Upload
others
View
7
Download
1
Embed Size (px)
Citation preview
Copyright
by
Ajay Suri
2005
The Dissertation Committee for Ajay Suri Certifies that this is the approved version
of the following dissertation:
CLEANUP OF INTERNAL FILTER CAKE DURING FLOWBACK
Committee:
Mukul M. Sharma, Supervisor
Roger T. Bonnecaze
Daniel A. Hill
Carlos Torres-Verdin
Martin E. Chenevert
Steven L. Bryant
CLEANUP OF INTERNAL FILTER CAKE DURING FLOWBACK
by
Ajay Suri, B. Tech., M.S.
Dissertation
Presented to the Faculty of the Graduate School of
The University of Texas at Austin
in Partial Fulfillment
of the Requirements
for the Degree of
DOCTOR OF PHILOSOPHY
The University of Texas at Austin
December 2005
Dedication
This dissertation is dedicated to
The Supreme Spirit
The Ocean of Knowledge, Peace, Purity, Love, Happiness, Bliss, and Power
v
Acknowledgements
I would like to express my sincere gratitude to Dr. Mukul M. Sharma for
constantly inspiring, guiding and supporting me during the course of my research. I
found him very caring during my entire stay here at the university.
I would also like to thank Dr. Roger T. Bonnecaze, Dr. A. D. Hill, Dr. Steven L.
Bryant, Dr. Carlos Torres-Verdin, and Dr. Martin E. Chenevert for serving on the
committee.
Thanks to some of my colleagues, Jagan, Phani, Zongyu, Liu, and Baosheng for
their company and friendship.
Thanks to Reynaldo Casanova for providing the office supplies, to Roger
Terzian for providing the computer accessories and software, to Glenn Baum, Bob
Savicki and Tony Bermudez for setting the lab and for the friendship.
Lastly I would like to thank my brothers and sisters of my Brahmin family,
Sister Hansa, Brother Mark, Brother Mahesh, Brother Sachin and Brother Janardhan for
their constant love and support.
vi
CLEANUP OF INTERNAL FILTER CAKE DURING FLOWBACK
Publication No._____________
Ajay Suri, Ph.D.
The University of Texas at Austin, 2005
Supervisor: Mukul M. Sharma
The flow initiation pressure (FIP) is used as an estimate of the differential
pressure (between the reservoir and the well) required to initiate production. The
standard practice to measure FIP uses a constant flowback rate. This method is shown
to be inadequate to measure the FIP. An improved flowback method, which uses a
series of constant differential pressures, is used instead to measure the FIP. This method
closely represents the constant drawdown experienced between the reservoir and the
wellbore. In addition the permeability during flowback is measured at increasing
differential pressures, resulting in a spectrum of return permeability values.
Two types of drilling fluids (sized calcium carbonate and bentonite) are used for
conducting the filtration and flowback experiments for porous media ranging in
permeability from 4 to 1500 md. Both single-phase and two-phase experiments are
conducted in lab-simulated open-hole and perforated completions to better understand
the factors affecting the FIP and the return permeability spectra.
vii
We observe small values for FIP in all the experiments (considerably smaller
than those measured using the constant flowback method). The values of FIP yield
pressure gradients that are achievable in vertical wells but may not be easily achieved
in horizontal wells. The FIP and the return permeability spectra are controlled by the
cleanup of the internal filter cake. A Bingham fluid in a network of pores is used to
model the cleanup of the internal filter cake during flowback. The results indicate that
very large pressure gradients are required during flowback to cleanup the entire internal
filter cake. However, a pressure gradient of 10 psi / inch is found to yield a skin factor
< 1 for most open-hole completions. For perforated completions, pressure gradients up
to 20 psi / inch and flow rates up to 0.3 bbl/day/perf yield skin factors < 2.
viii
Table of Contents
List of Tables ..................................................................................................................xiii
List of Figures .................................................................................................................xvi
Chapter 1: Introduction ..................................................................................................1 1.1 Background...................................................................................................... 1 1.2 Definition of the Problem ................................................................................ 5 1.3 Outline of the Chapters .................................................................................... 7 References................................................................................................................. 8
Chapter 2: An Improved Laboratory Method to Estimate Flow Initiation Pressures and Return Permeabilities During Flowback ...................................11 2.1 Inroduction..................................................................................................... 11 2.2 Literature Review........................................................................................... 11
2.2.1 Flow Initiation Pressure ........................................................................ 11 2.2.2 Return Permeability .............................................................................. 15
2.3 Problem Description and Motivation............................................................. 17 2.4 Experimental Design...................................................................................... 18
2.4.1 Test Equipment ..................................................................................... 18 2.4.2 Core and Fluid Sample.......................................................................... 20 2.4.3 Test Procedure ...................................................................................... 21
2.5 Test Objectives............................................................................................... 26 2.6 Discussion of Experimental Results .............................................................. 26
2.6.1 Single-phase (Brine) Experiments ........................................................ 27 2.6.2 Two-phase (Brine + Oil) Experiments.................................................. 30 2.6.3 Comparison between Single-phase and Two-phase Flow Experiments33
2.7 Effect of Different Parameters on FIP and Return Permeability ................... 35 2.7.1 Effect of Flowback Condition (Constant Flow Rate vs. Constant
Pressure)................................................................................................ 36 2.7.2 Effect of External Filter Cake ............................................................... 36 2.7.3 Effect of Drill-in or Completion Fluid Type......................................... 37 2.7.4 Effect of Core Length ........................................................................... 38
ix
2.7.5 Effect of Back Pressure......................................................................... 38 2.7.6 Effect of Median Particle Size of the Bridging Agent.......................... 39
2.8 Application of Results To Estimate Skin Around Wells ............................... 39 2.9 Conclusions.................................................................................................... 44 References............................................................................................................... 81
Chapter 3: Role of Drill-in Fluid Components during Filtration and Flowback ....84 3.1 Introduction.................................................................................................... 84 3.2 Drill-in and Completion Fluid Components .................................................. 84
3.2.1 Bridging Additive ................................................................................. 86 3.2.2 Fluid Loss Control Additive ................................................................. 86 3.2.3 Rheology Control Additive................................................................... 87
3.3 Research Objective ........................................................................................ 87 3.4 Experimental Design...................................................................................... 88
3.4.1 Test Description and Fluid Design ....................................................... 88 3.4.2 Test Equipment ..................................................................................... 89 3.4.3 Test Procedure ...................................................................................... 89
3.5 Discussion of Experimental Results .............................................................. 90 3.5.1 Flow Initiation Pressure ........................................................................ 90 3.5.2 Return Permeability Ratio..................................................................... 91 3.5.3 Filtrate Loss .......................................................................................... 94
3.6 Effect of Drill Solids...................................................................................... 95 3.7 Comparison of Experimental Results with UTDamage................................. 96 3.8 Conclusions.................................................................................................... 96 References............................................................................................................. 108
Chapter 4: Filter Cake Yield Strength.......................................................................109 4.1 Introduction.................................................................................................. 109 4.2 Literature Review......................................................................................... 109 4.3 Motivation.................................................................................................... 111 4.4 Constant Strain Rheometer .......................................................................... 112
4.4.1 Principle of Measurement ................................................................... 113
x
4.4.2 Parallel Plate Geometry ...................................................................... 113 4.4.3 Theoretical Equations ......................................................................... 114 4.4.4 Sample Preparation ............................................................................. 115
4.5 Results and Discussion ................................................................................ 115 4.5.1 Dynamic Strain Sweep Test................................................................ 116 4.5.2 Linear Strain Test................................................................................ 117
4.6 Experimental Issues and Concerns .............................................................. 119 4.7 Conclusions.................................................................................................. 121 References............................................................................................................. 135
Chapter 5: Modeling the Cleanup of Internal Filter Cake during Flowback ........136 5.1 Introduction.................................................................................................. 136 5.2 Background and Literature Review ............................................................. 136 5.3 Model Development..................................................................................... 138
5.3.1 Bundle of Tubes Model ...................................................................... 139 5.3.2 Discussion on Bundle of Tubes Model Results .................................. 143 5.3.3 Comparison of Bundle of Tubes Model Results with Experimental
Results................................................................................................. 145 5.3.4 Three Dimensional Network Model with Effective Medium
Approximation .................................................................................... 148 5.3.5 Results and Discussion on Network Model ........................................ 156
5.4 Slow Cleanup of the Internal Filter Cake .................................................... 159 5.5 Conclusions.................................................................................................. 161 References............................................................................................................. 181
Chapter 6: Cleanup of Lab-Simulated Perforation Tunnels during Flowback .....183 6.1 Introduction.................................................................................................. 183 6.2 Background and Literature Review ............................................................. 183 6.3 Problem Description .................................................................................... 186 6.4 Objectives .................................................................................................... 186 6.5 Test Design .................................................................................................. 187
6.5.1 Lab-simulated Perforated Core and Core Holder ............................... 187 6.5.2 Rock Type and Fluid Type ................................................................. 187
xi
6.5.3 Test Procedure .................................................................................... 188 6.6 Discussion of Experimental Results ............................................................ 189
6.6.1 Single-phase Experiments................................................................... 189 6.6.2 Two-phase Experiments...................................................................... 194
6.7 Effect of Different Parameters ..................................................................... 196 6.7.1 Single-phase vs. Two-phase Flow ...................................................... 197 6.7.2 Effect of Completion Fluid Type........................................................ 197 6.7.3 Open-hole Completion vs. Perforated Completion............................. 198 6.7.4 Effect of Overbalance Pressure........................................................... 200 6.7.5 Effect of Perforation Dimensions ....................................................... 201 6.7.6 Single vs. Multiple Perforations ......................................................... 201
6.8 Application of Results To Estimate Skin In Perforated Completions ......... 201 6.9 Conclusions.................................................................................................. 202 References............................................................................................................. 225
Chapter 7: UTDamage: An Application to Model Both Filtration and Flowback and To Design Fluids ..........................................................................................226 7.1 Introduction.................................................................................................. 226 7.2 Background and Literature Review ............................................................. 226 7.3 Model Development..................................................................................... 227 7.4 UTDamage Vs. Experimental Results ......................................................... 243 7.5 Erosion Factor Model Vs. Bingham Model................................................. 244
Chapter 8: Conclusions ...............................................................................................255 8.1 Recommendations........................................................................................ 258 8.2 Future Work ................................................................................................. 258
xii
Appendix-A: Photograph of the lab-setup used in conducting the experiments ........... 260
Appendix-B: Plots for single-phase constant pressure flowback experiments simulating open-hole completion............................................................................................ 262
Appendix-C: Plots of two-phase constant pressure flowback experiments simulating open-hole condition .............................................................................................. 288
Appendix-D: Plots for experiments with flow back at constant rate to study the role of individual drill-in fluid components on formation damage .................................. 307
Appendix-E: Plots of single-phase filtration experiments conducted on cores with lab-simulated perforations with constant pressure flowback condition...................... 341
Appendix-F: Plots for two-phase constant pressure flowback experiments conducted on lab-simulated perforated cores.............................................................................. 369
Appendix-G: Detailed information of all the fluid filtration experiments with constant pressure flowback condition ................................................................................. 375
Appendix-H: Detailed information of all the fluid filtration experiments with constant rate flowback condition......................................................................................... 377
Nomenclature................................................................................................................. 379
Bibliography .................................................................................................................. 382
Vita ............................................................................................................................... 389
xiii
List of Tables
Table 2-1: Short and long core dimensions ........................................................................47
Table 2-2: Different core types used in the study ...............................................................47
Table 2-3: Formulation of a sized CaCO3 drill-in mud (9.5 ppg UltraCarb)......................48
Table 2-4: Rheology of CaCO3 drill-in mud using Fann viscometer .................................48
Table 2-5: Formulation of bentonite mud (10 ppg) ............................................................49
Table 2-6: Rheology of bentonite mud using Fann viscometer..........................................49
Table 2-7: Flow initiation pressure for single-phase flow and constant pressure
flowback experiments simulating open hole conditions. ................................50
Table 2-8: Summary of return permeability ratio for single-phase constant pressure
flowback tests simulating open hole conditions..............................................51
Table 2-9: API filtrate loss for single-phase flow and constant pressure flowback
experiments simulating open-hole conditions .................................................52
Table 2-10: Flow initiation pressure for two-phase flow experiments with constant
pressure flowback condition simulating open-hole conditions .......................53
Table 2-11: Summary of return permeability ratio for two-phase constant pressure
flowback tests simulating open-hole conditions .............................................54
Table 2-12: API filtrate loss for two-phase flow and constant pressure flowback
experiments simulating open-hole conditions .................................................55
Table 2-13: Comparison of FIP for single-phase vs. two-phase experiments with
constant pressure flowback conditions............................................................56
Table 2-14: Comparison of return permeability ratio for single-phase vs. two-phase
experiments with constant pressure flowback conditions ...............................57
Table 2-15: Comparison of FIP for constant rate vs. constant pressure flowback
condition for two-phase flow experiments ......................................................58
Table 2-16: Comparison of FIP, return permeability ratio and API filtrate loss for
bentonite mud and UltraCarb drill-in fluid......................................................59
Table 3-1: Formulation of a sized CaCO3 drill-in mud (9.5 ppg UltraCarb) .....................99
Table 3-2: Drill-in fluid formulation matrix .......................................................................99
xiv
Table 3-3: FIP, return permeability ratio and API filtrate loss for different drill-in fluid
formulations on Berea sandstone (Overbalance: 100 psi)...............................100
Table 3-4: Comparison of FIP, return permeability ratio and API filtrate loss for drill-in
fluid with and without revdust.........................................................................101
Table 3-5: Erosion factors used to fit the return permeability ratio obtained from
experiments with UTDamage for different drill-in fluids ...............................101
Table 4.1: Comparison of yield stress measurements done using dynamic strain sweep
test and linear strain test for different filter cake samples...............................123
Table 5-1: Depth of invasion of solids and polymers calculated from UTDamage for
different rocks used in conducting the experiments ........................................163
Table 6-1: Flow initiation pressure for single-phase flow and constant pressure
flowback experiments simulating perforated completion ...............................204
Table 6-2: Summary of return permeability ratio for single-phase constant pressure
flowback tests simulating open-hole completion ............................................205
Table 6-3: Summary of 30 minute fluid loss for lab simulated perforated cores with
single phase flow and constant pressure flowback condition..........................206
Table 6-4: Summary of FIP for lab simulated perforated cores with two phase flow and
constant pressure flowback condition .............................................................207
Table 6-5: Summary of return permeability ratio for two-phase constant pressure
flowback tests simulating open hole completion ............................................207
Table 6-6: Comparison of FIP for single phase vs. two phase experiments with constant
pressure flowback condition in lab-simulated perforated completions...........208
Table 6-7: Comparison of FIP and return permeability ratio between bentonite mud and
UltraCarb completion fluid in lab-simulated perforated completions.............208
Table B.1: List of all the single-phase, constant pressure flowback experiments,
simulating open-hole completion ....................................................................263
Table C.1: List of all the two-phase, constant pressure flowback experiments,
simulating open-hole completion ....................................................................289
xv
Table D.1: List of experiments with constant rate flowback condition to study the effect
of individual drill-in fluid components on FIP, return permeability and API
filtrate loss .......................................................................................................308
Table E.1: List of all the single-phase, constant pressure flowback experiments,
simulating perforated completions ..................................................................342
Table F.1: List of all the two-phase, constant pressure flowback experiments,
simulating lab-simulated perforated completion.............................................370
xvi
List of Figures
Figure 2-1: Flowback pressure profile with constant flow rate boundary condition to
calculate flow initiation pressure (FIP) ...........................................................60
Figure 2-2: Flow-back pressure profile with constant pressure boundary condition
(incremental pressure differentials) to calculate FIP.......................................60
Figure 2-3: Apparatus for fluid filtration and flowback test...............................................61
Figure 2-4: Apparatus for long core holder ........................................................................62
Figure 2-5: Steps used during mud filtration and flowback tests .......................................63
Figure 2-6: Pore volume distribution for different rocks obtained from mercury
penetrometer ....................................................................................................64
Figure 2-7: Top view of a limestone core after flowback at constant pressure (Mud
used: UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 1-phase flowLS-
12)....................................................................................................................64
Figure 2-8: Top view of a Berea core after flowback at constant pressure (Mud used:
UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 2-phase flow, BS-17).....65
Figure 2-9: Nugget sandstone core after flowback at constant pressure (Mud used:
UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 1-phase flow, NS-2).......65
Figure 2-10: Top view of an Aloxide core after flowback at constant pressure (Mud
used: UltraCarb-20 drill-in fluid, O.B. pressure = 100 psi, 1-phase flow,
AL-2) ...............................................................................................................66
Figure 2-11: Return permeability spectra for different permeability cores (single-phase
flow and constant flowback pressure). ............................................................66
Figure 2-12: Spurt loss vs. absolute permeability of different cores for single-phase
experiments simulating open hole conditions .................................................67
Figure 2-13: API Filtrate loss vs. absolute permeability of different cores for single-
phase experiments simulating open hole conditions .......................................67
Figure 2-14: Return permeability spectra for different permeability cores (two-phase
flow and constant flowback pressure) .............................................................68
Figure 2-15: Return permeability spectra for different permeability cores (two-phase
flow and constant flowback pressure) .............................................................68
xvii
Figure 2-16: Spurt loss vs. absolute permeability of different cores for two-phase
experiments simulating open hole conditions .................................................69
Figure 2-17: API Filtrate loss vs. absolute permeability of different cores for two-phase
experiments simulating open hole conditions .................................................69
Figure 2-18: Return permeability spectra in Nugget sandstone for single-phase flow and
two-phase flow ................................................................................................70
Figure 2-19: Comparison of return permeability spectra in Texas limestone for single-
phase vs. two-phase flow (constant pressure B.C.) .........................................70
Figure 2-20: Comparison of return permeability spectra in Berea sandstone for single-
phase vs. two-phase flow (constant pressure B.C.) .........................................71
Figure 2-21: Comparison of return permeability spectra in Aloxide (synthetic cores) for
single-phase vs. two-phase flow (constant pressure B.C.) ..............................71
Figure 2-22: Comparison of return permeability spectra in Boise sandstone for single-
phase vs. two-phase flow (constant pressure B.C.) .........................................72
Figure 2-23: Comparison of FIP between constant rate boundary condition (B.C.) and
constant pressure B.C. during flowback for Berea sandstone.........................72
Figure 2-24: Comparison of FIP and return permeability spectra for Berea sandstone
with and without external filter cake...............................................................73
Figure 2-25: Return permeability vs. differential pressure during flowback in short and
long Berea cores ..............................................................................................73
Figure 2-26: Return permeability vs. average flowback velocity for experiments
conducted on short and long Berea cores ........................................................74
Figure 2-27: Comparison of return permeability spectra for Berea sandstone with and
without back pressure (O.B. = 500 psi)...........................................................74
Figure 2-28: Comparison of return permeability spectra for Aloxide cores with
UltraCarb drill-in fluids with two different median sizes ...............................75
Figure 2-29: Comparison of return permeability spectra for Berea cores with UltraCarb
drill-in fluids with two different median sizes ................................................75
Figure 2-30: Skin with varying return permeability ratio of the near wellbore region.......76
xviii
Figure 2-31: Return permeability ration vs. average pressure gradients in Texas
limestone and Berea during flowback .............................................................76
Figure 2-32: Return permeability ratio vs. average pressure gradient in Boise sandstone
and Aloxide core during flowback ..................................................................77
Figure 2-33: Return permeability ration vs. average pressure gradients in Texas
limestone and Berea during flowback (Semi-log plot) ...................................77
Figure 2-34: Return permeability ratio vs. average pressure gradient in Boise sandstone
and Aloxide core during flowback (Semi-log plot).........................................78
Figure 2-35: Pressure gradient at the wellbore face at different steady state flow rates ....78
Figure 2-36: Return permeability ratio of inch long Texas limestone and Berea
sandstone core at different flowback rates (semi-log plot) .............................79
Figure 2-37: Return permeability ratio of Boise sandstone and Aloxide core at different
flowback rates (semi-log plot).........................................................................79
Figure 2-38: Return permeability ratio of Texas limestone and Berea sandstone core at
different flowback velocities (semi-log plot) ..................................................80
Figure 2-39: Return permeability ratio of Boise sandstone and Aloxide core at different
flowback velocities (semi-log plot) .................................................................80
Figure 3-1: Flowback pressure profile with constant flow rate boundary condition to
calculate flow initiation pressure (FIP) ...........................................................102
Figure 3-2: Flow initiation pressure (constant rate flow back) for Berea sandstone with
varying composition of the drill-in fluid .........................................................102
Figure 3-3: Return permeability ratio for Berea sandstone with varying median size of
bridging agents (bridging agent with no xanthan and no starch) ....................103
Figure 3-5: Return permeability ratio for Berea sandstone with varying median size of
bridging agents (bridging agent with xanthan but no starch) ..........................104
Figure 3-6: Return permeability ratio for Berea sandstone with varying median size of
bridging agents (bridging agent with xanthan and starch) ..............................104
Figure 3-7: Comparison of return permeability ratio at flow back rate = 1 cc/min for
Berea sandstone with varying drill-in fluid composition ................................105
xix
Figure 3-8: Comparison of return permeability ratio at flow back rate = 3 cc/min for
Berea sandstone with varying drill-in fluid composition ................................105
Figure 3-9: Comparison of return permeability ratio at flow back rate = 5 cc/min for
Berea sandstone with varying drill-in fluid composition ................................106
Figure 3-10: Comparison of API filtrate loss for different drill-in fluid compositions on
Berea sandstone...............................................................................................106
Figure 3-11: Comparison of return permeability ratio obtained from experiments and
from UTDAMAGE simulations......................................................................107
Figure 3-12: Comparison of API filtrate loss obtained from experiments and from
UTDAMAGE simulations...............................................................................107
Figure 4.1: Lifting up of the external filter cake during flowback. The internal filter
cake (roots holding the external filter cake) has cleaned up at point A ..........123
Figure 4.2: Lifting up and formation of pin-holes and cracks in the external filter cake
during flowback...............................................................................................123
Figure 4.3a: Photograph of ARES constant strain rheometer.............................................124
Figure 4.3b: Close up photograph of ARES constant strain rheometer with a parallel
plate (25 mm) apparatus ..................................................................................124
Figure 4.3c: Schematic of parallel plate apparatus in ARES constant strain rheometer ....125
Figure 4.4: Plot of visco-elastic parameters using dynamic strain sweep test in a
constant strain rheometer for UltraCarb-2 drill-in fluid filter cake.................125
Figure 4.5: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-2 drill-
in fluid filter cake ............................................................................................126
Figure 4.6: Plot of visco-elastic parameters using dynamic strain sweep test in a
constant strain rheometer for UltraCarb-12 drill-in fluid filter cake...............126
Figure 4.7: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-12 drill-
in fluid filter cake ............................................................................................127
Figure 4.8: Plot of visco-elastic parameters using dynamic strain sweep test in a
constant strain rheometer for UltraCarb-12 drill-in fluid filter cake...............127
Figure 4.9: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-12 drill-
in fluid filter cake ............................................................................................128
xx
Figure 4.10: Plot of visco-elastic parameters using dynamic strain sweep test in a
constant strain rheometer for UltraCarb-20 drill-in fluid filter cake...............128
Figure 4.11: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-20
drill-in fluid filter cake ....................................................................................129
Figure 4.12: Plot of stress vs. strain in a linear strain test using constant strain
rheometer for UltraCarb-2 drill-in fluid filter cake .........................................129
Figure 4.13: Plot of stress vs. strain in a linear strain test using constant strain
rheometer for UltraCarb-12 drill-in fluid filter cake .......................................130
Figure 4.14: Plot of stress vs. strain in a linear strain test using constant strain
rheometer for UltraCarb-12 drill-in fluid filter cake .......................................130
Figure 4.15: Plot of stress vs. strain in a linear strain test using constant strain
rheometer for UltraCarb-20 drill-in fluid filter cake .......................................131
Figure 4.16: Plot of stress vs. strain in a linear strain test using constant strain
rheometer for UltraCarb-20 drill-in fluid filter cake .......................................131
Figure 4.17: Plot of stress vs. strain in a linear strain test using constant strain
rheometer for bentonite mud filter cake ..........................................................132
Figure 4.18: Plot of stress vs. strain in a linear strain test using constant strain
rheometer for bentonite mud filter cake ..........................................................132
Figure 4.19: Plot of stress vs. strain in a linear strain test using constant strain
rheometer for bentonite mud filter cake ..........................................................133
Figure 4.20: Plot of stress vs. strain at a normal force equal to 500 gms in a linear strain
test for bentonite mud filter cake.....................................................................133
Figure 4.21: Yield strength of different muds using dynamic strain sweep test and linear
strain test..........................................................................................................134
Figure 5.1: Schematic of invasion of particles (solids and polymers) in porous medium
representing internal and external filter cake ..................................................164
Figure 5.2: Schematic of filter cake (internal and external) as a Bingham fluid ................165
Figure 5.3: Schematic of filter cake conceived as a Bingham fluid in a porous medium
represented by a bundle of tubes model ..........................................................166
xxi
Figure 5.4: Flow initiation pressure (FIP) as a function of the largest pore throat
diameter of the pores with varying thickness of the internal filter cake .........167
Figure 5.5: Pore volume distribution obtained from mercury penetrometer for Texas
limestone .........................................................................................................167
Figure 5.6: Pore volume distribution obtained from mercury penetrometer for Berea
sandstone .........................................................................................................168
Figure 5.7: Pore volume distribution obtained from mercury penetrometer for Boise
sandstone .........................................................................................................168
Figure 5.8: Plot comparing the pore volume distribution for different rocks obtained
from mercury penetrometer.............................................................................169
Figure 5.9: Return permeability ratio for Berea sandstone using bundle of tubes model
with varying thickness of the internal filter cake ............................................169
Figure 5.10: Return permeability ratio for Berea sandstone using bundle of tubes model
with varying cake yield strength .....................................................................170
Figure 5.11: Return permeability spectra for different rocks obtained from the bundle of
tubes model......................................................................................................170
Figure 5.12: Comparison of return permeability ratio obtained from bundle of tubes
model and experimental results for single phase flow in Texas limestone .....171
Figure 5.13: Comparison of return permeability ratio obtained from bundle of tubes
model and experimental results for single phase flow in Berea sandstone .....171
Figure 5.14: Comparison of return permeability ratio obtained from bundle of tubes
model and experimental results for single phase flow in Boise sandstone .....172
Figure 5.15: Schematic of a core before flowback for calculating differential pressure
across the internal filter cake (damaged zone) ................................................172
Figure 5.16: Return permeability in the damaged zone with different depths for Nugget
sandstone (NS-2) .............................................................................................173
Figure 5.17: Schematic of a porous medium represented by a two-dimensional network
of pore throats plugged with internal filter cake. Please note that in the
actual network model the pore throats are of varied sizes. .............................174
xxii
Figure 5.18: A schematic of the distribution of the internal filter cake (as a Bingham
fluid) and the flowback fluid (brine) in the pores during flowback ................175
Figure 5.19: Accessible fraction of pore throats for a Bethe tree with Z = 5 to represent
the accessibility fraction of a three dimensional network with Z = 6 .............176
Figure 5.20: Probability function for pore throat radius for Berea sandstone calculated
from volume size distribution obtained from mercury penetrometer..............176
Figure 5.21: Return permeability for a network model with varying coordination
number (without accessibility function)..........................................................177
Figure 5.22: Return permeability for a network model with varying coordination
number (with accessibility function) ...............................................................177
Figure 5.23: Comparison of bundle of tubes model with the network model (the
network model approaches the bundle of tubes model when z approaches
infinity) ............................................................................................................178
Figure 5.24: Return permeability for a network model with varying pore throat length....178
Figure 5.25: Return permeability obtained from experiments conducted on Berea
sandstone and from the network model...........................................................179
Figure 5.26: Pressure gradients across the internal filter cake with different thickness
(calculated from NS-2 return permeability data and the two zone model) .....179
Figure 5.27: Pressure gradients vs. return permeability ratio of the damaged zone
(calculated for NS-2 using the two zone model) .............................................180
Figure 5.28: Ratio of the flow rate of the flowback fluid (Newtonian) to the flow rate of
the internal filter cake (Bingham fluid) ...........................................................180
Figure 6-1: Schematic of a lab-simulated single perforation in a core ...............................209
Figure 6-2: Schematic of the long core holder with a lab-simulated single perforation.....210
Figure 6-3: Top view of a 1 in. limestone core with lab simulated perforation (1/4 X 1/2
in.) before flowback at constant pressure (LS-9) ............................................211
Figure 6-4: Top view of a 1 in. limestone core with lab simulated perforation (1/4 X 1/2
in.) after flowback at constant pressure (LS-9) ...............................................211
Figure 6-5: Top view of a long Berea core with lab simulated perforation (1/8 X 1 in.)
after flowback at constant pressure (BS-long-#11) .........................................212
xxiii
Figure 6-6: Top view of a long Berea core with lab simulated perforation (1/8 X 2 in.)
after flowback at constant pressure (BS-long-#12) .........................................212
Figure 6-7: Top view of a long Berea core with lab simulated perforation (1/4 X 1 in.)
after flowback at constant pressure (BS-long-#13) .........................................213
Figure 6-8: Top view of a long Berea core with lab simulated perforation (1/4 X 2 in.)
after flowback at constant pressure (BS-long-#14) .........................................213
Figure 6-9: Top view of a long Berea core with lab simulated perforation (3/8 X 1 in.)
after flowback at constant pressure (BS-6-13-04-#8) .....................................214
Figure 6-10: Return permeability spectra for Berea with different perforation
dimensions (single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid) ......214
Figure 6-11: Semi-log plot for return permeability in Berea with different perforation
dimensions (single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid) ......215
Figure 6-12: Return permeability ratio in the first 2 inches of Berea cores (single-phase
flow, O.B: 100 psi, UltraCarb-2 drill-in fluid) ................................................215
Figure 6-13: Semi-log plot for return permeability for the first 2 inches in Berea cores
(single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)..........................216
Figure 6-14: Return permeability spectra for Berea with varying flowback rate (single-
phase flow, const. pressure b.c, O.B: 100 psi, UltraCarb-2 drill-in fluid) ......216
Figure 6-15: Semi-log plot for return permeability for Berea with flowback rate (single-
phase flow, const. pressure b.c, O.B: 100 psi, UltraCarb-2 drill-in fluid) ......217
Figure 6-16: Semi-log plot for return permeability for Berea with flowback rate (single-
phase flow, const. pressure b.c, O.B: 100 psi, UltraCarb-2 drill-in fluid) ......217
Figure 6-17: Semi-log plot for return permeability in 1st 2 inches of the Berea core
(single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)..........................218
Figure 6-18: Top and side view of a short Berea core with three drilled holes to
represent lab-simulated perforations ...............................................................218
Figure 6-19: Return permeability spectra for lab-simulated open-hole completion vs.
lab-simulated perforated completions in long Berea cores (6 inch long)........219
Figure 6-20: Return permeability vs. flowback pressure for open-hole and perforated
completions (lab-simulated) in short Berea sandstone cores (1 inch long).....219
xxiv
Figure 6-21: Return permeability vs. flowback velocity for open-hole and perforated
completions (lab-simulated) in short Berea sandstone cores (1 inch long).....220
Figure 6-22: Return permeability vs. flowback pressure for open-hole and perforated
completions (lab-simulated) in short Texas limestone cores (1 inch long).....220
Figure 6-23: Return permeability vs. flowback rate for open-hole and perforated
completions (lab-simulated) in short Texas limestone cores (1 inch long).....221
Figure 6-24: Return permeability vs. flowback velocity for open-hole and perforated
completions (lab-simulated) in short Texas limestone cores (1 inch long).....221
Figure 6-25: Return permeability with varying flowback pressure in Boise sandstone
with lab-simulated perforations at two different O.B. pressures (Mud used:
UltraCarb-20) ..................................................................................................222
Figure 6-26: Return permeability spectra for two different perforated completions (lab-
simulated) with different lengths.....................................................................222
Figure 6-27: Return permeability spectra for two different perforated completions (lab-
simulated) with different diameter ..................................................................223
Figure 6-28: Return permeability spectra for the first two inches of cores with different
perforated completions as a function of average pressure gradient ................223
Figure 6-29: Estimate of skin factor for perforated completions with a depth of damage
equal to 2 inches ..............................................................................................224
Figure 6-30: Return permeability spectra for perforated completions in the first 2 inches
as a function of flow rate through the perforation tunnels ..............................224
Figure 7.1: Schematic of invasion of particles (solids and polymers) in porous medium
representing internal and external filter cake ..................................................246
Figure 7.2: Happel 's Sphere-in-cell porous media model representing the grain and the
pore throat........................................................................................................247
Figure 7.3 (a): Initial saturation of fluids in the core..........................................................248
Figure 7.3 (b): Fluid saturations after invasion of mud filtrate...........................................248
Figure 7.4: Erosion factors used in UTDamage to match the experimental data (BS-4-2-
04-I: UltraCarb-2 drill-in fluid on a short Berea core) ....................................249
xxv
Figure 7.5: Erosion factors used in UTDamage to match the experimental data (BS-6-5-
04-#5: UltraCarb-2 drill-in fluid on a long Berea core) ..................................249
Figure 7.6: Erosion factors used in UTDamage to match the experimental data (All
single-phase experiments using Berea sandstone and UltraCarb-2 drill-in
fluid) ................................................................................................................250
Figure 7.7: Plot of erosion factor used in UTDamage to match the return permeability
data for Texas limestone (LS-1: 1-P flow with UltraCarb-2 drill-in fluid).....250
Figure 7.8: Plot of erosion factor used in UTDamage to match the return permeability
data for Texas limestone (LS-12: Two-phase flow with UltraCarb-2 drill-in
fluid) ................................................................................................................251
Figure 7.9: Erosion factors for single-phase flow and two-phase flow return
permeabilities for Texas limestone cores (LS-1: 1-P, LS-12: 2-P
experiment)......................................................................................................251
Figure A.1: Photograph of the filtration and flow back apparatus .....................................261
Figure B-1: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Nugget sandstone (NS-2) .......................................................264
Figure B-2: Return permeability spectra with incremental differential pressures for
Nugget sandstone (NS-2) ................................................................................264
Figure B-3: Static filtration of UltraCarb-2 on Nugget sandstone simulating open hole
completion (NS-2) ...........................................................................................265
Figure B-4: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Texas limestone (LS-1) ..........................................................266
Figure B-5: Return permeability spectra with incremental differential pressures for
Texas limestone (LS-1) ...................................................................................266
Figure B-6: Static filtration of UltraCarb-2 on Texas limestone simulating open hole
completion (LS-1) ...........................................................................................267
Figure B-7: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Texas limestone (LS-13) ........................................................268
Figure B-8: Return permeability spectra with incremental differential pressures for
Texas limestone (LS-13) .................................................................................268
xxvi
Figure B-9: Static filtration of UltraCarb-2 on Texas limestone simulating open hole
completion (LS-13) .........................................................................................269
Figure B-10: Flowback rate at incremental differential pressures after filtration with
bentonite on Texas limestone (LS-5) ..............................................................270
Figure B-11: Return permeability spectra with incremental differential pressures for
Texas limestone (LS-5) ...................................................................................270
Figure B-12: Static filtration of bentonite mud on Texas limestone simulating open hole
completion (LS-5) ...........................................................................................271
Figure B-13: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-4-2-04-I) ..............................................272
Figure B-14: Return permeability spectra with incremental differential pressures for
Berea sandstone (BS-4-2-04-I)........................................................................272
Figure B-15: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole
completion (BS-4-2-04-I)................................................................................273
Figure B-16: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on a long Berea sandstone (BS-4-29-04-long-3) ........................274
Figure B-17: Return permeability spectra for incremental differential pressures in a
long Berea core (BS-long-3) ...........................................................................274
Figure B-18: Static filtration of UltraCarb-2 on a long Berea core simulating open hole
completion (BS-long-3)...................................................................................275
Figure B-19: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on a long Berea sandstone (BS-4-29-04-long-4) ........................276
Figure B-20: Return permeability spectra for incremental differential pressures in a
long Berea core (BS-4-29-04-long-4) .............................................................276
Figure B-21: Static filtration of UltraCarb-2 on a long Berea sandstone simulating open
hole completion (BS-4-29-04-long-4).............................................................277
Figure B-22: Flowback rate at incremental differential pressures after filtration on a
long Berea sandstone with external filter cake removed (BS-4-29-04-long-
5)......................................................................................................................278
xxvii
Figure B-23: Return permeability spectra for incremental differential pressures in a
long Berea core with external filter cake removed (BS-4-29-04-long-5) .......278
Figure B-24: Static filtration of UltraCarb-2 on a long Berea core simulating open hole
completion (BS-4-29-04-long-5).....................................................................279
Figure B-25: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on a Boise sandstone (Bo-1) .....................................................280
Figure B-26: Return permeability spectra with incremental differential pressures for
Boise sandstone (Bo-1) ...................................................................................280
Figure B-27: Static filtration of UltraCarb-20 on Boise sandstone simulating open hole
completion (Bo-1) ...........................................................................................281
Figure B-28: Flowback rate at incremental differential pressures after filtration with
bentonite mud on Boise sandstone (Bo-2) ......................................................282
Figure B-29: Return permeability spectra with incremental differential pressures for
Boise sandstone (Bo-2) ...................................................................................282
Figure B-30: Static filtration of bentonite mud on Boise sandstone simulating open hole
completion (Bo-2) ...........................................................................................283
Figure B-31: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Aloxide core (Al-1) ................................................................284
Figure B-32: Return permeability spectra with incremental differential pressures for
Aloxide core (Al-1) .........................................................................................284
Figure B-33: Static filtration of UltraCarb-2 on Aloxide core simulating open hole
completion (Al-1) ............................................................................................285
Figure B-34: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Aloxide core (Al-2) ..............................................................286
Figure B-35: Return permeability spectra with incremental differential pressures for
Aloxide core (Al-2) .........................................................................................286
Figure B-36: Static filtration of UltraCarb-20 on Aloxide core simulating open hole
completion (Al-2) ............................................................................................287
Figure C-1: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Nugget sandstone (NS-3) .......................................................290
xxviii
Figure C-2: Return permeability spectra with incremental differential pressures for
Nugget sandstone (NS-3) ................................................................................290
Figure C-3: Static filtration of UltraCarb-2 on Nugget sandstone simulating open hole
completion (NS-3) ...........................................................................................291
Figure C-4: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Texas limestone (LS-12) ........................................................292
Figure C-5: Return permeability spectra with incremental differential pressures for
Texas limestone (LS-12) .................................................................................292
Figure C-6: Static filtration of UltraCarb-2 on Texas limestone simulating open hole
completion (LS-12) .........................................................................................293
Figure C-7: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-11-11-03-I) ..........................................294
Figure C-8: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole
completion (BS-11-11-03-I)............................................................................294
Figure C-9: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Berea sandstone (BS-21)......................................................295
Figure C-10: Return permeability spectra with incremental differential pressures for
Berea sandstone (BS-21) .................................................................................296
Figure C-11: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole
completion (BS-21) .........................................................................................296
Figure C-12: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-17)........................................................297
Figure C-13: Return permeability spectra with incremental differential pressures for
Berea sandstone (BS-17) .................................................................................298
Figure C-14: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole
completion (BS-17) .........................................................................................298
Figure C-15: Flowback rate at incremental differential pressures after filtration with
UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea sandstone (BS-19).........299
Figure C-16: Return permeability spectra with incremental differential pressures for
Berea sandstone (BS-19) .................................................................................300
xxix
Figure C-17: Static filtration of UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea
sandstone simulating open hole completion (BS-19)......................................300
Figure C-18: Flowback rate at incremental differential pressures after filtration with
UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea sandstone (BS-20).........301
Figure C-19: Return permeability spectra with incremental differential pressures for
Berea sandstone (BS-20) .................................................................................302
Figure C-20: Static filtration of UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea
sandstone simulating open hole completion (BS-20)......................................302
Figure C-21: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Aloxide core (AL-3).............................................................303
Figure C-22: Return permeability spectra with incremental differential pressures for
Aloxide core (AL-3)........................................................................................304
Figure C-23: Static filtration of UltraCarb-20 on Aloxide core simulating open hole
completion (AL-3)...........................................................................................304
Figure C-24: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Boise sandstone (Bo-7) ........................................................305
Figure C-25: Return permeability spectra with incremental differential pressures for
Boise sandstone (Bo-7) ...................................................................................306
Figure C-26: Static filtration of UltraCarb-20 on Boise sandstone simulating open hole
completion (Bo-7) ...........................................................................................306
Figure D-1: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (BS-4-16-03-II) ....................................................310
Figure D-2: Static filtration of UltraCarb-2 on Berea sandstone simulating open-hole
completion (BS-4-16-03-II) ............................................................................310
Figure D-3: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (BS-8-27-03-III)...................................................311
Figure D-4: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-27-03-III) .............................................................................312
Figure D-5: Static filtration of UltraCarb-2 on Berea sandstone simulating open-hole
completion (BS-8-27-03-III) ...........................................................................312
xxx
Figure D-6: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (no starch) (BS-4-21-03-II)..................................313
Figure D-7: Static filtration of UltraCarb-2 (no starch) on Berea sandstone simulating
open-hole completion (BS-4-21-03-II) ...........................................................314
Figure D-8: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (no xanthan) (BS-4-21-03-III) .............................314
Figure D-9: Static filtration of UltraCarb-2 (no xanthan) on Berea sandstone simulating
open-hole completion (BS-4-21-03-III) ..........................................................315
Figure D-10: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (no xanthan and starch) (BS-6-8-03-IV)..............315
Figure D-11: Static filtration of UltraCarb-2 (no xanthan and starch) on Berea
sandstone simulating open-hole completion (BS-6-8-03-IV) .........................316
Figure D-12: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (no xanthan and starch) (BS-6-8-03-V) ...............316
Figure D-13: Static filtration of UltraCarb-2 (no xanthan and starch) on Berea
sandstone simulating open-hole completion (BS-6-8-03-V)...........................317
Figure D-14: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 (BS-6-8-03-VI) ..................................................318
Figure D-15: Static filtration of UltraCarb-12 on Berea sandstone simulating open-hole
completion (BS-6-8-03-VI) .............................................................................318
Figure D-16: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 without starch (BS-6-8-03-IX)...........................319
Figure D-17: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-6-8-03-IX) ...............................................................................319
Figure D-18: Static filtration of UltraCarb-12 without starch on Berea sandstone
simulating open-hole completion (BS-6-8-03-IX) ..........................................320
Figure D-19: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 without xanthan (BS-6-8-03-VIII) .....................321
Figure D-20: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-6-8-03-VIII) ............................................................................321
xxxi
Figure D-21: Static filtration of UltraCarb-12 without xanthan on Berea sandstone
simulating open-hole completion (BS-6-8-03-VIII) .......................................322
Figure D-22: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 without xanthan and starch (BS-6-8-03-VII) .....323
Figure D-24: Static filtration of UltraCarb-12 without xanthan and starch on Berea
sandstone simulating open-hole completion (BS-6-8-03-VII) ........................324
Figure D-25: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 with RevDust (BS-10-2-03-I) ............................325
Figure D-26: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-10-2-03-I) ................................................................................325
Figure D-27: Static filtration of UltraCarb-12 with RevDust on Berea sandstone
simulating open-hole completion (BS-10-2-03-I) ...........................................326
Figure D-28: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 (BS-8-27-03-II) ..................................................327
Figure D-29: Return permeability on Berea sandstone at different flowback rates after
filtration with UltraCarb-20 (BS-8-27-03-II) ..................................................327
Figure D-30: Static filtration of UltraCarb-12 with RevDust on Berea sandstone
simulating open-hole completion (BS-10-2-03-I) ...........................................328
Figure D-31: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 without starch (BS-8-11-03-IX).........................329
Figure D-32: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-11-03-IX) .............................................................................329
Figure D-33: Static filtration of UltraCarb-20 without starch on Berea sandstone
simulating open-hole completion (BS-8-11-03-IX) ........................................330
Figure D-34: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 without xanthan (BS-8-11-03-XII) ....................331
Figure D-35: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-11-03-XII)............................................................................331
Figure D-36: Static filtration of UltraCarb-20 without xanthan on Berea sandstone
simulating open-hole completion (BS-8-11-03-XII).......................................332
xxxii
Figure D-37: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 without xanthan and starch (BS-8-11-03-X)......333
Figure D-38: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-11-03-X) ..............................................................................333
Figure D-39: Static filtration of UltraCarb-20 without xanthan on Berea sandstone
simulating open-hole completion (BS-8-11-03-X) .........................................334
Figure D-40: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 with RevDust (BS-10-7-03-I) ............................335
Figure D-41: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-10-7-03-I) ................................................................................335
Figure D-42: Static filtration of UltraCarb-20 with RevDust on Berea sandstone
simulating open-hole completion (BS-10-7-03-I) ...........................................336
Figure D-43: Differential pressure profile during flowback on Berea sandstone after
filtration with Brine (BS-8-27-03-I)................................................................337
Figure D-44: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-27-03-I) ................................................................................337
Figure D-45: Static filtration of Brine on Berea sandstone simulating open-hole
completion (BS-8-27-03-I)..............................................................................338
Figure D-46: Differential pressure profile during flowback on Berea sandstone after
filtration with Brine and pH buffer (BS-8-11-03-XIII)...................................339
Figure D-47: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-11-03-XIII) ..........................................................................339
Figure D-48: Differential pressure profile during flowback on Boise sandstone after
filtration with UltraCarb-20 (Bo-3) .................................................................340
Figure D-49: Static filtration of UltraCarb-20 on Boise sandstone simulating open-hole
completion (Bo-3) ...........................................................................................340
Figure E-1: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Texas limestone with lab simulated perforation (LS-9).........343
Figure E-2: Return permeability spectra with incremental differential pressures for
Texas limestone with lab simulated perforation (LS-9) ..................................343
xxxiii
Figure E-3: Static filtration of UltraCarb-2 on Texas limestone simulating open hole
completion (LS-9) ...........................................................................................344
Figure E-4: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea core with lab simulated perforation (BS-2-2-04-I) ......345
Figure E-5: Return permeability spectra with incremental differential pressures for
Berea sandstone with lab simulated perforation (BS-2-2-04-I) ......................345
Figure E-6: Static filtration of UltraCarb-2 on Berea sandstone with lab simulated
perforation (BS-2-2-04-I) ................................................................................346
Figure E-7: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-6-5-04-long-6) .....................................347
Figure E-8: Return permeability spectra with incremental differential pressures for
Berea sandstone (BS-6-5-04-long-6)...............................................................347
Figure E-9: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole
completion (BS-6-5-04-long-6).......................................................................348
Figure E-10: Flowback rate at incremental differential pressures on Berea sandstone
with a lab simulated perforation (BS-6-5-04-long-7)......................................349
Figure E-11: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-6-5-04-long-7) ..........349
Figure E.12: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated
perforation (BS-6-5-04-long-7) .......................................................................350
Figure E-13: Flowback rate at incremental differential pressures on Berea sandstone
with a lab simulated perforation (BS-6-13-04-long-8)....................................351
Figure E-14: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-6-13-04-long-8).........351
Figure E-15: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated
perforation (BS-6-13-04-long-8) .....................................................................352
Figure E-16: Flowback rate at incremental differential pressures on Berea sandstone
with a lab simulated perforation (BS-6-13-04-long-9)....................................353
Figure E-17: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-6-13-04-long-9).........353
xxxiv
Figure E-18: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated
perforation (BS-6-13-04-long-9) .....................................................................354
Figure E-19: Flowback rate at incremental differential pressures on Berea sandstone
with a lab simulated perforation (BS-6-29-04-long-10)..................................355
Figure E-20: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-6-29-04-long-10).......355
Figure E-21: Static filtration of UltraCarb-2 on a long Berea core simulating open hole
completion (BS-6-29-04-long-10)...................................................................356
Figure E-22: Flowback rate at incremental differential pressures on Berea sandstone
with a lab simulated perforation (BS-long-11)................................................357
Figure E-23: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-long-11) ....................357
Figure E-24: Static filtration of UltraCarb-2 on a long Berea core simulating open hole
completion (BS-long-11).................................................................................358
Figure E-25: Flowback rate at incremental differential pressures on Berea sandstone
with a lab simulated perforation (BS-long-12)................................................359
Figure E-26: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-long-12) ....................359
Figure E-27: Static filtration of UltraCarb-2 on a long Berea core simulating open hole
completion (BS-long-12).................................................................................360
Figure E-28: Flowback rate at incremental differential pressures on Berea sandstone
with a lab simulated perforation (BS-long-13)................................................361
Figure E-29: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-long-13) ....................361
Figure E-30: Static filtration of UltraCarb-2 on a long Berea core simulating open hole
completion (BS-long-13).................................................................................362
Figure E-31: Flowback rate at incremental differential pressures on Berea sandstone
with a lab simulated perforation (BS-long-14)................................................363
Figure E-32: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-long-14) ....................363
xxxv
Figure E-33: Static filtration of UltraCarb-2 on a long Berea core simulating open hole
completion (BS-long-14).................................................................................364
Figure E-34: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Boise sandstone with a lab simulated perforation (Bo-4) ....365
Figure E-35: Return permeability spectra with incremental differential pressures for
Boise sandstone with a lab simulated perforation (Bo-4) ...............................365
Figure E-36: Static filtration of UltraCarb-20 on a long Berea core simulating open hole
completion (Bo-4) ...........................................................................................366
Figure E-37: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Boise sandstone with a lab simulated perforation (Bo-6) ....367
Figure E-38: Return permeability spectra with incremental differential pressures for
Boise sandstone with a lab simulated perforation (Bo-6) ...............................367
Figure E-39: Static filtration of UltraCarb-20 on a long Berea core simulating open hole
completion (Bo-6) ...........................................................................................368
Figure F-1: Flowback rate at incremental differential pressures after filtration with
bentonite mud on Berea sandstone (BS-12-22-03-I).......................................371
Figure F-2: Return permeability spectra with incremental differential pressures for
Berea sandstone (BS-12-22-03-I)....................................................................371
Figure F-3: Static filtration of bentonite mud on Berea sandstone simulating open hole
completion (BS-12-22-03-I)............................................................................372
Figure F-4: Flowback rate at incremental differential pressures after filtration with
bentonite mud on Berea sandstone (BS-12-15-03-I).......................................373
Figure F-5: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-12-08-03) .............................................374
1
Chapter 1: Introduction
1.1 BACKGROUND
Fluids are used in oil and gas wells for various well operations such as drilling,
completion and stimulation. According to the nature of the operation these fluids are
classified as drilling fluids, completion fluids, or stimulation fluids. In the early history of
the oil industry, the major focus was mainly on drilling and hence most of the
advancement took place on drilling fluids 1, 2. Drilling fluids have many functions, such
as: 1) clean the broken rock fragments beneath the bit, 2) carry those cuttings to the
surface, and 3) exert sufficient pressure against the formation fluids to prevent them from
flowing into the well bore.
