UNIVERSITY OF CALGARY Drill Cuttings, Petrophysical, … · methodology developed in this thesis allows for complete formation evaluation and ... thank Dr. Roberto ... Paul Glover,

UNIVERSITY OF CALGARY

Drill Cuttings, Petrophysical, and Geomechanical Models for Evaluation of Conventional

and Unconventional Petroleum Reservoirs

by

Bukola Korede Olusola

A THESIS

SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL

FULFILMENT OF THE REQUIREMENT FOR THE DEGREE OF MASTER OF

SCIENCE

DEPARTMENT OF CHEMICAL AND PETROLEUM ENGINEERING

CALGARY, ALBERTA

SEPTEMBER, 2013

© Bukola Korede Olusola 2013

ii

ABSTRACT

This thesis concentrates on some of the aspects of a ‘Total Petroleum System’ including

natural gas and oil stored in conventional and unconventional reservoirs.

The original contributions of this thesis include:

1) The use of electromagnetic mixing rules for construction of dual and triple

porosity models with a view to quantifying matrix, fracture and non-effective porosity

and the porosity exponent (m) of naturally fractured reservoirs.

2) The use of electromagnetic mixing rules for construction of dual and triple

porosity models with a view to quantify the water saturation exponent (n) and to estimate

the wettability of reservoir rocks in naturally fractured reservoirs.

3) Measurements of porosity and permeability in drill cuttings collected directly in a

horizontal well. Although these measurements have been carried out previously in drill

cuttings collected in vertical and deviated wells, this is the first time that they are

performed in horizontal well drill cuttings.

The models developed in Items 1 and 2 are compared successfully against core laboratory

data. Water and/or oil stored in each of the porous media considered in the models,

affects rock wettability and consequently the values of n. Robustness of the models is

important because, in practice, while logging a well in a naturally fractured reservoir, the

tool will probably go through some intervals with only matrix porosity; some intervals

with matrix porosity and fractures, some with matrix porosity and isolated porosity; and

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some intervals with matrix, fractures and non-connected porosities. As there are

variations in the contribution of each porosity system with depth, there are also variations

in m with depth that have to be taken into account.

The laboratory measurements of porosity and permeability from drill cuttings mentioned

above in Item 3 were conducted at the University of Calgary. Based on a thorough review

of literature this is the first time that this measurements are conducted in drill cuttings

samples collected in horizontal wells.

Starting with only drill cuttings measurements of porosity and permeability, the

methodology developed in this thesis allows for complete formation evaluation and

geomechanical analysis through the use of a successive approach for determination of

several parameters of interest including pore throat aperture radius (rp35), water

saturation, porosity exponent (m), true formation resistivity, capillary pressure, Knudsen

number, depth to the water contact (if present), construction of Pickett plots, Young’s

Modulus, Poisson’s ratio and brittleness index throughout the horizontal length of the

well, and for locating the best hydraulic fracture initiation points during multi-stage

fracturing jobs.

It is concluded that the use of electromagnetic mixing rules and drill cuttings provide a

valuable and practical addition for quantitative characterization of conventional and

unconventional petroleum reservoirs.

iv

ACKNOWLEDGEMENT

I will like to specially thank Dr. Roberto Aguilera for giving me an opportunity to join

the GFREE (Geoscience, Formation Evaluation, Reservoir Drilling, Completion and

Stimulation, Reservoir Engineering, Economics and Externalities) research team at the

University of Calgary. I sincerely appreciate all his efforts in guiding and supervising my

work and also ensuring the successful completion of my thesis. I feel privileged to have

had Dr. Roberto Aguilera as my supervisor on this research.

Parts of this work were funded by the Natural Sciences and Engineering Council of

Canada (NSERC agreement 347825-06), ConocoPhillips (agreement 4204638), Alberta

Innovates Energy and Environmental Solutions (AERI agreement 1711), the Schulich

School of Engineering at the University of Calgary and Servipetrol Ltd. Darcylog

equipment for measuring permeabilities from drill cuttings was provided by Roland

Lenormand of Cydarex in Paris. GOHFER software was provided by Barree &

Associate. Their contributions are gratefully acknowledged. Also, special thanks to past

and present GFREE research team members at the University of Calgary for their

consistent academic support and advice.

I also specially thank my wife, daughter and family for their moral support.

v

DEDICATION

I dedicate this achievement to my family in Calgary and Nigeria especially to my wife,

daughter, parents and sisters.

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TABLE OF CONTENTS

Abstract ............................................................................................................................... ii

Acknowledgement ............................................................................................................. iv

Dedication ............................................................................................................................v

Table of Contents ............................................................................................................... vi

List of Tables ..................................................................................................................... ix

List of Figures and Illustrations ......................................................................................... xi

List of Symbols, Abbreviations and Nomenclature………………………………….….xix

Chapter One: INTRODUCTION .........................................................................................1

1.1 JUSTIFICATION ..........................................................................................................1

1.2 OBJECTIVES ................................................................................................................5

1.3 GEOLOGICAL BACKGROUND OF STUDY AREA ................................................5

1.3.1 Study Area ..............................................................................................................8

1.4 RESEARCH APPROACH ............................................................................................9 1.4.1 Laboratory Work .....................................................................................................9

1.4.2 Analytical Model Development ..............................................................................9 1.4.3 Petrophysical and Geomechanical Evaluation ......................................................10

1.4.4 Hydraulic Fracturing and Simulation ...................................................................10

1.5 TECHNICAL PUBLICATIONS .................................................................................12

Chapter Two: LITERATURE REVIEW ...........................................................................14

2.1 OVERVIEW ................................................................................................................14

2.1.1 Drill Cuttings ........................................................................................................14 2.1.2 Porosity Exponent (m) ..........................................................................................19 2.1.3 Water Saturation Exponent (n) .............................................................................24 2.1.4 Petrophysical and Geomechanical Evaluation ......................................................28 2.1.5 Hydraulic Fracturing .............................................................................................32

Chapter Three: METHODOLOGY ...................................................................................39

3.1 LABORATORY WORK .............................................................................................39

3.1.1 Sample Collection .................................................................................................40 3.1.2 Microscopic Analysis ...........................................................................................41 3.1.3 Measurable Sample Collection .............................................................................43 3.1.4 Cleaning, Drying, and Weighting of Sample ........................................................45 3.1.5 Porosity Measurement ..........................................................................................46

3.1.6 Screening of Samples Prior to Permeability Measurement ..................................53 3.1.7 Permeability Measurement ...................................................................................53

Chapter Four: POROSITY EXPONENT...........................................................................58

vii

4.1 THE CONCERNS .......................................................................................................58

4.2 USE OF ELECTROMAGNETIC UNIFIED MIXING RULE FOR BUILDING

DUAL AND TRIPLE POROSITY MODELS .........................................................59 4.2.1 Maxwell Garnett Electromagnetic Mixing Rule ...................................................61 4.2.2 Bruggeman Electromagnetic Mixing Rule ...........................................................66

4.2.3 Coherent Potential Electromagnetic Mixing Rule ................................................68

4.3 MODEL DEVELOPMENT .........................................................................................69 4.3.1 Derivation of Maxwell Garnett Mixing Rule Extension to Matrix and Non-

Connected Vugs .....................................................................................................69 4.3.2 Maxwell Garnett Mixing Rule Extension to Matrix and Fractures ......................71

4.3.3 Bruggeman Mixing Rule Extension to Matrix and Non-Connected Vugs ...........72 4.3.4 Coherent Potential Mixing Rule Extension to Matrix and Non-Connected

Vugs .......................................................................................................................74

4.4 MODEL VALIDATION .............................................................................................75

4.4.1 Comparison of Available Models .........................................................................75 4.4.2 Comparison with Core Data .................................................................................83

Chapter Five: WATER SATURATION EXPONENT(n) .................................................91

5.1 THE CONCERNS .......................................................................................................91

5.2 THEORETICAL MODELS.........................................................................................91

5.2.1 Dual Porosity (Matrix and Isolated Porosity) .......................................................93

5.2.2 Dual Porosity (Matrix and Fracture Porosity) ......................................................97 5.2.3 Triple Porosity (Matrix, Isolated and Fracture Porosity) ....................................100

5.3 MODEL VALIDATION ...........................................................................................101

5.3.1 First Step: Single Porosity Reservoirs (matrix porosity) ....................................102 5.3.2 Second Step: Dual Porosity Reservoirs (Matrix and Isolated Porosity or

Matrix and Fracture Porosity) ..............................................................................111 5.3.3 Third Step: Triple Porosity Reservoirs (Matrix, Isolated and Fracture

Porosities) ............................................................................................................118 ..........................................................................................................................................121 Chapter Six: PETROPHYSICAL AND GEOMECHANICAL EVALUATION ............122

6.1 OVERVIEW ..............................................................................................................122

6.2 PETROPHYSICAL EVALUATION BASED ON DRILL CUTTINGS ..................122

6.2.1 Case Study: Drill Cuttings Collected in Horizontal Well ...................................122 6.2.2 Porosity ...............................................................................................................124 6.2.3 Permeability ........................................................................................................125 6.2.4 Pore Throat Aperture Radii .................................................................................125

6.2.5 Porosity Exponent ( ) ........................................................................................127 6.2.6 Irreducible Water Saturation ...............................................................................128

6.2.7 True Formation Resistivity .................................................................................131

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6.2.8 Capillary Pressure ...............................................................................................132 6.2.9 Distinguishing Between Viscous and Diffusion-Like Flow ...............................133 6.2.10 Location of Water Contact ................................................................................135 6.2.11 Flow (or Hydraulic) Units .................................................................................136 6.2.12 Construction of Pickett Plots ............................................................................137

6.3 GEOMECHANICS BASED ON DRILL CUTTINGS .............................................145 6.3.1 Brittleness Index .................................................................................................146

Chapter Seven: HYDRAULIC FRACTURE DESIGN OPTIMIZATION USING DRILL

CUTTINGS ......................................................................................................................157

7.1 HYDRAULIC FRACTURING OF TIGHT GAS RESERVOIRS ............................157

7.1.1 Hydraulic Fracture Design Using Drill Cuttings ................................................158

7.2 MODEL DEVELOPMENT .......................................................................................161 7.2.1 Data Input and Processing ..................................................................................161 7.2.2 Calibration of GOHFER Generated Data with Drill Cuttings Data ...................163

7.2.3 Multi-Stage Hydraulic Fracture Treatment Design ............................................169

7.3 RESULTS ..................................................................................................................171

Chapter Eight: CONCLUSION AND RECOMMENDATIONS ....................................175

8.1 DRILL CUTTINGS ...................................................................................................175

8.2 POROSITY EXPONENT (M) ...................................................................................175

8.3 WATER SATURATION EXPONENT (N) ..............................................................177

8.4 PETROPHYSICAL AND GEOMECHANICAL EVALUATION ...........................178

8.5 HYDRAULIC FRACTURING AND MODELING .................................................179 References ........................................................................................................................181

APPENDIX A: SCREEN SHOTS OF PERMEABILITY MEASUREMENTS USING

DARCYLOG ...................................................................................................................196

APPENDIX B: RELEVANT EQUATIONS ……………………….……………...…..225

APPENDIX C: ANGLE BETWEEN FRACTURES AND DIRECTION OF CURRENT

FLOW………………………………………………………………………..…….…...226

APPENDIX D: WELL CONFIGURATION FOR INITIAL DESIGN………………...227

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LIST OF TABLES

Table 3.1— FRAC VALUE ESTIMATION AT A GIVEN DEPTH FOLLOWING

MICROSCOPIC ANALYSIS OF DRILL CUTTINGS (Adapted from Ortega

and Aguilera, 2012) .................................................................................................. 42

Table 3.2— RESULTS OF LABORATORY WORK ON DRILL CUTTINGS

(DETERMINATION OF POROSITY) .................................................................... 52


(DETERMINATION OF PERMEABILITY) .......................................................... 57

Table 5.1—RESULTS FOR SINGLE POROSITY RESERVOIR WHEN ISOLATED

POROSITY IS EQUAL TO ZERO AND MATRIX POROSITY IS EQUAL TO

THE TOTAL POROSITY ...................................................................................... 104

Table 5.2—RESULTS FOR SINGLE POROSITY RESERVOIR WHEN

FRACTURE POROSITY IS EQUAL TO ZERO AND MATRIX POROSITY IS

EQUAL TO THE TOTAL POROSITY ................................................................. 105

Table 5.3—RESULTS FOR SINGLE POROSITY RESERVOIR WHEN ISOLATED

POROSITY IS EQUAL TO ZERO AND MATRIX POROSITY IS EQUAL TO

THE TOTAL POROSITY ...................................................................................... 107

Table 5.4— RESULTS FOR SINGLE POROSITY RESERVOIR WHEN


EQUAL TO THE TOTAL POROSITY ................................................................. 110

Table 5.5— RESULTS FOR DUAL POROSITY RESERVOIR WITH MATRIX

AND ISOLATED POROSITY ............................................................................... 113

Table 5.6 — RESULTS FOR DUAL POROSITY RESERVOIR WITH MATRIX

AND ISOLATED POROSITY ............................................................................... 114

Table 6.1— PETROPHYSICAL DATA FOR WESTERN CANADA

SEDIMENTARY BASIN TIGHT GAS SANDSTONE. THE HORIZONTAL

WELL POROSITY AND PERMEABILITY DATA FROM DRILL CUTTINGS

(COLUMN 2 & 3) ARE OBTAINED FROM LABORATORY WORK AND IT

IS USED AS A STARTING POINT IN DETERMINING OTHER

PETROPHYSICAL DATA (COLUMN 5 TO 11) USING EMPIRICAL

EQUATIONS. ......................................................................................................... 123

Table 6.2— GEOMECHANICAL DATA FOR WESTERN CANADA



(COLUMN 3) ARE OBTAINED FROM LABORATORY WORK AND IT IS

USED AS A STARTING POINT IN DETERMINING OTHER

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PETROPHYSICAL DATA (COLUMN 4 TO 12) USING EMPIRICAL

EQUATIONS. ......................................................................................................... 148

Table 7.1—BOTTOM HOLE PUMP SCHEDULE ....................................................... 169

Table 7.2— SIMULATION OUTPUT FROM INITIAL MODEL DESIGN BASED

ON SYMMETRICAL DISTANCES FOR HYDRAULIC FRACTURE

INITIATION. .......................................................................................................... 173

Table 7.3— SIMULATION OUTPUT FROM RE-DESIGN MODEL BASED ON

HYDRAULIC FRACTURE INITIATIONS FROM THE CUTTINGS-BASED

CUT-LOG. .............................................................................................................. 174

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LIST OF FIGURES

Figure 1.1— Distribution of world proved oil reserves in 1992, 2002, and 2012

(Adapted from BP Statistical Review of World Energy. June, 2013). ....................... 1

Figure 1.2 — Distribution of world proved natural gas reserves in 1992, 2002, and

2012 (Adapted from BP Statistical Review of World Energy. June, 2013). .............. 2

Figure 1.3—Location of western Canada sedimentary basin and other major

sedimentary basins in North America (Zaitlin and Moslow, 2006). ........................... 6

Figure 1.4—Map of western Canada sedimentary basin (Adapted from Moslow,

University of Calgary Presentation, 2013). ................................................................. 6

Figure 1.5— Stratigraphic framework of the Nikanassin group (Adapted from Stott,

1998; Miles, 2010; and Solano, 2010). ....................................................................... 7

Figure 1.6—Typical wireline log section through the Nikanassin group in the study

area 66-0W6 (Miles, 2010). ........................................................................................ 8

Figure 1.7— Location of Study Area (Red Rock Field) shaded in Light Blue (Adapted

from Solano, 2010). .................................................................................................... 9

Figure 2.1— Example of the use of drill cuttings to analyse shale caving types and

wellbore stability prediction (source: www.geomi.com). ......................................... 16

Figure 2.2—Example of Cut-Log showing the brittleness index, permeability and

Frac-Value (Adapted from Ortega and Aguilera, 2012). .......................................... 18

Figure 2.3—Main sources of data concerning sub-surface rocks (Source: Dr. Paul

Glover, Petrophysics MSc course notes, University of Laval, Quebec, Canada,

2013) ......................................................................................................................... 29

Figure 2.4 —Example of a non-fractured reservoir (upper schematic) and a fractured

reservoir (lower schematic). The upper schematic represents radial fluid flow

(red arrows) into the well (circle) from a smaller area of the reservoir. The lower

schematic represents a hydraulically fractured reservoir that allows linear fluid

flow (red arrows) from a larger area of the reservoir into the fracture and finally

into the wellbore. This leads to an increase in recovery (API, 2009). ...................... 33

Figure 2.5—Example of an open rock with well-rounded ceramic proppants keeping

the fracture open (Adapted from thorsoil.com). ....................................................... 34

Figure 2.6—Example of a multistage hydraulic fracturing operation. Halliburton’s

Swell packer systems isolating various zones of a horizontal wellbore (open

hole) that will be stimulated (Adapted from www.egyptoil-gas.com). .................... 35

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Figure 2.7‒ Example of horizontal well contacting a large area of the reservoir layer.

The vertical well in the right can only contact a smaller area of the reservoir

(Adapted from API, 2009). ....................................................................................... 36

Figure 3.1—Example of drill cuttings under a 10x microscope (Source:

http://en.wikipedia.org/wiki/Drill_cuttings, 2013 ). ................................................. 39

Figure 3.2—Labeled (well name and measured depth) vials containing drill cutting

samples. ..................................................................................................................... 40

Figure 3.3— Identifying structural features through drill cuttings. (a)The upper right

corner shows a planar (flat surface), and unmineralized drill cuttings sample. (b)

The lower right shows drill cutting samples with mineral infill or linings. (c)

Upper left shows loose, clear, euhedral quartz crystal in sandstone. (d) Lower

left shows a fracture set with mineral infill (Adapted from Hews, 2011). ............... 41

Figure 3.4—Chart for visual estimation of percentages of minerals in rock sections.

The interpretation is extended in this work to represent sizes of drill cutting

samples (Terry and Chillingar, 1955). ...................................................................... 43

Figure 3.5—Material safety data sheet for Toluene ......................................................... 46

Figure 3.6—Apparatus for measuring saturated weight of drill cuttings (Adapted from

Ortega, 2012). ........................................................................................................... 47

Figure 3.7—Apparatus for measuring immersed weight based on Archimedes

principle. The Immersed weight is used to determine the bulk volume of the drill

cuttings using Eq. 3.2 (Adapted from Ortega, 2012). ............................................... 50

Figure 3.8— The left side shows the diagram of the spring and bellow system while

the right side shows the Darcylog Equipment (Adapted from Lenormand and

Fonta, 2007). ............................................................................................................. 54

Figure 4.1—Schematic of mixture for spherical inclusions with permittivity εi that

occupy random positions in a host environment of permittivity εe. The mixture

effective permittivity is εeff (Sihvola, 1999). ............................................................. 59

Figure 4.2— Chart for determining m as a function of non-connected vug porosity

(nc) or fracture porosity (2) for the case in which mb= 2.0. Petrophysical model

is developed on the basis of the Electromagnetic Mixing Rule (Maxwell Garnett,

vs = 0). ....................................................................................................................... 64

Figure 4.3— Chart for determining m as a function of non-connected vug

porosity(nc) and fracture porosity(2) for the case in which mb = 2.0.

Petrophysical model developed on the basis of the Unified Electromagnetic

Mixing Rule (Maxwell Garnett, vs = 0). ................................................................... 66

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porosity(nc) for the case in which mb = 2.0. Petrophysical model developed on

the basis of the Unified Electromagnetic Mixing Rule (Bruggeman, vs = 2). .......... 67

Figure 4.5—Chart for determining m as a function of non-connected vug porosity(nc)

for the case in which mb = 2.0. Petrophysical model developed on the basis of

the Unified Electromagnetic Mixing Rule (Coherent Potential, vs = 3). .................. 69

Figure 4.6—Comparison chart for determining m as a function of non-connected vug

porosity (nc) for the case in which mb = 2.0. Petrophysical model developed on

the basis of the Unified Electromagnetic Mixing Rule -Maxwell Garnett( vs = 0),

Bruggeman (vs = 2) and Coherent Potential (vs = 3). ................................................ 76

Figure 4.7— Comparison of dual porosity models made out of matrix and fractures or

matrix and non-connected vugs from various theories show good agreement.

Porosity exponent of the matrix mb = 2.0. Maxwell Garnet and Aguilera’s

equations for calculating m are explicit. Berg’s solution uses an iteration

procedure and for the vugs case assumes an infinite value of mv (in reality it

assumes mv = 1E35 in a spread sheet for the above curves in the right hand side

of the graph). ............................................................................................................. 78

Figure 4.8—Comparison of models based on the Unified Electromagnetic Mixing

Rule (Maxwell Garnett, vs = 0) represented by the solid lines and Berg effective

medium theory (x symbol). Comparison is made for naturally fractured

reservoirs and reservoirs with vugs (mb = 2.0, mv =1.5, mf =1.0). According to

Berg, small values of mv might be indicative of connected (or partially

connected) vugs. ....................................................................................................... 79

Figure 4.9—Comparison of models based on the Electromagnetic Mixing Rule, vs = 0

(solid lines) and Aguilera fracture dip model, θ = 90°- fracture dip (x symbol).

Comparison is made for naturally fractured reservoirs (mb = 2.0, fracture dip,

0°). ............................................................................................................................. 80

Figure 4.10—Comparison of triple porosity models based on the Electromagnetic

Mixing Rule, vs = 0 (solid lines) and Berg’s effective medium theory (x symbol).

Comparison is good (mb = 2.0, mv =1.5, mf =1.0, θ’ = 90°). ..................................... 81

Figure 4.11—Comparison of models based on the Electromagnetic Mixing Rule, vs =

2 (solid lines) and Berg’s effective medium theory (x symbol). Comparison is

for reservoirs with non-connected vugs (mb = 2.0, mv =1.5). ................................... 82


3 (solid lines) and Berg’s effective medium theory (x symbol). Comparison is

for reservoirs with non-connected vugs (mb = 2.0, mv =1.5). ................................... 83

xiv

Figure 4.13—Comparison of limestone core data from well A (Ragland, 2002) and

dual porosity models made out of matrix and fractures developed by Aguilera

and Aguilera (2003), Berg (2006) and this study (Maxwell Garnett, vs = 0).The

open red circles show the absolute error as compared with core data. The mean

absolute percentage error (MAPE) is 1.84%. ............................................................ 85

Figure 4.14—Comparison of limestone core data from well B (Ragland, 2002) and


and Aguilera (2003), Berg (2006) and this study(Maxwell Garnett, vs = 0). The

blue data point enclosed in a red square corresponds to a sample where

approximately 64% of the pore system is dominated by non-connected moldic

pores (Ragland 2002). The MAPE is 7.15% ............................................................. 86

Figure 4.15—Comparison of limestone core data from well J (Ragland, 2002) and



blue data point enclosed in a red square with m = 1.63 shows an error in the

order of 20%. This sample is characterized by a connected moldic pore system

that reduces significantly the value of m (Ragland 2002). The MAPE is equal

7.40%. ....................................................................................................................... 87

Figure 4.16—Comparison of dolomite core data from well C (Ragland, 2002) and



error is generally less than 10%. The MAPE is 4.91%. ............................................ 88

Figure 4.17—Comparison of dolomite core data from well E (Ragland, 2002) and


and Aguilera (2003), Berg (2006) and this study (Maxwell Garnett, vs = 0). The

largest errors correspond to data points enclosed in red squares. These are

dominated by either connected and interparticle pore system (lower values of m)

or non-connected moldic pore systems (larger values of m) (Ragland 2002). The

MAPE is equal to 7.67%. .......................................................................................... 89

Figure 4.18—Comparison of tight gas sandstone core data from wells in the

Mesaverde formation (Byrnes et al., 2006) and triple porosity models made out

of matrix, fractures and slots, and non-connected porosity developed by Al-

Ghamdi et al. (2011), Berg (2006) and this study(Maxwell Garnett, vs = 0). The

error is generally less than 10%. The MAPE is equal to 3.58% .............................. 90

Figure 5.1— Comparison of Eq. 5.19 for matrix and isolated porosity using nc = 0

and preferentially oil-wet core data published by Sweeney and Jennings (1960).

The blue diamonds represent core data, the black open diamonds represent other

data from the dual porosity model used to match the core data. All the core data

points are matched. The red squares correspond to data calculated for illustration

purposes in Table 5.3 for samples 1 to 5. ............................................................... 108

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Figure 5.2— Comparison of Eq. 5.33 for matrix and fractures using 2 = 0 and

preferentially water-wet core data published by Sweeney and Jennings (1960).

The blue diamond’s represent core data, the black open diamonds represent other

data from the dual porosity model used to match the core data. All the core data

points are matched. The red squares correspond to data calculated for illustration

purposes in Table 5.4 for samples 1 to 5. ............................................................... 111

Figure 5.3— Graph of versus developed with the use of the dual porosity

model for matrix and isolated porosity (Eq. 5.17). The chart shows the effects of

increasing isolated porosity (PHINC) on while keeping matrix porosity

constant at b = 0.315 Matrix and composite system (vugs+matrix) are oil wet. .. 113


model for matrix and fractures (Eq. 5.32). The chart shows the effects of

increasing fracture porosity (PHI2) on while keeping matrix porosity constant

at b = 0.315 Matrix and composite system (matrix plus fractures) are water wet. 115

Figure 5.5— Plot of versus for a dual porosity model made up of matrix and

isolated porosity (red squares) and comparison with core data (single porosity

model). For the same resistivity index, water saturations are smaller in the case

of the dual porosity model. Matrix and the composite system (matrix + vugs) are

oil wet. ..................................................................................................................... 116


fracture porosity (red squares) and comparison against core data (single porosity

model). For the same resistivity index, water saturations are larger in the case of

the dual porosity model for the example at hand. The slope values indicate that

the matrix and the composite system are preferentially water wet. ........................ 118

Figure 5.7— Graph of versus using Eqs. 5.34 and 5.35 for the case of a triple

porosity model. The chart shows the combined effects of isolated porosity and

fracture porosity on Matrix porosity (b) is maintained constant at 0.315 in

this case. .................................................................................................................. 120

Figure 5.8— Graph of versus calculated for a triple porosity model (red

squares). The calculated results are compared against core data represented by

black squares (single porosity model). For the same resistivity index the water

saturation of the triple porosity model is generally larger than Sw from cores

(single porosity). ..................................................................................................... 121

Figure 6.1—Plot of porosity exponent ( versus porosity ( . The porosity

exponent was determined using Byrnes empirical correlation (Eq. 6.2). ............... 128

Figure 6.2— Buckles plot. The red circles represent porosity and permeability data

from drill cuttings. Lines of constant permeability are represented by solid lines.

The red circles and solid lines are determined using Eq. 6.4. The dashed lines

xvi

represent the constant values of the product of porosity and irreducible water

saturation also known as Buckles number. All water saturations are irreducible

since the wells have not produced any water for several years. ............................. 130

Figure 6.3— Plot of capillary pressure (Pc) vs. irreducible water saturation (Swi). Pc

was determined using Eq. 6.7 and Swi was obtained using Eq. 6.4 based on

knowledge of porosity and permeability from drill cuttings................................... 133

Figure 6.4—Chart for estimating pore throat apertures on the basis of permeability

and porosity. The green triangular symbols represent data obtained from drill

cuttings. Nikanassin flow units are dominated by microports. Source of template:

Aguilera (2003). ...................................................................................................... 137

Figure 6.5— Pickett plot including lines of constant water saturation. The black

circles represent drill cuttings data from a horizontal well drilled in the

Nikanassin group of the WCSB. ............................................................................. 141

Figure 6.6— Pickett plot including lines of constant water saturation and constant

permeability. The black circles represent drill cuttings data from a horizontal

well drilled in the Nikanassin group of the WCSB. ................................................ 141

Figure 6.7—Pickett plot including lines of constant water saturation, constant

permeability, and constant capillary pressure. The black circles represent the

drill cuttings data from a horizontal well drilled in the Nikanassin Group of the

WCSB. .................................................................................................................... 142


permeability, and constant pore throat radius. The black circles represent drill

cuttings data from a horizontal well drilled in the Nikanassin group of the

WCSB. .................................................................................................................... 142


permeability and constant height above the water contact. The black circles

represent drill cuttings data from a horizontal well drilled in the Nikanassin

group of the WCSB. ................................................................................................ 144

Figure 6.10—Pickett plot including constant lines of water saturation and constant

Knudsen number. The black circles represent drill cuttings data from a

horizontal well drilled in the Nikanassin group of the WCSB. .............................. 145

Figure 6.11—Plot of ( ) versus ( ) for the Nikanassin formation using data

from an offset vertical well (Ortega and Aguilera, 2012). ...................................... 149

Figure 6.12—Cross plot of Young Modulus (YM) versus Poisson’s ratio (PR). The

porosity and bulk density values from drill cuttings (WCSB) were used as input

data in calculating the YM and PR using Eq.6.22 and Eq. 6.27 respectively. ........ 152

xvii

Figure 6.13—Empirical log-log cross plot of porosity from drill cuttings versus

Poisson’s ratio (PR) results in a nearly straight line (R2 = 0.9999). Thus porosity

can be used for obtaining a reasonable estimate of Poisson’s ratio in those cases

where compressional and shear velocities are not available. .................................. 155

Figure 7.1— Example of fracture network created by hydraulic fracturing operation

(Source: fracfocus.org, 2013).................................................................................. 157

Figure 7.2— Track 2 shows a good comparison between drill cuttings data (DTC-

Lab-Dark blue line between the depth interval of 3095-3205m MD) and DTC-

Sonic Log(Green).The track scale is 120-420 us/m.(Adapted from Ortega et al.

2012). ...................................................................................................................... 159

Figure 7.3 — Wellbore survey for horizontal Well A 3953 MD / 3115m TVD and

reference Well B 3240m MD / 3192m TVD. ......................................................... 163

Figure 7.4 — Calibration of compressional travel time DTCGR from GOHFER

(orange Line) with DTCLab extracted from drill cuttings (blue line). The 2

curves are shown in Track 2. .................................................................................. 165

Figure 7.5 — Calibration of Poisson’s ratio PRGR from GOHFER (orange Line) with

PRLab (blue line) extracted from drill cuttings. The 2 curves are shown on Track

2. .............................................................................................................................. 166

Figure 7.6 — Calibration of dynamic Young Modulus YMEGR from GOHFER

(Orange Line) with YMELab (pink line). The 2 curves are shown on Track 2...... 167

Figure 7.7— Example of grid setup showing grid properties such as total closure

stress, brittleness factor, permeability and static young modulus . The reference

well (well B) data was used to populate the grid properties from surface to

3225m MD while the remaining depth interval to 3950m MD that represents the

horizontal section was populated using the horizontal well (well A) data. ............ 168

Figure 7.8 — Cut-Log with three parameter tracks ranging from 3200 to 3900m MD.

