Upload
lamkhanh
View
223
Download
1
Embed Size (px)
Citation preview
* Mark of Schlumberger
IMPERIAL COLLEGE LONDON
Department of Earth Science and Engineering
Centre for Petroleum Studies
Wireline Formation Testers Analysis with Deconvolution
By
Joelle Mitri
A report submitted in partial fulfillment of the requirements for the award of the degree of
Master of Science in Petroleum Engineering
September 2013
ii Wireline Formation Testers Analysis with Deconvolution
DECLARATION OF OWN WORK
I declare that this thesis Wireline Formation Testers Analysis with Deconvolution is entirely
my own work and that where any material could be construed as the work of others, it is fully cited and
referenced, and/or with appropriate acknowledgement given.
Signature:
Name of student: Joelle Mitri
Names of supervisors: Prof. Alain C. Gringarten and Lekan Aluko (Petro-vision)
Wireline Formation Testers Analysis with Deconvolution iii
ACKNOWLEDGEMENT
To my parents and sisters, for their continuous and invariable support of my endeavors, in literally all
four corners of the world.
To my boyfriend, for his impatience, a constant reminder of what life is really about.
To Professor Alain C. Gringarten from Imperial College London, and Lekan Aluko from Petro-vision, for
their technical advice and guidance.
To Irina Kostyleva and Olakunle Ogunrewo, PHD students at Imperial College, for their precious time
and valuable discussions.
To Dr. Cosan Ayan from Schlumberger Data Consulting, for providing real data and motivation.
A Sincere Thank you,
Joelle
iv Wireline Formation Testers Analysis with Deconvolution
TABLE OF CONTENTS
DECLARATION OF OWN WORK ..............................................................................................................................................II
ACKNOWLEDGEMENT .......................................................................................................................................................... III
JOELLE ................................................................................................................................................................................. III
TABLE OF CONTENTS ........................................................................................................................................................... IV
LIST OF FIGURES ................................................................................................................................................................... V
LIST OF TABLES ..................................................................................................................................................................... V
ABSTRACT.......................................................................................................................................................................... 1
INTRODUCTION ................................................................................................................................................................ 1
MODEL DESIGN AND VERIFICATION .......................................................................................................................... 2
LIMITED-ENTRY WELL WITH C & S, HOMOGENOUS, INFINITE LATERAL EXTENT ........................................................................ 3 LIMITED-ENTRY WELL WITH C & S, RADIAL COMPOSITE, INFINITE LATERAL EXTENT ................................................................ 4 LIMITED-ENTRY WELL WITH C & S, RADIAL COMPOSITE (WITH FILTRATE INVASION), INFINITE LATERAL EXTENT .................... 5
DISCUSSION AND CONCLUSION ................................................................................................................................... 9
NOMENCLATURE ........................................................................................................................................................... 10
APPENDICES ........................................................................................................................................................................ 13
A- APPENDIX: MILESTONES .................................................................................................................................................. 13 B- APPENDIX: CRITICAL LITERATURE REVIEW ...................................................................................................................... 14
Wireline Formation Testers Analysis with Deconvolution v
LIST OF FIGURES FIGURE 1 SCHEMATIC OF THE DUAL-PACKER/PROBE CONFIGURATION (NOT DRAWN TO SCALE) .......................................................................... 3 FIGURE 2 CROSS-SECTION: 3-D RADIAL GRID (R,Θ,Z) ................................................................................................................................ 3 FIGURE 3 DUAL-PACKER (PA) AND OBSERVATION PROBE (PS) PRESSURES .................................................................................................... 3 FIGURE 4 EFFECT OF VARYING KV ON DUAL PACKER RESPONSE (A, LEFT) AND OBSERVATION PROBE (B, RIGHT), HOMOGENOUS CASE .......................... 4 FIGURE 5 EFFECT OF VARYING KHI/KHU ON DUAL PACKER RESPONSE (A, LEFT) AND OBSERVATION PROBE (B, RIGHT), RADIAL COMPOSITE ..................... 4 FIGURE 6 EARLY AND LATE TIME MATCH OF THE RADIAL COMPOSITE MODEL, DUAL-PACKER (A, LEFT), OBS. PROBE (B, RIGHT) ................................. 4 FIGURE 7 EFFECT OF VARYING THE RADIUS OF INVASION ON DUAL-PACKER (A,LEFT) AND OBS. PROBE (B,RIGHT) RESPONSES, RADIAL COMPOSITE ....... 5 FIGURE 8 EFFECT OF VARYING THE RADIUS OF INVASION ON DUAL-PACKER (A,LEFT) AND OBS. PROBE (B,RIGHT) RESPONSES, RADIAL COMPOSITE WITH
FILTRATE INVASION ..................................................................................................................................................................... 5 FIGURE 9 EFFECT OF VARYING THE RADIUS OF INVASION ON DUAL-PACKER (A, LEFT) AND OBS. PROBE (B,RIGHT) RESPONSES, COMPOSITE WITH FILTRATE
INVASION, NARROW FORMATION DAMAGE. .................................................................................................................................... 6 FIGURE 10 COMPARING THREE CASES: 14GK, FORMATION DAMAGE, 13D, FORMATION DAMAGE AND INVASION, 13DF NARROW FORMATION
DAMAGE, FILTRATE INVASION ....................................................................................................................................................... 6 FIGURE 11 DECONVOLUTION OF CASE 13DF, RECONVOLVED P(T) AT PROBE (A, LEFT TOP) AT PACKER (B, LEFT BOTTOM); DECONVOLVED DERIVATIVE AT
PROBE (C, RIGHT TOP) AT PACKER (D, RIGHT BOTTOM) ....................................................................................................................... 7 FIGURE 12 RESULT OF DECONVOLUTION, RADIAL COMPOSITE MODEL WITH NO INVASION. PI=4855.67 PSIA...................................................... 7 FIGURE 13 CASE B: LOG-LOG PLOT OF BU 1,2,3,4. RADIAL COMPOSITE MODEL INITIALIZED WIT INVASION OF 61" (DUAL PACKER RESPONSE) ......... 8 FIGURE 14 CASE B RADIAL COMPOSITE MODEL INITIALIZED WIT INVASION OF 61". BUS 2-3-4 PI=4855.14 PSIA (AS FOUND BY DECONVOLUTION) .. 8 FIGURE 15 CASE B: RADIAL COMPOSITE MODEL INITIALIZED WIT INVASION OF 61". BUS 2-3-4. FORCED PI TO PI=4855.67 PSIA. ........................ 8 FIGURE 16 CASE B: INVASION OF 61" BUILD-UP 3-4 (SAPHIR) FORCED PI=4855.4 PSIA. .............................................................................. 9 FIGURE 17 RECONSTRUCTION OF DECONVOLUTION WITH BUILD-UPS 3&4(ABOVE). CLOSE-UP ON BUILD-UPS 2-3&4 (BELOW) ............................ 9 FIGURE 18 RECONSTRUCTION OF DECONVOLUTION WITH BUILD-UPS 2-3&4 (ABOVE). CLOSE-UP ON BUILD-UPS 2-3&4 (BELOW) ...................... 10
LIST OF TABLES TABLE 1 FORMATION AND FLUID PROPERTIES, ......................................................................................................................................... 3
* Mark of Schlumberger
CID 00777981
Wireline Formation Testers Analysis with Deconvolution Joelle Mitri, SPE, Imperial College of London
Copyright 2013, Society of Petroleum Engineers This paper was prepared as a requirement for the MSc of Petroleum Engineering at the Imperial College of London, 11-13 September 2013.