Because of an overbalance pressure, wellbore fluids invade the formation during
drilling, completion or stimulation operations. The invasion of fluids and solids into the
formation is a multi-component filtration problem studied and presented by Suri 3.
Invasion of solids, polymer and filtrate into the formation reduces the ability of the
formation to produce. This is because the pores are plugged by the solids and polymers
from the wellbore fluids. The different mechanisms of formation damage can be
summarized as follows 4, 5 :
1. Mechanically Induced:
a. Solids and Polymer Invasion
b. Fines Migration
c. Phase Trapping (water block, gas breakout, condensate banking)
d. Stress Induced
2. Chemically Induced
a. Rock – Fluid Incompatibility
2
i. Clay Swelling
ii. Clay Deflocculation
iii. Formation Dissolution
iv. Chemical Adsorption
b. Fluid – Fluid Incompatibility
i. Solids Precipitation
ii. Wettability Alteration
iii. Wax Deposition
iv. Asphaltene Formation
3. Biologically Induced
4. Thermally Induced
It is believed that the predominant form of near wellbore formation damage is the
invasion of solids and polymers into the formation 6, 7. The invasion of the fluid leads to
the formation of an internal filter cake and an external filter cake. To minimize the
formation damage caused by fluid invasion, Suri and Sharma 8 presented strategies for
sizing solids in the drilling and completion fluids. The filter cake (internal and external)
that can restrict the production during flowback, strengthens the well bore 9 as well.
One of the strategies adopted to prevent formation damage caused by drilling and
completion fluids is to operate the well with an under-balanced mud column which
prevents any invasion of the well bore fluid into the formation. Unfortunately, this
operation is risky in high pressure wells. This method requires the use of special
equipment and trained crews, and may not be economically feasible. Using low density
drill-in fluids can cause severe washouts and bit-balling. In most wells, an overbalanced
column must be maintained in the well, and thus complete prevention of impairment due
3
to solids and filtrate invasion seems impossible. Another strategy to prevent any invasion
of solids into the formation is to use “clear” brines which, in theory, have no solids and,
therefore, cannot damage the formation due to the internal and external filter cake
deposition. But in practice, all field brines contain solids, although the amount may be
very small. The particles contaminating the brine may come from the source water or
from the sacked salt, or they may be picked up in tank trucks or rig pits. Even if extreme
care is taken to remove the contaminating solids at the surface, enough solids may be
picked up on the way down the tubing to cause considerable impairment. Therefore, there
is always going to be some invasion of solids and filtrate into the formation from the
wellbore fluids leading to a build-up of an internal and an external filter cake.
To design drilling and completion fluids for the pay-zone, both the drilling and
the productivity objectives need to be considered. The drilling and productivity objectives
are summarized as follows:
1. Drilling objectives:
• Well-bore stability
• Shale inhibition
• Hole cleaning
• Good lubricity
• Drag and torque mitigation
• High rate of penetration subject to safety, environmental and cost constraints
2. Productivity objectives:
• Minimum invasion of the well-bore fluid (solids and filtrate) into the
formation
4
• Thin, tough and ultra-low permeable external filter cake build up for
minimum fluid leak-off
• Low flow initiation pressure and large return permeabilities during production
In recent years, a new class of drilling fluids has been developed (drill-in fluids)
with special consideration for the productivity objectives. These drill-in fluids form filter
cakes that can be dissolved in acids. Sized CaCO3 and sized salt drill-in fluids are two of
the most commonly used fluids of this kind. Another advantage in using these fluids is
that the size of the solids in these fluids can be designed according to the formation pore
size distribution which would result in more effective bridging of the particles at the
formation face resulting in minimum invasion of the solids and polymers into the
formation. Polymers are added to these drill-in fluids to meet the drilling objectives and
for building an ultra-low permeable external filter cake to minimize the filtrate loss.
A fluid used in a well during completion or work-over operations is called a
completion fluid. Completion fluids remain in contact with the productive pay-zone for
days in a static and an overbalanced condition. The completion fluids used today are
broadly categorized into water-based fluids, oil-based fluids, foams, and emulsions. A
detailed overview of completion fluids is provided by Al-Riyamy 10. Water-based fluids
(brines) are the most commonly used completion fluids.
In the past, the use of oil-based drilling fluids had simplified many drilling
operations that involve water sensitive shales, hole stability issues, friction related
problems etc. However, disposal of the used oil-mud and the oil-soaked cuttings has
become a challenge because of environmental concerns 11, 12.
5
1.2 DEFINITION OF THE PROBLEM
Zain and Sharma 13 clearly showed that the external filter cake does not play any
role during flowback and that it is the solids and polymer invasion which determines the
flow initiation pressure and the return permeability. Therefore, it is expected that after the
well is drilled, completed and put back on production, the internal filter cake be
completely removed leaving behind a formation with clean pores. Breakers such as
hydrochloric acid or an oxidative solution can be used to remove the filter cakes.
However the use of breakers has resulted only in a marginal improvement in the return
permeability. Some of the reasons for the ineffectiveness of the breakers are:
1. The breakers usually have an insufficient contact time with the filter cakes to dissolve
them completely.
2. The breakers can be partially spent with other downhole materials such as tubing,
hydrocarbons, and other components in the well-bore and as a result may not come in
contact with the target zone.
3. The breakers might be ineffective in dissolving the polymers (starch, xanthan etc.)
which cause the most damage.
Some of the concerns in using the breakers are:
1. The breakers may lead to the damage of the downhole materials.
2. The breakers may lead to formation damage.
3. The use of breakers might be uneconomical.
4. The breakers (acids and oxidizers) could be unsafe and hazardous to handle.
5. The breakers could be unfriendly to the environment.
Recently environmentally friendly breakers are formulated which can attack the
polymer in the muds 14. These polymer linkage-specific enzymes offer a safe, effective
alternative to conventional cleanup methods that usually consist of oxidizers such as
6
bleach and acid. These enzymes has none of the “side effects” associated with non-
specific reactants such as premature reaction, corrosive damage to down hole tools and
tubular goods, and disposal problems. Enzyme such as α-amylase targets the starch in the
filter cake as starch acts as a binder for the calcium carbonate and other solids in the
fluid15.
However, even if the breakers can dissolve both the external and the internal filter
cake completely, and be environmentally friendly, there is a significant risk of invasion
of these breakers into the formation which can lead to more damage to the formation.
Therefore, it is still common to flow the wells back naturally (by reducing the well bore
pressure to a value lower than the average reservoir pressure) than to use special acids,
breakers or enzymes to cleanup the filter cakes. Hence, in this dissertation we intend to
look at the cleanup of the near wellbore region during production without the use of
breakers. The motivation behind the research can be listed as follows:
1. There is no exhaustive study available that quantifies the damage caused by the more
commonly used drill-in and completion fluids on cores with a wide range of
permeability. This quantification of the damage can aid in determining if breakers are
required or not in a particular situation.
2. The standard practice is to use a constant rate during flowback to estimate the FIP and
the return permeability to quantify the damage, with the goal of determining the
drawdown requirements for a well (to initiate production) and to determine the flow
rate of the hydrocarbons into the well for a given drawdown. However, this method is
inadequate in representing the wellbore condition during flowback since flow into a
wellbore occurs at constant drawdown. Chapter 2 discusses this inadequacy in more
detail.
7
3. There is no study data in the literature to evaluate the formation damage caused by
the more commonly used water-based completion fluids in perforated completions.
4. There is no model for the cleanup of the formation damage (internal filter cake)
during flowback (when the well is put on production).
The cleanup of the internal filter cake is postulated to be the controlling factor in
determining the flow initiation pressure (FIP) and the return permeability during
flowback. We intend to find the key parameters which determine the cleanup of the
internal filter cake and using these key parameters make recommendations for designing
less damaging drill-in and completion fluids.
1.3 OUTLINE OF THE CHAPTERS
In this work, cleanup of the internal filter cake during flowback is studied.
Chapter 2 presents an improved laboratory method to estimate the FIP and return
permeabilities during flowback (which is used to quantify the damage caused by the
formation of an internal filter cake into the porous medium). This improved flowback
method is used to measure the FIP and return permeabilities in cores with a wide range of
permeability and for commonly used drill-in and completion fluids. Chapter 3 evaluates
the different components used in the drill-in and completion fluids from the formation
damage stand point. Chapter 4 presents yield strength measurements for filter cakes for
two more commonly used water-based muds. These yield strength measurements are
used to model the cleanup of the internal filter cake and to make recommendations to
better design the drill-in and completion fluids. Chapter 5 presents models for cleanup of
the internal filter cake during flowback. Chapter 6 presents an experimental study on the
cleanup of the filter cakes in the lab-simulated perforated completions. Chapter 7 presents
UTDamage, a filtration and flowback simulator to design drill-in and completion fluids.
8
Finally chapter 8 presents the overall conclusions and recommendations to design drill-in
and completion fluids to minimize formation damage and to maximize well productivity.
REFERENCES
1. Gray, George R., Darley, H.C.H., and Rogers, Walter F.: “Composition and
Properties of Oil Well Drilling Fluids,” Fourth edition, Gulf Publishing Company,
Book Division, Houston, London, Paris, Tokyo.
2. Chilingarian, G. V., and Vorabutr, P.: “Drilling and drilling fluids,” updated textbook
edition, Elsevier, Amsterdam-Oxford-New York, 1983.
3. Suri, A.: “A Model for Multi-Component Filtration” MS Thesis, The University of
Texas at Austin, December 2000.
4. Qutob, Hani, et al.: “Underbalanced Drilling; Remedy for Formation Damage, Lost
Circulation, and Other Related Conventional Drilling Problems,” paper 88698
presented at the 11th Abu Dhabi International Petroleum Exhibition and Conference
held in Abu Dhabi, U.A. E., 10-13 October 2004
5. Kruger, R. F.: “An Overview of Formation Damage and Well Productivity in Oil
Field Operations,” JPT, February 1986, 131-152, SPE 10029
6. Browne, S. V., and Smith, P. S.: “Mud cake Clean up to Enhance the Productivity of
Horizontal Wells,” paper SPE 27350 presented at the SPE Formation Damage
Control Symposium held in Lafayette, 9-10 Feb., 1994
7. Browne, S. V., et al.: “Simple Approach to the Cleanup of Horizontal Wells With
Prepacked Screen Completions,” paper SPE 30116 presented at the SPE Formation
Damage Control Symposium held in The Hague, The Netherlands, 15-16 May, 1995
8. Suri, A., and Sharma, M.M.: “Strategies for Sizing Particles in Drilling and
Completion Fluids,” paper SPE 87676 published in SPEJ, March 2004
9
9. Aston, M. S., et al.: “Drilling Fluids for Wellbore Strengthening,” paper IADC/SPE
87130 presented at the IADC/SPE Drilling Conference held in Dallas, Texas, U.S.A.,
2-4 March, 2004
10. Al-Riyamy, K.: “Synthesis and Characterization of Reversible Emulsions:
Application to Completion Fluids,” dissertation presented to the faculty of the
graduate school of The University of Texas at Austin, May 2000
11. Davidson, E., et al.: “Challenging Reservoir Drilling Conditions Overcome by
Engineered Water Based Drill-In Fluids,” paper AADE-04-DF-HO-03 presented at
AADE 2004 Drilling Fluids Conference, held at the Radisson Astrodome in Houston,
Texas, U.S.A., April 6-7, 2004
12. Cameron, C., et al.: “Water-Based Drilling Fluid Helps Achieve Oil-Mud
Performance,” paper AADE-04-DF-HO-03 presented at AADE 2004 Drilling Fluids
Conference, held at the Radisson Astrodome in Houston, Texas, U.S.A., April 6-7,
2004
13. Zain, M. Z., and Sharma, M. M.: “Mechanisms of Mud Cake Removal During
Flowback,” SPE Drilling and Completion, December 2001
14. Sanders, M. W., et al.: “A Quantitative Method for Estimating a-Amylase-Based
Enzyme Concentrations in Wellsite Field Samples and its Application on a Gravel
Pack Completion,” paper AADE-04-DF-HO-35 presented at the 2004 AADE Drilling
Fluids Conference, held at the Radisson Astrodome in Houston, Texas, April 6-7,
2004
15. Suhy, Thomas, et al.: “Application of Polymer Specific Enzymes To Cleanup Drill-In
Fluids,” paper SPE 51094 presented at the SPE Eastern Regional Meeting held in the
Pittsburgh, PA, 9-11 November 1998
10
16. Bailey et al.: “Particulate Invasion From Drilling Fluids,” paper SPE 51094 presented
at the SPE Eastern Regional Meeting held in the Pittsburgh, PA, 9-11 November
1998
17. Kruger, R. F.: “An Overview of Formation Damage and Well Productivity in Oil
Field Operations,” JPT, February 1986, 131-152, SPE 10029
11
Chapter 2: An Improved Laboratory Method to Estimate Flow Initiation Pressures and Return Permeabilities During Flowback
2.1 INRODUCTION
This chapter presents an improved laboratory method, to estimate the flow
initiation pressure (FIP), needed to initiate flow of hydrocarbons from the reservoir into
the wellbore during production. Using this method, a spectrum of return permeabilities
during flowback is also calculated, at increasing flowback pressures.
First a background on the importance of the FIP and the return permeabilities is
presented. Then a literature review on the standard practices used to estimate the FIP and
the return permeability is presented. The motivation behind improving the standard
practices is discussed. The improved flowback test method is presented in detail,
followed by a list of test objectives. Results are discussed for both single-phase and two-
phase flow experiments in cores with a wide range of permeabilities and with more
commonly used muds. The effect of different parameters on the FIP and the return
permeability is discussed. Finally the tests results are applied to vertical and horizontals
wells for field recommendations.
2.2 LITERATURE REVIEW
2.2.1 Flow Initiation Pressure
In 1994 Browne et al.1 presented data on several British Petroleum operated non-
perforated horizontal wells in the North Sea that did not produce from the entire
completed interval. They believed that geological variation and partial cleanup of the
drilling-mud filter cake were the two main reasons for the reduced production. Based on
12
their hypothesis of partial cleanup of filter cakes they suggested laboratory based mud-
cake cleanup tests. Their objectives for formulating mud-cake lift-off tests were:
1) To design filter cakes which need low differential pressure to lift-off,
2) To find out if the filter cakes can be readily removed by fluids,
3) To maximize productivity from horizontal or high angle well bore sections.
The term “lift-off pressure” was first used for estimating the minimum differential
pressure required to initiate flow in a well. More recently “flow initiation pressure” has
been used instead 2. It was not made clear 1 whether the cake lift-off tests were done
under constant flowback rate or constant flowback pressure. I assume that the tests were
done at constant flowback rates based on their subsequent paper 2 in which they used
constant flowback rate for measuring the flow initiation pressure.
Figure 2.1 shows a typical differential pressure profile during a cake lift-off /
flowback test done at a constant flowback rate. It shows ∆P readings recorded as oil is
injected in the reverse direction at an injection rate of 5 ml/min after mud filtration was
conducted at 100 psi on Berea sandstone. As the fluid is flowed back (after mud
filtration), a peak injection pressure, ∆Pmax, is quickly reached, followed by a gradual
decrease until a stabilized pressure ∆Pfinal is obtained. The difference between the peak
pressure and the stabilized pressure is defined as the flow initiation pressure (FIP), ∆Pfi
(equation 2.1). The purpose of determining this laboratory-measured FIP was to estimate
the magnitude of the minimum drawdown pressure required to lift the external filter cake
off and thereby initiate production in a well.
∆Pfi = ∆Pmax - ∆Pfinal (2.1)
13
Browne et al.1, 2 showed that the lift-off pressure depends on the permeability of
the rock and the type of mud used. Their laboratory studies showed that low permeability
reservoirs have significantly larger lift-off pressures than larger permeability sections.
Bailey et al 3 used the term flow initiation pressure (FIP) instead of lift-off
pressure to estimate differential pressure required to initiate flow during flowback. They
presented laboratory data on filter cake strength and its relation to cleanup by back
production for typical reservoir drilling fluids. They showed that FIP is linearly
dependent on filter cake yield strength irrespective of the composition of the water-base
mud.
Ryan et al. 4 indicated that oil-based muds have smaller FIP than water-based
muds. They found that complete external filter cake removal is not necessary to produce
oil through the cake.
Zain and Sharma 5 studied external filter cake behavior by measuring the
flowback pressure profile after mud filtration at constant flow rate. They found that the
external filter cake plays no role in determining the FIP and return permeability. Rather it
is solids and filtrate invasion, which determine the flowback pressure profile during
production.
Rana and Sharma 6 worked on finding the relative importance of solids and
filtrate invasion on the FIP. They showed that for low permeability rocks and small
mobility ratios, relative permeability effects play a dominant role in determining the
flowback pressure profile while for high permeability rocks (>100 md) and large mobility
ratios, both the internal filter cake and relative permeability effects play a significant role.
Alfenore et al. 7 suggested using an ultra low flow rate (0.1 cm3/min) for the
flowback rate to measure FIP. Their results show that oil-based muds have smaller FIP
values than those obtained with water-based muds.
14
Ladva et al. 8 studied the effect of permeability, core length, mud type, and
flowback rate on FIP and provided possible explanations for why FIP is found to be
larger in low permeability cores as compared to high permeability cores in constant
flowback experiments. They used a very small flowback rate of 0.1 cm3/min for
determining the FIP. Their results suggested that the external filter cake does not play a
significant role in determining FIP and that two-phase flow results in larger FIP
compared to single-phase flow. They concluded that core length and velocity of the
flowback fluid will alter the value of FIP and that a drawdown test method is preferred
which will better approximate the conditions observed at the onset of production in a real
well.
Gruber et al. 9 recommended a constant pressure flowback method over a constant
rate flowback method to be consistent with the application of a drawdown in a well. They
found that a minimum “threshold pressure” was required for the fluid to start flowing
upon imposing a differential pressure and measuring the resultant flow rate. Regain
permeability was found to improve with increasing pressure differentials and with
increasing volumetric throughput. They found the maximum threshold pressure to be
approximately 6 psi for cores with an absolute permeability of 30 md using two different
muds. In their subsequent paper 10 they found the “threshold pressure” to have a well
defined inverse relationship with permeability, especially in carbonate cores. In this paper
they found threshold pressures as high as 30 psi for cores with an absolute permeability
of 1 md. They suggested capillary pressure to be the cause of these larger threshold
pressures.
To date almost all the studies for determining FIP have used a constant rate
flowback procedure 1-7 rather than a constant pressure flowback condition 9, 10 to estimate
the drawdown required to initiate production in a well.
15
2.2.2 Return Permeability
Return permeability is defined as the effective permeability to hydrocarbons
during production. The return permeability determines the oil flow rate into a well for a
given drawdown (pressure difference between the reservoir and the well). The standard
practice for measuring return permeability uses a constant flowback rate. Oil is flowed in
the reverse direction to mud filtration at a constant rate while the pressure profile is
recorded until a stable pressure drop across the core is obtained. Figure 2.1 shows a
typical flowback pressure profile at a constant flowback rate used in laboratory studies.
The return permeability ratio is calculated at a specific flowback rate and signifies the
extent of cleanup at a particular flow rate. The return permeability ratio is calculated by
dividing the stabilized ∆P reading before filtration by the stabilized ∆P reading during
flowback (after filtration) at a given flow rate:
Return permeability ratio = ∆P initial / ∆P final (2.2)
The return permeability calculated by the above method is flow rate dependent 5.
However, oil wells in the field are usually produced at fixed drawdowns that approximate
a constant pressure boundary condition. This suggests the use of constant pressure
differentials across the core during flowback instead of using a constant flow rate to
determine the return permeability ratio. Figure 2.2 shows a typical flowback profile for a
constant pressure flowback condition.
Today horizontal wells are increasingly used in oilfield developments to
maximize well productivity, access widely spread reserves, or reduce water and gas
coning by reducing drawdown. Browne and Smith11 showed that these benefits require
the horizontal well sections to be flowing without significant near well bore damage.
16
Ryan et al.12 presented a major joint industry project to study the effectiveness of
different mud cleanup techniques (acids, breakers, solvents) for horizontal wells. The
results of their studies indicate that there is no single best technique for the cleanup of
uncemented / open hole horizontal wells. They concluded that a ‘universally’ non-
damaging mud system or cleanup technique is unlikely to exist. Reservoir specific testing
is required to establish damage levels. They also concluded that:
1. Complete external filter cake removal is not necessary to produce oil through the
cake.
2. High solids loadings in the mud system were found not to adversely effect oil
production through the mud cake.
3. Aggressive breakers (acid) effectively clean the well bore and screens but can
generate increases in fluid losses.
4. Whole mud has a greater impact on sand control screen damage than filter cake back
production.
6. Oil-based muds show smaller breakthrough pressures (FIP) and lower damage levels
(larger return permeability) than water-based muds.
7. Most of the breakers were found to increase the breakthrough pressure (FIP) than to
reduce them.
8. Breakers behaved differently for different mud systems with significant reductions in
damage levels found in many cases but, conversely some mud breaker combinations
increased damage.
Marshall et al.13 presented a detailed comparative study on return permeability.
Their objective was to standardize formation damage testing to select the appropriate
drilling fluid and/or cleanup technique. They presented an extensive laboratory study,
17
based on a refined recommended practice for the determination of return permeability.
They found a wide variation in the results from different laboratories which didn’t allow
for a good level of repeatability and reproducibility.
Alfenore et al.15 have shown that the flowing area ratio between a typical vertical
perforated well and a horizontal open hole completion is ~50/1, resulting in a fluid
velocity ratio to be ~13/1. This would suggest using a 13 times smaller flowback rate for
determining the return permeability ratio for horizontal wells compared to the flowback
rate used for determining return permeability ratio for vertical wells. Assessing return
permeability ratios at elevated drainage rates for horizontal open hole situations would be
irrelevant. Their results showed that oil-based muds (OBM) clean-up faster and easier as
compared to water-based muds (WBM).
Various authors16, 17 have shown the importance of designing drilling and
completion fluids for minimum formation damage. Some authors18, 19 have also presented
models for particulate invasion from drilling fluids into the formation. Suri and Sharma20
presented a rigorous multi-component model to predict the invasion of solids and
considered build-up of both the external and internal filter cake. Their model can be used
to design the mean particle size of the bridging agents to effectively bridge the formation
pores and also filter the polymers in the external filter cake.
2.3 PROBLEM DESCRIPTION AND MOTIVATION
The term flow initiation pressure (FIP) is defined in the literature as the difference
between the peak differential pressure and the stabilized differential pressure across a
core during flowback. The standard practice for estimating FIP is to flowback at a
constant rate after mud filtration. Figure 2.1 shows a typical flowback pressure profile at
constant rate that is used to determine FIP.
18
It is also found that at different flowback rates, different FIP values are observed,
resulting in a non-unique value for estimating flow initiation in a well during production.
There should be a unique value of drawdown required to initiate flow for a given
formation, mud, overbalance pressure and flowback fluid. Various authors have
suggested using a very small flowback rate to estimate FIP. Even a very small flowback
rate would give an approximate FIP that would be rate dependent.
Since flowback in oil and gas wells occurs at constant drawdown (constant
differential pressure between the reservoir and the wellbore), it is more reasonable to
measure the flow initiation at constant differential pressures. Therefore, to estimate the
flow initiation pressure, we conduct constant pressure flowback experiments instead of
constant rate flowback experiments. The constant pressure flowback experiment better
approximates the conditions observed at the onset of production in a real well than the
constant rate flowback experiment. Figure 2.2 shows measured flowback rates at a series
of increasing pressure differentials to determine the FIP and to measure the return
permeability spectra.
2.4 EXPERIMENTAL DESIGN
2.4.1 Test Equipment
A schematic of the experimental setup is shown in Figure 2.3. Two different sized
core holders were used in the apparatus to accommodate for two different core plug sizes.
The short core holder accommodates a 2.5 inches diameter, 1.0 inch core long core plug,
and approximately 110 ml of fluid inside the filter cell. The filtration unit can be heated
up to 350oF and can withstand a maximum filtration pressure of 1300 psi. The long core
holder can accommodate a core plug 2.0 inch in diameter, and up to 12 inches in length.
A hollow cylindrical sleeve with 2.0 inch diameter and ¼ inch thickness was specially
19
designed to hold fluid (drill-in or completion fluid) in the long core holder. The main
purpose behind setting up a long core apparatus was to be perform filtration experiments
on cores having long simulated perforations. It also enabled us to study the depth of
damage caused by solids and polymers (internal filter cake) and filtrate invasion by
recording pressure readings at 2 inch intervals along the length of the core. Figure 2.4
shows a schematic of the long core apparatus. In the short core holder the cores are
epoxied on the sides to restrict any flow between the core and the sides of the cell. The
long core holder uses confining pressure on a rubber sleeve around the core to restrict
flow between the core and the sides of the sleeve. The following is a list of items used to
conduct the mud filtration and flowback experiments:
1. Short HPHT core holder
2. Long HPHT core holder
3. Beckman pump (constant rate condition)
4. Highly sensitive pressure reducing regulator (constant drawdown condition)
5. Accumulators
6. Back pressure regulator
7. Pressure gauges
8. 1/8 inch tubing
9. 2 way valves
10. 3 way valves
11. Pressure transducers
12. Validyne interface
13. Data acquisition computer
14. Data acquisition software (Softwire, Sartoconnect)
15. Electronic balance
16. Dessicator
17. Vacuum pump
18. High pressure source (compressed N2 gas cylinder)
20
Actual photographs of the main equipment and tools used to conduct the
experiments are shown in Appendix-A.
2.4.2 Core and Fluid Sample
Table 2.1 shows the dimensions of the two different sized core plugs used in the
experiments. The dimensions for the shorter core were 2.5 inch diameter and 1 inch
length and the dimensions for the longer core were 2 inch diameter and 6 inch length.
Table 2.2 shows five different rock types used in the study with a permeability range of 4
md to 1500 md. The five rock types used are:
1. Nugget sandstone (4 md),
2. Texas limestone (25 md),
3. Berea sandstone (200 md),
4. Synthetic Aloxide (1000 md), and
5. Boise sandstone (1000 md).
Figure 2.6 shows the pore volume distribution obtained from mercury
penetrometer for some of the rocks used. The larger permeability rocks have a larger
median pore diameter. Texas limestone has a median pore diameter of 0.711 microns,
Berea sandstone has a median pore diameter of 13.5 microns, and Boise sandstone has a
median pore diameter of 17.6 microns.
Two types of fluids were used for the filtration experiments. Table 2.3 shows the
fluid components and their concentration used in formulating the UltraCarb drill-in fluid.
Table 2.4 shows the fluid rheology for the UltraCarb fluid. Table 2.5 shows the fluid
components for the bentonite mud while Table 2.6 shows its rheology.
21
Fluids used for the flowback were: 1) 3% brine solution for single-phase flow
experiments, 2) a non-corrosive and non-reactive oil distillate (Exxsol D110) was used
for the two-phase flow experiments.
2.4.3 Test Procedure
Figure 2.5 shows a schematic of the experimental procedure used for the mud
filtration and flowback test. The detailed procedure is explained step by step as follows:
1. Obtain core plugs of desired dimensions. Clean and dry them in an oven (at 100oC)
for at least 24 hours.
2. Apply a thin layer of epoxy on the side of the short core plug to avoid flow through
the sides of the plug. The epoxy layer is necessary for the small core filtration unit as
it does not have the option of confining pressure but depends only on the two rubber
O-rings each set on the top and bottom of the plug for sealing the sides. The long core
plugs don’t need epoxy as the long core apparatus uses a Viton sleeve confining
pressure to seal the sides of the core.
3. Vacuum the core plugs with 3 % NaCl brine for at least 12 hours.
4. Install the fully saturated core plug in the filter cell followed by the fluid distribution
end cap. Tightly set all cap-locking screws to ensure complete sealing of the side of
the plug while using the short core holder.
5. Inject brine (3 % NaCl) from bottom to top of the core plug at rates from 1 to 10
ml/min as seen in Step 1 of Figure 2.5 (simulating flow from the formation to the well
22
bore). Record differential pressures readings (∆P) continuously until a stabilized ∆P is
reached for the different injection rates.
6. Plot the injected flow rate vs. the measured stabilized differential pressure across the
core. Fit a straight line through all the data points assuming Darcy’s law:
Pmq ∆= (2.3)
where q is the flow rate in cc/min, ∆P is the differential pressure in psi and m is
the slope given by the following equation
1 96.456
k AmLµ
= (2.4)
where k is the permeability in md, A is the area in inch2, µ is the viscosity of the
injected fluid in cp and L is the length of the core in inch.
7. For two-phase experiments inject Exxsol D110 (oil) at a injection rate of 1 ml/min
from top to bottom of the core for piston like displacement of water with oil. After 3-
4 hours of injection increase the flow rate to 10 ml/min and continue flowing for an
hour or so until the pressure drop across the core is stabilized. After that the plug is
assumed to be at irreducible water saturation.
8. Inject Exxsol from bottom to top at rates from 1 to 10 ml/min as seen in Step 1 of
Figure 2.5 (simulating flow from the formation to the well bore). Record differential
pressures readings (∆P) continuously until a stabilized ∆P is reached for the different
23
injection rates. Calculate effective permeability to oil assuming linear Darcy flow
(step 6).
9. Dismantle the filter cell. Pour mud out of the cell. Please note that to pour the mud
out of the filtration cell, the core plug has to be taken out from the filtration cell. This
exposes the core plug to atmosphere. Therefore, it is important to perform this step as
quickly as possible to avoid any drying of the core.
10. Apply a desired filtration (overbalance) pressure using a nitrogen line (Step 2). Open
the valve at the bottom of the cell to allow fluid loss. Collect and record mud filtrate
volume every minute for 30 minutes and every hour for 16 hrs using an electronic
balance connected to a PC.
11. Slowly bleed off the filtration pressure inside the filter cell to atmospheric pressure.
12. Use Exxsol D110 for two-phase flowback experiments and 3 % brine solution for
single-phase flowback experiments. Details of the flowback procedure are provided
in Sub-Sections 2.4.3.1 and 2.4.3.2 below.
2.4.3.1 Constant Pressure Flow-back Procedure
1. Make sure all the lines are liquid filled, specially the outlet line which is open to
atmosphere in case of no back flow pressure. Apply a constant pressure (~ 1 psi) at
the bottom of the core using a sensitive pressure regulator. Monitor the outlet to
check if there is any flow. Keep the flowback differential pressure constant at 1 psi
for 10 minutes and keep monitoring any flow at the outlet.
24
2. In case of no flow, slowly increment the pressure at the bottom of the core using the
pressure regulator to 2 psi and hold it constant for 10 minutes while monitoring the
outlet. Repeat the above step by incrementing the flowback differential pressure by 1
psi until there is some measurable flow.
3. The differential pressure at which there is flow observed at the outlet is recorded as
the flow initiation pressure (FIP). The fluid from the outlet is collected using a
balance and the data is transferred from the balance to a computer electronically to
calculate the flowback rate. The pressure is held constant until the flowback rate
becomes constant.
4. Increment the flowback differential pressure in small steps (1-2 psi) to study the
cleanup behavior of the internal and external filter cake. Figure 2.2 shows a plot of
incremental flowback differential pressures and measured flow rates with time.
Increment ∆P slowly (1-5 psi) until 20 psi is reached and keep recording the flow rate
until rates are stabilized. Apply larger increments of about 10-20 psi after reaching a
flowback differential pressure of 20 psi. Keep incrementing the ∆P up to a maximum
desired flowback differential pressure. In most of our experiments we applied a
maximum of 100 psi flowback differential pressure.
5. Calculate the return permeability spectra using the following steps:
• Tabulate the flowback results as follows: The applied flowback differential
pressure values (∆Pflowback) and the corresponding measured flowback rates (q
flowback). Calculate the ideal differential pressure for the different recorded
flowback rates as given by:
25
m
flowbackideal
qP∆ = (2.5)
where m is given by Equation 2.4.
• Calculate return permeability ratio for different applied flowback differential
pressures by using the following equation:
Return Permeability Ratio ideal
flowback
PP∆
=∆
(2.6)
• Plot the return permeability ratios vs. the applied differential pressures. This plot
provides return permeability spectra for incrementing drawdowns.
2.4.3.2 Constant Rate Flowback Procedure
1. Inject fluid (oil for two-phase and brine for single-phase) from the bottom of the cell
at a constant rate of 1 ml/min. Monitor and record ∆P readings until stabilized
readings are observed.
2. Increase the flowback rate to 3 ml/min and then 5 ml/min and record the flowback
differential pressures until stabilized readings are observed for each rate.
3. Calculate the return permeability ratio for the different flowback rates using equation
3.1.
Finally, dismantle the filter cell and record observations for the external filter
cake such as thickness, rupture, cracks, and partial or total removal. Photograph the filter
cake and the core.
26
2.5 TEST OBJECTIVES
1. Study the effect of core permeability on FIP and return permeability spectra.
2. Study the effect of flowback condition (constant rate vs. constant pressure) on FIP
and return permeability spectra.
3. Study the effect of different fluids (sized CaCO3 drill-in fluid and bentonite mud) on
FIP and return permeability spectra.
4. Study the effect of single vs. two-phase flow on FIP and return permeability spectra.
5. Compare FIP and return permeability spectra for constant pressure flowback
experiments with constant rate flowback experiments.
6. Study the leak-off behavior of different drill-in fluids on different permeability cores.
7. Study the effect of overbalance pressure on FIP and return permeability spectra.
8. Study the effect of back pressure on the removal of internal and external filter cake
(FIP and return permeability spectra).
2.6 DISCUSSION OF EXPERIMENTAL RESULTS
We conducted single-phase and two-phase filtration and flowback experiments on five
different cores and with two different fluids. We measured and reported the following
parameters for all the experiments:
1. Flow initiation pressure
2. Return permeability ratio vs. flowback differential pressure
3. Filtrate loss during mud overbalance
27
2.6.1 Single-phase (Brine) Experiments
The motivation behind conducting single-phase experiments was to obtain results
that would help us understand the flowback problem better. Some factors which can
determine the FIP and the return permeability spectra are:
1. External filter cake properties.
2. Internal filter cake properties.
3. Capillary pressure curves for the rock.
4. Relative permeability curves for the rock.
In this set of experiments the flowback problem is simplified by having to
understand the effect of only the external and internal filter cake in determining the FIP
and return permeability as there are no capillary pressure and relative permeability effects
due to two-phase flow.
Table B.1 in Appendix-B shows a list of all the single-phase constant-pressure
flowback experiments conducted, together with a summary of results. Subsequently,
three plots are shown for each of the experiments conducted:
1) Applied differential pressure and measured flow rates vs. time during
flowback,
2) Return permeability ratio vs. applied differential pressure, and
3) Filtrate loss vs. square root of time.
A brief discussion is also presented in Appendix-B for some of the experiments
after the plots.
28
2.6.1.1 Flow Initiation Pressure
Table 2.7 shows a summary of flow initiation pressures (FIP) for single-phase
constant pressure flowback experiments. Five different types of cores with permeability
ranging from 4 md to 1500 md (Nugget sandstone (4 md), Texas limestone (25 md),
Berea sandstone (200 md), Boise sandstone (1000 md), and Aloxide (1500 md)) were
used with UltraCarb drill-in fluid and bentonite mud. An overbalance pressure of 100 psi
and static filtration time equal to 16 hrs was used for most of the experiments. The
maximum FIP for all the single-phase flow experiments with short cores (1 inch in
length) and appropriate sized fluids resulted in a value of 4 psi. However, upon using
UltraCarb-2, the FIP for Aloxide core (1500 md) resulted in a much larger value of 8 psi.
This suggests that larger FIP values are obtained if the bridging solids are not correctly
sized for the porous medium. The bridging additive particle size was changed from
median size of 2 microns to 20 microns to minimize the invasion of solids and polymers
into the core. Using UltraCarb-20 for Aloxide and Boise sandstone, resulted in a FIP
value smaller than 4 psi. The results indicate that the FIP values are independent of the
rock permeability if the solids are sized properly.
Figures 2.7 to 2.10 show photographs of cores (Texas limestone, Berea sandstone,
Nugget sandstone and Aloxide) after flowback at constant pressure. It can be seen that
the external filter cake detaches from the surface of the cores but doesn’t break into
pieces while allowing flow.
2.6.1.2 Return Permeability Spectra
Table 2.8 shows return permeability ratios for four different flowback differential
pressures (FIP, 20 psi, 50 psi, and 100 psi) for most of the single-phase constant pressure
flowback experiments simulating open-hole conditions. For larger permeability cores
29
(Aloxide, and Boise sandstone), the maximum flowback differential pressure applied was
equal to 50 psi. The flow rates for larger permeability rocks were so high that the
accumulators holding the flowback fluid emptied out very quickly. It is observed in the
table that most of the return permeability improvement is at or below 20 psi of applied
flowback differential pressure. Appendix-B shows return permeability spectra for all the
single-phase flowback tests. A return permeability spectra is a plot between return
permeability ratios vs. applied differential pressures during flowback. All return
permeability spectra are found to be S-shaped.
Figure 2.11 compares the return permeability spectra for all the single-phase
flowback experiments on different rocks using UltraCarb-2 drill-in fluid. The return
permeability ratios for cores with absolute permeability less than 200 md (Nugget
sandstone, Texas limestone and Berea sandstone) are found to reach values above 50% at
larger differential pressures. This suggests a significant amount of natural cleanup of the
damage in cores with permeability less than 60 md at larger differential pressures. But for
Aloxide core with an absolute permeability of more than a Darcy, the return permeability
ratios are found to be quite poor (< 10 %). This indicates that the solids were not sized
correctly for the larger permeability cores which resulted in large invasion of solids and
polymers. In such cases acidizing may be required to improve the return permeability. In
general, the return permeability ratios are found to be larger for cores with smaller
permeability. This indicates that the cores with small absolute permeability were less
damaged than the cores with large absolute permeabilities. The return permeability ratios
are observed to attain an asymptotic value with increasing flowback differential pressures
for all the experiments.
30
2.6.1.3 Filtrate Loss
Table 2.9 shows spurt loss and 30 minute API filtrate loss for single-phase
filtration experiments simulating an open-hole completion. The API filtrate loss is based
on a 3 inch diameter filter paper for standard reporting. Figure 2.12 and 2.13 show plots
of spurt loss and API filtrate loss vs. the absolute permeability of the cores used to
conduct the single-phase experiments. It can be seen that the cores with larger
permeability show larger spurt loss and filtrate loss than cores with smaller permeability
for the same filtration fluid. Bentonite muds result in larger filtrate loss than UltraCarb
drill-in fluids.
Appendix-B contains plots for cumulative filtrate loss with square root of time for
all the single-phase filtration experiments. The plot shows a linear increase of cumulative
filtrate loss with square root of time that can be expressed as:
w spQ C t Q= + (2.8)
Where Qsp is called the spurt loss and Cw the leak-off coefficient.
2.6.2 Two-phase (Brine + Oil) Experiments
The motivation behind conducting two-phase experiments was to closely
represent the actual flow conditions around a wellbore where there are at least two-phases
(water and oil) present during production.
Table C.1 in Appendix-C shows the list of all the two-phase constant pressure
flowback experiments simulating open-hole completion with results summarized. shown
Three plots are shown for each of the experiments conducted: 1) applied differential
pressure and measured flow rates vs. time during flowback, 2) return permeability ratio
31
vs. applied differential pressure, and 3) filtrate loss vs. square root of time. A brief
discussion is also presented for some of the experiments after their plots.
2.6.2.1 Flow Initiation Pressure
Table 2.10 shows a summary of flow initiation pressures (FIP) for two-phase
constant pressure flowback experiments. Five different types of cores with permeability
ranging from 4 md to 1500 md (Nugget sandstone (4 md), Texas limestone (25 md),
Berea sandstone (200 md), Boise sandstone (1000 md), and Aloxide (1500 md)) were
used with UltraCarb drill-in fluid. An overbalance pressure of 100 psi and static filtration
time equal to 16 hrs was used for most of the experiments. The maximum FIP observed
for the two-phase flow experiments was 7 psi. The FIP for two-phase flow experiments
were slightly larger than the FIP found for similar single-phase flow experiments. This
indicates that an additional differential pressure is required to initiate flow because of
capillary pressure and relative permeability effects in two-phase flow. As in the single-
phase flow experiments, the two-phase flow experiments did not show any correlation
between rock permeability and the FIP.
2.6.2.2 Return Permeability Spectra
Table 2.11 shows the return permeability ratios at four different flowback
differential pressures (FIP, 20 psi, 50 psi, and 100 psi) for the two-phase constant
pressure flowback experiments simulating open-hole conditions. For larger permeability
cores (Aloxide, and Boise sandstone), the maximum flowback differential pressure
applied was 50 psi. It can be observed in the table that the return permeability
improvement is more gradual as compared to single-phase experiments. We still observe
that most of the permeability improvement occurs at or below 20 psi of applied flowback
32
differential pressure. Appendix-C shows the return permeability spectra for all the two-
phase flowback tests. The return permeability spectra for the two-phase experiments are
also found to be S-shaped.
Figure 2.14 compares the return permeability spectra for the two-phase flowback
experiments conducted on Texas limestone and Berea sandstone one inch cores with
UltraCarb-2 drill-in fluid. It is observed that the return permeability improvement is more
gradual as compared to the return permeability spectra for single-phase experiments.
However, the return permeability ratios are found to be larger for cores with smaller
permeability as observed in the single-phase experiments. Similar trend is observed in
experiments conducted on Boise sandstone and Aloxide cores with UltraCarb-20 drill-in
fluid as shown in Figure 2.15. The return permeability spectra are S-shaped and are
asymptotic with increasing flowback differential pressures for all the experiments.
2.6.2.3 Filtrate Loss
Table 2.12 shows spurt loss and 30 minute API filtrate loss for two-phase
filtration experiments simulating open-hole conditions. Figure 2.16 and 2.17 show plots
of spurt loss and API filtrate loss vs. the absolute permeability of the cores used to
conduct the two-phase experiments. Similar observations to single-phase filtration
experiments are seen where larger permeability cores show larger spurt loss and filtrate
loss than smaller permeability cores when using the same filtration fluid. Appendix-C
contains plots for cumulative filtrate loss with square root of time for all the two-phase
filtration experiments. The plots again show a linear increase of cumulative filtrate loss
with square root of time. This indicates the formation of an external filter cake early in
the filtration process.
33
2.6.3 Comparison between Single-phase and Two-phase Flow Experiments
Table 2.13 shows comparison of FIP between single-phase and two-phase flow
experiments. We observe that the FIP is larger for smaller permeability cores in two-
phase flow tests than single-phase flow tests. This is attributed to the additional capillary
pressure required to initiate flow in two-phase flow experiments. However, for larger
permeability cores the FIP is either equal or slightly larger for single-phase flow
experiments than two-phase flow experiments. This is attributed to deeper invasion of
internal filter cake in single-phase flow experiments during mud filtration. The shallower
invasion of the internal filter cake in two-phase flow experiments especially in large
pores is attributed to the resistance imposed by oil in the core to filtrate invasion.
Table 2.14 shows a comparison of return permeability ratios for single-phase and
two-phase flow experiments. We observe that the return permeabilities are larger for two-
phase flow tests than single-phase flow tests. Figure 2.18 to Figure 2.22 show plots
comparing return permeability spectra for single-phase vs. two-phase flow experiments
conducted on cores with different permeability.
Figure 2.18 shows plots of return permeability spectra for single-phase flow and
two-phase flow experiments conducted on Nugget sandstone cores. The single-phase
flow experiment resulted larger return permeability ratios than two-phase flow
experiments for the entire applied differential pressure range. The mud overbalance
during filtration in the two-phase experiment was equal to 140 psi as compared to 100 psi
used in the single-phase experiment. Also while conducting the two-phase experiment,
the bottom of the core came in contact with the drill-in fluid while pouring the mud out
from the filter cell. These two reasons might have caused smaller return permeability
ratios in the two-phase flow experiment than single-phase flow experiment.
34
Figure 2.19 shows plots of return permeability spectra for single-phase flow and
two-phase flow experiments conducted on Texas limestone cores. The single-phase flow
experiment had larger return permeability ratios than two-phase flow experiments up to
about 10 psi of applied differential pressure during flowback. For differential pressures
larger than about 10 psi, the return permeability ratios were observed to be larger for two-
phase flow experiment than single-phase flow experiment. The single-phase return
permeability did not improve after a differential pressure of about 10 psi or larger. This
indicated significant damage in the core used in for the single-phase flow experiment. I
repeated the single-phase flow experiment to confirm the results and obtained nearly
identical spectrum as shown in the figure. This confirmed that significant damage is
caused in Texas limestone cores in single-phase flow experiments. The reasons behind
this large damage in single-phase experiments are unclear.
Figure 2.20 shows plots of return permeability spectra for single-phase flow and
two-phase flow experiments conducted on Berea sandstone cores. From the figure we
observe that the two return permeability spectrums obtained from single-phase and two-
phase flow experiments are very similar.
Figure 2.21 shows plots of return permeability spectra for single-phase flow and
two-phase flow experiments conducted on Aloxide cores. As we can see in the figure, the
two-phase flow experiment yielded larger return permeability ratios than single-phase
flow experiments for the entire applied differential pressure range. The following could
be one of the possible reasons behind larger return permeability in two-phase flow
experiment than single-phase flow experiment. In two-phase flow experiment, most of
the large pores are filled with oil while the smaller pores are filled with brine before
filtration. In single-phase flow experiments both the large and small pores are filled with
brine before filtration. During filtration the water based mud tries to invade the pores due
35
to the overbalance pressure. In single-phase experiments all the pores are invaded by the
filtration fluid. But in two-phase experiments, due to capillary pressure the larger pores
still remain filled with oil while the smaller pores are invaded with the fluid containing
solids and polymers. The large pores in two-phase flow experiments are not invaded to
the extent they are invaded in the single-phase flow experiments. Hence the return
permeability which is more governed by the flow through the large pores is larger in two-
phase flow experiments than in single-phase flow experiments.
Figure 2.22 shows plots of return permeability spectra for single-phase flow and
two-phase flow experiments conducted on Boise sandstone cores. As we can see in the
figure, the two-phase flow experiment yielded larger return permeability ratios than
single-phase flow experiments for the entire applied differential pressure range.
2.7 EFFECT OF DIFFERENT PARAMETERS ON FIP AND RETURN PERMEABILITY
The effect of the following different parameters on FIP and return permeability spectra
are analyzed for the single and two-phase flow experiments:
1. Flow-back condition (constant pressure vs. constant rate)
2. External filter cake
3. Fluid type (drill-in fluid vs. bentonite mud)
4. Core length (1 inch core vs. 6 inch core)
5. Back pressure (No back pressure vs. 500 psi back pressure)
6. Median particle size of the bridging agent
36
2.7.1 Effect of Flowback Condition (Constant Flow Rate vs. Constant Pressure)
Figure 2.23 shows a comparison of FIP for constant flow rate and constant
pressure conditions during flowback in Berea sandstone cores. We can see that the FIP is
larger for the constant flow rate test than for the constant pressure flowback test. The FIP
is equal to 14 psi for the test with constant flow rate while the FIP is equal to only 7 psi
for the constant pressure case.
Table 2.15 shows a comparison of FIP for the constant flow rate tests and
constant pressure flowback tests for two-phase flow experiments. We can see that the
constant flow rate tests yield much larger FIP values than constant pressure tests. These
large FIP values are not valid and would give a very high estimate of the drawdown
required to initiate flow from the reservoir into a well. This would require the use of
artificial cleaning methods if the reservoir is depleted and is not able to provide the
required estimated drawdown. It is, therefore, recommended that constant rate
experiments not be used to estimate FIP since they can yield unreasonably high values.
2.7.2 Effect of External Filter Cake
Zain and Sharma showed that the external filter cake plays no role in determining
the flow initiation pressure. However, they conducted tests using a constant rate condition
during flowback. Tests with constant pressure flowback condition are conducted to verify
if there is any effect of external filter cake on FIP and return permeability.
Two long core experiments are conducted to study the effect of external filter
cake on FIP. In one of the experiments the flowback is done with the external filter cake
while in the other the external filter cake is mechanically scraped before flowback. For
both the experiments, the FIP value is found to be equal to 2 psi. Figure 2.24 shows FIP
and return permeability ratios during flowback for Berea cores with and without external
37
filter cake. It can be seen clearly that the two return permeability spectras are very
similar. Hence, the external filter cake is found to have no effect on the FIP and return
permeability spectrum. The presence of the external filter cake can have a large impact
on plugging of screens and liners and on the injectivity of injection wells. It should be
noted that for the acid or solvents to come into contact with the internal filter cake, either
the external filter cake should be mechanically removed or it should be dissolved
completely.
2.7.3 Effect of Drill-in or Completion Fluid Type
Table 2.16 shows a comparison of FIP, maximum return permeability ratio, and
API filtrate loss for UltraCarb drill-in fluid and a bentonite mud.
Flow initiation pressure: We found FIP equal to 1 psi for both UltraCarb-2 drill-in
fluid and bentonite mud on Texas limestone cores (~ 25 md). However, bentonite mud
gave a smaller FIP value equal to 1 psi for Boise sandstones (~ 1 Darcy) as compared to
the FIP value of 3 psi for UltraCarb-20 drill-in fluid. In conclusion, we observed an
insignificant effect of mud type on FIP on different permeability cores.