Track 1 is the brittleness index, track 2 is permeability and track 3 is the Frac-

Value. Higher values of all three parameters are desired but two high values are

still acceptable. The blue color represents the zones suitable for optimum

fracture initiation and the color intensity is intentionally related to better

conditions. ............................................................................................................... 170

Figure 7.9—Comparison of cumulative gas production profile between the Initial

Design and the Re-design case using Cut-Log. The two cases involved a seven

stage fracture treatment but the fracture initiation zones for the two cases are

different. The Re-design case shows a better performance for the 364 days of

production forecast; these performance shows that selecting symmetrical

distances for hydraulic fracture initiation, as done commonly in the oil and gas

industry due to data scarcity, is not optimum. Better performance is obtained

xviii

selecting those zones with high brittleness index, permeability and Frac-Value in

the Cut-Log, parameters obtained from drill cuttings in this study. ....................... 172

xix

LIST OF ABBREVIATIONS, NOMENCLATURE, AND SYMBOLS

Nomenclature

A = Empirical parameter function of saturation (Kwon et al 1975)

a = Constant in formation factor equation, dimensionless

A= Function of water saturation in Pickett and Kwon empirical equation

B = Empirical parameter in permeability correlation

BRITi = Brittleness Index, dimensionless

BV = Bulk Volume, cubic centimeter

C = Degrees Celsius

C = Parameter function of type of fluid (Morris et al. 1967)

constant1= Empirical constant (A determination)

constant2 = Empirical constant (A determination)

DT= Wave traveling delta time, (μs/m) and (μs/ft)

DTC =Compressional wave slowness (μs/m) and (μs/ft)

DTCGR =Compressional wave slowness from gamma ray data (μs/m) and (μs/ft)

DTCLab =Compressional wave slowness from drill cuttings (μs/m) and (μs/ft)

DTf = Fluid Compressional slowness, (μs/m) and (μs/ft)

DTma = Matrix Compressional slowness (μs/m) and (μs/ft)

DTS= Shear wave slowness, (μs/m) and (μs/ft)

F = Formation factor, dimensionless

f = Volume fraction of the spherical inclusion

G =Rigidity Modulus, (psi) and (GPa)

xx

I = Resistivity Index, dimensionless

k = Absolute permeability, md

kx= Absolute permeability in x direction, md

ky= Absolute permeability in y direction, md

kz= Absolute permeability in z direction, md

Kn =Knudsen number, dimensionless

L = Characteristic length (Knudsen number calculation), m

m = Triple/dual porosity exponent for the reservoir, dimensionless

mb= Matrix block porosity exponent attached only to the matrix system, dimensionless

mf = Fracture block porosity exponent attached only to the fracture system, dimensionless

n = Water saturation exponent, dimensionless

nb = Water saturation exponent attached only to the matrix system, dimensionless

nb’ = Water saturation exponent in electromagnetic mixing rule triple porosity formula

NA= Avogadro's constant, 1/mol

Pc = Capillary pressure, psi

PHI = Porosity, fraction

PR = Poisson's Ratio, fraction

PRGR = Poisson's Ratio from gamma ray data, fraction

PRLab = Poisson's Ratio from drill cuttings, fraction

PRbrit = Poisson’s Ratio brittleness term, fraction

r = Radius of a capillary tube, μm

r35 = Winland's average pore throat radius at 35th percentile mercury saturation, μm

xxi

Rg= Universal gas constant, Pa.m3/mol.K

rp35= Average pore throat radius at 35% mercury saturation, microns

Rt = True resistivity of a porous media at a brine saturation ( , (Ω.m)

= Resistivity of the matrix system at reservoir temperature when it’s 100% saturated

with water of resistivity , (Ω.m)

= Water resistivity at reservoir temperature, (Ω.m)

= Resistivity of the spherical inclusions (water phase)

= Resistivity of the composite system at reservoir temperature when it’s 100%

saturated with water of resistivity , (Ω.m)

= Resistivity of the composite system (matrix and fractures) at θ= 0 when it’s 100%

saturated with water of resistivity , (Ω.m)

= Resistivity of the composite system (matrix and fractures) at θ= 90 when it’s

100% saturated with water of resistivity , (Ω.m)

Rw = Water resistivity, ohm.m

Sirr = Irreducible Water Saturation, fraction

Sw = Water Saturation, fraction

Swi = Irreducible Water Saturation, fraction

Swirr= Irreducible Water Saturation, fraction

Sw = Water saturation, fraction

Swb = Water saturation attached only to the matrix system, fraction

Swnc = Water saturation attached only to the isolated porosity system, fraction

Sw2 = Water saturation attached only to the fracture porosity system, fraction

xxii

Swb’ = Water saturation in electromagnetic mixing rule triple porosity formula; the water

saturation of nb’, fraction

T = Temperature, K

V = Sonic wave velocity, ft/s

Vc = Compressional wave velocity, ft/s

Vs = Shear wave velocity, ft/s

v = partitioning coefficient, fraction

vnc= Lucia’s isolated porosity ratio, fraction

vs = Sihvola dimensionless parameter in unified mixing formula

YM = Young's Modulus, (psi) and (GPa)

YMbrit =Young’s Modulus Brittleness term, fraction

YMd= Dynamic Young’s Modulus, (psi) and (GPa)

YMEGR= Dynamic Young’s Modulus from gamma ray data, (psi) and (GPa)

YMELab= Dynamic Young’s Modulus from drill cuttings, (psi) and (GPa)

YMs= Static Young’s Modulus, (psi) and (GPa)

YMs_max= Maximum Static Young’s Modulus, (psi) and (GPa)

YMs_min = Minimum Static Young’s Modulus, (psi) and (GPa)

Greek Symbols

= Permittivity

εi = Permittivity for spherical inclusions

εe = Permittivity for background material (host)

xxiii

εeff =Effective permittivity of the mixtures

= Real part of the dielectric permittivity

θ = Aguilera’s, angle between fracture and current flow direction

= Bulk density, g/cm3

= Conductivity

= Conductivity for spherical inclusions

= Conductivity for background material (host)

= Conductivity of mixtures (composite system)

= Conductivity of water phase

= Conductivity of the composite system (matrix and fractures) in parallel at θ= 0

= Conductivity of the composite system (matrix and fractures) in series at θ= 90

σ = Interfacial tension, dyne/cm

σh = Minimum in-situ horizontal stress, psi

σH = Maximum in-situ horizontal stress, psi

σv = Vertical stress or overburden stress, psi

δ = Collision diameter, m

θ = Interface contact angle, degrees

θ’ = Berg’s angle that the current makes with the normal to a fracture

λ = Molecular mean free path, m

π= Pi number, dimensionless

μ = Viscosity, mPa.s

= Porosity from laboratory test on drill cuttings, fraction

ϕ = Total porosity, fraction

xxiv

ϕb =Matrix block porosity attached to the bulk volume of the matrix system, fraction

ϕ2 = Fracture block porosity attached to the bulk volume of the composite system,

fraction

ϕm = Matrix block porosity attached to the bulk volume of the composite system, fraction

ϕnc = Isolated block porosity attached to the bulk volume of the composite system,

fraction

= Angular frequency

Abbreviations

API= American Petroleum Institute

ASCII= American Standard Code for Information Interchange

GFREE=Geoscience, Formation Evaluation, Reservoir Drilling, Completion and

Stimulation, Reservoir Engineering, Economics and Externalities

LHS= Left Hand Side

RHS= Right Hand Side

PHINC= Isolated Porosity

PHI2= Fracture Porosity

WCSB= Western Canada Sedimentary Basin

1

Chapter One: INTRODUCTION

1.1 Justification

As at the end of 2012 the total world proved oil reserves stood at 256.33 billion cubic

metres (Fig. 1.1) and the total world proved natural gas reserves at 187.3 trillion cubic

meters (Fig. 1.2). This proved reserves of oil and natural gas represents the quantities

found both in conventional and unconventional petroleum reservoirs. Proved reserves of

oil and natural gas are generally defined as those quantities that geological and

engineering information indicate with reasonable certainty can be recovered in the future

from known reservoirs under existing economic and operating conditions (BP Statistical

Review of World Energy, June, 2013).

Figure 1.1— Distribution of world proved oil reserves in 1992, 2002, and 2012

(Adapted from BP Statistical Review of World Energy. June, 2013).

2

Figure 1.2 — Distribution of world proved natural gas reserves in 1992, 2002, and

2012 (Adapted from BP Statistical Review of World Energy. June, 2013).

As evidenced in Fig. 1.1 and Fig. 1.2 the quantity of proved oil and natural gas reserves

continues to increase from year to year due to technological advancements. However,

significant challenges remain especially in quantitative evaluation of conventional and

unconventional petroleum reservoirs. Some of the questions this research addresses for

contributing to the solution of these challenges include: (1) Is there an alternate and

reliable direct source of information, apart from well logs, seismic data, or core data,

which can be added for quantitative formation evaluation?, (2) how does the porosity

exponent (m) change with depth in reservoirs with complex pore structures?, (3) what is

the water saturation exponent (n) in heterogeneous reservoirs with mixed wettability?,

and (4) in the absence of well logs and/or core data, is it still possible to design an

3

hydraulic fracture model that will improve the success probabilities of the stimulation

job?.

The answers to these questions will help to increase the accuracy of reservoir properties

required for determining petroleum reserves in conventional and unconventional

reservoirs. This will also serve as a means of improving recovery from challenging

reservoirs, hence reducing the number of unproven reserves.

Therefore, the justification for this thesis is to address these challenges (question 1 to 4)

and offer possible solutions. It does so by considering that all hydrocarbons and reservoir

types can be integrated under the umbrella of ‘Total Petroleum Systems’. That is the

premise for being able to integrate in this thesis conventional and unconventional

reservoirs. Aguilera (2010, 2013) set up the stage for this integration by considering flow

units: from conventional to tight gas to shale gas to tight oil to shale oil reservoirs, as a

means for characterizing these types of reservoirs and estimating potential production

rates.

An excellent explanation of the Petroleum System has been presented by Magoon and

Beaumont (1999). “The Petroleum System is a unifying concept that encompasses all of

the disparate elements and processes of petroleum geology including a pod of active

source rock and all genetically related oil and gas accumulations.”

The Petroleum System includes all the geologic elements and processes required for an

oil and gas accumulation to exist. The word ‘petroleum’ includes high concentrations of

4

any of the following substances: (1) Thermal and biological hydrocarbon gas found in

conventional reservoirs as well as in unconventional reservoirs (gas hydrates, tight

reservoirs, fractured shale, and coal). (2) Condensates. (3) Crude oils. (4) Natural

bitumen. The word ‘system’ describes the interdependent elements and processes that

form the functional unit that creates hydrocarbon accumulations.

Magoon and Beaumont (1999) indicate that the essential elements of a Petroleum System

include the following: (1) Source rock. (2) Reservoir rock. (3) Seal rock. (4) Overburden

rock. The Petroleum System includes two processes: (1) Trap formation. (2) Generation–

migration–accumulation of hydrocarbons. These essential elements and processes must

be correctly placed in time and space so that organic matter included in a source rock can

be converted into a petroleum accumulation. A Petroleum System exists wherever all

these essential elements and processes are known to occur or are thought to have a

reasonable chance or probability to occur (Aguilera, 2013).

The segments of the Total Petroleum System described above, dealing with conventional

oil in carbonate reservoirs and natural gas in tight reservoirs are the primary concern of

this thesis. The significant paradigm shift is that tight rocks that could not produce any

petroleum in the past or were nearly impermeable ‘seals’ are now economic reservoir

rocks (Aguilera, 2013).

5

1.2 Objectives

Part of the objectives of the GFREE (Geoscience, Formation Evaluation, Reservoir

Drilling, Completion and Stimulation, Reservoir Engineering, Economics and

Externalities) research group at the University of Calgary is to understand the reservoir

rocks through their characterization, and develop new petrophysical models and concepts

to facilitate optimal recovery of petroleum from challenging reservoir rocks.

As continuation of the GFREE research program, the primary objectives of this research

are to:

Extend the use of drill cuttings-based petrophysical and geomechanical evaluation

methods to a horizontal well that penetrates a tight gas reservoir.

Develop new petrophysical models for calculating the porosity exponent (m) in

dual and triple porosity reservoirs.

Develop new petrophysical models for calculating the water saturation exponent

(n) in dual and triple porosity reservoirs with mixed wettability.

Design a multi-stage hydraulic fracture model using drill cuttings data to improve

recovery from the Nikanassin formation

1.3 Geological Background of Study Area

Zaitlin and Moslow (2006) reviewed the deep basin gas reservoirs of the western Canada

sedimentary basin (WCSB) as shown in Fig. 1.3 and Fig.1.4. The western Canada deep

basin is mapped northward from the United States-Montana border into the northeastern

part of British Columbia, Canada. This is a regional extensive hydrocarbon saturated

6

area, abnormally pressured, thermally matured, composed of Mesozoic to Paleozoic

clastics rocks with low permeability and little or no water production.

Figure 1.3—Location of western Canada sedimentary basin and other major

sedimentary basins in North America (Zaitlin and Moslow, 2006).

Figure 1.4—Map of western Canada sedimentary basin (Adapted from Moslow,

University of Calgary Presentation, 2013).

7

The Nikanassin rocks in the WCSB are dominated by a sandstone sequence. The

Nikanassin spreads above the Fernie shale and below the Cadomin conglomerate

(Mackay, 1930; Stott, 1998). The Nikanassin Group represents a significant tight gas

resource and is composed by the following three formations: Monteith, Beattie Peaks,

and Monach (Fig. 1.5 and Fig. 1.6). The horizontal well evaluated in this study

penetrates the Monteith formation and the collected drill cutting samples are also from

this same formation. The Monteith formation is the oldest of the three and generally

decreases in thickness from west to east. It is made up of a succession of very fine to fine

grain sandstones but has variable amounts of coarser grained quartzose sandstone,

siltstone, mudstone and carbonaceous rocks (Stott, 1998; Solano, 2010). Detailed

description of this formation was done by Solano (2010).

Figure 1.5— Stratigraphic framework of the Nikanassin group (Adapted from Stott,

1998; Miles, 2010; and Solano, 2010).

8

Figure 1.6—Typical wireline log section through the Nikanassin group in the study

area 66-0W6 (Miles, 2010).

1.3.1 Study Area

With the aid of stratigraphic correlation and mapping of three major coarsening-up,

siliciclastic sequences, the Monteith formation was divided into Red rock, Wapiti and

Knopcik field (Miles, 2009, 2010; Solano, 2010). The study area for the present work is

in the Red Rock Field in Alberta (Canada) where drill cuttings were collected at different

depths in the horizontal well (referred as well A in Chapters 3 and 7 ) (Fig. 1.7).

9

Figure 1.7— Location of Study Area (Red Rock Field) shaded in Light Blue

(Adapted from Solano, 2010).

1.4 Research Approach

The research work in this thesis can be summarised under four main components listed

below:

1.4.1 Laboratory Work

Carry out laboratory measurement on drill cuttings to determine porosity and

permeability.

1.4.2 Analytical Model Development

Develop new petrophysical models to estimate the porosity exponent (m) in dual

and triple porosity reservoirs using electromagnetic mixing rules.

10

Develop new petrophysical models to estimate the water saturation exponent (n)

in dual and triple porosity reservoirs with mixed wettability using electromagnetic

mixing rules.

Both m and n exponents in Archie’s equation used for determining the formation factor

and water saturation.

1.4.3 Petrophysical and Geomechanical Evaluation

Use drill cuttings data to perform complete petrophysical and geomechanical

evaluations of a horizontal well that penetrates a tight gas Nikanassin reservoir.

1.4.4 Hydraulic Fracturing and Simulation

Use drill cuttings data to design a multi-stage hydraulic fracture model to

optimize production from a tight gas reservoir and simulate production for 364

days.

The above topics are discussed in this thesis throughout seven chapters. Chapter One (this

chapter) presents an introduction to drill cuttings, petrophysical, and geomechanical

models for evaluation of conventional and unconventional petroleum reservoirs.

Chapter Two discusses an overview of the work done by several researchers and can be

broadly grouped into five categories: (1) Drill cuttings, (2) Porosity exponent, (3) Water

11

saturation exponent, (4) Petrophysical and geomechanical evaluation, and (5) Hydraulic

fracturing and simulation

Chapter Three discusses the methodology used in the laboratory at the University of

Calgary to determine porosity and permeability from drill cuttings samples. Results are

also presented in this chapter.

Chapter Four develops new petrophysical methods with the use of electromagnetic

mixing rules for determining the porosity exponent (m) in reservoirs represented by dual

(matrix and non-connected vugs or matrix and fractures) and /or triple porosity models

(matrix, fractures and non-connected vugs). This chapter also includes the models

validation with core data from carbonate and tight gas reservoirs.

Chapter Five also uses electromagnetic mixing rules to develop new petrophysical

models capable of estimating the water saturation exponent ( ) in heterogeneous

reservoirs with mixed wettability. The reservoirs are represented by dual porosity (matrix

and fractures or matrix and isolated porosity) and triple porosity (matrix, fractures and

isolated porosity) models. This chapter also include the model validation with core data

from preferentially oil-wet and water-wet reservoirs.

Chapter Six presents a case study on petrophysical and geomechanical evaluation of

horizontal wells in the tight gas Nikanassin Group of the WCSB using drill cuttings.

Their utilization as an aid in performing complete quantitative petrophysical and

12

geomechanical evaluations is also discussed. This includes measurements in the

laboratory of porosity and permeability, which allow determining pore throat apertures,

capillary pressures, irreducible water saturation, porosity exponent (m), true formation

resistivity, location of water contact, Knudsen’s number, Young Modulus, Poisson’s

ratio, and brittleness index.

Chapter Seven discusses the application of hydraulic fracturing as a means of optimizing

production from tight gas reservoirs using drill cuttings. Two cases are compared: One

with and one without the use of drill cuttings for selecting fracture initiation zones in a

horizontal well drilled in the lower Nikanassin Group of the western Canada sedimentary

basin.

Chapter Eight contains a summary of the thesis’s finding, conclusions and

recommendations.

1.5 Technical Publications

Parts of this research work have been accepted for presentation at the following

international conferences:

Olusola, B. K., Yu, G., Aguilera, R. 2012. The Use of Electromagnetic Mixing

Rules for Petrophysical Evaluation of Dual and Triple Porosity Reservoirs. Paper

SPE 162772-PP presented at the SPE Canadian Unconventional Resources

Conference., Calgary, Canada. Oct - Nov. In press: SPE Reservoir Evaluation &

Engineering-Formation Evaluation

13

Olusola, B. K, Aguilera, R. 2013. How to Estimate Water Saturation Exponent in

Dual and Triple Porosity Reservoirs with Mixed Wettability. Paper SPE 167213-

MS prepared for SPE Canadian Unconventional Resources Conference., Calgary,

Canada. Oct - Nov.

Olusola, B. K, Aguilera, R. 2013. A Case Study on Formation Evaluation of

Horizontal Wells in the Tight Gas Nikanassin Group of the Western Canada

Sedimentary Basin Using Drill Cuttings. Paper SPE 167214-MS prepared for SPE

Canadian Unconventional Resources Conference., Calgary, Canada. Oct - Nov.

14

Chapter Two: LITERATURE REVIEW

2.1 Overview

This chapter presents an overview of the work done by several researchers and can be

broadly grouped into five categories: (1) Drill cuttings, (2) Porosity exponent, (3) Water

saturation exponent, (4) Petrophysical and geomechanical evaluation, and (5) Hydraulic

fracturing and simulation. In reality, there are interdependencies between each of these

five categories but for the purpose of this thesis, each category is treated as a distinct

topic in order to provide the reader with a basic overview of the impact of each category

on petroleum reservoirs.

2.1.1 Drill Cuttings

Drill cuttings are produced as the rock is broken by the action of the drilling bit

advancing through rock or soil. The cuttings are usually carried to the surface by drilling

fluid circulating up from the drill bit to the surface. Drill cuttings are separated from the

drilling fluid at the surface using shale shakers, de-sanders and de-silters.

At the rig site, drill cuttings are commonly monitored and examined by mud loggers, mud

engineers, pore pressure specialists and other on-site personnel. These professionals make

a record (a well log) of the formations penetrated at various depths; and various

properties including among others drill-cuttings composition, size, shape, color, texture,

and hydrocarbon content (http://www.glossary.oilfield.slb.com, 2013).

http://www.glossary.oilfield.slb.com/

15

In the petroleum industry, this record is often called a mud log. The quality of mud

logging data is highly dependent on the well site personnel technical skills and

experience. The quality of the mud log data can be improved through detailed cutting

selection and analysis. Many visual inspections are focused on the large cutting samples

because they are the easiest to manipulate with tweezers and picks but in reality, the

larger drill cuttings samples may not be representative of the interval of interest due to

many factors including lack of structural features that indicates the presence of vugs or

fractures, this structural features will be explained further in chapter two (Georgi et al.,

1993). Based on experiments performed by GFREE members at the University of

Calgary, drill cuttings samples equal to or greater than 1mm can provide representative

values of porosity and permeability for the intervals of interest.

Mud log data provides direct source of information about the formation and helps to

answer certain questions that well logs data cannot explain during formation evaluation.

Fig. 2.1 shows how shapes of drill cutting samples are used to predict the sub-surface

stress and recommends solutions to avoid wellbore stability problems during drilling

operations, for example platy or tabular caving samples at the shale shakers may indicate

the drill bit has penetrated a weakly bedded or fissile subsurface rock

16

Figure 2.1— Example of the use of drill cuttings to analyse shale caving types and

wellbore stability prediction (source: www.geomi.com).

2.1.1.1 Drill Cuttings based Formation Evaluation

High quality formation evaluation data is critical for successful development of oil and

gas fields especially in tight gas reservoirs where this information is required as input

data for building hydraulic fracturing models. Formation evaluation data assists in

identifying zones that are brittle, permeable and suitable for stimulation in order to

improve oil and gas recovery.

Historically, the methods used to obtain petrophysical formation evaluation data has been

limited to well logs and cores but recently, advances in technology have made the use of

17

drill cuttings possible for obtaining formation evaluation data. An example is provided by

the Darcylog; an equipment designed by the French Institute of Petroleum (IFP) that uses

the liquid pressure pulse method for determining permeability from drill cuttings.

The Darcylog equipment ensures effective flow inside the cuttings by compression of the

residual gas that the drill cuttings contain. The equipment is especially suited for

measuring permeability in reservoir rocks that cannot be measured by gas pressure test

(Lenormand and Fonta, 2007). The Darcylog, explained in chapter three is used for the

experimental work carried out in this thesis.

Talabani and Thamir (2004) designed equipment (Portable Permeameter) that allows

measuring vector permeability in a piece of drill cutting. The recommended average size

of drill cutting samples is 0.32 x 0.5 x 0.5 cm. According to Talabani and Thamir (2004),

three points are chosen and marked perpendicular to each other to measure permeability

of the drill cutting sample. The three points represents permeability in three directions

(kx, ky, and kz). Once the permeability measurement is completed after injecting gas

through a probe at certain pressure, two permeability measurement will be close or

identical (plane k: kx and ky) while the last permeability measurement will be different

(kz).

Drill cuttings can also detect micro fractures in some cases but most of the in-situ micro

fractures and slot porosities are destroyed by the action of the bit during drilling

operations (Ortega and Aguilera, 2012). Micro fractures, when present in large quantities,

can significantly improve fluid flow into the wellbore from the reservoir. Hews (2012)

recommends a staining technique such as the use of Rhodamine B dye to identify micro

18

fracture porosity in drill cuttings. Hews (2012) also presents procedures to evaluate drill

cuttings and identify structural features using a standard binocular microscope. Some of

the features that can be identified include fracture sets with mineral lining, fracture sets

with planar, unmineralized surfaces, brecciation, micro faulting, slickensides,

crenulations in shales, and loose mineral crystals.

Ortega and Aguilera (2012) adapted the drill cuttings evaluation procedure of Hews

(2012) to develop the Cut-Log. The Cut-Log is made of three main parameters

(brittleness Index, permeability and Frac Value) that can be used as a guide in selecting

optimum locations for initiating hydraulic fractures in vertical and horizontal wells. An

example of the Cut-Log is presented in Fig 2.2. The shades of green show the optimum

locations for performing multi-stage fracturing in a Nikanassin horizontal well.

Figure 2.2—Example of Cut-Log showing the brittleness index, permeability and

Frac-Value (Adapted from Ortega and Aguilera, 2012).

19

Egermann et al. (2004), Lenormand and Fonta (2007); Solano (2010); Ortega (2012); and

Zambrano (2013) have used drill cuttings to effectively characterize tight gas sandstone

and carbonate reservoirs. In a recent work by Ortega (2012) he concluded that in the

absence of well logs and cores; quantitative petrophysical evaluation can presently be

considered a possibility owing to the fact that permeability and porosity can now be

measured directly from drill cuttings. However, his study as well as works by Solano

(2010), and Zambrano (2013) were performed on drill cuttings from vertical and deviated

wells drilled in the tight gas Nikanassin group of the western Canada sedimentary basin.

In the present study the methodology is extended to drill cuttings collected in a horizontal

well drilled in the same formation. The benefit of this work is that it provides direct

information about reservoir properties of the horizontal well to be stimulated using

hydraulic fracturing technology.

2.1.2 Porosity Exponent (m)

Understanding of the role played by vuggy and naturally fractured reservoirs on

hydrocarbon recovery has changed over the past few years as a thorough petrophysical

knowledge of this reservoir properties has helped to improve estimates of hydrocarbons-

in-place and recoveries. This has happened for example in the case of ‘unconventional’

reservoirs.

When conducting petrophysical evaluation in a tight gas reservoir, an accurate value of

the porosity exponent (m) is important because variations in m change significantly the

water saturation values and therefore affect the hydrocarbons-in-place estimates. In

20

general, decrease in m tends to reduce the computed water saturation values. It has been

demonstrated in the literature (Al-Ghamdi et al., 2012) that petrophysical evaluation

techniques that uses a constant porosity exponent for all depths will likely magnify the

errors in the calculated water saturation value especially in tight reservoirs with low

porosity. Laboratory studies by Byrnes et al. (2006) show that m tends to become lower

as porosity decreases in the Mesaverde formation of the United Sates.

Archie (1942) studied a group of core samples and observed that m ranged between 1.8

and 2.0 for consolidated sandstones and that for loosely or partly unconsolidated

sandstone the value of m was as low as 1.3. Archie expressed the formation factor, F, as

follows (Eq. 2.1):

…………………………………………………………..….Eq. 2.1

Towle (1962) investigated the porosity exponent and discovered that one of the reasons m

varies is because of changes on the type of pore system, e.g. inter-granular, inter-

crystalline, vuggy or fractured. Towle’s investigation of reservoirs containing vugs

showed that m values were larger than usual ranging from 2.67 to > 7.3. He concluded

that the vuggier the rock, the higher the value of m.

Lucia (1983, 1992) showed that the porosity exponent of carbonate rocks was related to

particle size, amount of inter-particle porosity, amount of non-connected vug porosity,

and the presence or absence of connected vugs. Lucia defined vuggy porosity as that pore

space larger than or within the particles of rock. A common characteristic was the

presence of leached particles, fractures, and large irregular cavities.

21

Lucia described the interconnectivity of vugs in two general ways: (1) Vugs connected

only through the interparticle/matrix pore network (isolated, non-connected or non-

touching vugs) and (2) Vugs connected to each other (connected or touching vugs).

Values of the porosity exponent were related to a vug porosity ratio (vnc) which he

defined as non-connected vug porosity (non-touching vugs) divided by total porosity. He

further observed that m became larger as the vug porosity ratio increased. This

observation was based on data from the Smackover dolomite in the Bryans Mill field,

Texas; Mississippian dolomite of the Harmattan field, Alberta; Magnolia field and

Quitman field in Texas, and Snipe Lake field in Canada.

In Lucia’s work, the term non-connected vugs refers to vugs that are not touching each

other; but each vug is connected to the matrix pore system, hence making it possible for

the vuggy space to be filled with water or hydrocarbon during migration and

accumulation processes. Non-connected vugs are usually formed through diagenetic

processes by which selective fabric (carbonates and evaporite minerals) is dissolved and

removed, thus creating and modifying pore spaces in reservoir rocks (Lucia, 1992).

Aguilera and Aguilera (2004) developed a triple porosity model for evaluation of

naturally fractured reservoirs. They assumed that the matrix and fractures have

conductivities that are connected in parallel and the combined matrix and fractures are

connected in series with the non-connected vugs. An improved triple porosity model

using the same assumptions was developed by Al-Ghamdi et al. (2011). Values obtained

22

from this model matched reasonably well petrographic work and core data and indicated

that m can be smaller than, equal to or larger than the porosity exponent of only the

matrix system, mb, depending on the contribution of non-connected vugs and fractures to

the total porosity system of the reservoir.

Aguilera and Aguilera (2009, 2010) developed a model for petrophysical evaluation of

dual-porosity naturally fractured reservoirs that included the angle between the fracture

and the direction of current flow, θ, between 0o and 90

o. They used the Maxwell Garnett

mixing formula for calculating effective permittivity of a system with aligned ellipsoids

and depolarization factors equal to 0 and 1 that led to the parallel and series resistance

networks required to establish the matrix and fracture relationships (Eq. 2.2 to Eq. 2.4).

They concluded that the change in angle θ between the fracture and the direction of

current flow had significant impact on the value of m. Their theoretical model was used

as part of the validation of the dual porosity (matrix and fractures) model developed in

this paper.

[

]

( ………………………………………...……………….Eq. 2.2

(

……………………………………………………...Eq. 2.3

( ………....…..…………………..……………Eq. 2.4

Berg (2006) developed an equation that calculates the effects of fractures or vugs on the

total porosity exponent (m) of the composite system for a dual porosity reservoirs using

effective medium theory. He further extended the method to calculate the triple porosity

23

exponent, m. The model works by calculating first the dual porosity exponent, m, for the

combination of matrix (bulk) porosity and vugs using Eq. 2.5 and then using the

calculated dual porosity exponent, m as mb, and the total porosity of the dual porosity

model ϕ as ϕb along with a porosity exponent of only the fractures, mf, to calculate the

triple porosity exponent, m, with Eq. 2.6. Berg’s model has been used as part of the

validation of the dual and triple porosity models based on electromagnetic mixing rules

developed in this thesis.

( (

)

……………………………………….…….Eq. 2.5

……………..……………………………………….Eq. 2.6

Berg’s model is very useful as it allows introduction of the porosity exponents for the

fractures (mf) and vugs (mv). Most generally mf is assumed to be equal to 1.0 but it can

reach as high as 1.2 or 1.3 depending on the amount of fracture tortuosity in the fractures.

When mv is infinite (actually in an excel sheet a very large value, for example mv = 1E35)

Berg’s model provides approximately the same results as other models discussed in this

thesis.

Berg suggests that small values of mv might be indicative of connected vugs where

electric current has to contend with tortuosity of the vugs until the vugs approach the

shape of smooth tubes in which case the porosity exponent would be 1.0 as in the case of

smooth fractures. The problem is that the starting point of effective medium theory

assumes that the inclusions in the host material are not connected. So thinking in terms of

24

connected ‘inclusion’ vugs using the effective medium theory appears contradictory. A

further problem from a practical point of view is thinking in terms of mv for a vug. How

to determine it? What does it mean? The assumption of mv being infinite is intuitively

correct for the unlikely case of truly isolated vugs (how do they form and fill with

hydrocarbons if they are truly isolated? So this is arguably an abstract case. But

additional work in the subject is warranted.

There are also excellent contributions along the same lines by Sen et al. (1981) for

various types of sedimentary rocks and fused glass beads; Rasmus and Kenyon for

ooilitic reservoirs (1985); Focke and Munn (1987) for limestones and dolomites; Lucia

(1983) for carbonates; and Kennedy and Herrick (2004) for non-shaly sandstones. The

new method developed in this thesis for petrophysical analysis can handle with the use of

one single equation the individual mixing rules of Maxwell, Bruggeman and Coherent

potential. The unified equation can further handle matrix, fracture and non-connected vug

porosity as well as calculate the porosity exponent (m) of the total porosity system

represented by dual or triple porosity reservoir systems.

2.1.3 Water Saturation Exponent (n)

One of the key petrophysical parameters when evaluating reserves estimates is water

saturation; water saturation relies on the water saturation exponent (n) and resistivity

index (I) using Archie’s equation (Eq. 2.7)

(

)

…………………………………………………………………Eq. 2.7

25

where is the water saturation, is the resistivity of the porous media when

completely saturated with brine, is the true resistivity of a porous media at a brine

saturation ( , is the resistivity index, and is the water saturation exponent; a

dimensionless empirical parameter (Archie, 1942). The resistivity index ( ) is readily

available from resistivity well logs but the water saturation exponent can only be

correctly determined through laboratory work. The water saturation exponent ( appears

equal to two (2) for clean, consolidated, and water-wet sandstones (Archie, 1942) and has

been assumed equal to two (2) in many petrophysical evaluation methods but in reality n

is not constant but varies as a function of different factors including fluid distribution in

the pore spaces and rock wettability.

Many researchers have conducted experimental work to show that the water saturation

exponent truly varies as a function of the preferential wetting of the porous rock to water

or oil. Donaldson and Siddiqui (1989) performed some experiments on some Berea and

Elgin core samples and found that the water saturation exponent range from less than two

(2) to eight (8). They later concluded that the relationship between wettability and n is

linear and that oil/water/ rock systems have more preference for water as the temperature

is increased.

Sweeney and Jennings (1960) carried out resistivity measurements on some porous

carbonate rocks by varying the amounts of electrolyte and aliphatic hydrocarbon; this was

done to make the carbonate surface either preferentially water wet or oil wet. They

observed that the resistivity data obtained from preferentially water-wet samples were

26

considerably different from the resistivity data obtained from preferentially oil-wet

samples; thereby leading to different n values. The data from of Sweeney and Jennings

(1960) laboratory work have been used to validate the models developed in this thesis.

Morgan and Pirson (1964) examined the effect of fractional wettability on ; they

prepared unconsolidated sand packs in capillary pressure resistivity cells using mixtures

covering the entire wettability spectrum. They saturated each pack with brine and then

displace the packs with oil at progressive stages; at each stage the water saturation value

was measured and the n value for each pack was determined. They recorded n values

ranging from 2.48 to 25.17 at different wettability condition. Therefore, wettability is a

major controlling factor on n.

