IMPERIAL COLLEGE LONDON · IMPERIAL COLLEGE LONDON ... Wireline Formation Testers Analysis with Deconvolution By ... FIGURE 1 SCHEMATIC OF THE DUAL-PACKER/PROBE CONFIGURATION

* 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


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


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


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)


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


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?


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

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si]

14AK: PA Di=0.79" (ref)

14CK: PA Di=4.16"

14EK: PA Di=23.5"

14GK: PA Di=61"


1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]

0.1

1

10

Pre

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si]

14AK: PS Di=0.79" (ref)

14CK: PS Di=4.16"

14EK: PS Di=23.5"

14GK: PS Di=61"


1E-5 1E-4 1E-3 0.01 0.1 1Time [hr]

1

10

100

Pre

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re [p

si]

13A: PA Di=12.4"

13B: PA Di=23.5"

13C: PA Di=34.8" (ref)

13D: PA Di=61"


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"


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]: ?????




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"


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"


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)


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)


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


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


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


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



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]


320

325

330

Pre

ssu

re [b

ara

]


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

]


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

]




Comment [ACG19]: I disagree. The pressure data are incorrect to start with

Comment [ACG20]: Same comment

Comment [ACG21]: ????


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

]


0 0.1 0.2 0.3 0.4 0.5

Time [Day]

02.5

Liq

uid

ra

te [m

3/D

]


330

332

334

Pre

ssu

re [b

ara

]


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

]



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


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.


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.

http://www.onepetro.org.iclibezp1.cc.ic.ac.uk/mslib/app/Preview.do?paperNumber=00071574&societyCode=SPE






http://www.onepetro.org.iclibezp1.cc.ic.ac.uk/mslib/app/Preview.do?paperNumber=SPE-84290-PA&societyCode=SPE










http://www.onepetro.org/mslib/app/Preview.do?paperNumber=SPE-123982-MS&societyCode=SPE




http://www.onepetro.org/mslib/app/Preview.do?paperNumber=SPE-149567-PA&societyCode=SPE





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.


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


This paper presents a method to output estimates for bias and confidence intervals of the parameters


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.


SPE: 84290-PA (2005)

“Practical application of pressure-rate deconvolution to analysis of real well tests”

Authors: Michael M. Levitan


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.


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.

Documents

IMPERIAL COLLEGE LONDON · IMPERIAL COLLEGE LONDON ... Wireline Formation Testers Analysis with Deconvolution By ... FIGURE 1 SCHEMATIC OF THE DUAL-PACKER/PROBE CONFIGURATION