Abstract
Wireline Formation Testers (WFTs) technology evolved considerably over the last 50 years following the developments in
exploration frontiers. Deeper waters and increasingly more challenging environments drove the rising demand for complete
and efficient reservoir characterisation. From the introduction of the Formation Tester in 1955 providing one sample per
descent, to the Repeat Formation Tester (RFT*) in 1975, and the Modular Formation Dynamics Tester (MDT*) in 1991, WFT
toolstrings today can combine up to 30 different modules and provide days of continuous reservoir evaluation.
This was coupled with the development of Crystal Quartz Gauges (CQG*) with improved accuracy and dynamic response, as
well as reliable Tough Logging Conditions (TLC*). TLC conveyance technology enables these tools to be run on drill pipe
while still connected to the wireline, therefore eliminating the weight limitation and reducing the fishing risk. On deep water
operations, development/marginal wells and in environmentally sensitive areas, cost and flaring constraints may render a well
testing operation uneconomic or impossible. With much diversity and reliability, WFT services namely, Interval Pressure-
Transient Tests (IPTTs), emerged as substitutes to conventional well testing under these conditions. IPTTs combine a dual-
packer module, isolating a one-meter interval of formation, with traditionally one or two vertical observation probes; . the The
resulting transient behaviour matches that of a limited-entry well.
This study looks into the analysis of both synthetic and real pressure transient data obtained from IPTTs, using the latest Well
Test Analysis (WTA) tool: Deconvolution. Deconvolution transforms the pressure and variable-rate history of a given well
into a constant-rate drawdown with a duration equivalent to that of the entire test. This increased depth of investigation may
reveal or confirm critical boundary conditions that are otherwise not detected when interpreting individual flow periods.
Another powerful advantage of deconvolution is its ability to correct for erroneous rates which heavily compromise
conventional WTA techniques such as the superposition function. Although deconvolution was introduced in the literature as
early as 1949, its application only came recently after a reliable algorithm was implemented by von Shcroeter, Hollaender, and
Gringarten in 2001.
In principle, deconvolution can be equally applied to IPTTs; however, the openhole conditions which govern a WFT operation
challenge this undertaking: They involve withdrawal of drilling mud trapped in the interval, clean-up of near-wellbore
invasion and ultimately sampling of native reservoir fluid. The Duhamel integral underlying the theory of deconvolution,
pertains to a linear system which is therefore not entirely satisfied by IPTTs. Through forward modeling, interpretation and
sensitivity runs, it is found that invasion exhibits skin-like effects in early-time transients as well as inconsistent late-time
behaviors on the deconvolved derivative. Excluding cleanup and contaminated flow periods eliminates this inconsistency but
fails to reconstruct the correct pressure history.
Introduction
WFT operations require careful planning and execution as well as a complete understanding of client objectives and
borehole conditions. MDT* is a versatile family of tools: probes, packers, pumps, downhole fluid analyzers, sample chambers;
robust yet precise engineering designed to meet a wide spectrum of formation and fluid properties. Dual-packers, also known
as straddle-packers, provide a flow area a thousand times larger than that of a standard probe, which allows for higher flow
rates and reduced drawdowns. They were mainly designed to test thin laminated beds, unconsolidated formations, low
permeability formations and fluids at bubble point pressures; additional applications include stress testing and mini-frac. In
homogenous layers equally, they provide dynamically-controlled pressure tests, and are combined with vertical probes to
deliver interference tests that allow for the direct measurement of vertical and horizontal permeabilities.
IPTTs theory and interpretation are well-established in the literature and are continually explored and revisited as new
2 Wireline Formation Testers Analysis with Deconvolution
technologies emerge; additional accounts can be found in (Zimmerman et al. (1990); Goode et al. (1991, 1992); Pop et al.
(1993); Ayan et al. (1996). Applications of IPTTs also include layer productivity estimation prior to completion (Da Prat et
al.1999) and multiphase flow properties derivation by combining resistivity measurements of invasion with IPTT cleanup
process (Zeybek et al. 2001). Understanding the invasion and cleanup processes is not only critical to WFT operations but to
the overall productivity of the well.
Dynamic mud invasion occurs during the drilling process, it continues after the mud cake has been formed and drilling
stopped in a process referred to as filtration or static invasion. Shortly after drilling the formation, the mud cake develops as a
result of the suspension of mud particles in the pore space, which leads to further accumulation of solids on the inner wall of
the well. Devoid of solids, filtrate continues to invade the formation at rates proportional to the permeability of the mud cake.
This results in formation damage in the invaded zone, reducing permeability, porosity and in some cases altering wettability
(Shuang 1990). It has been reported in the literature that relying uniquely on uninvaded formation and fluid properties to
analyze WFT data can incur an error of 100% and lead to underestimating permeability by a factor of 3.6 (Goode et al. 1996).
The invasion process depends on many factors namely: pressure differential between the hydrostatic and formation
pressures, shear rate, mud solid content, mud type, formation permeability, absolute temperature and time sequential. As a
result, modeling invasion is a very complicated task; it is governed by dynamic flow as well as capillary pressures and gravity
effects. However, the process itself is not of prime importance to our study but the resulting reservoir conditions prior to WFT
and their effect on pressure transients. To model the effect of invasion, several studies assumed negligible capillary pressures
and gravity effects as well as negligible formation damage, reducing it to a miscible or immiscible flow (Phelps et al. 1984;
Hammond 1991; Zeybek et. al 2001). Goode et al. (1996) developed an analytical model of a two-region problem, the invaded
and uninvaded regions, with different vertical and horizontal mobilities and compressibilities. The study investigates the effect
of this invasion on the sink, horizontal and vertical probes in a Multi-probe WFT, assuming a sharp invasion front and a
piston-like displacement in a single homogenous layer. Gök et al. (2003) developed this model to include dual-packer as well
as multi-probe WFT in single and multilayer systems. However, the basic assumption has been that the invasion front is static
during the WFT which is not the case on dual-packer operations where cleanup is expected and fluid contamination is
monitored in real-time. Alpak et al. (2006) and Malik et al. (2007) used compositional simulators to model the cleanup process
and match their simulations to real Gas-Oil Ratio (GOR) and probe transient data.