Return permeability spectra: The return permeability ratios are found to be better
for bentonite mud as compared to UltraCarb drill-in fluids for both Texas limestone cores
and Boise sandstone. This result was surprising considering the fact that drill-in fluids are
so much more expensive than bentonite muds and are supposed to be less damaging. One
advantage offered by drill-in fluids is that they are easier to remove by stimulation fluids.
Fluid loss: Bentonite muds have a larger fluid loss as compared to UltraCarb drill-
in fluids. As a result, the thickness of the external filter cake formed by bentonite muds
was much larger compared to the thickness of the external filter cake formed by the
UltraCarb drill-in fluid.
38
2.7.4 Effect of Core Length
We used a 6 inch long and 2 inch in diameter Berea core to find out if there is any
effect of core length on FIP. We found the FIP to be equal to 3 psi for the 6 inch long
core, which is comparable to the FIP value of 4 psi for the short Berea core. Hence, no
effect of core length was observed on FIP. This was because FIP depends on the depth of
the internal filter cake, yield strength of the internal filter cake and the pore size
distribution of the rock. All the factors mentioned above are expected to be
approximately equal in the both the short and long core experiments.
Figure 2.25 compares return permeability spectra for experiments conducted on
short and long Berea cores. We can see that the return permeability spectra are quite
different for the two cases. But if we plot the return permeability for the first 2 inches of
the long core the plot shifts toward the short core return permeability spectra. We need to
compute the permeability of the top one inch of the longer core to be able to compare its
return permeability spectra with the short 1 inch core. Unfortunately, we only made
measurements at every two inch intervals in long core experiments. Figure 2.26 shows a
plot comparing the return permeability spectra for the short and long Berea cores with
average flowback velocity on the x-axis. We observe similar trends as in Figure 2.25
showing very little overlap between the short and long core return permeabilities. The
two spectra come close to each other when the permeability of the first 2 inches of the
long core is plotted as seen in Figures 2.25 and 2.26.
2.7.5 Effect of Back Pressure
Figure 2.27 shows a comparison of return permeability spectra for Berea cores
with and without back pressure during flowback. We can observe an insignificant
difference between the two spectra. Hence, we conclude that back pressure has no
39
measurable effect on FIP and return permeability. This means that lab-experiments can
be done without applying any back pressure to characterize formation damage due to
drill-in and completion fluids, which would ease in setting up and conducting the
experiments.
2.7.6 Effect of Median Particle Size of the Bridging Agent
Figure 2.28 shows a comparison of return permeability spectra for UltraCarb drill-
in fluids with two different median size particles on Aloxide core samples. We can
observe larger FIP and smaller return permeability ratios when UltraCarb-2 (median size
= 2 microns) is used than when UltraCarb-20 (median size = 20 microns) is used on
Aloxide cores. Similar trend is seen in Figure 2.29 which shows the return permeability
spectra for UltraCarb-2 and UltraCarb-20 drill-in fluids on Berea core samples.
The external filter cake didn’t lift-off at all when UltraCarb-2 drill-in fluid was
used but it lifted-off completely when UltraCarb-20 drill-in fluid was used. We attribute
this lift-off in the case of UltraCarb-2 drill-in fluid to a much deeper and denser internal
filter cake. The external filter cake is being held to the rock surface by roots (internal
filter cake) which penetrate much deeper into the pores of the rock as compared to the
UltraCarb-20. As a result pin holes are formed in UltraCarb-2 filter cake during flowback
while the external filter cake is still held in place by the internal roots.
2.8 APPLICATION OF RESULTS TO ESTIMATE SKIN AROUND WELLS
The return permeability spectra can be used to estimate the skin around the
wellbores due to the damage caused by the drill-in and completion fluids. The skin is
calculated using the Hawkin’s formula:
40
( 1)(ln )d
d w
rkSkink r
= − (2.9)
where kd/k is taken equal to the return permeability ratio and rd is taken equal to
the sum of the wellbore radius and the length of the core (which was equal to 1 inch for
the short core experiments). We make two approximations in using the return
permeability data to calculate skin around wellbores: 1) The return permeability ratio
(kd/k) in a radial well is approximately equal to the return permeability ratio in the
flowback experiments with linear flow geometry; 2) The depth of damage in a radial well
is approximately equal to the depth of damage in the flowback experiments with linear
flow (which is equal to 1 inch). The approximations will hold well if the depth of damage
is small. Substituting k/kd with the return permeability ratio (RPR) and depth of damage
equal to the length of the core (1 inch), we obtain:
11( 1)(ln )w
w
rSkinRPR r
+= − (2.10)
where RPR is the return permeability ratio and rw is the radius of the well in
inches. Figure 2.30 shows a plot of skin with varying return permeability ratios for a
damaged depth of 1 inch for different well radii. We can see in the above figure that
below a return permeability ratio of 20 % the skin values becomes large.
Figures 2.31 and 2.32 show return permeability ratios at increasing pressure
gradients during flowback in one inch cores with different absolute permeabilities. The
average pressure gradients were calculated by dividing the applied differential pressures
during flowback by the length of the core. Figures 2.33 and 2.34 show the above plots of
return permeability ratio as a function of the log of the average pressure gradient applied
during flowback. We observe in the above figures that a minimum pressure gradient
equal to 10 psi/inch during flowback yields a return permeability ratio larger than 20 %
41
for all the four different types of cores with different permeabilities. Therefore, wells
flowing below a pressure gradient of 10 psi/inch are most likely to be damaged (with skin
factor > 1) and need artificial cleaning methods (acids, mutual solvents, enzymes) to
further improve the return permeability of the near wellbore region.
The following equation is used to calculate the pressure gradient at the wellbore
face for a single well located at the center of a cylindrical, homogeneous and isotropic
reservoir and which is produced instantaneously at a constant rate, q:
2173.94 exp( )
2 4t w
w wr
c rdp q Bdr kh r kt
φµµπ
−= (2.11)
The above equation is the solution of the diffusivity equation for radial flow in an
infinite acting reservoir. It can be observed that the exponential term in the Eq. (2.11) is
smaller than 1, therefore the maximum pressure gradient at the wellbore face is given by:
173.942w wr
dp q Bdr kh r
µπ
= (2.12)
The above equation is essentially Darcy’s law for radial flow at steady state. The
term dp/dr is the pressure gradient in psi/inch, q is the flow rate in STB/day, µ is the
viscosity of the flowing phase in cp, B is the formation volume factor for the flowing
phase in RB/STB, k is the permeability of the near wellbore region in md, and rw is the
radius of the well in ft. For a vertical well h is the thickness of the pay zone while for a
horizontal well h is equal to the length of the horizontal well, both in ft. The pressure
gradient at the wellbore face is directly proportional to the flow rate, viscosity of the
flowback fluid, and the formation volume factor and is inversely proportional to the
42
permeability, wellbore radius, and the thickness of the pay zone in a vertical well or the
length in the horizontal wells.
Figure 2.35 shows a plot of the pressure gradient at the wellbore face for a typical
vertical and a horizontal well with varying flow rates at steady state. The above plot
suggests that the near wellbore region can experience a wide range of pressure gradients
depending upon the flow rate. However, we can observe that the pressure gradients are
between 0.5 to 50 psi/inch in a vertical well (the rates are considered in the range of 100-
10000 STB/day) and 0.1 to 10 psi/inch in a horizontal well (the rates are considered in
the range of 1000-100000 STB/day). Typical values for permeability, viscosity, radius of
the well, formation volume factor, thickness of the pay zone in the vertical well and
length of the horizontal well were chosen as shown in the Figure 2.35 to calculate the
pressure gradients at the wellbore face.
We consider the average pressure gradients applied in the flowback experiments
to closely represent the pressure gradients in a radial well at the wellbore face. The
minimum average pressure gradient (10 psi/inch) which is needed to establish a good
return permeability (> 20 %) of the near wellbore region is in the range of the steady state
pressure gradients (0.5 – 50 psi/inch) for vertical wells. This means that there can be a
significant amount of damage present in the near wellbore region depending upon the
flow rates / pressure gradients in these wells. For the horizontal wells the average
pressure gradient (10 psi/inch) is the upper limit of the approximate pressure gradients
(0.1 to 10 psi/inch) which is required for low skin (return permeability ratio >20%).
Therefore, horizontal wells are most likely damaged even at large flow rates.
Eq. (2.12) assumes a constant permeability of the reservoir to calculate the
pressure gradients at the wellbore face. However the near wellbore permeability is not
constant during production because of the internal filter cake. Therefore, the pressure
43
gradients calculated using Eq. (2.12) will be different from the actual pressure gradients
at the wellbore face during production.
Another approach is to use the flow rate instead of the pressure gradient to
estimate the skin factor. The flow rates can be measured at the wellbore and therefore can
be used to estimate the amount of cleanup for a given flowrate. Figures 2.36 and 2.37
show the average return permeability ratios for inch long cores (Texas limestone, Berea
sandstone, Boise sandstone and Aloxide) at different steady state flowback rates. These
plots can be used to estimate return permeability of the near wellbore region instead of
using the pressure gradient values. For Texas limestone a flowback rate of 1 ml/min
yields a return permeability ratio larger than 20 %, while for Berea sandstone a flowback
rate of 10 ml/min is needed to achieve a return permeability ratio larger than 20 %. For
Boise sandstone a flowback rate of 10 ml/min yields a return permeability ratio larger
than 20 %, while for Aloxide core a flowback rate of 100 ml/min is needed to achieve a
return permeability ratio larger than 20 %.
Figures 2.38 and 2.39 show average return permeability ratios for inch long cores
(Texas limestone, Berea sandstone, Boise sandstone and Aloxide) at different steady state
flowback velocities. The flowback velocities were computed by dividing the flowback
rates by the total area of the top face of the cores. To achieve a return permeability ratio
larger than 20 %, an average flowback velocity of 0.02 cm/min is needed for Texas
limestone, 0.2 cm/min for Berea sandstone, 0.2 cm/min for Boise sandstone and 1
cm/min for Aloxide.
For a specific formation, drill-in fluid and an over-balance pressure, a constant
pressure flowback experiment should be conducted to obtain the return permeability
spectra as a function of average pressure gradient or the average flow rate. The return
44
permeability spectra will give us an estimate of the average pressure gradient needed for
a good return permeability of the near wellbore region.
2.9 CONCLUSIONS
1. Constant pressure flowback experiments result in much smaller FIP values than
constant rate flowback experiments. Constant rate flowback experiments yield
artificially large FIP values that are not representative of values relevant to the field.
2. No correlation is found between FIP and rock permeability for both single-phase and
two-phase flow experiments. However, the FIP for two-phase flow experiments in
small permeability rocks is found to be slightly larger than the FIP values obtained for
single-phase flow experiments because of capillary pressure and relative permeability
effects.
3. Flow initiation pressure (FIP) depends upon the extent and depth of internal damage
(internal filter cake) and does not depend on the external filter cake. FIP will be larger
if the particles in the drill-in fluid are not sized according to the rock permeability
(pore throat size). This causes deeper invasion of solids (larger thickness of the
internal filter cake).
4. Permanent damage to the core is dominated by the internal filter cake, a thin layer of
cake residue inside the porous medium. The return permeability spectra obtained
from the two-phase experiments is similar to the return permeability spectra obtained
from the single-phase experiments. For cores with large permeabilities (Aloxide and
Boise sandstone) the return permeabilities in two-phase experiments are found to be
larger than the single-phase return permeabilities. For cores with small permeabilities
(Texas limestone) and at small flowback pressures the return permeabilities in two-
45
phase flow experiments are found to be smaller than the single-phase return
permeabilities. However at large flowback pressures the single-phase return
permeabilities are found to be smaller than the two-phase return permeabilities. For
Berea sandstone the two spectra (single-phase and two-phase) are found to be very
similar indicating that the cleanup is controlled by the internal filter cake.
5. We recommend using a median size for the bridging additive equal to the median
pore-throat size of the formation for optimizing the return permeability and fluid loss.
If the pore throat size distribution of the formation is very broad then we recommend
using a combination of two or three different median sized bridging agents.
6. Core length plays insignificant role in determining the FIP. However the return
permeability ratios should be calculated at equal intervals in cores with different
lengths to compare the return permeabilities.
7. Back pressure on the external filter cake plays no role in determining the FIP and
return permeability.
8. The return permeability spectra, when plotted as a function of applied differential
pressure during flowback are consistently S-shaped. Return permeability spectrum is
a more meaningful measure of the formation damage than the FIP value. The return
permeability spectra can be used to evaluate the formation damage potential of
different drill-in and completion fluids.
9. The return permeability spectra can be used to estimate the skin in vertical and
horizontal wells as a function of the pressure gradient at the wellbore face or the flow
velocity of the hydrocarbons into the well. A pressure gradient of approximately 10
46
psi/inch or a flowback velocity of 1 cm/min is needed at the wellbore face to obtain a
skin factor < 1 for most formations completed open-hole provided the solids are
correctly sized according to the formation permeability or pore size distribution.
47
Table 2-1: Short and long core dimensions
Core type Core length (inch)
Core diameter (inch)
Short core 1 2.5
Long core 6 2
Table 2-2: Different core types used in the study
No. Core name Average porosity (%)
Av. absolute permeability
(md)
1 Nugget sandstone 14 4
2 Texas Limestone 29 25
3 Berea sandstone 20 200
4 Boise sandstone 28 1000
5 Aloxide 44 1500
48
Table 2-3: Formulation of a sized CaCO3 drill-in mud (9.5 ppg UltraCarb)
Composition
Field units
Laboratory units
Brine 0.98 bbl of9.7 ppg NaCl brine
343 ml of 16.4% NaCl brine
Viscosifier (Xanthan) 1 ppb
1 gram / 350 ml
FL-7 Plus (Starch) 7 ppb
7 grams / 350 ml
pH buffer 2 ppb
2 grams / 350 ml
Sized CaCO3 with median size of particles (2, 5, 12, 20 microns)
22 ppb
22 grams / 350 ml
Table 2-4: Rheology of CaCO3 drill-in mud using Fann viscometer
Rotational speed
(rpm)
Dial reading
(lbf / 100 sq. ft.)
600 43
300 32
200 24
100 18
6 8
3 7
Plastic viscosity
11 cp
Yield point
21 lbf/100 sq. ft.
pH 9.5
49
Table 2-5: Formulation of bentonite mud (10 ppg)
Composition
Field units
Laboratory units
NaCl 10.5 ppb
(10.5 gms) / 350 ml (3% by wt.)
Bentonite 22 ppb
22 gram / 350 ml
Ligno-sulfonate 3.5 ppb
3.5 grams / 350 ml (1% by wt.)
pH buffer 2 ppb
2 grams / 350 ml
Table 2-6: Rheology of bentonite mud using Fann viscometer
Rotational speed
(rpm)
Dial reading
(lbf / 100 sq. ft.)
600 23
300 13
Plastic viscosity
10 cp
Yield point
5 lbf/100 sq.ft.
pH 9
50
Table 2-7: Flow initiation pressure for single-phase flow and constant pressure flowback experiments simulating open hole conditions.
Core Type
Mud used
Core Dimensions (Dia. X Len.)
[inches]
Completion type simulated
FIP
[psi]
Nugget sandstone
(4 md)
UltraCarb-2*
Short core 2.5 X 1
Open hole 2
UltraCarb-2*
Open hole 1
UltraCarb-2* (Repeat
experiment)
Open hole 2
Texas limestone
(25 md)
Bentonite
Short core 2.5 X 1
Open hole 1
Short core 2.5 X 1
Open hole 4
Long core 2 X 6
Open hole 2
Berea sandstone
(200 md)
UltraCarb-2*
Long core 2 X 6
Open hole (external filter cake removed)
2
UltraCarb-20*
Open hole 3 Boise sandstone
(1000 md) Bentonite
Short core 2.5 X 1
Open hole 1
UltraCarb-2*
Open hole 8 Aloxide (Synthetic)
(1500 md) UltraCarb-20*
Short core 2.5 X 1
Open hole 4
* The number represents the median size of CaCO3 particles Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
51
Table 2-8: Summary of return permeability ratio for single-phase constant pressure flowback tests simulating open hole conditions
Return permeability ratio (%)
Core Type
Mud used
Core Dimensions
(Dia. X Len.)
[inches]
Lab Simulated
Completion type At
(FIP) At 20 psi
At 50 psi
At 100 psi
Nugget sandstone
(4 md)
UltraCarb-2*
Short core 2.5 X 1
Open hole 2.5 (2)
60.8 68.8 72.3
UltraCarb-2*
Open hole 33.88(1)
54.3 56.5 56.6
UltraCarb-2* (Repeat
experiment)
Open hole 30.39 (2)
54 55 55
Texas Limestone
(25 md)
Bentonite
Short core 2.5 X 1
Open hole 38.1 (1)
100 100 100
Short core2.5 X 1
Open hole 0.9 (4)
50.4
Open hole 36.3 (3)
58 64.1 70
Berea Sandstone (200 md)
UltraCarb-2*
Long core 2 X 6
Open hole (w/o filter
cake)
34.3 (2)
60.7 68.2 73
UltraCarb-20*
17 (3)
18.8 13.2 Boise sandstone (1000 md)
Bentonite
Short core 2.5 X 1
Open hole
1.41 (1)
12 (2)
22 (10)
UltraCarb-2*
0.003 (8)
1.2 (16)
1.7 (20)
5.2 (50)
Aloxide (1000 md)
UltraCarb-20*
Short core 2.5 X 1
Open hole
.04 (4)
2.3 (7)
7 (20)
7.3 (50)
* The number represents the median size of CaCO3 particles Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
52
Table 2-9: API filtrate loss for single-phase flow and constant pressure flowback experiments simulating open-hole conditions
Core Type
Mud used
Core Dimensions
(Dia. X Len.)
[inches]
Completion type
simulated
API Spurt loss
[ml]
API filtrate
[ml] Nugget
sandstone (4 md)
UltraCarb-2*
Short core 2.5 X 1
Open hole 0 3.74
UltraCarb-2*
Open hole 0.23 4.79
UltraCarb-2* (Repeat
experiment)
Open hole 0.2 4.55
Texas limestone
(25 md)
Bentonite
Short core 2.5 X 1
Open hole 0.7 22.4
Short core 2.5 X 1
Open hole 0.2 4.65 Berea sandstone
(200 md)
UltraCarb-2*
Long core 2 X 6
Open hole 0.8 6.37
UltraCarb-20*
Open hole 0.47 4.16 Boise sandstone
(1000 md) Bentonite
Short core 2.5 X 1
Open hole 0.71 31.1
UltraCarb-2*
Open hole 3.62 14.9 Aloxide (Synthetic)
(1500 md) UltraCarb-20*
Short core 2.5 X 1
Open hole 1.04 8.04
* The number represents the median size of CaCO3 particles Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
53
Table 2-10: Flow initiation pressure for two-phase flow experiments with constant pressure flowback condition simulating open-hole conditions
Core Type
Mud used
Core Dimensions (Dia. X Len.)
[inches]
Completion type simulated
FIP
[psi]
Nugget sandstone
(4 md)
UltraCarb-2*
Short core 2.5 X 1
Open hole 6
Texas limestone
(25 md)
UltraCarb-2*
Short core 2.5 X 1
Open hole
2
UltraCarb-2*
Open hole 7
UltraCarb-2* (Repeat
experiment)
Open hole 4
Berea sandstone
(200 md)
UltraCarb-20*
Short core 2.5 X 1
Open hole 4
Boise sandstone
(1000 md)
UltraCarb-20*
Short core 2.5 X 1
Open hole 2
Aloxide (Synthetic)
(1500 md)
UltraCarb-20*
Short core 2.5 X 1
Open hole 3
* The number represents the median size of CaCO3 particles Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
54
Table 2-11: Summary of return permeability ratio for two-phase constant pressure flowback tests simulating open-hole conditions
Return permeability ratio (%)
Core Type
Mud used
Core Dimensions
(Dia. X Len.)
[inches]
Lab Simulated
Completion type At
(FIP) At 20 psi
At 50 psi
At 100 psi
Nugget sandstone
(4 md)
UltraCarb-2*
Short core 2.5 X 1
Open hole 1 (6)
18 38 48
Texas Limestone
(25 md)
UltraCarb-2*
Short core 2.5 X 1
Open hole 1 (2)
63 82 93
UltraCarb-2*
Open hole 25 (7)
>29
UltraCarb-2* (Repeat
experiment as above)
Open hole 0.452(4)
46 62 72
Berea Sandstone
(200 md)
UltraCarb-20*
Short core 2.5 X 1
Open hole 3.64 (4)
69 82
Boise sandstone (1000 md)
UltraCarb-20*
Short core 2.5 X 1
Open hole 35 (2)
84 96
Aloxide
(1500 md)
UltraCarb-20*
Short core 2.5 X 1
Open hole 2.1 (3)
25 26.5
* The number represents the median size of CaCO3 particles Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
55
Table 2-12: API filtrate loss for two-phase flow and constant pressure flowback experiments simulating open-hole conditions
Core Type and
Permeability
Mud used
Core Dimensions (Dia. X Len.)
[inches]
API Spurt loss
[ml]
API filtrate
[ml]
Nugget sandstone
(4 md)
UltraCarb-2*
Short core 2.5 X 1
0 3.82
Texas limestone
(25 md)
UltraCarb-2*
Short core 2.5 X 1
0.18 4.83
UltraCarb-2*
0.26 5.47
UltraCarb-2* (Repeat
experiment for above)
0.57 4.6
Berea sandstone
(200 md)
UltraCarb-20*
Short core 2.5 X 1
0.13 3.02
Boise sandstone
(1000 md)
UltraCarb-20*
Short core 2.5 X 1
0.65 3.23
Aloxide (Synthetic)
(1500 md)
UltraCarb-20*
Short core 2.5 X 1
1.1 5.6
* The number represents the median size of CaCO3 particles Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
56
Table 2-13: Comparison of FIP for single-phase vs. two-phase experiments with constant pressure flowback conditions
FIP [psi]
Core Type
Mud used
Core Dimensions (Dia. X Len.)
[inches] Single-phase
(Flowback fluid: 3 % brine)
Two-phase (Flowback
fluid: Exxsol)
Nugget Sandstone
(4 md)
UltraCarb-2
2.5 X 1 (Short core)
2 6
Texas limestone
(25 md)
UltraCarb-2
2.5 X 1 (Short core)
1 2
Berea sandstone
(200 md)
UltraCarb-2
2.5 X 1 (Short core)
7 7
Aloxide
(1000 md)
UltraCarb-20
2.5 X 1 (Short core)
4 3
Boise sandstone
(1000 md)
UltraCarb-20
2.5 X 1 (Short core)
3 2
57
Table 2-14: Comparison of return permeability ratio for single-phase vs. two-phase experiments with constant pressure flowback conditions
Return permeability ratio at the maximum applied differential
pressure [%]
Core Type
Mud used
Core Dimensions (Dia. X Len.)
[inches]
Single-phase (Flowback fluid:
3 % brine)
Two-phase (Flowback
fluid: Exxsol)
Nugget Sandstone
(4 md)
UltraCarb-2
2.5 X 1 (Short core)
72.3 (100 psi)
48.4* (100 psi)
Texas limestone
(25 md)
UltraCarb-2
2.5 X 1 (Short core)
56.6 (100 psi)
93 (100 psi)
Berea sandstone
(200 md)
UltraCarb-2
2.5 X 1 (Short core)
50.4 (20 psi)
72 (100 psi)
Aloxide
(1000 md)
UltraCarb-20
2.5 X 1 (Short core)
7.3 (50 psi)
26.5 (50 psi)
Boise sandstone
(1000 md)
UltraCarb-20
2.5 X 1 (Short core)
13.2 (50 psi)
96 (50 psi)
* The overbalance pressure was equal to 140 psi for this experiment. For rest of the experiments the mud overbalance pressure was equal to 100 psi.
58
Table 2-15: Comparison of FIP for constant rate vs. constant pressure flowback condition for two-phase flow experiments
FIP [psi]
Core Type
Mud used
Core Dimensions (Dia. X Len.)
[inches] Constant Rate
Flowback condition
(Rate: ml/min)
Constant Pressure
Flowback condition
Nugget Sandstone
(4 md)
Ultra-Carb
2.5 X 1 (Short core)
121 (5 ml/min)* 6
Texas limestone
(25 md)
Ultra-Carb
2.5 X 1 (Short core)
5.5 (1 ml/min)*
44 (5 ml/min)*
78 (20 ml/min)*
2
Berea sandstone
(200 md)
Ultra-Carb
2.5 X 1 (Short core)
14 (5 ml/min)* 7
Aloxide
(1000 md)
Ultra-Carb
2.5 X 1 (Short core)
21 (5 ml/min)*
38 (20 ml/min)*
3
* Reference: Zain and Sharma 5 Note: The mud overbalance pressure was equal to 100 psi for all the experiments.
59
Table 2-16: Comparison of FIP, return permeability ratio and API filtrate loss for bentonite mud and UltraCarb drill-in fluid
FIP [psi]
Return permeability ratio (%)
30 minute API filtrate loss [ml]
Core Dimensions (Dia.X Len.)
and Type Bentonite UltraCarb Bentonite UltraCarb Bentonite UltraCarb
Short (2.5”X 1”)
Texas Limestone
(25 md)
1 1 38.1 33.8 22.37 4.79
Short (2.5”X 1”)
Boise sandstone (1000 md)
1
3 22 19 31.1 4.16
60
0
2
4
6
8
10
12
14
16
18
20
0 20 40 60 80 100 120 140Time (min)
Mea
sure
d P
ress
ure
Diffe
rent
ial (
psi)
∆P peak = 18.4 psi
∆P f inal = 4.8 psi
FIP = ∆P peak - ∆P final = 13.6 psi
Flowrate = 5 ml/min
Figure 2-1: Flowback pressure profile with constant flow rate boundary condition to
calculate flow initiation pressure (FIP)
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140Time (min)
Appl
ied
Pre
ssur
e D
iffer
entia
l (ps
i)
0
2
4
6
8
10
12
14
16
Mea
sure
d Ra
te (m
l/min
)
Const Pressure Flowback rate
FIP = 7 psi
kreturn = 25%
kreturn = 29%
Figure 2-2: Flow-back pressure profile with constant pressure boundary condition
(incremental pressure differentials) to calculate FIP.
61
Figure 2-3: Apparatus for fluid filtration and flowback test
Pressure transducer
Data acquisition
systems
Liquid pump 0.1 - 28 ml/min
Graduated cylinder for static filtration
High pressure gas line
o-ring Core plug (2.5” x 1”)
Fluid distribution end
Fluid Space
Fluid outlet during flow back
Pressure bleed off line
Electronic Balance
Pressure regulator
Fluid accumulator
Constant pressure flow back line
Constant rate flow back line
Modified HPHT Filtration Cell
62
Pressure taps
Borehole sleeve
Core
Confining liquid
Rubber sleeve
Completion fluid
Stationary end cap
End spacer
Dynamic end cap
End spacer
2 in.
Min
imum
: 1.3
5 in
.
.97
in.
17 in
.
1.35
in. 1
in.
2.15
in.
2 in
. 1.
85 in
.
Max
imum
: 6.3
in.
6 in
.
Perforation
Figure 2-4: Apparatus for long core holder
63
Flow-back with oil for 2-phase experiments Brine flow for single-phase exp.
Step 3: FIP & Return permeability
Flow oil for two-phase experiments Flow brine for single-phase experiments
Step 1: Initial permeability
Over-balance pressure
Fluid
Step 2: Static filtration
External filter cake
Boundary Condition: Constant pressure / Constant rate
Record fluid loss for 16 hours
Record differential pressure & flow rate during flow-back
Figure 2-5: Steps used during mud filtration and flowback tests
64
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.01 0.1 1 10 100 1000Pore diameter (µm)
Nor
mal
ized
Intr
usio
n Vo
lum
e (m
l/g)
Berea sandstone Median = 13.5 µm
Boise sandstone Median = 17.6 µm
Texas Limestone Median = 0.7 µm
Figure 2-6: Pore volume distribution for different rocks obtained from mercury
penetrometer
Figure 2-7: Top view of a limestone core after flowback at constant pressure (Mud used: UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 1-phase flowLS-12)
65
Figure 2-8: Top view of a Berea core after flowback at constant pressure (Mud used: UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 2-phase flow, BS-17)
Figure 2-9: Nugget sandstone core after flowback at constant pressure (Mud used: UltraCarb-2 drill-in fluid, O.B. pressure = 100 psi, 1-phase flow, NS-2)
66
Figure 2-10: Top view of an Aloxide core after flowback at constant pressure (Mud used: UltraCarb-20 drill-in fluid, O.B. pressure = 100 psi, 1-phase flow, AL-2)
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100Flowback Pressure (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
Aloxide, kabs = 1313 md
Berea sandstone, kabs = 60 md
Texas limestone, kabs = 24 md
Nugget sandstone, kabs = 4 md
UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiSingle-phase flow (brine)
Figure 2-11: Return permeability spectra for different permeability cores (single-phase
flow and constant flowback pressure).
67
0
1
2
3
4
0 250 500 750 1000 1250 1500
Absolute Permeability (md)
Spur
t los
s (m
l)
UltraCarb-2 Bentonite UltraCarb-20
Figure 2-12: Spurt loss vs. absolute permeability of different cores for single-phase
experiments simulating open hole conditions
0
5
10
15
20
25
30
35
0 250 500 750 1000 1250 1500
Absolute Permeability (md)
30 M
inut
e AP
I Filt
rate
Los
s (m
l)
UltraCarb-2 Bentonite UltraCarb-20
Figure 2-13: API Filtrate loss vs. absolute permeability of different cores for single-phase
experiments simulating open hole conditions
68
0
20
40
60
80
100
0 20 40 60 80 100 120 140Flowback Pressure (psi)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Berea sandstone, kef f (oil) = 129 md
Texas limestone, kef f (oil) = 15 md
UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow
Figure 2-14: Return permeability spectra for different permeability cores (two-phase flow
and constant flowback pressure)
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100Flowback Pressure (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Aloxide, kabs = 1313 md
Berea sandstone, kabs = 60 md
Texas limestone, kabs = 24 md
Nugget sandstone, kabs = 4 md
UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiSingle-phase flow (brine)
Figure 2-15: Return permeability spectra for different permeability cores (two-phase flow
and constant flowback pressure)
69
0
0.2
0.4
0.6
0.8
1
1.2
0 200 400 600 800 1000
Effective Permeability to Oil (md)
Spur
t los
s (m
l)
UltraCarb-2 (OB=100 psi) UltraCarb-20 (OB=100 psi)
Figure 2-16: Spurt loss vs. absolute permeability of different cores for two-phase
experiments simulating open hole conditions
0
1
2
3
4
5
6
0 200 400 600 800 1000
Effective Permeability to Oil (md)
30 M
inut
e A
PI F
iltra
te L
oss
(ml)
UltraCarb-2 (OB=100 psi) UltraCarb-20 (OB=100 psi)
Figure 2-17: API Filtrate loss vs. absolute permeability of different cores for two-phase
experiments simulating open hole conditions
70
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Two-phase flow (O.B. = 140 psi)
Single-phase flow(O.B. = 100 psi)
Figure 2-18: Return permeability spectra in Nugget sandstone for single-phase flow and
two-phase flow
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
Two-phase flow
Single-phase flow
Figure 2-19: Comparison of return permeability spectra in Texas limestone for single-
phase vs. two-phase flow (constant pressure B.C.)
71
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Single-phase flow (UltraCarb-2)
Two-phase flow (UltraCarb-2)
Two-phase flow (UltraCarb-20)
Figure 2-20: Comparison of return permeability spectra in Berea sandstone for single-
phase vs. two-phase flow (constant pressure B.C.)
0
5
10
15
20
25
30
0 10 20 30 40 50 60Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
Two-phase flow
Single-phase flow
Figure 2-21: Comparison of return permeability spectra in Aloxide (synthetic cores) for
single-phase vs. two-phase flow (constant pressure B.C.)
72
0
10
20
30
40
50
60
0 10 20 30 40 50 60Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Two-phase flow
Single-phase flow
Figure 2-22: Comparison of return permeability spectra in Boise sandstone for single-
phase vs. two-phase flow (constant pressure B.C.)
0
2
4
6
8
10
12
14
16
18
20
0 20 40 60 80 100 120 140
Time (min)
∆p
(psi
)
0
2
4
6
8
10
12
14
16
Rat
e (m
l/min
)
Const Pressure Const Rate
FIP (constant pressure b.c.) = 7 psi
kreturn = 25%
kreturn = 29%
kreturn = 26% at q = 5 ml / min
FIP (constant rate b. c.) = 14 psi
Figure 2-23: Comparison of FIP between constant rate boundary condition (B.C.) and
constant pressure B.C. during flowback for Berea sandstone
73
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
with external filter cakewithout external filter cakewith external filter cake (repeat experiment)
Figure 2-24: Comparison of FIP and return permeability spectra for Berea sandstone with
and without external filter cake
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Berea long core (diameter = 2 in., length = 6 in.)
Berea short core (dia. = 2.5 in., length = 1 in.)
Berea long core with K calculated for the first two inches of the core
Figure 2-25: Return permeability vs. differential pressure during flowback in short and
long Berea cores
74
0
10
20
30
40
50
60
70
80
90
100
0 0.5 1 1.5 2 2.5 3Average Flowback Velocity (cm/min)
Retu
rn P
erm
eabi
lity
Rat
io (%
)Berea long core (diameter = 2 in., length = 6 in.)
Berea short core (dia. = 2.5 in., length = 1 in.)
Berea long core with K calculated for the first two inches of the core
Figure 2-26: Return permeability vs. average flowback velocity for experiments
conducted on short and long Berea cores
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
No back pressure
Back pressure = 500 psi
Figure 2-27: Comparison of return permeability spectra for Berea sandstone
with and without back pressure (O.B. = 500 psi)
75
0
1
2
3
4
5
6
7
8
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
UltraCarb-20 (Median size = 20 microns)
UltraCarb-2 (Median size = 2 microns)
Figure 2-28: Comparison of return permeability spectra for Aloxide cores with UltraCarb
drill-in fluids with two different median sizes
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100Flowback Pressure (psi)
Ret
urn
Perm
eabi
lity
Ratio
(%)
UltraCarb-2* drill-in fluid
UltraCarb-20* drill-in fluid
* Median size of the bridging agent
Figure 2-29: Comparison of return permeability spectra for Berea cores with UltraCarb
drill-in fluids with two different median sizes
76
0
1
2
3
4
5
6
0 20 40 60 80 100Return Permeability Ratio (%)
Skin
Depth of damage = 1 inch
radius of well (rw) = 3 inch
rw = 4 inch
rw = 6 inch
Figure 2-30: Skin with varying return permeability ratio of the near wellbore region
0
20
40
60
80
100
0 20 40 60 80 100 120 140Average Pressure Gradient During Flowback (psi/inch)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Berea sandstone, kef f (oil) = 129 md
Texas limestone, kef f (oil) = 15 md
UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow
Figure 2-31: Return permeability ration vs. average pressure gradients in Texas limestone
and Berea during flowback
77
0
20
40
60
80
100
0 10 20 30 40 50 60Average Pressure Gradient During Flowback (psi/inch)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Aloxide, kef f (oil) = 965 md
Boise sandstone, kef f (oil) = 600 md
UltraCarb-20 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow
Error = -20%
Error = 20%
Figure 2-32: Return permeability ratio vs. average pressure gradient in Boise sandstone
and Aloxide core during flowback
0
20
40
60
80
100
1 10 100 1000Average Pressure Gradient During Flowback (psi/inch)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Berea sandstone, kef f (oil) = 129 md
Texas limestone, kef f (oil) = 15 md
UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow
Figure 2-33: Return permeability ration vs. average pressure gradients in Texas limestone
and Berea during flowback (Semi-log plot)
78
0
20
40
60
80
100
1 10 100Average Pressure Gradient During Flowback (psi/inch)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Aloxide, kef f (oil) = 965 md
Boise sandstone, kef f (oil) = 600 md
UltraCarb-20 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow
Error = -20%
Error = -20%
Figure 2-34: Return permeability ratio vs. average pressure gradient in Boise sandstone
and Aloxide core during flowback (Semi-log plot)
0.01
0.1
1
10
100
10 100 1000 10000 100000Flow Rate (bpd)
dp/d
r (ps
i/inc
h) a
t the
Wel
lbor
e Fa
ce
Radial well Horizontal well
ko = 200 mdµ = 0.74 cpBo = 1.3 RB/STBrw = 0.25 fth (radial well) = 50 ftlength of hor. well = 2000 ft
Figure 2-35: Pressure gradient at the wellbore face at different steady state flow rates
79
0
20
40
60
80
100
0.001 0.01 0.1 1 10 100 1000Flowback Rate (ml/min)
Ret
urn
Perm
eabi
lity
Ratio
(%)
Berea sandstone, kef f (oil) = 129 md
Texas limestone, kef f (oil) = 15 md
UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow
Figure 2-36: Return permeability ratio of inch long Texas limestone and Berea sandstone
core at different flowback rates (semi-log plot)
0
20
40
60
80
100
1 10 100 1000Flowback Rate (ml/min)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
Aloxide, kef f (oil) = 965 md
Boise sandstone, kef f (oil) = 600 md
UltraCarb-20 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow
Error = -20%
Error = 20%
Figure 2-37: Return permeability ratio of Boise sandstone and Aloxide core at different
flowback rates (semi-log plot)
80
0
20
40
60
80
100
0.0001 0.001 0.01 0.1 1 10Flowback Velocity (cm/min)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Berea sandstone, kef f (oil) = 129 md
Texas limestone, kef f (oil) = 15 md
UltraCarb-2 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow
Figure 2-38: Return permeability ratio of Texas limestone and Berea sandstone core at
different flowback velocities (semi-log plot)
0
20
40
60
80
100
0.01 0.1 1 10 100Flowback Velocity (cm/min)
Ret
urn
Perm
eabi
lity
Ratio
(%)
Aloxide, kef f (oil) = 965 md
Boise sandstone, kef f (oil) = 600 md
UltraCarb-20 drill-in fluidOverbalance pr. = 100 psiTwo-phase flow
Error = -20%
Error = 20%
Figure 2-39: Return permeability ratio of Boise sandstone and Aloxide core at different
flowback velocities (semi-log plot)
81
REFERENCES
1. Browne, S. V., and Smith, P. S.: “Mud cake Clean up to Enhance the Productivity of
Horizontal Wells,” paper SPE 27350 presented at the SPE Formation Damage
Control Symposium held in Lafayette, 9-10 Feb., 1994
2. Browne, S. V., et al.: “Simple Approach to the Cleanup of Horizontal Wells With
Prepacked Screen Completions,” paper SPE 30116 presented at the SPE Formation
Damage Control Symposium held in The Hague, The Netherlands, 15-16 May, 1995
3. Bailey, L., et al.: “Filter cake Integrity and Reservoir Damage,” paper SPE 39429
presented at the 1998 SPE International Symposium on Formation Damage Control
held in Lafayette, 18-19 February, 1998
4. Ryan, D. F., et al.: “Mud Clean-Up in Horizontal Wells: A Major Joint Industry
Study,” paper SPE 30528 presented at the SPE Annual Technical Conference and
Exhibition held in Dallas, USA, 22-25 October, 1995
5. Zain, M. Z., and Sharma, M. M.: “Cleanup of Wall-Building Filter Cakes,” paper
SPE 56635 presented at the SPE Annual Technical Conference and Exhibition held in
Houston, Texas, 3-6 October, 1999
6. Roy, S. R., and Sharma, M. M.: “The Relative Importance of Solids and Filtrate
Invasion on the Flow Initiation Pressure,” paper SPE 68949 presented at the
European Formation Damage Conference held in The Hague, The Netherlands, 21-22
May, 2001
7. Alfenore, J., et al.: “What really Matters In our Quest of Minimizing Formation
Damage In Open Hole Horizontal Wells,” paper SPE 54731 presented at the
European Formation Damage Conference held in The Hague, The Netherlands, 31
May – 1 June, 1999
82
8. Ladva, J. K. H., et al.: “Multiphase Flow and Drilling-Fluid Filtrate Effects on the
Onset of Production,” paper SPE 58795 presented at the SPE International
Symposium on Formation Damage Control, Lafayette, Louisiana, 23-24 Feb., 2000
9. Gruber, N. G., and Adair, K. L.: “New Laboratory Procedures for Evaluation of
Drilling Induced Formation Damage and Horizontal Well Performance,” paper JCPT
Volume 34, No. 5, May 1995
10. Gruber, N. G., and Adair, K. L.: “New Laboratory Procedures for Evaluation of
Drilling Induced Formation Damage and Horizontal Well Performance: An Update,”
paper SPE 37139 presented at the SPE International Conference on Horizontal Well
Technology held in Calgary, Canada, 18-20 November, 1996
11. Browne, S. V., and Smith, P. S.: “Mud cake Clean up to Enhance the Productivity of
Horizontal Wells,” paper SPE 27350 presented at the SPE Formation Damage
Control Symposium held in Lafayette, 9-10 Feb., 1994
12. Ryan, D. F., et al.: “Mud Clean-Up in Horizontal Wells: A Major Joint Industry
Study,” paper SPE 30528 presented at the SPE Annual Technical Conference and
Exhibition held in Dallas, USA, 22-25 October, 1995
13. Marshall, S. D., et al,: “Return Permeability: A Detailed Comparative Study,” paper
SPE 54763 presented at the SPE European Formation Damage Conference held in
The Hague, The Netherlands, 31 May - 1 June 1999
14. Zain, M. Z., and Sharma, M. M.: “Cleanup of Wall-Building Filter Cakes,” paper
SPE 56635 presented at the SPE Annual Technical Conference and Exhibition held in
Houston, Texas, 3-6 October, 1999
15. Zain, M. Z., and Sharma, M. M.: “Mechanisms of Mud Cake Removal During
Flowback,” SPE Drilling and Completion, December 2001
83
16. Alfenore, J., et al.: “What really Matters In our Quest of Minimizing Formation
Damage In Open Hole Horizontal Wells,” paper SPE 54731 presented at the
European Formation Damage Conference held in The Hague, The Netherlands, 31
May – 1 June, 1999
17. Smith, P. S., et al.: “Drilling Fluid Design to Prevent Formation Damage in High
Permeability Quartz Arenite Sandstones,” paper SPE 36430 presented at the Annual
Technical Conference and Exhibition held in Denver, Colorado, U.S.A., 6-9 October
1996
18. Kalpakci, B., et al.: “A Systematic Approach for Selection of Drill-in Fluids and
Cleanup Options for Minimum Formation Damage in Horizontal Well: A Case Study
for Paloma Field, Bolivia,” paper SPE 53948 presented at the SPE Latin American
and Caribbean Petroleum Engineering Conference held in Caracas, Venezuela, 21-23
April, 1999
19. Bailey, L., et al.: “Particulate Invasion From Drilling Fluids,” paper SPE 54762
presented at the SPE European Formation Damage Conference held in The Hague,
The Netherlands, 31 May -1 June, 1999
20. Suri, A., and Sharma, M.M.: “Strategies for Sizing Particles in Drilling and
Completion Fluids,” paper SPE 68964 presented at the SPE European Formation
Damage Conference held in The Hague, The Netherlands, 21–22 May 2000
84
Chapter 3: Role of Drill-in Fluid Components during Filtration and
Flowback
3.1 INTRODUCTION
In this chapter, we evaluate the formation damage potential of different
components used in water-based drill-in and completion fluids. First a literature review of
past studies on the major components used in water-based drill-in and completions fluids
(starch, xanthan and calcium carbonate) is presented. A total of 12 fluid formulations are
designed to study the formation damage potential of individual components. Results are
presented and discussed for each of these formulations. UTDamage is used to simulate
the experiments. A quantitative match for the return permeabilities and a qualitative
match for the filtrate loss is found between the two. Finally, conclusions are presented
and recommendations are provided to better design drill-in and completion fluids for
minimizing formation damage.
3.2 DRILL-IN AND COMPLETION FLUID COMPONENTS
The components used in drilling and completion fluids have been changing since
the beginning of the oil industry. In the early years water was used as the only component
in the fluid to clean the bore hole by circulating it through the drill pipe and out through
the annulus. Gray and Darley 1 have presented a detailed history on the development of
drilling fluids technology. Drilling muds on the broadest level can be classified as: water-
based muds, oil-based muds, and gas-based muds. They can be further classified into sub
categories according to the specific components used in the mud for a desired purpose.
85
After the advent of horizontal drilling technology and multi-lateral drilling
through the pay-zone, careful thought was given to mud formulations based on
productivity concerns. A new class of drilling fluids was developed for use when drilling
through the pay-zone. These fluids were called drill-in fluids. A drill-in fluid (DIF) is
defined as a drilling / completion fluid, specially formulated to optimize well
productivity. Like standard drilling fluids, DIF’s provide lubricity, inhibition, solids
suspension, and borehole stability. Additionally, they are also formulated to protect
producing intervals by: (1) mechanically sealing exposed pore space openings in
boreholes by forming thin, tough and impermeable filter cakes; (2) stabilizing the
wellbore during completion by strengthening the wellbore; (3) allowing easy cleanup
after drilling and completion.
Most DIF’s contain solid materials such as sized calcium carbonate or sized salt.
Solids are used as bridging agents to plug the surface of a formation matrix and as
weighting material to control formation pressure. Drill-in fluids use viscosifiers such as
biopolymers to provide gel strength and to improve the carrying of the drill solids to the
surface. They also use fluid loss control agents to reduce the fluid loss from the well bore
to the formation. The important components of the more commonly used water based
DIF’s are as follows:
1. Base brines (Na, Ca, K, and cesium chlorides, bromides, halides and formates) to
meet the density and formation compatibility requirements.
2. Sized salt/CaCO3 as bridging additives.
4. Modified starch for controlling fluid loss.
3. Polymers (usually Xanthan) for desired rheology and viscosity behavior.
5. pH buffer for desired alkalinity requirements.
86
The three main additives (bridging additive, fluid loss control additive, and the
rheology control additive) are discussed in more detail below:
3.2.1 Bridging Additive
Sized calcium carbonate and sized salt are the two most common bridging
additives used in drill-in fluids. Sized calcium carbonate is used even more widely than
sized salt. The use of calcium carbonate was proposed as a weighting material because it
can be dissolved in hydrochloric acid. It is readily available as ground limestone or oyster
shell. It can also be used as a substitute for barite in oil-based muds as it disperses more
readily in oil than barite. Its specific gravity is between 2.6 and 2.8 which limit the
maximum density of drill-in fluid to about 12 lb/gal. There are two advantages of using
sized calcium carbonate particles in drill-in fluids: 1) the particles are acid soluble which
provides an option of dissolving the filter cake using acids before production, and 2) the
particles are available with different median sizes which can be used to match the pore
throat or permeability of the formation to be drilled for minimizing invasion.
3.2.2 Fluid Loss Control Additive
Starch is the most common fluid loss control additive used in drilling or drill-in
fluids. It was the first organic polymer used in substantial quantities in mud. The
widespread use of starch decreased as other polymers (notably CMC) were introduced.
Starch is still the most economical filtration loss control additive for strongly alkaline and
salt saturated muds. However starch is subject to fermentation by many microorganisms
(yeasts, molds, bacteria). To avoid this, the mud is saturated with salt or the pH is kept
around 12. A biocide needs to be added if the mud with starch is to be used for several
days. Starch can also break down at high temperatures and at high circulation rates.
87
Numerous modifications and derivatives of starch are proposed and used in drill-in fluids.
For example a fermentation-resistant starch is prepared by blending moist starch (about
20 % water) with 3 % bis (2-hydroxy, 3,5-dichlorophenyl) sulfide, and passing the
mixture under pressure through a heated extruder1. Gums, polyanionic cellulose, sodium
polyacrylonitrile, oil are some other additives which are also used to control fluid loss
from the well into the formation.
3.2.3 Rheology Control Additive
Xanthan polymer is used as the most common rheology control additive in drill-in
fluids. It was introduced as a drilling fluids component in the mid 1960s under the name
“XC polymer” and its use has increased noticeably since 1970. It is a water soluble
polysaccharide produced by bacterial action (genus Xanthomonas) on carbohydrates. The
most important property of xanthan in its application to drill-in fluids is that it builds
viscosity at low concentrations as compared to gums or other viscosifiers. It acts as an
excellent suspending agent for drill cuttings and surpasses any other polymer used in
drilling or drill-in fluids. It displays excellent shear thinning properties with apparent
viscosity markedly lower at high shear rates than measured at low shear rates. Cross
linking with chromic ion significantly increases viscosity. There is a small effect of pH
on viscosity in the range of 7 -11. It shows negligible sign of degradation at high
temperatures. Other rheology control additives used in drilling fluids are CMC, gums,
and HEC.
3.3 RESEARCH OBJECTIVE
There has been no study done in evaluating the effect of individual components in
drill-in fluids from a productivity stand point. The main idea behind studying the role of
88
individual components in drill-in fluids was to have a clear picture of how each
component affects production and if we can design drill-in fluids better using that
understanding. The research objective is to experimentally evaluate the effect of the
following drilling fluid components on FIP and return permeability ratio: Bridging
additive, fluid loss control additive, and rheology control additive.
3.4 EXPERIMENTAL DESIGN
3.4.1 Test Description and Fluid Design
Table 3.1 shows the composition of UltraCarb drill-in fluid with all the
components. For studying the effect of individual components we formulated the drill-in
fluid with different combinations of components by taking out one of the three main
components in one formulation. Table 3.2 shows the different drill-in fluid formulations
used in evaluating the effect of different components. The different drill-in fluid
formulations are described below in detail:
1. Drill-in fluid with no fluid loss control agent (starch) and no rheology control agent
(xanthan polymer). Only sized calcium carbonate was added to brine with the pH
buffer (see Table 3.1).
2. Drill-in fluid with no rheology control agent (xanthan polymer). Sized calcium
carbonate along with fluid loss control agent (starch) was added to brine with the pH
buffer (see Table 3.1).
3. Drill-in fluid with no fluid loss control agent (starch). Sized calcium carbonate along
with the rheology control agent (xanthan polymer) was added to brine with the pH
buffer (see Table 3.1).