Wettability is defined as the tendency of a particular fluid to spread on or adhere to a

solid surface in the presence of other immiscible fluids. In a rock/oil/brine system; when

the rock is water-wet; there is a tendency for water to occupy the small pores and also

make contact with most of the rock surfaces. For an oil-wet rock the reverse is true.

When the rock has no strong affinity for either water or oil; the system is defined as

having neutral (or intermediate) wettability (Anderson, 1986).

Apart from oil-wet, water-wet, and neutral-wet systems; there is also another type of

wettability known as fractional wettability in which some parts of the rock have affinity

for water while other parts have affinity for oil (Morgan and Pirson, 1964). The idea of

fractional wettability (also called heterogeneous, spotted, or Dalmatian wettability) was

27

also proposed by Brown and Fatt (1956). Fractional wettability is conceptually different

from intermediate wettability, which assumes that all parts of the rock surface have slight

but equal affinity for either water or oil (Anderson, 1986).

Salathiel (1973) introduced the concept of mixed wettability as a special type of

fractional wettability in which the oil-wet surfaces form continuous paths through the

larger pores. In this condition, the fine pores and grains contacts would be water-wet and

contain no oil while the surfaces of the larger pores would be strongly oil-wet. Mixed

wettability is different from fractional wettability because fractional wettability does not

imply specific locations for the oil-wet surfaces nor continuous oil-wet paths but that a

portion of the rock is strongly water-wet while the rest is strongly oil-wet. Salathiel

(1973) explained that the generation of mixed wettability conditions in the reservoir may

result from the following process: originally water is present in the larger pores, small

capillaries and at grain contacts and the reservoir is water-wet, but as oil accumulates in

the reservoir, it displaces the water from the larger pores while the water in the small

capillaries and at grain contacts are retained due to capillary forces.

As this fluid migration and displacement process continues for a long period of time,

some organic material from the oil will deposit on the rock surfaces in direct contact with

the oil and the larger pores will become strongly oil-wet. This last process results in a

mixed wettability condition. Melrose (1982) and Hall et al. (1983) further describe that

the water films in the originally water-wet reservoir becomes thinner and thinner as more

oil accumulates in the reservoir. At a time when the water film thickness is reduced to a

28

critical thickness, the water film become unstable in the larger pores (only part of the

total pore surface area is affected) after which it will rupture and give way for the

displacing oil to contact the rock.

However, most studies carried out on reservoirs with mixed wettability condition are

laboratory studies with limited work done on estimating using analytical method. To

contribute to the solution of this concern, we utilize electromagnetic mixing rules to

develop new petrophysical models capable of estimating the water saturation exponent

( ) in heterogeneous reservoirs with mixed wettability. The reservoirs are represented by

dual porosity (matrix and fractures or matrix and isolated porosity) and triple porosity

(matrix, fractures and isolated porosity) models. In our petrophysical model, we follow

the concept of mixed wettability proposed by Salathiel, 1973; Melrose, 1982; and Hall et

al., 1983. We assume that the larger pores represent the isolated porosity (non-connected

vugs or isolated porosity) and the small capillaries and grain contacts represent fractures

and matrix porosity respectively.

2.1.4 Petrophysical and Geomechanical Evaluation

2.1.4.1 Petrophysical Evaluation

Petrophysical evaluation can be described as the process of sub-surface data acquisition,

processing and interpretation to detect and quantify oil and gas reserves in the rock

adjacent to a well (Wikipedia, 2013). Petrophysical evaluation techniques are used to

answer basic questions, such as:

What does the reservoir contain: water or hydrocarbons?

29

If hydrocarbons, oil or gas?

How much is there?

Where is it? And how to get it out?

What type of rock is there and what are its properties?

Fig. 2.3 shows the main sources of data used in the oil and gas industry for petrophysical

evaluation. Generally, the more sources of data are available for a particular reservoir the

more accurate and reliable the petrophysical evaluation results.

Figure 2.3—Main sources of data concerning sub-surface rocks (Source: Dr. Paul

Glover, Petrophysics MSc course notes, University of Laval, Quebec, Canada, 2013)

2.1.4.1.1 Archie’s Equation

Archie (1942) introduced empirical equations that became the keystone of log analysis

(See Eq. 2.8 to Eq. 2.10). The equations are still used till date to determine water

saturation in hydrocarbon reservoirs.

30

(

)

…………………………..……………………………………………Eq. 2.8

…………………………………………………………………………...…Eq. 2.9

(

)

…………………………………….………………………………….Eq. 2.10

Archie’s equations produce acceptable results in “clean” (shale free) formations but they

produces questionable results in heterogeneous and complex reservoirs. The application

of Archie’s equation requires knowledge of the parameters in Eqs. 2.8 to 2.10. Most of

the parameters especially the resistivity parameters can be determined from field

measurements and /or log analysis estimations but the porosity exponent (m) and

particularly the water saturation exponent (n) are difficult to estimate in tight formations.

As a result assumed values are assigned based on experience of the petrophysicist or

geoscientist. The problem is that and values can change continuously with depth

especially in heterogeneous and complex reservoirs. Thus the assigned constant value for

the whole reservoir is misleading since it either overestimates or underestimates the water

saturation value. This affects the reserves estimates in conventional and unconventional

petroleum reservoirs.

To accommodate this deficiency, a new petrophysical model is developed in this thesis

using electromagnetic mixing rules proposed by Sihvola (1999). The petrophysical model

allows the estimation of and in reservoirs made up of dual porosity (matrix and

fractures or matrix and isolated porosity) and triple porosity (matrix, fractures and

isolated porosity) systems. These petrophysical models are validated with core data with

31

a good level of accuracy. The models development is explained in detail in chapters four

and five.

2.1.4.1.2 Pickett Plot

Pickett (1973) devised a formation evaluation interpretive technique using cross plots of

log responses. In his approach resistivity is plotted against porosity values on log-log

coordinates. The result is straight lines for zones with constant water saturation (for

example Sw = 100%). Hydrocarbon-bearing intervals fall to the right of the 100% water

saturation line. Pickett’s plot is based on Archie’s (1942) equations (Eq. 2.8 to Eq. 2.10),

which can be rearranged to obtain:

( ………………………………………..Eq. 2.11

The conventional construction of a Pickett plot requires the availability of porosity and

resistivity logs. In this thesis, these logs are not available for the horizontal well under

consideration, and the Pickett plot is built on the basis of data extracted from drill

cuttings. Use of Pickett plot is illustrated in chapter six of this thesis.

2.1.4.2 Geomechanical Evaluation

Geomechanical evaluation of conventional and unconventional reservoirs is used to

predict important rock mechanics parameters, such as in-situ rock stresses, Young

Modulus, Poisson’s ratio and brittleness index. These parameters are useful for designing

hydraulic fracture treatments. Some important work along these lines has been

contributed by Barree et al. (2009) for stress and rock property profiling for

unconventional reservoir simulation; Mullen et al. (2007) for determination of

32

mechanical rock properties for stimulation design in the absence of sonic logs; Aoudia

and Miskimins (2010) for statistical analysis on the effects of mineralogy on rock

mechanical properties of the Woodford shale; and Ortega and Aguilera (2012) for

evaluating the impact of drill cuttings on the design of multi-stage hydraulic fracturing

jobs in tight gas formations. Chapter six of this thesis shows an application of drill

cuttings based geomechanical evaluation to characterize the tight gas reservoir considered

in this study.

2.1.5 Hydraulic Fracturing

The use of hydraulic fracturing technology started in the 1940s (King, 2012). Without

hydraulic fracturing it would have been impossible to recover hydrocarbons such as oil

and gas from tight reservoirs with permeabilities equal to or smaller than 0.1 md (Center

for Energy, 2013). Permeability is a rock property and defines the ability of a fluid to

flow through porous media. This porous media must have interconnected pores for the

fluids to travel through a tortuous path to reach the wellbore. Tight gas reservoirs have

low permeabilities. Without using hydraulic fracturing technology, it is impossible to

recover economically gas or oil from these types of reservoirs (API, 2009).

Hydraulic fracturing removes the skin effect of a wellbore (Economides et. al. 1994),

creating a high conductivity path that covers a long distance and extends from the

wellbore to the hydrocarbon reservoir. This fractured path allows reservoir fluids to flow

more easily from the reservoir, into the fracture, and finally into the wellbore. Fig. 2.4

33

shows a comparison of fluid flow between a well completed without hydraulic fracturing

and a well completed using hydraulic fracturing technology (API, 2009).

Figure 2.4 —Example of a non-fractured reservoir (upper schematic) and a

fractured reservoir (lower schematic). The upper schematic represents radial fluid

flow (red arrows) into the well (circle) from a smaller area of the reservoir. The

lower schematic represents a hydraulically fractured reservoir that allows linear

fluid flow (red arrows) from a larger area of the reservoir into the fracture and

finally into the wellbore. This leads to an increase in recovery (API, 2009).

2.1.5.1.1 Hydraulic Fracturing Process

The hydraulic fracturing process involves injecting specialized fluids down the wellbore

and through perforations in the casing (or open hole) to the reservoir. The fluid is injected

at pressures high enough to cause tensile failure of the rock (Economides et al., 1994).

This process is known as “breaking down” the formation. As additional fluids are

injected at the propagating pressure, the rock continues to open and the fracture continues

to propagate into the reservoir. During this process, measured amounts of proppants, such

as sand, are added into the injected fluid. When the fluid injection is stopped and the

excess pressure is removed, the proppants keep the fractured path open (Fig. 2.5),

34

allowing the oil or gas (also water) to easily flow through the conductive (fractured) path

(API, 2009).

Figure 2.5—Example of an open rock with well-rounded ceramic proppants keeping

the fracture open (Adapted from thorsoil.com).

2.1.5.1.2 Multistage Hydraulic Fracturing

Multistage hydraulic fracturing is shown in Fig. 2.6 and refers to the process whereby

multiple fractures are created along the horizontal section of the wellbore in a

consecutive manner. The operation is carried out by first isolating and fracturing the

deepest segment of the horizontal wellbore, after which the depth before the deepest

segment is treated; this process continues upwards until the last segment (shallowest

depth) is treated (ERCB, 2011).

35

Figure 2.6—Example of a multistage hydraulic fracturing operation. Halliburton’s

Swell packer systems isolating various zones of a horizontal wellbore (open hole)

that will be stimulated (Adapted from www.egyptoil-gas.com).

Ortega and Aguilera (2012) developed a new methodology to improve multistage

hydraulic fracturing design using drill cuttings. This is valuable particularly in those

cases where log and core data are scarce or unavailable. The methodology selects the

optimum locations to initiate each hydraulic fracturing stage.

2.1.5.1.3 Horizontal Wells

Many tight gas reservoirs that are candidates for hydraulic fracturing are drilled using

horizontal well technology. This allows optimum formation area penetration and

maximum gas and oil recovery. The use of horizontal well technology started in the

1930s (King, 2012). Horizontal well technology with directional survey technology

allows drilling multiple horizontal wells from a single surface location, thereby reducing

http://www.egyptoil-gas.com/

36

time spent on moving rigs to different surface locations and reducing the footprint and

environmental problems.

Tight gas reservoirs are candidates for horizontal well technology because horizontal

wells allow a large area of the reservoir to be placed in contact with the wellbore (Fig.

2.7); horizontal wells make it possible to create a complex fracture network in the tight

reservoir using multistage hydraulic fracturing technology.

Figure 2.7‒ Example of horizontal well contacting a large area of the reservoir

layer. The vertical well in the right can only contact a smaller area of the reservoir

(Adapted from API, 2009).

37

2.1.5.1.4 3D Hydraulic Fracture Simulation Software

Robust hydraulic fracture simulation software requires a model that can be used to

analyze, target and optimize hydraulic fracturing design, and predict well production.

Several years ago, simple two-dimensional (2D) models were used in the petroleum

industry to simulate hydraulic fracturing in unconventional reservoirs. The 2D model is

based on the concept that the fluid pumped into the rock is directly related to the fracture

geometry. The limitation of the 2D model is that it imposes unrealistic height restrictions

that are often not representative of the formation.

This limitation led to the development of pseudo three-dimensional (P3D) and fully

three-dimensional (3D) models. The 3D models require more reservoir input data and

greater computational time (Christopher et al. 2007). There are many commercial 3D

models for hydraulic fracturing including Stimplan, Fracpro, and GOHFER (Grid-

Oriented Hydraulic Fracture Extension Replicator). GOHFER is used in this thesis.

GOHFER is a well-known robust simulator used to model complex hydraulic fractures in

tight gas and oil reservoirs. GOHFER is a planar 3D geometry, finite difference hydraulic

fracturing modeling software and has a fully coupled fluid/solid transport simulator.

GOHFER was developed by Dr. Bob Barree & Associates in association with Stim-Lab,

a division of Core Laboratories. GOHFER uses a regular grid structure to describe the

reservoir; this grid structure permits vertical and lateral variations, multiple perforated

intervals as well as single and bi-wing asymmetric fractures to model the most complex

reservoirs. The software is capable of modeling multiple fracture initiation sites

38

simultaneously and shows diversion between perforations. GOHFER handles elastic rock

displacement calculations as well as a planar finite difference grid for the fluid flow

calculations. At each grid cell variables such as pressure, width, fluid composition,

proppant concentration, shear rate, fluid age, viscosity, velocity, and proppant

concentration are defined. The robustness of GOHFER to handle hydraulic fracturing

design, modeling and production forecast makes it a valuable tool in this research

(GOHFER user manual version 8.1.5, 2013).

39

Chapter Three: METHODOLOGY

3.1 Laboratory Work

Due to technology advancements, drill cuttings are gaining recognition and acceptance as

a direct source of information for quantitative petrophysical analysis. Petrophysical data

such as porosity and permeability are now measurable in the laboratory by the GFREE

team at the University of Calgary with minimal error. Fig. 3.1 shows an example of drill

cuttings examined under a microscope that include red, brown and gray shales, limestone,

sand grain, consolidated sand and limestone conglomerate with imbedded glauconitic.

Figure 3.1—Example of drill cuttings under a 10x microscope (Source:

http://en.wikipedia.org/wiki/Drill_cuttings, 2013 ).

This chapter discussed the following laboratory steps leading to the evaluation of drill

cuttings (Adapted from Ortega, 2012):

http://en.wikipedia.org/wiki/Drill_cuttings

40

Sample collection

Microscopic analysis

Measurable sample selection

Cleaning and drying of sample

Porosity measurement

Screening of samples prior to permeability measurement

Permeability measurement

Also, good practice to follow while doing this laboratory work was recommended.

3.1.1 Sample Collection

During drilling operations at the rig site; the mud logger picks samples of drill cuttings at

regular intervals for lithology identification and, generally verifies his/her interpretation

with available well site data such as a gamma ray log. These samples are usually taken at

5m intervals after which they are washed and preserved in vials. To preserve the identity

of the samples, each vial is labeled. The common label information on the vial includes

well name and measured depth (Fig. 3.2).

Figure 3.2—Labeled (well name and measured depth) vials containing drill cutting

samples.

41

3.1.2 Microscopic Analysis

Hews (2009-2012) showed that microscopic analysis of drill cuttings provides

information that permits identification of many structural features including fractures,

vugs, lost circulating materials, and shale beddings .

Figure 3.3— Identifying structural features through drill cuttings. (a)The upper

right corner shows a planar (flat surface), and unmineralized drill cuttings sample.

(b) The lower right shows drill cutting samples with mineral infill or linings. (c)

Upper left shows loose, clear, euhedral quartz crystal in sandstone. (d) Lower left

shows a fracture set with mineral infill (Adapted from Hews, 2011).

Ortega and Aguilera (2012) developed the concept of ‘Frac Value’ using drill cuttings.

The Frac Value represents the mean value of three features obtained through visual

inspection of drill cuttings: (1) Fracture sets with mineral lining. (2) Fracture sets with

planar; unmineralized surfaces. (3) Loose mineral crystals (Table 3.1 and Fig. 3.3).

The Frac Value is expressed in percentage using as a base a chart by Terry and Chillingar

(1955) presented in Fig. 3.4. This allows visual estimation of percentages of drill cutting

42

chips in laboratory. Therefore, microscopic analysis is carried out for each drill cuttings

sample to obtain its Frac Value. This information is compared with a brittleness index

and permeability and the integrated information is useful for identifying fracture

initiation zones during hydraulic fracturing design job. Ortega and Aguilera (2012) used

this concept to show how production can be improved from the Nikanassin formation by

pointing to optimum locations to initiate multi-stage hydraulic fractures in horizontal

wells.

Petrographic work involving thin section image analysis of drill cuttings can also serve as

a means of identifying isolated porosity from drill cuttings.

Table 3.1— FRAC VALUE ESTIMATION AT A GIVEN DEPTH FOLLOWING

MICROSCOPIC ANALYSIS OF DRILL CUTTINGS (Adapted from Ortega and

Aguilera, 2012)

SAMPLE None 1-5% 6-10% 11-15% 15%+

0 1 2 3 4

FEATURE A

FEATURE B

FEATURE B

FRAC_VALUE Mean Value

43

Figure 3.4—Chart for visual estimation of percentages of minerals in rock sections.

The interpretation is extended in this work to represent sizes of drill cutting samples

(Terry and Chillingar, 1955).

3.1.3 Measurable Sample Collection

Obtaining an amount of sample that meets the criteria for porosity and permeability

measurement is important. This step is actually tedious and time consuming but the work

is important as it simplifies other steps that follows in the laboratory procedure by

providing only drill cuttings that can be used for both porosity and permeability

measurements. This laboratory step is divided into two stages:

44

3.1.3.1 Stage 1:

This involves sieving the drill cuttings to remove samples with sizes greater than 5mm

and lower than 1mm from the rest of the samples. To save time, it is important to start

with this sieving process first, previous to the other steps explained below as this helps to

concentrate on samples that meet the criteria for porosity and permeability measurements.

Drill cuttings samples less than 1mm are difficult to handle when removing the excess

brine from the surfaces of the saturated drill cuttings as the small samples tend to enter

into the material (soft paper or sponge) used in removing the excess water. Also, smaller

samples tend to be unstable and float while measuring the immersed weight of the

drilling cuttings using Archimedes principle, hence introducing errors into the

measurement. Larger samples (more than 5mm) are acceptable for porosity measurement

but it is beyond the domain of application of Darcylog for measuring permeability.

Therefore, since managing time is essential to the success of this laboratory work,

isolating samples with sizes outside the range of application is important.

3.1.3.2 Stage 2:

Sandstone is the reservoir rock in the Nikanassin Group. This stage involves the picking

and isolation of non-reservoir (non-sandstone) rocks and foreign materials (for example

metals from the drilling string) from the entire sample of drill cuttings. Non-reservoir

rocks such as shale, quartz, lost circulation materials (L.C.M.) are removed from the

sample of drill cuttings to end up with only samples that are sandstone chips between

1mm to 5mm in size.

45

3.1.4 Cleaning, Drying, and Weighting of Sample

Cleaning the drill cutting samples is essential as this helps to remove remaining fluids

and any foreign dirt from the pore space of the drill cuttings. According to Gant and

Anderson (1988), mixtures or series of solvents are generally more effective than using a

single solvent. In their work, they orderly ranked the effectiveness of solvents after

performing a 12-hour solvent evaluation of dolomite cores using Dean Stark extraction

method and demonstrated that a 50% toluene and 50% methanol (mixture) is highly

effective in cleaning core samples. They reached their conclusion because toluene

removed the hydrocarbons and some weakly polar compounds, and methanol removed

the dissolved precipitated salt and polar compounds.

Therefore, in this work we utilize a 50% - 50% mixture of toluene and methanol to clean

the drill cutting samples. The process involves soaking the drill cuttings for at least 30

minutes in this cleaning solvent and then gently stirring the drill cuttings inside the glass

bottle. Once the cleaning solvent appears dirty, the solvent is poured into a waste

container and a new cleaning solvent is used for rinsing the drill cuttings. This process is

repeated continuously until the rinsing solvent is clean.

In the case of drill cuttings used in this work, most of the cleaning had been done at the

rig site and so the cleaning done at the laboratory was not overly time consuming. After

cleaning, the drill cuttings are poured into a glass bottle, which is placed in the oven for

about 3 hours at 110oC. The drying temperature is selected using the boiling point of the

46

highest solvent in the mixture as a guide (the toluene used in this experiment has a

boiling point of 110.60 oC). Fig. 3.5 shows the material safety data sheet for toluene

where the boiling point is stated. After drying the drill cuttings, they are weighted and the

dry weight is recorded. This measured weight is later used for calculating porosity.

Figure 3.5—Material safety data sheet for Toluene

(Adapted from http://kni.caltech.edu/facilities/msds/toluene.pdf ).

3.1.5 Porosity Measurement

The laboratory procedure outlined in the American Petroleum Institute recommended

practice 40 (API RP-40) for core analysis was adapted to determine porosity in the drill

cuttings. According to API RP-40, porosity is defined as the ratio of void space volume

to the bulk volume of the whole rock. Porosity measurement is important since it is used

in estimating the initial hydrocarbons-in-place using volumetric method. Eqs. 3.1 to 3.2

were used to determine from drill cuttings pore volume, bulk volume and porosity,

respectively.

(

…………………….….…….. Eq. 3.1

http://kni.caltech.edu/facilities/msds/toluene.pdf

47

(

…………………........…………Eq. 3.2

(

………………..………………………………Eq. 3.3

Prior to the calculation using Eq. 3.1 to Eq. 3.3, the saturated weight followed by the

immersed weight was measured as explained next.

3.1.5.1 Saturated Weight

3.1.5.1.1 Apparatus

Analytical mass balance accurate to 1 milligram

Beaker that can hold de-aerated liquid under vacuum

Test tbe with tap (125 milli-litre)

Vacuum pump

Brine composed of 20 grams of sodium chloride (NaCl) in one litre of distilled

water

Drill cutting basket for holding cuttings in the beaker

Figure 3.6—Apparatus for measuring saturated weight of drill cuttings (Adapted

from Ortega, 2012).

48

3.1.5.1.2 Procedure

Re-measure and record the weight of the dry and cleaned drill cuttings (Column 3

of Table 3.2)

Pour the drill cuttings inside the cuttings basket

Place the drill cutting basket inside the beaker, the beaker can contain five (5) drill

cutting basket at a time

Fill the test tube with 125 milliliter of brine of known density (1.023g/cc)

Place the test tube on top of the beaker such that it seals the beaker

Apply a high vacuum on the beaker for about 15 minutes

Open the tap on the test tube to allow the brine to flow into the beaker containing

the drill cuttings until the drill cuttings have been completely submerged in the

brine

The drill cuttings are allowed to saturate for at least 45 minutes

The drill cuttings basket is removed from the beaker

The drill cuttings are placed on a paper sheet to remove excess water on the

surface of the drill cuttings

The saturated cuttings are placed on the mass balance and the saturated weight is

recorded (column 4 of Table 3.2)

The difference in weight between the saturated weight and dry weight is divided

by the density of the saturant to obtain the pore volume (column 6 of Table 3.2)

49

3.1.5.1.3 Recommendation

The following recommendation will minimize potential sources of error:

Distilled water must be used in preparing the brine since un-distilled water may

introduce impurities that may plug the pores of the drill cuttings

Extreme care should be taken to prevent the brine from contacting air in the

beaker as this will impair the saturation process

The excess brine on the saturated drill cuttings must be removed in order to

minimize error when measuring the saturated weight

3.1.5.2 Immersed Weight

3.1.5.2.1 Apparatus

Analytical mass balance accurate to one milligram

Transparent liquid container

Drill cuttings basket for holding drill cuttings during suspension

Brine made up of 20 grams of sodium chloride (NaCl) in one litre of distilled

water

50

Figure 3.7—Apparatus for measuring immersed weight based on Archimedes

principle. The Immersed weight is used to determine the bulk volume of the drill

cuttings using Eq. 3.2 (Adapted from Ortega, 2012).

3.1.5.2.2 Procedure

Fill the liquid container with brine of known density (1.023g/cc)

Suspend the empty drill cutting basket with a fine wire and lower it into the liquid

container

Tare the weight of the balance until it reads zero

Remove the empty drill cuttings basket from the liquid container and pour the

drill cuttings inside it

Re-suspend the drill cuttings basket containing the drill cuttings using the fine

wire and lower it into the liquid container

After the weight is stabilized, record the immersed weight (column 5 of Table

3.2)

The immersed weight is divided by the density of immersion liquid to get the bulk

volume (column 7 of Table 3.2)

51

3.1.5.3 Porosity Calculation

The ratio of pore volume to bulk volume is determined to yield the porosity of the

drill cuttings sample. Columns 8 or 9 of Table 3.2 show the determined porosity

values.

3.1.5.4 Recommendation

Ensure the analytical mass balance is tared with empty drill cuttings basket inside

the liquid container so that accurate immersed weight can be obtained

Fill the liquid container to a level that allows it to have some room to

accommodate increase in liquid level in the container due to buoyancy effects

3.1.5.5 Results

Results of the experimental work on drill cuttings up to the determination of porosity are

presented in Table 3.2. The table includes the identification of the samples in column 1,

bottom depth of sample collection in column 2, column 3 shows the measured dry

weight, column 4 contains the measured saturated weight, column 5 has the measured

immersed weight, column 6 has the calculated pore volume, column 7 shows the

calculated bulk volume, and columns 8 and 9 shows the determined porosity quantified in

fraction and percentage, respectively.

52


(DETERMINATION OF POROSITY)

1 2 3 4 5 6 7 8 9

Sample

No.

Bottom

Depth

MD (m)

Dry Weight (g)Saturated Weight

(g)

Immersed Weight

(g)

Pore Volume(PV)

(cc)

Bulk

Volume(BV)

(cc)

Porosity=

(PV/BV)

(fraction)

Porosity (%)

1 3185.0 1.594 1.643 0.743 0.048 0.734 0.066 6.595

2 3190.0 1.981 2.030 0.773 0.048 0.764 0.063 6.339

3 3195.0 3.113 3.198 1.307 0.084 1.291 0.065 6.503

4 3200.0 1.841 1.883 0.799 0.041 0.789 0.053 5.257

5 3202.5 2.084 2.143 0.901 0.058 0.890 0.065 6.548

6 3205.0 1.642 1.711 0.653 0.068 0.645 0.106 10.567

7 3207.5 1.616 1.675 0.681 0.058 0.673 0.087 8.664

8 3210.0 1.415 1.469 0.599 0.053 0.592 0.090 9.015

9 3217.5 1.061 1.095 0.496 0.034 0.490 0.069 6.855

10 3220.0 1.075 1.121 0.470 0.045 0.464 0.098 9.787

11 3225.0 1.710 1.780 0.708 0.069 0.699 0.099 9.887

12 3235.0 1.154 1.191 0.567 0.037 0.560 0.065 6.526

13 3265.0 2.257 2.334 0.891 0.076 0.880 0.086 8.642

14 3285.0 2.878 3.048 1.137 0.168 1.123 0.150 14.952

15 3290.0 3.634 3.755 1.446 0.120 1.428 0.084 8.368

16 3295.0 3.933 4.023 1.625 0.089 1.605 0.055 5.538

17 3300.0 4.391 4.550 1.751 0.157 1.730 0.091 9.081

18 3305.0 5.009 5.145 1.998 0.134 1.974 0.068 6.807

19 3310.0 5.063 5.174 2.040 0.110 2.015 0.054 5.441

20 3315.0 3.329 3.411 1.316 0.081 1.300 0.062 6.231

21 3320.0 2.833 2.954 1.154 0.120 1.140 0.105 10.485

22 3325.0 1.200 1.245 0.469 0.044 0.463 0.096 9.595

23 3345.0 1.307 1.378 0.585 0.070 0.578 0.121 12.137

24 3355.0 2.085 2.148 0.819 0.062 0.809 0.077 7.692

25 3435.0 1.992 2.045 0.874 0.052 0.863 0.061 6.064

26 3440.0 2.100 2.156 0.850 0.055 0.840 0.066 6.588

27 3445.0 1.595 1.650 0.650 0.054 0.642 0.085 8.462

28 3450.0 9.469 9.762 3.812 0.289 3.766 0.077 7.686

29 3455.0 7.040 7.166 2.808 0.124 2.774 0.045 4.487

30 3460.0 1.664 1.699 0.671 0.035 0.663 0.052 5.216

31 3665.0 1.449 1.475 0.641 0.026 0.633 0.041 4.056

32 3690.0 1.329 1.379 0.721 0.049 0.712 0.069 6.935

33 3710.0 9.801 9.994 3.913 0.191 3.865 0.049 4.932

34 3715.0 7.958 8.105 3.188 0.145 3.149 0.046 4.611

35 3720.0 9.529 9.728 3.871 0.197 3.824 0.051 5.141

36 3725.0 8.613 8.845 3.537 0.229 3.494 0.066 6.559

37 3730.0 6.447 6.648 2.579 0.199 2.548 0.078 7.794

38 3735.0 5.751 5.872 2.273 0.120 2.245 0.053 5.323

39 3740.0 5.973 6.133 2.367 0.158 2.338 0.068 6.760

40 3745.0 2.120 2.176 0.879 0.055 0.868 0.064 6.371

41 3750.0 6.534 6.624 2.570 0.089 2.539 0.035 3.502

42 3755.0 7.127 7.250 2.799 0.122 2.765 0.044 4.394

43 3760.0 4.595 4.687 1.792 0.091 1.770 0.051 5.134

44 3765.0 4.398 4.482 1.744 0.083 1.723 0.048 4.817

45 3770.0 6.724 6.857 2.683 0.131 2.650 0.050 4.957

46 3775.0 3.663 3.760 1.435 0.096 1.418 0.068 6.760

47 3785.0 4.243 4.359 1.762 0.115 1.741 0.066 6.583

48 3790.0 2.986 3.031 1.239 0.044 1.224 0.036 3.632

49 3800.0 1.170 1.198 0.567 0.028 0.560 0.049 4.938

50 3820.0 1.889 1.933 0.765 0.043 0.756 0.058 5.752

51 3835.0 2.943 3.028 1.279 0.084 1.263 0.066 6.646

52 3845.0 1.048 1.070 0.619 0.022 0.611 0.036 3.554

53 3850.0 5.572 5.710 2.257 0.136 2.230 0.061 6.114

54 3855.0 4.369 4.517 1.765 0.146 1.744 0.084 8.385

55 3860.0 3.367 3.452 1.385 0.084 1.368 0.061 6.137

56 3865.0 2.333 2.403 0.958 0.069 0.946 0.073 7.307

57 3880.0 2.771 2.862 1.082 0.090 1.069 0.084 8.410

58 3885.0 2.979 3.043 1.174 0.063 1.160 0.055 5.451

59 3890.0 2.626 2.709 1.018 0.082 1.006 0.082 8.153

60 3895.0 2.607 2.685 1.067 0.077 1.054 0.073 7.310

61 3900.0 2.203 2.268 0.871 0.064 0.860 0.075 7.463

62 3930.0 3.907 4.030 1.621 0.122 1.601 0.076 7.588

63 3935.0 3.145 3.223 1.273 0.077 1.258 0.061 6.127

64 3940.0 5.075 5.214 2.057 0.137 2.032 0.068 6.757

65 3945.0 3.006 3.102 1.262 0.095 1.247 0.076 7.607

66 AVERAGE 3.574 3.668 1.455 0.093 1.438 0.069 6.892

TABLE 3.2 —RESULTS OF LABORATORY WORK ON DRILL CUTTINGS

53

3.1.6 Screening of Samples Prior to Permeability Measurement

After going through the previous procedures and calculating the porosity of each drill

cutting sample, we are now equipped with all required information necessary to

determine if some of the drill cuttings meet the criteria to be used for measuring

permeability using Darcylog equipment. In this step, drill cutting samples with porosity

less than 5% and occupying less than half of the drill cutting cell (basket) are not

included for permeability measurement due to Darcylog limitations (www.cydarex.fr,

2013).

3.1.7 Permeability Measurement

Darcylog equipment for measuring permeability in drill cuttings was designed and is

patented by the French Petroleum Institute, and is built by Cydarex (Paris, France) (Fig.

3.8). According to Lenormand and Fonta (2007), the concept of liquid pressure pulse is

used in Darcylog equipment in such a way that an effective flow inside the pores of the

drill cuttings by compression of residual gas inside the cuttings can be achieved. A

viscous liquid (in this work a mixture of 90% glycerol and 10% distilled water) is used as

displacing fluid in such a way that the pressure decrease in the rock is slowed down.