In this study, we neglect gravity and capillary effects and we model a two-phase flow process in a two-zone radial
composite model representing invaded and non-invaded zones. We investigate the effect of Water-Based Mud (WBM)
invasion of an oil reservoir flowing above the bubble point pressure, by varying anisotropy, the radius of invasion, viscosity
and compressibility of the invading fluid and monitoring transient pressures at the dual-packer and observation probe in a
single finite homogenous layer. Finally, the transient data is analyzed using the latest WTA technique: Deconvolution.
Deconvolution was first introduced in the literature by van Everdingen and Hurst (1949) as an adaptation of the Duhamel
Principle of heat conduction, but it wasn’t until 2001 that the first robust algorithm was implemented by von Schroeter et al.
(2001). This algorithm presented several advancements over existing Spectral and Time-Domain methods and was
characterized by: a novel encoding of the solution, regularization by curvature to maintain a degree of smoothness in the result,
a total least-squares formulation to account for errors in pressure and rate data, and confidence intervals and error estimates for
the results. Since, many improvements and applications were suggested to the algorithm and continuous efforts made to
encourage reservoir engineers to make use of this powerful technique (von Schroeter et al. 2004; Levitan 2005; Levitan et. al
2006; Gringarten 2006, 2010). Recently, a modification of this algorithm was presented by Pimonov et al. (2009); it enables
the user to define different error estimates to different parts of the data as mitigation to unreliable pressure and rate data as well
as inconsistencies with the reservoir model. Onur et al. (2011) presented a modification to the latter for multiwell-interference
tests and IPTTs by replacing the rate signal with the observation probe signal thus eliminating the errors and uncertainty
associated with the flow-rate.
Using generated synthetic and real data sets, we investigate the reliability and viability of the deconvolution under different
invasion conditions using the algorithm developed by von Shroeter et al. (2004).
Model Design and Verification
The IPTT response we aim to reproduce is that of a dual-packer/probe configuration. The inflatable packers isolate an
interval of 3.2ft (0.98m) in the standard configuration that can be extended to 5.2, 8.2 or 11.2ft (1.58, 2,5 or 3.41m)
(Schlumberger 2002, 2011). Fig. 1 represents the schematic of this configuration and defines the model parameters h, hw, zw, ri,
Di, used throughout the paper.
The IPTT model is implemented, using the commercial simulator Eclipse*100 in fully-implicit blackoil mode
(Schlumberger Information Solutions 2010), to examine the effects of varying formation and invasion parameters on the
transient data. A 3-D radial grid (r,θ,z) represents a 10-meter thick homogenous layer and extends 500 m away from a vertical
Comment [ACG1]: Use this
presentation for citing references. “et al.” must be in italic
Comment [ACG2]: Where are they?
Wireline Formation Testers Analysis with Deconvolution 3
1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]
0.01
0.1
1
10
Pre
ssu
re [p
si]
1A: PS Kv:50mD
1A: PA Kv:50mD (ref)
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
well. A well diameter of 8.5in (0.216m) is set throughout the study. The distance away from the borehole is chosen such that
the pressure disturbance does not reach the boundary for the duration of the test.
With the inner and outer radii of the grid defined, 50 layers make up the radial dimension r following a geometric series;
this ensures the near wellbore area is well defined.
At the observation probe, for an 8.5” hole, 30 divisions with dθ=12°, result in a cell dimension of 1” equivalent to the
diameter of the probe; while the dual packer is azimuthally symmetric. It was found however, that with 8 azimuthal
divisions and dθ=45°, the signal at the probe is equally reproduced and additional computational efficiency is achieved.
In the z direction, the grid consists of 107 layers; the dual-packer interval is equally divided into 36 layers while the probe
occupies a single layer, one inch in thickness. The remaining layers increase logarithmically away from the interval and
probe sections. A cross-section of the grid is shown in Fig. 2.
Table 1 summarizes the main rock and fluid properties of the model. Since we are measuring and interpreting downhole
pressures and rates, the total depth of the well and the absolute depth of the model are of no consequence.
On the following tests, the model is run over a 2.4hr constant-rate drawdown period followed by a buildup of equal
duration. The time steps vary logarithmically and a flow rate of 5m3/day is set throughout. The elements of the final model are
built and tested systematically starting with a homogenous limited-entry well, to radial composite and finally invaded radial
composite.
Limited-entry well with C & S, homogenous, infinite lateral extent
In a limited entry test such as the IPTT with the dual-packers positioned in the middle of the layer, the early-time flow
regime is spherical (-1/2 slope); once the upper and lower boundaries of the layer are reached, radial flow stabilization is
established. The model transients at the dual-packer and observation probe are matched using Saphir (Kappa Engineering
2012), for kv=50md and kh=100md, as shown in Fig. 3.
Table 1 Formation and Fluid Properties,
homogenous case
Uninvaded Zone Properties
φ 0.18
μo (cp) 1.142
kh (md) 100
kv (md) 50
ct (bar -1
) 1.27E-4
Swc 0.22
Sor 0.35
Figure 3 Dual-packer (PA) and Observation probe (PS) pressures
and derivatives. kh=100md.
Figure 1 Schematic of the dual-packer/probe
configuration (not drawn to scale) Figure 2 Cross-section: 3-D Radial grid (r,θ,z)
Formatted: Highlight
4 Wireline Formation Testers Analysis with Deconvolution
Fig. 4a and Fig. 4b demonstrate the effect of varying the kv/kh ratio on the dual-packer and observation probe responses
respectively. As the vertical permeability decreases, the radial flow stabilization is delayed; the time it takes pressure
disturbance to reach the vertical boundaries increases.
Figure 4 Effect of varying kv on dual packer response (a, left) and observation probe (b, right), homogenous case
Limited-entry well with C & S, radial composite, infinite lateral extent
We model the invaded and non-invaded zones as co-centric zones around the wellbore with different properties. For a fixed
radius of damaged formation ri, we vary the permeability ‘damage’, which is the ratio of khi to khu. The assumption is that the
drilling and invasion process has altered the vertical and horizontal permeabilities equally and so the kv/ kh ratios are constant.