4. Drill-in fluid with all the components.
89
Each of the above 4 formulations were made for three different median sizes (2
micron, 12 micron, and 20 micron) of bridging additive. Hence a total of 12 drill-in fluid
formulations were made to study the effect of these components on FIP and return
permeability. Two more experiments were also conducted: 1) with only brine and 2) with
brine and pH buffer to measure FIP and return permeability ratio.
3.4.2 Test Equipment
The experimental set up used in conducting the experiments was the same as
presented in Chapter 2. Figure 2.3 in Chapter 2 shows the schematic of the experimental
set up. Berea cores with diameter 2.5 inch and length equal to 1 inch were used in the
modified HPHT API filtration cell. The temperature used in the early experiments was
equal to 150 oF to simulate reservoir conditions but later, after we found that the effect of
high temperature on filter cake removal to be negligible, experiments were conducted at
room temperature (75 oF).
3.4.3 Test Procedure
The test procedure used in conducting the experiments is outlined in Chapter 2,
Section 2.3.5. In brief, Berea cores were first vacuum saturated in 3% brine and then
Exxsol D-110 (oil distillate) was flowed until an irreducible water saturation was
achieved. The initial effective permeability to oil for the core was calculated. A static
filtration test at an overbalance of 100 psi was conducted with the drill-in fluid on top of
the core for a filtration time of 16 hours. The fluid loss was recorded during that time to
calculate the standard API 30 minute fluid loss for each drill-in fluid formulation. After
filtration, a flow back test was conducted at a constant rate and the differential pressure
profile was recorded across the core. Figure 3.1 shows a typical plot of the differential
90
pressure profile across the core during flowback after filtration. The flow initiation
pressure (FIP) is defined as the difference between the peak pressure and the stabilized
pressure.
3.5 DISCUSSION OF EXPERIMENTAL RESULTS
We measure and report the following parameters for all the two-phase (brine and
Exxsol D-110) filtration and flow back experiments:
1. Flow initiation pressure
2. Return permeability ratio
3. API filtrate loss
Table 3.3 shows the results for peak pressure during flow back, FIP, return
permeability ratio, and API filtrate loss for all the experiments. Appendix D shows plots
of differential pressure profile across the core during flowback and filtrate loss vs. square
root of time during static filtration for all the tests. The FIP, return permeability ratio, and
the filtrate loss for all the experiments are discussed below.
3.5.1 Flow Initiation Pressure
Figure 3.2 shows a bar graph comparing the FIP for four different compositions of
drill-in fluids: (1) only bridging additive, (2) bridging additive and fluid loss control
additive (starch), (3) bridging additive and rheology control additive (xanthan), (4)
bridging additive, fluid loss control additive (starch), and rheology control additive
(xanthan). Each of these four compositions was formulated for three median sizes (2 µm,
12 µm, 20 µm) of bridging additive, with a total of 12 fluid formulations. We can see that
the largest FIP is found for drill-in fluid formulations (3) and (4) which have xanthan
91
polymer. Drill-in fluid formulation number (2), which is made up of bridging additive
and starch, shows the smallest FIP in comparison to the rest of the drill-in fluid
formulations. We attribute this small FIP to minimum invasion of particles/polymers for
this formulation into Berea cores. It could also be that the internal filter cake formed from
this drill-in fluid formulation has the lowest yield strength, which would also result in a
small FIP. Most likely the product of depth of invasion of solids and the yield strength of
the internal filter cake is minimum for this fluid formulation. Because FIP is directly
proportional to the product of the yield strength of the internal filter cake and the depth of
the internal filter cake. The dependence of FIP on the yield strength and the depth of
internal filter cake is discussed in detail in Chapter 5.
3.5.2 Return Permeability Ratio
The return permeability ratio is defined in equation 2.6 of Chapter 2. Return
permeability ratio depends on the flow rate in flow back experiments done at constant
rate. The following sections present return permeability ratios for different drill-in fluid
formulations.
3.5.2.1 Drill-in Fluid Formulation 1 (Only Bridging Additive)
Figure 3.3 shows a bar graph for return permeability ratio for drill-in fluid
formulation (1) for the three different median sizes (2 µm, 12 µm, 20 µm) of bridging
additive and at three different flow rates (1ml/min, 3 ml/min, 5 ml/min). The graph
clearly shows that the drill-in fluid with a median size equal to 12 microns results in the
largest return permeability ratio. The fluid with median size equal to 12 microns is closest
in size to the median pore throat size of Berea sandstone (13.5 microns) than the median
sizes (2 µm and 20 µm) of the other two formulations. This would have led to the most
92
effective bridging with fluid with median size equal to 12 microns with minimum
invasion of solids and filtrate into the rock. As a result the return permeability ratio was
the largest for the fluid with median size equal to 12 microns.
It can also be seen in Figure 3.3 that the return permeability ratios are larger with
larger flowback rates for all fluid formulations. This observation is consistent with the
earlier observations presented by Zain and Sharma 2.
3.5.2.2 Drill-in Fluid Formulation 2 (Bridging Additive + Fluid Loss Control Additive)
Figure 3.4 shows a bar graph for return permeability ratio for drill-in fluid
formulation (2) for the three different median sizes (2 µm, 12 µm, 20 µm) of bridging
additive and at three different flow rates (1ml/min, 3 ml/min, 5 ml/min). The graph
clearly shows that the drill-in fluid with bridging agents with a median size equal to 20
microns results in the largest return permeability ratio. I assume that the addition of
starch to sized CaCO3 particles with a fixed median size must have reduced the overall
median size of the mixture. This reduction in an overall median size of the particles might
have approached a median size closer to the median pore throat size of Berea sandstone.
As a result there was minimum invasion of the fluid into the Berea core which led to the
largest return permeability ratio compared to the return permeability ratios obtained using
other fluid formulations.
3.5.2.3 Drill-in Fluid Formulation 3 (Bridging Additive + Rheology Control Additive)
Figure 3.5 shows a bar graph for return permeability ratio for drill-in fluid
formulation (3) for the three different median sizes (2 µm, 12 µm, 20 µm) of bridging
additive and at three different flow rates (1ml/min, 3 ml/min, 5 ml/min). The graph
93
clearly shows that the drill-in fluid with bridging agents with a median size of 20 microns
results in the largest return permeability ratio. Addition of xanthan polymer (size of few
microns) to calcium carbonate particles with a median size of 20 microns reduced the
median size of the overall mixture. This reduction in an overall median size might have
approached a median size very close to the median pore throat size of Berea sandstone.
As a result there was minimum invasion of the fluid into the Berea core which led to the
largest return permeability ratio compared to the return permeability ratios obtained using
other fluid formulations.
3.5.2.4 Drill-in Fluid Formulation 4 (Bridging Additive + Fluid Loss Control Additive + Rheology Control Additive)
Figure 3.6 shows a bar graph for return permeability ratio for drill-in fluid
formulation (4) for the three different median sizes (2 µm, 12 µm, 20 µm) of bridging
additive and at three different flow rates (1ml/min, 3 ml/min, 5 ml/min). The graph shows
that the drill-in fluid with bridging agents with a median size equal to 12 microns results
in the largest return permeability ratio. The drill-in fluid with a median size equal to 20
microns results in a slightly smaller return permeability ratio than the fluid with bridging
agents with a median size equal to 12 microns. This result was different from the results
obtained when only one of the additives (xanthan or starch) was added to the sized
CaCO3 particles. This suggests that addition of both the additives to the sized CaCO3
particles with a median size of 12 microns did not reduce the median size of the overall
mixture but kept the median size close to the median pore throat size of Berea sandstone.
It could be that the two polymers when mixed together results in a larger median size
than their individual median sizes because of some form of linking or interaction.
94
3.5.2.5 Comparison of Return Permeability Ratio for the Different Drill-in Fluid Formulations
Figure 3.7, 3.8, and 3.9 show bar graphs of return permeability ratio for the four
different drill-in fluid formulations at three different flow back rates (1ml/min, 3 ml/min,
and 5 ml/min). All the three figures clearly indicate that drill-in fluid formulation number
3 (bridging additive + xanthan) has the smallest return permeability ratio. This indicates
that xanthan polymer is the most damaging of all the constituents and must have invaded
the most into the rock compared to the other components during filtration. This deep
invasion is assumed to be because of the small size of xanthan polymer. It could also be
that the xanthan polymer forms an internal filter cake with large yield strength which
would make the cleanup of the internal filter cake difficult. Drill-in fluid formulation
number 2 (bridging additive + starch) shows large return permeability ratio which is
approximately the same as drill-in fluid formulation 4 (bridging additive + starch +
xanthan). This suggests that starch is very less damaging and doesn’t invade much into
the formation. Not only it doesn’t invade into the formation but it also restricts xanthan to
invade into the formation. The drill-in fluid formulation number 1 (only bridging
additive) shows the largest return permeability ratio with a median size of 12 µm
compared to all the other drill-in fluid formulations. This is because there are no
polymers in this fluid which can invade deep into the rock which can cause significant
permanent damage to the rock.
3.5.3 Filtrate Loss
Figure 3.10 shows a bar graph comparing API filtrate loss for the four different
compositions of drill-in fluids as presented in Table 3.2 for three median sizes of bridging
additive. The largest API filtrate loss is found for drill-in fluid formulation number 1 with
95
only sized CaCO3 particles and no additives, while the smallest API filtrate loss is found
for the drill-in fluid formulation number 4 with all the components. This is because the
drill-in fluid formulation number 1 resulted in the thickest and largest permeability filter
cake while the drill-in fluid formulation number 4 made the thinnest and smallest
permeability filter cake. The polymer additives can fit into the pores of the filter cake
made from the bigger sized CaCO3 particles which will lower the porosity and the
permeability of the filter cake resulting in a reduced leak-off. Appendix D shows plots for
filtrate loss vs. square root of time for all the twelve tests. The filtrate loss shows a linear
fit with square root of time.
3.6 EFFECT OF DRILL SOLIDS
10 ppb RevDust was added to UltraCarb drill-in fluid to simulate drill solids in a
clean mud to represent the mud in a wellbore. Static filtration experiments with an
overbalance of 100 psi on Berea sandstone were conducted with UltraCarb-12 and
UltraCarb-20 drill-in fluids with and without RevDust. Table 3.4 compares the FIP,
return permeability ratio and API filtrate loss for both the cases (with and without
RevDust) for both the drill-in fluids. It can be seen in the table that the FIP is larger for
the drill-in fluids with RevDust than for the drill-in fluids without RevDust. However, the
return permeability ratio is found to be also slightly larger for drill-in fluid with RevDust
than for drill-in fluid without RevDust. The 30 minute API filtrate loss is found to be
approximately the same for both the cases. Hence there is not much effect of addition of
RevDust to clean drill-in fluids.
96
3.7 COMPARISON OF EXPERIMENTAL RESULTS WITH UTDAMAGE
A multi-component filtration model developed by Suri and Sharma 3 was used to
simulate the filtration and flowback experiments. The model needs an empirical constant
called erosion factor to determine the return permeability ratio during flow back. The
erosion factor is defined as the ratio of fractional volume of the particles resuspended at
the onset of flowback from the total volume of the deposited particles in the porous
medium after filtration. If all the deposited particles remain deposited at the onset of
flowback then erosion factor is equal to zero. If all the deposited particles are
resuspended at the onset of flowback then erosion factor is equal to 1. Table 3.5 shows
the erosion factors used in fitting the model results with the experimental results. I have
chosen one erosion factor for one kind of fluid formulation to fit the return permeability
ratio data. Figure 3.11 shows a bar graph of return permeability ratio obtained from
UTDamage and from the experiments. The model results match quite well with the
experimental results for return permeability ratios.
Figure 3.12 shows a bar graph of API filtrate loss obtained from UTDamage and
from the experiments. The model results match quite well with the experimental results
for return permeability ratios but match the filtrate loss only qualitatively. Hence,
UTDamage needs to be improved estimating the external filter cake permeability to
match the fluid loss during filtration.
3.8 CONCLUSIONS
1. UltraCarb-12 drill-in fluid resulted in the smallest FIP, largest return permeability
ratio and smallest API filtrate volume in comparison to UltraCarb-2 and UltraCarb-20
drill-in fluids for Berea sandstone. Therefore, a median size of the bridging additive
equal to the median pore throat size of the formation is recommended rather than
97
using the 1/3rd rule (which says the median size of the bridging additive should be
equal to the 1/3rd of the median size of the pore throat of the rock).
2. Xanthan polymer is the most damaging component among all the drill-in fluid
components tested. The drill-in fluid with xanthan shows the smallest return
permeability ratio among all the formulations.
3. Starch is a relatively less damaging component. It not only invades very little into the
formation but it also seems to restrict xanthan polymer from damaging the formation.
Therefore to minimize damage, it is recommended that within acceptable rheological
parameter requirements, more starch and less xanthan should be used in drill-in and
completion fluids.
4. Drill-in fluids with no starch and no xanthan polymer result in a smaller FIP and a
larger return permeability ratio than using the whole mud. However the API filtrate
loss is 50-100 times larger than the API filtrate loss with the whole mud.
5. Addition of RevDust to the drill-in fluid results in larger FIP than the FIP from the
clean drill-in fluid. However, the return permeability is also found to be larger as
compared to the clean fluid.
6. A quantitative match is found between UTDamage and the experimental results for
return permeability ratio. However, a value for erosion factor, an empirical constant is
needed to fit the results. A qualitative match is found between UTDamage and the
experimental results for API filtrate loss. The model to estimate the external filter
cake permeability in UTDamage needs to be modified to better fit the fluid loss
results.
98
99
Table 3-1: Formulation of a sized CaCO3 drill-in mud (9.5 ppg UltraCarb)
Composition
Field Scale
Laboratory Scale
Brine 0.98 bbl of9.7 ppg NaCl brine
343 ml of 16.4% NaCl brine
Viscosifier (Xanthan) 1 ppb
1 gram / 350 ml
FL-7 Plus (Starch) 7 ppb
7 grams / 350 ml
pH buffer 2 ppb
2 grams / 350 ml
Sized CaCO3 with median size of particles (2, 5, 12, 20 microns)
22 ppb
22 grams / 350 ml
Table 3-2: Drill-in fluid formulation matrix
Drill-in Fluid
Formulation
Drill-in Fluid Composition
1
Only bridging additive (no xanthan and no starch)
(Brine + pH buffer + Sized CaCO3)
2
Bridging additive with starch (no xanthan)
(Brine + pH buffer + Sized CaCO3 + starch)
3
Bridging additive with xanthan (no starch)
(Brine + pH buffer + Sized CaCO3 + xanthan)
4
Bridging additive with starch and xanthan
(Brine + pH buffer + Sized CaCO3 + starch + xanthan)
100
Table 3-3: FIP, return permeability ratio and API filtrate loss for different drill-in fluid formulations on Berea sandstone (Overbalance: 100 psi)
Test No. Mud Used
Av. Brine Perm (md)
Av. oil Perm (md)
Av. Porosity
Core Sample Name
Peak pressure
(psi)
FIP (psi)
Return perm (%)
API filtrate (ml)
1 UltraCarb-2 (all components) 60 N/A 0.17 BS-4-16-03-II 11.9 8.95 N/A 6.15
2 UltraCarb-2 (all components) 247 217 0.19 BS-8-27-03-III 18.27 13.9 26 6
3 UltraCarb-2 (no starch) 60 N/A 0.20 BS-4-21-03-II 13.3 10.8 14 25.3
4 UltraCarb-2 (no xanthan) 60 N/A 0.19 BS-4-21-03-III 6.2 3.57 13.1 17.2
5 UltraCarb-2
(no starch and no xanthan) 186 129 0.20 BS-6-8-03-IV 2.1 0.3 29 321
6 UltraCarb-2
(no starch and no xanthan) 130 87 0.20 BS-6-8-03-V 2.5 0 22 304
7 UltraCarb-12 (all components) 190 134 0.19 BS-6-8-03-VI 9.52 7.33 33.9 3.62
8 UltraCarb-12 (no starch) 128 92 0.17 BS-6-8-03-IX 29 20 29 48.9
9 UltraCarb-12 (no xanthan) 252 162 0.19 BS-6-8-03-VIII 7.47 4.07 47 23.7
10 UltraCarb-12
(no starch and no xanthan) 85 70.5 0.20 BS-6-8-03-VII 12.53 6.53 70 435.7
11 UltraCarb-12 + RevDust 233 214 0.21 BS-10-2-03-I 13.47 10.2 36 3.98
12 UltraCarb-20 (all components) 247 199 0.20 BS-8-27-03-II 13.44 9.97 33.4 4.5
13 UltraCarb-20 (no starch) 535 287 0.19 BS-8-11-03-XI 7.01 4.71 41.2 25.13
14 UltraCarb-20 (no xanthan) 291 166 0.19 BS-8-11-03-XII 7.59 4.36 53.1 27.7
15 UltraCarb-20
(no starch and xanthan) 142 128 0.20 BS-8-11-03-X 9.39 5 44.8 515
16 UltraCarb-20 + RevDust 272 184 0.21 BS-10-7-03-I 15 11.5 39 4.44
17 Brine 223 188 0.19 BS-8-27-03-I 5.71 2.51 52 951
18 Brine + pH Buffer 231 176 0.19 BS-8-11-03-
XIII 4.95 2.35 72
101
Table 3-4: Comparison of FIP, return permeability ratio and API filtrate loss for drill-in fluid with and without revdust
FIP [psi]
Return permeability ratio (%)
30 minute API filtrate loss [ml]
Drill-in fluid
Without RevDust
With RevDust
Without RevDust
With RevDust
Without RevDust
With RevDust
UltraCarb-12*
7.33 10.2 33.9 36 3.62 3.98
UltraCarb-20*
9.97
11.53 33.4 39 4.5 4.44
* The number denotes the median size of the bridging agent (calcium carbonate)
Table 3-5: Erosion factors used to fit the return permeability ratio obtained from experiments with UTDamage for different drill-in fluids
Drill-in fluid formulations Erosion factor
All formulations with UltraCarb-2
0.9
All formulations with UltraCarb-12
0.3
All formulations with UltraCarb-20
0.1
102
0
2
4
6
8
10
12
14
16
18
20
0 20 40 60 80 100 120 140Time (min)
Mea
sure
d P
ress
ure
Diffe
rent
ial (
psi)
∆P peak = 18.4 psi
∆P f inal = 4.8 psi
FIP = ∆P peak - ∆P final = 13.6 psi
Flowrate = 5 ml/min
Figure 3-1: Flowback pressure profile with constant flow rate boundary condition to
calculate flow initiation pressure (FIP)
0
5
10
15
20
25
Only UltraCarb UltraCarb +Starch
UltraCarb +Xanthan
UltraCarb +Starch +XanthanVarying Composition of Drill-in Fluid
Flow
Initi
atio
n Pr
essu
re (p
si)
UltraCarb-2 UltraCarb-12 UltraCarb-20
Figure 3-2: Flow initiation pressure (constant rate flow back) for Berea sandstone with
varying composition of the drill-in fluid
103
0
10
20
30
40
50
60
70
80
2 12 20Median Size of Bridging Additive (microns)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
1 ml/min 3 ml/min 5 ml/min
Figure 3-3: Return permeability ratio for Berea sandstone with varying median size of
bridging agents (bridging agent with no xanthan and no starch)
0
10
20
30
40
50
60
2 12 20Median Size of Bridging Additive (microns)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
1 ml/min 3 ml/min 5 ml/min
Figure 3-4: Return permeability ratio for Berea sandstone with varying median size of
bridging agents (bridging agent with starch but no xanthan)
104
0
10
20
30
40
50
2 12 20
Median Size of Bridging Additive (microns)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
1 ml/min 3 ml/min 5 ml/min
Figure 3-5: Return permeability ratio for Berea sandstone with varying median size of
bridging agents (bridging agent with xanthan but no starch)
0
10
20
30
40
50
2 12 20Median Size of Bridging Additive (microns)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
1 ml/min 3 ml/min 5 ml/min
Figure 3-6: Return permeability ratio for Berea sandstone with varying median size of
bridging agents (bridging agent with xanthan and starch)
105
0
10
20
30
40
50
60
70
Only UltraCarb UltraCarb +Starch
UltraCarb +Xanthan
UltraCarb +Starch +XanthanVarying Composition of Drill-in Fluid
Ret
urn
Perm
eabi
lity
Rat
io (%
)
UltraCarb-2 UltraCarb-12 UltraCarb-20
Figure 3-7: Comparison of return permeability ratio at flow back rate = 1 cc/min for
Berea sandstone with varying drill-in fluid composition
0
10
20
30
40
50
60
70
80
Only UltraCarb UltraCarb +Starch
UltraCarb +Xanthan
UltraCarb +Starch +XanthanVarying Composition of Drill-in Fluid
Ret
urn
Perm
eabi
lity
Rat
io (%
)
UltraCarb-2 UltraCarb-12 UltraCarb-20
Figure 3-8: Comparison of return permeability ratio at flow back rate = 3 cc/min for
Berea sandstone with varying drill-in fluid composition
106
0
10
20
30
40
50
60
70
80
Only UltraCarb UltraCarb +Starch
UltraCarb +Xanthan
UltraCarb +Starch +XanthanVarying Composition of Drill-in Fluid
Ret
urn
Perm
eabi
lity
Rat
io (%
)
UltraCarb-2 UltraCarb-12 UltraCarb-20
Figure 3-9: Comparison of return permeability ratio at flow back rate = 5 cc/min for
Berea sandstone with varying drill-in fluid composition
1
10
100
1000
Only UltraCarb UltraCarb +Starch
UltraCarb +Xanthan
UltraCarb +Starch +XanthanVarying Composition of Drill-in Fluid
API
Filt
rate
Los
s (c
u. c
ms)
UltraCarb-2 UltraCarb-12 UltraCarb-20
Figure 3-10: Comparison of API filtrate loss for different drill-in fluid compositions on
Berea sandstone
107
0
20
40
60
80
100
Exp Model Exp Model Exp Model
2 12 20Median Size of Bridging Additive (microns)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
Only UltraCarb UltraCarb + StarchUltraCarb + Xanthan UltraCarb + Starch + Xanthan
Figure 3-11: Comparison of return permeability ratio obtained from experiments and
from UTDAMAGE simulations
0.01
0.1
1
10
100
1000
Exp Model Exp Model Exp Model
2 12 20Median Size of Bridging Additive (microns)
API
Filt
rate
Los
s (c
u.cm
s)
Only UltraCarb UltraCarb + StarchUltraCarb + Xanthan UltraCarb + Starch + Xanthan
Figure 3-12: Comparison of API filtrate loss obtained from experiments and from
UTDAMAGE simulations
108
REFERENCES
1. Darley, H. C. H. and Gray, George R.: “Composition and Properties of Drilling and
Completion Fluids,” fifth edition, Gulf Publishing Company
2. Zain, M. Z., and Sharma, M. M.: “Cleanup of Wall-Building Filter Cakes,” paper
SPE 56635 presented at the SPE Annual Technical Conference and Exhibition held in
Houston, Texas, 3-6 October, 1999
3. Suri, A. and Sharma, M. M.: “Strategies for Sizing Particles in Drilling and
Completion Fluids,” paper SPE 87676 published in March 2004 SPE Journal
109
Chapter 4: Filter Cake Yield Strength
4.1 INTRODUCTION
This chapter reports the yield strength measurements of filter cake samples
prepared using UltraCarb drill-in fluids and bentonite muds. A constant strain rheometer
with parallel plate geometry is used to conduct both linear strain tests and dynamic strain
sweep tests. Complementary results are obtained from the two tests. The yield strength
values obtained in this chapter are used in Chapter 5 to model the cleanup of the internal
filter cake during flowback. A list of issues faced is discussed to provide guidance for the
future use of the rheometer to measure the filter cake yield strength.
4.2 LITERATURE REVIEW
The external filter cake formed should be thin, tough and highly impermeable to
seal the well bore during drilling, completion and work over operations. During
production we require the external filter cake to let the well flow freely without the need
for expensive cleanup treatments. The external filter cake either detaches from the
formation (lifts-off) or ruptures (blistering and pin holing) during production 1. Figures
4.1 and 4.2 show cartoons of external filter cake lifting-up and having pin holes and
cracks. Although the ultimate productivity is determined by the residual damage of the
near well bore region, the lift-off pressure is crucial to bringing the well on-stream; if it
exceeds the expected drawdown breakers will be required.
Very high flow initiation pressures (FIP) were observed 1 for carbonate mud with
ultra-fine particles and a mean size of 3.9 microns as compared to other carbonate muds
with larger particle sizes. The terms lift-off pressure and FIP are used interchangeably in
the literature. Bailey et al. 1 presented laboratory data on filter cake yield strength for
110
bentonite, polymer, and mixed metal hydroxide-bentonite (MMH) muds with barite and
carbonate as weighting agents. It was found that FIP is linearly dependent on filter cake
yield strength irrespective of water-based mud type or the nature and size of the
weighting agent and its concentration. A hole punch method was used for measuring the
filter cake yield strength.
Cerasi et al.2 presented a more detailed explanation of external filter cake failure.
According to them the filter cake’s initial failure is characterized by localized loss of
adhesion between the cake and the rock substrate. At low differential pressures, pinholes
appear directly above these detached areas whereas at high drawdowns, the deformed
zones grow in size and merge, leading to complete or partial cake lift-off. A parallel plate
configuration in a constant stress rheometer from Bohlin instruments was used to
measure the filter cake yield strength. They also measured the visco-elastic properties of
the filter cake such as the elastic modulus G’ (storage modulus), viscous modulus G”
(loss modulus) and phase angle. The cross over point between G’ and G” was used as a
means to calculate an approximate yield stress value. The main method used to measure
the yield strength was to apply a stress ramp and measure the shear rate. At stresses
smaller than the yield stress the shear rates will be vanishingly small indicating very high
viscosity values but on reaching the yield point (yield stress) the instantaneous viscosity
will drop by a few orders of magnitude indicating yielding of the filter cake. Oil-based
muds were found to have lower yield stress values as compared to water based muds.
Zain et al.3, 4 conducted filtration and constant rate flow back experiments to study
the behavior of filter cakes by measuring the flowback pressure profile after mud
filtration. They found similar flow back pressure profiles with and with out the external
filter cake. They concluded that the external filter cake plays no role in determining the
FIP and return permeability ratio but rather the solids and filtrate invasion into the pores
111
of the rock, which determine the flowback pressure profile during production. They
proposed a simple mathematical model for determining FIP based on Bingham fluid flow
as shown in equation 4.1.
(4.1)
p y2
p p
vdP dL 18000 d 2700 d
µ τ= +
where dp/dL is the pressure gradient, µp is the viscosity, v is the velocity, dp is the pore
diameter, and τy is the yield stress. As we can see from Equation 4.1, if there is no flow
then the pressure gradient required to initiate flow depends directly on the yield stress of
the internal filter cake and inversely on the pore diameter. The invaded polymer and
solids inside the pores of a rock forming the internal filter cake is assumed to behave as a
Bingham fluid with yield strength. The pores are assumed to be cylindrical tubes with
diameter equal to the mean pore throat diameter of the rock.
To conclude, two very different views have been presented above by authors (1-2)
and authors (3-4) to understand the mechanisms behind the flow initiation pressure (FIP).
The first view suggests that cake-rock adhesion and cake-cake adhesion control the
flowback behavior and looked at the failure of the external filter cake while the second
view suggested solids and filtrate invasion into the pores to control the flowback
behavior.
4.3 MOTIVATION
The experiments conducted by Zain and Sharma 4 clearly show that the external
filter cake does not play any role in determining the flowback pressure profile. We have
also shown the same in Chapter 2 by conducting flowback experiments with constant
pressure boundary conditions. We are convinced that it is the internal filter cake and not
the external filter cake which determines the flow initiation pressure and return
112
permeability. Therefore, to estimate the FIP and return permeability spectra,
understanding the cleanup of the internal filter cake is more important than understanding
the break down of the external filter cake. The breaking down of the external filter cake is
important from the stand point that removal of the external filter cake may lead to
plugging of screens or other flow devices in the well. In that case, pinholes or formation
of blisters in the external filter cake would be better than complete lifting up of the
external filter cake. Understanding the formation of pinholes and blistering is less
relevant to the scope of this work. However, Cerasi et al.2 have presented the mechanism
and modeling of external filter cake failure.
To determine FIP and return permeability the author assumes the invaded solids
and polymers to be represented as an internal filter cake similar to the external filter cake
but squeezed into the pores of the rock. It is assumed that the internal filter cake will
behave like a Bingham fluid with a shear yield strength. This shear yield strength can
then be related to FIP using Equation 4.1 and also to the return permeability which is
discussed in detail in Chapter 5. Hence the objective in this Chapter is to quantify the
shear yield strength of the external filter cake as an approximation for the shear yield
strength of the internal filter cake to predict the FIP and return permeability.
4.4 CONSTANT STRAIN RHEOMETER
A constant strain rheometer from TA Instruments is used to measure the yield
strength of external filter cakes produced by sized CaCO3 drill-in fluid (UltraCarb) and
bentonite muds on API filter press. As mentioned before the motivation behind making
these measurements is to find a relationship (if any), between flow initiation pressure,
return permeability and the yield strength of the external filter cake. The yield stress is
113
defined as the stress which marks the transition between the elastic region where the cake
behaves like a solid and plastic flow where the cake will behave more like a thick liquid.
4.4.1 Principle of Measurement
The constant strain rheometer can subject a sample to either dynamic (sinusoidal)
or steady (linear) shear strain (deformation), and measure the resultant torque exerted by
the sample in response to the shear strain. Shear strain is applied by a motor and torque is
measured by a transducer. Figure 4.3a shows a picture of the instrument. Figure 4.3b
shows a close up picture of the parallel plate assembly used in the experiments to
measure the yield strength of filter cakes.
In the dynamic mode (sinusoidal strain) the motor begins all tests at the motor
zero position and drives symmetrically about motor zero position to the strain
commanded by the user using RHIOS software. The motor is labeled with graduations
indicating 0.1, 0.25 and 0.5 radians from motor zero position. The maximum angular
deflection of the motor is 0.5 radians from either side of motor zero.
In the steady mode the motor can begin a test from any position, rotating either
clockwise or counter clockwise, as specified by the user, to apply linear strain to the
sample.
4.4.2 Parallel Plate Geometry
A parallel plate geometry was used to measure the yield stress of the filter cake
samples. Two different pairs of circular plates were available for the parallel plate
geometry, one with 25 mm diameter and the other with 50 mm diameter. We chose the 25
mm diameter plates so that we require smaller filter cake samples. Figure 4.3c shows a
114
schematic of the parallel plate apparatus with a description of the functionality of the
plates.
4.4.3 Theoretical Equations
The average shear stress on the top plate is given by the following equation:
(4.2)( ) ( )( ) stress k Mττ =
where M is the torque measured by the transducer connected to the top plate in g-
cm and kτ is a stress constant as given below
3
2 (4.3)
10
cGR
kτ
π=
⎛ ⎞⎜ ⎟⎝ ⎠
where Gc is the gravitational constant which is equal to 98.07 (SI units) and 980.7
in cgs units, and R is the radius of the plates in mm.
The strain applied to the sample through the bottom plate is given by the
following equation:
(4.4)( ) ( )( ) strain kγγ θ=
where θ is the angle of the bottom plate with respect to its initial position in
radians and kγ is a strain constant as given below
(4.5) R
Hkγ =
115
where R is the radius of the plates and Η is the gap between the plates.
The visco-elastic parameters G’ and G” are given by the following equations. G’
is called the elastic (storage) modulus while G” is called the viscous (loss) modulus.
cos ( ) (4.6) G τδγ
′ =
sin ( ) (4.7) G τδγ
′′ =
where δ is the phase angle (phase shift between stress and strain vectors).
4.4.4 Sample Preparation
API filter cells were used to prepare the filter cake samples. An overbalance of
100 psi was applied for a filtration time equal to 16 hours. 3 1/2" (9 cm) diameter, and 2.7
micron pore size filter papers (OFITE brand, part number: 140-55) were used to prepare
the external filter cakes. UltraCarb drill-in fluid and bentonite muds were used as the
filtration fluids with composition given in Table 2.2 of chapter 2.
4.5 RESULTS AND DISCUSSION
The following subsections provide and discusses the results obtained using the
dynamic strain sweep test and the linear strain test to measure the filter cake yield
strength.
116
4.5.1 Dynamic Strain Sweep Test
In the dynamic strain sweep test the sample was strained sinusoidally with
increasing amplitude (strain) at a constant frequency. The sample was kept between the
two parallel and circular plates. The top plate was used to apply a normal force and to
create a static boundary condition at the top of the sample. The bottom plate was used to
apply the strain to the sample by rotating back and forth sinusoidally at a specified
frequency. The minimum strain and maximum strain were specified in the RHIOS
software as the lower and upper limit for the strain. It was assumed that there was no
slippage between the top and bottom surface of the filter cake samples and the plates.
Figure 4.4 shows a plot of visco-elastic parameters (elastic modulus and viscous
modulus) for a dynamic strain test on a filter cake sample prepared from UltraCarb-2
drill-in fluid at a frequency of 0.1 rad/sec. The plot shows a higher elastic modulus than
viscous modulus at early strain values indicating the filter cake behave predominantly
elastically at small strains. After increasing the strain amplitude to a certain value the
elastic modulus falls sharply and becomes smaller than the viscous modulus. This clearly
shows a transition of filter cake behavior from elastic to plastic at well-defined yield
strength. It is assumed that the filter cake predominantly behaves as an elastoplastic
material with a well defined yield point at the transition point between the elastic and
plastic regimes. At sufficiently small strain it behaves predominantly elastically, and after
the yield point the filter cake behaves predominantly as a plastic material. Figure 4.5
shows a plot of stress vs. strain for the same experiment with the maximum stress
denoting the yield stress of the filter cake. The yield stress for the filter cake sample was
found to be equal to 418 Pascals as shown in Figure 4.5.
Figures 4.6 - 4.9 show results for two dynamic strain sweep tests done on filter
cake samples prepared using UltraCarb-12 (Median particle size: 12 microns) drill-in
117
fluid. The yield stress values were found to be equal to 353 Pascals and 248 Pascals in the
two tests. The yield stress values for UltraCarb-12 filter cakes are lower than, the yield
stress values for UltraCarb-2 filter cakes.
Figure 4.10 and 4.11 show results for a dynamic strain sweep test done on filter
cake samples prepared using UltraCarb-20 (median particle size: 20 microns) drill-in
fluid. The yield stress was found to be equal to 268 Pascals as seen in Figure 4.11. The
yield stress value for UltraCarb-20 is lower than the yield stress value of UltraCarb-12
samples. The yield stress varied as follows: UltraCarb-2 > UltraCarb-12 > UltraCarb-20.
The filter cake samples with smallest median particle size had the largest yield stress.
4.5.2 Linear Strain Test
In the linear strain test the sample was sheared linearly with time (either
clockwise or counter clockwise). The parallel plate geometry used in this test had plates
with diameter equal to 25 mm. A normal force approximately equal 100 gram force was
applied on the filter cake samples through the top plate.
Figure 4.12 shows a plot of measured stress vs. applied linear strain on a filter
cake sample prepared from UltraCarb-2 drill-in fluid. The gap between the two plates
was 1.31 mm. The applied linear strain with time is given by the following equation:
-41 * 10 t where 0 t 1000 (4.8)γ = ≤ ≤
where unit of strain is % and time is in seconds. A linear rise in stress can be seen in the
plot with applied linear strain indicating elastic behavior of the sample up to the yield
point. Considering the sample to be elastic and obeying Hook’s law of elasticity in this
region the maxima is taken to be equal to the yield or tensile strength of the filter cake.
The yield stress for the UltraCarb-2 drill-in fluid filter cake sample was found to equal to
118
439 Pascals. This value is comparable to the yield stress value of 418 Pascals measured
using the dynamic strain sweep test.
Figure 4.13 and 4.14 show results of two linear strain tests performed on
UltraCarb-12 drill-in fluid filter cake samples. The yield stress values were found to be
equal to 243 Pascals and 194 Pascals in the two tests. Figure 4.15 and 4.16 show results
of two linear strain tests performed on UltraCarb-20 drill-in fluid filter cake samples. The
yield stress values were found to be equal to 236 Pascals and 288.5 Pascals in the two
tests. Figure 4.17 - 4.19 show results of three linear strain tests performed on bentonite
mud filter cake samples. The yield stress values were found to be equal to 738 Pascals,
835 Pascals and 807 Pascals. The bentonite mud filter cake samples were much thicker
than the UltraCarb-2, 12, 20 drill-in fluid filter cake samples. The gap between the
parallel plates varied between 6.4 and 6.6 mm for the bentonite filter cake tests. The plot
shows a maxima or a turning point at 738 Pascals. The terms yield strength and yield
stress are used synonymously here. Figure 4.20 shows the effect of higher applied normal
force (500 grams) on bentonite filter cake samples. The yield stress is found to be equal
to 944 Pascals which is larger than the yield stress values with 100 grams of applied
normal force.
Figure 4.21 shows average yield strength of different filter cake samples prepared
from bentonite mud and the UltraCarb drill-in fluids. It can be seen that the filter cakes
made from bentonite muds have much higher yield strength than filter cakes made from
UltraCarb drill-in fluids. The figure also compares the yield strength values obtained
from the dynamic strain sweep test and the linear strain test. It can be seen that the two
different measurement techniques (dynamic strain sweep test and linear strain test) yield
approximately the same values. Hence the two tests can be used as complimentary tests.
Table 4.1 presents the yield strength values of the filter cakes from different muds.
119
4.6 EXPERIMENTAL ISSUES AND CONCERNS
The following experimental issues were encountered in conducting the tests:
1) Did the shear occur inside the filter cake, i.e. at the cake/cake interface or did it occur
at the cake/metal interface (slipping of the filter cake)?
The shear at the cake/metal interface means slipping between the filter cake and
the metal plates. This condition is unwanted as the objective is to measure the shear yield
stress of the filter cake which requires shearing to occur at the cake/cake interface. To our
advantage, the filter cake samples were found to adhere well to the metal plates. However
the bottom plate which was used to apply strain to the filter cake samples was doubted for
some slippage between the filter cake and the plate. To minimize slipping between the
filter cake sample and the bottom metal plate, multiple tests were conducted by varying
the normal force applied on top of the filter cake samples. A normal force of 100 grams
was found to minimize the slipping between the filter cake samples and the metal plates
without damaging the sample. A particle depleted zone between the filter cake samples
and the plates is postulated especially for the filter cake samples prepared using
UltraCarb drill-in fluids. This is because the UltraCarb fluid filter cakes can bend which
might lead to no contact zones at some places between the filter cakes samples and the
metal plates. Therefore, the actual shear strength of the filter cake samples obtained from
UltraCarb drill-in fluid could be slightly larger than the measured yield strength.
To further check for slipping between the filter cake and the metal plates, tests
were conducted on filter cake samples with and without the filter paper attached to the
samples. Similar results for the yield stress measurements were found for samples with
and without the filter paper attached to the filter cake. Tests were also conducted using
different filter papers and again similar results were obtained for the filter cake samples
120
with different filter papers. Therefore it was concluded that the filter cake samples were
mostly sheared in the bulk i.e. at the cake/cake interface and may have slipped minimally
at some places because of a particle depleted zone between the filter cake and the metal
plates.
2) Removal of filter cake sample from the filter paper. Is it necessary?
Tests were performed with and without filter paper and similar results were
obtained. Hence filter cake samples were not removed from the filter paper to avoid any
damage to the filter cake samples. It is recommended that the filter paper may not be
removed for measuring the yield strength of the filter cake samples using the rheometer.
3) Drying of the filter cake sample.
Tests were designed so as to finish in the minimum time to minimize the effect of
drying on the filter cake samples. A trial-and-error method was used for this.
a. Dynamic strain sweep test: An optimum frequency for the dynamic sweep was
found to avoid drying of the sample (which needed higher frequency) and to
avoid slipping between the sample and the plates (which needed lower
frequency). Initial tests were done at a frequency of 10 radians/sec but consistent
results were not found because of slipping. Finally a frequency of 0.1 radians/sec
was found to give consistent results for all the samples. The maximum time was
about 30 minutes for the sample to yield with minimum effect of drying and to
avoid any slipping.
b. Linear strain test: Similarly for the linear strain test, a maximum time of about 30
minutes was chosen initially to minimize the effect of drying. With trial-and-
error, the time was reduced to about 5 minutes for the samples to yield.
121
4) Yield stress measurements are sensitive to the applied normal force.
A trial-and-error method was used to find the optimum normal force that needs to
be applied to the filter cake samples to satisfy the following two conditions. First, there
should be complete contact between the sample’s top surface and the top plate. Secondly,
the sample should not be extruded with the application of the normal force.
5) Filter cake preparation requires that the excess mud left from the filtration test on top
of the filter cake be removed.
The excess mud from the top of each cake sample was carefully removed by
dabbing the cake samples with a paper towel. The excess mud was soaked repeatedly into
fresh paper towels until no more liquid is visible on top of the sample.
4.7 CONCLUSIONS
1. The yield strength of different filter cake samples obtained from bentonite muds and
UltraCarb drill-in fluids are successfully measured using a constant strain rheometer.
2. Two different methods (dynamic strain sweep test and linear strain test) are found to
compliment the yield strength measurements. The linear strain test is recommended
over the dynamic strain sweep test to measure the filter cake yield strength. This is
because the time required to finish the linear strain test is found less than the dynamic
strain sweep test which minimizes the drying of the filter cake sample. If other visco-
elastic properties are required to be measured then the dynamic strain sweep test is
recommended.
3. The yield strength of bentonite mud filter cakes is found to be larger than the yield
strength of the filter cake samples prepared using UltraCarb drill-in fluid.
122
4. Filter cake samples prepared from calcium carbonate drill-in fluid with the smallest
median particle size (2 microns) resulted in larger yield strength values as compared
to CaCO3 drill-in fluids with larger median particle size. This is consistent with the
experimental results obtained in Chapter 2 for the return permeabilities using drill-in
fluids with two different sizes. The drill-in fluid with a median size of two microns
resulted in smaller return permeabilities than the drill-in fluid with a median size of
20 microns. This supports the hypothesis that the cleanup of the internal filter cake
depends strongly on the yield strength of the filter cake.
5. The yield strength measurement values obtained can be used to estimate the FIP and
the return permeability spectra for different drill-in and completion fluids. Drill-in
and completion fluids with small yield strength values are recommended because a
large yield strength value suggests a large pressure gradient needed to cleanup the
internal filter cake.
123
Table 4.1: Comparison of yield stress measurements done using dynamic strain sweep test and linear strain test for different filter cake samples
Yield Stress (Pascals) Mud used to form the
filter cake sample Dynamic strain
sweep test
Linear strain
test
Bentonite mud 800*
UltraCarb-2 418 439*
UltraCarb-12 300* 225*
UltraCarb-20 268 263*
* Mean values calculated using two repeated experiments
Figure 4.1: Lifting up of the external filter cake during flowback. The internal filter cake
(roots holding the external filter cake) has cleaned up at point A
Figure 4.2: Lifting up and formation of pin-holes and cracks in the external filter cake
during flowback
Rock Flow-back
External filter cake with pin holes and cracks
Rock Flow-back
Lifted external filter cake
124
Figure 4.3a: Photograph of ARES constant strain rheometer
Figure 4.3b: Close up photograph of ARES constant strain rheometer with a parallel plate
(25 mm) apparatus
125
Figure 4.3c: Schematic of parallel plate apparatus in ARES constant strain rheometer
10
100
1000
10000
0.1 1 10 100 1000Strain (%)
(Pas
cals
)
G' (Elastic modulus) G" (Viscous Modulus)
Frequency = 0.1 rad/s
Figure 4.4: Plot of visco-elastic parameters using dynamic strain sweep test in a constant
strain rheometer for UltraCarb-2 drill-in fluid filter cake
Filter cake (sample)
Top plate is kept stationary and the torque is measured by the transducer
Bottom plate is rotated to apply a strain to the sample
Normal force is applied
126
10
100
1000
1 10 100 1000Strain (%)
Stre
ss (P
a)
Frequency = 0.1 rad/sYield stress = 418 Pascals
Figure 4.5: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-2 drill-in
fluid filter cake
10
100
1000
10000
0.1 1 10 100 1000Strain (%)
(Pas
cals
)
G' Pa G" Pa
Frequency = 0.1 rad/sStress at cross-over = 374 Pa
Figure 4.6: Plot of visco-elastic parameters using dynamic strain sweep test in a constant
strain rheometer for UltraCarb-12 drill-in fluid filter cake
127
10
100
1000
1 10 100 1000Strain (%)
Stre
ss (P
a)
Frequency = 0.1 rad/sYield stress = 353 PascalsStrain at yield point = 6.34 %
Figure 4.7: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-12 drill-in
fluid filter cake
10
100
1000
10000
0.1 1 10 100 1000Strain (%)
(Pas
cals
)
G' Pa G" Pa
Frequency = 0.1 rad/sStress at cross over point = 232 Pa
Figure 4.8: Plot of visco-elastic parameters using dynamic strain sweep test in a constant
strain rheometer for UltraCarb-12 drill-in fluid filter cake
128
10
100
1000
1 10 100 1000Strain (%)
Stre
ss (P
a)
Frequency = 0.1 rad/sYield stress = 248 PascalsStrain at yield point = 20 %
Figure 4.9: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-12 drill-in
fluid filter cake
10
100
1000
10000
0.1 1 10 100Strain (%)
(Pas
cals
)
G' Pa G" Pa
Frequency = 0.1 rad/sCross over stress = 262 Pa
Figure 4.10: Plot of visco-elastic parameters using dynamic strain sweep test in a constant
strain rheometer for UltraCarb-20 drill-in fluid filter cake
129
10
100
1000
1 10 100Strain (%)
Stre
ss (P
a)
Frequency = 0.1 rad/sYield stress = 268 PaStrain at yield point = 20 %
Figure 4.11: Plot of stress vs. strain in a dynamic strain sweep test for UltraCarb-20 drill-
in fluid filter cake
0
100
200
300
400
500
0 20 40 60 80 100 120Strain (%)
Stre
ss (P
asca
ls)
Yield stress: 439 PascalsStrain at yield point: 30%Normal force = 100 gramsGap = 1.31 mm
Figure 4.12: Plot of stress vs. strain in a linear strain test using constant strain rheometer
for UltraCarb-2 drill-in fluid filter cake
130
0
50
100
150
200
250
300
350
400
0 20 40 60 80 100 120Strain (%)
Stre
ss (P
asca
ls)
Yield stress: 243 PascalsStrain at yield point: 12.85%Normal force = 100 gramsGap = 1.096 mm
Figure 4.13: Plot of stress vs. strain in a linear strain test using constant strain rheometer
for UltraCarb-12 drill-in fluid filter cake
0
50
100
150
200
250
0 50 100 150Strain (%)
Stre
ss (P
asca
ls)
Yield stress: 194 PascalsStrain at yield point: 49.6%Normal force = 100 gramsGap = 1.586 mm
Figure 4.14: Plot of stress vs. strain in a linear strain test using constant strain rheometer
for UltraCarb-12 drill-in fluid filter cake
131
0
50
100
150
200
250
0 50 100 150 200Strain (%)
Stre
ss (P
asca
ls)
Yield stress: 236 PascalsStrain at yield point: 21.4%Normal force = 100 gramsGap = 1.069 mm
Figure 4.15: Plot of stress vs. strain in a linear strain test using constant strain rheometer
for UltraCarb-20 drill-in fluid filter cake
0
50
100
150
200
250
300
350
0 50 100 150 200Strain (%)
Stre
ss (P
asca
ls)
Yield stress: 288.5 PascalsStrain at yield point: 34.2%Normal force = 100 gramsGap = 1.22 mm
Figure 4.16: Plot of stress vs. strain in a linear strain test using constant strain rheometer
for UltraCarb-20 drill-in fluid filter cake
132
0
100
200
300
400
500
600
700
800
0 2 4 6 8 10 12Strain (%)
Stre
ss (P
asca
ls)
Yield Strength = 738 PascalsStrain at yield point = 3.6%Normal force = 100 gmsGap = 6.551 mm
Figure 4.17: Plot of stress vs. strain in a linear strain test using constant strain rheometer
for bentonite mud filter cake
0
100
200
300
400
500
600
700
800
900
0 2 4 6 8 10 12Strain (%)
Stre
ss (P
asca
ls)
Yield Strength = 835 PascalsStrain at yield point = 2.4 %Normal force = 100 gmsGap = 6.466 mm
Figure 4.18: Plot of stress vs. strain in a linear strain test using constant strain rheometer
for bentonite mud filter cake
133
0
100
200
300
400
500
600
700
800
900
0 1 2 3 4 5 6
Strain (%)
Stre
ss (P
asca
ls)
Yield Strength = 807 PaStrain at yield point = 3%Normal force = 100 gmsGap = 6.414 mm
Figure 4.19: Plot of stress vs. strain in a linear strain test using constant strain rheometer
for bentonite mud filter cake
0
100
200
300
400
500
600
700
800
900
1000
0 2 4 6 8 10 12 14Strain (%)
Stre
ss (P
asca
ls)
Yield Strength = 944 PascalsStrain at break point = 2.8%Normal force = 500 gmsGap = 3.685 mm
Figure 4.20: Plot of stress vs. strain at a normal force equal to 500 gms in a linear strain
test for bentonite mud filter cake
134
0
200
400
600
800
1000
Bentonite UltraCarb-2 UltraCarb-12 UltraCarb-20
Yiel
d St
reng
th (P
asca
ls)
Dynamic Strain Sweep Test Linear Strain Test
Error = 20%For all the bars
Figure 4.21: Yield strength of different muds using dynamic strain sweep test and linear
strain test
135
REFERENCES
1. Bailey, L., et al.: “Filter cake Integrity and Reservoir Damage,” paper SPE 39429
presented at the 1998 SPE International Symposium on Formation Damage Control
held in Lafayette, 18-19 February, 1998
2. Cerasi, P., et al.: “Measurement of the Mechanical Properties of Filtercakes,” paper
SPE 68948 presented at the 2001 SPE European Formation Damage Conference held
in The Hague, The Netherlands, 21-22 May, 2001
3. Zain, M. Z., and Sharma, M. M.: “Cleanup of Wall-Building Filter Cakes,” paper
SPE 56635 presented at the SPE Annual Technical Conference and Exhibition held in
Houston, Texas, 3-6 October, 1999
4. Zain, M. Z., and Sharma, M. M.: “Mechanisms of Mud Cake Removal During
Flowback,” SPE Drilling and Completion, December 2001
5. Lakes S. R.: “Viscoelastic solids,” published by CRC press.
136
Chapter 5: Modeling the Cleanup of Internal Filter Cake during Flowback
5.1 INTRODUCTION
A literature review of the existing models for flowback (with a focus on cleanup
of the formation damage) is presented. The motivation behind developing a new model
for the cleanup of the internal filter cake is discussed. A bundle of tubes model is
presented to calculate the FIP and the return permeabilities during flowback. Results
from the bundle of tubes model are presented along with a parametric study. The model
results are compared with the experimental results presented in Chapter 2. The
motivation behind developing a network model is presented. A parametric study for the
network model is also presented. The network model results are compared with the
experimental results.