During the displacement process the pressure versus time is recorded by the equipment

and the volume of oil invading into the pores of the cuttings is derived from the

calibration of the spring/bellow system. After the displacement process, a numerical

simulation model based on equations describing the flow of a viscous liquid in a

compressible medium of spherical geometry is used to calculate the permeability by

http://www.cydarex.fr/

54

matching the simulated model data with the experimental model data. A rule of thumb is

to use the beginning of the curve corresponding to more than 1/3 of the total curve. For

more details please refer to Lenormand and Fonta (2007).

Figure 3.8— The left side shows the diagram of the spring and bellow system while

the right side shows the Darcylog Equipment (Adapted from Lenormand and Fonta,

2007).

3.1.7.1 Apparatus

Darcylog

Pump

Viscous liquid (mixture of 90% glycerol and 10% distilled water) suitable for

tight formation since the rate of invasion also depends on fluid viscosity

(Lenormand and Fonta, 2007)

Glass bottle for holding drill cuttings

55

3.1.7.2 Procedure

Pour some quantity of the viscous liquid inside the glass bottle containing the drill

cuttings and stir gently to remove excess air in the pores of the drill cuttings

Open the cover of the drill cutting cell and open all valves i.e. valve 1 to 3

After 30 minutes pour the drill cutting samples inside the drill cuttings basket and

place it in the drill cutting cell of the Darcylog and cover it but not tightly

Using Darcylog software, click start data display from the data acquisition

window to monitor the real-time pressure and temperature

Input required drill cuttings information (well information, porosity, dry weight,

range of cuttings diameter, grain density, temperature, and viscosity) into the

software, and save this information because it will be used for the simulation run

Apply some pressure via the pump to the Darcylog equipment to remove any

trapped air in the circulating system of the Darcy Log

Stop the pump, close the cover of the cutting cell completely

With valve 1 remaining open ,close valves 2 and 3

Apply pressure between 9.5 to10 bars to the pressure cell using the pump

Close valve 1 and wait for few minutes to allow the pressure in the cell to

stabilized

Start recording data from the Darcylog software and open only valve 2

The apparatus will record the measured pressure versus time

Stop the recording after about 100 seconds and match the simulated data with the

experimental data to determine the permeability

56

Remove the drill cuttings basket from the cuttings cell and repeat the same step to

determine the permeability of the next sample

3.1.7.3 Recommendation

1. Ensure the temperature in the input data window is updated to the present liquid

temperature as the experiment continues, as this is used to determine the liquid

viscosity

2. Ensure to gently stir the drill cuttings in the container after pouring the liquid into

it to remove excess air to avoid crushing the drill cuttings samples

3. Ensure the Darcylog equipment is not pressurized for more than 10 bars to avoid

liquid leakage and rupturing of the cylinders in the equipment

3.1.7.4 Results

Results of the experimental work on drill cuttings up to the determination of permeability

are presented in Table 3.3. The table includes the identification of the samples in column

1, bottom depth of sample collection in column 2, column 3 shows the viscosity of the

viscous liquid measured by Darcylog, column 4 contains the temperature of the viscous

liquid measured by Darcylog, column 5 has the outside gas volume which represents the

volume of gas in the outer side of the cuttings fragments or gas trapped between the

rubber seals and Darcylog valves, column 6 contains the initial gas saturation, this values

refers to the gas trapped inside the drill cutting fragments after the spontaneous

imbibition process, column 7 has the porosity values mentioned in previous section and

column 8 contains the determined permeability from drill cuttings. Appendix A shows

screenshots of the best fit between simulated and experimental data.

57


(DETERMINATION OF PERMEABILITY)

1 2 3 4 5 6 7 8

Sample

No.

Bottom Depth

MD (m)Viscosity (cp) Temp.(deg C)

Outside Gas

Volume (mm3)

Initial Gas

Saturation

(fraction)

Porosity (fraction) K (md)

1 3185.0 154.4 23.8 8.8 0.075 0.066 0.031

2 3190.0 152.2 24.0 11.5 0.067 0.063 0.022

3 3195.0 151.1 24.1 15.0 0.076 0.065 0.030

4 3200.0 151.1 24.1 10.4 0.098 0.053 0.038

5 3202.5 151.1 24.1 106.5 0.085 0.065 0.056

6 3205.0 152.2 24.0 56.0 0.062 0.106 0.088

7 3207.5 151.1 24.1 23.0 0.067 0.087 0.079

8 3210.0 158.8 23.4 139.2 0.097 0.090 0.216

9 3217.5 159.9 23.3 16.2 0.050 0.069 0.025

10 3220.0 159.9 23.3 43.5 0.071 0.098 0.017

11 3225.0 162.2 23.1 13.4 0.042 0.099 0.017

12 3235.0 161.1 23.2 7.0 0.120 0.065 0.069

13 3265.0 156.6 23.6 14.0 0.082 0.086 0.058

14 3285.0 156.6 23.6 11.9 0.060 0.150 0.064

15 3290.0 161.1 23.2 80.0 0.108 0.084 0.078

16 3295.0 159.9 23.3 10.0 0.136 0.055 0.032

17 3300.0 158.8 23.4 135.0 0.125 0.091 0.190

18 3305.0 158.8 23.4 30.4 0.141 0.068 0.109

19 3310.0 158.8 23.4 12.0 0.150 0.054 0.055

20 3315.0 159.9 23.3 8.6 0.148 0.062 0.062

21 3320.0 158.8 23.4 38.0 0.085 0.105 0.069

22 3325.0 157.7 23.5 7.5 0.082 0.096 0.046

23 3345.0 157.7 23.5 95.0 0.102 0.121 0.150

24 3355.0 158.8 23.4 9.6 0.040 0.077 0.025

25 3435.0 157.7 23.5 8.3 0.117 0.061 0.065

26 3440.0 157.7 23.5 8.7 0.105 0.066 0.048

27 3445.0 157.7 23.5 6.8 0.074 0.085 0.051

28 3450.0 157.7 23.5 8.6 0.029 0.077 0.010

29 3460.0 157.7 23.5 9.8 0.066 0.052 0.020

30 3690.0 151.1 24.1 7.7 0.058 0.069 0.023

31 3710.0 157.7 23.5 11.8 0.088 0.05 0.030

32 3715.0 156.6 23.6 75.5 0.078 0.05 0.029

33 3720.0 156.6 23.6 7.9 0.080 0.051 0.025

34 3725.0 156.6 23.6 68.0 0.065 0.066 0.028

35 3730.0 156.6 23.6 41.0 0.058 0.078 0.036

36 3735.0 155.5 23.7 8.7 0.059 0.053 0.010

37 3740.0 153.3 23.9 26.8 0.044 0.068 0.018

38 3745.0 153.3 23.9 120.0 0.100 0.064 0.066

39 3760.0 154.4 23.8 114.0 0.082 0.051 0.057

40 3765.0 153.3 23.9 12.0 0.076 0.048 0.018

41 3770.0 153.3 23.9 57.5 0.077 0.050 0.012

42 3775.0 153.3 23.9 12.0 0.050 0.068 0.015

43 3785.0 153.3 23.9 11.5 0.055 0.066 0.016

44 3820.0 157.7 23.5 12.8 0.052 0.058 0.019

45 3835.0 155.5 23.7 12.2 0.015 0.066 0.011

46 3855.0 153.3 23.9 125.0 0.091 0.084 0.184

47 3860.0 153.3 23.9 18.2 0.069 0.061 0.020

48 3865.0 153.3 23.9 14.2 0.051 0.073 0.015

49 3880.0 153.3 23.9 8.8 0.037 0.084 0.012

50 3885.0 153.3 23.9 9.0 0.072 0.055 0.020

51 3890.0 153.3 23.9 8.0 0.049 0.082 0.017

52 3895.0 154.4 23.8 8.8 0.046 0.073 0.015

53 3900.0 154.4 23.8 10.2 0.053 0.075 0.016

54 3930.0 154.4 23.8 7.0 0.035 0.076 0.010

55 3935.0 154.4 23.8 9.2 0.048 0.061 0.014

56 3940.0 153.3 23.9 28.6 0.045 0.068 0.020

57 3945.0 153.3 23.9 88.5 0.058 0.076 0.080

AVERAGE 155.8 23.7 33.0 0.075 0.047

TABLE 3.3—RESULTS OF LABORATORY WORK ON DRILL CUTTINGS

58

Chapter Four: POROSITY EXPONENT

4.1 The Concerns

The understanding of the role played by vuggy and naturally fractured reservoirs in

hydrocarbon recovery has improved significantly over the past few years as thorough

petrophysical knowledge of reservoir properties has helped to improve estimates of

petroleum-in-place and recoveries. This has happened for example in the case of

‘unconventional’ reservoirs. When conducting petrophysical evaluation in a tight gas

reservoir, an accurate value of the porosity exponent (m) is very important because

variations in this exponent will change the calculated water saturation and therefore affect

the petroleum-in-place estimates. In general, a decrease in m tends to reduce the

computed water saturation values.

A detailed literature review (Chapter 2) demonstrated that petrophysical evaluation

techniques that uses a constant porosity exponent for all depths will likely magnify the

errors in the calculated water saturations especially in tight reservoirs with low porosity.

To address this concern, we develop as part of the present research petrophysical models

that takes into consideration the individual porosity components in heterogeneous

reservoirs for estimating the value of m to be used in log interpretation.

This chapter dicusses the development of the petrophysical model for determining m in a

reservoir represented by dual (matrix and non-connected vugs or matrix and fractures)

59

and /or triple porosity reservoir (matrix, fractures and non-connected vugs/or isolated

porosity).

4.2 Use of Electromagnetic Unified Mixing Rule for Building Dual and Triple

Porosity Models

The dielectric mixing rules of Maxwell Garnett rule, Bruggeman formula and Coherent

potential approximation are unified into one family by Sihvola (1999). The unified

mixing formula assumed a spherical geometry in three dimensions in which isotropic

spherical inclusions with permittivity ԑi occupy random positions in an isotropic host

environment with permittivity ԑe (Fig. 4.1).

Figure 4.1—Schematic of mixture for spherical inclusions with permittivity εi that

occupy random positions in a host environment of permittivity εe. The mixture

effective permittivity is εeff (Sihvola, 1999).

The unified formula is expressed as:

(

( )…………………………………Eq. 4.1

εe

εi

60

Where f is the volume fraction occupied by a spherical inclusion, and vs is a Sihvola

dimensionless parameter. Using different value of the individual mixing rules can be

recovered; for example when vs = 0 in Eq.4.1 gives the Maxwell Garnett rule, vs = 2 leads

to the Bruggeman equation, and vs = 3 simplifies to the Coherent potential

approximation.

In the present work, the term permittivity relates to a material’s capacity to allow (or

“permit’) an electric field. In order to replace the permittivity term with conductivity

equivalences, we use the complex dielectric permittivity which is defined as (Seybold,

2005):

(

) ……….…………………………………………………………..Eq.

4.2

where is the real part of the dielectric permittivity, =√-1, is the conductivity, and

is the angular frequency. At low frequencies ( approaches zero), the conductivity term

in Eq. 4.2 becomes large, and dominates the complex dielectric permittivity ( ). Based

on these observations Sihvola’s unified mixing formula can be recast for the special case

of low frequency where it becomes defined in terms of the porosity exponent (m) that is

familiar to petrophysics practitioners. As a result can be replaced with their

conductivity terms at low frequencies in Eq. 4.1. The same type of reasoning has been

presented by Rasmus and Kenyon (1985).

61

Also, to convert the unified Eq. 4.1 to standard petroleum nomenclature, we assigned

Sihvola’s permittivity notation the following petrophysical equivalences: host

environment permittivity (ԑe) to be equivalent to the conductivity of the matrix porosity;

the spherical inclusions permittivity (ԑi ) corresponds to the water phase, the volume

fraction ( f ) is equal to non-connected vugs or fracture porosity depending on the model,

and the effective permittivity (ԑeff ), which is the summation of the host and the inclusion

is equivalent to the conductivity of the total porosity of the composite system. Since

resistivity is the inverse of conductivity, the permittivity terms in Eq. 4.1 are re-written

with their resistivity value equivalent during the petrophysical model development in

order to relate it to Archie’s empirical equation.

A good match between the theoretical and laboratory values of porosity exponent

presented later in the section dealing with ‘comparison with core data’ lends empirical

evidence that this substitution is valid. Development of the petrophysical equations are

presented in detail later in this chapter (section 4.5). The equivalences between individual

mixing rules, dual and triple porosity models are presented next.

4.2.1 Maxwell Garnett Electromagnetic Mixing Rule

Sihvola (1999) Unified Mixing Rule, when in Eq. 4.1, leads to the Maxwell

Garnett equation:

(

( ………………………………………………………Eq. 4.3

62

Maxwell Garnett developed his famous equation by considering the effective dielectric

constant of a medium where metal spheres occupy a given fraction of the host medium

(Maxwell, 1904). The positions of the spheres are random. The same randomness

assumption is used in the case of the non-connected vugs considered in this chapter.

4.2.1.1 Dual Porosity (Matrix and Non-Connected Vugs)

This model represents the matrix and any type of non-connected porosity that can occur

in a given reservoir. But for simplicity we refer to non-connected vugs throughout this

chapter. For example in the case of carbonate rocks; intragranular, ooilitic, moldic, and/

or fenestral porosity are the mathematical equivalent of non-connected (or isolated) vugs.

In this case the summation of matrix and non-connected vugs is equal to the total porosity

(ϕ) of the system. In the case of tight gas formations isolated non-effective porosity is the

mathematical equivalent of non-connected vugs. When the permittivity terms in Eq. 4.3

are replaced by their respective conductivity and resistivity terms (inverse of

conductivity), all resistivities cancel out as shown in Section 4.5.1 and we end up with

Eq. 4.4, which is a function of porosities at different scales and porosity exponents. The

equation allows calculating m of the composite system of matrix and non-connected vugs

from the equation:

[

((

(

( ( )]

( ………………………………………...Eq. 4.4

where ϕnc is the non-connected vug porosity, ϕb is matrix porosity attached (or scaled) to

the bulk volume of only the matrix block and mb is the porosity exponent of the matrix.

63

The right hand side of Fig. 4.2 shows values of m calculated with the use of Eq. 4.4 for

various values of total and non-connected porosities. The consistency of the model is

demonstrated by the fact that all lines become horizontal when the value of non-

connected porosity becomes equal to the total porosity (matrix porosity is zero). This is

an indication that the model predicts a value of infinity for m of non-connected vugs.

4.2.1.2 Dual Porosity (Matrix and Fractures)

Eq. 4.5 is an adaptation of Eq. 4.3 developed in this paper to construct a model that

incorporates fracture and matrix porosities:

( (

( …………………………………………….Eq. 4.5

where αt is a dimensionless parameter representing the volume fraction of the host and

the inclusion phase, expressed by the empirical equation:

……………………………………….Eq. 4.6

The equation was developed as part of this research by determining the αt that gave a

fracture porosity equal to the total porosity (matrix porosity is zero); then the respective

fracture porosity was correlated with αt using a polynomial regression that led to Eq. 4.6.

Eq. 4.6 is valid for ϕ2 smaller than 0.1 which covers most cases of practical importance.

When the permittivity terms in Eq. 4.6 are replaced by their respective conductivities

(and resistivities), all resistivities cancel out as shown in Section 4.5.2. This leads to Eq.

4.7 that calculates the dual porosity exponent (m) in reservoirs made out of matrix and

fracture porosity.

64

[ ( ] (

[ ( ] (

( ……………………………………….…Eq. 4.7

Results from Eq. 4.7 are presented in the left hand side of Fig. 4.2. Values of m are

shown as a function of total and fracture porosities. Note that m = 1.0 when the fracture

porosity is equal to total porosity. Thus, in this model the porosity exponent of the

fractures is equal to 1.0. This equation was compared with Aguilera’s (2006, 2009)

petrophysical model that considers the effect of the angle between the fracture and the

direction of current flow on the porosity exponent, and Berg’s (2006) effective medium

petrophysical model that includes the angle that the normal to the fracture makes with the

current flow. It is concluded that the porosity exponent obtained with the petrophysical

model represented by Eq. 4.7 calculates about the same m when the angle, θ = 0°, using

Aguilera (mf =1.0) (2009, 2010) and Berg petrophysical model (θ’ = 90°, mf =1.0).

Figure 4.2— Chart for determining m as a function of non-connected vug porosity

(nc) or fracture porosity (2) for the case in which mb= 2.0. Petrophysical model is

0.0001

0.001

0.01

0.1

1

1.0 1.5 2.0 2.5 3.0

Tota

l Po

rosi

ty, φ

Dual Porosity Exponent, m

ɸ2=0.01

ɸ2=0.015

ɸ2=0.001

ɸ2=0.0001

ɸnc=0.050

ɸnc=0.010

ɸnc=0.0010

ɸnc=0.0001

65

developed on the basis of the Electromagnetic Mixing Rule (Maxwell Garnett, vs =

0).

4.2.1.3 Triple Porosity (Matrix, Non Connected Vugs and Fractures)

Aguilera and Aguilera (2004) developed a triple porosity model for evaluation of

naturally fractured reservoirs, which was subsequently improved by Al-Ghamdi et al.

(2011). The basic assumptions are that the matrix and fractures have conductivities that

are connected in parallel; and the combined matrix and fractures are connected in series

with the non-connected vugs. Berg (2006) provided another way of quantifying the same

triple porosity model parameters with the use of Eqs. 2.5 and 2.6 as discussed in Chapter

two. This chapter uses the same methodology proposed by Berg as follows: (1) calculate

a porosity exponent mb’ using Eq. 4.8; note that Eq. 4.8 has the same form as Eq. 4.4 but

ϕ and m are replaced with ϕb’ and mb’. (2) Transfer the parameter mb’ and ϕb’ into Eq. 4.7

to replace mb and ϕb, respectively. This results in Eq. 4.9 from which the triple porosity

exponent, m is calculated.

[

((

(

( ( )]

(

…………………………………….Eq. 4.8

[ ( ] (

[ ( ] (

( ……………………………………….Eq. 4.9

Fig. 4.3 shows an example of triple porosity results under the assumption that vs is equal

to zero (Maxwell Garnett). Note that the value of m for the triple porosity model can be

bigger, equal to, or smaller than mb depending on the contribution of matrix, non-

connected vugs and fractures to the total porosity system.

66


porosity(nc) and fracture porosity(2) for the case in which mb = 2.0. Petrophysical

model developed on the basis of the Unified Electromagnetic Mixing Rule (Maxwell

Garnett, vs = 0).

4.2.2 Bruggeman Electromagnetic Mixing Rule

Use of the Unified Mixing Rule, when in Eq. 4.1 results in the Bruggeman

equation:

(

( )…………………………………..Eq. 4.10

When the permittivity terms in Eq. 4.10 are replaced by the corresponding conductivity

and resistivity terms, all the resistivities cancel out as shown in Section 4.5.3 and we

obtain Eq. 4.11 that allows calculation of the dual porosity exponent (m) for reservoirs

with matrix and non-connected vug porosities:

0.01

0.1

1

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0To

tal P

oro

sity

, φ

Triple Porosity Exponent, m

ɸnc=0.1,ɸ2=0.01

ɸnc=0.075,ɸ2=0.01

ɸnc=0.05,ɸ2=0.01

ɸnc=0.01,ɸ2=0.01

ɸnc=0.02,ɸ2=0.01

67

(

)………………………...………………..Eq. 4.11

This equation cannot be solved explicitly to estimate the porosity exponent (m) as in the

case of the Maxwell Garnett approach. An iterative approach has to be used by assuming

m in the right hand side and calculating m in the left hand side until a minimum

acceptable error is accepted. Microsoft Excel Solver was utilized for this purpose. Fig.

4.4 shows an example of calculated results using Eq. 4.11.


porosity(nc) for the case in which mb = 2.0. Petrophysical model developed on the

basis of the Unified Electromagnetic Mixing Rule (Bruggeman, vs = 2).

0.01

0.1

1

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Tota

l Por

osit

y, ɸ

Dual Porosity Exponent,m

ɸnc=0.125

ɸnc=0.010

ɸnc=0.050

ɸnc=0.075

ɸnc=0.100

68

4.2.3 Coherent Potential Electromagnetic Mixing Rule

When vs = 3 the unified mixing formula (Eq. 4.1) leads to the Coherent potential mixing

rule:

(

( )…………………………………..Eq. 4.12

Development of the above equation is presented in section 4.5.4. As in the previous

cases, when the permittivity terms in Eq. 4.12 are replaced by conductivity and resistivity

terms, the resistivities cancel out. The result is Eq. 4.13 that allows calculating the dual

porosity exponent (m) for reservoirs represented by matrix and non-connected vug

porosities:

[

(

)]

(

)………………….......…………………..Eq. 4.13

As in the case of the Bruggeman model this equation cannot be solved directly to

estimate the porosity exponent (m). An iterative method is required. Microsoft Excel

Solver has been utilized in this thesis. Fig. 4.5 shows an example of calculated results

using Eq. 4.13.

69

Figure 4.5—Chart for determining m as a function of non-connected vug

porosity(nc) for the case in which mb = 2.0. Petrophysical model developed on the

basis of the Unified Electromagnetic Mixing Rule (Coherent Potential, vs = 3).

4.3 Model Development

4.3.1 Derivation of Maxwell Garnett Mixing Rule Extension to Matrix and Non-

Connected Vugs

The unified mixing formula according to Sihvola (1999) is stated as follows:

(

( )……………………...………….Eq. 4.14

When, the unified mixing formula (Eq. 4.14) leads to the Maxwell Garnett mixing

rule as follows:

(

( …………………………………………………...….Eq. 4.15

0.01

0.1

1

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Tota

l Por

osit

y, φ


ɸnc=0.125

ɸnc=0.010

ɸnc=0.050

ɸnc=0.075

ɸnc=0.100

70

By expansion of Eq. 4.15 we obtain:

( )( ( )( …………….…………Eq. 4.16

Factorization of Eq. 4.16 leads to:

[ ( ( ] [ ( ] ( …………….Eq. 4.17

[ ( (

( ( ]………………………………………….……Eq. 4.18

which is the Maxwell Garnett’s permittivity of the host is assumed in this chapter to

be equal to the conductivity of the rock matrix while is assumed to be equivalent to

the conductivity of the composite system. Therefore the basic Archie’s equations for only

matrix and composite system can be written respectively as follows:

…………………………………………..………………..Eq. 4.19

……………………………………..………………………Eq. 4.20

………………………………………………………...…Eq. 4.21

…………………….……………………………………..Eq. 4.22

Permittivity of the inclusion phase, which has a volume fraction , is assumed to

represent the water phase in the non-connected vugs and is written as:

……………………………………………………………………..Eq. 4.23

Replacing the permittivity with conductivity and using standard petrophysical resistivity

notation (the inverse of conductivity); and replacing with nc transforms equations (Eq.

4.18) to (Eq. 4.23) into:

71

[

(

(

(

(

]…………………………………….……Eq. 4.24

[

(

(

(

(

] ……………………………………..Eq. 4.25

leading to:

[

(

(

( ( ]……………...………………………..Eq. 4.26

[

(

(

( ( ]

( …………………………………………..Eq. 4.27

This is the dual porosity exponent equation for the non-connected vugs and matrix

porosity presented in Eq. 4.4 of this chapter.

4.3.2 Maxwell Garnett Mixing Rule Extension to Matrix and Fractures

Maxwell Garnett equation (Eq. 4.18), used for development of the dual porosity exponent

for matrix and non-connected vugs (Eq. 4.27), has been extended in this section to

provide an equation for a dual porosity model made out of matrix and fractures as

follows:

(

………………………………………….………Eq. 4.28

Eq. 4.28 can be expanded:

( )( ( ( )( ………………….Eq. 4.29

72

( ( ( ) ( ( ))

( ( ( ) ( ( ))………..……………………..……Eq. 4.30

Replacing permittivity with conductivity, using standard petrophysical resistivity notation

(the inverse of conductivity) and replacing with 2 transforms Eq. 4.30 to Eq. 4.31:

(

(

( )

(

(

( )

…………………………..…...Eq. 4.31

[

(

( ]

(

(

…………………….……….Eq. 4.32

leading to:

[ ( ] (

( ( ) ( ………...……………………………….Eq. 4.33

[ ( ] (

[ ( ] (

( …………………………...……………..Eq. 4.34

where (for 0.0001 ≤ ϕ2 ≤ 0.1 )…………...……….Eq. 4.35

The extension of the Maxwell Garnett mixing formula represented by Eq. 4.35 is the

same as Eq. 4.7 in this chapter for the case of a dual porosity model represented by

matrix and fractures.

4.3.3 Bruggeman Mixing Rule Extension to Matrix and Non-Connected Vugs

When, the Sihvola’s (1999) unified mixing formula, Eq. 4.14 leads to the

Bruggeman mixing rule as follows:

73

(

( )…………………………………...Eq. 4.36

………………………………………….……………..Eq. 4.37

By factorization we obtain:

( …………………………………..…………..Eq. 4.38


(the inverse of conductivity) and replacing with nc transforms Eq. 4.38 to Eq. 4.39:

(

)……………………………………...…....Eq. 4.39

(

)

………………………………………..Eq. 4.40

[

(

)]…………………………………..Eq. 4.41

leading to:

(

)………………...………………………..Eq. 4.42

This is the dual porosity exponent equation presented in Eq. 4.11 for the non-connected

vugs and matrix porosity system developed starting with the Bruggeman mixing formula.

The equation has to be solved by iterations to obtain the value of m for the composite

system of matrix and non-connected vugs.

74

4.3.4 Coherent Potential Mixing Rule Extension to Matrix and Non-Connected Vugs

When, the unified mixing formula, Eq. 4.14 results to the Coherent potential

mixing rule as follows:

(

( )……………………………….…..Eq. 4.43

……………………………………………..……….Eq. 4.44

[ ( ] [ ( ]……....Eq. 4.45


(the inverse of conductivity) and replacing with nc transforms Eq. 4.45 to Eq. 4.46.

[

(

)]

[

(

)]…………………………………………..………….Eq. 4.46

[

(

)]

[

(

)]………………………………………….….Eq. 4.47

(

)

[ (

)]

(

)

[

( )]……………………….………………Eq. 4.48

(

)

and we obtain:

75

[ (

)]

[

( )]………………………………………...……….Eq. 4.49

[

(

)]

(

)………………………...………………..Eq. 4.50

This is the dual porosity exponent equation for the non-connected vugs and matrix

porosity system presented in section 4.2.3 as Eq. 4.13.

4.4 Model Validation

4.4.1 Comparison of Available Models

Sihvola’s (1999) unified equation for handling the three electromagnetic mixing rules

was used to develop petrophysical means of estimating the porosity exponent of dual and

triple porosity models made out of matrix, non-connected vugs and natural fractures.

Only the Maxwell Garnett mixing rule has been extended to determine the porosity

exponent in reservoirs made out of matrix and fractures but the three electromagnetic

mixing rules have been used to determine the porosity exponent in reservoirs made out of

matrix and non-connected vugs. The three rules provide consistent results but the

difference between the three models gets bigger as the value of the non-connected

porosity gets bigger than 0.1. This is shown in Fig. 4.6.

76

Figure 4.6—Comparison chart for determining m as a function of non-connected

vug porosity (nc) for the case in which mb = 2.0. Petrophysical model developed on

the basis of the Unified Electromagnetic Mixing Rule -Maxwell Garnett( vs = 0),

Bruggeman (vs = 2) and Coherent Potential (vs = 3).

However, models based on the assumption of parallel and series resistors and the

Maxwell Garnett mixing rule are easier to run as the calculations for determining m are

explicit. On the other hand the Bruggeman, Berg and Coherent potential models require

iterative procedures for calculating m. The porosity exponent of the matrix (mb) is

assumed to be equal to 2.0 in all these comparisons. Key equations that link matrix,

fracture and non-connected porosity are presented in APPENDIX B.

0.01

0.1

1

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Tota

l P

oro

sity

, Ф

Comparison of Dual Porosity Exponent,m for Different EMR Models

Vs=0,PHINC=0.05

Vs=0,PHINC=0.010

Vs=0,PHINC=0.10

Vs=0,PHINC=0.075

Vs=2.0,PHINC=0.10

vs=2.0,PHINC=0.050

Vs=2.0,PHINC=0.010

Vs=3.0,PHINC=0.10

Vs=3.0,PHINC=0.050

Vs=3.0,PHINC=0.010

Vs=3.0,PHINC=0.075

Vs=2.0,PHINC=0.075

ɸnc=0.100

ɸnc=0.050

ɸnc=0.010

ɸnc=0.075

77

Fig. 4.5 to 4.6 discussed previously show charts for evaluating the dual and triple

porosity exponent for reservoirs represented by matrix, vugs and /or fracture porosity.

Fig. 4.7 shows a comparison of dual porosity models based on three different theories:

Maxwell Garnett (this study, Eq. 4.4 and Eq. 4.7); Aguilera and Aguilera (2003) and

Berg (2006). In all cases the porosity exponent of the matrix (mb) is equal to 2.0. All the

models give essentially the same values of m for the case of fractures and matrix as

shown in the left hand side of the graph. The first two methods allow calculation of m

explicitly. Berg’s m values are calculated by an iteration procedure. In the case of matrix

and non-connected vugs Berg’s iteration procedure uses an infinite value of the porosity

exponent of the vugs (actually mv = 1E35 in an Excel spread sheet). There are some

differences in the case of the dual porosity models made out of matrix and vugs. Aguilera

and Aguilera (2003) and Berg (2006) provide the same results for the cases involving

matrix and fractures. Eq. 4.4 based on Maxwell Garnett (vs = 0) for matrix and non-

connected vugs gives m values that are somewhat smaller at large total porosities. These

smaller values can be matched with Berg’s model when mv is made equal to 1.5.

78

Figure 4.7— Comparison of dual porosity models made out of matrix and fractures

or matrix and non-connected vugs from various theories show good agreement.

Porosity exponent of the matrix mb = 2.0. Maxwell Garnet and Aguilera’s equations

for calculating m are explicit. Berg’s solution uses an iteration procedure and for the

vugs case assumes an infinite value of mv (in reality it assumes mv = 1E35 in a spread

sheet for the above curves in the right hand side of the graph).

Fig. 4.8 shows a good comparison of models based on the Unified Electromagnetic

Mixing Rule (Maxwell Garnett, vs = 0) represented by the solid lines and Berg’s effective

medium theory (X symbol). The comparison is made for naturally fractured reservoirs

and reservoirs with vugs (mb = 2.0, mv =1.5, mf =1.0). Berg suggests that values such as

mv =1.5 could be indicative of connected vugs (as opposed to mv being infinite). It could

be, but the problem from a practical point of view is the quantification of the porosity

exponent (mv) for vugs.

0.0001

0.001

0.01

0.1

1

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0

Tota

l Po

rosi

ty, Ф

Maxwell PHINC=0.10

Maxwell PHINC=0.05

Maxwell PHINC=0.010

Maxwell PHI2=0.01

Maxwell PHI2=0.001

Maxwell PHI2=0.0001

Aguil_PHINC=0.10

Aguil_PHINC=0.05

Aguil_PHINC=0.01

AGUIL PHI2=0.01

AGUIL PHI2=0.001

AGUIL Phi2=0.0001

Berg PHIV=0.10

Berg PHIV=0.05

Berg PHIV=0.010

Berg PHI2 =0.01

Berg Phi2=0.001

Berg PHI2=0.0001

ɸnc=0.100

ɸnc=0.050

ɸnc=0.010

ɸ2=0.01

ɸ2=0.001

ɸ2=0.0001

Dual Porosity Exponent, m

79

Figure 4.8—Comparison of models based on the Unified Electromagnetic Mixing

Rule (Maxwell Garnett, vs = 0) represented by the solid lines and Berg effective

medium theory (x symbol). Comparison is made for naturally fractured reservoirs

and reservoirs with vugs (mb = 2.0, mv =1.5, mf =1.0). According to Berg, small values

of mv might be indicative of connected (or partially connected) vugs.

Fig. 4.9 compares results obtained with the model developed in this paper (Eq. 4.7) for

dual porosity (matrix and fractures) and Aguilera’s model with a fracture angle between

the fracture and the direction of current flow equal to 0°. Fracture porosities in the graph

are equal to 0.0150, 0.010, 0.0010, and 0.0001.

80


0 (solid lines) and Aguilera fracture dip model, θ = 90°- fracture dip (x symbol).

Comparison is made for naturally fractured reservoirs (mb = 2.0, fracture dip, 0°).