This is demonstrated in Fig. 5a and Fig. 5b on the dual-packer and observation probe responses respectively. The effect of the
formation damage is the alteration of the spherical flow -1/2 slope into a step change; the greater the damage, the larger the
step on the derivative response.
Figure 5 Effect of varying khi/khu on dual packer response (a, left) and observation probe (b, right), radial composite
As shown in Fig.6a and Fig.6b, the early time response matches the invaded zone properties (homogenous model with
invasion zone properties) while the late time behavior is that of the uninvaded zone (match of a homogenous model with
uninvaded zone properties). The match comparison was done using Interpret (Paradigm 2010).
Figure 6 Early and late time match of the radial composite model, dual-packer (a, left), obs. Probe (b, right)
1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]
0.1
1
10
Pre
ssu
re [p
si]
1A: PA Kv:50mD
1B: PA Kv:10mD
1C: PA Kv:20mD
1D: PA Kv:100mD (ref)
1E: PA Kv:200mD
1F: PA Kv:500mD
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]
0.01
0.1
1
Pre
ssu
re [p
si]
1A: PS Kv:50mD
1B: PS Kv:10mD
1C: PS Kv:20mD
1D: PS Kv:100mD (ref)
1E: PS Kv:200mD
1F: PS Kv:500mD
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]
1
10
100
Pre
ssu
re [p
si]
3A: PA Kvi5 Khi10
3B: PA Kvi10 Khi20
3C: PA Kvi25 Khi50
3D: PA Kvi33 Khi66
3E: PA Kvi50 Khi100 (ref)
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]
0.01
0.1
1
Pre
ssu
re [p
si]
3B: PS Kvi10 Khi20
3C: PS Kvi25 Khi50
3D: PS Kvi33 Khi66
3E: PS Kvi50 Khi100 (ref)
3A: PS Kvi5 Khi10
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
kv 50mD kh100mD Derivative Match
kv 5mD kh 10mD Derivative Match
3A: Radial Composite, kvi 5mD, khi 10mD
kv 50mD k
h100mD Match
kv 5mD k
h 10mD Match
3A: Radial Composite, kvi 5mD, khi 10mD
Comment [ACG3]: Why not use kh?
Wireline Formation Testers Analysis with Deconvolution 5
For the same invaded and uninvaded zone permeabilities, we vary the radius of the damaged formation; the results are
shown in Fig. 7a and Fig. 7b for the dual-packer and obs. probe respectively. The literature suggests that ideally we wouldn’t
expect the radius of invasion to extend beyond 48” (Hammond 1991, Phelps 1984, Gök 2003) (values greater than that are for
illustration purposes). It is interesting to see as will be pointed out later, that while the dual-packer response shows greater
variation, in the early times, to the extent of formation damage, the observation probe exhibits little change; the shallow
depths, Di= 0.79”, 4.16” and 23.5”, meet at the spherical flow -1/2 slope. The permeabilities used to demonstrate this example
were: kvu=5 md, khu=50 md, kvi=1.5 md and khi=15 md.
Figure 7 Effect of varying the radius of invasion on dual-packer (a,lefta, left) and obs. probe (b, right) responses, Radial Composite
Limited-entry well with C & S, radial composite (with filtrate invasion), infinite lateral extent
We now investigate the radial composite model with formation damage and presence of mud filtrate. Previous studies
assumed sharp and constant invasion fronts corresponding to the formation damage zones. We take a more realistic approach
by first simulating the invasion as a water injection process varying the time of invasion. The resulting gradual saturation
profiles are then used to initialize the model. As a result, it is not less obvious as to where what the extent of the damaged
formation should be; here we adopt two methods and explore the difference. In the first, we choose the radius of invasion and
formation damage at the point where water saturation is 50%. The second approach uses a narrower front and assumes a radius
of invasion and damage at 65% water saturation, which corresponds to 1-Sor. For disambiguation, we will now refer to the
radius formation damage radius as rf and to that of filtrate invasion as ri; Di and Df are the distances measured from the
wellbore wall as per Fig. 1.
The invasion front is not assumed to be stationary and so, given the same drawdown duration, the breakthrough of native
fluid will vary considerably; this will be illustrated when we vary native and invasion fluid parameters next. For the same
values of permeabilities of as in figures 7a and 7b, we illustrate the effect of varying the invasion radius with filtrate invasion.
We illustrate the first method whereby the formation damage extends to the limit of 50% filtrate saturation in Fig. 8a and Fig.
8b for the dual-packer and obs. probe respectively. The second method is illustrated in Fig. 9a and Fig. 9b.
Figure 8 Effect of varying the radius of invasion on dual-packer (a, left) and obs. probe (b, right) responses, Radial Composite with
filtrate invasion
1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]
1
10
100
Pre
ssu
re [p
si]
14AK: PA Di=0.79" (ref)
14CK: PA Di=4.16"
14EK: PA Di=23.5"
14GK: PA Di=61"
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]
0.1
1
10
Pre
ssu
re [p
si]
14AK: PS Di=0.79" (ref)
14CK: PS Di=4.16"
14EK: PS Di=23.5"
14GK: PS Di=61"
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]
1
10
100
Pre
ssu
re [p
si]
13A: PA Di=12.4"
13B: PA Di=23.5"
13C: PA Di=34.8" (ref)
13D: PA Di=61"
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
1E-3 0.01 0.1 1Time [hr]
1
10
Pre
ssu
re [p
si]
13B: PS Di=23.5"
13C: PS Di=34.8" (ref)
13D: PS Di=61"
13E: PS Di=177"
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
Comment [ACG4]: I am not sure I understand the difference. Is this a three-
region radial composite?
Comment [ACG5]: Do you mean “not” or “less”?
Comment [ACG6]: ?????
Formatted: Highlight
Formatted: Highlight
6 Wireline Formation Testers Analysis with Deconvolution
Figure 9 Effect of varying the radius of invasion on dual-packer (a, left) and obs. probe (b,right) responses, Composite
with filtrate invasion, Narrow formation damage.
Figure 10 Comparing three cases: 14GK, Formation damage, 13D, Formation Damage and Invasion, 13DF Narrow
Formation Damage, filtrate invasion
Putting all the model parameters together in comparison we note from Fig.10a (the dual-packer response) that the two
cases with similar formation damage model namely 14GK and 13D, have similar shape, the difference being that the invasion
acts like a skin in early time. Reducing the damaged formation zone (as in 13DF case) changed the radial composite model and
led to overall a higher oil production from the simulated run. The same was run on a model with higher permeabilities, the
same behavior was observed but the cleanup was slower. At the observation probe, the difference is minimal as shown in
Fig.10b suggesting the observation probe is less affected by invasion.
