Deconvolution of Well Test Data from the E-M Gas ... · iii [Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)]

IMPERIAL COLLEGE LONDON

Department of Earth Science and Engineering

Centre for Petroleum Studies

Deconvolution of Well Test Data from the E-M Gas

Condensate Field (South Africa)

By

Eduard Rinas

A report submitted in partial fulfilment of the requirements for the award of the degree of

Master of Science in Petroleum Engineering

September 2011

ii [Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)]

DECLARATION OF OWN WORK

I declare that this thesis Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)

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: Eduard Rinas

Names of supervisors: Prof. Alain C. Gringarten and Dr. Thabo Kgogo

iii [Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)]

ACKNOWLEDGEMENT

I would like to express a sincere gratitude to the following people who made the writing of this thesis

possible:

Professor Alain C. Gringarten from Imperial College London, whose professional advice and supervision

guided me to completion of this thesis.

Special thanks go to Dr. Thabo Kgogo from PetroSA, whose comments and instructions helped me

enormously to complete this work.

Also I would like to thank Olakunle Ogunrewo, PhD, student of Imperial College London, for his

continuous helpfulness and advice in solution of subject-specific issues and questions.

Moreover, I would like to mention that I am very grateful to all my classmates to have worked and to stay

together during this unforgettable academic year at Imperial College London.

And of course my sincere thanks to my father, mother and brother who always supported and motivated

me in all aspects during my studies at Imperial College London.

iv [Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)]

TABLE OF CONTENTS

DECLARATION OF OWN WORK............................................................................................................................................. ii

ACKNOWLEDGEMENT ........................................................................................................................................................... iii

TABLE OF CONTENTS ............................................................................................................................................................. iv

LIST OF FIGURES ...................................................................................................................................................................... v

LIST OF TABLES ....................................................................................................................................................................... vi

Abstract ......................................................................................................................................................................................... 1

Introduction ................................................................................................................................................................................... 1

Concept of deconvolution ............................................................................................................................................................. 2

Duhamel’s principle .................................................................................................................................................................. 2

Deconvolution as a nonlinear TLS problem .............................................................................................................................. 2

E-M field overview ....................................................................................................................................................................... 3

Statement of paper concern ....................................................................................................................................................... 4

Methodology ................................................................................................................................................................................. 5

Data management ...................................................................................................................................................................... 5

Evaluation of the prepared data prior to deconvolution ............................................................................................................ 5

Determination of initial reservoir pressure ................................................................................................................................ 6

Deconvolution ........................................................................................................................................................................... 6

Verification of deconvolution ................................................................................................................................................... 6

Analysis of unit-rate pressure drawdown .................................................................................................................................. 6

Application of obtained model to measured pressure data ........................................................................................................ 6

Analysis results ............................................................................................................................................................................. 6

Conclusions and recommendations ............................................................................................................................................. 14

NOMENCLATURE .................................................................................................................................................................... 16

LIST OF REFERENCES ............................................................................................................................................................ 16

APPENDICES ............................................................................................................................................................................ 17

APPENDIX A (Table of milestones in deconvolution of well test data) ................................................................................ 18

APPENDIX B (Critical literature review) ............................................................................................................................... 20

APPENDIX C (Practical application of deconvolution in the past) ........................................................................................ 28

APPENDIX D (Zones encountered while drilling the wells) .................................................................................................. 30

APPENDIX E (Reported reservoir and well parameters) ....................................................................................................... 31

APPENDIX F (Received pressure data for 3 E-M field development wells) ......................................................................... 32

APPENDIX G (Pressure and rate histories for three E-M-Field development wells) ............................................................. 33

APPENDIX H (Log-log rate validation & superposition plots) .............................................................................................. 36

APPENDIX I (Deconvolution of well test data from each well) ............................................................................................ 40

APPENDIX J (Pressure history matches) ............................................................................................................................... 46

APPENDIX K (Rate history matches) .................................................................................................................................... 48

APPENDIX L (Unit-rate pressure drawdown analysis results) .............................................................................................. 49

APPENDIX M (Analysis of measured pressure data in three wells) ...................................................................................... 56

APPENDIX N (Comparison between the deconvolved derivatives in well E-M03P) ............................................................ 65

APPENDIX O (Determination of initial reservoir pressure using Kappa engineering software Saphir) ................................ 65

v [Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)]

LIST OF FIGURES Figure 1: E-M field location map [17] ................................................................................................................................................................ 4 Figure 2: Cross section E-M4 to E-M6 [1] ......................................................................................................................................................... 4 Figure 3: E-M field polygon map and three located wells [15] .......................................................................................................................... 5 Figure 4: Example of a deconvolved derivative providing explanation for each label ....................................................................................... 6 Figure 5: Well E-M02Pa - log-log rate validation plot, normalized to flow period 19: useful build-ups up to the last build-up 833 of the