Fig. 4.10 presents a comparison of triple porosity models based on the electromagnetic

mixing rule, vs = 0 (solid lines), and Berg’s effective medium theory (X symbol). The

comparison is very good as results are approximately the same. The graph is developed

for mb = 2.0, mv =1.5, mf =1.0, θ = 90°.

81

Figure 4.10—Comparison of triple porosity models based on the Electromagnetic

Mixing Rule, vs = 0 (solid lines) and Berg’s effective medium theory (x symbol).

Comparison is good (mb = 2.0, mv =1.5, mf =1.0, θ’ = 90°).

Fig. 4.11 is a comparison of models based on the Unified Electromagnetic Mixing Rule,

Bruggeman’s equation (vs = 2) and Berg’s effective medium theory (X symbol).

Comparison is for reservoirs with matrix and non-connected vugs (mb = 2.0, mv =1.5).

82

Figure 4.11—Comparison of models based on the Electromagnetic Mixing Rule, vs

= 2 (solid lines) and Berg’s effective medium theory (x symbol). Comparison is for

reservoirs with non-connected vugs (mb = 2.0, mv =1.5).

Fig. 4.12 shows a comparison of models based on the Electromagnetic Mixing Rule for

the coherence potential approximation ( vs = 3) and Berg’s effective medium theory (X

symbol). The comparison is good for the assumed values of mb = 2.0 and mv =1.5.

0.010

0.100

1.000

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Tota

l P

oro

sity

Ф


ɸnc=0.010

ɸnc=0.125

ɸnc=0.100

ɸnc=0.075

ɸnc=0.050

83

Figure 4.12—Comparison of models based on the Electromagnetic Mixing Rule, vs

= 3 (solid lines) and Berg’s effective medium theory (x symbol). Comparison is for

reservoirs with non-connected vugs (mb = 2.0, mv =1.5).

4.4.2 Comparison with Core Data

A key component of this thesis is the comparison of the model developed in this study

and previous models with core data. An excellent data bank for carbonate reservoirs has

been presented by Ragland (2002). In her work values of the porosity exponent were

calculated from laboratory resistivity and porosity data and compared to thin section

analyses of the same pore systems. Ragland’s data base for limestone and dolomite

reservoirs are used for comparison with the theoretical models presented in this chapter.

Equally outstanding is a data bank presented by Byrnes et al. (2006) for the case of tight

gas sandstones in the Mesaverde formation of the United States. The data of Byrnes et al.

(2006) are also used for comparison purposes in this section. All comparisons show that

0.010

0.100

1.000

2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0

Tota

l Po

rosi

ty Ф


ɸnc=0.100

ɸnc=0.075

ɸnc=0.050

ɸnc=0.010

84

the theoretical methods provide good results that match the core data. The advantage of

the explicit methods (Aguilera and Aguilera, 2003; this study) is that they are easier to

use. Berg’s porosity exponent for the fractures is assumed to be equal to 1.0. Berg’s

porosity exponent for the vugs is assumed to be 1.5 in the case of the triple porosity

example.

The difference between the porosity exponent from core data and the model introduced in

this study is generally small as shown by the absolute error scale (%) on the secondary

vertical axis and the open red circles at the bottom of Fig. 4.13 to Fig. 4.18. Some data

points with higher error represent pore systems with different characteristics such as non-

connected moldic pore systems, partially connected moldic and interparticle pore systems

discussed by Ragland (2002). The error value is calculated by considering that m from

core data is the correct value.

4.4.2.1 Limestone Reservoirs

Wells A, B, and J of Ragland’s (2002) data base are used in this case. The comparison of

laboratory data and three different theoretical models are presented in Fig. 4.13, Fig. 4.14

and Fig. 4.15. . The partitioning coefficient (v) mentioned in the title of these figures is

equal to fracture porosity divided by the total porosity. The values of v and mb are

selected in such a way that they provide a good fit of the core data. The theoretical

models were developed by Aguilera and Aguilera (2003), Berg (2006) and in this study

using the unified mixing model (Sihvola, 1999) and vs = 0, which leads to the Maxwell

Garnett equation. The Maxwell Garnett and Aguilera’s models are explicit and permit

85

determination of the porosity exponent (m) without any trial and error. Berg’s curve was

developed with an iteration procedure.

All the theoretical models do a good job in well A (Fig. 4.13). The difference between the

m values from core data and the model introduced in this study (Maxwell Garnett with vs

= 0) is less than 10% as shown by the error scale. The mean absolute percentage error

(MAPE) for this case is 1.84%.

Figure 4.13—Comparison of limestone core data from well A (Ragland, 2002) and

dual porosity models made out of matrix and fractures developed by Aguilera and

Aguilera (2003), Berg (2006) and this study (Maxwell Garnett, vs = 0).The open red

circles show the absolute error as compared with core data. The mean absolute

percentage error (MAPE) is 1.84%.

Fig. 4.14 shows the difference between m from core data and the theoretical model for

well B. The absolute error is generally less than 10%. The data point enclosed in the red

square has an m from cores equal to 2.40. In his case the error is slightly larger than 10%.

The reason for the difference is that about 64% of the pore system in this sample is

0

10

20

30

40

50

60

70

80

90

100

1.0

1.5

2.0

2.5

3.0

0.14 0.16 0.18 0.20 0.22 0.24 0.26

Err

or,

%

Du

al P

oro

sit

y E

xp

on

en

t,m

Total Porosity

Well A Limestone,mb =2.15,v=0.025

Maxwell Vs=0

Ragland's m,cores,2002

Aguilera &Aguilera,2003

Berg's 2006

Error: Core data-Maxwell

86

dominated by a non-connected moldic pore system (Ragland 2002). The MAPE in this

well is 7.15%

Figure 4.14—Comparison of limestone core data from well B (Ragland, 2002) and


Aguilera (2003), Berg (2006) and this study(Maxwell Garnett, vs = 0). The blue data

point enclosed in a red square corresponds to a sample where approximately 64% of

the pore system is dominated by non-connected moldic pores (Ragland 2002). The

MAPE is 7.15%

The difference between m from core data and the model introduced in this study

corresponds to an error smaller than 10% for well J as shown in Fig. 4.15. The data point

enclosed in the red square shows an m equal to 1.63 and an errror that is in the order of

20%. This data point corresponds to a sample characterized by a connected moldic pore

system (Ragland 2002) which reduces significantly the core value of m. The MAPE for

the sample population of this well is 7.40%.

87

Figure 4.15—Comparison of limestone core data from well J (Ragland, 2002) and


Aguilera (2003), Berg (2006) and this study(Maxwell Garnett, vs = 0). The blue data

point enclosed in a red square with m = 1.63 shows an error in the order of 20%.

This sample is characterized by a connected moldic pore system that reduces

significantly the value of m (Ragland 2002). The MAPE is equal 7.40%.

4.4.2.2 Dolomite Reservoirs

Wells C and E of Ragland’s (2002) data are used in this case. The comparison of m

values from core data and the same theoretical models mentioned above is good as shown

on Fig. 4.16 and Fig. 4.17. Another example using a triple porosity model has been

presented by Al-Ghamdi et al. (2011).

Fig. 4.16 shows the difference between m from core data and the Maxwell Garnett

model. The comparison is good with an error that is generally less than 10%. The MAPE

is 4.91%.

88

Figure 4.16—Comparison of dolomite core data from well C (Ragland, 2002) and


Aguilera (2003), Berg (2006) and this study(Maxwell Garnett, vs = 0). The error is

generally less than 10%. The MAPE is 4.91%.

The errors stemming from differences between m from core data and the model

introduced in this study are generally less than 10% as shown in Fig. 4.17. The data

points enclosed in red squares correspond to m values equal to 2.26, 2.91, 2.81 and 2.21.

In these cases the errors are above 10%. These data points correspond to samples

dominated by connected and interparticle pore systems or moldic pore systems (Ragland

2002). The MAPE for this case including all samples is 7.67%.

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

1.0

1.5

2.0

2.5

3.0

0.00 0.02 0.04 0.06 0.08 0.10

Err

or,

%

Du

al

Po

rosit

y E

xp

on

en

t,m

Total Porosity

Well C Dolomite,mb =3.0,v=0.016

Maxwell Vs=0



Berg's 2006

Error Value: Core data-Maxwell

89

Figure 4.17—Comparison of dolomite core data from well E (Ragland, 2002) and


Aguilera (2003), Berg (2006) and this study (Maxwell Garnett, vs = 0). The largest

errors correspond to data points enclosed in red squares. These are dominated by

either connected and interparticle pore system (lower values of m) or non-

connected moldic pore systems (larger values of m) (Ragland 2002). The MAPE is

equal to 7.67%.

4.4.2.3 Tight Gas Sandstone

In this case m data based on core analysis published by Byrnes et al. (2006) are compared

against theoretical models developed by Al-Ghamdi et al. (2011), Berg (2006) and in this

study using the unified mixing model (Sihvola, 1999) and vs = 0, which leads to the

Maxwell Garnett equation but now considering a triple porosity model. The comparison

with all three models is good as shown on Fig. 4.18. The error is generally less than 10%.

The MAPE is 3.58%.

APPENDIX B shows relevant equations that (Aguilera and Aguilera, 2003, 2004) are useful

during the calculations to maintain consistency in the scaling of porosity.

0

10

20

30

40

50

60

70

80

90

100

1.0

1.5

2.0

2.5

3.0

0.10 0.12 0.14 0.16 0.18

Err

or,

%

Du

al P

oro

sit

y E

xp

on

en

t,m

Total Porosity

Well E Dolomite,mb =2.7,v=0.015

Maxwell Vs=0



Berg's 2006


90

Figure 4.18—Comparison of tight gas sandstone core data from wells in the

Mesaverde formation (Byrnes et al., 2006) and triple porosity models made out of

matrix, fractures and slots, and non-connected porosity developed by Al-Ghamdi et

al. (2011), Berg (2006) and this study(Maxwell Garnett, vs = 0). The error is

generally less than 10%. The MAPE is equal to 3.58%

0

10

20

30

40

50

60

70

80

90

100

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

0.00 0.05 0.10 0.15

Err

or,

%

Tri

ple

Po

rosit

y E

xp

on

en

t,m

Total Porosity

Comparison of Petrophysical Model with Tight Sandstone Reservoir Core Data

Maxwell Vs=0

Mesaverde m,core data

Al-Ghamdi 2011

Berg's 2006


91

Chapter Five: WATER SATURATION EXPONENT

5.1 The Concerns

A detailed literature review (Chapter 2) demonstrated that the water saturation exponent

( ) is not constant in petroleum reservoirs but varies as a function of different factors

including fluid distribution in the pore spaces and rock wettability. However, most

studies carried out on petroleum reservoirs with mixed wettability condition are

laboratory studies with limited work done for estimating . To contribute to the solution

of this concern, we present in this chapter how we used electromagnetic mixing rules to

develop a new petrophysical model capable of estimating in heterogeneous reservoirs

with mixed wettability. The reservoirs are represented by dual porosity (matrix and

fractures or matrix and isolated porosity) and triple porosity (matrix, fractures and

isolated porosity) models. In our petrophysical model, we follow the concept of mixed

wettability proposed by Salathiel, 1973; Melrose, 1982; and Hall et al., 1983. This

concept was explained in Chapter 2.

5.2 Theoretical Models

The three models developed in this chapter are as follows: (1) Petrophysical model for

calculating values of n in reservoirs made up of matrix and isolated porosity, (2)

Petrophysical model for calculating values of n in reservoirs made up of matrix and

fracture porosities, and (3) Petrophysical model for calculating n in reservoirs made up of

matrix, isolated and fracture porosities.

92

To use the three petrophysical models proposed in this study, the porosity exponent (m)

representing these multi-porosity reservoirs is required as input data. To accomplish this

task; we used two recent petrophysical models (Eq. 5.1 and Eq. 5.2) that can determine

m for dual and triple porosity reservoirs. These models have been validated with core

data and proven to estimate with reasonable certainty the multi-porosity values of m

(Aguilera, 2009, 2010; Olusola et al., 2013). Eq. 5.1 was developed using the

electromagnetic mixing formula of Maxwell Garnett (Olusola et al., 2012). It calculates

m for a dual porosity system made up of matrix and any type of non-connected or isolated

porosity. For example in the case of carbonate rocks, intragranular, ooilitic, moldic, and/

or fenestral porosity are the mathematical equivalent of isolated porosity. In the case of

this dual porosity model the summation of matrix and isolated porosity is equal to the

total porosity ϕ of the system.

[

((

(

( ( )]

( ……………...…………………………………Eq. 5.1

Eq. 5.2 is used to determine the m value of a dual-porosity model made up of matrix and

fractures (Aguilera and Aguilera, 2009, 2010). This case includes an angle θ between the

fracture and the direction of current flow (0o to 90

o).

[

]

( ……………………………………………...………………….Eq. 5.2

where,

(

………………………………………………………….……Eq. 5.3

( ………...……………………………….……………Eq. 5.4

93

Values of m from the above equations are used in the determination of n. The next

section explains the development of the petrophysical model that determines n in dual

and triple porosity reservoirs.

5.2.1 Dual Porosity (Matrix and Isolated Porosity)

The dielectric mixing rules of Maxwell Garnett, Bruggeman and Coherent Potential

approximation were unified into one family (Eq. 5.5) by Sihvola (1999). The unified

mixing formula assumes a spherical geometry in three dimensions in which isotropic

spherical inclusions with permittivity ԑi occupy random positions in an isotropic host

environment with permittivity ԑe . In this present work, the term permittivity relates to a

material’s capacity to allow (or “permit’) an electric field (Olusola et al. 2013).

( )

( ) …………………………...……………….Eq. 5.5

where f is the volume fraction occupied by a spherical inclusion, is the effective

permittivity, and vs is a Sihvola dimensionless parameter. Using different value of the

individual mixing rules can be recovered; for example when vs = 0 in Eq. 5.5 it gives the

Maxwell Garnett formula (Eq. 5.6):

[ ( (

( ( ]……………………………………………..…………Eq. 5.6

Recently, Olusola et al. (2013) used Eq. 5.6 to develop a petrophysical model that

determines the porosity exponent m in dual and triple porosity reservoirs. The model

compares well with core data and petrophysical models developed by Berg (2006),

94

Aguilera and Aguilera (2003, 2009) and Al-Ghamdi et al. (2011). To convert Eq. 5.6 to

oil and gas notation, we assigned Sihvola’s notation the following petrophysical

equivalences: host environment permittivity (ԑe) to be equivalent to the conductivity of

the matrix porosity; the spherical inclusions permittivity (ԑi ) corresponds to the

conductivity of the inclusion phase, the volume fraction f is equal to isolated porosity

( , and the effective permittivity (ԑeff) is equivalent to the conductivity of the total

porosity system. In order to replace the permittivity term with conductivity equivalences,

we use the complex dielectric permittivity which is defined as (Seybold, 2005):

(

) …………………..…………………………………..…..Eq. 5.7

where is the real part of the dielectric permittivity, =√-1, is the conductivity, and

is the angular frequency. At low frequencies ( approaches zero), the conductivity term

in Eq. 5.7 becomes large, and dominates the complex dielectric permittivity ( ). Based

on these observations, Eq. 5.6 can be recast for the special case of low frequency where it

becomes defined in terms familiar to petrophysics practitioners. As a result permittivity

terms can be replaced with their conductivity terms at low frequencies in Eq. 5.6 to yield

Eq. 5.8 (Olusola et al., 2013). The same type of reasoning using the complex dielectric

permittivity has been presented by Rasmus and Kenyon (1985), and Sihvola (1999).

[ ( (

( ( ]……….…………………………………………Eq. 5.8

Now, to use Eq. 5.8 to develop a model that estimates the water saturation exponent in a

dual porosity reservoir with mixed wettability; it is important to note that the term

wettability in this work refers to (1) the wetting preference of the rock and (2) the fluid in

contact with the rock at any given time. Also, except when stated otherwise; the concept

95

of mixed wettability as used in this chapter refers to a reservoir condition in which the

matrix porosity is water wet, the isolated porosity is oil wet and that the inclusion phase

is completely filled with oil. The conductivity terms in Eq. 5.8 can also be written using

standard petrophysical notation in terms of resistivity, which is the inverse of

conductivity. This allows expressing Archie’s-types relationships in standard form as

follows (Eq. 5.9 and 5.10):

For the composite system:

……………………………………………………………Eq. 5.9

For the host environment (matrix):

………………………………………………………....Eq. 5.10

and for the inclusion phase:

………………………………………….……………………Eq. 5.11

Also, an averaging equation for water saturation in a dual porosity reservoir made up of

matrix and isolated porosity can be written as,

( …………………………………..................……..Eq. 5.12

where is the water saturation in the isolated porosity and is the isolated porosity

ratio (ratio of the isolated porosity to the total porosity of the composite system). Eq. 5.12

is written such that if the average equation will represent that of a single

porosity (matrix porosity) reservoir, i.e.

…………………….……..……………..……………………………..Eq. 5.13

If (i.e. isolated pores filled completely with oil), Eq. 5.12 can be re-arranged to

yield:

96

(

( )…………….………….….…………………….……………….Eq. 5.14

Eq. 5.14 can be related to the reservoir condition in which the conductivity of the

inclusion phase is very low ( ≈ 0). Inserting Eqs. 5.9, 5.10, and 5.11 into Eq. 5.8 leads

to:

[

(

(

(

(

]……….……Eq. 5.15

cancels out of Eq. 5.15 leading to:

[ (

(

( (

]………………….……Eq. 5. 16

Re-arranging Eq. 5.16 results in:

[

[

]

(

(

( ( ]

[ ( ] ………………..……………………………………..…Eq. 5.17

Eq. 5.16 can be re-written in terms of the resistivity index as expressed in Eq. 5.18 to

give Eq. 5.19

…………………………………………………………………………Eq. 5.18

[ (

(

( (

] ( …………………..……Eq. 5.19

Eqs. 5.17 and 5.19 represent the petrophysical model used to determine the water

saturation exponent n in a dual porosity reservoir represented by matrix and isolated

porosity with mixed wettability. The two equations (Eqs. 5.17 and Eq. 5.19) give the

same results. Availability of data will direct which model to use for determining the

97

water saturation exponent n. The method on how to use the models will be explained

further in the model validation section of this chapter.

5.2.2 Dual Porosity (Matrix and Fracture Porosity)

To develop a model that determines the water saturation exponent (n) in a dual porosity

reservoir made up of matrix and fractures, we start with Eqs. 5.20 and 5.21 which

represent the effective permittivities of mixtures. From Maxwell Garnett formulas with

aligned ellipsoids, the depolarization factor is equal to zero in Eq. 5.20 and equal to 1.0 in

Eq. 5.21 (Sihvola, 1999):

( …………………………………………………..…….Eq. 5.20

( ………………………………………………...………......…Eq. 5.21

Based on the complex dielectric permittivity reasoning stated above and expressed in Eq.

5.7, the permittivity terms in Eq. 5.20 and 5.21 are replaced with their conductivity terms

at low frequencies but written in their equivalent resistivity terms in Eqs. 5.22 and 5.23:

(

……………………………..……..…..…….Eq. 5.22

(

…………………….………………..………...…..Eq. 5.23

and

………………………………………………………………...... Eq. 5.24

Eqs. 5.22 and 5.23 can be combined to give the total conductivity (inverse of resistivity)

of the system for current flowing at any angle ( with respect to the fractures (Eq. 5.25);

98

except when stated otherwise the angle ( between the fracture and the direction of

current flow has been taken to be 0o throughout this chapter so that the tortuosity is equal

to one (1.0) and the fracture porosity exponent, mf =1.0. Appendix C shows a schematic

of the angle between fractures and the direction of current flow.

(

) (

) ………………………………...…………Eq. 5.25

Therefore;

(

(

) (

(

) ………...…………Eq. 5.26

An averaging equation for water saturation in a dual porosity reservoir made up of matrix

and fracture porosity can be written as

( ……….…………………………………………...........Eq. 5.27

where is the water saturation in fractures and is the fracture porosity ratio (ratio of

the fracture porosity to the total porosity of the composite system) . If in Eq. 5.27

the average equation will represent that of a single porosity (matrix porosity) reservoir,

i.e.,

…………………….…………………….…………..…………………Eq. 5.28

Also, if (i.e. fractures are filled completely with water), Eq. 5.28 can be re-

arranged such that,

(

( ……………………..………………………………………………Eq. 5.29

Inserting Eqs. 5.9, 5.10 and 5.24 into Eq. 5.26 leads to:

(

(

)

99

(

(

) .………………………...……Eq. 5.30

cancels out of Eq. 5.30 resulting in:

[( (

)

(

(

) ]…......................................................Eq. 5.31

To obtain the water saturation exponent (n) in dual porosity system represented by matrix

and fracture porosities, Eq. 5.31 is re-arranged to yield Eq. 5.32:

[

([( ⟨(

⟩) ]

[

(

) (

] )]

[ ( ] ……………………………….………………….…Eq. 5.32

To include the resistivity index, Eq. 5.31 can be re-written as expressed in Eq. 5.33

using :

[( (

)

(

(

) ] ( ……………………………………………Eq. 5.33

100

Eqs. 5.32 and 5.33 represent the petrophysical model used to determine n in a dual

porosity reservoir made up of matrix and fracture porosities with mixed wettability. Eqs.

5.32 and 5.33 give the same results. Availability of data will direct which model to use

for determining the water saturation exponent. This will be explained further in the

modeling section of this chapter.

5.2.3 Triple Porosity (Matrix, Isolated and Fracture Porosity)

To determine the triple water saturation exponent n in a reservoir with mixed wettability;

the following steps are taken:

(1) Calculate a water saturation exponent nb’ using Eq. 5.34; note that Eq. 5.34 has the

same form as Eq. 5.17 but and n are replaced with ’ and nb’,

(2) Transfer the parameters ’ and nb’ into Eq. 5.32 to replace Swb and nb, respectively.

This results in Eq. 5.35 from which the triple porosity water saturation exponent (n) is

calculated. Berg (2006) and Olusola et al. (2013) followed a similar approach to

determine the triple porosity exponent (m) by using two dual porosity models.

[

[

]

(

(

( ( ] [ ( ]

………

……………………………………………………………………………….....….Eq. 5.34

101

[

([( ⟨(

⟩) ]

[

(

) (

] )] [ ( ] ………………….……Eq. 5.35

5.3 Model Validation

An essential part of this chapter is the validation of the models and their application to

mixed wettability reservoirs using core data published by Sweeney and Jennings (1960).

The intergranular core plugs studied by Sweeney and Jennings (1960) include twenty five

one-inch diameter core plugs, three-inches long with porosity values in the range of 11.8

to 31.5%. Throughout this chapter we demonstrate the use of the single, dual and triple

porosity models using a matrix porosity ( of 31.5%. Note that is scaled to the bulk

volume of only the matrix block.

Crossplots of resistivity index ( ) versus water saturation ( ) are used to validate the

models developed in this chapter. Since the available core data represent a single porosity

reservoir (Sweeney and Jennings do not mention fractures or isolated porosity); we

validate the models by converting the dual and triple porosity equations into a single

porosity model by making This corroborates that the dual and triple

porosity models developed in this study also apply to the case where there is only matrix

porosity. The single porosity model can next be extended to reservoirs made up of dual or

102

triple porosity systems. Three steps, one for each type of porosity, and various methods

are shown next for validation purposes.

5.3.1 First Step: Single Porosity Reservoirs (matrix porosity)

The first validation step of the methodology presented in this chapter is explained using

two methods for determining n; the first method uses water saturation while the second

method uses the resistivity index. Both methods are for single porosity reservoirs.

5.3.1.1 First Method: Use of Sw for Determining n

As indicated previously the available core data and wettability studies are for a single

porosity reservoir; therefore the core data water saturation ( is equal to the saturation

of the matrix block (Swb) and the matrix block porosity (b) can be handled with a dual

porosity model assuming that the isolated and fracture porosities are equal to zero (nc =

2 = 0).

5.3.1.1.1 Dual Porosity Model for matrix and isolated porosity system:

To convert the dual porosity model representing matrix and isolated porosity (Eq. 5.17)

to a single porosity model, we assume in Eq. 5.17. Columns 1 to 12 in Table

5.1 show results of the various petrophysical parameters determined for 5 samples.

Colum 1 presents the core porosities that correspond to matrix porosities scaled to the

103

bulk volume of only the matrix blocks ( b). For example, for sample No. 1,

Since the calculations are for only the matrix, vnc and as shown in

columns 2 and 3. matrix porosity scaled to the bulk volume of the composite system of

matrix and isolated porosity (m) is calculated with the use of equation B-2 in the

Appendix, and is shown in column 4. Total porosity scaled to the bulk volume of the

composite system of matrix and isolated porosity () is calculated with the use of

equation B-3 in the Appendix, and is shown in column 5. The porosity exponent of only

the matrix (mb = 2.01) is obtained from core data and is shown in column 6. The dual

porosity exponent (m) in column 5 is determined using Eq. 5.1. In this case, m= mb

because we are dealing with a single porosity reservoir.

The results presented on columns 9 to 12 of Table 5.1 show that and

indicating that the dual porosity model is robust and estimates the water saturation and

water saturation exponent correctly in the case of a single porosity reservoir. Since the

isolated porosity is zero in this dual porosity case, a value of Swnc is mathematically

needed. In this case, as shown in column 8. can be any other number

depending on the wettability conditions of the rocks . Water saturation in the matrix

block (Swb) is taken from the core data and is presented in column 9. The matrix block

water saturation exponent ( ) in column 10 is equal to the water saturation exponent

from core data and is also the same as calculated using Eq. 5.18. The values of nb range

between 3.92 and 4.50 suggesting the presence of a rock that is preferentially oil wet.

Water saturation ( ) in column 11 is calculated from Eq. 5.12 and in column 12 is

determined using Eq. 5.17.

104


ISOLATED POROSITY IS EQUAL TO ZERO AND MATRIX POROSITY IS

EQUAL TO THE TOTAL POROSITY

5.3.1.1.2 Dual Porosity Model for matrix and fracture porosity system:

To use the dual porosity model representing matrix and fracture porosity (Eq. 5.32) in a

conventional single porosity reservoir, we assume in Eq. 5.32. Table 5.2

(columns 1 to 12) shows results for petrophysical parameters determined in the following

manner: starting with column 1 assume that the porosity attached to the bulk volume of

only the matrix system is the core porosity ( as shown on column 2. For a

single porosity reservoir (column 3), it can also be determined using equation B-4

in the Appendix. and in columns 4 and 5 are determined from equations B-5 and

B-6 in the Appendix, respectively. Column 6 is the matrix porosity exponent attached to

only the matrix system (mb = 1.57). The dual porosity exponent (m) in column 7 is

determined using Eq. 5.2. Since this is a single porosity system, m= mb.

Since this is a dual porosity model where 2 is zero there is a mathematical need for

water saturation in the fractures. In this case is assumed equal to 1.0 as shown in

column 8. However, can be any other number depending on wettability conditions

Sample No. 1 2 3 4 5 6 7 8 9 10 11 12

ɸb Vnc ɸnc ɸm ɸ mb m Swnc Swb nb Sw n

1 0.315 0 0 0.315 0.315 2.01 2.01 0 0.22 4.41 0.22 4.41

2 0.315 0 0 0.315 0.315 2.01 2.01 0 0.23 4.50 0.23 4.50

3 0.315 0 0 0.315 0.315 2.01 2.01 0 0.25 4.25 0.25 4.25

4 0.315 0 0 0.315 0.315 2.01 2.01 0 0.26 3.92 0.26 3.92

5 0.315 0 0 0.315 0.315 2.01 2.01 0 0.26 4.40 0.26 4.40

105

and the angle between fractures and direction of flow ( ). Water saturation in the matrix

( ) in column 9 is given by the core data water saturation. The matrix block water

saturation exponent ( ) in column 10 is equal to the water saturation exponent from core

data. Water saturation ( ) in column 11 is calculated from Eq. 5.27 and in column 12

is determined using Eq. 5.32. The results of Table 5.2 show that and

indicating that the dual porosity model is robust and calculates Sw and n correctly in the

case of a single porosity reservoir.




5.3.1.2 Second Method: Use of I for Determining n


This second method also uses a dual porosity model for determination of n in a single

porosity reservoir. In this case the resistivity index ( is known and some of the

calculations require an iteration procedure. To convert the dual matrix and isolated

porosity model to a single porosity model is made equal to zero in Eq. 5.19. Table

5.3 (columns 1 to 15) shows results of the calculated petrophysical parameters for 5

Sample No. 1 2 3 4 5 6 7 8 9 10 11 12

ɸb V ɸ2 ɸm ɸ mb m Sw2 Swb nb Sw n

1 0.315 0 0 0.315 0.315 1.57 1.57 1 0.69 2.40 0.69 2.40

2 0.315 0 0 0.315 0.315 1.57 1.57 1 0.70 2.38 0.70 2.38

3 0.315 0 0 0.315 0.315 1.57 1.57 1 0.72 2.15 0.72 2.15

4 0.315 0 0 0.315 0.315 1.57 1.57 1 0.84 2.59 0.84 2.59

5 0.315 0 0 0.315 0.315 1.57 1.57 1 0.95 3.46 0.95 3.46

106

samples determined in the following manner: A value of from core data is

introduced in column 1.

Since there is no isolated porosity, as shown in columns 2 and 3 (see also

equation B-1 in the Appendix). Porosities and in columns 4 and 5 are determined

from equations B-2 and B-3 in the Appendix. Column 6 represents the matrix porosity

exponent attached only to the matrix system (mb = 2.01) determined from core data. The

dual porosity exponent (m) shown in column 7 is determined using Eq. 5.1. The result is

that m equals mb validating the use of the dual porosity equation for calculating m values

in single porosity systems.

The dual porosity model requires mathematically water saturation in the isolated porosity.

For this case it assumed that as shown in column 8. However, can be any

other value depending on the rock wettability conditions. Water saturations in the matrix

blocks ( ) in column 9 are obtained via an iteration procedure. The water saturation

exponent of the matrix blocks ( ) shown in column 10 are taken from cores. They range

between 3.92 and 4.50 suggesting that the rock is preferentially oil wet.

The resistivity index (I) in column 11 is also taken from the core data. Columns 12 and

13 are determined using Eq. 5.19. To use Eq. 5.19 iterations are run to determine the

unknown value of that makes the right hand side (RHS) of Eq. 5.19 equal to the left

hand side (LHS). In this work we used Microsoft Excel Solver package. To use this

package we followed these steps:

107

(1) Input available data into Eq. 5.19 and assume any reasonable value greater than zero

for .

(2) Set up as a constraint: LHS = RHS. (3) Run the iterations until reaching convergence;

at convergence LHS =RHS. The result from Eq. 5.19 is unique since it depends on a

constant resistivity index at each depth in the well.


determined with the use of Eq. 5.18. The results of Table 5.3 show that and

indicating that the matrix-isolated dual porosity model is robust and capable of

calculating correct values of n for single porosity reservoirs.


ISOLATED POROSITY IS EQUAL TO ZERO AND MATRIX POROSITY IS


Fig. 5.1 shows a comparison of results from this dual porosity model (with nc = 0) and

core data (single porosity) published by Sweeney and Jennings (1960) for preferentially

oil-wet rocks. The blue diamonds in the graph correspond to core data, the black open

diamonds represent calculated parameters to match the core data, and the numbered red

square symbols represent the calculated values shown in Table 5.3 (samples 1 to 5) for

Sample No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

ɸb Vnc ɸnc ɸm ɸ mb m Swnc Swb nb I LHS RHS Sw n

1 0.315 0 0 0.315 0.315 2.01 2.01 0 0.22 4.41 805.85 0.10 0.10 0.22 4.41

2 0.315 0 0 0.315 0.315 2.01 2.01 0 0.23 4.50 753.78 0.10 0.10 0.23 4.50

3 0.315 0 0 0.315 0.315 2.01 2.01 0 0.25 4.25 349.40 0.10 0.10 0.25 4.25

4 0.315 0 0 0.315 0.315 2.01 2.01 0 0.26 3.92 192.88 0.10 0.10 0.26 3.92

5 0.315 0 0 0.315 0.315 2.01 2.01 0 0.26 4.40 354.43 0.10 0.10 0.26 4.40

108

illustration purposes. The red squares make it easier for the readers to compare the

calculations presented in Table 5.3 with the graph shown in Fig. 5.1.

Figure 5.1— Comparison of Eq. 5.19 for matrix and isolated porosity using nc = 0

and preferentially oil-wet core data published by Sweeney and Jennings (1960). The

blue diamonds represent core data, the black open diamonds represent other data

from the dual porosity model used to match the core data. All the core data points

are matched. The red squares correspond to data calculated for illustration

purposes in Table 5.3 for samples 1 to 5.