5.2 BACKGROUND AND LITERATURE REVIEW
When a well is put back on production, there is usually an external filter cake on
the wellbore face and an internal filter cake (invaded solids and polymer) in the rock
matrix. These filter cakes are formed because of the excess pressure in the wellbore
during drilling and completion operations. To produce hydrocarbons from the formation
into the well, the pressure in the wellbore is reduced to below the formation pressure.
How do these filter cakes cleanup? What is the return permeability as a function of
applied drawdown (pressure difference between the well and the reservoir). Chapter 2
presented experimental data on return permeabilities as a function of differential
pressures across different permeability rocks during flowback. In this chapter we model
the return permeability spectra as a function of differential pressure for different
137
permeability cores during flowback. Below is a brief review of the literature on the
modeling of the cleanup of formation damage during production.
Ding et al.1 presented a numerical model to simulate a) fluid invasion and
permeability damage during filtration and b) natural cleanup of damage during flowback
when the well is put on production. Their objective was to predict well performance of
horizontal wells as a function of pressure drawdown. They conducted laboratory tests to
obtain data for external filter cake permeability, damaged permeability during invasion
and final return permeability during flowback. For two-phase flow, their model also
requires the reservoir oil/fluid filtrate relative permeability curves for both the drilling
mud filtrate phase and flowback production phase. They used the model to investigate the
influence of different parameters such as relative permeability curves, external filter cake
permeability, flow initiation pressure, depth of internal filter cake, overbalance pressure,
and drilling fluid circulation rate. They found the end point relative permeability for oil
during drainage to be the most influential parameter on horizontal well performance.
However, the model did not include the cleanup of the internal filter cake which we
believe is a crucial factor in determining the return permeability as a function of applied
drawdown during production.
Suri and Sharma 2 presented a model to predict the permeability reduction in the
near wellbore region during mud filtration and the improvement in permeability during
production. Figure 5.1 shows a schematic of their conceptual model. Their model
accounted for both the internal filtration and the external filtration of particles. Internal
filtration led to deposition of particles on the surface of the grains, while external
filtration led to the development of an external filter cake consisting of filtered particles
of different sizes. For flowback, they defined a parameter, the “erosion factor”, for
simulating resuspension of deposited particles from the rock grains. The “erosion factor”
138
was defined as the ratio of the volume of particles resuspended during flowback to the
total volume of particles deposited during mud filtration. If all the particles are eroded
from the surface of the grains and are resuspended in the fluid then the erosion factor is
equal to one. An erosion factor equal to zero means that all the particles remain deposited
on the grain surface during flowback and that there will be no improvement in the
permeability during flowback. However, they did not present any method to predict or
estimate the erosion factor for a given mud, formation, and flowback conditions.
Zain and Sharma 3 proposed a simplified model for cleanup of the internal filter
cake. This model can be used to estimate the flow initiation pressure. However, they did
not extend the model to predict the return permeability spectra.
Rana and Sharma 4 also presented a flowback model based entirely on relative
permeability effects and did not consider cleanup of the internal filter cake. Their model
considers flowback at constant rate and can be used to predict the FIP at constant rate.
No model is found which focuses on the cleanup of the damage (internal filter
cake) as a function of applied drawdown during flowback. Below is a simple model
presented which considers the cleanup of the internal filter cake and computes the return
permeability as a function of the applied drawdown.
5.3 MODEL DEVELOPMENT
The invasion of solids and polymers into the porous medium can be thought of as
occurring in two zones: 1) an internal filter cake which consists of solids, polymers and
filtrate from the mud as a homogenous pore-filling paste, 2) loose particles (solids and
polymers) and fluid filtrate that penetrates deeper into the formation but does not fill up
the entire pore space. Figure 5.2 shows a schematic of this conceptual model representing
the external filter cake, internal filter cake, and loose solids and polymers ahead of the
139
internal filter cake. The depth of the internal filter cake is usually a few millimeters while
the fine particles and mud filtrate penetrate much deeper into the formation. We focus on
the removal of the pore-filling internal filter cake since it offers a much larger flow
resistance than the dispersed fines that penetrate deeper into the formation.
We assume the internal filter cake to behave like a Bingham fluid with a finite
yield stress. The cleanup of the internal filter cake is controlled by the removal of this
Bingham fluid out of the pores during flowback. We consider the following two models
to represent the porous medium: 1) a bundle of tubes model, and 2) 3-D network of pore
throats model. The pore size distribution of the porous medium is represented by the pore
size distribution data obtained from mercury penetrometer data for three different rock
samples: 1) Texas Limestone, 2) Berea sandstone, and 3) Boise sandstone.
5.3.1 Bundle of Tubes Model
In the bundle of tubes model the porous medium is represented by cylindrical
tubes with varying diameter. In this simple model of the porous medium the tubes are
parallel to each other and are connected only at the two ends (inlet and outlet). Figure 5.3
shows a schematic of the bundle of tubes representation of the porous medium with the
external filter cake and the internal filter cake. The following assumptions are made in
representing the structure of the internal filter cake: 1) the internal filter cake is a
homogeneous paste, 2) the rhelogical properties of the internal filter cake are the same or
proportional to the properties of the external filter cake so that the yield strength of the
internal filter cake is taken to be approximately equal to the yield strength of the external
filter cake, and 2) the depth of the internal filter cake is the same for tubes of all sizes.
The flow rate (q) of a Newtonian fluid in a tube of radius r is given by Hagen
Poisuellie’s law as followed:
140
4
8r Pq
Lπ
µ∆
= (1)
where r is the radius of the tube, µ is the viscosity of the fluid, L is the length of
the tube and ∆P is the pressure gradient across the tube. The flow rate for a bundle of
tubes with a continuous distribution of diameter from 0 to infinity can be given by the
following equation:
4
0( )
8r Pq f r dr
Lπ
µ∞ ∆
= ∫ (2)
where f (r) is the number/frequency distribution of the radius of the tubes. Note
that the boundary condition is that the pressure difference across the bundle of tubes is a
constant.
For a real porous medium (rock matrix), the flow rate is given by Darcy’s law as
followed:
kA Pq
Lµ∆
= (3)
Comparing Eq. 2 and Eq. 3, we obtain the permeability for the bundle of tubes
model:
4
0( )
8rk f r drA
π∞= ∫ (4)
141
where f (r) is the number frequency distribution of the radius of the tubes, k is the
permeability of the porous medium, and A is the area of the porous medium, which is
given by the following equation:
2
0( )A r f r drπ
φ∞
= ∫ (5)
We assume that before a differential pressure is applied across the core during
flowback, all the tubes are filled with the internal filter cake up to a fixed distance d and
beyond that the tubes are filled with a Newtonian fluid (brine/oil). The internal filter cake
in a tube of radius r, is assumed to flow (internal filter cake is assumed to behave like a
Bingham fluid) if the pressure difference across the tube is more than a minimum
pressure gradient. The minimum pressure gradient for a tube of radius r filled with a
Bingham fluid is given by the following equation:
2
f
dPrτ
∆ = (6)
where τ is the yield strength of the Bingham fluid, d is the thickness of the
internal filter cake, and rf is the radius of the tube. The Bingham fluid will flow in the
tubes whose radius is larger than rf and will not flow in tubes whose radius is smaller than
rf. There will be a transient period during which the Bingham fluid will be flowing out
through the tubes till the tube is completely cleaned up of the internal filter cake. Finally,
the flow will reach a steady state when the flowing Bingham fluid is pushed completely
out of the porous medium in tubes with radius larger than rf. At steady state the flowback
fluid, which is assumed as a Newtonian fluid will be flowing through tubes with radius
larger than rf and the tubes with radius smaller than rf will not allow any flow through
142
them. The return permeability for the bundle of tubes, at a fixed applied pressure gradient
is, therefore, given by the following equation:
4
4
0
( )( )
( )return
frr f r dr
k Pr f r dr
∞
∞∆ =∫
∫ (7)
where 2f
LrP
τ=
∆ (8)
Eq. 7 is the ratio of the total flow rate through tubes with radius rf to R (the tubes
which have cleaned up) to the total possible flow rate if all the tubes were cleaned up.
The flow initiation pressure for the bundle of tubes model is given by the pressure
gradient which results in initiating flow in the pore with the largest radius. The flow
initiation pressure (FIP) can be calculated using the following equation:
2 dFIPRτ
= (9)
where R is the radius of the largest pore in a media. Figure 5.4 shows the FIP as a
function of the largest pore throat diameter for different thickness of the internal filter
cake. The FIP increases with increasing thickness of the internal filter cake and decreases
with the increasing largest pore diameter of a rock. The yield strength of the internal filter
cake was taken equal to 400 Pascals (for UltraCarb-2 drill-in fluid) as presented in
Chapter 4.
We used the mercury penetrometer to obtain the pore size distribution of the
different rock samples. The mercury penetrometer gives the volume size distribution of
the pores for a given rock sample rather than its number size distribution of the pores. To
convert the volume size distribution to number distribution data, we need a relation
143
between the volume and the number of the pores. We assume that the relation between
the volume and the number of pores for the actual rock samples to be the same as for a
bundle of tubes. For a bundle of tubes, the volume of a tube is proportional to the square
of its radius, and is independent of the length of the tubes (because all the tubes are of
constant length). Equation (7) is modified to include the volume size distribution in the
equation as followed:
2
2
0
( )( )
( )return
frr V r dr
k Pr V r dr
∞
∞∆ =∫
∫ (10)
where V(r) is the volume distribution of the rock sample. We can see in the above
equation that the return permeability is a function of pressure drop across the bundle of
tubes. Figures 5.5, 5.6, and 5.7 show plots of volume distribution for Texas limestone,
Berea sandstone and Boise sandstone obtained from mercury injection data. Figure 5.8
shows the above three plots together for a comparison. The Texas limestone has a median
volume pore size of 0.71 microns, the Berea sandstone has a median volume pore size of
13.5 microns, and the Boise sandstone has a median volume pore size of 17.6 microns.
5.3.2 Discussion on Bundle of Tubes Model Results
The three factors which determine the return permeability in a bundle of tubes
model are: 1) the thickness of the internal filter cake, 2) the filter cake yield strength, and
3) the pore size distribution of the rock.
5.3.2.1 Effect of Depth of Internal Filter Cake
Figure 5.9 shows the calculated return permeability with varying pressure drop for
a bundle of tubes representation of Berea sandstone. The three return permeability curves
144
shown in the figure are for three different assumed thicknesses of the internal filter cake.
Larger internal filter cake thickness results in smaller return permeabilities at a fixed
pressure drop across the bundle of tubes. The yield strength of the internal filter cake is
assumed to be equal to 400 pascals (approximate yield strength of UltraCarb drill-in
fluids as presented in Chapter 4).
5.3.2.2 Effect of Filter Cake Yield Strength
Figure 5.10 shows return permeability vs. pressure drop across a bundle of tubes
model for Berea sandstone with varying yield strength of the internal filter cake. Larger
filter cake yield strength results in smaller return permeabilities at a fixed pressure drop.
The thickness of the internal filter cake is equal to 2 mm (approximate depth of damage
calculated using UTDamage) for all the three plots.
5.3.2.3 Effect of Pore Size Distribution
Figure 5.11 shows return permeability vs. pressure drop across a bundle of tubes
model for three different rock samples with varying pore size distribution. The three rock
samples chosen were Texas limestone, Berea sandstone, and Boise sandstone for which
we have measured the pore size distribution. We can see that for a pore size distribution
with a larger median, larger return permeabilities are obtained at a fixed pressure drop.
The filter cake yield strength is taken equal to 400 pascals and the thickness of the
internal filter cake is taken equal to 2 mm in calculating the return permeability spectra
using the bundle of tubes model. The pore size distribution for Texas limestone shows the
minimum cleanup and requires very higher pressure drops for complete cleanup.
145
5.3.3 Comparison of Bundle of Tubes Model Results with Experimental Results
Bailey et al. presented that the most of the damage due to invasion of particulate
from drilling fluids is approximately 15 mm deep in from the surface of the rock. The
amount of particulate invasion decreases exponentially with distance in the rock. The
volume of solids deposited / trapped is very high within the first few mms and is reduced
to very small values at large depths into the core.
UTDamage calculates the depth of invasion of solids and polymers in cores
during filtration. We used UTDamage to estimate the thickness of the internal filter cake
for different rocks with different drill-in fluids. Table 5.1 shows range of the depth of
solids and polymer invasion in rocks with different permeability (calculated using
UTDamage). This range of invasion of solids and polymer invasion was taken as an
estimate of the range of thickness of the internal filter cake.
The yield strength of the internal filter cake is taken to be approximately 400
pascals which was estimated using a constant strain rheometer for filter cake samples
prepared from UltraCarb drill-in fluids (presented in Chapter 4).
After obtaining an estimate for the three parameters needed in the bundle of tubes
model (thickness of the internal filter cake, yield strength of the internal filter cake, and
the pore size distribution of the rock), we computed the return permeability ratio for the
different rock samples to compare with the experimental results. Figures 5.12, 5.13 and
5.14 show return permeability obtained from the bundle of tubes model and from the
flowback experiments conducted on Texas limestone, Berea sandstone and Boise
sandstone cores. The comparison between the model results and the experimental results
show a good match for Berea sandstone and Texas limestone cores but not for Boise
sandstone cores. The large permanent damage in Boise sandstone (small return
permeability ratio) was quite different from the model prediction. The bundle of tubes
146
model predict 100 % return permeability ratio at large differential pressures. However
the experimental results do not show complete clean up (i.e. 100% return permeability) at
large pressures. It should be noted that the return permeability calculated is an average
return permeability for the entire one inch core. But actually the return permeability
would vary with distance in the core. The return permeability would be very small in the
first few millimeters and would increase with increasing distance into the core. However,
the return permeability for a bundle of tubes is independent of the length of the tubes.
In conducting the experiments, the pressures are recorded at the two ends of the
short core (1 inch in length) and at intervals of 2 inches in using the long cores (6 inch in
length). We do not have the return permeability data with varying distance in the core. I
believe that to compare the return permeability ratio calculated from the bundle of tubes
model with the return permeability ratio obtained from the experiments, we should
consider the return permeability of the front end of the core (which would have the
internal filter cake) and not the average return permeability of the whole core.
To estimate the return permeability of the first few millimeters of the core, we
hypothesized two zones in the core. Figure 5.15 shows a schematic of a core with two
zones: 1) a zone with the internal filter cake (damaged zone), and 2) an undamaged zone.
In reality there will be some damage in the undamaged zone as well (due to solids,
polymers and filtrate). But most of the damage would be due to the internal filter cake
(which is plugging the entire pore space of the rock) as compared to the solids and
polymers penetrating deep into the formation and plugging only some part of the pore
space. Therefore, we assume that there is no damage in the undamaged zone and that the
permeability of the undamaged zone is equal to the initial permeability of the rock. The
pressure drop across the damaged zone can be calculated by subtracting the pressure drop
147
across the undamaged zone from the pressure drop across the whole core during
flowback and can be written as:
D FB U DP P P∆ = ∆ − ∆ (11)
where ∆PFB is the differential pressure across the core during flowback. ∆PUD is
the pressure drop across the undamaged zone, which can be calculated using the
following equation:
96.456 ( )U D FB
UD
L dP qk A
µ −∆ = (12)
where qFB is the measured flow rate in cc/min at a specific applied differential
pressure ∆PFB (in psi) during flowback, KUD is the initial undamaged permeability of the
core in md, µ is the viscosity of the flowback fluid in cp, L is the length of the core in
inches, and d is the thickness of the damaged zone in inches. We assume that the
thickness of the damaged zone is the same as the thickness of the internal filter cake. The
return permeability of the damaged zone (with the internal filter cake) can be calculated
using the following equation:
96.456/ (%) *100D FBD
dk k qA P
µ=
∆ (13)
Figure 5.16 shows the return permeability ratio of the damaged zone with varying
depths of damage (thickness of the internal filter cake). We can see that the return
permeability ratio of the damaged zone is much smaller than the average return
permeability of the whole core. Hence the two zone model suggests even smaller return
permeability ratios for the damaged zone (across the internal filter cake) as compared to
148
the return permeability of the entire core during flowback. This suggests even lesser clean
up of the cores closer to the rock face during flowback.
We now present a three dimensional network model to represent the porous
medium. This model is more generic than the bundle of tubes model.
5.3.4 Three Dimensional Network Model with Effective Medium Approximation
The network model used to represent the porous medium consists of a regular
array of variable sized pore throats and pore bodies interconnected to each other as shown
in Figure 5.17. The figure shows the pore bodies and pore throats with uniform size for
ease of presentation. However the pore throats sizes in the network model are considered
to be distributed according to a certain pore size distribution. The flow is considered in
the pore throats with a varied size distribution. Koplik3 applied the effective medium
theory (E.M.T.) to flow in porous media and showed that the E.M.T. provides an
excellent approximation to flow in two-dimensional (2-D) networks. Rossen et al.4
applied the E.M.T. to predict the single and two-phase flow of Bingham fluids in natural
fractures. They found the minimum pressure gradient for flow of Bingham fluid in a
fracture with an aperture distribution to depend primarily on the widest portion of the
aperture distribution. Fractures with narrow aperture distribution are easily plugged by
Bingham fluids as compared to fractures with broad aperture distribution.
The basic idea of E.M.T. in its application to flow in porous medium is to replace
the random microscopic flow conductances (which depends on a pore throat chosen
randomly from a distribution) with a certain mean flow conductance value so that the
mean field produced by the random flow conductances is the same as that produced when
all parameters have this mean value. By integrating local fluctuations and equating them
to zero, Kirkpatrick showed that sufficiently away from the percolation threshold, the
149
effective medium flow conductance (average flow conductance) of a network symbolized
as gm can be obtained by solving the following equation:
0( ) 0
( 1)2
m
m
g g G g dgZg g
∞ −=
+ −∫ (14)
where the network of pore throats is represented by randomly distributed
cylindrical tubes with varying radius but a constant length. G (g) dg is the probability of a
pore throat having a flow conductance between g and g + dg which is equal to f (r) dr ,
the probability of a pore throat having a radius between r and r + dr, i.e. ( ) = ( )G g dg f r dr (the fundamental transformation law of probabilities).
All the pore throats are completely filled by the Bingham fluid, which is used to
represent the internal filter cake before flowback. We consider modeling cleanup of the
internal filter cake in single-phase flow experiments, where brine is the displacing fluid
while the Bingham fluid (internal filter cake) is the displaced fluid.
A pore throat in the network can only allow flow if the pressure difference across
it is more than the pressure difference given by the following equation:
2
f
LPrτ
∆ = (15)
where τ is the yield stress of the Bingham fluid in the pore throat, L is the length
of the pore throat and ∆P is the pressure difference across the pore throat. The fraction of
pores with radius >= rf can allow flow while the other pore throats with radius < rf can
not allow flow. The fraction of pore throats which can allow flow is denoted by Xf, which
can be calculated by the following equation:
150
( )f
frX f r dr
∞
= ∫ (16)
However, in the network model, the above fraction of pore throats, Xf which can
allow flow are not completely accessible by the displacing fluid as opposed to the bundle
of tubes model. The fraction of pore throats which are accessible from this allowed
fraction of pores is given by the accessibility function for a network:
, ( )ad f fX X X= (17)
where Xa (Xf) is the accessibility function and Xd,f is the fraction of accessible
pore throats which can flow. The accessibility function gives the fraction of pore throats
which are accessible from the total number of pore throats which can allow flow. Figure
5.18 shows a schematic of the fluid (internal filter cake and brine) distribution in the
pores with a size distribution during flowback. To compute the accessibility function for
a three dimensional pore throat network, Monte Carlo simulations on computer generated
samples would be needed. This would be a very tedious and involved task, which we
wish to omit. Moreover, the accessibility function calculated would depend on the
computer generated sample networks and would change each time the sample network is
changed. The reason behind using E.M.T. was to avoid performing computer simulations
but to use a quick and easy semi-analytical model for flow of a Bingham fluid in a
network to model internal cake cleanup. To simplify the problem, we are going to use the
accessibility function for a Bethe tree for the accessibility function of a network with
same percolation thresholds. It has been shown by Heiba et al. 5 that Bethe trees with
same percolation thresholds as of a network gives very similar accessibility functions. A
Bethe tree is an endlessly branching structure similar to the branches of a tree that lack
151
reconnections. The accessibility function for a Bethe tree with local coordination Z is
given by the following equation5:
( )a fX X = (18)
where X* is the root of the following equation:
( 2) ( 2)*(1 *) (1 ) 0b b
f fZ ZX X X X− −− − − = (19)
The above eq. (18) vanishes as Xf approaches 0 or 1. The bond percolation
threshold for the Bethe tree is given by:
1
( 1)cb
XZ
=−
(20)
The local coordination number for a Bethe tree (ZB) and the average coordination
number of the three-dimensional network (Z) are related as followed:
11.5bZZ = + (21)
Heiba et al.5 have shown that aside from the shift in the bond percolation
threshold Xc, the accessibility function Xa (X) and the normalized conductivity K (X) / K
(1) of three dimensional networks and Bethe trees are qualitatively similar. They
illustrated the above similarity by comparing Xa (X) and K (X) / K (1) for a Bethe tree of
(2 2)( 2)*1 , f f c
f
bb
ZZXX X X
X
−−⎡ ⎤
− ≥⎢ ⎥⎢ ⎥⎣ ⎦
0 , f cX X<
152
local coordination number (Zb = 5) and the six-coordinated three dimensional simple
cubic network (Z = 6). The percolation threshold (Xc) for the Bethe tree with (Zb = 5) is
equal to 0.25, while Xc for the simple cubic network (Z = 6) was taken close to 0.25 for
the comparison. Their results showed a very good match for the accessibility function Xa
(X) and the normalized conductivity K (X) / K (1) between the cubic network and the
Bethe tree. Figure 5.19 shows a plot between accessibility fraction of pore throats and the
allowable fraction of pore throats. The allowable fraction of pore throats was calculated
using eq. (16) and the corresponding accessibility fraction of pore throats was calculated
using eqs. (18-21). The figure shows that the accessibility fraction of pore throats is zero
until the allowable fraction of pore throats reaches a certain threshold (minimum fraction
of allowable fraction of pore throats).
The flow conductance (g) of a pore throat is defined as follows:
q g P= ∆ (22)
where ∆P is the pressure difference across the pore throat, q is the flow rate of the
phase whose flow conductance is to be evaluated and g is the flow conductance for the
pore throat. Relating eq. (1) and eq. (12), we calculate the flow conductance for the pore
throat, which is given as followed:
4
4
8rg Cr
lπ
µ= = (23)
In the above eq. (13), r is the radius of the pore throat, l is the length of the pore
throat, µ is the viscosity of the phase whose flow conductance is to be evaluated, and C is
a constant. The pore throats in the network are assumed to have a size distribution f (r)
153
with random connectivity. We are considering brine as one phase and the Bingham fluid
(internal filter cake) as the second phase. Brine is displacing the Bingham fluid from the
pore throats.
The flow conductivity distribution function for the displacing phase (brine) during
flow back is given by the following equation:
d, f , ,G (g) ( ) (1 ) ( )d f d f fX G g X gδ= + − (24) The first term , , ( )d f d fX G g denotes the conductance distribution of the displacing
fluid through the pore throats which allow flow and are accessible. The second term (1 ) ( )fX gδ− denotes the conductance distribution of the displacing fluid through the
pore throats which don’t allow flow. All the inaccessible pore throats will be filled with
the Bingham fluid, while all the accessible pores will be filled with brine. ( )gδ is the
Dirac delta function, whose value is equal to 1 when g is equal to 0 and is equal to 0
when g is not equal to 0. The probability of allowed conditional flow conductance of the
displacing phase (brine) used in eq. (24) can be written as following:
, , ( )d f d fdrG f rdg
= (25)
, ( )d ff r = (26)
,1 ( )d f
f
drG f rX dg
= (27)
1 ( ) ff
f r r rX
≥
0 fr r<
154
d, f ,1G (g) ( ) (1 ) ( )d f f
f
drX f r X gX dg
δ= + − (28)
Substituting eq. (28) into eq. (14), we get the following equation:
,0
1 ( ) (1 ) ( ) 0( 1)2
md f f
fm
g g drX f r X g dgz X dgg gδ
∞ ⎡ ⎤−+ − =⎢ ⎥
⎢ ⎥⎣ ⎦+ −∫ (29)
,
0
( ) (1 ) ( ) 0( 1)2
d fmf
fm
Xg g f r dr X g dgz Xg gδ
∞ ⎡ ⎤−+ − =⎢ ⎥
⎢ ⎥⎣ ⎦+ −∫ (30)
, ,0
( ) (1 ) ( ) 0( 1) ( 1)2 2
f
fm m
d f d f fr
m m
rg g g gX f r dr X g dgz zg g g g
δ∞ − −
+ − =+ − + −
∫ ∫ (31)
,0
( ) (1 ) ( ) 0( 1) ( 1)2 2
f
fm m
d f ffr
m m
rg g g gf rX dr X g dgz zXg g g g
δ∞ − −
+ − =+ − + −
∫ ∫ (32)
( )g r = (33)
Substituting g from eq. (33) into eq. (32), we get the following:
, (1 )
( ) 0( 1) ( 1)2 2
f
d f fm
f rm
X Xg g f r drz zX g g
∞ −−− =
+ − −∫ (34)
4 fCr r r≥
0 fr r<
155
The flow of Bingham fluid starts when the network reaches its percolation
threshold, i.e. the accessible fraction of pore throats which can allow flow and are
connected will become greater than zero. The displacement of the Bingham fluid
(internal filter cake) by the displacing fluid (brine) would continue until the pore throats
containing the Bingham fluid allow flow and are connected. This would mean cleaning
up of the damage (internal filter cake) and gain in return permeability of the network. At
some point, the pore throats containing the Bingham fluid will become isolated and hence
inaccessible to the flow paths. The inaccessible fraction of pore throats containing the
Bingham fluid will also be given by a threshold fraction as followed:
,n f cX X= (35)
where X c is the percolation threshold of the network given by eq. (19) and Xn,f is
the inaccessible fraction of pore throats containing the Bingham fluid.
Discretizing eq. (33) to include the measured discrete pore radii distribution of
different rocks obtained from mercury penetrometer and to fit the experimental data, we
obtain the following equation:
4
,1
4
(1 )( )( ) 0
( 1) ( 1)2 2
Nd f fi m
i i ii nff
i m
X XCr g f r r rz zX Cr g+
=
−−− − =
+ − −∑ (36)
If we take the coordination number (z) for the network equal to 6, then the above
equation is reduced to:
4
,14
(1 )( )( ) 0
2 2
Nd f fi m
i i ii nff i m
X XCr g f r r rX Cr g +
=
−−− − =
+∑ (37)
where fX is also discretized and is given by the following equation:
156
1( )( )N
f i i ii nf
X f r r r+=
= −∑ (38)
where i = nf gives the pore throat radius equal to rf in the pore throat radii
distribution as given by the following equation:
( ) ( ) [1, ]if r f r where i N= = (39)
The return permeability ratio of the network is the ratio of the conductivity of the
displacing fluid to the total conductivity, when all the pores are conductive and is given
by the following equation:
/ /o m mofbk k g g= (40)
where mog is obtained from the following equation:
4
140
( )( ) 02
Ni mo
i i ii i mo
Cr g f r r rCr g +
=
−− =
+∑ (41)
It is interesting to note that this model is equivalent to flow of water in an oil wet
rock, where water is the conductive phase (representing brine) and oil is the non-
conductive phase (representing the Bingham fluid/internal filter cake).
5.3.5 Results and Discussion on Network Model
Equations (36-41) are solved in Excel using Solver to calculate the return
permeability for a network (representing the porous medium) filled with a Bingham fluid
157
(representing the internal filter cake) as a function of pressure gradient across the
network. A uniform pressure gradient is assumed in the network which means that there
is an equal amount of pressure difference across all the pore throats (as the pore throats
are considered to be of equal length). Figure 5.20 shows the probability distribution
function for the number of pores with varying radius for Berea sandstone. This number
distribution was used to represent the number distribution of the pore throats in the
network model to model the flowback of brine.
Figure 5.21 shows a plot of return permeability ratio calculated with varying
pressure difference across the pore throats (without taking the accessibility function into
account) for networks with different coordination numbers. At large pressure difference
across the pore throats, we find complete cleanup of the Bingham fluid from the network
(100% return permeability ratio). Next we use the accessible fraction instead of the
allowable fraction in calculating the return permeability ratio of the network (using Eq.
17). Figure 5.22 shows return permeability ratio for a network with varying pressure
difference across the pore throats (using accessibility function) for different coordination
numbers. The above figure shows the return permeability ratios to reach an asymptotic
value at large pressure differences across the pore throats. However, both the figures
show return permeabilities to be small for small coordination numbers at equal pressure
difference across the pore throats. Figure 5.23 shows that at very large coordination
numbers the return permeability curve obtained from the network model approach the
return permeability curve obtained from the bundle of tubes model. This is consistent
with the fact that the bundle of tubes model is a network with a coordination number
approaching infinity.
Figure 5.24 shows a plot of return permeability ratio for a network with increasing
pressure difference in pore throats with different lengths. A network with shorter pore
158
throats results in larger return permeabilities as compared to a network with longer pore
throats for the same pressure difference across the pore throats. This trend is consistent
with the fact that pore throats with a larger length need a larger pressure difference to
push a Bingham fluid through it as given by Eq. (15).
Figure 5.25 shows plots of return permeability ratios obtained from experiments
conducted on Berea sandstone and return permeability ratios obtained from the network
model. The model shows a good qualitative match with the experiments, but predicts
much larger FIP and much faster cleanup as compared to the experimental results. The
network model return permeability curve is much narrower than the experimental return
permeability curve which is much broader. However it should be noted that the pressure
difference across the pore throats in the network model is assumed to be equal to the
applied differential pressure across the cores during flowback in obtaining the match
between the model and the experiments.
The network model predicts FIP values in the range of 1 to 20 psi for networks
with pore throats with length equal to 100 microns. The corresponding pressure gradients
for these FIP values would be in the range of 250 – 5000 psi/inch. These pressure
gradients are very large as compared to the steady state pressure gradients in typical
vertical or horizontal wells as shown in Figure 2.26 of Chapter 2. There are two reasons
for this difference. One reason is the poor estimate of E.M.T. for flow in networks near
the percolation threshold and the second reason is that the pressure gradients calculated
for vertical or horizontal wells in Chapter 2 assume uniform permeability around the
wellbore. However, we know that the permeability near the wellbore is very small
(because of the damage) and increases with increasing radius away from the wellbore.
Therefore, we use the two zone model presented earlier in Section 5.2.3, to estimate the
pressure gradients across the internal filter cake with varying thickness. The single-phase
159
return permeability ratio data for Nugget sandstone (NS-2) is taken and the two zone
model is applied to calculate the pressure gradients across the internal filter cake. Figure
5.26 shows a plot of pressure gradients across the damaged zone (internal filter cake)
with varying thickness. It can be clearly seen that the pressure gradients across the
internal filter cake increases with decreasing thickness. The pressure gradients across the
internal filter cake with thickness equal to 100 microns are larger than 1000 psi/inch as
shown in Figure 5.26. These pressure gradients are comparable to the pressure gradients
estimated by the network model across pore throats to initiate flow. However the return
permeability ratios for the damaged zone calculated using the two zone model are very
small as seen in Figure 5.27. If the thickness of the internal filter cake (damaged zone) is
equal to 100 microns then the return permeability ratio of the damaged zone is only about
1% even at a pressure gradient of 7000 psi/inch. This suggests that there is very little
cleanup of the internal filter cake during flowback. To validate these small return
permeabilities, differential pressures need to be recorded for the first few millimeters
while conducting the flowback experiments.
5.4 SLOW CLEANUP OF THE INTERNAL FILTER CAKE
Both the single-phase and two-phase experiments show that the flow rates did not
stabilize instantly when the flowback pressures were incremented but took very long time
to stabilize. Two-phase experiments showed even larger time scale of cleanup than the
single-phase experiments. This is because two-phase experiments had relative
permeability effects along with the cleaning of the pores whereas in single-phase
experiments only the cleaning of the pores was taking place.
For most of the experiments, about 1000 pore volumes of the fluid were flowed
across the thin layer of the core with the internal filter cake during flowback for the flow
160
rates to reach a steady state. We wish to look at the reasons as to why there was slow
cleanup of the internal filter cake in both the single-phase and two-phase experiments to
explain the large amount of pore volumes needed during flowback for the rates to
stabilize. Below is the explanation for the slow cleanup of the internal filter cake.
The volume flow rate of a Bingham fluid which is used to model the cleanup of
the internal filter cake can be calculated using the following equation:
i0 when i oq τ τ= < (42)
4
4i
i i
4 1(1 ( ) ( ) ) when 8 3 3
i o oi o
rq Pl
π τ τ τ τµ τ τ
= − + ∆ > (43)
where qi is the volume flow rate of the Bingham fluid (representing the internal filter
cake), ri is the radius of the capillary tube (representing the pores), ∆P is the differential
pressure across the capillary (representing the flowback differential pressure), and τi is
the shear stress at the wall of the capillary given by:
i 2
i iPrl
τ ∆= (44)
If the shear stress at the wall of a pore is less than the yield strength of the
Bingham fluid then there is no flow as shown in Eq. (42). If the shear stress at the wall of
the pore is larger than the yield strength of the Bingham fluid then the flow is given by
Eq. (43).
The flow rate of a Newtonian fluid (representing the flowback fluid) is given by
the following equation:
161
4
8i
i newtonian
r PqL
πµ
∆= (45)
The ratio of the volume flow rate of a Newtonian fluid (i.e. the flowback fluid) to
the flow rate of a Bingham fluid (i.e. the internal filter cake) for a given pressure drop
across pores with radius ri is calculated using Eq. (43) and Eq. (45) and is given by:
i4
i i
1 when 4 1(1 ( ) ( ) )3 3
i newtoniano
o oi bingham
τ ττ ττ τ
= >− +
(46)
Figure 5.28 shows a plot of the ratio of the flow rate of a Newtonian fluid to the
flow rate of a Bingham fluid as a function of τo/τi (ratio of the yield stress at the wall of a
capillary tube to the yield strength of the Bingham fluid). The figure clearly shows that
for τo/τi values close to 1 (i.e. when the shear stress at the wall is barely equal to the
yield strength of the Bingham fluid), qnewtonian/qbingham is very large (i.e. the flow of
Bingham fluid is very small compared to the flow rate of the Newtonian fluid). This large
difference in the flow rates between the two fluids explains the slow cleaning up of the
internal filter cake (Bingham fluid) as compared to the measured rates for the flowback
fluid (Newtonian fluid).
5.5 CONCLUSIONS
1 The return permeability spectra obtained from the bundle of tubes model compares
qualitatively with the return permeability spectra obtained from the experiments
conducted on inch long Berea sandstone and Texas limestone cores. However, the
bundle of tubes model predicts complete cleanup (100% return permeability) at large
162
differential pressures whereas the experimental results does not show complete
cleanup even at large differential pressures during flowback.
2 A network model is also found to match qualitatively with the experimental results.
The network model can capture the asymptotic values for the return permeabilities
observed in the flowback experiments. The network model indicates the requirement
of very large pressure gradients to cleanup the internal filter cake. Therefore, the
permeability across the first few millimeters in a core during flowback is needed to
further validate the network model.
163
Table 5-1: Depth of invasion of solids and polymers calculated from UTDamage for different rocks used in conducting the experiments
Core type Drill-in fluid Depth of internal filter
cake (mm)
Nugget sandstone (4 md) UltraCarb-2 0.1 - 0.5
Texas limestone (25 md) UltraCarb-2 0.5 - 2.5
Berea sandstone (200 md) UltraCarb-2 1 - 5
Boise sandstone (1000 md) UltraCarb-20 1 - 10
Aloxide (1500 md) UltraCarb-20 1 - 15
164
∆h = Thickness of an external cake layer, k = Permeability of an external cake layer dg = Average grain diameter of an external cake layer
Figure 5.1: Schematic of invasion of particles (solids and polymers) in porous medium
representing internal and external filter cake
∆h1, k1,dg1
∆h2, k2,dg2
Depth of damage
Formation grains
Mud particles and polymers
165
Figure 5.2: Schematic of filter cake (internal and external) as a Bingham fluid
Formation grains
Internal filter cake
External filter cake
Loose particles
Formation grains
Internal filter cake
External filter cake
Loose particles
166
Figure 5.3: Schematic of filter cake conceived as a Bingham fluid in a porous medium
represented by a bundle of tubes model
External Filter Cake
Internal Filter Cake
167
0
1
2
3
4
5
6
7
8
9
10
30 40 50 60 70 80 90 100Largest Pore Throat Diameter (µm)
FIP
(psi
)d = 0.2 mm d = 0.5 mm d = 1 mm
Yield strength of the internal filter cake = 400 Pascals
Figure 5.4: Flow initiation pressure (FIP) as a function of the largest pore throat diameter
of the pores with varying thickness of the internal filter cake
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.001 0.01 0.1 1 10 100 1000Pore Diameter (µm)
Pore
Vol
ume
(ml/g
)
Figure 5.5: Pore volume distribution obtained from mercury penetrometer for Texas
limestone
FIP (Experiments) = 1 – 8 psi FIP (Model) = 0.5 – 8 psi
168
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.001 0.01 0.1 1 10 100 1000Pore Diameter (µm)
Pore
Vol
ume
(ml/g
)
Figure 5.6: Pore volume distribution obtained from mercury penetrometer for Berea
sandstone
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.01 0.1 1 10 100 1000Pore Diameter (µm)
Pore
Vol
ume
(ml/g
)
Figure 5.7: Pore volume distribution obtained from mercury penetrometer for Boise
sandstone
169
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.01 0.1 1 10 100 1000
Pore Diameter (µm)
Nor
mal
ized
Por
e Vo
lum
eBerea sandstone Median = 13.5 µm
Boise sandstone Median = 17.6 µmTexas Limestone
Median = 0.7 µm
Figure 5.8: Plot comparing the pore volume distribution for different rocks obtained from
mercury penetrometer
0
20
40
60
80
100
120
0 20 40 60 80 100∆P (psi)
k/ko
(%)
Thickness of the internal filter cake (d) = 1 mmd = 2.5 mmd = 5 mm
Cake's yield strength = 400 Pascals
Figure 5.9: Return permeability ratio for Berea sandstone using bundle of tubes model
with varying thickness of the internal filter cake
170
0
20
40
60
80
100
120
0 50 100 150 200∆P (psi)
k/ko
(%)
Filter cake's yield strength = 100 PaFilter cake's yield strength = 500 PaFilter cake's yield strength = 1000 Pa
Thickness of the internal filter cake = 2 mm
Figure 5.10: Return permeability ratio for Berea sandstone using bundle of tubes model
with varying cake yield strength
0
20
40
60
80
100
120
0 50 100 150 200∆P (psi)
k/ko
(%)
Berea sandstone Texas limestone Boise sandstone
Cake's yield strength = 400 PascalsDepth of internal filter cake = 2mm
Figure 5.11: Return permeability spectra for different rocks obtained from the bundle of
tubes model
171
0
20
40
60
80
100
120
0 20 40 60 80 100∆P (psi)
k/ko
(%)
Thickness of the internal filter cake (d) = 0.5 mmd = 1 mmd = 2.5 mmExperimental Results
Cake's yield strength = 400 Pascals
Figure 5.12: Comparison of return permeability ratio obtained from bundle of tubes
model and experimental results for single phase flow in Texas limestone
0
20
40
60
80
100
120
0 20 40 60 80 100∆P (psi)
k/ko
(%)
Thickness of the internal filter cake (d) = 1 mmd = 2.5 mmd = 5 mmExperimental Results
Filter cake's yield strength = 400 Pascals
Figure 5.13: Comparison of return permeability ratio obtained from bundle of tubes
model and experimental results for single phase flow in Berea sandstone
172
0
20
40
60
80
100
120
0 50 100 150 200∆P (psi)
k/ko
(%)
Thickness of the internal filter cake (d) = 1 mmd = 5 mmd = 10 mmExperimental Results
Filter cake's yield strength = 400 Pascals
Figure 5.14: Comparison of return permeability ratio obtained from bundle of tubes
model and experimental results for single phase flow in Boise sandstone
Figure 5.15: Schematic of a core before flowback for calculating differential pressure
across the internal filter cake (damaged zone)
Internal filter cake (Damaged zone)
Undamaged zone
Core length – d
Core length
d
d = thickness of the internal filter cake
∆Pdamage
∆Pundamaged
173
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Rat
io (%
)Across the whole core (1 inch)Across first 0.5 mm of the core (d)d = 2.5 mmd = 5 mm
Figure 5.16: Return permeability in the damaged zone with different depths for Nugget
sandstone (NS-2)
174
Figure 5.17: Schematic of a porous medium represented by a two-dimensional network of
pore throats plugged with internal filter cake. Please note that in the actual network model the pore throats are of varied sizes.
Inte
rnal
filte
r ca
ke
External filter cake
175
Figure 5.18: A schematic of the distribution of the internal filter cake (as a Bingham fluid) and the flowback fluid (brine) in the pores during flowback
r f
f ( r )
Small pores occupied by the Bingham fluid (internal filter cake) (1-X d, f)
Large pores drained by the displacing fluid (Brine) (X d, f)
r
Inaccessible pores containing Bingham fluid (X f – X d, f)
X f = Allowable fraction of pore-segments for the displacing fluid
X d, f = Accessible fraction of pore-segments from the allowable fraction for the displacing fluid
176
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1Xf (Allowable Fraction of Pore Throats)
XA
(Acc
essi
ble
Frac
tion
of P
ore
Thro
ats)
Figure 5.19: Accessible fraction of pore throats for a Bethe tree with Z = 5 to represent
the accessibility fraction of a three dimensional network with Z = 6
0
0.5
1
1.5
2
2.5
3
3.5
0.1 1 10 100 1000
Pore Throat Diameter (µm)
Pro
babi
lity
func
tion
f(d)
Figure 5.20: Probability function for pore throat radius for Berea sandstone calculated
from volume size distribution obtained from mercury penetrometer
177
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200∆P Across Pore Throat (psi)
k/ko
z=4 z=6 z=8 z=12
Filter cake yield strength = 400 PaPore throat length = 100 microns
Figure 5.21: Return permeability for a network model with varying coordination number
(without accessibility function)
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100∆P Across Pore Throat (psi)
k/ko
z=4 z=6 z=8 z=12
Filter cake yield strength = 400 PaPore throat length = 100 microns
Figure 5.22: Return permeability for a network model with varying coordination number
(with accessibility function)
178
0
0.2
0.4
0.6
0.8
1
0 10 20 30 40 50 60∆P Across Pore Throat (psi)
k/ko
Filter cake yield strength = 400 PaPore throat length = 100 microns
Bundle of tubes model
Network model (z = 12)Network model (z = 6)
Network model (z = 50)
Figure 5.23: Comparison of bundle of tubes model with the network model (the network
model approaches the bundle of tubes model when z approaches infinity)
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100∆P Across Pore Throat (psi)
k/ko
Filter cake yield strength = 400 PaZ (Coordination number) = 6
Pore throat length (L) = 10 microns
L = 50 microns
L = 100 microns
Figure 5.24: Return permeability for a network model with varying pore throat length
179
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80∆P (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
Berea short core (dia. = 2.5 inch, length = 1 inch)
Berea long core (dia. = 2 inch, length = 6 inch)
Berea long core with K and ∆P calculated only at the first two inches of the core
Network model (z=6, Pore throat length = 50 microns, τ = 400 Pa)
Figure 5.25: Return permeability obtained from experiments conducted on Berea
sandstone and from the network model
1
10
100
1000
10000
0 20 40 60 80 100 120
Applied Differential Pressure During Flowback (psi)
Pres
sure
Gra
dien
t Acr
oss
the
Inte
rnal
Fi
lter C
ake
(psi
/inch
)
Across the whole core (1 inch)Thickness of the internal filter cake (d) = 5 mmd = 1 mmd = 0.1 mm (100 microns)
Figure 5.26: Pressure gradients across the internal filter cake with different thickness
(calculated from NS-2 return permeability data and the two zone model)
180
1
10
100
1000
10000
0.01 0.1 1 10 100
Return Permeability Ratio (%)
Pres
sure
Gra
dien
t Acr
oss
the
Inte
rnal
Fi
lter C
ake
(psi
/inch
)
Across the whole core (1 inch)Thickness of the internal filter cake (d) = 5 mmd = 1 mmd = 0.1 mm (100 microns)
Figure 5.27: Pressure gradients vs. return permeability ratio of the damaged zone
(calculated for NS-2 using the two zone model)
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
1 1.1 1.2 1.3 1.4τi/τo
q new
toni
an/q
bing
ham
Figure 5.28: Ratio of the flow rate of the flowback fluid (Newtonian) to the flow rate of
the internal filter cake (Bingham fluid)
181
REFERENCES
1. Ding, Y., et al.: “Modeling of Both Near-Wellbore Damage and Natural Cleanup of
Horizontal Wells Drilled With Water-Based Drilling Fluids,” paper SPE 88807
revised for publication from paper 73733, presented at the SPE Formation Damage
Control Symposium held in Lafayette, Louisiana, 20-21 Feb., 2002
2. Suri, A., and Sharma, M.M.: “Strategies for Sizing Particles in Drilling and
Completion Fluids,” paper SPE 68964 presented at the SPE European Formation
Damage Conference held in The Hague, The Netherlands, 21–22 May 2000
3. Zain, M. Z., and Sharma, M. M.: “Mechanisms of Mud Cake Removal During
Flowback,” SPE Drilling and Completion, December 2001
4. Roy, S. R., and Sharma, M. M.: “The Relative Importance of Solids and Filtrate
Invasion on the Flow Initiation Pressure,” paper SPE 68949 presented at the
European Formation Damage Conference held in The Hague, The Netherlands, 21-22
May, 2001
5. Koplik, J.: “Creeping Flow in Two-Dimensional Networks,” Journal of Fluid
Mechanics, v.119, p.219 (1982)
6. Rossen, W. R., and Kumar, Arun T. A.: “Single- and Two-phase Flow in Natural
Fractures,” paper SPE 24915 presented at the 67th Annual Technical Conference and
Exhibition of the Society of Petroleum Engineers, Washington, DC, Oct. 4-7, 1992
7. Heiba, A. A., et al.: “Percolation Theory of Two-phase Relative Permeability,” paper
SPE 11015 presented at the 57th Annual Technical Conference and Exhibition of the
Society of Petroleum Engineers of AIME, held in New Orleans, Lafayette, September
26-29, 1982
182
8. Wang, Y.: “A Three-Dimensional Network Model for Porous Media,” M.S. Thesis,
The University of Texas at Austin, August 1988
183
Chapter 6: Cleanup of Lab-Simulated Perforation Tunnels during Flowback
6.1 INTRODUCTION
This chapter presents a study on the cleanup of lab-simulated perforation tunnels
during flowback. A background and a literature review on the fluids used in perforated
completions are presented first. The motivation for the experimental study and the
objectives of the study are presented thereafter. Both single-phase and two-phase flow
experiments are designed using lab-simulated perforated completions with different
dimensions (length and diameter of the perforation) to understand the cleanup during
flowback in these completions. The results for the FIP and return permeabilities in both
single-phase and two-phase experiments are presented and discussed. The effect of
different parameters on the FIP and return permeability ratio is also presented and
discussed. The results of the experiments are applied for field use and rule of thumbs are
provided for cleanup in perforated completions.
6.2 BACKGROUND AND LITERATURE REVIEW Fluids used during and after perforating a well are usually referred to as kill-pills.
Kill-pills can be water-based or oil-based. A typical water-based kill-pill consists of a
brine that meets density requirements, a xanthan polymer for viscosity control, a starch
polymer for fluid loss control and sized calcium carbonate for bridging at the pore
throats. The water-based kill-pill can have the same ingredients as a water-based drill-in
fluid mentioned in Chapter 2 except of drill-solids. A typical oil-based kill-pill consists of
a base oil, an emulsifier package, brine as an internal phase, barite or sized calcium
184
carbonate to meet density and bridging requirements, and lime and organophilic clay for
alkalinity and viscosity, respectively. In addition fluid loss control additives are also
added in oil-based muds.
Jiang et al.1 conducted formation damage tests using both water-based and oil-
based kill-pills on Clashach sandstone with drilled tunnels (1 cm in diameter and ~3.3 cm
in depth) simulating perforations. The results from all the tests which used oil-based kill-
pills showed return permeability ratios from 52% to 80%. However the return
permeability ratios were greatly reduced to about 10% when zinc debris (to simulate
perforating gun debris) was incorporated into the oil-based kill-pills. Water-based kill-pill
results for return permeability ratio were not affected by the addition of the zinc debris.
All the tests which used water-based kill-pills showed return permeability ratios from
69% to 91%. However, they recommended using low solids oil-based kill-pills with
charges that produce zinc debris. The water-based muds have chemical reactions that
significantly increase the fluid loss due to gas evolution from the mixture with zinc debris
although these interactions have little effect on return permeability.