Applying deconvolution to the dual-packer and probe transients from case 13DF reveals a late time inconsistency on the
dual-packer signal and a poor reconstructed pressure while the result of deconvolution at the probe was satisfactory (Figs. 11a,
11b, 11c, 11d).
Deconvolution of synthetic data
We simulate a sampling WFT sampling consisting of the following schedule of drawdowns (DDs) and build-ups (BPs):
Duration
(hrs)
Rate
(Rm3/D)
1.26 3.55
0.17 0
3.80 3.15
0.15 0
3.80 1.32
0.55 0
0.79 3.46
0.32 5.3
1.05 0
1E-4 1E-3 0.01 0.1 1 10Time [hr]
1
10
100
Pre
ssu
re [p
si] 13AF: PA Di=12.4" Df=0.79" (ref)
13BF: PA Di=23.5" Df=2.84"
13CF: PA Di=34.8" Df=4.16"
13DF: PA Di=61" Df=12.4"
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
1E-3 0.01 0.1 1 10Time [hr]
0.1
1P
ressu
re [p
si]
13BF: PS Di=23.5" Df=2.84" (ref)
13CF: PS Di=34.8" Df=4.16"
13DF: PS Di=61" Df=12.4"
13EF: PS Di=177" Df=34.8"
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
1E-5 1E-4 1E-3 0.01 0.1 1 10 100 1000Time [hr]
1
10
100
Pre
ssu
re [p
si]
14GK: PA Di=61"
13D: PA Di=61" Df=61"
13DF: PA Di=61" Df=12.4" (ref)
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
0.01 0.1 1 10 100Time [hr]
0.1
1
10
Pre
ssu
re [p
si]
14GK: PS Di=61"
13D: PS Di=61" Df=61"
13DF: PS Di=61" Df=12.4" (ref)
Log-Log plot: p-p@dt=0 and derivative [psi] vs dt [hr]
Comment [ACG7]: Difficult to
distinguish 14GK from 13DF. Change the colors
Comment [ACG8]: Not identified on the figure
Comment [ACG9]: The correct nomenclature is “skin effect” or “skin factor”
Comment [ACG10]: Which deconvolution software did you use? What
did you deconvolve, the DD and the BU or just the BU?
Comment [ACG11]: This seems to be due to an erroneous simulated pressure at
the beginning. The simulated pressure goes down and up at the beginning. This is not
physical and should be checked.
Formatted: para, Indent: First line: 0cm
Comment [ACG12]: This is not a typical schedule for a sampling MDT.
Usually, there is a pre-test at the beginning
and another one at the end
Wireline Formation Testers Analysis with Deconvolution 7
Figure 11 Deconvolution of case 13DF, Reconvolved p(t) at probe (a, left top) at packer (b, left bottom); Deconvolved derivative at
probe (c, right top) at packer (d, right bottom)
First we apply deconvolution in the presence of a damaged formation damage but in the absence of invasion fluid for easier
comparison with the final model. Fig. 12 shows the Deconvolved deconvolved derivative which is consistent with the
individual BUs. Next we initialize our model with filtrate invasion, ri=61”, the resulting BUs are shown in Fig.13. Although
the build-ups will eventually converge at late times, early times shows that invasion acts like a skin effect., Buildup#1 is the
most affected because the previous clean-up was not sufficient. Fig.14 illustrates the result of Deconvolution of build-ups 2-3-
4 which exhibits an inconsistent late time behavior.
Nu, Lambda and Pi were varied. Fig.15 shows a slightly better match still with a hump after varying Pi. Increasing the
smoothness or increasing Pi doesn’t correct this hump, it only rotates it. This also confirms that the second clean-up was no
effective either. Deconvolution of Build-ups 3&4 is shown in Fig.16 gave ais satisfactory result. However, this result does not
reconstruct successfully the Drawdown responses or the build-ups that were affected by invasion and not included in the
Deconvolution as shown in Figs.17 and 18. It behaves like the well was never invaded. A similar behavior was reported in
Levitan (2005, Fig.5) when deconvolving flow periods with changing wellbore storage.
Figure 12 Result of Deconvolution, Radial composite model with no invasion. Pi=4855.67 psia.
4838
4848
Pre
ssu
re [p
sia
]
Reconvolved p(t) response
0 2 4
Time [hr]
-12.50
12.5
Liq
uid
ra
te [S
TB
/D]
History plot (Pressure [psia], Liquid rate [STB/D] vs Time [hr])
1E-3 0.01 0.1 1Time [hr]
0.1
1
10
Pre
ssu
re [p
si]
Log-Log deconv olution plot: p-p@dt=0 and deriv ativ e [psi] v s dt [hr]
4600
4700
4800
Pre
ssu
re [p
sia
]
0 2 4
Time [hr]
-12.50
12.5
Liq
uid
ra
te [S
TB
/D]
History plot (Pressure [psia], Liquid rate [STB/D] v s Time [hr])
1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]
1
10
100
Pre
ssu
re [p
si]
Log-Log deconvolution plot: p-p@dt=0 and derivative [psi] vs dt [hr]
1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1Time [Day]
0.01
0.1
1
10
Pre
ssure
[bar]
Deconvolution
Log-Log deconvolution plot: p-p@dt=0 and derivative [bar] vs dt [Day]
Comment [ACG13]: Show!
Comment [ACG14]: Don’t use the future tense
Comment [ACG15]: Have you tried to deconvolve one BU at a time, and all the
data (DDs and BUs)?
Comment [ACG16]: Do not use capital letters for this and similar words
Comment [ACG17]: The figures show a lack of match at the beginning which is
clearly associated with erroneous simulated
pressures.
Comment [ACG18]: My recollection is that the deconvolved derivative is not
correct at early times is skin effects or
wellbore coefficients are different in different flow periods. This is of little
concern as we do have the actual derivative
data at early times. We are mainly interested in late time derivative beyond
what is available in the individual flow
periods
8 Wireline Formation Testers Analysis with Deconvolution
Figure 13 CASE B: Log-Log plot of BU 1,2,3,4. Radial composite model
initialized wit invasion of 61" (dual packer response)
Figure 14 CASE B Radial composite model initialized wit invasion of 61". BUs 2-3-4
Pi=4855.14 psia (as found by Deconvolution)
Figure 15 CASE B: Radial composite model initialized wit invasion of 61". BUs 2-3-4.
Forced Pi to Pi=4855.67 psia.