To convert this dual porosity model into a single porosity petrophysical model we assume

in Eq. 5.33. Table 5.4 (columns 1 to 15) shows petrophysical parameters

determined for this case in the following manner: The porosity attached only to the

matrix system ( shown in column 1 is from unfractured cores. Column 2 is

determined using equation B-4 in the Appendix. For a single porosity reservoir as

1

10

100

1000

0.1 1

Re

sist

ivit

y R

ati

o

Fractional Water Saturation(Sw)

1 253

4

109

shown in column 3. Porosities and in column 4 and 5 are determined from equation

B-5 and B-6 (Appendix), respectively. Column 6 is the matrix porosity exponent attached

only to the matrix system (mb = 1.57). The dual porosity exponent (m) in column 7 is

determined using Eq. 5.2. For this case, m= mb because we are dealing with a single

porosity system.

Since this is a dual porosity model where 2 is zero there is a mathematical need for

water saturation in the fractures. In this case is assumed equal to 1.0 as shown in

column 8 indicating thus water wet fractures. However, can be any other value

depending on wettability conditions of the fractures and the angle between fractures and

direction of flow ( ). Water saturation in the matrix ( ) in column 9 is obtained via

iteration and in column 10 is the water saturation exponent from core data. The small

values of nb (1.37 to 1.53) indicate that the matrix is preferentially water wet. The

resistivity index (I) in column 11 is taken from core data, columns 12 and 13 are

determined using Eq. 5.33. This involves iterations to determine the unknown value

( ) that will make the RHS = LHS in Eq. 5.33. In this work we used Microsoft Excel

Solver package and the following steps: (1) Input available data into Eq. 5.33 and assume

any reasonable value greater than zero for . (2) Set up a constraint: LHS = RHS. (3)

Run iterations until attaining convergence at LHS = RHS. The iteration result from Eq.

5.33 is unique since it depends on a constant resistivity index at each depth in the well.


determined using Eq. 5.18. The results in Table 5.4 show that and

indicating that the dual porosity model is capable of calculating water saturation and the

110

water saturation exponent correctly in single porosity reservoirs. For this example, =

90o

in Eq. 5.33. The model (Eq. 5.33) is capable of running iterations without any

convergence problem with .

Table 5.4— RESULTS FOR SINGLE POROSITY RESERVOIR WHEN



Fig. 5.2 shows a comparison of results from this dual porosity model (with 2 = 0) and

core data (single porosity) published by Sweeney and Jennings (1960) for preferentially

water-wet rocks. The blue diamonds in the graph correspond to core data, the black open

diamonds represent the calculated parameters that match the core data, and the numbered

red square symbols represent the calculated values shown in Table 5.4 (samples 1 to 5)

for illustration purposes. The red squares make it easier for the readers to compare the

calculations presented in Table 5.4 with the graph shown in Fig. 5.2.

Sample No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

ɸb V ɸ2 ɸm ɸ mb m Sw2 Swb nb I LHS RHS Sw n

1 0.315 0 0 0.315 0.315 1.57 1.57 1 0.15 1.37 13.32 0.16 0.16 0.15 1.37

2 0.315 0 0 0.315 0.315 1.57 1.57 1 0.15 1.54 18.18 0.16 0.16 0.15 1.54

3 0.315 0 0 0.315 0.315 1.57 1.57 1 0.16 1.56 16.79 0.16 0.16 0.16 1.56

4 0.315 0 0 0.315 0.315 1.57 1.57 1 0.19 1.40 9.94 0.16 0.16 0.19 1.40

5 0.315 0 0 0.315 0.315 1.57 1.57 1 0.20 1.53 12.17 0.16 0.16 0.20 1.53

111

Figure 5.2— Comparison of Eq. 5.33 for matrix and fractures using 2 = 0 and

preferentially water-wet core data published by Sweeney and Jennings (1960). The

blue diamond’s represent core data, the black open diamonds represent other data

from the dual porosity model used to match the core data. All the core data points

are matched. The red squares correspond to data calculated for illustration

purposes in Table 5.4 for samples 1 to 5.

5.3.2 Second Step: Dual Porosity Reservoirs (Matrix and Isolated Porosity or Matrix

and Fracture Porosity)

The second validation step of the dual porosity models developed in this chapter is

explained using two methods; the first method shows how to determine the water

saturation exponent (n) using water saturation values while the second step shows how to

use resistivity index values to determine the water saturation exponent (n).


As indicated previously the available core data and wettability studies are for a single

porosity reservoir; therefore the core water saturations are equal to the saturation of the

1

10

100

1000

0.1 1

Resi

stiv

ity R

atio


5

4

3

1

2

112

matrix blocks (Swb) and the porosity of cores is equal to the matrix block porosity (b).

Furthermore it was shown previously that single porosity can be handled with a dual

porosity model assuming that the isolated and fracture porosities are equal to zero (nc =

2 = 0). In this second step we investigate the effects of isolated and fracture porosities

greater than zero on and .


In this example we assume in the dual porosity model made out of matrix

and isolated pores (Eq. 5.17). Each data value in Table 5.5 (columns 1 to 12) is

calculated using the first method explained previously in the section “First Step: Single

Porosity Reservoirs (matrix porosity).” In this case Sw is known. The only difference is

that now for illustration purposes (rather than zero) in Table 5.5. The water

saturation in the isolated porosity (Swnc) shown in column 8 is equal to zero. Thus the

isolated porosity is full of oil and is oil-wet. Also oil-wet is the matrix as the values of nb

in column 10 are large (3.92 to 4.50). The effects of increasing isolated porosity (PHINC)

on the water saturation exponent are shown on Fig. 5.3. The plot was constructed using

data developed with the use of the dual porosity model for matrix and isolated porosity

represented by Eq. 5.17 under the assumption that nb is equal to 4.0.

113

Table 5.5— RESULTS FOR DUAL POROSITY RESERVOIR WITH MATRIX

AND ISOLATED POROSITY


model for matrix and isolated porosity (Eq. 5.17). The chart shows the effects of

increasing isolated porosity (PHINC) on while keeping matrix porosity constant at

b = 0.315 Matrix and composite system (vugs+matrix) are oil wet.


This case is handled assuming in the dual porosity model made out of matrix

and fractures (Eq. 5.32). Each data value in Table 5.6 (columns 1 to 12) is determined

using the first method explained previously in the section “First Step: Single Porosity

Reservoirs (matrix porosity).” The only difference is that now for illustration purposes

(rather than zero) in Table 5.6.

Sample No. 1 2 3 4 5 6 7 8 9 10 11 12

ɸb Vnc ɸnc ɸm ɸ mb m Swnc Swb nb Sw n

1 0.315 0.143 0.050 0.299 0.349 2.01 2.06 0 0.22 4.41 0.19 4.14

2 0.315 0.143 0.050 0.299 0.349 2.01 2.06 0 0.23 4.50 0.20 4.21

3 0.315 0.143 0.050 0.299 0.349 2.01 2.06 0 0.25 4.25 0.22 3.97

4 0.315 0.143 0.050 0.299 0.349 2.01 2.06 0 0.26 3.92 0.22 3.67

5 0.315 0.143 0.050 0.299 0.349 2.01 2.06 0 0.26 4.40 0.23 4.10

1.5

2.5

3.5

4.5

0.0 0.2 0.4 0.6 0.8 1.0

Wat

er S

atur

atio

n Ex

pone

nt,n

Water Saturation

PHINC=0.025

PHINC=0.050

PHINC=0.075

PHINC=0.100

nb = 4.0

114

The water saturation in the fracture porosity (Sw2) shown in column 8 is equal to 1. Thus

the fracture porosity is full of water and is water-wet. The matrix has intermediate

wettability as the values of nb in column 10 are moderate (2.15 to 3.46).

The effects of increasing fracture porosity (PHI2) on the water saturation exponent are

shown on Fig. 5.4. The plot was constructed using data developed with the use of the

dual porosity model for matrix and fractures represented by Eq. 5.32 under the

assumption that nb is equal to 4.0. The value of n for the composite system shown in

column 12 ranges between 1.75 and 2.92 suggesting a system that is preferentially water

wet with the possible exception of sample 5. Fig. 5. 4 (matrix and fracture porosity) has

an opposite slope compared to Fig. 5.3 (matrix and isolated porosity) because the Sw2 is

equal to one in Fig. 5.4 while Swnc is equal to zero in Fig. 5.3.

Table 5.6 — RESULTS FOR DUAL POROSITY RESERVOIR WITH MATRIX

AND ISOLATED POROSITY

Sample No. 1 2 3 4 5 6 7 8 9 10 11 12

ɸb V ɸ2 ɸm ɸ mb m Sw2 Swb nb Sw n

1 0.315 0.143 0.050 0.299 0.349 1.57 1.51 1 0.69 2.40 0.73 1.90

2 0.315 0.143 0.050 0.299 0.349 1.57 1.51 1 0.70 2.38 0.74 1.90

3 0.315 0.143 0.050 0.299 0.349 1.57 1.51 1 0.72 2.15 0.76 1.75

4 0.315 0.143 0.050 0.299 0.349 1.57 1.51 1 0.84 2.59 0.87 2.16

5 0.315 0.143 0.050 0.299 0.349 1.57 1.51 1 0.95 3.46 0.96 2.92

115


model for matrix and fractures (Eq. 5.32). The chart shows the effects of increasing

fracture porosity (PHI2) on while keeping matrix porosity constant at b = 0.315 Matrix and composite system (matrix plus fractures) are water wet.


5.3.2.2.1 Dual Porosity for matrix and isolated porosity system:

In this section, we assume in the dual porosity model made out of matrix and

isolated pores (Eq. 5.19). The matrix porosity (b) is maintained constant at 0.315. We

follow similar calculation steps as shown previously in the second method in the section

“First Step: Single Porosity Reservoirs (matrix porosity).” In this method the resistivity

index (I) is known.

0.0

1.0

2.0

3.0

4.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Wate

r S

atu

rati

on

Exp

on

en

t,n

Water Saturation

PHI2=0.025

PHI2=0.050

PHI2=0.075

PHI2=0.100

nb = 4.0

116

The red squares in Fig. 5.5 show a cross plot of the calculated water saturation against the

resistivity index (red squares). The isolated porosity is 100% saturated with oil. Also

shown for comparison are the oil wet data (black diamonds) extracted from core analysis

(single porosity model) by Sweeney and Jennings (1960). These core data was also

shown on Fig. 5.1. In this case, for the same resistivity index the values of water

saturation are lower in the case of the dual porosity model.

In both cases the slopes of the linear trends for matrix and composite systems are steep (n

> 7) indicating that both the matrix and composite system (matrix and isolated pores) are

preferentially oil wet.


isolated porosity (red squares) and comparison with core data (single porosity

model). For the same resistivity index, water saturations are smaller in the case of

the dual porosity model. Matrix and the composite system (matrix + vugs) are oil

wet.

1

10

100

1000

0.1000 1.0000

Res

isti

vity

Rat

io


Dual Porosity Model

Single Porosity Model

117

5.3.2.2.2 Dual Porosity for matrix and fracture porosity system:

In this section, we assume in the dual porosity system made out of matrix and

fractures (Eq. 5.33). We follow similar calculation steps as shown previously in the

second method in the section “First Step: Single Porosity Reservoirs (matrix porosity).”

In this method the resistivity index (I) is known.

The red squares in Fig. 5.6 show a cross plot of the calculated water saturation values vs.

resistivity index. Also shown for comparison (black diamonds) are the data extracted

from core analysis (single porosity model) published by Sweeney and Jennings (1960).

As opposed to the previous dual porosity model (oil wet matrix and isolated pores), for

the same resistivity index the values of water saturation are larger in the case of the dual

porosity model made out of matrix and fractures. This is because the angle between the

fractures and the direction of flow was taken as 90o for this case.

In the case of core experiments (single porosity model), also shown in Fig. 5.2, the

average value of n is 1.666 (R2 = 0.86) indicating a system that is preferentially water

wet. In the case of the dual porosity model the slope is steeper with an average value of n

equal to 2.22 (R2 = 0.896) indicating that both the matrix and composite system (matrix

and fractures combined) are preferentially water wet.

118


fracture porosity (red squares) and comparison against core data (single porosity

model). For the same resistivity index, water saturations are larger in the case of the

dual porosity model for the example at hand. The slope values indicate that the

matrix and the composite system are preferentially water wet.

5.3.3 Third Step: Triple Porosity Reservoirs (Matrix, Isolated and Fracture Porosities)

The third step is treated using two methods. The first method shows how to determine the

water saturation exponent (n) using water saturation values (Sw) while the second method

shows how to use resistivity index values (I) to determine the water saturation exponent

(n). Both methods are for a triple porosity reservoir system that include matrix, isolated

and fracture porosities.

y = x-2.222

R² = 0.8964

y = x-1.666

R² = 0.8633

1

10

100

0.1 1.0

Re

sist

ivit

y In

dex

(I)

Fractional Water Saturation (Sw)

Dual Porosity Model


119


In this section, to determine the triple water saturation exponent in a reservoir with mixed

wettability. The approach involves the following steps:

(1) Calculate an intermediate water saturation exponent nb’ using Eq. 5.34. Note that Eq.

5.34 has the same form as Eq. 5.17 and all the petrophysical parameters are determined in

the same way as done previously for the dual porosity model represented by isolated and

matrix porosities (first method).

(2) Transfer the parameter ’ and nb’ from Eq. 5.34 into Eq. 5.35 making ’ =

and nb’ = n. Use Eq. 5.35 to calculate the triple porosity water saturation exponent (n).

Note that Eq. 5.35 has the same form as Eq. 5.32. All the other petrophysical parameters

beyond Swb and nb are determined in the same way as was done with the dual porosity

model represented by fractures and matrix porosity (first method).

(3) Prepare a cross plot of water saturation exponent (n) versus water saturation as shown

on Fig. 5.7. This provides a good visualization of the calculations. The matrix porosity

(b) in the graph is 0.315, fracture porosity (2 ) is 0.01 and the isolated porosities (nc )

are 0.025, 0.05, 0.075, and 0.1.

120

Figure 5.7— Graph of versus using Eqs. 5.34 and 5.35 for the case of a triple

porosity model. The chart shows the combined effects of isolated porosity and

fracture porosity on Matrix porosity (b) is maintained constant at 0.315 in this

case.


In this example matrix porosity (b) is equal to 0.315 and . The matrix

system (core) is oil wet as well as the isolated vugs which have a water saturation of zero

(100% oil). The fractures are water wet with a water saturation of 1. The calculations are

as in the second method for the single porosity reservoir case but

in Eq. 5.34

and Eq. 5.35. The calculated results are plotted as red squares in Fig. 5.8. A comparison

is made with core data from an oil wet system (black squares), which corresponds to only

matrix (core, single porosity model). Contrary to the case shown on Fig. 5.5, for the same

1.5

2.5

3.5

0.0 0.2 0.4 0.6 0.8

Wa

ter

Satu

rati

on

Exp

on

en

t,n

Water Saturation

PHINC=0.025,PHI2=0.01

PHINC=0.050,PHI2=0.01

PHINC=0.075,PHI2=0.01

PHINC=0.100,PHI2=0.01

nb = 4.0

121

resistivity index, water saturations are higher in the triple porosity than in the single

porosity model. The overall triple porosity system is oil wet with values of n greater than

7.

Figure 5.8— Graph of versus calculated for a triple porosity model (red

squares). The calculated results are compared against core data represented by

black squares (single porosity model). For the same resistivity index the water

saturation of the triple porosity model is generally larger than Sw from cores (single

porosity).

1.0000

10.0000

100.0000

1000.0000

0.1000 1.0000

Re

sist

ivit

y R

atio


Triple Porosity Model


122

Chapter Six: PETROPHYSICAL AND GEOMECHANICAL EVALUATION

6.1 Overview

This chapter presents a case study on petrophysical and geomechanical evaluation of

horizontal wells in the tight gas Nikanassin Group of the WCSB using drill cuttings. The

advantages of measuring porosity and permeability from drill cuttings has also been

discussed as they provide an aid in performing a complete quantitative petrophysical and

geomechanical evaluation of reservoirs in those cases where well logs and/or core data

are not available. Several empirical equations using porosity and permeability data for

calculating capillary pressure, irreducible water saturation, porosity exponent (m), pore

throat aperture radius, true formation resistivity, location of water contact, Knudsen’s

number, Young Modulus, Poisson’s ratio, and brittleness index have been used to

characterize this tight gas formation

6.2 Petrophysical Evaluation Based on Drill Cuttings

6.2.1 Case Study: Drill Cuttings Collected in Horizontal Well

Column 1 of Table 6.1 identifies 57 drill cutting samples considered in this study. The

measured depth in Column 2 represents the bottom depth where the drill cutting samples

were collected in the horizontal well.

123

Table 6.1— PETROPHYSICAL DATA FOR WESTERN CANADA



(COLUMN 2 & 3) ARE OBTAINED FROM LABORATORY WORK AND IT IS

USED AS A STARTING POINT IN DETERMINING OTHER PETROPHYSICAL

DATA (COLUMN 5 TO 11) USING EMPIRICAL EQUATIONS.

1 2 3 4 5 6 7 8 9 10 11

Sample

No.

BOTDepth

MD (m)

Ф (Drill

Cuttings)

K (md)

(Drill

Cuttings)

rp35

(μm)m

Swi

(fraction)F

Rt

(ohm.m)

Pc (Hg-Air)

(Psi)Kn

1 3185.0 0.066 0.031 0.239 1.827 0.129 143.61 231 7101 0.00052

2 3190.0 0.063 0.022 0.208 1.823 0.136 152.61 221 7442 0.00060

3 3195.0 0.065 0.030 0.237 1.825 0.125 146.74 247 7478 0.00053

4 3200.0 0.053 0.038 0.290 1.801 0.059 201.16 1254 22116 0.00043

5 3202.5 0.065 0.056 0.313 1.826 0.094 145.19 416 9297 0.00040

6 3205.0 0.106 0.088 0.309 1.866 0.314 66.22 22 1204 0.00041

7 3207.5 0.087 0.079 0.322 1.852 0.183 92.65 82 2903 0.00039

8 3210.0 0.090 0.216 0.497 1.855 0.125 86.71 157 3608 0.00025

9 3217.5 0.069 0.025 0.213 1.831 0.161 135.22 146 5443 0.00059

10 3220.0 0.098 0.017 0.153 1.861 0.568 75.49 8 891 0.00082

11 3225.0 0.099 0.017 0.152 1.861 0.586 74.20 8 850 0.00082

12 3235.0 0.065 0.069 0.344 1.826 0.084 145.97 515 10271 0.00036

13 3265.0 0.086 0.058 0.280 1.851 0.212 93.04 63 2595 0.00045

14 3285.0 0.150 0.064 0.229 1.885 1.044 35.92 1 211 0.00055

15 3290.0 0.084 0.078 0.325 1.849 0.166 98.13 103 3394 0.00039

16 3295.0 0.055 0.032 0.262 1.807 0.075 186.63 765 16195 0.00048

17 3300.0 0.091 0.190 0.468 1.855 0.136 85.67 132 3314 0.00027

18 3305.0 0.068 0.109 0.415 1.830 0.075 136.72 588 10136 0.00030

19 3310.0 0.054 0.055 0.337 1.805 0.054 191.47 1400 21839 0.00037

20 3315.0 0.062 0.062 0.335 1.821 0.077 156.66 638 12199 0.00037

21 3320.0 0.105 0.069 0.278 1.865 0.347 67.11 18 1132 0.00045

22 3325.0 0.096 0.046 0.241 1.859 0.325 78.08 24 1454 0.00052

23 3345.0 0.121 0.150 0.369 1.874 0.365 52.04 13 782 0.00034

24 3355.0 0.077 0.025 0.202 1.842 0.227 112.57 65 3185 0.00062

25 3435.0 0.061 0.065 0.346 1.818 0.069 163.22 798 14105 0.00036

26 3440.0 0.066 0.048 0.291 1.827 0.103 143.83 347 8497 0.00043

27 3445.0 0.085 0.051 0.267 1.850 0.212 96.34 65 2719 0.00047

28 3450.0 0.077 0.010 0.134 1.842 0.359 112.72 28 2216 0.00093

29 3460.0 0.052 0.020 0.218 1.800 0.079 203.38 740 17735 0.00057

30 3690.0 0.069 0.023 0.204 1.832 0.174 132.79 125 4988 0.00061

31 3710.0 0.049 0.030 0.268 1.792 0.055 219.90 1525 27055 0.00047

32 3715.0 0.046 0.029 0.272 1.783 0.045 240.89 2260 36506 0.00046

33 3720.0 0.051 0.025 0.243 1.798 0.068 207.59 994 20747 0.00052

34 3725.0 0.066 0.028 0.229 1.826 0.133 144.82 218 6991 0.00055

35 3730.0 0.078 0.036 0.237 1.843 0.197 110.21 84 3467 0.00053

36 3735.0 0.053 0.010 0.158 1.802 0.119 197.58 347 12227 0.00079

37 3740.0 0.068 0.018 0.185 1.829 0.182 138.21 119 5094 0.00068

38 3745.0 0.064 0.066 0.341 1.823 0.080 151.45 582 11281 0.00037

39 3760.0 0.051 0.057 0.352 1.798 0.045 207.98 2102 29029 0.00036

40 3765.0 0.048 0.018 0.215 1.789 0.066 227.17 1122 24630 0.00058

41 3770.0 0.050 0.012 0.177 1.793 0.088 218.38 650 18320 0.00071

42 3775.0 0.068 0.015 0.170 1.829 0.199 138.21 100 4736 0.00073

43 3785.0 0.066 0.016 0.178 1.827 0.178 143.99 128 5494 0.00071

44 3820.0 0.058 0.019 0.204 1.812 0.109 176.59 372 11029 0.00061

45 3835.0 0.066 0.011 0.149 1.828 0.221 141.91 85 4527 0.00084

46 3855.0 0.084 0.184 0.478 1.849 0.109 97.79 225 4739 0.00026

47 3860.0 0.061 0.020 0.203 1.819 0.129 160.30 252 8326 0.00062

48 3865.0 0.073 0.015 0.165 1.837 0.252 122.25 59 3297 0.00076

49 3880.0 0.084 0.012 0.140 1.849 0.429 97.31 18 1568 0.00090

50 3885.0 0.055 0.020 0.214 1.805 0.090 190.95 555 14444 0.00059

51 3890.0 0.082 0.017 0.166 1.847 0.328 102.41 30 2082 0.00076

52 3895.0 0.073 0.015 0.165 1.837 0.252 122.16 58 3290 0.00076

53 3900.0 0.075 0.016 0.168 1.839 0.260 118.20 54 3067 0.00075

54 3930.0 0.076 0.010 0.135 1.840 0.345 115.08 31 2352 0.00093

55 3935.0 0.061 0.014 0.173 1.819 0.154 160.69 184 7273 0.00073

56 3940.0 0.068 0.020 0.194 1.829 0.172 138.28 131 5321 0.00065

57 3945.0 0.076 0.080 0.343 1.841 0.123 114.62 206 5342 0.00036

58 AVERAGE 0.073 0.047 0.253 1.831 0.195 137.14 381 8553 0.00055

124

6.2.2 Porosity

Porosity which represents the amount of void space in a bulk volume of rock is

considered as a measure of the storage capacity of the rock since it is capable of holding

fluids (Ahmed 2006). Porosity is an important rock property, cheaper to measure and

most readily used to correlate with other rock properties such as permeability and pore

throat aperture that are more expensive to obtain.

In this case study, we provide support to the conclusion that measuring porosity from

drill cuttings is an important step to complete petrophysical evaluation of reservoirs in the

absence of well logs or cores. The porosity values obtained from drill cuttings closely

match those from well log data (Ortega and Aguilera, 2012); therefore we anticipate that

future quantitative formation evaluation work will also include drill cuttings. Care will

always have to be exercised in tight reservoirs because in all probability some of the slot

porosity and micro-fractures will be destroyed by the action of the drilling bit, but drill

cuttings can still provide relevant quantitative information as shown in this case study

using drill cuttings collected in a horizontal well. Furthermore they can provide structural

information (Hews, 2012) that is very relevant for estimating the Frac Value (Ortega and

Aguilera, 2012). The third column in Table 6.1 shows the laboratory porosity values

from drill cuttings.

125

6.2.3 Permeability

Permeabilities were determined using Darcylog equipment patented by the Institut

Français du Pétrole (IFP) and methodologies presented by Egermann et al. (2002) and

Lenormand et al. (2007). Nikanassin data (Solano, 2010; Ortega, 2012) confirmed the

reliability of permeability measurements from drill cuttings. These permeabilities are

most likely associated with the matrix system since micro fractures are probably not

preserved in drill cuttings. Permeability is a function of many petrophysical variables

including grain size, pore-throat aperture, porosity, pore architecture and irreducible

water saturation. Among these independent variables porosity represents the most easily

measured variable used for predicting permeability (Byrnes, 2005). Column 4 in Table

6.1 show the laboratory permeabilities from drill cuttings determined in this study.

6.2.4 Pore Throat Aperture Radii

Pore throat size represents one of the dominant variables that control permeability in low

permeability rocks (Byrnes, 2005). Pore throat aperture is generally estimated from

mercury injection test but this test is expensive to acquire and the chemical element in

mercury is not environmentally friendly due to its toxic nature. Therefore, empirical

equations relating pore throat aperture to less expensive parameters such as permeability

and porosity are generally used to estimate the pore throat aperture (Pittman, 1992).

126

The Washburn equation shows a relationship that determines the pore aperture radius in

porous rocks after conducting mercury injection test in the laboratory (Washburn, 1921).

H. D. Winland (1980s) of Amoco Research Department (Tulsa, Oklahoma) used

Washburn equation and performed mercury injection tests on sandstones from 14

formations. These 14 formations which age range from Ordovician to Tertiary include

Simpson, Delaware, Tensleep, Nugget, Cotton Valley, Muddy, Meserverde, Terry, First

Wall Creek, Second Wall Creek, Frontier, Montrose, Vicksburg, and Frio Sandstones.

From this mercury injection test, Winland established an empirical correlation that relates

porosity and permeability to pore throat size. 202 porosity (data range from 3.3% to 28%)

and uncorrected air permeability (data range from 0.05 to 998md) data sets was used in

his analysis (Pittman, 1992).

A similar equation (Eq. 6.1) that relates porosity and permeability to pore throat aperture

was developed by Aguilera (2002):

[

]

.......................................................................................... Eq. 6.1

This equation is rigorously valid between 30 to 90% water saturation, but in practice we

have been able to extend it beyond those limits with reasonable results for the tight

formations we are studying in the GFREE research group (Aguilera 2002 and Ortega et al

2013). The porosity and permeability obtained from drill cuttings were used to estimate

the pore throat radii (rp35) shown in Column 5 of Table 6.1.

127

6.2.5 Porosity Exponent ( )

Data from the Mesaverde tight gas formation in the United States was used by Byrnes et

al. (2006) to develop the following empirical correlation for calculating the porosity

exponent ( ):.

…………………………………..…………………………….… Eq. 6.2

A crossplot of Eq. 6.2 is shown in Fig. 6.1. Given that porosity exponent ( ) data are not

available in the study area and that there are some similarities between the Nikanassin

and Mesaverde continuous accumulations, the above equation was used to generate

porosity the exponent ( data shown in column 6 of Table 6.1.

128

Figure 6.1—Plot of porosity exponent ( versus porosity ( . The porosity

exponent was determined using Byrnes empirical correlation (Eq. 6.2).

6.2.6 Irreducible Water Saturation

Low permeability gas-production sandstone reservoirs are typically known for high

capillary pressure due to the small pore throat size of the reservoir rocks. Since

irreducible water saturation affects the gas recovery from low permeability reservoirs; it

is essential to account for the presence of this water. In conventional reservoirs

irreducible water saturation is defined as the saturation at which a further increase in

capillary pressure does not significantly decrease the water saturation (Byrnes, 2005). In

129

the case of tight gas sandstones it is possible to have from very small to nearly 100%

water saturation at irreducible conditions.

Morris and Biggs (1997) developed an empirical equation to estimate permeability for

formations at irreducible condition. They expressed the correlation of log derived values

of water saturation (Sw) versus porosity ( ) as:

…………………………………………………………………………Eq. 6.3

In Eq. 6.3, k = formation permeability, milidarcies, Swi = water saturation at irreducible

saturation, i.e., it corresponds to the beginning of krw equal to zero and c equal to a

constant whose value depends on the density of the type of hydrocarbon occupying the

formation. For the case of medium gravity oil (≈25o API), c = 250, and for dry gas at

shallow depth, c = 79. Since the formation under study is a tight gas formation, a constant

value of c = 79 was used in this work.

This correlation is applicable in this case study because for several years of gas

production from the Nikannasin tight gas sandstone, the water production has been zero.

This indicates that the formation has immobile water even in zones with high values of

water saturation (Solano el al., 2011 ; Ortega and Aguilera, 2013). Therefore, Eq. 6.3 can

be written to calculate the irreducible water saturation from:

130

………………………………………………………………………. Eq. 6.4

The calculated values of irreducible water saturation are presented in column 7 of Table

6.1.

Figure 6.2— Buckles plot. The red circles represent porosity and permeability data

from drill cuttings. Lines of constant permeability are represented by solid lines.

The red circles and solid lines are determined using Eq. 6.4. The dashed lines

represent the constant values of the product of porosity and irreducible water

saturation also known as Buckles number. All water saturations are irreducible

since the wells have not produced any water for several years.

Morris and Biggs (1967) also corroborated Buckles’ (1965) observation that the product

of porosity and water saturation was approximately constant for intervals at irreducible

water saturation. Since porosity and permeability (columns 3 and 4 in Table 6.1) are

131

obtained from drill cuttings, and the tight gas formation under consideration does not

produce any water, it is possible to estimate irreducible water saturation with the use of

Eq. 6.4. Porosity, permeability and Buckles number are introduced in Fig. 6.2; the

increasing Buckles number is indicative of increasing reservoir heterogeneity (not

moveable water) since the Nikanassin tight gas formation is known for zero water

production (Solano et al., 2011).

6.2.7 True Formation Resistivity

True formation resistivity is an important parameter in petrophysical evaluation of

hydrocarbon reservoirs (Archie, 1942). It is also important in the construction of Pickett

plots.

Archie established that the ratio of resistivity of a completely brine saturated rock ( ) to

the resistivity of the brine ( saturating the rock is equal to the formation factor ( ).

He also observed that has a linear relationship with porosity:

..............................................................................................................Eq. 6.5

Eq. 6.5 was used for calculating the values of F shown in column 8 of Table 6.1. Next,

values of were calculated as shown in column 9 using irreducible water saturations

values from column 7, m values from column 6, formation water resistivity Rw = 0.038

ohm-m (at 100o C of temperature) and constant a=1, with the use of the equation (Archie,

1942):

132

…………………………..……………………………………Eq. 6.6

where is the water saturation exponent (assumed equal to in this study). Eq. 6.6 can

be applied in this study because the drill cuttings used in the laboratory for determination

of porosity and permeability are clean sandstone samples.

6.2.8 Capillary Pressure

A discontinuity in pressure exists between two immiscible fluids that are in contact. This

pressure difference is generally known as capillary pressure and commonly defined as the

difference in pressure across the interface between two fluids that are not miscible

(Ahmed, 2006). Capillary pressure shown in column 10 of Table 6.1 was calculated from

Eq. 6.7 (Aguilera, 2002):

[ ] ( ⁄ )

…………………………………..…………….Eq. 6.7

where Sw is water saturation (fraction). In order to extend Eq. 6.7 to this study, we

replaced the water saturation (Sw) with irreducible water saturation (Swi). This is valid

because several years of gas production from the Nikannasin formation have resulted in

zero water production, which indicates that the formation is at irreducible water

saturation (Solano el al., 2011; Ortega and Aguilera, 2013).

133

The trend line fit between the capillary pressure and irreducible water saturation was

performed using the power regression option in excel (Fig. 6.3). Strictly, however,

separate capillary pressures have to be developed for each value of porosity and

permeability. For the case at hand, the results are similar to the regression line.

Figure 6.3— Plot of capillary pressure (Pc) vs. irreducible water saturation (Swi). Pc

was determined using Eq. 6.7 and Swi was obtained using Eq. 6.4 based on

knowledge of porosity and permeability from drill cuttings.