Chang et al.2 (2003) conducted experiments which simulated the field conditions
when perforating in overbalance in a well. They investigated oil-based muds, low solids
oil-based muds, and water-based kill-pills formulated from formates and bromide brines
to evaluate damage caused by these fluids during overbalanced perforation operations.
Their conclusions were:
1. Oil-based kill fluids are capable of controlling leak-off effectively when perforating
overbalance. The perforation and the adjacent formation is also easily cleaned up
185
when using these oil-based fluids. The filtrate leaking into the formation does not
cause relative permeability reduction.
2. Oil-based kill fluids perform better in preventing productivity impairment than water-
based fluids in oil wells (even when the fluid losses are equal).
3. The productivity impairment from water-based kill-pills is a function of leak off. The
more fluid loss to the formation, the lower the perforation permeability. Therefore,
being able to control fluid loss when using a water-based fluid is a key factor in
minimizing formation damage.
4. There are two major mechanisms of damage to perforations by water-based kill-pills.
The first is the relative permeability damage induced by the brine filtrate, the second
is the tough and elastic filter cake built inside the perforation tunnel. The toughness of
the filter cake is enhanced by increasing polymer, polymer residue, and solids
concentration in the cake when leak-off increases – high leak-off results in the
formation of a thick filter cake.
Chang et al.3 (2005) conducted experiments simulating field conditions to
recommend field practice for overbalanced perforating. They considered the three most
common field practices for perforating in overbalance and investigated the effect of
perforation pressure dynamics on fluid loss, different kill-pills (oil-based mud, low solid
oil-based mud, and water-based kill-pills) and finally provided design guidelines for
production optimization. They concluded that building an effective filter cake is the key
to controlling fluid loss which is the main factor in determining productivity in perforated
completions. They used a constant rate flowback condition rather than constant pressure
186
flowback condition to estimate the flow initiation pressure (FIP) and to measure the
return permeability during flowback.
6.3 PROBLEM DESCRIPTION
All the tests in the literature simulating perforated completions have used a
constant rate flowback condition to estimate FIP. As mentioned in Chapter 2, a constant
pressure flowback condition will better approximate the FIP. In addition, there is no
study in the literature, which shows how return permeability improves with drawdown
for perforated completions. Return permeability spectra, as obtained here, can be used as
a guide for determining if artificial cleanup methods for a given formation, mud system
and field conditions are needed or not.
6.4 OBJECTIVES
The objectives of the experiments conducted on lab-simulated perforated cores
are as follows:
1. Measure FIP and return permeability spectra for lab-simulated perforated cores with
different permeability using a constant pressure flowback condition.
2. Study the effect of single-phase flow vs. two-phase flow in lab-simulated perforated
completion.
3. Study the effect of different parameters such as: perforation dimensions, completion
fluid type (sized CaCO3 fluid vs. bentonite mud), and overbalance on FIP and the
return permeability.
187
6.5 TEST DESIGN
6.5.1 Lab-simulated Perforated Core and Core Holder
To simulate perforations, holes were drilled through the cores before conducting
the experiments. The cores were epoxied on the top to create a no flow boundary before
drilling the hole. Figure 6.1 shows a schematic of a lab-simulated single perforation. The
perforation diameters were varied from 1/8 inch to 3/8 inch, while the lengths were
varied from ½ inch to 2 inches to represent different perforation dimensions.
Two different sized core holders were used to accommodate two different core
sizes. The short core holder accommodates a 2.5 inches diameter, 1.0 inch core long core
plug, and approximately 110 ml of fluid inside the filter cell. The long core holder can
accommodate a core plug 2.0 inch in diameter, and up to 12 inch in length. The main
purpose behind setting up a long core apparatus was to be conduct filtration experiments
on cores having long, lab-simulated, perforations. It also enabled us to study the depth of
damage caused by solids and polymers (internal filter cake) and filtrate invasion by
recording pressure readings at 2 inch intervals along the length of the core. Figure 6.2
shows a schematic of the long core apparatus. In the short core holder the cores are
epoxied on the sides to restrict any flow between the core and the sides of the cell. The
long core holder uses confining pressure on a rubber sleeve around the core to restrict
flow between the core and the sides of the sleeve.
6.5.2 Rock Type and Fluid Type
Three different rock types were used in the study with a permeability range of 25
md to 1000 md. The three rock types used are: 1) Texas limestone (25 md), 2) Berea
sandstone (200 md), and 3) Boise sandstone (1000 md).
188
Two types of fluids were used for the filtration experiments. Table 2.3 in Chapter
2 shows the fluid components and their concentration used in formulating the UltraCarb
drill-in fluid. Table 2.4 in Chapter 2 shows the fluid rheology for the UltraCarb fluid.
Table 2.5 in Chapter 2 shows the fluid components for the bentonite mud and Table 2.6
in Chapter 2 shows its rheology.
Fluids used for the flowback were: 1) 3% brine solution for single-phase flow
experiments, 2) a non-corrosive and non-reactive oil distillate (Exxsol D110) for two-
phase flow experiments.
6.5.3 Test Procedure
The test procedure used for conducting the experiments is outlined in detail in
Chapter 2 Section 2.4.3. We used a constant pressure condition during flowback.
The return permeability ratio at different applied flowback differential pressures
was calculated using the following equation:
Return Permeability Ratio ideal
flowback
PP∆
=∆
(6.1)
where ∆Pideal is the pressure drop across the lab-simulated perforated core before
mud filtration and ∆Pflowback is the pressure drop across the lab-simulated perforated core
after mud filtration at a given rate. Plotting return permeability ratio for different
differential pressures across the core during flowback yields a return permeability spectra
curve.
189
The lab-simulated perforated cores were visually examined before and after
flowback to observe the filter cake condition. Photographs of the filter cake along with
the core were taken before and after the flowback.
6.6 DISCUSSION OF EXPERIMENTAL RESULTS
Single-phase and two-phase filtration experiments on three different types of
cores with permeability ranging from 25 md to 1000 md and two different types of fluids
were conducted on the lab-simulated perforated cores. We measured, reported, and
analyzed the following parameters:
1. Flow initiation pressure
2. Return permeability ratio vs. flowback differential pressure
3. Filtrate loss during mud filtration
6.6.1 Single-phase Experiments
The motivation behind conducting single-phase experiments was to obtain results
that would help us understand the cleanup of perforations better. In this set of
experiments the flowback problem is simplified by having to understand the effect of
only the external and internal filter cake on FIP and return permeability as there are no
capillary pressure and relative permeability effects due to two-phase flow.
Table E.1 in Appendix-E shows a list of all the single phase constant pressure
flowback experiments conducted on lab-simulated perforated completions. Subsequently
three plots are shown for each of the experiments conducted: 1) applied differential
pressure and measured flow rates vs. time during flowback, 2) calculated return
permeability ratio vs. applied differential pressure during flowback, and 3) measured
190
filtrate loss vs. square root of time. A brief discussion is also presented for some of the
experiments after the plots.
6.6.1.1 Flow Initiation Pressure
Table 6.1 shows a summary of the flow initiation pressures (FIP) for single-phase
constant pressure flowback experiments simulating perforated completions. Three
different types of cores with permeability ranging from 25 md to 1000 md (Texas
limestone (25 md), Berea sandstone (200 md), and Boise sandstone (1000 md)) were
used with UltraCarb drill-in fluid. An overbalance pressure of 100 psi and static filtration
time equal to 16 hrs was used for all the experiments. For Texas limestone and Berea
sandstone the median size of bridging agent in the UltraCarb completion fluid was equal
to 2 microns while for Boise sandstone the median size of bridging agent was equal to 20
microns. The bridging additive particle size was changed from a median size of 2
microns to 20 microns to minimize the invasion of solids and polymers into the cores
with large permeability.
Figure 6.3 shows a photograph of a short (2.5 inch diameter and 1 inch length)
Texas limestone core with a 1/4 inch diameter and ½ inch long lab-simulated perforation
in the middle after mud filtration with UltraCarb-2 completion fluid. It can be seen that
the hole is completely plugged with the external filter cake. Figure 6.4 shows a
photograph of the same core after flowing back with brine. We can see that the external
filter cake is lifted-off partially but still remains in the perforation tunnel after flowback.
Figure 6.5 shows a photograph of a long (2 inch diameter and 6 inch long) Berea
core with a 1/8 inch diameter and 1 inch long, lab-simulated perforation after flowback
with brine. The lab-simulated perforation was plugged by the external filter cake after
mud filtration with UltraCarb-2 completion fluid. However, after flowing back with brine
191
the external filter cake was entirely removed from the hole as seen in Figure 6.5. A
similar observation was made for a long Berea core with a lab-simulated perforation
diameter equal to 1/8 inch and length equal to 2 inches. Figure 6.6 shows a photograph
where the external filter cake is broken into pieces. Figures 6.7 and 6.8 show photographs
of long Berea cores with lab-simulated perforations with diameter equal to ¼ inch and
lengths equal to 1 inch and 2 inch respectively. It can be seen in the figures that the
external filter cake plugs came out from the hole after flowback in both the cores.
However for a long Berea core with a lab-simulated perforation with diameter equal to
3/8 inch, the external filter cake remained in the hole as seen in Figure 6.9.
The maximum FIP for all the single-phase flow experiments on lab-simulated
perforated cores was 14 psi. The FIP was found to be significantly different for lab-
simulated perforations with diameter 1/8 inch as compared to perforations with diameter
larger than 1/8 inch. It was found that for small diameter perforations (up to 1/8 inch) the
FIP values were large. For perforation sizes larger than 1/8 inch, the FIP values were
quite small and ranged between 1 psi and 4 psi. The small FIP values were comparable to
the FIP values for the open-hole case with no perforations. The cake formed in small
diameter perforations completely plugged the tunnel when the thickness of the cake
became equal to the perforation radius. The large FIP values in small diameter
perforations are a result of the additional pressure drop required to push the plug out of
the perforation tunnel to initiate flow. Both internal and external filter cakes played a role
in determining FIP for perforations with small diameter. In the case of larger diameter
perforations, the external filter cake was only formed along the walls of the perforation
tunnel and did not pose any additional resistance during flowback.
In general, perforations with a diameter larger than twice the external filter cake
thickness had small FIP values and that the external filter cake did not play any role in
192
determining the FIP. The flowback through perforations with large diameter is achieved
similar to the open-hole flowback case (pin-holes or partial lift-off of the external filter
cake at small flowback pressures). But perforations with diameter smaller or equal to
twice the external filter cake thickness can have large FIP values and that the external
filter cake will play a significant role in determining the FIP. For perforations with small
diameter the flow is initiated after some part of the plug (external filter cake) is removed
from the tunnel. At large flowback pressures the entire external filter cake lifts off and the
whole plug (external filter cake) is removed from the perforation tunnel.
6.6.1.2 Return Permeability Spectra
Table 6.2 shows return permeability ratios at four different flowback differential
pressures (FIP, 20 psi, 50 psi, and 100 psi) for all the single-phase (3% brine) constant
pressure flowback experiments simulating perforated completions at an overbalance of
100 psi. We can see in the table that most of the return permeability improvement is at 20
psi of the applied flowback differential pressure for almost all the experiments.
Figure 6.10 shows the return permeability spectra for all the single-phase
flowback experiments conducted on Berea cores with different dimensions of lab-
simulated perforations. The mud used for all the tests was UltraCarb-2 drill-in fluid at an
overbalance of 100 psi. The plot shows that most of the permeability is recovered within
20 psi of applied differential pressure during flowback. The plot is S-shaped for most of
the cases and the return permeability ratios are asymptotic to a return permeability ratio
ranging between 60 to 70 % except for the case with a ¼ inch diameter and 2 inch long
perforation. The return permeability spectrum for ¼ inch diameter and 2 inch long
perforation was found to be significantly different from the rest of the return permeability
spectra. Figure 6.11 shows a semi-log plot version of the above plot which shows that the
193
return permeability ratios are approximately linear with the log of the differential
pressure. Figure 6.12 shows return permeability ratios for the first 2 inches of the core in
6 inch long Berea cores with different lab-simulated perforations. Figure 6.13 shows a
semi-log plot for the above data. The return permeability ratios for the first two inches of
the core are much smaller than return permeability ratios for the whole core (6 inches
long). This is because most of the damage occurs in the first two inches of the cores (area
around the perforation tunnel).
Figure 6.14 shows a plot of return permeability ratio with measured flowback
rates for Berea with different lab-simulated perforations. The return permeability ratios
approach asymptotic values at larger flowback rates. When plotted as a semi-log plot the
return permeability spectra becomes linear as seen in Figure 6.15. We observe that at a
flowback rate of 2 ml/min the return permeability ratios are larger than 20 % and at a
flowback rate of 10 ml/min the return permeability ratios are larger than 40 % for all the
experiments.
We computed the average velocity of the flowback fluid through the perforations
for all the tests by dividing the total measured flowback rate by the surface area of the
perforation tunnel. Figure 6.16 shows a plot of return permeability ratio with the log of
the average velocity of the flowback fluid. We can observe in the figure that a flowback
velocity of 0.5 cm/min results in return permeability ratios larger than 20 % for all the
experiments. At a flowback velocity of 2 cm/min the return permeability ratios are larger
than 40 % for all the cases. Figure 6.17 shows return permeability spectra for the first two
inches of the perforated cores with varying flowback velocity.
A flow rate of 10 ml/min or an average velocity of 2 cm/min in all the lab-
simulated perforated completions with single-phase flow resulted in a significant
improvement in the return permeability ratio.
194
6.6.1.3 Filtrate Loss
Table 6.3 shows 30 minute filtrate loss for all the single-phase filtration
experiments simulating perforation completions. It can be seen that the lab-simulated
perforations with large (diameter or length) leading to a larger exposed surface area of the
rock yields larger filtrate loss than in smaller diameter or smaller length perforations.
Appendix-E contains plots for cumulative filtrate loss with square root of time for
all the tests. The plots show a linear increase of cumulative filtrate loss with square root
of time, and can be expressed as:
w spQ C t Q= + (6.1)
Where Qsp is called the spurt loss and Cw, the slope of the line, is called the leak-
off coefficient.
However the volume of filtrate loss is very small and is in the range of 0 to 2 ml
for 30 minutes filtration in all the single-phase experiments (see Table 6.3). This is
because of the small surface area of the rock exposed to the completion fluid during
overbalance. Therefore, the damage caused by the filtrate invasion in perforated
completions should be potentially small.
6.6.2 Two-phase Experiments
The motivation behind conducting two-phase experiments was to closely
represent the actual field conditions where there is usually oil and water both present
during production.
Table F.1 in Appendix-F shows three two-phase constant pressure flowback
experiments conducted on cores with simulated perforations. Subsequently shown are
plots for each of the experiments conducted. All the tests were done on short Berea cores
195
at an overbalance of 100 psi. The third test was done on a core with multiple perforations.
Figure 6.18 shows a schematic of the core with three perforations.
6.6.2.1 Flow Initiation Pressure
The FIP for two-phase flow filtration experiments with lab-simulated perforations
and done at constant pressure flowback condition are shown in Table 6.4. Small Berea
core plugs with 1/8 inch diameter and ½ inch long holes were used to simulated
perforations. In one of the tests bentonite mud was used as the filtration fluid and in the
other one UltraCarb-2 completion fluid was used. A FIP of 15 psi was observed when
UltraCarb-2 drill-in fluid was used as compared to a FIP of 14 psi when bentonite mud
was used. In case of Berea core plug with 3 lab-simulated perforations, the FIP was found
to be equal to 8 psi, a value less than the FIP values for single perforation.
The FIP values for two-phase flow experiments were larger than the FIP values
for corresponding single-phase flow experiments on Berea cores with lab-simulated
perforations with diameter 1/8 inch and length equal to ½ inch. This suggests the
additional differential pressure required to initiate flow is because of capillary pressure
and relative permeability effects in two-phase flow.
6.6.2.2 Return Permeability Spectra
Table 6.5 shows return permeability ratios for the two-phase constant pressure
flowback experiments simulating perforated completion. It is observed that the return
permeability improvement is more gradual in two-phase experiments as compared to
single-phase experiments. For the case of Berea core with three perforations, the return
permeability improvement is even more gradual (Figure F-1 in Appendix F) than single
perforation cases (Figure F-4 and Figure F-5). It is possible that the perforation tunnels
196
were getting cleaned up one by one. Figure F-2 in Appendix-F shows a plot of return
permeability ratio with applied differential pressure for Berea core with 3 lab-simulated
perforations. We can see that the return permeability ratio is increasing linearly with
applied differential pressure and is not S-shaped. Figure F-2 in Appendix-F shows that
the flow rates were still increasing and had not stabilized at the end of each pressure step
change. The maximum unstabilized flow rates at different applied differential pressures
were used to calculate the return permeability ratio. This could be a possible explanation
for the return permeability spectra to be not S-shaped in case of multiple perforations.
6.6.2.3 Filtrate Loss
Figure F-3 in Appendix-F shows plot for cumulative filtrate loss with square root
of time for two-phase filtration experiments on Berea core with 3 lab-simulated
perforations. The plot shows a linear increase of cumulative filtrate loss with square root
of time. This suggests that the leak-off behavior in perforations is similar to the leak-off
behavior in open-hole completions. Therefore the formation of the filter cake in
perforations is similar to the formation of the filter cake in open-hole completions. The
leak-off volume at large times can therefore be estimated by extending the straight line fit
in the filtrate loss plot.
6.7 EFFECT OF DIFFERENT PARAMETERS
The effect of the following different parameters on FIP and return permeability spectra
are analyzed:
1. Single-phase vs. two-phase flow
2. Completion fluid (sized CaCO3 vs. bentonite mud)
3. Completion type (open hole vs. perforated completion (lab-simulated))
197
4. Overbalance pressure
5. Perforation dimensions (length and diameter of the drilled hole)
6. Single vs. multiple perforations
6.7.1 Single-phase vs. Two-phase Flow
Table 6.6 shows a comparison of FIP observed for single phase flow experiments
and two-phase flow experiments conducted on lab-simulated perforated cores. The FIP
for two-phase flow experiments is larger than the FIP for single-phase flow experiments.
We attribute the reason for larger FIP in two-phase flow than single-phase flow to
additional pressure required to overcome capillary forces and relative permeability effects
in two-phase flow. However the return permeability ratio was found to be larger in the
two-phase experiments than the single-phase experiments at the same flowback pressure.
6.7.2 Effect of Completion Fluid Type
Table 6.7 shows a comparison of FIP and return permeability ratio for UltraCarb-
2 completion fluid and bentonite mud when used on Berea cores with same hole sizes and
similar test conditions. Bentonite mud showed smaller FIP and larger return permeability
ratios as compared to UltraCarb-2 completion fluid. This is a similar result to what was
observed in for lab-simulated open-hole completions that the bentonite mud performed
better than the UltraCarb fluid in terms of both FIP and return permeability ratio.
However the fluid loss is larger for bentonite mud as compared to the fluid loss from
UltraCarb-2.
198
6.7.3 Open-hole Completion vs. Perforated Completion
The flow area in open-hole completions is much larger than the flow area in
perforated completions. Therefore the amount of fluid invasion (solids, polymers, and
filtrate) into the formation in open-hole completions will be much larger than the amount
of fluid invasion in perforated completions. Tables 2.9 and 2.12 in Chapter 2 (filtrate loss
in open-hole completion) and Table 6.3 (filtrate loss in perforated completion) clearly
show that the volume of fluid loss in open-hole completions is much larger than the fluid
loss in lab-simulated perforated completions.
The FIP values for the lab-simulated perforated completions with diameter larger
than 1/8 inch are found to be comparable with the FIP values obtained for the lab-
simulated open-hole completions. The FIP is a function of the diameter of the largest
pore throat of the media, the depth of the internal filter cake and the yield strength of the
internal filter cake assuming that there is no resistance offered by the external filter cake.
All the parameters should be about the same in both the lab-simulated open-hole
completion and lab-simulated perforated completion because the same core type, drill-in
fluid and the overbalance was applied in the two completions. However the FIP values
are found to be much larger in the lab-simulated perforated completions with diameter
equal to 1/8 inch. This is because there is an additional flow resistance offered by the
external filter cake in a form of a plug in addition to the internal filter cake in these small
diameter perforations.
Figure 6.19 shows three return permeability spectra, one for a lab-simulated open-
hole completion and two for the lab-simulated perforated completions (with two different
perforation dimensions). All the experiments were conducted on 6 inch long Berea cores
with UltraCarb-2 drill-in fluid at an overbalance of 100 psi. It can be clearly seen in the
above figure that the return permeability ratios for the lab-simulated perforated
199
completions are smaller than the return permeability ratios obtained for the lab-simulated
open-hole completions at an equal flowback pressure. The smaller return permeabilities
in the perforated completions compared to the return permeabilities in the open-hole
completion suggests less cleanup of the internal filter cake around the perforation tunnels.
We believe that this could be because of the geometry of the perforations. The tip of the
perforation tunnel is closer to the bottom face of the core than the rest of the area around
the perforation tunnel. The pressure is raised at the bottom face (reservoir side) of the
core during flowback. Before the flow is initiated the pressure gradient across the internal
filter cake around the perforation tunnel is the same. Once the flow is initiated at some
part of the perforation (i.e. some part of the internal filter cake is cleaned up around the
tunnel), the pressure gradients around the tunnel are distributed unevenly around the
perforation tunnel. The pressure gradients will be larger near the tip of the tunnel and
smaller away from the tunnel (closer to the top face of the core). Most of the flow will
take place from the tip of the tunnel and therefore the pressure gradients experienced by
the internal filter cake away from the tip of the tunnel will be small. Whereas in the lab-
simulated open-hole completions there will be a much more uniform pressure gradient
across the whole area at the top face of the core even after flow has initiated leading to a
better cleanup of the internal filter cake. This uneven distribution of pressure gradients
around the perforation tunnel during flowback might be one possible explanation of
lower return permeabilities in perforated completions compared to the open-hole
completion.
Figure 6.20 shows return permeability spectra for Berea core with open-hole and
lab-simulated perforated completions. It can be clearly seen in the figure that the FIP is
smaller for the open-hole case than the perforated case. This is because the hole diameter
was equal to 1/8 inch in the perforation completion leading to extra resistance imposed by
200
the external filter cake in the perforation tunnel. However at large flowback pressures the
return permeabilities are approximately the same in the two completions. Figure 6.21
shows the same two return permeability spectra but now as a function of the average
flowback velocity. The flowback velocities are smaller in the open-hole case than the
flowback velocities in the lab-simulated perforated case because of the small flow area in
the later case. However the two spectra show a similar cleanup behavior of the internal
filter cake as a function of the flowback velocity.
Figure 6.22 shows return permeability spectra for Texas limestone core with
open-hole and lab-simulated perforated completions. It can be clearly seen in the figure
that the FIP is small (~ 1 psi) for both the open-hole and the perforated completion.
However the return permeabilities are slightly larger for the open-hole case than the
perforated case initially. However at large flowback pressures the return permeabilities
for the perforated completion is larger than the open-hole completion. This could be
because of permanent damage to the core in the open-hole completion. We do not
understand the reason behind the permanent damage to the core in the open-hole
completion. Figures 6.23 and 6.24 show return permeability spectra for the two
completions as a function of the flowback rate and the average flowback velocities.
6.7.4 Effect of Overbalance Pressure
Figure 6.25 shows a comparison of the return permeability spectra for two
different overbalance pressures (100 psi and 500 psi) in Boise sandstone cores with lab-
simulated perforations (1/8 inch diameter and ½ inch long). It can be clearly seen in the
figure that larger overbalance results in a larger FIP and lower return permeabilities than
smaller overbalance. This suggests that the kill pills or the completion fluids should be
kept at low overbalance pressures in perforated completions.
201
6.7.5 Effect of Perforation Dimensions
Figure 6.26 shows a comparison of return permeability spectra for lab-simulated
perforations with different lengths. The figure shows that the return permeability spectra
are about the same for the two cases which suggests that the length of the perforation
does not play a significant role in the cleanup of the internal filter cake.
Figure 6.27 shows a comparison of return permeability spectra for lab-simulated
perforations with different hole diameter. The figure shows that at small flowback
pressures the perforations with large hole diameter cleanup easily and yield large return
permeabilities but at large flowback pressures the return permeabilities are about the
same for all the perforations with different hole diameter.
6.7.6 Single vs. Multiple Perforations
A lab-simulated single perforation (1/8 inch in diameter and ½ inch long) in Berea
sandstone core resulted in a FIP of 14 psi (see Figure F-4) while a Berea core with three
perforations in parallel (see Figure 6.18) resulted in a FIP of 8 psi (see Figure F-1). Even
though the FIP for the multiple perforation case was smaller than the FIP for the single
perforation case, it took a longer time to clean the 3 perforations than the single
perforation during flowback. The return permeability of the core with a single-perforation
was also larger than the return permeability of the core with 3 perforations at an equal
flowback pressure.
6.8 APPLICATION OF RESULTS TO ESTIMATE SKIN IN PERFORATED COMPLETIONS
Figure 6.29 shows a plot of skin calculated using Hawkin’s formula with a depth of
damage equal to 2 and for different return permeability ratios for the damaged zone. It
can be clearly seen that to obtain a skin factor < 2, the return permeability ratio should be
202
larger than 20 % in the damaged zone. Figure 6.30 shows a plot of the flow rates during
cleanup of the internal filter cake vs. the obtained return permeability ratios. We can
clearly see in Figure 6.30 that to obtain a return permeability ratio of 20 %, the flow rates
should be larger than 0.3 bbl/day/perf for all perforated completions. Therefore, to obtain
a significant cleanup (skin factor < 2) the perforations should flow at a rate mentioned
above. If the flow rates are smaller than 0.3 bbl/day/perf then we can assume that the skin
factor around the perforations is larger than 2. The data can also be used to estimate the
skin factor for perforated completions, if the flow rates are known.
6.9 CONCLUSIONS
1. Lab-simulated perforated completions with perforation diameter larger than 1/8 inch
resulted in FIP values similar to FIP values obtained from experiments conducted on
lab simulated open-hole completions. The external filter cake played a significant role
in case of lab-simulated perforations with diameter equal to 1/8 inch. If the external
filter cake thickness becomes equal or greater than the radius of the perforation
tunnel, additional pressure is required to push the external filter cake plug. Therefore
perforations with large hole diameter are recommended.
2. The FIP’s for two-phase flow experiments are found to be slightly larger than the
single-phase flow experiments for lab-simulated perforated completions. This is
consistent with the experimental results obtained for lab-simulated open-hole
completions as presented in Chapter 2.
3. The average return permeability spectra for lab-simulated perforated cores, when
plotted as a function of applied differential pressure is consistently S-shaped similar
to the results obtained for cores with lab-simulated open-hole completion. Perforated
203
completions are also permanently damaged similar to the open-hole completions
because of the incomplete removal of the internal filter cake leading to asymptotic
values for the return permeabilities at large flowback pressures.
4. Overbalance pressure plays a significant role in determining the FIP and return
permeability spectra in perforated completions. A large overbalance pressure results
in a large FIP and a smaller return permeability ratio compared to a small overbalance
pressure.
5. The perforation tunnel length doesn’t seem to play a significant role in determining
the FIP and the return permeability ratio during flowback in perforated completions.
6. Bentonite mud performed better than UltraCarb-2 drill-in fluid on Berea sandstone in
terms of FIP and return permeability for cores with lab-simulated perforated
completion. However bentonite mud resulted in a much larger fluid loss than
UltraCarb-2 drill-in fluid.
7. The data presented in this chapter can be used to determine the return permeability
ratio in perforated completions for a given perforation size and the drawdown /
average flow velocity / average flow rate. A flowback rate of 0.3 bbl/day/perf yielded
in a skin factor < 2 in all perforated completions.
204
Table 6-1: Flow initiation pressure for single-phase flow and constant pressure flowback experiments simulating perforated completion
Core Type
Mud used
Core Dimensions (Dia. X Len.)
[inches]
Lab-simulated Perforation dimensions
(Dia. X Length)
[inches]
FIP
[psi] Texas
limestone (25 md)
UltraCarb-2*
Short core 2.5 X 1
(1/4 X 1/2) 1
Short core 2.5 X 1
(1/8 X 1/2) 10
(1/8 X 1) 4
(1/8 X 1)** 12
(1/8 X 2) 3
(1/8 X 2)** 14
(1/4 X 1) 4
(1/4 X 1)** 2
(1/4 X 2) 1.5
(1/4 X 2)** 1
Berea sandstone (200 md)
UltraCarb-2*
Long core 2 X 6
(3/8 X 1) 3.5
Boise sandstone (1500 md)
UltraCarb-20*
Short core 2.5 X 1
(1/8 X ½) 2
* The number represents the median size of CaCO3 particles ** Repeat experiment Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the
experiments.
205
Table 6-2: Summary of return permeability ratio for single-phase constant pressure flowback tests simulating open-hole completion
Return permeability ratio (%)
Core Type
Mud used
Core Dimensions
(Dia. X Len.)
[inches]
Lab-simulated
Perforation dimensions
(Dia.X Len.) [inches]
At (FIP)
At 20 psi
At 50 psi
At 100 psi
Texas Limestone
(25 md)
UltraCarb-2* Short core 2.5 X 1
(1/4 X 1/2) 7.7 (1)
64.3 74.8 78.9
Short core2.5 X 1
(1/8 X 1/2) 41.9 (10)
56.1 77.1 100
(1/8 X 1) 0.2 (4)
46.3 64.7 73
(1/8 X 1)** 1.4 (10)
66.8 91 96
(1/8 X 2) 3.2 (3)
59.7 71.1 74.1
(1/8 X 2)** 55.4 (14)
62.5 76 78.9
(1/4 X 1) 11.4 (4)
42.8 59.4 64
(1/4 X 1)** 0.7 (2)
47.7 61.7 74.4
(1/4 X 2) 56.6 (1)
86.4 86.6 87
(1/4 X 2)** 80 (1.5)
86 93 93
Berea Sandstone (200 md)
UltraCarb-2* Long core
2 X 6
(3/8 X 1) 13.7 (3.5)
46.5 55.2 63
Boise sandstone (1000 md)
UltraCarb-20*
Short core 2.5 X 1
(1/8 X 1/2) 1 (2)
38
* The number represents the median size of CaCO3 particles. ** Repeat experiment Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
206
Table 6-3: Summary of 30 minute fluid loss for lab simulated perforated cores with single phase flow and constant pressure flowback condition
Core Type
Mud used
Core Dimensions (Dia. X Len.)
[inches]
Lab-simulated Perforation dimensions
(Dia. X Length)
[inches]
30 Minute Filtrate Loss
[ml]
Texas limestone (25 md)
UltraCarb-2*
Short core 2.5 X 1
(1/4 X 1/2) 0.16
Short core 2.5 X 1
(1/8 X 1/2) 0.05
(1/8 X 1) 0.5
(1/8 X 1)** 0.46
(1/8 X 2) 0.87
(1/8 X 2)** 1.06
(1/4 X 1) 0.89
(1/4 X 1)** 0.99
(1/4 X 2) 1.92
(1/4 X 2)** 1.72
Berea sandstone (200 md)
UltraCarb-2*
Long core 2 X 6
(3/8 X 1) 1.15
Boise sandstone (1500 md)
UltraCarb-20*
Short core 2.5 X 1
(1/8 X ½) 0.12
* The number represents the median size of CaCO3 particles ** Repeat experiment Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
207
Table 6-4: Summary of FIP for lab simulated perforated cores with two phase flow and constant pressure flowback condition
Core Type
Mud used
Core Dimensions (Dia. X Len.)
[inches]
Perforation dimensions
(Dia. X Length)
[inches]
FIP
[psi]
UltraCarb-2* (1/8 X 1/2) 15
(1/8 X 1/2) 14
Berea sandstone (200 md)
Bentonite
Short core 2.5 X 1
3 Perforations (1/8 X 1/2)
8
* The number represents the median size of CaCO3 particles Note: The mud overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
Table 6-5: Summary of return permeability ratio for two-phase constant pressure flowback tests simulating open hole completion
Return permeability ratio (%)
Core Type
Mud used
Core Dimensions
(Dia.X Len.)
[inches]
Lab-simulated
Perforation dimensions (Dia.X Len)
[inches]
At (FIP)
At 10 psi
At 12 psi
At 14 psi
UltraCarb-2
Short core 2.5 X 1
(1/8 X 1/2) >*56 (15)
(1/8 X 1/2) >*72 (14)
>*72
Berea Sandstone (200 md)
Bentonite Short core 2.5 X 1
3 Perforations (1/8 X 1/2)
>*25 (8)
>*33 >*44 >*55
* The > sign represents that the rate during flowback was still increasing and would have resulted in a calculation of a larger return permeability than cited. The overbalance pressure was equal to 100 psi and the temperature was 75 oF for all the experiments.
208
Table 6-6: Comparison of FIP for single phase vs. two phase experiments with constant pressure flowback condition in lab-simulated perforated completions
FIP [psi]
Core Type
Mud used
Core Dimensions
(Dia. X Len.)
[inches]
Perforation dimensions
(Dia. X Length)
[inches]
Single phase (Flowback fluid: 3 %
brine)
Two phase (Flowback
fluid: Exxsol)
Berea sandstone
(200 md)
UltraCarb-2
2.5 X 1 (Short core)
(1/8 X ½) 10 15
Table 6-7: Comparison of FIP and return permeability ratio between bentonite mud and UltraCarb completion fluid in lab-simulated perforated completions
FIP
[psi] Return permeability ratio
(%) Core Type and Permeability
Core dimensions
[inches]
Perforation dimensions
[inches] Bentonite UltraCarb-2 Bentonite UltraCarb-2
Berea sandstone (200 md)
(2.5” X 1”)
(1/8” X ½”)
14
15
72
56
209
mud cake
Escaid flow
Measure Flow rate
Apply constant pressure / Constant flow back rate
Top view of the core
Side view of the core
Impermeable Epoxy Perforation
mud cake
Escaid flow
mud cake
Escaid flow
Measure Flow rate
Apply constant pressure / Constant flow back rate
Top view of the core
Side view of the core
Impermeable Epoxy Perforation
mud cake
Escaid flow
Figure 6-1: Schematic of a lab-simulated single perforation in a core
210
Pressure taps
Borehole sleeve
Core
Confining liquid
Rubber sleeve
Completion fluid
Stationary end cap
End spacer
Dynamic end cap
End spacer
2 in.
Min
imum
: 1.3
5 in
.
.97
in.
17 in
.
1.35
in. 1
in.
2.15
in.
2 in
. 1.
85 in
.
Max
imum
: 6.3
in.
6 in
.
Perforation
Figure 6-2: Schematic of the long core holder with a lab-simulated single perforation
211
Figure 6-3: Top view of a 1 in. limestone core with lab simulated perforation (1/4 X 1/2 in.) before flowback at constant pressure (LS-9)
Figure 6-4: Top view of a 1 in. limestone core with lab simulated perforation (1/4 X 1/2 in.) after flowback at constant pressure (LS-9)
212
Figure 6-5: Top view of a long Berea core with lab simulated perforation (1/8 X 1 in.) after flowback at constant pressure (BS-long-#11)
Figure 6-6: Top view of a long Berea core with lab simulated perforation (1/8 X 2 in.) after flowback at constant pressure (BS-long-#12)
213
Figure 6-7: Top view of a long Berea core with lab simulated perforation (1/4 X 1 in.)
after flowback at constant pressure (BS-long-#13)
Figure 6-8: Top view of a long Berea core with lab simulated perforation (1/4 X 2 in.) after flowback at constant pressure (BS-long-#14)
214
Figure 6-9: Top view of a long Berea core with lab simulated perforation (3/8 X 1 in.) after flowback at constant pressure (BS-6-13-04-#8)
0
20
40
60
80
100
0 20 40 60 80 100Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-10: Return permeability spectra for Berea with different perforation dimensions
(single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)
215
0
20
40
60
80
100
1 10 100Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-11: Semi-log plot for return permeability in Berea with different perforation
dimensions (single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)
0
20
40
60
80
100
0 10 20 30 40 50 60Differential Pressure Across First 2 inches of the Core (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-12: Return permeability ratio in the first 2 inches of Berea cores (single-phase
flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)
216
0
20
40
60
80
100
0.1 1 10 100Differential Pressure Across First 2 inches of the Core (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-13: Semi-log plot for return permeability for the first 2 inches in Berea cores
(single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)
0
20
40
60
80
100
0 30 60 90Measured Flow back Rate (ml/min)
Retu
rn P
erm
eabi
lity
Ratio
(%)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-14: Return permeability spectra for Berea with varying flowback rate (single-
phase flow, const. pressure b.c, O.B: 100 psi, UltraCarb-2 drill-in fluid)
217
0
20
40
60
80
100
0.01 0.1 1 10 100Measured Flow back Rate (ml/min)
Ret
urn
Perm
eabi
lity
Ratio
(%)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-15: Semi-log plot for return permeability for Berea with flowback rate (single-
phase flow, const. pressure b.c, O.B: 100 psi, UltraCarb-2 drill-in fluid)
0
20
40
60
80
100
0.01 0.1 1 10 100Average Velocity Through The Perforation (cm/min)
Retu
rn P
erm
eabi
lity
Ratio
(%)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-16: Semi-log plot for return permeability for Berea with flowback rate (single-
phase flow, const. pressure b.c, O.B: 100 psi, UltraCarb-2 drill-in fluid)
218
0
20
40
60
80
100
0.01 0.1 1 10 100Average Velocity Through The Perforation (cm/min)
Ret
urn
Perm
eabi
lity
Ratio
in F
irst T
wo
Inch
es o
f The
Cor
e (%
)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-17: Semi-log plot for return permeability in 1st 2 inches of the Berea core
(single-phase flow, O.B: 100 psi, UltraCarb-2 drill-in fluid)
1/8 in.
2.5
inch
es
1/2 in
1 in.
Figure 6-18: Top and side view of a short Berea core with three drilled holes to represent lab-simulated perforations
Top view of the coreSide view of the core
Drilled holes to simulate perforations
Epoxy to seal the top of the core
219
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120Applied Differential Pressure During Flowback (psi)
k/ko
(%)
Lab-simulated open-hole completionPerf. dimensions: 1/8" diameter, 1" lengthPerf. dimensions: 1/4" diameter, 1" length
Figure 6-19: Return permeability spectra for lab-simulated open-hole completion vs. lab-
simulated perforated completions in long Berea cores (6 inch long)
0
20
40
60
80
100
120
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Open-hole
Perforated (1/8"X1/2")
Berea sandstoneUltraCarb-2 drill-in fluidO.B. Pressure = 100 psi
Figure 6-20: Return permeability vs. flowback pressure for open-hole and perforated
completions (lab-simulated) in short Berea sandstone cores (1 inch long)
220
0
20
40
60
80
100
120
0.001 0.01 0.1 1 10 100
Average Flowback Velocity (cm/min)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Open-hole Perforated (1/8"X1/2")
Berea sandstoneUltraCarb-2 drill-in fluidO.B. Pressure = 100 psi
Figure 6-21: Return permeability vs. flowback velocity for open-hole and perforated
completions (lab-simulated) in short Berea sandstone cores (1 inch long)
0
10
20
30
40
50
60
70
80
90
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
Open-hole
Perforated (1/4"X1/2")
Texas LimestoneUltraCarb-2 drill-in fluidO.B. Pressure = 100 psi
Figure 6-22: Return permeability vs. flowback pressure for open-hole and perforated
completions (lab-simulated) in short Texas limestone cores (1 inch long)
221
0
10
20
30
40
50
60
70
80
90
0.01 0.1 1 10 100Measured Flowback Rate (ml/min)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
Open-hole Perforated (1/4"X1/2")
Texas LimestoneUltraCarb-2 drill-in fluidO.B. Pressure = 100 psi
Figure 6-23: Return permeability vs. flowback rate for open-hole and perforated
completions (lab-simulated) in short Texas limestone cores (1 inch long)
0
10
20
30
40
50
60
70
80
90
0.01 0.1 1 10 100Average Flowback Velocity (cm/min)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Open-hole Perforated (1/4"X1/2")
Texas LimestoneUltraCarb-2 drill-in fluidO.B. Pressure = 100 psi
Figure 6-24: Return permeability vs. flowback velocity for open-hole and perforated
completions (lab-simulated) in short Texas limestone cores (1 inch long)
222
0
5
10
15
20
25
30
35
40
45
0 10 20 30 40 50 60 70Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
) O.B. pressure = 100 psi
O.B. pressure = 500 psi
Figure 6-25: Return permeability with varying flowback pressure in Boise sandstone with
lab-simulated perforations at two different O.B. pressures (Mud used: UltraCarb-20)
0
20
40
60
80
100
1 10 100Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
1/8 1
1/8 1(Repeat)
1/8 2
1/8 2(Repeat)
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-26: Return permeability spectra for two different perforated completions (lab-
simulated) with different lengths
223
0
20
40
60
80
100
1 10 100Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Ratio
(%)
1/8 1
1/4 1
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-27: Return permeability spectra for two different perforated completions (lab-
simulated) with different diameter
0
20
40
60
80
100
0.1 1 10 100Average Pressure Gradient (psi/inch)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-28: Return permeability spectra for the first two inches of cores with different
perforated completions as a function of average pressure gradient
224
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100Return Permeability Ratio (%)
Skin
Depth of damage = 2 inch
radius of well (rw) = 4 inch
rw = 4 inch
rw = 6 inch
Figure 6-29: Estimate of skin factor for perforated completions with a depth of damage
equal to 2 inches
0
20
40
60
80
100
0.001 0.01 0.1 1
Flow rate (bbl/day/perforation)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
1/8 1
1/8 2
1/4 1
1/4 2
3/8 1
Perf. Dim. Dia. Len. (in.) (in.)
Figure 6-30: Return permeability spectra for perforated completions in the first 2 inches
as a function of flow rate through the perforation tunnels
225
REFERENCES
1. Jiang, P., et al.: “New Low-Solids OBM Demonstrates Improved Returns as
Perforating Kill-pill,” paper SPE 73709 presented at the SPE International
Symposium and Exhibition on Formation Damage Control held in Lafayette,
Louisiana, 20-21 February 2002.
2. Chang, F. F., et al.: “Perforating in Overbalance – Is it really sinful?,” paper SPE
82203 presented at the SPE European Formation Damage Conference held in The
Hague, The Netherlands, 13-14 May 2003.
3. Chang, F. F., et al.: “Recommended Practice for Overbalanced Perforating in Long
Horizontal Wells,” paper SPE 94596 presented at the SPE European Formation
Damage Conference held in Scheveningen, The Netherlands, 25-27 May 2005.
226
Chapter 7: UTDamage: An Application to Model Both Filtration and
Flowback and To Design Fluids
7.1 INTRODUCTION
In this chapter, an overview of UTDamage (a multi-component filtration model)
is presented first. The model is used to match with the experimental results presented in
Chapter 2 to develop strategies for designing drill-in and completion fluids. The erosion
factors for the different muds are calculated by matching the model results with the
experimental results. However, no clear trend was found for the erosion factors for
different muds. In the end the erosion factor model in UTDamage is compared with the
Bingham model presented in Chapter 5. A discussion on the pros and cons for the two
flowback models is presented.
7.2 BACKGROUND AND LITERATURE REVIEW
Suri and Sharma1 presented a model to predict the permeability reduction in the
near wellbore region during mud filtration and permeability improvement during
production. Figure 7.1 shows a schematic of their conceptual model. The model accounts
for the development of both the internal and the external filter cakes during filtration.
During flowback, a parameter called “erosion factor” is defined for simulating cleanup of
deposited particles inside the porous medium. The “erosion factor” is defined as the ratio
of the volume of particles resuspended during flowback to the total volume of particles
deposited during mud filtration. If all the particles are eroded from the surface of the
grains and are resuspended in the fluid then the erosion factor is equal to one. An erosion
factor equal to zero means that all the particles remain deposited on the surface of the
227
grains during flowback. As a result, there is no improvement in the permeability during
flowback.
A Visual Basic application called UTDAMAGE 2.0 is developed to design and
evaluate drill-in and completion fluids for minimum formation damage. The application
sizes bridging solids in drill-in fluids to minimize solids invasion into the formation. The
program also evaluates the formation damage potential of a given drill-in or completion
fluid. The porosity and permeability reduction in the formation is estimated both during
filtration and production. The program accounts for both the external filter cake and the
internal filter cake build up. The application can be used for: 1) designing drill-in and
completion fluids and 2) estimating permeability distribution around the wellbore in oil-
wells during mud overbalance and during production.
7.3 MODEL DEVELOPMENT
A filtration model was developed 2 that estimates the reduction in porosity and
permeability due to invasion of particles from the mud into the formation. A description
of the model formulation is given in the following section.
A general conservation equation for particles within a certain size range can be
written as:
0)()..( =+∂∂
+∇−∇ iiiii ct
cDcu σφ (1)
where u is the Darcy velocity, ci is the volume fraction (per unit pore volume) of
suspended particles of the ith species (particles within a certain size range) in the fluid, Di
is the dispersion coefficient of the ith species, φ is the porosity of the formation and σi is
228
the volume fraction of deposited particles of the ith species in the porous medium per unit
bulk volume.
The above equation is simplified with the following approximations:
1 Incompressible flow (for both the fluid and the particles (solids/polymers) in the
mud).
2 Dispersion is neglected (diffusion is negligible for particles larger than 1µm).
3 The porosity of the medium changes due to the deposition of particles and can be
calculated as follows:
tti
∂∂
−=∂∂ σφ (2)
4 The particle deposition term dσi/dt is assumed to follow an empirical relation
proposed by Iwasaki (1937) :
iii uc
dtd λσ
= (3)
where λ is the filtration coefficient with units of (1/length).
The volumetric concentration of particles in the fluid is assumed to be low
(c<<1). With the above assumptions Equation (1) for each species reduces to,
0. =+∂∂
+∇ iii
i uctccu λφ (4)
A semi-empirical equation based on extensive computer simulations conducted by
Rajagopalan and Tien (1976) was used to calculate the filtration coefficient for each
species. The following equation gives an approximate closed form solution for the initial
229
collection efficiency in deep bed filtration by using Happel’s model. Figure 7.2 shows the
Happel's sphere-in-cell porous media model used in the model. The volume of the liquid
shell covering the solid grain is such that the volume of this liquid shell divided by the
total volume of the Happel’s sphere-in-cell is equal to the porosity of the porous medium.
3/23/14.038/158/1 4104.272.0
2.1 −−− +×+= PESRGSRLOSi NANNANNAη (5)
where AS is Happel’s geometric parameter and ηi is the collection efficiency of
the ith species and is given as the ratio of trapped particle concentration to the inlet
particle concentration in an unit bed element and is defined as,
cell sHappel' thecell sHappel' thecell sHappel' the /)( enteringileavingienteringii ccc −=η (6)
and NLO (London group), NR (relative size group), NG (gravity group), and NPE
(Peclet number) are dimensionless groups for the ith species and are defined as,
ua
HNi
LO 29πµ= (7)
µ
ρρu
gaN fii
G 9)(2 2 −
= (8)
BM
gPE D
udN = (9)
g
piR d
dN = (10)
230
The above equation for the collector efficiency is valid for NR<0.18 i.e. when the
mud particles are less than one-fifth the size of the rock grains and when there is no
energy barrier for particle deposition on the rock grains. The difference in the diameter of
the solid grain and the diameter of the Happel’s sphere-in-cell is used to represent the
pore throat diameter of the porous medium.
For a Happel cell, the relation between λi and ηi can be written as
ig
i dηφλ
2)1(3 3/1−
= (11)
Substituting equation (11) in equation (4) and assuming u and φ to be a function
of only space and not time, we get an analytical solution, which is quasi-linear in
concentration. The solution to the above equation for the ith species in linear and radial
flow geometry in one dimension was obtained using Laplace transforms.
7.3.1 Solution for Mud Filtration in Linear Geometry
For linear flow in one dimension, the following initial and boundary conditions
are used for the ith species
( ,0) 0ic x = (Initial condition) (12)
( )(0, )i i inc t c= (Boundary condition) (13)
where ci(in) is the concentration of the ith species at the face of the formation.
The solution obtained for the injection of the ith species is,
231
0),( =txci uxt φ
< (14)
)exp(),( )( xctxc iinii λ−= uxt φ
> (15)
This solution for the concentration of the ith species can be used to calculate the
total deposited concentration (σ) by using the deposition rate of the ith species in the
porous medium:
dttxuctx i
t
ii ),(),(0∫= λσ (16)
∑=
=N
ii txtx
0
),(),( σσ (17)
),()0,(),( txftf o σφφ −= (18)
A permeability reduction model due to particle deposition based on the Kozeny-
Carman equation as proposed by Pang (1996) is used. The permeability reduction can be
broken into three parts; namely reduced porosity (kdp), increased surface area (kds), and
increased tortuosity (kdt). The reduced permeability can then be written as,
dtdsdpo kkkkk =/ (19)
⎟⎟⎠
⎞⎜⎜⎝
⎛
−
−=
23
23
)1()1(
φφφφ
o
odpk (20)
232
2
)(0
)/()1(
1
)1/(1
⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢
⎣
⎡
−+
−+=
∑=
ipgo
iN
i
ods
ddk
φσ
φσ (21)
⎟⎟⎠
⎞⎜⎜⎝
⎛+
=βσ1
1dtk (22)
The damage factor (β) is introduced as an empirical parameter which accounts for
the change in tortuosity as particles deposit on the rock grains. The initial grain diameter ( god ) of the porous medium is calculated using the
Carmen-Kozeny equation as given below
o
ogo
kdφ
200= (23)
where ko is in md and dgo is in microns.
Based on Happel’s sphere-in-cell model, the pore throat diameter ( thd ) of the
porous medium is defined as the difference between the diameter of the Happel cell and
the diameter of the solid grain with deposited particles, if any. This can be seen in Figure
7.2, and is given by,
[ ]3/13/1 ))1/((1(1
)1( dpo
goth
dd φφ
φ−−−
−= (24)
233
where oφ is the initial porosity of the medium, φ is the new porosity of the
medium after deposition of particles and φ dp is the porosity of the deposited particles on
the cake grains.