1E-5 1E-4 1E-3 0.01 0.1Time [Day]
0.1
1
10
Pre
ssure
[bar]
build-up #1
build-up #2
build-up #3
build-up #4 (ref)
Log-Log plot: dp and dp' normalized [bar] vs dt
1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1Time [Day]
0.01
0.1
1
10
Pre
ssure
[bar]
Deconvolution
Log-Log deconvolution plot: p-p@dt=0 and derivative [bar] vs dt [Day]
1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1Time [Day]
0.01
0.1
1
10
Pre
ssu
re [b
ar]
Deconvolution
Log-Log deconvolution plot: p-p@dt=0 and derivative [bar] vs dt [Day]
Wireline Formation Testers Analysis with Deconvolution 9
Figure 16 CASE B: Invasion of 61" Build-up 3-4 (saphir) Forced Pi=4855.4 psia.
Figure 17 Reconstruction of Deconvolution with Build-ups 3&4(Above). Close-up on Build-ups 2-3&4 (Below)
Discussion and Conclusion
In this study we investigated water invasion in an oil interval flowing at pressures above the bubble point. The reduction
in permeability of the invaded zone due to bridging and solids was modeled as a radial composite system and verified. Radius
of invasion, mobility ratio and Diffusivity were varied between the invaded and non-invaded zones. It was found that the dual-
packer response is more affected by invasion in early times than the response seen at the observation probe.
A job was simulated with various rates and cleanup and build up periods and deconvolution applied systematically on the
pressure signal of the dual-packer. As expected, invasion imposed a non-linear system and a Deconvolution applied on the
entire dataset yielded erroneous results and the effect was seen on early as well as late times. The length of the cleanup period
is clearly the most important factor in getting the most out of subsequent flow periods with deconvolution. Smaller
permeabilities result in faster cleanup with greater drawdown. In a real well situation, the quality of the mudcake also plays a
big role in recharging the invasion and effective cleanup (supercharging) .
Applying deconvolution on this inconsistent data set yielded a consistent deconvolved derivative when applying it on
buildups after sufficient cleanup has been made; that means after the effect of invasion have has been reduced or eliminated.
As a result, the reconstructed pressure has no memory of invasion and does not match the actual signal.
As a way forward, having showed the more consistent data quality at the probe, it would be interesting to apply the
algorithm by replacing rates with the signal at the observation probe.
1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1
Time [Day]
0.01
0.1
1
10
100
Pre
ssu
re [b
ar]
Log-Log deconvolution plot: p-p@dt=0 and derivative [bar] vs dt [Day]
320
325
330
Pre
ssu
re [b
ara
]
Reconvolved p(t) response
0 0.2 0.4
Time [Day]
-2.50
Liq
uid
ra
te [m
3/D
]
History plot (Pressure [bara], Liquid rate [m3/D] vs Time [Day])
328
333
Pre
ssu
re [b
ara
]
Reconvolved p(t) response
0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5
Time [Day]
0
2.5
Liq
uid
ra
te [m
3/D
]
History plot (Pressure [bara], Liquid rate [m3/D] vs Time [Day])
Formatted: Highlight
Formatted: Highlight
Comment [ACG19]: I disagree. The pressure data are incorrect to start with
Comment [ACG20]: Same comment
Comment [ACG21]: ????
10 Wireline Formation Testers Analysis with Deconvolution
Figure 18 Reconstruction of Deconvolution with Build-ups 2-3&4 (Above). Close-up on Build-ups 2-3&4 (Below)
Nomenclature
D1 = Distance from middle of dual-packer interval to probe, L, m (ft)
Di = Extent of invasion measured from the borehole wall, L, in
Df = Extent of formation damage measured from the borehole wall, L, in
h = Thickness of homogenous layer, L, m
hw = Thickness of the dual-packer interval, L, m (ft)
k = Permeability, L2, md
M = Mobility ratio, ratio
p = Pressure m/Lt2, psia
ri = Radius of invasion measured from the center of the wellbore, L, in
rf = Radius of formation damage measured from the center of the wellbore, L, in
t = Time, t, hours
zw = Distance from middle of dual-packer interval to bottom boundary, L, m(ft)
μ = mobility, L3t/m, md/cp
dθ = Angle of grid azimuthal division, angle, deg
μo = Oil viscosity, m/Lt, cp
μw = Water viscosity, m/Lt, cp
μ = Fluid viscosity, m/Lt, cp
φ = porosity, L3/L
3, fraction
Subscripts
h Horizontal
i Invaded Zone
u Uninvaded Zone
v Vertical
322
327
332
Pre
ssu
re [b
ara
]
Reconvolved p(t) response
0 0.1 0.2 0.3 0.4 0.5
Time [Day]
02.5
Liq
uid
ra
te [m
3/D
]
History plot (Pressure [bara], Liquid rate [m3/D] vs Time [Day])
330
332
334
Pre
ssu
re [b
ara
]
Reconvolved p(t) response
0.22 0.24 0.26 0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48
Time [Day]
-2.50
2.5
Liq
uid
ra
te [m
3/D
]
History plot (Pressure [bara], Liquid rate [m3/D] vs Time [Day])
Wireline Formation Testers Analysis with Deconvolution 11
References
Alpak, F.O., Elshahawi, H., and Hashem, M. Compositional Modeling of Oil-base Mud-Filtrate Cleanup During Wireline
Formation Tester Sampling. 2006. Paper SPE 100393 presented at the SPE Annual Technical Conference and Exhibition,
San Antonio, Texas, 24-27 September. http://dx.doi.org/10.2118/100393-MS.
Ayan, C., Douglas, A., and Kuchuk, F.J. 1996. A Revolution in Reservoir Characterization. Schlumberger Middle East Well
Evaluation Review 16: 42–55.
Da Prat, G., Colo, C., Martinez, R., Cardinali, G., and Conforto, G. 1999. A New Approach To Evaluate Layer Productivity
Before Well Completion. SPE Res Eval & Eng 2 (1): 75-84. SPE-54672-PA. http://dx.doi.org/10.2118/54672-PA
Gök, I.M., Onur, M., Hegeman, P.S., and Kuchuk, F.J. 2003. Effect of an Invaded Zone on Pressure Transient Data From
Multi-Probe and Packer-Probe Wireline Formation Testers in Single and Multilayer Systems. Paper SPE 84093 presented
at the SPE Annual Technical Conference and Exhibition, Denver, 5–8 October. http://dx.doi.org/10.2118/84093-PA.
Goode, P.A., Pop, J.J., and Murphy, W.F. 1991. Multiple-Probe Formation Testing and Vertical Reservoir Continuity. Paper
SPE 22738 presented at the SPE Annual Technical Conference and Exhibition, Dallas, 6–9 October.
http://dx.doi.org/10.2118/22738-MS.