6.2.9 Distinguishing Between Viscous and Diffusion-Like Flow

A thorough understanding of gas flow through micro or nano scale pore space (tight

porous media) is important for improving techniques that will ensure economic flow rates

and recoveries from tight formations (Rahmanian et al., 2013). Knudsen number has been

recognized as a flow regime indicator that helps to understand the flow regime (viscous

or diffusion-like flow or maybe a combination of the two) in tight formations. Knudsen

134

number is defined in gas dynamics as the ratio of the molecular mean free path ( ) to

some characteristics length ( ). The molecular mean free path ( ) is the average

distance covered by a moving molecule between successive collisions that modify its

direction or energy or its other properties. The characteristics length ( ) depends on the

type of problem under consideration and the flow geometry (Knudsen, 1909, after

Kennard, 1938, Klinkenberg, 1941, Rahmanian et al., 2013).

Four different flow regimes have been recognized in gas dynamics of porous media and

the value of Knudsen number (Kn) helps to identify these flow regimes: Continuum flow

(Kn<0.01), slip flow (0.01<Kn<0.1), transition flow (0.1<Kn<10), and free molecular flow

(Kn>10).

The basic data and the assumed gas mixture parameters used in this work were published

originally by Javadpour et al. (2007) and have been used by Ortega and Aguilera (2013).

Several researchers including Winland (in Kolodzie, 1980), Pittman (1992), Aguilera

(2002), Byrnes (2005), and Ortega and Aguilera (2013) have shown the relation between

porosity, permeability, and pore throat radii. The pore throat radius (rp35) is used to

calculate Knudsen number in this study. Hence, another benefit of measuring porosity

and permeability from drill cuttings in the laboratory is that it serves as an aid for

determining the dominant flow regime in a reservoir especially for areas where well logs

or core data is scarce. For the tight gas sandstone considered in this study, continuum-

135

flow condition is the dominant flow regime as evidenced by the Kn values calculated

using Eq. 6.7 and 6.8, and shown in Table 6.1, column 11.

…………………………………………………………………...…Eq. 6.7

( ) is expressed as

√ ……………………………………………… ……..……… Eq. 6.8

where is the universal gas constant (Pa.m3/mol.K), is temperature

(K), is Avogadro’s number, is the

average collision diameter of the gas molecules (gm), and is pressure in

the porous media (Pa).

6.2.10 Location of Water Contact

Water contact refers to the elevation above which a gas-water contact or oil-water contact

can be found in a reservoir. However, the Nikanassin formation is a tight gas continuous

accumulation characterized by lack of a water leg. In the Nikanassin formation water is

found above gas due to very low permeability and capillary pressure effects (Masters,

1979; Ramirez and Aguilera, 2011). However, for reservoirs with water below the gas

bearing zone it is possible to make an estimate of the water contact depth with the use of

136

Eq. 6.9 (Aguilera and Ortega, 2013). Note that this estimate starts with the evaluation of

drill cuttings in the laboratory.

……………………………………………..…………………………Eq. 6.9

where h is water contact depth in feet and Pc is capillary pressure in psi.

6.2.11 Flow (or Hydraulic) Units

Flow unit is a reservoir subdivision defined on the basis of similar pore type (Hartmann

and Beaumont, 1999). Data from carbonate and sandstone reservoirs was originally used

by H.D. Winland of Amoco (Kolodzie, 1980) to develop flow units on the basis of pore

throat apertures. Following Winland’s format Aguilera (2003) developed the template

presented in Fig. 6.4, which includes pore throat apertures ( ) as a function of porosity

and permeability. The triangles in the graph correspond to porosities and permeabilities

from the drill cutting samples evaluated in this study. The crossplot indicates that

Nikanassin flow units are dominated by micro pore throats (microports). In this case,

hydraulic fracturing stimulation is required to attain commercial production.

137

Figure 6.4—Chart for estimating pore throat apertures on the basis of permeability

and porosity. The green triangular symbols represent data obtained from drill

cuttings. Nikanassin flow units are dominated by microports. Source of template:

Aguilera (2003).

6.2.12 Construction of Pickett Plots

Pickett (1973) devised a formation evaluation interpretation technique using crossplots of

log responses. His approach indicates that a log-log crossplot of Rt vs. porosity should

result in a straight line with a negative slope equal to the porosity exponent ( ) for

intervals with constant water saturation. Pickett’s plot is based on Archie’s (1942)

equations:

0.001

0.010

0.100

1.000

10.000

100.000

1000.000

10000.000

0.000 5.000 10.000 15.000 20.000 25.000 30.000

Pe

rme

ab

ilit

y, k

ma

x (

mD

)

Porosity (%)

© Servipetrol, 2003

CHART FOR ESTIMATING PORE THROAT APERTURE (Source: Aguilera, CSEG Recorder, Feb 2003)

rp35

20

10

4

2

1

0.5

0.2

me

ga

po

rtsm

acro

po

rtsm

eso

po

rtsm

icrop

orts

0.1

138

…………………………………………………………………….……Eq. 6.10

( ……………………………………………………….................Eq. 6.11

………………………………………………………………………Eq. 6.12

Combining and rearranging Eqs. 6.10 to 6.12 yield:

( ……………………………………..…Eq. 6.13

The conventional construction of a Pickett plot requires the availability of porosity and

resistivity logs. In the present case study, these logs are not available and the Pickett plot

is built on the basis of data extracted from drill cuttings. The 100% water saturation

straight line is drawn by knowing the value of the porosity exponent m, the formation

water resistivity and the value of a (used in Eq. 6.12). For the purpose of the present work

a is assumed to be equal to 1.0, n is assumed equal to m = 1.83 (column 6, Table 6.1).

The water resistivity Rw is equal to 0.038 ohm-m at reservoir temperature (100 C). Fig.

6.5 shows the drill cuttings-based Pickett Plot for the tight gas formation under

consideration built with the porosity and true resistivity data shown in Table 6.1.

In order to construct lines of constant permeability on a Pickett plot, Aguilera (1990)

derived an equation (Eq. 6.14) that indicates that a cross-plot of Rt versus on log-log

139

coordinates should result in a straight line with a slope equal to -3n-m for intervals at

irreducible water saturation with constant k and constant aRw.

( [ (

⁄ ]

………………...……………Eq. 6.14

Fig. 6.6 shows the same Pickett plot presented in Fig. 6.5 but now including lines of

constant permeability. The black circles are drill cuttings data and follow same trend as

some of the lines of constant permeability. Constant permeability values equal to 0.005,

0.05, 0.5 and 5md are plotted on the Pickett plot, the cuttings data fall between the lines

of constant permeability ranging between 0.005 and 0.5 md. The interpretation of Pickett

plot is facilitated by these lines of constant permeability. For instance, note the red square

enclosing a black circle (drill cuttings sample No. 39 in Table 6.1) in Fig. 6.6. From the

graph the interpreter can assign a value slightly larger than 0.05md to this sample. The

actual value is 0.057md as shown in column 4 of Table 6.1.

The construction of the Pickett plot is extended next to include lines of constant capillary

pressure using Eq. 6.15 (Aguilera, 2002). Results are shown in Fig. 6.7 where the black

dot inside the red square corresponds to Sample No. 6 (Table 6.1, column 10). Sample 6

has a porosity of 0.106, a permeability of 0.088 md, a true formation resistivity of 22

ohm-m and a mercury /air capillary pressure of 1204 psi. The same values can be

observed in the Pickett plot shown in Fig. 6.7.

140

( ([ ][ ]

) ……….…Eq. 6.15

Lines of constant pore throat radius (r, microns) can also be included in the Pickett plot

as shown on Fig. 6.8 Eq. 6.15 that was used for constructing lines of constant capillary

pressure can be modified by introducing the Washburn (1921) pore throat equation. This

modification results in the following equation:

( ([ ] [ (

)

]

) ..……Eq. 6.16

For intervals with constant pore throat radius and constant aRw, the crossplot of Rt versus

on log-log coordinates results in a straight line with a slope equal to ( )

(Ortega and Aguilera, 2013). These lines were constructed with the use of Eq. 6.16 based

on the assumption that the mercury/air interfacial tension (IFT) is 480 dyne/cm, and the

mercury/air contact angle is 140o.

141

Figure 6.5— Pickett plot including lines of constant water saturation. The black

circles represent drill cuttings data from a horizontal well drilled in the Nikanassin

group of the WCSB.

Figure 6.6— Pickett plot including lines of constant water saturation and constant

permeability. The black circles represent drill cuttings data from a horizontal well

drilled in the Nikanassin group of the WCSB.

0.01

0.10

1.00

0.01 0.10 1.00 10.00 100.00 1,000.00 10,000.00

Ф

Rt, ohm*m

Cuttings Based Pickett Plot (WCSB)

Cuttings Data

Sw=100%

Sw=50%

Sw=25%

Sw=12.5%

Sw=5%

aRw=0.038

aRw=0.038ohm-m

142


permeability, and constant capillary pressure. The black circles represent the drill

cuttings data from a horizontal well drilled in the Nikanassin Group of the WCSB.


permeability, and constant pore throat radius. The black circles represent drill

cuttings data from a horizontal well drilled in the Nikanassin group of the WCSB.

143

To construct constant lines of constant height above the water table in a Pickett plot in

gas reservoirs where an aquifer is present ( ), the capillary pressure in Eq. 6.15 is

substituted with

to give Eq. 6.17

( ([ ] [ (

)

]

) ……..Eq. 6.17

where represents the height in feet above the free water level when capillary pressure is

equal to zero and is mercury-air capillary pressure (psi). The example shown in Fig.

6.9, generated with the use of Eq. 6.17, is presented for illustration purposes only.

However, as mentioned previously in this study one of the characteristics of the

Nikanassin continuous gas accumulation is the lack of a water leg. This has been

corroborated as water-free throughout several years of production from a Nikanassin area

covering more than 15,000 km2 (Solano et al., 2011).

Lines of constant Knudsen number can also be constructed on a Pickett plot with the use

of the equation (Ortega and Aguilera, 2013):

(

([ ][ ] [ ( ( ⁄ ( )⁄ ]

)………………Eq. 6.18

144

The equation indicates that a crossplot of Rt versus on log-log coordinates should result

in a straight line with a slope equal to ( ) (Ortega and Aguilera, 2013) for

intervals with constant aRw. Fig. 6.10 shows the Pickett plot constructed with lines of

constant Knudsen’s number using Eq. 6.18. The drill cuttings data fall between the lines

of Kn equal to 1E-4 and 1E-2. Thus for the tight gas sandstone considered in this study,

continuum-flow is the dominant regime as evidenced in the Pickett plot shown in Fig.

6.10.


permeability and constant height above the water contact. The black circles

represent drill cuttings data from a horizontal well drilled in the Nikanassin group

of the WCSB.

0.01

0.10

1.00

0.01 0.10 1.00 10.00 100.00 1,000.00 10,000.00

Ф

Rt, ohm*m

Cuttings Based Pickett Plot (WCSB)

Cuttings Data

Sw=100%

Sw=50%

Sw=25%

Sw=12.5%

Sw=5%

k=5md

k=0.5md

k=0.05md

k=0.005md

aRw=0.038

h1=1600 ft

h2 = 800ft

h3 = 400 ft

h4 = 200 ft

h5 = 100 ft

h6 = 50 ft

h7 = 25 ft

h8 = 10 ft

aRw=0.038ohm-m

145

Figure 6.10—Pickett plot including constant lines of water saturation and constant

Knudsen number. The black circles represent drill cuttings data from a horizontal

well drilled in the Nikanassin group of the WCSB.

6.3 Geomechanics Based on Drill Cuttings

Column 1 of Table 6.2 identifies 65 drill cutting samples from a horizontal well used in

this study. Column 2 shows the collection measured depth. As in the case of the

formation evaluation presented above, the drill-cuttings based methodology is not meant

to replace detailed geomechanical studies but to provide estimates of basic parameters for

designing hydraulic fracturing jobs, particularly in those situations where core and log

data are scarce such as the case of some horizontal wells. This facilitates the success of

the operations by pointing to ideal locations for fracture initiation (Ortega and Aguilera,

2012).

146

6.3.1 Brittleness Index

Brittleness index serves as a good indicator for identifying lithological zones suitable for

well stimulation (hydraulic fracturing). Poisson’s ratio and Young’s Modulus are key

mechanical properties that are combined to determine the brittleness index. Poisson’s

ratio indicates the tendency of the rock to fail under stress while Young’s Modulus

indicates the resistance of the rock to deformation which helps to maintain a fracture after

well stimulation (Rick et al., 2008). Therefore, for optimal hydraulic fracturing design in

tight formations the intervals with high brittleness index (high Young’s Modulus and low

Poisson’s ratio) must be selected as zones of interest for initiation of hydraulic fractures.

Furthermore, the more brittle the tight formation, the more likely for these intervals to be

naturally fractured (Ortega and Aguilera, 2012).

The porosity data obtained from laboratory work (column 3 in Table 6.2) performed on

drill cuttings can serve as raw data for calculation of the compressional travel time ( )

shown in column 4 of Table 6.2. In this study DTC is calculated using the sonic log

equation published by Raymer et al. (1980):

(

……………………….…………………………Eq. 6.19

The Raymer et al.(1980) equation has been shown previously to work well for the lower

Nikanassin formation (Ortega and Aguilera, 2012). Also needed is the shear wave

traveling time ( ). In the absence of shear wave information, the Nikanassin empirical

147

correlation shown on Fig. 6.11 can be used as a good approximation as the coefficient of

determination R2 is equal to 0.89 (Ortega and Aguilera, 2012). The linear trend in Fig.

6.11 is represented by the equation:

………………………………………………..…Eq. 6.20

148

Table 6.2— GEOMECHANICAL DATA FOR WESTERN CANADA



(COLUMN 3) ARE OBTAINED FROM LABORATORY WORK AND IT IS

USED AS A STARTING POINT IN DETERMINING OTHER PETROPHYSICAL

DATA (COLUMN 4 TO 12) USING EMPIRICAL EQUATIONS.

1 2 3 4 5 6 7 8 9 10 11 12

Sample

No.

Bottom

Depth

MD (m)

PHILab

(fraction)

DTC

(us/ft)

DTS

(us/ft)PR G (E6 psi)

YM

Dynamic

(E6 psi)

YM Static

Eissa

(E6psi)

PR-BRIT

(%)

YM -BRIT

(%)

BRIT-

Index(%)

1 3185.0 0.07 60.12 95.04 0.17 3.65 8.52 5.91 64.46 68.48 66.47

2 3190.0 0.06 59.84 94.33 0.16 3.71 8.62 5.98 67.09 70.98 69.03

3 3195.0 0.07 60.02 94.79 0.17 3.67 8.55 5.93 65.39 69.37 67.38

4 3200.0 0.05 58.65 91.34 0.15 3.95 9.08 6.30 78.78 81.75 80.27

5 3202.5 0.07 60.07 94.91 0.17 3.66 8.54 5.92 64.93 68.94 66.93

6 3205.0 0.11 64.77 106.80 0.21 2.89 6.99 4.85 29.35 32.83 31.09

7 3207.5 0.09 62.48 101.02 0.19 3.23 7.69 5.34 44.95 49.20 47.07

8 3210.0 0.09 62.90 102.07 0.19 3.17 7.56 5.24 41.91 46.08 44.00

9 3217.5 0.07 60.41 95.78 0.17 3.59 8.41 5.83 61.84 65.98 63.91

10 3220.0 0.10 63.82 104.40 0.20 3.03 7.27 5.04 35.49 39.38 37.44

11 3225.0 0.10 63.94 104.70 0.20 3.01 7.24 5.02 34.69 38.53 36.61

12 3235.0 0.07 60.04 94.85 0.17 3.67 8.55 5.93 65.17 69.16 67.16

13 3265.0 0.09 62.46 100.95 0.19 3.24 7.70 5.34 45.14 49.40 47.27

14 3285.0 0.15 70.48 121.21 0.24 2.24 5.59 3.88 0.00 0.00 0.00

15 3290.0 0.08 62.14 100.15 0.19 3.29 7.81 5.41 47.56 51.87 49.71

16 3295.0 0.06 58.96 92.11 0.15 3.89 8.96 6.22 75.64 78.91 77.27

17 3300.0 0.09 62.98 102.26 0.19 3.15 7.53 5.23 41.35 45.50 43.43

18 3305.0 0.07 60.36 95.64 0.17 3.61 8.43 5.85 62.32 66.44 64.38

19 3310.0 0.05 58.85 91.84 0.15 3.91 9.00 6.25 76.72 79.89 78.30

20 3315.0 0.06 59.72 94.02 0.16 3.73 8.67 6.01 68.21 72.03 70.12

21 3320.0 0.10 64.67 106.54 0.21 2.91 7.02 4.87 29.97 33.51 31.74

22 3325.0 0.10 63.59 103.81 0.20 3.06 7.34 5.09 37.06 41.03 39.04

23 3345.0 0.12 66.74 111.78 0.22 2.64 6.46 4.48 17.89 20.31 19.10

24 3355.0 0.08 61.36 98.18 0.18 3.42 8.07 5.60 53.74 58.07 55.90

25 3435.0 0.06 59.53 93.56 0.16 3.77 8.74 6.06 69.96 73.68 71.82

26 3440.0 0.07 60.11 95.03 0.17 3.65 8.52 5.91 64.53 68.55 66.54

27 3445.0 0.08 62.25 100.42 0.19 3.27 7.77 5.39 46.73 51.02 48.87

28 3450.0 0.08 61.35 98.16 0.18 3.42 8.07 5.60 53.80 58.12 55.96

29 3455.0 0.04 57.83 89.26 0.14 4.14 9.42 6.54 87.72 89.64 88.68

30 3460.0 0.05 58.61 91.23 0.15 3.96 9.10 6.31 79.24 82.16 80.70

31 3665.0 0.04 57.38 88.12 0.13 4.25 9.61 6.67 92.97 94.14 93.55

32 3690.0 0.07 60.50 96.00 0.17 3.58 8.38 5.81 61.05 65.21 63.13

33 3710.0 0.05 58.31 90.46 0.14 4.03 9.23 6.40 82.48 85.06 83.77

34 3715.0 0.05 57.96 89.60 0.14 4.11 9.37 6.50 86.24 88.36 87.30

35 3720.0 0.05 58.53 91.02 0.15 3.98 9.13 6.34 80.09 82.93 81.51

36 3725.0 0.07 60.08 94.94 0.17 3.66 8.53 5.92 64.82 68.83 66.83

37 3730.0 0.08 61.48 98.47 0.18 3.40 8.03 5.57 52.80 57.12 54.96

38 3735.0 0.05 58.73 91.52 0.15 3.94 9.06 6.28 78.03 81.08 79.55

39 3740.0 0.07 60.30 95.51 0.17 3.62 8.45 5.86 62.79 66.89 64.84

40 3745.0 0.06 59.87 94.42 0.16 3.70 8.61 5.97 66.76 70.66 68.71

41 3750.0 0.04 56.80 86.66 0.12 4.39 9.87 6.84 100.00 100.00 100.00

42 3755.0 0.04 57.73 89.02 0.14 4.16 9.46 6.56 88.83 90.61 89.72

43 3760.0 0.05 58.52 91.01 0.15 3.98 9.14 6.34 80.17 83.00 81.58

44 3765.0 0.05 58.18 90.15 0.14 4.06 9.28 6.43 83.82 86.24 85.03

45 3770.0 0.05 58.33 90.53 0.15 4.02 9.21 6.39 82.19 84.80 83.50

46 3775.0 0.07 60.30 95.51 0.17 3.62 8.45 5.86 62.79 66.89 64.84

47 3785.0 0.07 60.11 95.01 0.17 3.65 8.52 5.91 64.58 68.60 66.59

48 3790.0 0.04 56.94 87.00 0.13 4.36 9.81 6.80 98.32 98.62 98.47

49 3800.0 0.05 58.31 90.48 0.14 4.03 9.22 6.40 82.41 85.00 83.70

50 3820.0 0.06 59.19 92.70 0.16 3.84 8.87 6.15 73.31 76.78 75.04

51 3835.0 0.07 60.18 95.19 0.17 3.64 8.50 5.89 63.94 67.99 65.97

52 3845.0 0.04 56.86 86.80 0.12 4.38 9.84 6.83 99.32 99.45 99.38

53 3850.0 0.06 59.59 93.70 0.16 3.76 8.72 6.05 69.43 73.18 71.31

54 3855.0 0.08 62.16 100.20 0.19 3.28 7.80 5.41 47.41 51.71 49.56

55 3860.0 0.06 59.61 93.76 0.16 3.75 8.71 6.04 69.19 72.95 71.07

56 3865.0 0.07 60.92 97.07 0.18 3.50 8.23 5.71 57.41 61.68 59.54

57 3880.0 0.08 62.19 100.27 0.19 3.28 7.79 5.40 47.18 51.48 49.33

58 3885.0 0.05 58.86 91.87 0.15 3.91 9.00 6.24 76.60 79.78 78.19

59 3890.0 0.08 61.89 99.52 0.18 3.33 7.89 5.47 49.49 53.82 51.66

60 3895.0 0.07 60.92 97.08 0.18 3.50 8.22 5.70 57.38 61.64 59.51

61 3900.0 0.07 61.10 97.51 0.18 3.47 8.16 5.66 55.92 60.21 58.06

62 3930.0 0.08 61.24 97.87 0.18 3.44 8.11 5.63 54.73 59.04 56.88

63 3935.0 0.06 59.60 93.74 0.16 3.75 8.71 6.04 69.30 73.05 71.17

64 3940.0 0.07 60.30 95.50 0.17 3.62 8.45 5.86 62.82 66.91 64.87

65 3945.0 0.08 61.26 97.93 0.18 3.44 8.11 5.62 54.55 58.86 56.70

149

Strictly, if the formation of interest is anisotropic to velocity, then the relationship of

vertical slowness to porosity is not applicable in the horizontal well. However, previous

Nikanassin work (Ortega and Aguilera, 2012) suggests that the empirical correlations

presented here provide a good approximation to DTC and DTS.

Figure 6.11—Plot of ( ) versus ( ) for the Nikanassin formation using data

from an offset vertical well (Ortega and Aguilera, 2012).

The correlation presented in Fig. 6.11 makes the estimation of ( ) possible (Column 5,

Table 6.2). Calculation of compressional wave velocities ( and shear wave

velocities ( are obtained from the following equation:

150

(μsec/ft) and

(μsec/ft) ……………………………………Eq. 6.21

Using (ft/sec) and (ft/sec) from Eq. 6.21, it is possible to estimate values of

Poisson’s ratio (column 6 in Table 6.2) from the equation:

………………………………………… …………………..…Eq. 6.22

The bulk density ( is calculated from:

……………………………………………………….Eq. 6.23

The dry weight and bulk volume parameters in Eq. 6.23 are measured in the laboratory

using drill cuttings. Shear or Rigidity Modulus, G (column 7, Table 6.2) is calculated

from (Barree, 2011):

………………..…………………………………………Eq. 6.24

The dynamic Young’s Modulus, YMd (column 8, Table 6.2) is determined from:

( …………………………………………………………Eq. 6.25

151

Mullen et al. (2007) worked on determining the mechanical rock properties for

stimulation design in the absence of sonic log and presented a derived correlation for

estimating the static Young Modulus, YMs (Eq. 6.26) that can be applied to tight gas

sands, coals and shales. Similarly, he developed for the same purpose a modified form of

the Eissa and Kazi (1988) empirical equation (Eq. 6.27). This modified form of Eissa

and Kazi correlation was used in this study to convert the calculated dynamic Young’s

Modulus to the static Young’s Modulus. Results are shown in column 9, Table 6.2.

( ………………………………………………………… Eq. 6.26

( ( …………………………...………………Eq. 6.27

Fig. 6.12 shows a plot of Poisson’s ratio versus Eissa and Kazi static Young Modulus

developed from drill cuttings data, and a relative indication of the change in brittleness

and ductility. The data are presented in columns 6 and 9 of Table 6.2. For comparison

purposes, results from the Mullen et al. correlation (Eq. 6.26) are also included in Fig.

6.12. Aoudia et al. (2010) show a similar plot on the effects of mineralogy on rock

mechanical properties.

152

Figure 6.12—Cross plot of Young Modulus (YM) versus Poisson’s ratio (PR). The

porosity and bulk density values from drill cuttings (WCSB) were used as input

data in calculating the YM and PR using Eq.6.22 and Eq. 6.27 respectively.

Rickman et al. (2008) have developed a unitized Poisson’s ratio (PRbrit) and unitized

Young’s Modulus (YMbrit) on the basis of the maximum and minimum values of these

parameters with the use of Eq. 6.28 and Eq. 6.29. Since Poisson’s ratio and Young’s

Modulus are mathematically expressed in different units, it is important to unitize these

two mechanical properties. Results are presented in columns 10 and 11 of Table 6.2.

y = -3.0899E+07x + 1.1126E+07R² = 9.9902E-01

y = -2.3870E+07x + 9.8627E+06R² = 9.9713E-01

3.E+06

4.E+06

5.E+06

6.E+06

7.E+06

8.E+06

0.12 0.14 0.16 0.18 0.20 0.22 0.24

Sta

tic Y

ou

ng

Mo

du

lus

(E6

psi

)

Poisson's Ratio

Mullen

Eissa and Kazi

Linear (Mullen)

Linear (Eissa and Kazi)

Increasingbrittleness

Increasingductility

153

(

) …………………………………………………………Eq. 6.28

(

) ……………………………………………………Eq. 6.29

The arithmetic average of (column 10, Table 6.2) and (column 11, Table

6.2) yield the brittleness index ( ) expressed by:

……………………………….………………………Eq. 6.30

The brittleness index value obtained using Eq. 6.30 is a fraction and can be expressed as

a percentage if desired. Column 12 in Table 6.2 shows the brittleness Index values. A

ductile rock will have a brittleness index of zero or close to zero while a brittle rock will

have a brittleness index of one or close to one. In the case of the lower Nikanassin

formation considered in this study, the zones with high brittleness index correspond to

zones that may contain micro fractures and slot porosities. This might be supported by

fracture indicators such as the presence of lost circulation materials, loose crystals and

planar shape features in the corresponding drill cuttings samples.

In those cases where compressional and shear velocities are not available it is still

possible to obtain reasonable estimates of Poisson’s ratio and static Young Modulus

solely on the basis of porosity. This is demonstrated with the use of Fig. 6.13 that shows

154

a log-log crossplot of drill-cuttings porosity versus Poisson’s ratio (Data are extracted

from columns 3 and 6 of Table 6.2). The crossplot results in a nearly straight line with a

coefficient of determination (R2) equal to 0.9999. Thus based on this result, Poisson’s

ratio can be calculated for the study area considered in this paper from the best fit

equation obtained in Fig. 6.13:

…………...………………………………………………Eq. 6.31

where porosity is a fraction. Fig. 6.13 shows that a cross plot of static Young Modulus

versus Poisson’s ratio results in approximate straight line for each, Mullen et al. (2007)

and Eissa and Kazi (1988) correlations. In both cases R2 is greater than 0.99. Based on

these results, static Young Modulus can be calculated for the study area from the best fit

equations shown on Fig. 6.12:

( …………………..……………Eq. 6.32

( …………..…………Eq. 6.33

Having these results, the values of PRbrit, YMbrit and brittleness index are calculated with

the use of Eq. 6.28, 6.29 and 6.30. Results are not shown but they are very close to the

ones generated in Table 6.2. The bottom line of this approach is that important

geomechanical parameters can be estimated when only drill cuttings porosities (and for

that matter porosities from cores and/or logs) are available.

155

Figure 6.13—Empirical log-log cross plot of porosity from drill cuttings versus

Poisson’s ratio (PR) results in a nearly straight line (R2 = 0.9999). Thus porosity can

be used for obtaining a reasonable estimate of Poisson’s ratio in those cases where

compressional and shear velocities are not available.

Although the results are reasonable, it must be emphasized that the methods presented in

this chapter are not meant to replace detailed petrophysical and geomechanical studies

but to provide useful information when core and log data are scarce. To make the

methods presented in this chapter more valuable, even when core, log data and detailed

y = 0.6139x0.4798

R² = 0.9999

0.10

1.00

0.01 0.10 1.00

Po

isso

n's

Ra

tio

Porosity

Drill cuttings

Power (Drill cuttings)

156

studies are available, the methods presented above should still be implemented with a

view to calibrate the equations presented in this chapter for use in wells short of data.

157

Chapter Seven: HYDRAULIC FRACTURE DESIGN OPTIMIZATION USING

DRILL CUTTINGS

7.1 Hydraulic Fracturing of Tight Gas Reservoirs

A high performance reservoir can be described as a reservoir that can produce large

volumes of hydrocarbons at economic rates without performing some extraordinary

completion, stimulation and development practices. Unfortunately, tight gas reservoirs

cannot be described as a high performance reservoir because fluid flow from pore spaces

to wellbore is restricted; their low permeability nature typically equal to or smaller than

0.1 md is responsible for this restriction (Center for Energy, 2013). One of the well

stimulation methods recognized to optimize gas recovery from tight gas reservoirs is

hydraulic fracturing; this method involves the continuous injection of fluids containing

proppants and other chemical additives at a high pressure into tight rock; until it causes

“tensile failure” of the rock and creates a good fracture network (Economides et al.,

1994). This is illustrated in Fig. 7.1.

Figure 7.1— Example of fracture network created by hydraulic fracturing

operation (Source: fracfocus.org, 2013).

158

The starting point for designing a hydraulic fracture treatment is an understanding of the

in-situ stress profile. To determine the in-situ stress profile the mechanical rock

properties and the pore pressure variations throughout the wellbore are required (Mullen,

2007).

In this chapter, we discuss the application of drill cuttings in constructing a hydraulic

fracturing model for optimizing production from a tight gas reservoir. A comparison is

made of two cases: One with drill cuttings for estimating geomechanical properties to

select fracture initiation zones, and one without drill cuttings. The geomechanical data

used in this chapter are taken from Chapter six.

7.1.1 Hydraulic Fracture Design Using Drill Cuttings

A methodology for improving design of multi-stage hydraulic fracturing jobs in

horizontal wells using drill cuttings from vertical wells was developed by Ortega et al.

(2012). This methodology started with porosity data determined from drill cuttings to

estimate shear slowness (DTS) based on the knowledge of compressional wave travel

time (DTC). These data allowed estimating critical geomechanical parameters such as

Poisson’s ratio, Young’s Modulus, and Brittleness Index (see Chapter six for a complete

workflow of how the geomechanical properties are computed). Fig. 7.2, track 2 shows a

good comparison between the compressional wave travel time (DTC) data obtained from

a sonic well log and drill cuttings. This shows that drill cuttings data are reliable in

designing hydraulic fracturing jobs since subsequent geomechanical parameters used for

identifying fracture initiation zones depends on DTC value.

159

Figure 7.2— Track 2 shows a good comparison between drill cuttings data (DTC-

Lab-Dark blue line between the depth interval of 3095-3205m MD) and DTC-Sonic

Log(Green).The track scale is 120-420 us/m.(Adapted from Ortega et al. 2012).

2 1

160

Another important use of drill cuttings data is the generation of the Frac Value (Chapter

three), which is an aid in selecting the selecting the optimum points for fracture initiation

(Ortega et al., 2012). The Frac Value brings microscopic observations of structural

features on drill cuttings into an understandable and readable approach.

The Frac Value, brittleness index, and permeability from drill cuttings are incorporated

into a qualitative model called Cut-Log. The advantages of the Cut-Log as stated by

Ortega et al. (2012) are as follows:

Open-Hole Completions:

Optimized the fracture spacing between packers and number of fracturing stages

in the reservoir

Identify where to initiate the stimulation process using as a guide the brittleness

index, friction losses optimization and tortuosity reductions related to the initial

axial growth length (commonly occur in horizontal wells with vertical hydraulic

fractures; but transverse fractures are also desired and expected, Daneshy, 2011)

Identify where to increase volume of injected fracturing fluid and proppant

concentration

Cemented Casing/Liner Completions:

Maximize the success probability of the fracturing job by identifying where to

perforate

Optimize the number, length and spacing of perforation clusters (Beard, 2011) for

each stage

161

The next section shows how drill cuttings data was used to optimize hydraulic fracturing

design from a horizontal well that penetrates a tight gas reservoir in the Nikanassin Group

of the western Canada sedimentary basin.

7.2 Model Development

GOHFER simulator was used to build the hydraulic fracturing model and to generate

production forecasts. A significant amount of input data are required to build an accurate

model that describes properly the reservoir to be stimulated. Unfortunately, but typical of

way too many cases in the oil and gas industry, the horizontal well (well A) considered in

this study only has a gamma ray log. But fortunately there are drill cuttings (refer to

Table 6.2 in Chapter six). The cuttings data were used to populate the grid cells of

GOHFER to create a hydraulic fracturing model. The availability of this geomechanical

data sourced from drill cuttings in the absence of complete standard well logs and cores

serve as a means of emphasizing another benefit of measuring porosity and permeability

from drill cuttings.