The constraint for a given species to be allowed to enter the porous medium is
that it’s diameter (di) should be smaller than the pore throat diameter of the porous
medium.
ith dd > (25)
7.3.2 Build-up of an External Filter cake
The process of fluid invasion involves both solids invasion and external cake
filtration, i.e. some particles are trapped inside the porous medium, forming an internal
filter cake and some particles are retained on the face of the porous medium forming an
external filter cake. When the above condition is not met for a given species, then the
species is filtered out and starts to form an external filter cake. The thickness of the
external filter cake formed by the filtering species which are not able to enter into the
core in ∆t time is given by,
∑=
=N
niicake hh (26)
where mciii tuch φ/∆= (27)
where i = n refers to the smallest species filtered out and N refers to the largest
species in the suspension.
234
The initial porosity of the external mud cake is assumed to be of a hexagonal
packing of spheres (φmci=25.6%). The initial permeability of this new layer of external
filter cake is calculated from the modified Carmen-Kozeny equation given by Panda and
Lake (1994) as below,
⎥⎥⎦
⎤
⎢⎢⎣
⎡
+
++−
=22
23
2
32
)1(13
)1(72 PD
PDPD
mci
mcipi C
CCdk
γφτ
φ (28)
where CDP is the coefficient of variation of the psd, and the total cake
permeability is given by
∑
=
= N
ni i
icake
kh
hk (29)
Dewan and Chenevert (2000) have shown that the external cake porosity is a
function of the pressure across it. The following equation has been used to account for the
cake compressibility as proposed by them,
ν
φφ
)()(
tPt
mc
mcimc = (30)
where ν is an exponent in the range of 0.1 - 0.2 (based on porosity – permeability
cross plots for shaly sand).
As the species filtering into the core have to first filter through the external filter
cake the constraint imposed by equation (25) also has to be satisfied by these species in
235
the external filter cake if present in order to filter through and deposit in the porous
medium. The ( thd ) used in equation (25) would be of the external filter cake for the
species to filter through.
The boundary for the species filtering into the porous medium is a moving
boundary as the external filter cake is growing. The boundary condition of constant
concentration of any species is given on the face of the external filter cake as,
)(),0( inii ctc = at X = 0 (31)
where cakehxX += (32)
i.e. the origin for the x axis is moved to the face of the external filter cake formed
at each time step.
As the external filter cake also now acts as a porous medium with species filtering
in and depositing in it, equations (33) and (34) will govern the filtration process. The
filtration coefficient will of course be different in the external filter cake because of the
different grain size (which is equal to the mean size of the species being filtered out).
0),( =tXci frontXX > (33)
[ ])(exp),( 1.0
)( jjji
X
jinii XXctXc
front
−−= +=
∏ λ frontXX < (34)
where cakefront hutX += φ/ (35)
236
where i refers to the species number and j refers to the external cake layer number
starting from the face of the external cake. The internal filtration process continues until
no more species can fulfill the pore throat constraint as given by equation (25).
7.3.3 Effect of Relative Permeability on Solids and Filtrate Invasion
The formation is assumed to be at some specified initial water saturation. The
initial saturation of water (Swi) and HC (1-Swi) in the formation is provided as an input
to the program. Invasion of the mud filtrate is assumed to be piston like. The oil
saturation is reduced to the residual oil saturation (Sor) behind the filtrate front (XF). In
front of filtrate front, oil and water saturations remain equal to their initial saturations.
The relative permeability of water at (Swi) and (1-Sor) and relative permeability of oil at
(Soi) is also provided in the program by the user.
Figure 7.3 (a) shows a linear core before the filtrate invasion and Figure 7.3 (b)
shows the core after the filtrate has invaded it. The filtrate front (XF) in a linear core is
calculated using equation (31) and the flow rate is calculated using equation (32).
)1( SwiSorAQ
X LF −−
=φ
(36)
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛+⎟⎟
⎠
⎞⎜⎜⎝
⎛++−
⎥⎦
⎤⎢⎣
⎡+∆
=
−Soiroi
o
wSwirwi
Sorrwd
F
cake
cakeF
o
Soiro
w
Swirwi
kkkkkk
XkX
XL
kkPAk
q||
|)(
||
1 µµ
µµ (37)
where XF = distance of the filtrate front from the core inlet.
QL = Cumulative filtrate leak-off.
Sor = Residual oil saturation.
237
Swi = Initial water saturation in the core.
ki = Initial permeability of the core.
krw|Swi = Relative permeability of water at Swi.
kro|Soi = Relative permeability of oil at Soi.
krw|1-Sor = Relative permeability of water at residual oil saturation.
Xcake = Thickness of the external filter cake.
kcake = Average permeability of the external filter cake.
kd = Average permeability of the core behind the filtrate front.
q = filtrate flow rate at a given time.
7.3.4 Solution for Flowback in Linear Geometry
We are ultimately interested in obtaining the return permeability when the well is
put back on production. The return permeability for linear flow is calculated using the
same mass balance approach except that the flow is reversed. The following initial and
boundary conditions, now apply,
φσα /*),()0,( iiibi txxc = (Initial condition) (38)
where cbi is the initial suspended particle concentration of the ith species during
flowback and σi is the trapped/deposited concentration of ith species obtained from the
solution of the inflow case for ith species. *it is the transition time for the ith species
after which it started to build an external filter cake (internal filtration of the ith species
stopped).
As some of the deposited particles from each species are eroded during flowback
of the formation fluids, an empirical erosion factor (αi) is introduced where αi<=1. αi=1
implies that all trapped particles from the ith species are resuspended during flowback,
238
while αi=0 implies that none of the trapped particles from the ith species are resuspended.
Since this profile is found to be well represented by an exponential relation, it is fitted to
the following form:
)exp()0,( xbAxc iibi −= for x < xfi (39)
where Ai and bi are the fitted constants for ith species initial suspended particle
concentration profile ( bic ) and xfi is the depth of invasion of the ith species.
The boundary condition for the suspended particle concentration of the ith species
is specified as,
0),( =txc fibi , (40)
i.e. liquid with no suspended particles is flowed back.
The solution for the back flow case for the ith species can also be obtained by
using Laplace transforms,
0),( =txcbi )( xxu
t fi −>φ (41)
))(exp()exp(),( tbuxbAtxc iiiibi +−−= λφ
)( xxu
t fi −<φ (42)
dttxcutx bi
t
bi ),( ),( i0
λσ ∫= (43)
239
The porosity and flowback permeability is then calculated using the same
equations (equations 18-22) as used for the mud inflow case.
7.3.5 Solution for Mud Filtration in Radial Geometry
For a radial flow geometry, with the following initial and boundary conditions for
each species,
0),( =orci (Initial condition) (44)
)(),( iniwi ctrc = (Boundary condition) (45)
where ci(in) is the concentration of the ith species at the face of the formation.
Both theory and experiments show that λ depends on velocity. Assuming a
power-law dependence of λ upon u as shown below
uua γλ −= (46)
where a and uγ are empirical constants, and in radial flow we know that
u(r) = q/A (47)
For a radial geometry the flow rate (q) is calculated using the following equation.
240
⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛+
⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜
⎝
⎛
++
⎥⎦
⎤⎢⎣
⎡+∆Π
=
−Soiroi
o
wSwirwi
Sorrwd
w
f
cake
cake
w
f
e
o
Soiro
w
Swirwi
kkkkkk
rr
krr
rr
kkPhk
q
|||
lnln)(ln
||2
1 µµ
µµ (48)
where rf = radius of the filtrate front.
re = radius of the drainage boundary.
rw = radius of the well-bore.
rcake = radius of the face of the external filter cake.
h = length of the pay-zone.
The solution obtained for a radial geometry at a constant injection rate is
0),( =trci , ur
rrt w )( 22 −<
φ (49)
⎥⎦
⎤⎢⎣
⎡−
+−
= ++ )()1(
)(exp),( 11
)(uu
uw
u
iinii rr
rr
ctrc γγγγ
λ,
urrrt w )( 22 −
>φ
(50)
The multi-component (species of different sizes) filtration through the external
cake in radial geometry would be given by,
0),( =tRci , frontRR > (51)
⎥⎥⎦
⎤
⎢⎢⎣
⎡−
+
−= ++
+=
∏ )()1(
)(exp),( 11
1,
0)(
uu
u
front
jjju
jjiR
jinii RR
R
RctRc γγ
γγ
λ, frontRR < (52)
241
where cakehrR += (53)
and so, cakefrontfront hrR += (54)
where i refers to the species number and j refers to the external cake layer number
starting from the face of the external cake.
7.3.6 Dynamic Filtration
Jiao and Sharma (1993) have shown that due to cross flow in the annular region
of the well-bore the maximum radius of particles which can be deposited on the well-bore
face forming the external filter cake can be obtained by
( )γφρ
ρ−⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛=
1323
1
maxuR
n
f
s (55)
particles larger than Rmax will be removed from the cake surface. This occurs
because there is a competing force between the shear force tending to entrain the particles
in the suspension and the normal drag force holding the particle on the cake surface.
7.3.7 Solution for Flowback in Radial Geometry
The return permeability for radial flow is calculated using the same mass balance
approach as used for the flowback case in linear geometry. The following initial and
boundary conditions, now apply,
φσα /*),()0,( iiibi trrc = (Initial condition) (56)
242
where cbi is the initial suspended particle concentration of the ith species during
flowback and σi is the trapped/deposited concentration of ith species obtained from the
solution of the inflow case for ith species. *it is the transition time for the ith species
after which it started to build an external filter cake (internal filtration of the ith species
was complete and stopped).
As some of the deposited particles from each species are eroded during flowback
of the formation fluids, an empirical erosion factor (αi) is introduced where αi ≤ 1. αi=1
implies that all trapped particles from the ith species are resuspended during flowback,
while αi=0 implies that none of the trapped particles from the ith species are resuspended.
Since this profile is found to be well represented by an exponential relation, it is fitted to
the following form:
)](exp[)0,( 22wiibi rrbArc −−= for r < rfi (57)
where Ai and bi are the fitted constants for ith species initial suspended particle
concentration profile ( bic ) and rfi is the depth of invasion of the ith species.
The boundary condition for the suspended particle concentration of the ith species
is specified as,
0),( =trc fibi , (58)
i.e. liquid with no suspended particles is flowed back. We have assumed ( uγ = 1)
in equation 46 in order to get an analytical solution for flowback in radial geometry.
ua
=λ (59)
243
The solution for the back flow case for the ith species can also be obtained by
using Laplace transforms,
0),( =trcbi )(2
22 rrru
t fiww
−>φ (60)
])2(exp[()0,(),( tbr
rurctrc iiww
bibi +−=λ
φ )(
222 rr
rut fi
ww
−<φ (61)
dttrcutr bi
t
bi ),( ),( i0
λσ ∫= (62)
The porosity and flowback permeability is then calculated using the same
equations (equations 18-22) as used for mud inflow.
7.4 UTDAMAGE VS. EXPERIMENTAL RESULTS
The erosion factor in UTDamage was tuned to match the return permeability
ratios obtained from experiments conducted on Berea sandstone and Texas limestone
cores. Figure 7.4 shows a plot of erosion factors used to match the return permeability
ratios at different flowback differential pressures for a short Berea core. Figure 7.5 shows
a similar plot of erosion factors used to match the return permeability ratios at different
flowback differential pressures for a long Berea core. Figure 7.6 shows a plot of erosion
factors needed to match the return permeability ratios for all the single phase experiments
conducted on Berea sandstone. It can be seen in the plot that the erosion factors are large
at large return permeabilities. Moreover, the plot shows that the erosion factors range
from 0.5 to 0.95 for Berea sandstone and UltraCarb-2 drill-in fluid.
244
Figure 7.7 and 7.8 shows plots of erosion factors tuned to match the return
permeability ratios for single-phase and two-phase experiments conducted on Texas
limestone cores. It can be observed in the plots that the erosion factor curves have a
similar shape as the return permeability curves and that the erosion factors are large at
large return permeabilities similar to the erosion factors trend found for Berea sandstone.
Figure 7.9 shows a comparison of the erosion factor plots for the single and two-phase
experiments. Similar match between UTDamage and other experiments can be obtained
by tuning the erosion factor. However, no clear trend for erosion factors is found for any
specific mud or rock type.
7.5 EROSION FACTOR MODEL VS. BINGHAM MODEL
The erosion factor model assumes the internal filter cake to be composed of
particles which are deposited in the porous media. These particles are eroded and
resuspended in the pore fluid at the onset of flowback. The Bingham model is based on
the assumption that the internal filter cake behaves as a Bingham fluid. The internal filter
cake can flow only if the applied pressure gradient is larger than the yield strength of the
internal filter cake. In applying both the models to cleanup of internal filter cake, it is
assumed that both the erosion factor and the yield strength of the Bingham fluid are
constant with in the damaged zone. In actuality this wouldn’t be the case, the erosion
factor or the yield strength of the Bingham fluid both would vary inside the damaged
zone with distance.
A better representation of the invaded solids would be a combination of both
loose deposited particles and a composite paste as shown in Figure 5.2 of Chapter 5. The
loose deposited particles deeper into the rock formation would be eroded and
resuspended into the flowback fluid while the internal filter cake (close to the rock face)
245
would need a certain threshold pressure gradient to flow. I believe that the Bingham
model can estimate the return permeabilities during flowback better than the erosion
factor model because most of the damage is caused by the internal filter cake and not by
the particles which have penetrated deeper into the formation.
The advantage of the erosion factor model with respect to its implementation is
that it is already incorporated in UTDamage and therefore can be used to fit the
experimental data. It is much simpler to use and has fewer variables than the Bingham
model. The shortcoming of using UTDamage is that it does not include the pore size
distribution of the formation and is only a one dimensional model. Also the return
permeabilities in UTDamage are found not to depend on the flowback pressure gradient
but only on the erosion factor value.
The advantage of the Bingham model presented in this dissertation is that it
includes the pore size distribution of the formation. However, the Bingham model is
currently not been combined with any filtration model. It is only a flowback model and
needs the thickness of the internal filter cake and the yield strength of the Bingham fluid
as input parameters to model flowback. The thickness of the internal filter cake can be
estimated by using UTDamage1 (as used in Chapter 5), X-ray imaging of thin sections of
the damaged cores 9, or by CAT scans. The yield strength of the internal filter cake can
be estimated using a constant strain rheometer (as shown in Chapter 4) or a constant
stress rheometer 10. The Bingham model needs to be combined with UTDamage to better
model the cleanup of the internal filter cake.
246
∆h = Thickness of an external cake layer, k = Permeability of an external cake layer dg = Average grain diameter of an external cake layer
∆h1, k1,dg1
∆h2, k2,dg2
Depth of damage
Formation grains
Mud particles and polymers
Figure 7.1: Schematic of invasion of particles (solids and polymers) in porous medium
representing internal and external filter cake
247
Limiting trajectory
Liquid Shell
Grain
b dg
(b,θS)
(ap+ac , π)
(r,θ)
Flow
Pore throat diameter (dth)
Figure 7.2: Happel 's Sphere-in-cell porous media model representing the grain and the pore throat
248
Figure 7.3 (a): Initial saturation of fluids in the core
XF
LCORE XCAKE
Sw = 1 Sw = 1 - Sor Sw = Swi
External filter cake
Uninvaded zone
Filtrate invaded zone
Figure 7.3 (b): Fluid saturations after invasion of mud filtrate
Where XCAKE = Cake thickness
XF = Distance of the filtrate front from the core inlet
LCORE = Length of the core
Sw = Water saturation
So = Oil saturation
Sor = Residual oil saturation
Swi = Initial water saturation in the formation
LCORE
Sw = SwiSo = 1 - Swi Core Inlet
249
0
10
20
30
40
50
60
0 5 10 15 20 25Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
0
0.2
0.4
0.6
0.8
1
Eros
ion
fact
or
Experimental result UTDamage Results Erosion factor
Figure 7.4: Erosion factors used in UTDamage to match the experimental data (BS-4-2-
04-I: UltraCarb-2 drill-in fluid on a short Berea core)
0
10
20
30
40
50
60
70
80
0 5 10 15 20 25Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
0
0.2
0.4
0.6
0.8
1
Eros
ion
fact
or
Experiment result UTDamage Results Erosion factor
Figure 7.5: Erosion factors used in UTDamage to match the experimental data (BS-6-5-
04-#5: UltraCarb-2 drill-in fluid on a long Berea core)
250
0
0.2
0.4
0.6
0.8
1
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Eros
ion
Fact
or
Long core exp. 1 Long core exp. 2 Short core exp. 1
Figure 7.6: Erosion factors used in UTDamage to match the experimental data (All
single-phase experiments using Berea sandstone and UltraCarb-2 drill-in fluid)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100Applied Differential Pressure (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Eros
ion
Fact
or
Experimental Data UTDamage Results Erosion Factor
Figure 7.7: Plot of erosion factor used in UTDamage to match the return permeability
data for Texas limestone (LS-1: 1-P flow with UltraCarb-2 drill-in fluid)
251
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140
Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Eros
ion
Fact
or
Experimental Results UTDamage Results Erosion Factor
Figure 7.8: Plot of erosion factor used in UTDamage to match the return permeability
data for Texas limestone (LS-12: Two-phase flow with UltraCarb-2 drill-in fluid)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120 140
Applied Differential Pressure During Flowback (psi)
Eros
ion
Fact
or
Single-phase experiment Two-phase experiment
Figure 7.9: Erosion factors for single-phase flow and two-phase flow return
permeabilities for Texas limestone cores (LS-1: 1-P, LS-12: 2-P experiment)
252
Nomenclature
φ : porosity
σ : specific deposit (volume of deposited particles per unit bulk volume)
u : darcy velocity
c : concentration of suspended fluid
λ : filtration coefficient
As : Happel’s geometric parameter
η : collection efficiency
NLO : London group
NR : Relative size group
NG : Gravity group
NPE : Peclet number
H : Hamakar constant for the particle medium system (~ 1*10-13 erg)
µ : plastic viscosity
ap : radius of the injected particle
ρp : injected particle density
ρf : fluid density
dg : grain diameter
DBM : Brownian diffusion coefficient
dp : diameter of the injected particle
fv : volume distribution function
rw : radius of the well
γu : velocity dependence parameter for filtration coefficient
Kdp : reduced porosity fraction
Kds : increased surface area fraction
Kdt : increased tortuosity fraction
P : pressure
dp : pore throat diameter
τy : mud cake yield point
253
Xd : depth of solids invasion, inch
ν : superficial flow velocity
h : cake thickness
φcrit : critical porosity
254
REFERENCES
1. Suri, A.: “A Model for Multi-Component Filtration” MS Thesis, The University of
Texas at Austin, December 2000.
2. Suri, A., and Sharma, M.M.: “Strategies for Sizing Particles in Drilling and
Completion Fluids,” paper SPE 87676 published in SPEJ, March 2004
3. Jiao, D. and Sharma, M.M.: ‘Mechanism of cake buildup in crossflow filtration of
colloidal suspension’, Journal of Colloid and Interfacial Science, 162, pp 454-462,
1994.
4. Khilar, K. C., et. al (1998): "Existence of a Critical Particle Concentration in
Plugging of a Packed Bed," AICHE J, April 1998, Vol. 44, No. 4, 978-81
5. Panda, M.N. and Lake, L.W.: ‘Estimation of single-phase permeability from
parameters of particle-size distribution’, AAPG Bulletin, V.78, No. 7, July 1994.
6. Rajagopalan, R. and Tien, C.: ‘Trajectory analysis of deep bed filtraiotn with sphere-
in cell model’, AIChE J, Vol. 22, No. 3, May 1976.
7. Scheuerman, R.F. and Berensen, B.M.: ‘Injection-water salinity, formation
pretreatment and well-operations fluid-selection guidelines’, JPT, July 1990.
8. Sharma, M.M. and Yortsos, Y.C.: ‘Transport of particulate suspensions in porous
media: Model formulation’, AIChE Journal, October 1987.
9. Bailey et al.: “Particulate Invasion From Drilling Fluids,” paper SPE 51094 presented
at the SPE Eastern Regional Meeting held in the Pittsburgh, PA, 9-11 November,
1998.
10. Cerasi, P., et al.: “Measurement of the Mechanical Properties of Filtercakes,” paper
SPE 68948 presented at the 2001 SPE European Formation Damage Conference held
in The Hague, The Netherlands, 21-22 May, 2001.
255
Chapter 8: Conclusions
1. Flow initiation pressures (FIP) are found to be considerably smaller with the constant
pressure flowback method compared to the constant rate flowback method. The
constant rate flowback method is found to be inadequate to estimate the FIP because
of two reasons: 1) the method yields FIP values which are rate dependent (which can
lead to very large FIP estimates) and 2) the constant rate flowback method does not
represent the wellbore condition during production.
2. An improved flowback method using constant differential pressures during flowback
is designed and used to estimate the FIP. Differential pressures are incremented in
steps to measure the return permeability spectra. The return permeability spectra,
when plotted as a function of applied differential pressure are consistently S-shaped.
3. Both single-phase (brine) and two-phase (oil and brine) experiments yielded small
and comparable values for the FIP. For very small permeability cores (Nugget
sandstone, 4 md), the FIP value for the two-phase flow experiment was slightly larger
than the FIP value obtained for a similar experiment but with single-phase flow.
4. The return permeability spectra can be used to evaluate the formation damage
potential of drill-in and completion fluids and to screen for the best fluids to use. The
return permeability spectra can be used to estimate the near wellbore permeability and
skin in vertical and horizontal wells.
5. The external filter cake is found to play no role in determining the FIP and the return
permeability spectra. The internal filter cake alone determines the FIP and return
permeabilities during flowback in open-hole completions.
256
6. Lab simulated perforated completions result in similar FIP values as lab simulated
open-hole completions. However, if the external filter cake thickness becomes equal
to or greater than the radius of the perforation tunnel (i.e. if the perforation tunnel is
completely plugged with the external filter cake) then an additional resistance is
imposed by the external filter cake in the form of a plug in the tunnel. This requires
additional pressure (larger FIP) to initiate production through these completely
plugged perforation tunnels. At small flowback pressures the return permeabilities in
lab-simulated perforated completions are found to be smaller than the return
permeabilities for the open-hole completions. This is because of the non-uniform
pressure gradients around the perforation tunnel compared to more uniform pressure
gradients across the internal filter cake in open-hole completions. However, at large
flowback pressures the return permeabilities in perforated completions are
comparable with the return permeabilities obtained in open-hole completions. This is
because a significant amount of internal filter cake is cleaned up at these large
pressure gradients in both the completions leading to similar return permeabilities.
7. A drill-in or a completion fluid with all the components (xanthan, starch, and sized
CaCO3) is the optimum fluid to use for maximizing return permeability and
minimizing fluid loss. Xanthan polymer causes the most damage while starch is
found to lower the FIP by minimizing the invasion of solids and polymers into the
formation and thus yielded larger return permeabilities.
8. Bentonite mud performed better than UltraCarb-2 drill-in fluid on Berea sandstone in
terms of FIP and return permeability. Using the median size of the bridging agent
equal or larger than the median size of the pore throat size of the formation (or mixing
257
two or three different grades of median sized bridging agents) in UltraCarb drill-in
fluids results in a lower FIP and larger return permeabilities. However, in terms of
fluid loss, bentonite mud does poorly (larger fluid losses than UltraCarb). The
external filter cakes formed from bentonite muds are much thicker than the external
filter cakes from UltraCarb drill-in fluids.
9. The yield strength of the external filter cake is measured using a constant strain
rheometer to model the cleanup of the internal filter cake to estimate the FIP and the
return permeabilities during flowback. Two different methods (dynamic strain sweep
test and linear strain test) were found to complement each other and provided
consistent yield strength measurements. However, the linear strain test is preferred
over the dynamic strain sweep test for measuring the yield strength of the filter cake
because it is quicker. Bentonite mud filter cakes are found to have larger shear
strength values than the filter cake samples prepared using UltraCarb drill-in fluids.
10. A bundle of tubes model and a network model with the effective medium
approximation is used to model the cleanup of the internal filter cake. A qualitative
match is found between the experiments and the models. The bundle of tubes model
predicts complete cleanup (100 % return permeability ratio) while the network model
captures the asymptotic values for return permeabilities (< 100 %) found in the
experiments.
11. Both the experimental results and the model results indicate that very large pressure
gradients are required to cleanup the internal filter cake completely. There will
always be some residual damage left in the near wellbore region due to the internal
filter cake. The near wellbore skin due to the internal filter cake is a function of the
258
drawdown or the flow rate. A pressure gradient of 10 psi/inch is required for a skin
factor < 1 in open-hole completions. For perforated completions a minimum
flowback velocity of 2 cm / min, or a flow rate of 0.3 bbl/day/perf or a pressure
gradient of 20 psi / inch is required to yield a skin factor < 2. The data presented can
be used to estimate the pressure gradient needed in wells to optimize production
while not failing the rock matrix and inducing sand production. The pressure
gradients required for small skin factors are achievable in vertical wells but may not
be easily achieved in horizontal wells.
1.1 RECOMMENDATIONS
1. We recommend using a median size for the bridging additive in drill-in and
completion fluids equal to the median pore-throat size of the formation for optimizing
the return permeability and fluid loss. The 1/3rd rule-of-thumb is not recommended
for determining the median size of the bridging agents. If the pore throat size
distribution of the formation is very broad then we recommend using a combination
of two or three different median sized bridging agents.
2. The skin around wells due to the internal filter cake should be calculated as a function
of the flow rate or the drawdown. The data presented (for a wide range of
permeability and for both open-hole and lab-simulated perforated completions) can be
used as a guide to estimate the skin factors in vertical and horizontal wells.
1.2 FUTURE WORK
1. Almost all the experiments in this study were conducted at an overbalance of 100 psi
during filtration. Large overbalance pressures can be applied during filtration in a
259
similar comprehensive experimental study to obtain more data (FIP and return
permeabilities).
2. Pressure measurements should be made at intervals of a few millimeters from the top
of the core to measure the differential pressure across this thin zone. These pressure
measurements can be used to further validate and tune the Bingham fluid model used
to represent the internal filter cake.
3. A similar comprehensive study can be done to estimate the FIP and return
permeability spectra for more commonly used oil-based and emulsion-based drill-in
and completion fluids.
260
Appendix-A: Photograph of the lab-setup used in conducting the experiments
261
Figure A.1: Photograph of the filtration and flow back apparatus
262
Appendix-B: Plots for single-phase constant pressure flowback experiments simulating open-hole completion
263
Table B.1: List of all the single-phase, constant pressure flowback experiments, simulating open-hole completion
Test No. Mud Used Rock Type
Av. Brine Perm (md)
Average Porosity
Overbalance (psi) Phase Core Type
Simulated Completion Type
Core Sample Name
1 UltraCarb-2 Nugget
sandstone 4 0.12 100 Single Short core Open hole NS-2
2 UltraCarb-2 Texas
limestone 24 0.28 100 Single Short core Open hole LS-1
3 UltraCarb-2 Texas
limestone 18 0.28 100 Single Short core Open hole LS-13*
4 Bentonite Texas
limestone 26 0.28 100 Single Short core Open hole LS-5
5 UltraCarb-2 Berea
sandstone 60 0.17 100 Single Short core Open hole BS-4-2-04-I
6 UltraCarb-2 Berea
sandstone 153 0.15 100 Single Long core Open hole BS-4-29-04-long-3
7 UltraCarb-2 Berea
sandstone 149 0.19 100 Single Long core Open hole BS-4-29-04-long-4
8 UltraCarb-2 Berea
sandstone 207 0.19 100 Single Long core Open hole BS-6-5-04-long-5
9 UltraCarb-20 Boise
sandstone 885 0.28 100 Single Short core Open hole Bo-1
10 Bentonite Boise
sandstone 982 0.28 100 Single Short core Open hole Bo-2
11 UltraCarb-2 Aloxide 960 0.44 100 Single Short core Open hole AL-1
12 UltraCarb-20 Aloxide 1313 0.44 100 Single Short core Open hole AL-2 * Experiment repeated to verify LS-1 experimental results.
264
Test No. 1
0
20
40
60
80
100
120
0 50 100 150 200 250Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
2
4
6
8
10
12
14
16
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 2 psi
Figure B-1: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Nugget sandstone (NS-2)
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120
Applied Differential Pressure (psi)
Ret
urn
Per
mea
bilit
y Ra
tio (%
)
Figure B-2: Return permeability spectra with incremental differential pressures for
Nugget sandstone (NS-2)
265
0
5
10
15
20
0 10 20 30 40Sqrt of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure B-3: Static filtration of UltraCarb-2 on Nugget sandstone simulating open hole
completion (NS-2)
Discussion on the experiment
Figure B.2 shows a plot of return permeability ratio vs. flowback pressure on short
Nugget core (2.5 in. in diameter and 1 in. in length). There was no flow observed below a
differential pressure of 2 psi during flowback. The flow starts at a flowback pressure of 2
psi, and stabilizes with a return permeability ratio of 2.5% indicating very little cleanup
of the core. Upon increasing the applied differential pressure in small increments, larger
return permeability ratio values are observed as shown in the Figure B.2. At a differential
pressure of 20 psi, the return permeability ratio came up to 60.8%. The plot shows a
linear relationship between differential pressure and return permeability ratio nearly up to
a differential pressure of 20 psi indicating most of the cleanup. At larger drawdowns the
return permeability ratio becomes asymptotic as seen in Figure B.2. At a differential
pressure of 100 psi during flowback the return permeability ratio was 72.3%.
266
Test No. 2
0
20
40
60
80
100
120
0 50 100 150Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 1 psi
Figure B-4: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Texas limestone (LS-1)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100
Applied Differential Pressure (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
Figure B-5: Return permeability spectra with incremental differential pressures for Texas
limestone (LS-1)
267
0
5
10
15
20
0 10 20 30 40Sqrt of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure B-6: Static filtration of UltraCarb-2 on Texas limestone simulating open hole completion (LS-1)
Discussion on the experiment
Figure B.5 shows a plot of return permeability ratio vs. flowback pressure on short Texas
limestone core (2.5 in. in diameter and 1 in. in length). As soon as a differential pressure
of 1 psi was applied, flow was observed. The flow was stabilized after some time with a
return permeability ratio of 33.8% indicating significant cleanup of the internal damage
in the core. Upon increasing the applied differential pressure in small increments, larger
return permeability ratio values are observed as shown in the Figure B.5. At a differential
pressure of 20 psi, the return permeability ratio came up to 54.3%. At larger drawdowns
the return permeability ratio remained nearly constant as can be seen in the Figure B.5.
At a differential pressure of 100 psi the return permeability ratio was 56.6%.
268
Test No. 3
0
20
40
60
80
100
120
0 10 20 30 40 50 60Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
5
10
15
20
25
30
35
40
45
50
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 2 psi
Figure B-7: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Texas limestone (LS-13)
0
20
40
60
80
100
0 20 40 60 80 100 120
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Figure B-8: Return permeability spectra with incremental differential pressures for Texas
limestone (LS-13)
269
0
5
10
15
20
0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure B-9: Static filtration of UltraCarb-2 on Texas limestone simulating open hole completion (LS-13)
Discussion on the experiment
Figure B.8 shows a plot of return permeability ratio vs. flowback pressure on short Texas
limestone core (2.5 in. in diameter and 1 in. in length). This experiment was conducted to
verify the results of earlier experiment (LS-1). The results indicate that the test results to
be very similar. This suggests that the tests are repeatable.
270
Test No. 4
0
10
20
30
40
50
60
0 10 20 30 40 50 60 70Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
80
90
Mea
sure
d Ra
te (m
l/min
)
Flowback started at ∆P = 1 psi
Figure B-10: Flowback rate at incremental differential pressures after filtration with
bentonite on Texas limestone (LS-5)
0
20
40
60
80
100
120
140
0 10 20 30 40 50 60
Applied Differential Pressure (psi)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Figure B-11: Return permeability spectra with incremental differential pressures for Texas limestone (LS-5)
271
0
20
40
60
80
0 5 10 15 20 25 30 35Sqrt of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure B-12: Static filtration of bentonite mud on Texas limestone simulating open hole
completion (LS-5)
Discussion on the experiment
Figure B.11 shows a plot of return permeability ratio vs. flowback pressure on short
Texas limestone core (2.5 in. in diameter and 1 in. in length). As soon as a differential
pressure of 1 psi was applied, flow was observed. The flow was stabilized after some
time with a return permeability ratio of 33.8% indicating significant cleanup of the
internal damage in the core. Upon increasing the applied differential pressure in small
increments, larger return permeability ratio values are observed as shown in Figure B.11.
At a differential pressure of 20 psi, the return permeability ratio came up to 100%. At
larger drawdowns the return permeability ratio remained nearly constant as can be seen in
the Figure B.11. At a differential pressure of 50 psi the return permeability ratio was
found to be more than 100%.
272
Test No. 5
0
5
10
15
20
25
0 50 100 150 200Time (min)
App
lied
Diff
eren
tial P
ress
ure
(psi
)
0
5
10
15
20
25
30
35
Mea
sure
d Ra
te (m
l/min
)
Flowback started at ∆P = 4 psi
Figure B-13: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-4-2-04-I)
0
10
20
30
40
50
60
0 5 10 15 20
Applied Differential Pressure (psi)
Ret
urn
Per
mea
bilit
y Ra
tio (%
)
Figure B-14: Return permeability spectra with incremental differential pressures for
Berea sandstone (BS-4-2-04-I)
273
0
1
2
3
4
0 2 4 6 8
Sqrt of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure B-15: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole completion (BS-4-2-04-I)
Discussion on the experiment
Figure B.14 shows a plot of return permeability ratio vs. flowback pressure on short
Berea core (2.5 in. in diameter and 1 in. in length). There was no flow observed below a
differential pressure of 4 psi during flowback. The flow starts at a flowback pressure of 4
psi, and stabilizes with a return permeability ratio of 0.9% indicating very little cleanup
of the core. Upon increasing the applied differential pressure in small increments, larger
return permeability ratio values are observed as shown in Figure B.14. At a differential
pressure of 20 psi, the return permeability ratio came up to 50.4%. The plot shows a
linear relationship between differential pressure and return permeability ratio. The
increasing linear trend suggests larger return permeabilities at differential pressure larger
than 20 psi during flowback.
274
Test No. 6
0
20
40
60
80
100
0 50 100 150 200 250 300 350 400Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
10
20
30
40
50
60
Mea
sure
d Ra
te (m
l/min
)
Flowback started at ∆P = 3 psi
Figure B-16: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on a long Berea sandstone (BS-4-29-04-long-3)
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100
Applied Differential Pressure (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
Figure B-17: Return permeability spectra for incremental differential pressures in a long
Berea core (BS-long-3)
275
0
2
4
6
8
10
12
0 5 10 15 20 25 30 35Sqrt of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure B-18: Static filtration of UltraCarb-2 on a long Berea core simulating open hole
completion (BS-long-3)
Discussion on the experiment
Figure B.17 shows results for return permeability ratio vs. flowback pressure in a long
Berea core (2 inch in diameter and 6 inch in length). The mud used was UltraCarb-2 for
the filtration step with an overbalance of 100 psi. The FIP was around 3 psi and the return
permeability ratio was 36.3% at FIP. Compared to the short Berea core experimental
results there was a significant amount of cleanup in the longer core. The short Berea core
showed a return permeability ratio of 0.9% at FIP while the longer core showed 36.3%.
The reason for the difference is not understood. Upon increasing the flowback pressure,
there was an increase in the return permeability ratio reaching an asymptotic value of
70% for the return permeability ratio.
276
Test No. 7
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250 300Time (min)
App
lied
Diff
eren
tial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 2 psi
Figure B-19: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on a long Berea sandstone (BS-4-29-04-long-4)
0
10
20
30
40
5060
70
80
90
100
0 20 40 60 80 100
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
For the whole core (0-6 inch)For the top 0-2 inch of the coreFor the middle 2-4 inch of the coreFor the bottom 4-6 inch of the core
Figure B-20: Return permeability spectra for incremental differential pressures in a long
Berea core (BS-4-29-04-long-4)
277
0
5
10
15
20
0 10 20 30 40 50 60Sqrt of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
The overbalance pressure got reduced to 20 psi overnight but w as again increased to 100 psi
Figure B-21: Static filtration of UltraCarb-2 on a long Berea sandstone simulating open hole completion (BS-4-29-04-long-4)
Discussion on the experiment
Another long core experiment was done on Berea core with additional pressure taps at 2
inch and 4 inch point of the 6 inch long core. The reason was to study how different parts
of the core are cleaned during flowback and to estimate the depth of damage. Figure B.20
shows the results indicating nearly no damage at the far end (4-6 inch) and the middle
part (2-4 inch) of the core with permeability recovery of approximately 100% value.
Most of the damage was observed only at the top of the core (0-2 inch) as can be seen in
Figure B.20. In this experiment also the average permeability recovery for the whole core
was asymptotic reaching approximately a maximum of 70%.
278
Test No. 8
0
10
20
30
40
50
60
70
80
0 10 20 30 40 50 60 70 80 90 100Time (min)
App
lied
Diff
eren
tial P
ress
ure
(psi
)
0
10
20
30
40
50
60
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 2 psi
Figure B-22: Flowback rate at incremental differential pressures after filtration on a long
Berea sandstone with external filter cake removed (BS-4-29-04-long-5)
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50 60 70 80
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
For the whole core (0-6 inch)For the top 0-2 inch of the coreFor the middle 2-4 inch of the coreFor the bottom 4-6 inch of the core
Figure B-23: Return permeability spectra for incremental differential pressures in a long
Berea core with external filter cake removed (BS-4-29-04-long-5)
279
0
4
8
12
16
0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure B-24: Static filtration of UltraCarb-2 on a long Berea core simulating open hole completion (BS-4-29-04-long-5)
Discussion on the experiment
Another long core experiment was done on Berea core but this time the external filter
cake was mechanically scraped from the top surface of the core before flow back. The
objective behind doing this was to study the role of external filter cake during flow back.
Figure B.23 shows the results of return permeability ratio vs. flow back pressure.
280
Test No. 9
0
10
20
30
40
50
60
0 10 20 30 40 50Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
50
100
150
200
250
300
350
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 3 psi
Figure B-25: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on a Boise sandstone (Bo-1)
0
5
10
15
20
25
0 10 20 30 40 50 60
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Figure B-26: Return permeability spectra with incremental differential pressures for
Boise sandstone (Bo-1)
281
0
5
10
15
20
25
30
0 10 20 30 40 50 60Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure B-27: Static filtration of UltraCarb-20 on Boise sandstone simulating open hole completion (Bo-1)
282
Test No. 10
0
2
4
6
8
10
12
0 20 40 60 80 100 120Time (min)
App
lied
Diff
eren
tial P
ress
ure
(psi
)
0
20
40
60
80
100
120
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 1 psi
Figure B-28: Flowback rate at incremental differential pressures after filtration with
bentonite mud on Boise sandstone (Bo-2)
0
5
10
15
20
25
30
0 2 4 6 8 10 12
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Figure B-29: Return permeability spectra with incremental differential pressures for
Boise sandstone (Bo-2)
283
0
20
40
60
80
0 5 10 15 20Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure B-30: Static filtration of bentonite mud on Boise sandstone simulating open hole completion (Bo-2)
284
Test No. 11
0
10
20
30
40
50
60
0 50 100 150 200 250 300Time (min)
Appl
ied
Diff
eren
tial P
ress
ure
(psi
)
0
20
40
60
80
100
120
140
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 8 psi
Figure B-31: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Aloxide core (Al-1)
0
1
2
3
4
5
6
0 10 20 30 40 50 60
Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
Figure B-32: Return permeability spectra with incremental differential pressures for
Aloxide core (Al-1)
285
0
10
20
30
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure B-33: Static filtration of UltraCarb-2 on Aloxide core simulating open hole completion (Al-1)
286
Test No. 12
0
10
20
30
40
50
60
0 50 100 150Time (min)
App
lied
Diffe
rent
ial P
ress
ure
(psi
)
0
50
100
150
200
250
300
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 4 psi
Figure B-34: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Aloxide core (Al-2)
0
1
2
3
4
5
6
7
8
0 10 20 30 40 50 60
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Figure B-35: Return permeability spectra with incremental differential pressures for
Aloxide core (Al-2)
287
0
5
10
15
20
0 10 20 30 40Sqrt of time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure B-36: Static filtration of UltraCarb-20 on Aloxide core simulating open hole completion (Al-2)
288
Appendix-C: Plots of two-phase constant pressure flowback experiments simulating open-hole condition
289
Table C.1: List of all the two-phase, constant pressure flowback experiments, simulating open-hole completion
Test No. Mud Used Rock Type
Average Brine Perm. (md)
Average Porosity
Over balance pressure
(psi) Phase Core TypeSimulated
Completion TypeCore Sample
Name
1 UltraCarb-2 Nugget
sandstone 26 0.13 140 Two Short core Open hole NS-3
2 UltraCarb-2 Texas
limestone 15
(keff oil) 0.30 100 Two Short core Open hole LS-12
3 UltraCarb-2 Berea
sandstone 285 0.20 100 Two Short core Open hole BS-11-11-03-I
4 UltraCarb-20 Berea
sandstone 146
(keff oil) 0.20 100 Two Short core Open hole BS-21
5 UltraCarb-2 Berea
sandstone 129
(keff oil) 0.20 100 Two Short core Open hole BS-17
6
UltraCarb-5(20%)
+12(60%) +20(20%)
Berea sandstone
144 (keff oil) 0.20 500 Two Short core Open hole BS-19
7
UltraCarb-5(20%)
+12(60%) +20(20%)
Berea sandstone
138 (keff oil) 0.20
500 (with 500
psi as back pressure Two Short core Open hole BS-20
8 UltraCarb-20 Aloxide 965
(keff oil) 0.42 100 Two Short core Open hole AL-3
9 UltraCarb-20 Boise
sandstone 600
(keff oil) 0.28 100 Two Short core Open hole Bo-7
290
Test No. 1
0
20
40
60
80
100
120
0 50 100 150 200Time (min)
App
lied
Diffe
rent
ial P
ress
ure
(psi
)
0
5
10
15
20
25
30
35
40
45
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 6 psi
Figure C-1: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Nugget sandstone (NS-3)
0
10
20
30
40
50
60
0 20 40 60 80 100 120
Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
Figure C-2: Return permeability spectra with incremental differential pressures for
Nugget sandstone (NS-3)
291
0
5
10
15
20
25
0 10 20 30 40Sqrt of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure C-3: Static filtration of UltraCarb-2 on Nugget sandstone simulating open hole completion (NS-3)
292
Test No. 2
0
20
40
60
80
100
120
140
0 50 100 150 200 250Time (min)
App
lied
Diffe
rent
ial P
ress
ure
(psi
)
0
5
10
15
20
25
30
35
40
45
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 2 psi
Figure C-4: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Texas limestone (LS-12)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Figure C-5: Return permeability spectra with incremental differential pressures for Texas
limestone (LS-12)
293
0
5
10
15
20
0 10 20 30 40Sqrt of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure C-6: Static filtration of UltraCarb-2 on Texas limestone simulating open hole
completion (LS-12)
294
Test No. 3
0
2
4
6
8
10
12
0 20 40 60 80 100 120 140
Time (min)
∆p
(psi
)
0
2
4
6
8
10
12
14
16
Rat
e (m
l/min
)
Const Pressure Flowback rate
FIP = 7 psi
kreturn = 25%
kreturn = 29%
Figure C-7: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-11-11-03-I)
0
10
20
30
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure C-8: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole completion (BS-11-11-03-I)
295
Test No. 4
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
50
100
150
200
250
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 4 psi
Figure C-9: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Berea sandstone (BS-21)
0
20
40
60
80
100
0 20 40 60 80 100
Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
296
Figure C-10: Return permeability spectra with incremental differential pressures for Berea sandstone (BS-21)
0
5
10
15
20
0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure C-11: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole completion (BS-21)
297
Test No. 5
0
20
40
60
80
100
120
0 20 40 60 80 100 120 140Time (min)
App
lied
Diff
eren
tial P
ress
ure
(psi
)
0
50
100
150
200
250
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 4 psi
Figure C-12: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-17)
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
298
Figure C-13: Return permeability spectra with incremental differential pressures for Berea sandstone (BS-17)
0
5
10
15
20
0 10 20 30 40Sqrt of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure C-14: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole completion (BS-17)
299
Test No. 6
0
20
40
60
80
100
120
0 50 100 150 200 250 300Time (min)
App
lied
Diffe
rent
ial P
ress
ure
(psi
)
0
50
100
150
200
250
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 4 psi
Figure C-15: Flowback rate at incremental differential pressures after filtration with
UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea sandstone (BS-19)
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
300
Figure C-16: Return permeability spectra with incremental differential pressures for Berea sandstone (BS-19)
0
5
10
15
20
25
0 10 20 30 40Sqrt of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure C-17: Static filtration of UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea
sandstone simulating open hole completion (BS-19)
301
Test No. 7
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 2 psi
Figure C-18: Flowback rate at incremental differential pressures after filtration with
UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea sandstone (BS-20)
0
10
20
30
40
50
60
70
0 5 10 15 20 25 30 35 40
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
302
Figure C-19: Return permeability spectra with incremental differential pressures for Berea sandstone (BS-20)
0
5
10
15
20
25
0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure C-20: Static filtration of UltraCarb-[2(20%) +12(60%) +20(20%)] on Berea
sandstone simulating open hole completion (BS-20)
303
Test No. 8
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100 120 140 160Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
50
100
150
200
250
300
350
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 3 psi
Figure C-21: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Aloxide core (AL-3)
0
5
10
15
20
25
30
0 10 20 30 40 50 60
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
304
Figure C-22: Return permeability spectra with incremental differential pressures for Aloxide core (AL-3)
0
5
10
15
20
0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure C-23: Static filtration of UltraCarb-20 on Aloxide core simulating open hole
completion (AL-3)
305
Test No. 9
0
5
10
15
20
25
30
35
40
45
50
0 10 20 30 40 50 60 70Time (min)
App
lied
Diff
eren
tial P
ress
ure
(psi
)
0
50
100
150
200
250
300
350
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 3 psi
Figure C-24: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Boise sandstone (Bo-7)
0
10
20
30
40
50
60
70
80
90
100
0 10 20 30 40 50
Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y Ra
tio (%
)
306
Figure C-25: Return permeability spectra with incremental differential pressures for Boise sandstone (Bo-7)
0
5
10
15
0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure C-26: Static filtration of UltraCarb-20 on Boise sandstone simulating open hole
completion (Bo-7)
307
Appendix-D: Plots for experiments with flow back at constant rate to study the role of individual drill-in fluid components on formation
damage
308
Table D.1: List of experiments with constant rate flowback condition to study the effect of individual drill-in fluid components on FIP, return permeability and API filtrate loss
Test No. Mud Used Rock
Type
Av. Brine Perm (md)
Average Porosity
Over balance
(psi)
Temp (oF)
Flowback rate
(ml/min)Phase Core
Dim.
Simulated Completion
Type
Core Sample Name
1 UltraCarb-2 Berea
sandstone 60 0.17 100 150 1 Two Short core Open-hole BS-4-16-03-II
2 UltraCarb-2 Berea
sandstone 247 0.19 100 150 5 Two Short core Open-hole BS-8-27-03-III
3 UltraCarb-2 (no starch)
Berea sandstone 60 0.20 100 150 1 Two
Short core Open-hole BS-4-21-03-II
4 UltraCarb-2 (no xanthan)
Berea sandstone 60 0.19 100 150 1 Two
Short core Open-hole BS-4-21-03-III
5
UltraCarb-2 (no starch and
xanthan) Berea
sandstone 186 0.20 100 75 1 Two Short core Open-hole BS-6-8-03-IV
6
UltraCarb-2 (no starch and
xanthan) Berea
sandstone 130 0.20 100 75 1 Two Short core Open-hole BS-6-8-03-V
7 UltraCarb-12 Berea
sandstone 190 0.19 100 75 1 Two Short core Open-hole BS-6-8-03-VI
8 UltraCarb-12
(no starch) Berea
sandstone 128 0.17 100 75 5 Two Short core Open-hole BS-6-8-03-IX
9 UltraCarb-12 (no xanthan)
Berea sandstone 252 0.19 100 75 5 Two
Short core Open-hole BS-6-8-03-VIII
10
UltraCarb-12 (no starch and
xanthan) Berea
sandstone 85 0.20 100 75 5 Two Short core Open-hole BS-6-8-03-VII
11 UltraCarb-12 +
RevDust Berea
sandstone 233 0.21 100 75 5 Two Short core Open-hole BS-10-2-03-I
12 UltraCarb-20 Berea
sandstone 247 0.20 100 75 5 Two Short core Open-hole BS-8-27-03-II
309
Test No. Mud Used Rock
Type
Av. Brine Perm (md)
Average Porosity
Over balance
(psi)
Temp (oF)
Flowback rate
(ml/min)Phase Core
Dim.