Goode, P.A. and Thambynayagam, R.K. 1992. Permeability Determination With a Multiprobe Formation Tester. SPE Form
Eval 7 (4): 297–303. SPE-20737-PA. http://dx.doi.org/10.2118/20732-PA.
Goode, P.A. and Thambynayagam, R.K.M. 1996. Influence of an Invaded Zone on a Multiprobe Formation Tester. SPE Form
Eval.11 (1): 31-40. SPE-23030-PA. http://dx.doi.org/10.2118/23030-PA
Gringarten, A.C. 2006. From Straight Lines to Deconvolution: The Evolution of the State-of-the Art in Well Test Analysis.
Paper SPE presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24-27 September;
2008. SPE Res Eval & Eng 11(1): 41-62. SPE-102079-PA. http://dx.doi.org/ 10.2118/102079-PA
Gringarten, A.C. 2010. Practical use of well test Deconvolution. Paper SPE 134534 presented at the SPE Annual Technical
Conference and Exhibition, Florence, Italy, 19-22 September. http://dx.doi.org/10.2118/134534-MS
Hammond, P.S. 1991. One- and Two-Phase Flow During Fluid Sampling by a Wireline Tool. Transport in Porous Media 6
(3): 299-330. http://dx.doi.org/10.1007/BF00208955.
Kappa Engineering. 2012. Ecrin v4.20.05 Integrated Software Platform for Dynamic Flow Analysis. Sophia Antipolis, France.
Levitan, M.M. 2005. Practical Application of Pressure/Rate Deconvolution to Analysis of Real Well Tests. SPE Res Eval &
Eng 8 (2): 113–121. SPE-84290-PA. http://dx.doi.org/10.2118/84290-PA.
Levitan, M.M., Crawford, G.E., and Hardwick, A. 2006. Practical Considerations for Pressure-Rate Deconvolution of Well-
Test Data. SPE J. 11 (1): 35–47. SPE-90680-PA. http://dx.doi.org/10.2118/90680-PA.
Malik, M., Torres-Verdín, C., Sepehrnoori, K., Dindoruk, B., Elshahawi, H., and Hashem, M. 2007. Field Examples Of
History Matching Of Formationtester Measurements Acquired In The Presence Of Oilbase Mud-Filtrate Invasion. Paper
presented at the SPWLA 48th
Annual Logging Symposium, Austin, Texas, June 3 – 6.
Onur, M., Ayan, C., Kuchuk, F.J. 2011. Pressure-Pressure Deconvolution Analysis of Multiwell-Interference and Interval-
Pressure-Transient-Tests. SPE Res Eval & Eng 14 (6): 652–662. SPE-149567-PA. http://dx.doi.org/ 10.2118/149567-PA.
Paradigm. 2010. Interpret, The Design and Analysis of Pressure Transients. Aberdeen, Scotland.
Phelps, G.D., Stewart, G., and Peden, J.M. 1984. The Analysis of the Invaded Zone Characteristics and Their Influence on
Wireline Log and Well-Test Interpretation. Paper SPE 13287 presented at the SPE Annual Technical Conference and
Exhibition, Houston, 16–19 September.
Pimonov, E., Ayan, C., Onur, M., and Kuchuk, F.J. 2009. A New Pressure/Rate-Deconvolution Algorithm to Analyze
Wireline Formation Tester and Well-Test Data. Paper SPE 123982 presented at SPE Annual Technical Conference and
Exhibition, New Orleans, 4–7 October. http://dx.doi.org/10.2118/123982-MS.
Pop, J.J., Badry, R.A., Morris, C.W., Wilkinson, D.J., Tottrup, P., and Jonas, J.K. 1993. Vertical Interference Testing With a
Wireline-Conveyed Straddle-Packer Tool. Paper SPE 26481 presented at the SPE Annual Technical Conference and
Exhibition, Houston, 3–6 October. http://dx.doi.org/10.2118/26841-MS.
Schlumberger Information Solutions. 2010. Eclipse 100, Version 2010.1., Houston.
Schlumberger. 2002. MDT Modular Formation Dynamics Tester.
http://www.slb.com/~/media/Files/evaluation/brochures/wireline_open_hole/insitu_fluid/mdt_brochure.pdf
Schlumberger. 2011. MDT Dual-Packer Module.
http://www.slb.com/~/media/Files/evaluation/product_sheets/wireline_open_hole/insitu_fluid/mdt_dual_packer_module_p
s.pdf
Shuang, J.P. 1990. Filtration Properties of Water Based Drilling Fluids. PhD dissertation, Heriott-Watt University, Edinburgh,
Scotland (October 1990).
van Everdingen, A. F. and Hurst, W. 1949. The Application of the Laplace Transformation to Flow Problems in Reservoirs.
Journal of Petroleum Technology 1(12): 305-324. http://dx.doi.org/10.2118/949305-G.
von Schroeter, T., Hollaender, F., and Gringarten, A.C. 2004. Deconvolution of Well Test Data as a Nonlinear Total Least
Squares Problem. SPE J. 9 (4): 375–390. SPE-77688-PA. http://dx.doi.org/10.2118/77688-PA.
Zeybek, M., Ramakrishnan, T.S., Al-Otaibi, S.S., Salamy, S.P., and Kuchuk, F.J. 2001. Estimating Multiphase Flow Properties
Using Pressure and Flowline Water-Cut Data from Dual Packer Formation Tester Interval Tests and Openhole Array
12 Wireline Formation Testers Analysis with Deconvolution
Resistivity Measurements,” paper SPE 71568 presented at the SPE Annual Technical Conference and Exhibition, New
Orleans, 30 September–3 October.
Zimmerman, T., MacInnis, J., Hoppe, J. and Pop, J. 1990. Application of Emerging Wireline Formation Testing Technologies.
Paper OSEA 90105 presented at the Offshore South East Asia Conference, Singapore, 4-7 December.
Wireline Formation Testers Analysis with Deconvolution 13
APPENDICES
A- APPENDIX: MILESTONES
Paper No Year Title Authors Contribution
71574
-MS 2001
Deconvolution of Well Test Data
as a Nonlinear Total Least
Squares Problem
Thomas von Schroeter,
Florian Hollaender, Alain
C. Gringarten
First introduction of a new method that demonstrates
Deconvolution as a separable nonlinear Total Least
Squares (TLS) problem. A modified error model
accounts for errors in both pressure and rate data.
This method enables to deconvolve smooth,
interpretable response functions from data with errors
of up to 10% in rates.