7.2.1 Data Input and Processing

Ideally, reservoir data such as rock mechanical properties are derived from cores and

openhole well logs, and the treatment data such as fluid properties, pumping rates,

proppant concentrations and quantity are provided by the service company.

162

GOHFER is built using log derived input data to generate rock elastic properties, porosity

and lithology. For optimum hydraulic fracturing design, the following data are required :

gamma ray (GR), neutron porosity (NPHI), bulk density (RHOB) , deep resistivity (ILD),

caliper (CAL), compressional travel time (DTC) and shear travel time (DTS) but in the

absence of standard log suite, the optimum minimum log suite required are gamma ray

(GR), neutron porosity (NPHI), and bulk density (RHOB).

Since these logs are not available for the hydraulic fracturing design in the horizontal

well considered in this study (Well A), a reference well (Well B) in the same geological

area was used to generate the grid properties in the vertical direction of the model while

the horizontal well data was superimposed along the bottom of the vertical grid.

Reference well B has gamma ray (GR), neutron porosity (NPHI), bulk density (RHOB),

deep resistivity (ILD), caliper (CAL), compressional travel time (DTC) and shear travel

time (DTS) data. This reference well data correspond to true vertical depth (TVD).

Porosity and permeability from drill cuttings, and geomechanical data extracted from

these properties were used for horizontal well A. Both Wells A and B are drilled

vertically from surface before they start deviating at 1710 m TVD and 1803 m TVD,

respectively. It is assumed that both wells have the same ‘zero’ level for TVD. Fig. 7.3

shows the wellbore survey for wells A and B.

163

Figure 7.3 — Wellbore survey for horizontal Well A 3953 MD / 3115m TVD and

reference Well B 3240m MD / 3192m TVD.

7.2.2 Calibration of GOHFER Generated Data with Drill Cuttings Data

The basic assumption is that data extracted from drill cuttings data represents the tight

gas reservoir accurately. As mentioned above, horizontal well A only has a gamma ray

(GR) log. The GR log was used by GOHFER to generate rock mechanical properties

using in-built correlations. The coefficients of the GR empirical equations for generating

rock mechanical properties such as Poisson’s ratio (PRGR), compressional travel time

(DTCGR), and dynamic Young Modulus (YMEGR) were calibrated with the

geomechanical data extracted from drill cuttings measurements of porosity and

164

permeability in the laboratory (Poisson’s ratio, PRLab; compressional travel time,

DTCLab; and dynamic Young Modulus, YMELab). Fig. 7.4 to 7.6 shows matches

between the GR GOHFER correlated curves and geomechanical data from the drill

cuttings.

Where in track 2 of Fig. 7.4,

DTCRESIST = DTC from resistivity, DTCPHIN = DTC from Neutron Porosity,

DTCACT = Actual DTC from Log, DTC PHIA = DTC from average porosity, DTCGR =

DTC from gamma ray, and DTCLab = DTC from drill cuttings. All these parameters are

expressed in microseconds per meter (µSec/m).

In track 2 of Fig. 7.5,

PRRESIST = PR from resistivity, PRPHIA = PR from average porosity, PRDTC = PR

from DTC Log, PRACT = Actual PR from Log, PRGR = PR from gamma ray, and

PRLab = PR from drill cuttings. All these parameters are expressed in fractions.

And in track 2 of Fig. 7.6,

YMERESIST = YME from resistivity, YMEPHIA = YME from average porosity,

YMEDTC = YME from DTC log, YMEACT = Actual YME from Log, YMEGR = YME

from gamma ray, and YMELab = YME from drill cuttings. All these parameters are

expressed in Giga Pascals (GPa).

165

Figure 7.4 — Calibration of compressional travel time DTCGR from GOHFER

(orange Line) with DTCLab extracted from drill cuttings (blue line). The 2 curves

are shown in Track 2.

1 2

166

Figure 7.5 — Calibration of Poisson’s ratio PRGR from GOHFER (orange Line)

with PRLab (blue line) extracted from drill cuttings. The 2 curves are shown on

Track 2.

1 2

167

Figure 7.6 — Calibration of dynamic Young Modulus YMEGR from GOHFER

(Orange Line) with YMELab (pink line). The 2 curves are shown on Track 2.

1 2

168

With the data input, and calibration process completed, the grid properties are populated

in the model. Fig. 7.7 show examples of the model populated with four grid properties.

Figure 7.7— Example of grid setup showing grid properties such as total closure

stress, brittleness factor, permeability and static young modulus . The reference well

(well B) data was used to populate the grid properties from surface to 3225m MD

while the remaining depth interval to 3950m MD that represents the horizontal

section was populated using the horizontal well (well A) data.

169

7.2.3 Multi-Stage Hydraulic Fracture Treatment Design

With the construction phase completed, the next step is to design the treatment

configuration. Two seven-stage hydraulic fracturing design cases were considered in this

work, Case I involves initiating fractures in the zones that were actually treated in

horizontal well A (shown in Appendix D). Case II involves using the Cut-Log (Fig. 7.8)

to determine zones where fractures can be initiated to improve gas recovery (i.e. re-

design case using drill cuttings data).

To emphasize the importance on production performance of fracture initiation points, a

constant pump schedule was used for the seven stages (Table 7.1) and the only variable

was the treated zones.

Table 7.1—BOTTOM HOLE PUMP SCHEDULE

1 2 3 4 5 6

FLUID FLUID CUM PROP PROP TOTAL B.H.

TYPE VOLUME FLUID TYPE CONC INJ. RATE

(m3) (m3)

Kg/m3 (m3/min)

PAD 34.4 34.4 None 0.0 9

2 58.5 92.9 100 MESH 50.0 9

3 31.7 124.6 None 0.0 9

4 75.6 200.2 40/70 SAND 25.0 9

5 83.5 283.7 40/70 SAND 50.0 9

6 68.9 352.6 None 0.0 9

7 80.1 432.7 40/70 SAND 25.0 9

8 79.1 511.8 40/70 SAND 50.0 9

9 34.6 546.3 40/70 SAND 75.0 9

10 62.2 608.6 None 0.0 9

11 62.4 670.9 40/70 SAND 50.0 9

12 55.7 726.7 40/70 SAND 75.0 9

13 44.6 771.3 40/70 SAND 100.0 9

SPACER 12.2 783.5 None 0.0 9

FLUSH 66.7 850.2 None 0.0 9

In Table 7.1, column 1 shows the sequence of operation, columns 2 and 3 show the

injected fluid volume, column 4 the type of proppant, column 5 the proppant

concentration, and column 6 shows the total bottom hole injection rate. Fig. 7.8 shows the

Cut-Log that was used as a guide in selecting zones with potential for high gas recovery.

170

Three parameter tracks ranging in depth from 3200m MD to 3900m MD are displayed in

Fig. 7.8. Track 1 is the brittleness index, track 2 is the permeability and track 3 is the Frac

Value. Higher values of all three parameters are desired but two high values are still

acceptable. The blue color represents the zones suitable for optimum fracture initiation

and the color higher intensity is intentionally related to better conditions.

Figure 7.8 — Cut-Log with three parameter tracks ranging from 3200 to 3900m

MD. Track 1 is the brittleness index, track 2 is permeability and track 3 is the Frac-

Value. Higher values of all three parameters are desired but two high values are still

acceptable. The blue color represents the zones suitable for optimum fracture

initiation and the color intensity is intentionally related to better conditions.

171

7.3 Results

The economic recovery of gas from tight gas reservoirs depends on successful

stimulation of wells using hydraulic fracturing techniques. The number of treatment

stages, the location, spacing, and number of hydraulic fractures created per stage; all

affect gas recovery. Therefore accurate modeling of hydraulic fractures is required to

predict production rates and to improve future stimulation strategies. Production forecasts

were carried out for the hydraulic fracture designs with and without the inclusion of drill

cuttings data. The results (shown for 364 days) highlight the importance of using drill

cuttings for selecting fracture initiation zones as opposed to using symmetric intervals for

multi-stage hydraulic fracturing, a common practice in the oil and gas industry due to

data scarcity.

Fig. 7.9 shows a comparison of results. The Re-design case based on drill cuttings shows

a better performance for the 364 days of production forecast Tables 7.2 and 7.3 shows

results for each hydraulic fracturing stage. Columns 2, 4, 6, 8, 10, 12, and 14 show the

cumulative gas production per stage, while columns 3, 5, 7, 9, 11, 13 and 15 show the

daily gas production rate for each fracture stage. Columns 16 and 17 show the total

cumulative gas production and the gas rate, respectively; these totals were determined by

adding the individual fracture stage cumulative gas production and rates.

172

Figure 7.9—Comparison of cumulative gas production profile between the Initial

Design and the Re-design case using Cut-Log. The two cases involved a seven stage

fracture treatment but the fracture initiation zones for the two cases are different.

The Re-design case shows a better performance for the 364 days of production

forecast; these performance shows that selecting symmetrical distances for

hydraulic fracture initiation, as done commonly in the oil and gas industry due to

data scarcity, is not optimum. Better performance is obtained selecting those zones

with high brittleness index, permeability and Frac-Value in the Cut-Log,

parameters obtained from drill cuttings in this study.

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

0.0 100.0 200.0 300.0 400.0

Cu

mu

lati

ve

Ga

s P

rod

uct

ion

, E

6 m

3

Time, days

Re-Design

Initial Design

173

Table 7.2— SIMULATION OUTPUT FROM INITIAL MODEL DESIGN BASED

ON SYMMETRICAL DISTANCES FOR HYDRAULIC FRACTURE

INITIATION.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

TimeCumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

0.000 0.004 4.318 0.004 4.318 0.004 4.317 0.026 25.848 0.026 25.939 0.003 3.074 0.002 1.527 0.069 69.341

1.000 0.008 3.963 0.008 3.963 0.008 3.963 0.049 23.450 0.050 23.533 0.006 2.618 0.003 1.313 0.132 62.803

2.100 0.012 3.669 0.012 3.669 0.012 3.669 0.073 21.412 0.073 21.441 0.008 2.270 0.004 1.169 0.195 57.299

3.310 0.017 3.454 0.017 3.454 0.017 3.483 0.097 19.969 0.097 20.039 0.011 2.004 0.005 1.078 0.260 53.481

4.641 0.021 3.319 0.021 3.319 0.021 3.347 0.122 18.936 0.123 18.962 0.013 1.863 0.007 1.027 0.328 50.773

6.105 0.026 3.190 0.026 3.190 0.026 3.216 0.149 18.067 0.149 18.129 0.016 1.732 0.008 0.979 0.399 48.503

7.716 0.031 3.115 0.031 3.115 0.031 3.090 0.177 17.378 0.177 17.403 0.018 1.651 0.010 0.933 0.474 46.685

9.487 0.036 2.993 0.036 2.993 0.036 3.018 0.206 16.784 0.207 16.808 0.021 1.574 0.011 0.889 0.553 45.059

11.436 0.042 2.923 0.042 2.923 0.042 2.947 0.238 16.244 0.239 16.267 0.024 1.500 0.013 0.862 0.639 43.666

13.579 0.048 2.855 0.048 2.855 0.048 2.878 0.272 15.720 0.272 15.742 0.027 1.430 0.015 0.835 0.729 42.315

15.937 0.054 2.788 0.054 2.788 0.054 2.766 0.308 15.244 0.308 15.266 0.030 1.407 0.017 0.809 0.826 41.068

18.531 0.061 2.722 0.061 2.722 0.062 2.701 0.346 14.783 0.347 14.804 0.034 1.341 0.019 0.783 0.930 39.856

21.384 0.069 2.659 0.069 2.659 0.069 2.637 0.387 14.335 0.388 14.355 0.038 1.320 0.021 0.759 1.040 38.724

24.523 0.077 2.596 0.077 2.596 0.077 2.576 0.431 13.915 0.431 13.935 0.042 1.258 0.023 0.735 1.158 37.611

27.975 0.086 2.535 0.086 2.535 0.086 2.515 0.477 13.453 0.478 13.472 0.046 1.239 0.026 0.712 1.284 36.461

31.772 0.095 2.436 0.095 2.436 0.095 2.456 0.527 13.059 0.528 13.078 0.051 1.219 0.028 0.729 1.419 35.413

35.950 0.105 2.379 0.105 2.379 0.105 2.399 0.579 12.625 0.580 12.643 0.055 1.162 0.031 0.707 1.561 34.294

40.545 0.116 2.323 0.116 2.323 0.116 2.343 0.636 12.256 0.637 12.273 0.061 1.144 0.035 0.685 1.716 33.347

45.599 0.127 2.269 0.127 2.269 0.127 2.251 0.696 11.849 0.697 11.865 0.066 1.126 0.038 0.663 1.878 32.292

51.159 0.139 2.216 0.139 2.216 0.139 2.198 0.759 11.455 0.761 11.471 0.073 1.109 0.042 0.680 2.051 31.345

57.275 0.153 2.129 0.153 2.129 0.153 2.147 0.827 11.075 0.828 11.091 0.079 1.057 0.046 0.659 2.239 30.287

64.003 0.167 2.079 0.167 2.079 0.167 2.096 0.899 10.707 0.901 10.722 0.086 1.040 0.050 0.639 2.437 29.362

71.403 0.182 2.031 0.182 2.031 0.182 2.015 0.976 10.352 0.977 10.366 0.094 1.024 0.055 0.619 2.647 28.438

79.543 0.197 1.951 0.197 1.951 0.198 1.967 1.057 10.008 1.059 10.022 0.102 1.008 0.059 0.599 2.869 27.506

88.497 0.214 1.906 0.214 1.906 0.215 1.921 1.144 9.676 1.146 9.689 0.110 0.961 0.065 0.616 3.108 26.675

98.347 0.233 1.861 0.233 1.861 0.233 1.846 1.236 9.317 1.237 9.330 0.120 0.946 0.071 0.597 3.363 25.758

109.182 0.252 1.788 0.252 1.788 0.253 1.803 1.333 9.007 1.335 9.020 0.130 0.931 0.077 0.579 3.632 24.916

121.100 0.273 1.760 0.273 1.760 0.273 1.718 1.436 8.673 1.439 8.685 0.140 0.887 0.084 0.560 3.918 24.043

134.210 0.295 1.678 0.295 1.678 0.295 1.692 1.546 8.351 1.548 8.363 0.152 0.859 0.091 0.543 4.222 23.164

148.631 0.319 1.652 0.319 1.652 0.318 1.612 1.662 8.041 1.664 8.053 0.164 0.833 0.099 0.526 4.545 22.369

164.494 0.344 1.574 0.344 1.574 0.344 1.587 1.785 7.743 1.787 7.754 0.176 0.807 0.107 0.543 4.887 21.582

181.943 0.370 1.500 0.370 1.500 0.370 1.513 1.914 7.425 1.917 7.436 0.191 0.824 0.116 0.526 5.248 20.724

201.138 0.398 1.477 0.398 1.477 0.399 1.489 2.051 7.121 2.054 7.131 0.206 0.798 0.126 0.510 5.632 20.003

222.252 0.428 1.408 0.428 1.408 0.429 1.419 2.195 6.815 2.198 6.824 0.222 0.773 0.136 0.494 6.036 19.141

245.477 0.459 1.342 0.459 1.342 0.460 1.353 2.346 6.522 2.350 6.531 0.240 0.749 0.148 0.478 6.462 18.317

271.024 0.492 1.279 0.492 1.279 0.493 1.289 2.504 6.191 2.508 6.199 0.258 0.726 0.159 0.464 6.906 17.427

299.127 0.526 1.219 0.526 1.219 0.527 1.229 2.670 5.876 2.674 5.885 0.278 0.703 0.172 0.449 7.373 16.580

330.039 0.562 1.162 0.562 1.162 0.564 1.171 2.842 5.578 2.846 5.586 0.299 0.681 0.185 0.421 7.860 15.761

364.000 0.600 1.107 0.600 1.107 0.602 1.116 3.020 5.251 3.025 5.259 0.321 0.660 0.200 0.438 8.368 14.938

STAGE 6 (3419)STAGE 1 (3876) STAGE 2 (3814) STAGE 3 (3708) STAGE 4 (3616) STAGE 5 (3511)

BASECASE-INITIAL DESIGN

STAGE 7 (3314) TOTAL

174

Table 7.3— SIMULATION OUTPUT FROM RE-DESIGN MODEL BASED ON

HYDRAULIC FRACTURE INITIATIONS FROM THE CUTTINGS-BASED

CUT-LOG.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

TimeCumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

CumGas

(e6m3)

Gas Rate

(e3m3/day)

0.000 0.023 22.690 0.021 20.606 0.026 26.052 0.002 1.527 0.002 1.527 0.002 1.527 0.002 1.527 0.076 75.456

1.000 0.043 20.585 0.039 18.694 0.050 23.635 0.003 1.313 0.003 1.313 0.003 1.313 0.003 1.313 0.144 68.166

2.100 0.064 18.876 0.058 17.179 0.073 21.535 0.004 1.169 0.004 1.169 0.004 1.169 0.004 1.169 0.212 62.266

3.310 0.086 17.715 0.078 16.089 0.098 20.126 0.005 1.078 0.005 1.078 0.005 1.078 0.005 1.078 0.283 58.242

4.641 0.108 16.798 0.098 15.256 0.123 19.045 0.007 1.027 0.007 1.027 0.007 1.027 0.007 1.027 0.356 55.207

6.105 0.131 16.126 0.119 14.645 0.150 18.171 0.008 0.979 0.008 0.979 0.008 0.979 0.008 0.979 0.433 52.858

7.716 0.156 15.511 0.142 14.087 0.178 17.479 0.010 0.933 0.010 0.933 0.010 0.933 0.010 0.933 0.515 50.809

9.487 0.183 15.012 0.166 13.620 0.208 16.881 0.011 0.889 0.011 0.889 0.011 0.889 0.011 0.889 0.602 49.069

11.436 0.211 14.557 0.192 13.221 0.240 16.304 0.013 0.862 0.013 0.862 0.013 0.862 0.013 0.862 0.695 47.530

13.579 0.242 14.116 0.219 12.833 0.273 15.811 0.015 0.835 0.015 0.835 0.015 0.835 0.015 0.835 0.793 46.100

15.937 0.274 13.703 0.249 12.457 0.309 15.301 0.017 0.809 0.017 0.809 0.017 0.809 0.017 0.809 0.899 44.697

18.531 0.309 13.355 0.280 12.092 0.348 14.838 0.019 0.783 0.019 0.783 0.019 0.783 0.019 0.783 1.012 43.417

21.384 0.346 12.964 0.314 11.785 0.389 14.389 0.021 0.759 0.021 0.759 0.021 0.759 0.021 0.759 1.133 42.174

24.523 0.385 12.584 0.350 11.440 0.433 13.967 0.023 0.735 0.023 0.735 0.023 0.735 0.023 0.735 1.261 40.931

27.975 0.427 12.215 0.388 11.105 0.479 13.503 0.026 0.712 0.026 0.712 0.026 0.712 0.026 0.712 1.396 39.671

31.772 0.472 11.857 0.429 10.779 0.529 13.108 0.028 0.729 0.028 0.729 0.028 0.729 0.028 0.729 1.544 38.660

35.950 0.520 11.510 0.473 10.464 0.582 12.673 0.031 0.707 0.031 0.707 0.031 0.707 0.031 0.707 1.701 37.475

40.545 0.572 11.173 0.519 10.157 0.639 12.301 0.035 0.685 0.035 0.685 0.035 0.685 0.035 0.685 1.868 36.371

45.599 0.627 10.845 0.569 9.860 0.699 11.893 0.038 0.663 0.038 0.663 0.038 0.663 0.038 0.663 2.047 35.250

51.159 0.685 10.528 0.622 9.571 0.763 11.498 0.041 0.642 0.042 0.680 0.042 0.680 0.042 0.680 2.236 34.279

57.275 0.747 10.178 0.679 9.253 0.831 11.116 0.046 0.660 0.046 0.659 0.046 0.659 0.046 0.659 2.440 33.184

64.003 0.814 9.880 0.739 8.982 0.903 10.747 0.050 0.639 0.050 0.639 0.050 0.639 0.050 0.639 2.656 32.165

71.403 0.884 9.552 0.804 8.684 0.980 10.390 0.054 0.619 0.055 0.619 0.055 0.619 0.055 0.619 2.886 31.102

79.543 0.960 9.235 0.872 8.395 1.062 10.045 0.059 0.600 0.059 0.599 0.059 0.599 0.059 0.599 3.131 30.072

88.497 1.040 8.928 0.945 8.149 1.148 9.673 0.065 0.617 0.065 0.616 0.065 0.616 0.065 0.616 3.393 29.215

98.347 1.125 8.632 1.023 7.879 1.240 9.351 0.071 0.598 0.071 0.597 0.071 0.597 0.071 0.597 3.671 28.251

109.182 1.215 8.345 1.105 7.617 1.338 9.004 0.077 0.579 0.077 0.579 0.077 0.579 0.077 0.579 3.966 27.282

121.100 1.311 8.068 1.193 7.334 1.442 8.705 0.084 0.561 0.084 0.560 0.084 0.560 0.084 0.560 4.281 26.348

134.210 1.413 7.800 1.286 7.091 1.552 8.382 0.091 0.543 0.091 0.543 0.091 0.543 0.091 0.543 4.614 25.445

148.631 1.522 7.511 1.384 6.842 1.668 8.071 0.098 0.526 0.099 0.526 0.099 0.526 0.099 0.526 4.968 24.528

164.494 1.636 7.232 1.489 6.601 1.791 7.740 0.107 0.544 0.107 0.543 0.107 0.543 0.107 0.543 5.344 23.746

181.943 1.758 6.978 1.599 6.317 1.921 7.453 0.116 0.527 0.116 0.526 0.116 0.526 0.116 0.526 5.742 22.853

201.138 1.886 6.678 1.716 6.095 2.057 7.118 0.126 0.510 0.126 0.510 0.126 0.510 0.126 0.510 6.163 21.931

222.252 2.021 6.391 1.839 5.833 2.201 6.812 0.136 0.494 0.136 0.494 0.136 0.494 0.136 0.494 6.605 21.012

245.477 2.163 6.116 1.969 5.583 2.353 6.520 0.147 0.479 0.148 0.478 0.148 0.478 0.148 0.478 7.076 20.132

271.024 2.313 5.854 2.106 5.343 2.511 6.189 0.159 0.464 0.159 0.464 0.159 0.464 0.159 0.464 7.566 19.242

299.127 2.469 5.556 2.248 5.072 2.676 5.874 0.172 0.449 0.172 0.449 0.172 0.449 0.172 0.449 8.081 18.298

330.039 2.632 5.274 2.397 4.814 2.848 5.576 0.185 0.421 0.185 0.421 0.185 0.421 0.185 0.421 8.617 17.348

364.000 2.802 5.006 2.552 4.570 3.027 5.249 0.200 0.439 0.200 0.438 0.200 0.438 0.200 0.438 9.181 16.578

STAGE 6 (3394) STAGE 7 (3299)

REDESIGN AFTER CUT-LOG

TOTALSTAGE 1 (3854) STAGE 2 (3746) STAGE 3 (3645) STAGE 4 (3446) STAGE 5 (3342)

175

Chapter Eight: CONCLUSION AND RECOMMENDATIONS

Conclusions stemming from this thesis are presented below separately for drill cuttings,

porosity exponent (m), water saturation exponent (n), petrophysics and geomechanical

evaluations, and finally hydraulic fracturing and modelling. This is followed by some

recommendations.

8.1 Drill Cuttings

1. Drill cuttings are powerful direct sources of information that can be used in the

laboratory for determining porosities and permeabilities of tight formations

penetrated by horizontal wells. This is of significant practical value particularly

because of the usual data scarcity in horizontal wells.

2. The data allow quantitative formation evaluation of horizontal wells even in the

absence of well logs. This includes the determination of pore throat aperture

radius (rp35), water saturation, porosity exponent (m), true formation resistivity,

capillary pressure, Knudsen number, depth to the water contact (if present) and

construction of Pickett plots.

3. The data also allow estimation of geomechanical properties including Poisson’s

ratio, Young’s Modulus, Brittleness Index, and a Cut-Log useful for determining

the optimum locations for initiating hydraulic fractures in multi-stage fracturing

jobs.

8.2 Porosity Exponent (m)

1. Sihvola’s unified electromagnetic mixing rules are shown to be applicable for

176

handling at once Maxwell Garnett, Bruggeman and the Coherent Potential

formulas.

2. These formulas have been used for developing new dual and triple porosity

models for calculation of the porosity exponent m in naturally fractured

reservoirs.

3. The models have been compared successfully with core data from limestones,

dolomites and tight sandstones. When applicable the models have also been

compared successfully with other theoretical models developed previously in the

literature.

4. The models are robust and can be used for any combination of porosities

(including one or two porosities equal to zero). This makes the models powerful

as they can be run throughout heterogeneous naturally fractured reservoirs

without a need for changing equations with depth.

5. The advantage of the petrophysical models based on the Maxwell Garnett

equation is that the calculation of m can be done explicitly without trial and error.

The Bruggeman and coherent potential formulas require an iteration procedure for

calculating m.

177

8.3 Water Saturation Exponent (n)

1. The same electromagnetic mixing rule mentioned above has been used for

developing new theoretical models for determining the water saturation exponent

(n) and water saturation (Sw) in dual and triple porosity reservoirs with mixed

wettability.

2. The dual and triple porosity models are robust and work correctly in the case of

single porosity (matrix) reservoirs when isolated and fracture porosities are equal

to zero. The single porosity model has been validated with the use of

preferentially oil wet and also preferentially water wet core data.

3. The models require water saturation of the matrix blocks or resistivity index as

input data. The value of n for dual and triple porosity reservoirs can be calculated

explicitly when water saturation of the matrix block (Swb) is known. However, an

iterative procedure is required when resistivity index of the matrix block or whole

block is used as input data.

4. Use of the models requires knowledge of the porosity exponent of the matrix (mb)

as well as the porosity exponent of the composite system (m). These parameters

are determined from petrophysical models for dual and triple porosity reservoirs

developed in this thesis with the use of the same electromagnetic mixing rules

mentioned above.

178

8.4 Petrophysical and Geomechanical Evaluation

1. Porosity and permeability data determined from drill cuttings of a horizontal well

have been used for complete petrophysical evaluation of a tight gas sandstone in

the Nikanassin Group.

2. Porosity data from drill cuttings can serve as input data for geomechanical

calculations and also serve as an aid in identifying zones with high brittleness

index. This increases the success probabilities of stimulation operations by

pointing to ideal locations for fracture initiation.

3. Starting with only drill cuttings, Pickett plots that include water saturation,

permeability, pore throat radii, capillary pressure, height above the water table,

and Knudsen numbers have been constructed.

4. For those cases where wells are short of data, a new method has been developed

for estimating Poisson’s ratio, static Young Modulus and brittleness index based

on knowledge of only porosity.

5. For the tight gas sandstone considered in this study, the dominant flow regime is

continuum-flow as evidenced by calculated Knudsen numbers.

6. The proposed drill cuttings-based petrophysical and geomechanical evaluations

are not meant to replace detailed studies when complete data sets are available.

179

But drill cuttings can provide good estimates of several important reservoir

parameters particularly in those cases where core and log data are scarce.

8.5 Hydraulic Fracturing and Modeling

1. A multi-stage hydraulically fractured horizontal well has been modeled

successfully using GOHFER. Drill cuttings data were used to calibrate

geomechanical correlations built in the simulator.

2. Grid properties in the hydraulic fracturing model were populated using data from

drill cuttings.

3. Design of hydraulic fracturing models using drill cuttings data can serve as an aid

in identifying optimum fracture initiation zones during multi-stage hydraulic

fracturing jobs. These zones can be at any distance to each other if wellbore

configuration allows.

4. Comparison of cumulative gas production profiles indicate that better

performance is obtained selecting those zones with high brittleness index,

permeability and Frac-Value in the Cut Log developed from drill cuttings. The

performance selecting symmetrical distances for hydraulic fracture initiation, as

done commonly in the oil and gas industry due to data scarcity, is not optimum.

Recommendations are as follows:

1. Extend the evaluation of drill cuttings to the case of petroleum shale reservoirs.

180

2. Conduct the evaluations at various confining pressures.

3. Use the results to develop petrophysical models for evaluation of shale petroleum

reservoirs.

4. Demonstrate that the drill cuttings based methodologies presented in this thesis

are applicable in the case of conventional reservoirs.

5. Extend the drill cuttings and petrophysical methodologies to the case of oil sands.

181

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196

APPENDIX A: SCREEN SHOTS OF PERMEABILITY MEASUREMENTS

USING DARCYLOG

Sample 1_ 3185m MD

Sample 2_ 3190m MD

197

Sample 3_ 3195m MD

Sample 4_ 3200m MD

198

Sample 5_ 3205.5m MD

Sample 6_ 3205m MD

199


Sample 8_ 3210m MD

200


Sample 10_ 3220.0 MD

201

Sample 11_ 3225MD

Sample 12_ 3235MD

202

Sample 13_ 3265MD

Sample 14_ 3285MD

203

Sample 15_ 3290MD

Sample 16_ 3295MD

204

Sample 17_ 3300MD

Sample 18_ 3305MD

205

Sample 19_ 3310MD

Sample 20_ 3315MD

206

Sample 21_ 3320MD

Sample 22_ 3325MD

207

Sample 23_ 3345MD

Sample 24_ 3355MD

208

Sample 25_ 3435MD

Sample 26_ 3440MD

209

Sample 27_ 3445MD

Sample 28_ 3450MD

210

Sample 29_ 3460MD

Sample 30_ 3690MD

211

Sample 31_ 3710MD

Sample 32_ 3715MD

Sample 33_ 3720MD

212

Sample 33_ 3720MD

Sample 34_ 3725MD

213

Sample 35_ 3730MD

Sample 36_ 3735MD

214

Sample 37_ 3740MD

Sample 38_ 3745MD

215

Sample 39_ 3760MD

Sample 40_ 3765MD

216

Sample 41_ 3770MD

Sample 42_ 3775MD

Sample 43_ 3785MD

217

Sample 43_ 3785MD

Sample 44_ 3820MD

218

Sample 45_ 3835MD

Sample 46_ 3855MD

219

Sample 47_ 3860MD

Sample 48_ 3865M

220

Sample 49_ 3880MD

Sample 50_ 3885MD

221

Sample 51_ 3890MD

Sample 52_ 3895MD

222

Sample 53_ 3900MD

Sample 54_ 3930MD

223

Sample 55_ 3935MD

Sample 56_ 3940MD

224

Sample 57_ 3945MD

225

APPENDIX B : RELEVANT EQUATIONS

The following equations (Aguilera and Aguilera, 2003, 2004) are useful for petrophysical

calculations in order to maintain consistency in the scaling of porosity.

For dual porosity models:

……….……………………………...………………………………………….(B-1)

( ………………..…………………...………………………..……………..(B-2)

( ………………………………………...……….……...(B-3)

………..…………….………………………………………………………….….(B-4)

( …………………………………………………………………….………..(B-5)

( ……………………………………………………...….....(B-6)

For triple porosity models:

( ……………………………….……..(B-7)

226

APPENDIX C : ANGLE BETWEEN THE FRACTURES AND DIRECTION OF

CURRENT FLOW

Schematics assumed that current direction is horizontal in all cases, and the angle θ in the

schematic corresponds to fracture dip. Case A shows the horizontal fracture with no

tortuosity (mf = 1.0), Case B shows horizontal fracture with tortuosity that leads to a

porosity exponent of the fractures (mf) equal to 1.3, Case C shows the non-horizontal

fracture (θ = 50°) with no tortuosity (mf = 1.0); the 50° angle leads to a pseudo fracture

porosity exponent (mfp) equal to 1.19, and Case D shows the non-horizontal fracture (θ =

50°) with tortuosity (mf = 1.3). The 50° angle leads to a pseudo fracture porosity

exponent (mfp) equal to 1.49. If the flow of current is vertical, the angle corresponds to

1.0 minus fracture dip (Adapted from Aguilera and Aguilera, 2006).

227

APPENDIX D : WELL CONFIGURATION FOR INITIAL DESIGN

Well A

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UNIVERSITY OF CALGARY Drill Cuttings, Petrophysical, … · methodology developed in this thesis allows for complete formation evaluation and ... thank Dr. Roberto ... Paul Glover,