Simulated Completion
Type
Core Sample Name
13 UltraCarb-20
(no starch) Berea
sandstone 535 0.19 100 75 5 Two Short core Open-hole BS-8-11-03-XI
14 UltraCarb-20 (no xanthan)
Berea sandstone 291 0.19 100 75 5 Two
Short core Open-hole BS-8-11-03-XII
15
UltraCarb-20 (no starch and
xanthan) Berea
sandstone 142 0.20 100 75 5 Two Short core Open-hole BS-8-11-03-X
16 UltraCarb-20 +
RevDust Berea
sandstone 272 0.21 100 75 5 Two Short core Open-hole BS-10-7-03-I
17 Brine Berea
sandstone 223 0.19 100 75 5 Two Short core Open-hole BS-8-27-03-I
18 Brine + pH
Buffer Berea
sandstone 231 0.19 100 75 5 Two Short core Open-hole BS-8-11-03-XIII
19 UltraCarb-20 Boise
sandstone 1121 0.29 100 75 5 SingleShort core Open-hole BS-8-11-03-XIII
310
Test No. 1
0
2
4
6
8
10
12
14
0 100 200 300 400Time (min)
Diffe
rent
ial p
ress
ure
durin
g flo
wba
ck
(psi
)
∆P (FIP) = 8.95 psi
Flowback rate = 1 ml/min
Figure D-1: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (BS-4-16-03-II)
0
5
10
15
20
25
0 5 10 15 20 25 30 35Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure D-2: Static filtration of UltraCarb-2 on Berea sandstone simulating open-hole completion (BS-4-16-03-II)
311
Test No. 2
0
2
4
6
8
10
12
14
16
18
20
0 100 200 300 400 500Time (min)
Diffe
rent
ial P
ress
ure
Dur
ing
Flow
back
(p
si)
3 ml / min
1 ml / min
5 ml / min
∆P (FIP) = 13.93 psi
Figure D-3: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (BS-8-27-03-III)
0
5
10
15
20
25
30
0 1 2 3 4 5 6Flowback Rate (ml/min)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
with external filter cake without external filter cake
312
Figure D-4: Return permeability spectra with varying flowback rates for Berea sandstone (BS-8-27-03-III)
0
5
10
15
20
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-5: Static filtration of UltraCarb-2 on Berea sandstone simulating open-hole completion (BS-8-27-03-III)
313
Test No. 3
0
2
4
6
8
10
12
14
0 100 200 300 400 500 600
Time (min)
Diff
eren
tial P
ress
ure
Duri
ng F
low
back
(p
si)
mud cake removed
∆P (FIP) = 10.78 psi
Kret (with mud cake) = 14.1 %Kret (w/o mud cake) = 20.0 %
Figure D-6: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (no starch) (BS-4-21-03-II)
0
5
10
15
20
0 2 4 6 8Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
314
Figure D-7: Static filtration of UltraCarb-2 (no starch) on Berea sandstone simulating open-hole completion (BS-4-21-03-II)
Test No. 4
0
1
2
3
4
5
6
7
0 50 100 150 200 250 300 350Time (min)
Diff
eren
tial P
ress
ure
Duri
ng F
low
back
(p
si)
mud cake removed
∆P (FIP) = 3.57 psi
Kret (with mud cake) = 13.1%Kret (w/o mud cake) = 13.8 %
Figure D-8: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (no xanthan) (BS-4-21-03-III)
0
10
20
30
40
0 4 8 12 16Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
315
Figure D-9: Static filtration of UltraCarb-2 (no xanthan) on Berea sandstone simulating
open-hole completion (BS-4-21-03-III)
Test No. 5
0
0.5
1
1.5
2
2.5
0 50 100 150 200 250 300
Time (min)
Diffe
rent
ial P
ress
ure
Dur
ing
Flow
back
(psi
)
∆P (FIP) = 0.3 psi
1 ml/min
Kreturn at 1 ml / min = 29 %Kreturn at 3 ml / min = 74 %
Flowback rate = 3 ml/min
Figure D-10: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (no xanthan and starch) (BS-6-8-03-IV)
316
0
20
40
60
80
100
0 1 2 3 4Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure D-11: Static filtration of UltraCarb-2 (no xanthan and starch) on Berea sandstone
simulating open-hole completion (BS-6-8-03-IV) Test No. 6
0
1
2
3
4
5
0 10 20 30 40 50 60 70 80Time (min)
Diff
eren
tial P
ress
ure
Dur
ing
Flow
back
(p
si)
3 ml/min
Flowback rate = 1 ml/min
Kreturn at 1 ml / min = 22 %Kreturn at 3 ml / min = 46 %
Figure D-12: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-2 (no xanthan and starch) (BS-6-8-03-V)
317
0
10
20
30
40
50
0 1 2 3Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-13: Static filtration of UltraCarb-2 (no xanthan and starch) on Berea sandstone
simulating open-hole completion (BS-6-8-03-V)
318
Test No. 7
0
2
4
6
8
10
0 20 40 60 80 100Time (min)
Diff
eren
tial P
ress
ure
Duri
ng F
low
back
(psi
)
Kreturn at 3 ml / min = 34 %
∆P (FIP) = 7.33 psi
Figure D-14: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 (BS-6-8-03-VI)
0
4
8
12
16
20
0 10 20 30 40
Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-15: Static filtration of UltraCarb-12 on Berea sandstone simulating open-hole
completion (BS-6-8-03-VI)
319
Test No. 8
0
5
10
15
20
25
30
0 50 100 150 200 250 300 350 400
Time (min)
Diff
eren
tial P
ress
ure
Duri
ng F
low
back
(psi
)
3 ml / min1 ml / min
Flowback rate = 5 ml / min
∆P (FIP) = 20 psi
Figure D-16: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 without starch (BS-6-8-03-IX)
0
5
10
15
20
25
30
35
0 2 4 6 8 10Flowback Rate (ml/min)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Figure D-17: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-6-8-03-IX)
320
0
10
20
30
40
50
60
0 2 4 6 8 10 12Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-18: Static filtration of UltraCarb-12 without starch on Berea sandstone simulating open-hole completion (BS-6-8-03-IX)
321
Test No. 9
0
1
2
3
4
5
6
7
8
0 20 40 60 80 100Time (min)
Diffe
rent
ial P
ress
ure
Durin
g Fl
owba
ck
(psi
)
3 ml / min
1 ml / min
Flowback rate = 5 ml / min
∆P (FIP) = 4 psi
Figure D-19: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 without xanthan (BS-6-8-03-VIII)
0
5
10
15
20
25
30
35
40
45
50
0 0.5 1 1.5 2 2.5 3 3.5Flowback Rate (ml/min)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Figure D-20: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-6-8-03-VIII)
322
0
20
40
60
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-21: Static filtration of UltraCarb-12 without xanthan on Berea sandstone simulating open-hole completion (BS-6-8-03-VIII)
323
Test No. 10
0
2
4
6
8
10
12
14
0 10 20 30 40 50Time (min)
Diffe
rent
ial P
ress
ure
Durin
g Fl
owba
ck (p
si)
3 ml / min
1 ml / min
Flowback rate = 5 ml / min
∆P (FIP) = 6.53 psi
Figure D-22: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 without xanthan and starch (BS-6-8-03-VII)
0
10
20
30
40
50
60
70
80
0 1 2 3 4 5 6Flowback Rate (ml/min)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Figure D-23: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-6-8-03-VII)
324
0
10
20
30
40
50
60
0 0.2 0.4 0.6 0.8 1 1.2
Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-24: Static filtration of UltraCarb-12 without xanthan and starch on Berea sandstone simulating open-hole completion (BS-6-8-03-VII)
325
Test No. 11
0
2
4
6
8
10
12
14
0 20 40 60 80 100 120Time (min)
Diffe
rent
ial P
ress
ure
Duri
ng F
low
back
(p
si)
3 ml / min
1 ml / min
∆P (FIP) = 10.2 psi
Flowback rate = 5 ml / min
Figure D-25: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-12 with RevDust (BS-10-2-03-I)
0
5
10
15
20
25
30
35
40
0 1 2 3 4 5 6Flowback Rate (ml/min)
Ret
urn
Perm
eabi
lity
Rat
io (%
) with external filter cake
without external filter cake
Figure D-26: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-10-2-03-I)
326
0
5
10
15
20
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-27: Static filtration of UltraCarb-12 with RevDust on Berea sandstone simulating open-hole completion (BS-10-2-03-I)
327
Test No. 12
0
2
4
6
8
10
12
14
0 25 50 75 100 125 150 175 200 225Time (min)
Diffe
rent
ial P
ress
ure
Dur
ing
Flow
back
(psi
)
3 ml / min
1 ml / min
Flowback rate = 5 ml / min
∆P (FIP) = 9.97 psi
Figure D-28: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 (BS-8-27-03-II)
0
5
10
15
20
25
30
35
40
0 1 2 3 4 5 6Flowback Rate (ml/min)
Retu
rn P
erm
eabi
lity
Rat
io (%
)
Figure D-29: Return permeability on Berea sandstone at different flowback rates after
filtration with UltraCarb-20 (BS-8-27-03-II)
328
0
5
10
15
20
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-30: Static filtration of UltraCarb-12 with RevDust on Berea sandstone simulating open-hole completion (BS-10-2-03-I)
329
Test No. 13
0
1
2
3
4
5
6
7
8
0 10 20 30 40 50 60 70Time (min)
Diffe
rent
ial P
ress
ure
Durin
g Fl
owba
ck (p
si)
3 ml / min
1 ml / min
Flowback rate = 5 ml / min
∆P (FIP) = 4.71 psi
Figure D-31: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 without starch (BS-8-11-03-IX)
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6Flowback Rate (ml/min)
Ret
urn
Per
mea
bilit
y R
atio
(%)
Figure D-32: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-11-03-IX)
330
0
10
20
30
40
50
0 4 8 12 16Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-33: Static filtration of UltraCarb-20 without starch on Berea sandstone simulating open-hole completion (BS-8-11-03-IX)
331
Test No. 14
0
1
2
3
4
5
6
7
8
0 20 40 60 80 100Time (min)
Diffe
rent
ial P
ress
ure
Duri
ng F
low
back
(p
si)
3 ml / min
1 ml / min
Flowback rate = 5 ml / min
∆P (FIP) = 4.36 psi
Figure D-34: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 without xanthan (BS-8-11-03-XII)
0
10
20
30
40
50
60
0 1 2 3 4 5 6Flowback Rate (ml/min)
Ret
urn
Per
mea
bilit
y Ra
tio (%
)
Figure D-35: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-11-03-XII)
332
0
10
20
30
40
50
0 5 10 15 20Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-36: Static filtration of UltraCarb-20 without xanthan on Berea sandstone simulating open-hole completion (BS-8-11-03-XII)
333
Test No. 15
0
1
2
3
4
5
6
7
8
9
10
0 20 40 60 80 100Time (min)
Diff
eren
tial P
ress
ure
Dur
ing
Flow
back
(p
si)
1 ml / min
Flowback rate = 5 ml / min
Figure D-37: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 without xanthan and starch (BS-8-11-03-X)
0
5
10
15
20
25
30
35
40
45
50
0 1 2 3 4 5 6Flowback Rate (ml/min)
Ret
urn
Per
mea
bilit
y Ra
tio (%
)
Figure D-38: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-11-03-X)
334
0
10
20
30
40
50
60
70
0 0.2 0.4 0.6 0.8 1 1.2
Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-39: Static filtration of UltraCarb-20 without xanthan on Berea sandstone simulating open-hole completion (BS-8-11-03-X)
335
Test No. 16
0
2
4
6
8
10
12
14
16
0 50 100 150 200Time (min)
Diffe
rent
ial P
ress
ure
Duri
ng F
low
back
(psi
)
3 ml / min
1 ml / min
Flowback rate = 5 ml / min
∆P (FIP) = 11.53 psi
Figure D-40: Differential pressure profile during flowback on Berea sandstone after
filtration with UltraCarb-20 with RevDust (BS-10-7-03-I)
0
5
10
15
20
25
30
35
40
45
50
0 1 2 3 4 5 6Flowback Rate (ml/min)
Ret
urn
Per
mea
bilit
y Ra
tio (%
)
Figure D-41: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-10-7-03-I)
336
0
5
10
15
20
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-42: Static filtration of UltraCarb-20 with RevDust on Berea sandstone simulating open-hole completion (BS-10-7-03-I)
337
Test No. 17
0
1
2
3
4
5
6
0 10 20 30 40 50 60Time (min)
Diff
eren
tial P
ress
ure
Duri
ng F
low
back
(p
si)
3 ml / min
1 ml / min
Flowback rate = 5 ml / min
∆P (FIP) = 2.51 psi
Figure D-43: Differential pressure profile during flowback on Berea sandstone after
filtration with Brine (BS-8-27-03-I)
0
10
20
30
40
50
60
0 1 2 3 4 5 6Flowback Rate (ml/min)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Figure D-44: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-27-03-I)
338
0
20
40
60
80
0 0.1 0.2 0.3
Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-45: Static filtration of Brine on Berea sandstone simulating open-hole completion (BS-8-27-03-I)
339
Test No. 18
0
1
2
3
4
5
6
0 10 20 30 40 50Time (min)
Diffe
rent
ial P
ress
ure
Dur
ing
Flow
back
(p
si)
Flowback rate = 5 ml / min
∆P (FIP) = 2.35 psi
Figure D-46: Differential pressure profile during flowback on Berea sandstone after
filtration with Brine and pH buffer (BS-8-11-03-XIII)
0
10
20
30
40
50
60
70
80
0 1 2 3 4 5 6Flowback Rate (ml/min)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
Figure D-47: Return permeability spectra with varying flowback rates for Berea
sandstone (BS-8-11-03-XIII)
340
Test No. 19
0
0.5
1
1.5
2
2.5
3
3.5
4
0 10 20 30 40 50 60 70Time (min)
Diffe
rent
ial P
ress
ure
Durin
g Fl
owba
ck (p
si)
∆PInitial = 0.09 psi
Return Perm = 10 %
∆PFinal = 0.97 psi
∆P(FIP) = 2.8 psi
Figure D-48: Differential pressure profile during flowback on Boise sandstone after
filtration with UltraCarb-20 (Bo-3)
0
5
10
15
20
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure D-49: Static filtration of UltraCarb-20 on Boise sandstone simulating open-hole
completion (Bo-3)
341
Appendix-E: Plots of single-phase filtration experiments conducted on cores with lab-simulated perforations with constant pressure flowback
condition
342
Table E.1: List of all the single-phase, constant pressure flowback experiments, simulating perforated completions
Test No. Mud Used Rock Type
Av. Brine Perm (md)
Average Porosity
Overbalance (psi) Phase Core Type
Simulated Completion Type
Core Sample Name
1 UltraCarb-2 Texas
limestone ~25 0.31 100 Single Short core
Single perforation (1/4" dia., 1/2"
len.) LS-9
2 UltraCarb-2 Berea
sandstone ~200 0.17 100 Single Short core
Single perforation (1/8" dia., 1/2"
len.) BS-2-2-04-I
3 UltraCarb-2 Berea
sandstone 187 0.19 100 Single Long coreSingle perforation
(1/8" * 1") BS-6-5-04-long-6
4 UltraCarb-2 Berea
sandstone 190 0.19 100 Single Long coreSingle perforation
(1/8" * 2") BS-6-5-04-7
5 UltraCarb-2 Berea
sandstone 216 0.20 100 Single Long coreSingle perforation
(3/8" * 1") BS-6-13-04-8
6 UltraCarb-2 Berea
sandstone 212 0.20 100 Single Long coreSingle perforation
(1/4" * 2") BS-6-13-04-9
7 UltraCarb-2 Berea
sandstone 207 0.20 100 Single Long coreSingle perforation
(1/4" * 1") BS-6-29-04-10
8 UltraCarb-2 Berea
sandstone 133 0.20 100 Single Long coreSingle perforation
(1/8" * 1") BS-long-11
9 UltraCarb-2 Berea
sandstone 175 0.20 100 Single Long coreSingle perforation.
(1/8" * 2") BS-long-12
10 UltraCarb-2 Berea
sandstone 144 0.19 100 Single Long coreSingle perforation.
(1/4" * 1") BS-long-13
11 UltraCarb-2 Berea
sandstone 174 0.19 100 Single Long coreSingle perforation.
(1/4" * 2") BS-long-14
12 UltraCarb-20 Boise
sandstone ~1000 0.29 100 Single Short coreSingle perforation. (1/8"dia., 1/2"len.) Bo-4
13 UltraCarb-20 Boise
sandstone ~1000 0.28 500 Single Short coreSingle perforation. (1/8"dia., 1/2"len.) Bo-6
343
Test No. 1
0
20
40
60
80
100
120
0 10 20 30 40 50 60 70Time (min)
App
lied
Diffe
rent
ial P
ress
ure
(psi
)
0
5
10
15
20
25
30
35
40
45
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 1 psi
Figure E-1: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Texas limestone with lab simulated perforation (LS-9)
0
20
40
60
80
100
0 20 40 60 80
Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y Ra
tio (%
)
Figure E-2: Return permeability spectra with incremental differential pressures for Texas
limestone with lab simulated perforation (LS-9)
344
0
0.4
0.8
1.2
1.6
0 10 20 30 40Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure E-3: Static filtration of UltraCarb-2 on Texas limestone simulating open hole completion (LS-9)
345
Test No. 2
0
10
20
30
40
50
60
70
80
90
100
0 50 100 150 200 250 300 350 400 450 500 550Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
10
20
30
40
50
60
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 10 psi
Figure E-4: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea core with lab simulated perforation (BS-2-2-04-I)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
Figure E-5: Return permeability spectra with incremental differential pressures for Berea
sandstone with lab simulated perforation (BS-2-2-04-I)
346
0
0.1
0.2
0.3
0.4
0 10 20 30 40
Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure E-6: Static filtration of UltraCarb-2 on Berea sandstone with lab simulated perforation (BS-2-2-04-I)
347
Test No. 3
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500Time (min)
Appl
ied
Diffe
rent
ial
Pres
sure
(psi
)
0
10
20
30
40
50
60
70
80
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 2 psi
Figure E-7: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-6-5-04-long-6)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
For the whole core (0-6 inch) For the top 0-2 inch of the coreFor the middle 2-4 inch of the core For the bottom 4-6 inch of the coreFor the top 0-1/8 inch of the core
Figure E-8: Return permeability spectra with incremental differential pressures for Berea
sandstone (BS-6-5-04-long-6)
348
0
0.5
1
1.5
2
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure E-9: Static filtration of UltraCarb-2 on Berea sandstone simulating open hole
completion (BS-6-5-04-long-6)
349
Test No. 4
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400Time (min)
Appl
ied
Diff
eren
tial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
80
90
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 3 psi
Figure E-10: Flowback rate at incremental differential pressures on Berea sandstone with
a lab simulated perforation (BS-6-5-04-long-7)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Ratio
(%)
For the whole core (0-6 inch)For the top 0-2 inch of the coreFor the middle 2-4 inch of the coreFor the bottom 4-6 inch of the core
Figure E-11: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-6-5-04-long-7)
350
0
1
2
3
4
0 10 20 30 40Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure E.12: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated perforation (BS-6-5-04-long-7)
351
Test No. 5
0
20
40
60
80
100
120
0 20 40 60 80 100 120Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
80
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 3.5 psi
Figure E-13: Flowback rate at incremental differential pressures on Berea sandstone with
a lab simulated perforation (BS-6-13-04-long-8)
0
20
40
60
80
100
120
0 20 40 60 80 100 120
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
For the whole core (0-6 inch) For the top 1/8-2 inch of the coreFor the middle 2-4 inch of the core For the bottom 4-6 inch of the coreFor the top 0-1/8 inch of the core For the top 0-2 inch of the core
Figure E-14: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-6-13-04-long-8)
352
0
2
4
6
0 10 20 30 40Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure E-15: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated perforation (BS-6-13-04-long-8)
353
Test No. 6
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120 140Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
20
40
60
80
100
120
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 1.5 psi
Figure E-16: Flowback rate at incremental differential pressures on Berea sandstone with
a lab simulated perforation (BS-6-13-04-long-9)
0
20
40
60
80
100
120
140
160
180
200
0 20 40 60 80 100 120Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y Ra
tio (%
)
For the whole core (0-6 inch) For the top 1/8-2 inch of the core
For the middle 2-4 inch of the core For the bottom 4-6 inch of the core
Figure E-17: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-6-13-04-long-9)
354
0
2
4
6
8
10
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure E-18: Static filtration of UltraCarb-2 on Berea sandstone with a lab simulated perforation (BS-6-13-04-long-9)
355
Test No. 7
0
20
40
60
80
100
120
0 50 100 150 200 250 300Time (min)
Appl
ied
Diff
eren
tial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
80
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 4 psi
Figure E-19: Flowback rate at incremental differential pressures on Berea sandstone with
a lab simulated perforation (BS-6-29-04-long-10)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
For the w hole core (0-6 inch) For the middle 2-4 inch of the core
For the bottom 4-6 inch of the core For the top 0-2 inch of the core
Figure E-20: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-6-29-04-long-10)
356
0
1
2
3
4
0 10 20 30 40Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure E-21: Static filtration of UltraCarb-2 on a long Berea core simulating open hole completion (BS-6-29-04-long-10)
357
Test No. 8
0
20
40
60
80
100
120
0 50 100 150 200 250Time (min)
App
lied
Diffe
rent
ial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
80
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 10 psi
Figure E-22: Flowback rate at incremental differential pressures on Berea sandstone with
a lab simulated perforation (BS-long-11)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
For the whole core (0-6 inch) For the middle 2-4 inch of the coreFor the bottom 4-6 inch of the core For the top 0-2 inch of the core
Figure E-23: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-long-11)
358
0
0.5
1
1.5
2
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure E-24: Static filtration of UltraCarb-2 on a long Berea core simulating open hole completion (BS-long-11)
359
Test No. 9
0
20
40
60
80
100
120
0 50 100 150 200 250 300Time (min)
Appl
ied
Diff
eren
tial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
80
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 14 psi
Figure E-25: Flowback rate at incremental differential pressures on Berea sandstone with
a lab simulated perforation (BS-long-12)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100 120
Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y R
atio
(%)
For the whole core (0-6 inch) For the middle 2-4 inch of the coreFor the bottom 4-6 inch of the core For the top 0-2 inch of the core
Figure E-26: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-long-12)
360
0
1
2
3
4
5
0 10 20 30 40Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure E-27: Static filtration of UltraCarb-2 on a long Berea core simulating open hole completion (BS-long-12)
361
Test No. 10
0
20
40
60
80
100
120
0 50 100 150 200 250 300 350 400Time (min)
Appl
ied
Diffe
retia
l Pre
ssur
e (p
si)
0
10
20
30
40
50
60
70
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 2 psi
Figure E-28: Flowback rate at incremental differential pressures on Berea sandstone with
a lab simulated perforation (BS-long-13)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
For the whole core (0-6 inch) For the middle 2-4 inch of the coreFor the bottom 4-6 inch of the core For the top 0-2 inch of the core
Figure E-29: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-long-13)
362
0
1
2
3
4
5
0 10 20 30 40Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure E-30: Static filtration of UltraCarb-2 on a long Berea core simulating open hole completion (BS-long-13)
363
Test No. 11
0
20
40
60
80
100
120
0 10 20 30 40 50Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
10
20
30
40
50
60
70
80
90
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 1 psi
Figure E-31: Flowback rate at incremental differential pressures on Berea sandstone with
a lab simulated perforation (BS-long-14)
0
10
20
30
40
50
60
70
80
90
100
0 20 40 60 80 100Applied Differential Pressure During Flowback (psi)
Ret
urn
Per
mea
bilit
y Ra
tio (%
)
For the whole core (0-6 inch) For the middle 2-4 inch of the coreFor the bottom 4-6 inch of the core For the top 0-2 inch of the core
Figure E-32: Return permeability spectra with incremental differential pressures for
Berea sandstone with a lab simulated perforation (BS-long-14)
364
0
2
4
6
8
0 10 20 30 40Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure E-33: Static filtration of UltraCarb-2 on a long Berea core simulating open hole completion (BS-long-14)
365
Test No. 12
0
5
10
15
20
25
30
0 20 40 60 80 100 120Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
20
40
60
80
100
120
140
160
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Figure E-34: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Boise sandstone with a lab simulated perforation (Bo-4)
0
5
10
15
20
25
30
35
40
45
0 5 10 15 20 25 30
Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Rat
io (%
)
Figure E-35: Return permeability spectra with incremental differential pressures for
Boise sandstone with a lab simulated perforation (Bo-4)
366
0
0.2
0.4
0.6
0.8
0 10 20 30 40Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure E-36: Static filtration of UltraCarb-20 on a long Berea core simulating open hole completion (Bo-4)
367
Test No. 13
0
10
20
30
40
50
60
70
80
0 50 100 150 200 250 300 350Time (min)
Appl
ied
Diffe
rent
ial P
ress
ure
(psi
)
0
50
100
150
200
250
300
350
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure Flowback rate
Flowback started at ∆P = 5 psi
Figure E-37: Flowback rate at incremental differential pressures after filtration with
UltraCarb-20 on Boise sandstone with a lab simulated perforation (Bo-6)
0
5
10
15
20
25
0 10 20 30 40 50 60 70 80
Applied Differential Pressure During Flowback (psi)
Ret
urn
Perm
eabi
lity
Ratio
(%)
Figure E-38: Return permeability spectra with incremental differential pressures for
Boise sandstone with a lab simulated perforation (Bo-6)
368
0
0.2
0.4
0.6
0.8
0 10 20 30Sqrt. of Time (min)1/2
Vol
ume
of F
iltra
te (m
l)
Figure E-39: Static filtration of UltraCarb-20 on a long Berea core simulating open hole completion (Bo-6)
369
Appendix-F: Plots for two-phase constant pressure flowback experiments conducted on lab-simulated perforated cores
370
Table F.1: List of all the two-phase, constant pressure flowback experiments, simulating lab-simulated perforated completion
Test No. Mud Used Rock Type
Av. Brine Perm (md)
Average Porosity
Over balance pressure
(psi) Phase Core TypeSimulated
Completion TypeCore Sample
Name
1 Bentonite Berea
sandstone Not
available 0.20 100 Two Short core3 Perforations
(1/8"dia.,1/2"len.) BS-12-22-03-I
2 Bentonite Berea
sandstone Not
available 0.20 100 Two Short coreSingle perforation (1/8"dia., 1/2"len.) BS-12-15-03-I
3 UltraCarb-2 Berea
sandstone Not
available 0.20 100 Two Short coreSingle perforation (1/8"dia., 1/2"len.) BS-12-08-03-I
371
Test No. 1
0
2
4
6
8
10
12
14
16
0 50 100 150 200 250 300 350 400Time (min)
Appl
ied
Diff
eren
tial P
ress
ure
(psi
)
0
2
4
6
8
10
12
14
16
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
Flowback started at ∆P = 8 psi
Figure F-1: Flowback rate at incremental differential pressures after filtration with
bentonite mud on Berea sandstone (BS-12-22-03-I)
0
20
40
60
80
100
0 5 10 15 20
Applied Differential Pressure During Flowback (psi)
Retu
rn P
erm
eabi
lity
Ratio
(%)
Figure F-2: Return permeability spectra with incremental differential pressures for Berea
sandstone (BS-12-22-03-I)
372
0
2
4
6
8
0 5 10 15 20 25Sqrt. of Time (min)1/2
Volu
me
of F
iltra
te (m
l)
Figure F-3: Static filtration of bentonite mud on Berea sandstone simulating open hole completion (BS-12-22-03-I)
373
Test No. 2
0
2
4
6
8
10
12
14
16
0 20 40 60 80 100 120 140 160Time (min)
App
lied
Diff
eren
tial P
ress
ure
(psi
)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Mea
sure
d R
ate
(ml/m
in)
Flowback pressure (psi) Flowback Rate (ml/min)
Kreturn = 72%
Flowback started at ∆P = 14 psi
Figure F-4: Flowback rate at incremental differential pressures after filtration with
bentonite mud on Berea sandstone (BS-12-15-03-I)
374
Test No. 3
0
2
4
6
8
10
12
14
16
0 100 200 300 400 500
Time (min)
App
lied
Diffe
rent
ial P
ress
ure
(psi
)
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Mea
sure
d Ra
te (m
l/min
)
Flowback pressure (psi) Flowback Rate (ml/min)
kreturn = 56 %
Flowback started at ∆P = 15 psi
Figure F-5: Flowback rate at incremental differential pressures after filtration with
UltraCarb-2 on Berea sandstone (BS-12-08-03)
375
Appendix-G: Detailed information of all the fluid filtration experiments with constant pressure flowback condition
376
Test No.M
ud UsedRock Type
Av. Brine Perm
(md)
Average Porosity
Overbalance (psi)
PhaseCore Type
Simulated Com
pletion TypeCore Sam
ple Name
FIP (psi)
Max return
perm (%
)
30 minute
API filtrate loss (m
l)Spurt loss (m
l)1
UltraCarb-2Nugget sandstone
40.12
100Single
Short coreOpen hole
NS-22
72.33.74
02
UltraCarb-2Nugget sandstone
260.13
140Two
Short coreOpen hole
NS-36
48.43.82
0
3UltraCarb-2
Texas limestone
240.28
100Single
Short coreO
pen holeLS-1
156.6
4.790.23
4UltraCarb-2
Texas limestone
180.28
100Single
Short coreO
pen holeLS-13 (Repeat)
255
4.550.2
5UltraCarb-2
Texas limestone
15 (keff oil)0.30
100Two
Short coreOpen hole
LS-122
92.84.84
0.36
BentoniteTexas lim
estone26
0.28100
SingleShort core
Open hole
LS-51
11722.4
17
UltraCarb-2Texas lim
estoneNA
0.31100
SingleShort core
Single perf. (1/4" dia. 1/2" len.)LS-9
178.9
0.160.1
8UltraCarb-2
Berea sandstone60
0.17100
SingleShort core
Open holeBS-4-2-04-I
450.4(20 psi)
4.650.2
9UltraCarb-2
Berea sandstoneNA
0.17100
SingleShort core
Single perf. (1/8" dia. 1/2" len.)BS-2-2-04-I
1096.8
0.020.01
10UltraCarb-2
Berea sandstone285
0.20100
TwoShort core
Open hole
BS-11-11-03-I7
29 (10)5.47
0.2611
BentoniteBerea sandstone
NA0.20
100Two
Short core3 Perf. (1/8"dia.1/2"len.)
BS-12-22-03-I8
55 (14)1.33
0.0612
BentoniteBerea sandstone
NA0.20
100Two
Short coreSingle perf. (1/8"dia.,1/2"len.)
BS-12-15-03-I14
72 (14)NA
NA13
UltraCarb-2Berea sandstone
NA0.20
100Two
Short coreSingle perf. (1/8"dia.,1/2"len.)
BS-12-08-03-I15
56 (15)NA
NA14
UltraCarb-2Berea sandstone
1530.15
100Single
Long coreO
pen hole BS-4-29-04-long-#3
367.8
6.390.63
15UltraCarb-2
Berea sandstone149
0.19100
SingleLong core
Open hole
BS-4-29-04-long-#42
765.46
0.5616
UltraCarb-2Berea sandstone
2070.19
100Single
Long coreO
pen holeBS-6-5-04-long-#5
271
6.370.88
17UltraCarb-2
Berea sandstone187
0.19100
SingleLong core
Single perf. (1/8" * 1")BS-6-5-04-long-#6
473
0.50NA
18UltraCarb-2
Berea sandstone190
0.19100
SingleLong core
Single perf. (1/8" * 2")BS-6-5-04-#7
374
0.87NA
19UltraCarb-2
Berea sandstone216
0.20100
SingleLong core
Single perf. (3/8" * 1")BS-6-13-04-8
3.563.1
1.15NA
20UltraCarb-2
Berea sandstone212
0.20100
SingleLong core
Single perf. (1/4" * 2")BS-6-13-04-9
<1.593
1.92NA
21UltraCarb-2
Berea sandstone207
0.20100
SingleLong core
Single perf. (1/4" * 1")BS-6-19-04-#10
464
0.89NA
22UltraCarb-2
Berea sandstone133
0.20100
SingleLong core
Single perf. (1/8" * 1")BS-1by8india-1indepth-#11
1096
0.46NA
23UltraCarb-2
Berea sandstone175
0.20100
SingleLong core
Single perf. (1/8" * 2")BS-1by8india-2indepth-#12
1478.9
1.06NA
24UltraCarb-2
Berea sandstone144
0.19100
SingleLong core
Single perf. (1/4" * 1")BS-1by4india-1indepth-#13
274.4
0.99NA
25UltraCarb-2
Berea sandstone174
0.19100
SingleLong core
Single perf. (1/4" * 2")BS-1by4india-2indepth-#14
187
1.72NA
25UltraCarb-2
Berea sandstone129(keff oil)
0.20100
TwoShort core
Open hole
BS-174
72.34.6
0.5726
2+12+20Berea sandstone
144(keff oil)0.20
500Two
Short coreOpen hole
BS-192
713.2
1.1627
2+12+20Berea sandstone
138(keff oil)0.20
500Two
Short coreOpen hole
BS-20 (Back pr = 500 psi)2
583.72
0.8128
UltraCarb-20Berea sandstone
146(keff oil)0.20
100Two
Short coreOpen hole
BS-214
853.41
0.13
29UltraCarb-20
Boise sandstone885
0.28100
SingleShort core
Open hole
Bo-13
204.16
0.4730
BentoniteBoise sandstone
9820.28
100Single
Short coreO
pen holeBo-2
125
31.10.68
31UltraCarb-20
Boise sandstoneNA
0.29100
SingleShort core
Single perf. (1/8"dia.,1/2"len.)Bo-4
238
0.120.015
32UltraCarb-20
Boise sandstoneNA
0.28500
SingleShort core
Single perf. (1/8"dia.,1/2"len.)Bo-6
521
0.10.018
33UltraCarb-20
Boise sandstone600(keff oil)
0.28100
TwoShort core
Open hole
Bo-72
953.23
0.65
34UltraCarb-2
Aloxide960
0.44100
SingleShort core
Open hole
AL-18
5 (50)14.9
3.6235
UltraCarb-20Aloxide
13130.44
100Single
Short coreOpen hole
AL-24
7.6 (50)8.04
1.0436
UltraCarb-20Aloxide
965 (keff oil)0.42
100Two
Short coreO
pen holeAL-3
326.5 (50)
5.61.1
377
Appendix-H: Detailed information of all the fluid filtration experiments with constant rate flowback condition
378
Test No.
Mud UsedRock Type
Av. Brine Perm (md)
Av. oil Perm (md)
Av. Porosity
Over balance
(psi)
Temp ( oF)
PhaseCore type*
Simulated Completion
Type
Core Sample Name
Flow back rate
(ml/min)
Peak pressure
(psi)
FIP (psi)
Return perm (%)
API filtrate (ml)
1UltraCarb-2
Berea sandstone60
N/A0.17
100150
TwoShort core
Open holeBS-4-16-03-II
111.9
8.95N/A
6.152
UltraCarb-2Berea sandstone
247217
0.19100
150Two
Short coreOpen hole
BS-8-27-03-III5
18.2713.93
266
3UltraCarb-2 (no starch)
Berea sandstone60
N/A0.20
100150
TwoShort core
Open holeBS-4-21-03-II
113.3
10.7814
25.34
UltraCarb-2 (no xanthan)Berea sandstone
60N/A
0.19100
150Two
Short coreOpen hole
BS-4-21-03-III1
6.23.57
13.117.2
5UltraCarb-2 (no starch and xanthan)
Berea sandstone186
1290.20
10075
TwoShort core
Open holeBS-6-8-03-IV
12.1
0.329
3216
UltraCarb-2 (no starch and xanthan)Berea sandstone
13087
0.20100
75Two
Short coreOpen hole
BS-6-8-03-V1
2.50
22304
7UltraCarb-12
Berea sandstone190
1340.19
10075
TwoShort core
Open holeBS-6-8-03-VI
39.52
7.3333.9
3.628
UltraCarb-12 (no starch)Berea sandstone
12892
0.17100
75Two
Short coreOpen hole
BS-6-8-03-IX5
2920
2948.9
9UltraCarb-12 (no xanthan)
Berea sandstone252
1620.19
10075
TwoShort core
Open holeBS-6-8-03-VIII
57.47
4.0747
23.710
UltraCarb-12 (no starch and xanthan)Berea sandstone
8570.5
0.20100
75Two
Short coreOpen hole
BS-6-8-03-VII5
12.536.53
70435.7
11UltraCarb-12 + RevDust
Berea sandstone233
2140.21
10075
TwoShort core
Open holeBS-10-2-03-I
513.47
10.236
3.98
12UltraCarb-20
Berea sandstone247
1990.20
10075
TwoShort core
Open holeBS-8-27-03-II
513.44
9.9733.4
4.513
UltraCarb-20 (no starch)Berea sandstone
535287
0.19100
75Two
Short coreOpen hole
BS-8-11-03-XI5
7.014.71
41.225.13
14UltraCarb-20 (no xanthan)
Berea sandstone291
1660.19
10075
TwoShort core
Open holeBS-8-11-03-XII
57.59
4.3653.1
27.715
UltraCarb-20 (no starch and xanthan)Berea sandstone
142128
0.20100
75Two
Short coreOpen hole
BS-8-11-03-X5
9.395
44.8515
16UltraCarb-20 + RevDust
Berea sandstone272
1840.21
10075
TwoShort core
Open holeBS-10-7-03-I
515
11.5339
4.44
17Brine
Berea sandstone223
1880.19
10075
TwoShort core
Open holeBS-8-27-03-I
55.71
2.5152
95118
Brine + pH BufferBerea sandstone
231176
0.19100
75Two
Short coreOpen hole
BS-8-11-03-XIII5
4.952.35
72
19UltraCarb-20
Boise sandstone1121
0.29100
75Single
Short coreOpen hole
Bo-35
3.762.8
9.834.52
379
Nomenclature
A : cross-section area of the core
As : Happel’s geometric parameter
ap : radius of the injected particle
c : concentration of suspended fluid
dp : pore throat diameter
dg : grain diameter
DBM : Brownian diffusion coefficient
dp : diameter of the injected particle
fv : pore volume distribution function
f (r) : probability distribution function for radii of pore-segments and
capillary tubes
g : pore-segment conductance
g m : effective mean conductance during flowback
g mo : effective mean conductance for single phase flow when all the
pore-segments are allowing flow and are accessible
G’ : elastic modulus
G” : viscous modulus
G (g) : single-phase conductivity distribution function
G d, f (g) : conductivity distribution function for the displacing fluid
G d, f (g) : allowable conductivity distribution function displacing fluid
h : cake thickness
H : Hamakar constant for the particle medium system (~ 1*10-13 erg)
k : permeability
Kdp : reduced porosity fraction
Kds : increased surface area fraction
Kdt : increased tortuosity fraction
l : length of pore-throats in a network and length of bundle of
capillary tubes
380
L : core length
NLO : London group
NR : Relative size group
NG : Gravity group
NPE : Peclet number
P : pressure
q : flow rate
Q : filtrate loss
Qsp : spurt loss
r : radius of pore-throats and capillary tubes
R : radius of the largest capillary tube
rw : radius of the well
u : darcy velocity
V (r) : probability distribution function for volume occupied by pore-
segments and capillary tubes
X f : fraction of pores allowed to flow and can have displacement of
the Bingham fluid by the displacing fluid
X d, f : fraction of pores accessible to flow and have displacement of the
Bingham fluid by the displacing fluid
X c : Percolation threshold for a Bethe tree, i.e. the maximum
inaccessible fraction of pores
Xd : depth of solids invasion, inch
Z : average coordination number of the three dimensional network
that approximates pore space topology
Z b : local coordination number of Bethe tree
Greek Symbols
∆P : pressure difference across pore-segments and capillary tubes
381
τ : yield stress
γ : strain
µ : viscosity
δ (g) : Dirac delta function
φ : porosity
σ : specific deposit (volume of deposited particles per unit bulk
volume)
λ : filtration coefficient
η : collection efficiency
ρp : injected particle density
ρf : fluid density
γu : velocity dependence parameter for filtration coefficient
ν : superficial flow velocity
φcrit : critical porosity
382
Bibliography
1. Al-Riyamy, K.: “Synthesis and Characterization of Reversible Emulsions:
Application to Completion Fluids,” dissertation presented to the faculty of the
graduate school of The University of Texas at Austin, May, 2000.
2. Alfenore, J., et al.: “What really Matters In our Quest of Minimizing Formation
Damage In Open Hole Horizontal Wells,” paper SPE 54731 presented at the
European Formation Damage Conference held in The Hague, The Netherlands, 31
May -1 June, 1999.
3. Aston, M. S., et al.: “Drilling Fluids for Wellbore Strengthening,” paper IADC/SPE
87130 presented at the IADC/SPE Drilling Conference held in Dallas, Texas, U.S.A.,
2-4 March, 2004.
4. Bailey, L., et al.: “Filter cake Integrity and Reservoir Damage,” paper SPE 39429
presented at the 1998 SPE International Symposium on Formation Damage Control
held in Lafayette, 18-19 February, 1998.
5. Bailey et al.: “Particulate Invasion From Drilling Fluids,” paper SPE 51094 presented
at the SPE Eastern Regional Meeting held in the Pittsburgh, PA, 9-11 November,
1998.
6. Browne, S. V., and Smith, P. S.: “Mud cake Clean up to Enhance the Productivity of
Horizontal Wells,” paper SPE 27350 presented at the SPE Formation Damage
Control Symposium held in Lafayette, 9-10 February, 1994.
383
7. Browne, S. V., et al.: “Simple Approach to the Cleanup of Horizontal Wells With
Prepacked Screen Completions,” paper SPE 30116 presented at the SPE Formation
Damage Control Symposium held in The Hague, The Netherlands, 15-16 May, 1995.
8. Cameron, C., et al.: “Water-Based Drilling Fluid Helps Achieve Oil-Mud
Performance,” paper AADE-04-DF-HO-03 presented at AADE 2004 Drilling Fluids
Conference, held at the Radisson Astrodome in Houston, Texas, U.S.A., April 6-7,
2004.
9. Cerasi, P., et al.: “Measurement of the Mechanical Properties of Filtercakes,” paper
SPE 68948 presented at the 2001 SPE European Formation Damage Conference held
in The Hague, The Netherlands, 21-22 May, 2001.
10. Chang, F. F., et al.: “Perforating in Overbalance – Is it really sinful?,” paper SPE
82203 presented at the SPE European Formation Damage Conference held in The
Hague, The Netherlands, 13-14 May, 2003.
11. Chang, F. F., et al.: “Recommended Practice for Overbalanced Perforating in Long
Horizontal Wells,” paper SPE 94596 presented at the SPE European Formation
Damage Conference held in Scheveningen, The Netherlands, 25-27 May, 2005.
12. Chilingarian, G. V., and Vorabutr, P.: “Drilling and drilling fluids,” updated textbook
edition, Elsevier, Amsterdam-Oxford-New York, 1983.
13. Darley, H. C. H. and Gray, George R.: “Composition and Properties of Drilling and
Completion Fluids,” fifth edition, Gulf Publishing Company.
14. Davidson, E., et al.: “Challenging Reservoir Drilling Conditions Overcome by
Engineered Water Based Drill-In Fluids,” paper AADE-04-DF-HO-03 presented at
384
AADE 2004 Drilling Fluids Conference, held at the Radisson Astrodome in Houston,
Texas, U.S.A., April 6-7, 2004.
15. Ding, Y., et al.: “Modeling of Both Near-Wellbore Damage and Natural Cleanup of
Horizontal Wells Drilled With Water-Based Drilling Fluids,” paper SPE 88807
revised for publication from paper 73733, presented at the SPE Formation Damage
Control Symposium held in Lafayette, Louisiana, 20-21 February, 2002.
16. Gray, George R., Darley, H.C.H., and Rogers, Walter F.: “Composition and
Properties of Oil Well Drilling Fluids,” Fourth edition, Gulf Publishing Company,
Book Division, Houston, London, Paris, Tokyo.
17. Gruber, N. G., and Adair, K. L.: “New Laboratory Procedures for Evaluation of
Drilling Induced Formation Damage and Horizontal Well Performance,” paper JCPT
Volume 34, No. 5, May, 1995.
18. Gruber, N. G., and Adair, K. L.: “New Laboratory Procedures for Evaluation of
Drilling Induced Formation Damage and Horizontal Well Performance: An Update,”
paper SPE 37139 presented at the SPE International Conference on Horizontal Well
Technology held in Calgary, Canada, 18-20 November, 1996.
19. Heiba, A. A., et al.: “Percolation Theory of Two-phase Relative Permeability,” paper
SPE 11015 presented at the 57th Annual Technical Conference and Exhibition of the
Society of Petroleum Engineers of AIME, held in New Orleans, Lafayette, September
26-29, 1982.
20. Jiang, P., et al.: “New Low-Solids OBM Demonstrates Improved Returns as
Perforating Kill-pill,” paper SPE 73709 presented at the SPE International
385
Symposium and Exhibition on Formation Damage Control held in Lafayette,
Louisiana, 20-21 February, 2002.
21. Jiao, D. and Sharma, M.M.: ‘Mechanism of cake buildup in crossflow filtration of
colloidal suspension’, Journal of Colloid and Interfacial Science, 162, pp 454-462,
1994.
22. Kalpakci, B., et al.: “A Systematic Approach for Selection of Drill-in Fluids and
Cleanup Options for Minimum Formation Damage in Horizontal Well: A Case Study
for Paloma Field, Bolivia,” paper SPE 53948 presented at the SPE Latin American
and Caribbean Petroleum Engineering Conference held in Caracas, Venezuela, 21-23
April, 1999.
23. Khilar, K. C., et. al (1998): "Existence of a Critical Particle Concentration in
Plugging of a Packed Bed," AICHE J, April 1998, Vol. 44, No. 4, 978-81.
24. Koplik, J.: “Creeping Flow in Two-Dimensional Networks,” Journal of Fluid
Mechanics, v.119, p.219, 1982.
25. Kruger, R. F.: “An Overview of Formation Damage and Well Productivity in Oil
Field Operations,” JPT, pp131-152, SPE 10029, February, 1986.
26. Ladva, J. K. H., et al.: “Multiphase Flow and Drilling-Fluid Filtrate Effects on the
Onset of Production,” paper SPE 58795 presented at the SPE International
Symposium on Formation Damage Control, Lafayette, Louisiana, 23-24 February,
2000.
27. Lakes S. R.: “Viscoelastic solids,” published by CRC press.
386
28. Marshall, S. D., et al,: “Return Permeability: A Detailed Comparative Study,” paper
SPE 54763 presented at the SPE European Formation Damage Conference held in
The Hague, The Netherlands, 31 May - 1 June, 1999.
29. Panda, M.N. and Lake, L.W.: ‘Estimation of single-phase permeability from
parameters of particle-size distribution’, AAPG Bulletin, V.78, No. 7, July, 1994.
30. Qutob, Hani, et al.: “Underbalanced Drilling; Remedy for Formation Damage, Lost
Circulation, and Other Related Conventional Drilling Problems,” paper 88698
presented at the 11th Abu Dhabi International Petroleum Exhibition and Conference
held in Abu Dhabi, U.A. E., 10-13 October, 2004.
31. Rajagopalan, R. and Tien, C.: ‘Trajectory analysis of deep bed filtraiotn with sphere-
in cell model’, AIChE J, Vol. 22, No. 3, May, 1976.
32. Rossen, W. R., and Kumar, Arun T. A.: “Single- and Two-phase Flow in Natural
Fractures,” paper SPE 24915 presented at the 67th Annual Technical Conference and
Exhibition of the Society of Petroleum Engineers, Washington, DC, Oct. 4-7, 1992.
33. Roy, S. R., and Sharma, M. M.: “The Relative Importance of Solids and Filtrate
Invasion on the Flow Initiation Pressure,” paper SPE 68949 presented at the
European Formation Damage Conference held in The Hague, The Netherlands, 21-22
May, 2001.
34. Ryan, D. F., et al.: “Mud Clean-Up in Horizontal Wells: A Major Joint Industry
Study,” paper SPE 30528 presented at the SPE Annual Technical Conference and
Exhibition held in Dallas, USA, 22-25 October, 1995.
387
35. Sanders, M. W., et al.: “A Quantitative Method for Estimating a-Amylase-Based
Enzyme Concentrations in Wellsite Field Samples and its Application on a Gravel
Pack Completion,” paper AADE-04-DF-HO-35 presented at the 2004 AADE Drilling
Fluids Conference, held at the Radisson Astrodome in Houston, Texas, April 6-7,
2004.
36. Scheuerman, R.F. and Berensen, B.M.: ‘Injection-water salinity, formation
pretreatment and well-operations fluid-selection guidelines’, JPT, July, 1990.
37. Sharma, M.M. and Yortsos, Y.C.: ‘Transport of particulate suspensions in porous
media: Model formulation’, AIChE Journal, October, 1987.
38. Smith, P. S., et al.: “Drilling Fluid Design to Prevent Formation Damage in High
Permeability Quartz Arenite Sandstones,” paper SPE 36430 presented at the Annual
Technical Conference and Exhibition held in Denver, Colorado, U.S.A., 6-9 October,
1996.
39. Suhy, Thomas, et al.: “Application of Polymer Specific Enzymes To Cleanup Drill-In
Fluids,” paper SPE 51094 presented at the SPE Eastern Regional Meeting held in the
Pittsburgh, PA, 9-11 November, 1998
40. Suri, A.: “A Model for Multi-Component Filtration” MS Thesis, The University of
Texas at Austin, December, 2000.
41. Suri, A., and Sharma, M.M.: “Strategies for Sizing Particles in Drilling and
Completion Fluids,” paper SPE 68964 presented at the SPE European Formation
Damage Conference held in The Hague, The Netherlands, 21–22 May, 2000.
388
42. Suri, A., and Sharma, M.M.: “Strategies for Sizing Particles in Drilling and
Completion Fluids,” paper SPE 87676 published in SPEJ, March, 2004.
43. Wang, Y.: “A Three-Dimensional Network Model for Porous Media,” M.S. Thesis,
The University of Texas at Austin, August, 1988.
44. Zain, M. Z., and Sharma, M. M.: “Mechanisms of Mud Cake Removal During
Flowback,” SPE Drilling and Completion, December, 2001.
45. Zain, M. Z., Suri, A., and Sharma, M. M.: “Mechanisms of Mud Cake Removal
During Flowback,” paper SPE 58797 presented at the SPE International Symposium
of Formation Damage Control held in Lafayette, Louisiana, 23-24 February, 2000.
46. Zain, M. Z., and Sharma, M. M.: “Cleanup of Wall-Building Filter Cakes,” paper
SPE 56635 presented at the SPE Annual Technical Conference and Exhibition held in
Houston, Texas, 3-6 October, 1999.
389
Vita
Ajay Suri was born in Delhi, India, on June 8 1975, as the son of Avinash
Chander Suri and Sita Rani. He received the degree of Bachelor of Technology in
petroleum engineering from the Indian School of Mines in 1998. In December 2000, he
graduated from the University of Texas at Austin with a MS in petroleum engineering.
He worked at Vignette Corporation from 2000 to 2001. In August 2002, he joined the
University of Texas at Austin to pursue a doctoral degree in petroleum engineering.
Permanent Address: A-41 Panchvati,
Near Azadpur,
Delhi, India - 110033
This dissertation was typed by Ajay Suri.