77688
-PA 2004
Deconvolution of Well Test Data
as a Nonlinear Total Least
Squares Problem
Thomas von Schroeter,
Florian Hollaender, Alain
C. Gringarten
Regulization of smoothness was modified. It
introduced bias and confidence intervals of signal.
84290
-PA 2005
Practical Application of
Pressure/Rate Deconvolution to
Analysis of Real Well Tests
Michael M. Levitan
Von Schroeter et al’s algorithm fails when used with
inconsistent data. The paper presents enhancement to
the existing deconvolution algorithm that allows it to
be used reliably with real test data.
23030
-PA 1996
Influence of an Invaded Zone on a
Multiprobe Formation Tester
Peter A. Goode
R.K. Michael
Thambynayagam
developed an analytical model of a two-region
problem, the invaded and uninvaded regions, with
different vertical and horizontal mobilities and
compressibilities. The study investigates the effect of
this invasion on the sink, horizontal and vertical
probes in a Multi-probe WFT, assuming a sharp
invasion front and a piston-like displacement in a
single homogenous layer
SPE-
84093
-PA
2006
Effect of an Invaded Zone on
Pressure-Transient Data From
Multiprobe and Packer-Probe
Wireline Formation Testers
Ihsan M. Gok, SPE, and
Mustafa Onur, SPE,
Istanbul Technical U.;
Peter S. Hegeman, SPE,
and Fikri J. Kuchuk, SPE,
Schlumberger
Discusses the effects of the invasion on Pressure
transient data (Probe and Dual Packer) and sets out to
model it using composite zones concentric with the
reservoir in order to estimate both invaded and non-
invaded properties.
90680
-PA 2006
Practical Considerations for
Pressure-Rate Deconvolution of
Well-Test Data
Michael M. Levitan, Gary
E. Crawford, Andrew
Hardwick
Paper presents how to recover the initial reservoir
pressure from well test data by use of Deconvolution.
It also introduces the application of Deconvolution
sequentially to individual build-ups.
SPE-
12398
2-MS
2010
A New Pressure Rate
Deconvolution Algorithm to
Analyze Wireline Formation
Tester and Well-Test Data
Evgeny Pimonov and
Cosan Ayan,
Schlumberger; Mustafa
Onur, Istanbul Technical
University; and Fikri
Kuchuk, Schlumberger
A modification to the algorithm of von Schroeter et al
is presented. it enables the user to define different
error estimates to different parts of the data as
mitigation to unreliable pressure and rate data as well
as inconsistencies with the reservoir model.
SPE-
14956
7-PA
2011
Pressure-Pressure Deconvolution
Analysis of Multiwell-Interference
and Interval-Pressure-Transient
Tests
M. Onur, Istanbul
Technical University; and
C. Ayan and F.J. Kuchuk,
Schlumberger
Onur et al. (2011) presented a modification to the
Pimonov 2009 algorithm for multiwell-interference
tests and IPTTs by replacing the rate signal with the
observation probe signal thus eliminating the errors
and uncertainty associated with the flow-rate.
14 Wireline Formation Testers Analysis with Deconvolution
B- APPENDIX: CRITICAL LITERATURE REVIEW
SPE: 71574-MS (2001)
Deconvolution of well test data as a nonlinear Total Least Squares problem
Authors: Thomas von Schroeter, Florian Hollaender, Alain C. Gringarten
Contribution to the understanding of deconvolution:
This algorithm presented several advancements over existing Spectral and Time-Domain methods and was characterized by: a
novel encoding of the solution, regularization by curvature to maintain a degree of smoothness in the result, a total least-
squares formulation to account for errors in pressure and rate data.
Objective of the paper:
To introduce a robust deconvolution algorithm
Methodology used:
Novel method of encoding the solution to eliminate the need for sign constraint. The algorithm calculates the natural
logarithm of the derivative instead of the derivative itself.
Minimization of an error measure function E by minimizing its three error sources: error in pressure (ε), error in rates
(δ) and smoothness term (Dz).
Conclusion reached:
If λ and ν should are selected carefully this algorithm was proved to be robust in deconvolving simulated and real test
data, allowing for errors in the measurement, up to 10%.
The result is a unit rate drawdown signal with a duration equivalent to that of the entire test.
Comments:
Needs to be applied carefully and with knowledge due to the subjective input of the user.
Wireline Formation Testers Analysis with Deconvolution 15
SPE: 77688-MS (2004)
“Deconvolution of well test data as a nonlinear Total Least Squares problem”
Authors: Thomas von Schroeter, Florian Hollaender, Alain C. Gringarten
Contribution to the understanding of deconvolution:
This paper presents a method to output estimates for bias and confidence intervals of the parameters
Objective of the paper:
Demonstration of improvements of deconvolution algorithm presented in SPE paper 71574-MS.
Reinforces the algorithm developed in 2001 by applying deconvolution to extensive data.
Methodology used:
In contrast to previous SPE paper 71574, assumption is made that the initial reservoir pressure is known
The original error weight (ν) is multiplied by a factor N/m in order to balance the effect of different sample sizes on
the pressure drop and derivative
Conclusion reached:
Eliminated the oscillations previously encountered by adding the regularization by curvature. It prevents the
flattening of the derivative while keeping it smooth.
Deconvolution can be applied to independent flow periods.
Deconvolution handles error and pressure errors very well.
The selection criteria of error weight (ν) and regularization parameter (λ) remains as a very subjective one.
Comments:
Care must be exercised when increasing the regularization parameter. Result constantly monitored and compared with
original data.
16 Wireline Formation Testers Analysis with Deconvolution
SPE: 84290-PA (2005)
“Practical application of pressure-rate deconvolution to analysis of real well tests”
Authors: Michael M. Levitan
Contribution to the understanding of deconvolution:
The paper states that the algorithm developed by von Schroeter et al. 2001 works well on consistent sets of pressure
and rate data. However, the algorithm fails when applied on inconsistent data set.
Inconsistency is given by skin factor or wellbore storage changing with time.
Objective of the paper:
Evaluate the application and limitations of the von Schroeter algorithm
Demonstrates some enhancements to the original algorithm for it to be applied reliably with inconsistent data sets
Methodology used:
Demonstrates the application and limitations of the deconvolution algorithm using several inconsistent data sets.
Conclusion reached:
For Inconsistent data sets, deconvolution produces correct results when applied to individual flow periods
The pressure data from a single flow period do not contain enough information to identify initial reservoir pressure
and to correct rates. Comparison of the deconvolved derivative from several flow periods is necessary to identify
initial reservoir pressure and model parameters.