production........................................................................................................................................................................................................... 7 Figure 6: Well E-M02Pa - superposition plot ..................................................................................................................................................... 7 Figure 7: Well E-M01P - log-log rate validation plot normalized to FP-91 ....................................................................................................... 8 Figure 8: Determination of initial reservoir pressure in well E-M02Pa through comparison of deconvolved derivatives of DST build-ups ..... 8 Figure 9: Well EM02Pa - deconvolution of flow periods corresponding to different stages of production ........................................................ 9 Figure 10: Well E-M01P - deconvolution of multi-flow periods .......................................................................................................................10 Figure 11: Well EM03P - deconvolution of flow periods during different stages of production .......................................................................10 Figure 12: Well EM02Pa - difference in % between actual measured pressure data and convolved pressures .................................................11 Figure 13: Well EM02Pa - rate history match for deconvolved derivative (1-873)[5,15,19-873]{1.00000E+09}3696.75 ...............................11 Figure 14: Well EM02Pa - drawdown resulted from deconvolution of all flow periods in one sweep..............................................................12 Figure 15: Well E-M02Pa - identification of flow regimes ...............................................................................................................................12 Figure 16: Well E-M02Pa - multilayer closed reservoir behavior .....................................................................................................................13 Figure 17: Well E-M02Pa - single layer closed reservoir behavior ...................................................................................................................13 Figure 18: Simulations of unit-rate drawdowns convolved from derivatives of different flow periods .............................................................13 Figure 19: Well E-M02Pa - pressure match of flow period 277 ........................................................................................................................13 Figure 20: Well E-M02Pa - single layer analysis applied to simulate entire pressure history ...........................................................................13 Figure 21: Well E-M02Pa - pressure match of flow period 277 ........................................................................................................................14 Figure 22: Well E-M02Pa - multilayer analysis applied to simulate entire pressure history .............................................................................14 Figure F-1: DST pressure data adjustment: green - first build-up in the production; red - original DST data; purple - adjusted DST data ......32 Figure G-1: Well E-M01P - pressure and rate history .......................................................................................................................................33 Figure G-2: Well E-M01P - DST Data ..............................................................................................................................................................33 Figure G-3: Well E-M02Pa - pressure and rate history .....................................................................................................................................34 Figure G-4: Well E-M02Pa - DST Data ............................................................................................................................................................34 Figure G-5: Well E-M03P - pressure and rate history .......................................................................................................................................35 Figure G-6: Well E-M03Pa - DST Data ............................................................................................................................................................35 Figure H-1: Well E-M01P - log-log rate validation plot ....................................................................................................................................36 Figure H-2: Well E-M01P - superposition plot .................................................................................................................................................36 Figure H-3: Well E-M02Pa - log-log rate validation plot, normalized to flow period 19: DST build-ups 5, 15 and 19 ....................................37 Figure H-4: Well EM02Pa - log-log rate validation plot, normalized to flow period 19: useful build-ups up to build-up 290 .........................37 Figure H-5: Well EM03P - log-log rate validation plot, normalized to FP 224 .................................................................................................38 Figure H-6: Well EM03P (pre-workover)- log-log rate validation plot, normalized to FP 224 .........................................................................38 Figure H-7: Well EM03P (post-workover) - log-log rate validation plot, normalized to FP 224 ......................................................................39 Figure H-8: Well E-M03P - superposition plot .................................................................................................................................................39 Figure I-1: Determination of initial reservoir pressure in well E-M01P through comparison of deconvolved derivatives of DST build-ups ..40 Figure I-2: Well E-M01P - deconvolution of FP 166 ........................................................................................................................................40 Figure I-3: Well E-M01P - deconvolution of FP 200 .......................................................................................................................................41 Figure I-4: Well E-M01P - deconvolution of FP 418 .......................................................................................................................................41 Figure I-5: Well E-M01P - deconvolution of flow periods during production phase 2 ....................................................................................42 Figure I-6: Well E-M02P - deconvolution of flow periods corresponding to production time period between 100 and 21200 hours...............42 Figure I-7: Well E-M02P - deconvolution of flow periods (mostly series of build-ups) corresponding to production time period between 100

and 73100 hours ................................................................................................................................................................................................43 Figure I-8: Well E-M02Pa - deconvolution of flow periods (mostly DST’s with individual build-up) corresponding to production time period

between 100 and 73100 hrs ...............................................................................................................................................................................43 Figure I-9: Well E-M03P - determination of initial reservoir pressure (3727 psia) ...........................................................................................44 Figure I-10: Well E-M03P - deconvolution of flow periods corresponding to pre-workover production period between 0 and 49700 hours

(except flow period 224) ...................................................................................................................................................................................44 Figure I-11: Well E-M03P - deconvolution of flow periods corresponding to post-workover production period 1 between 49700 and 68000

hours ..................................................................................................................................................................................................................45 Figure I-12: Well E-M03P - deconvolution of flow periods corresponding to post-workover production period 2 between 68000 and 93000

hours ..................................................................................................................................................................................................................45 Figure I-13: Well E-M03P - deconvolution of multi-flow periods ....................................................................................................................46 Figure J-1: Well EM01P - pressure history match .............................................................................................................................................46 Figure J-2: Well EM02Pa - pressure history match ...........................................................................................................................................47 Figure J-3: Well EM03P - pressure history comparison ....................................................................................................................................47 Figure J-4: Well EM-01P - difference in % between actual measured pressure data and convolved pressures .................................................48 Figure K-1: Well EM01P - rate history match for deconvolved derivative (1-878)[51,68,91,101-878] {2.5E+08}3798.00.............................48 Figure K-2: Well EM03P - Rate history match for deconvolved derivative (1-578)[11,16,20-578]{3.17653E+08}3727.00 ...........................49 Figure L-1: Well E-M01P - Analysis 1 of unit-pressure drawdown convolved from deconvolved derivative ..................................................49

vi [Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)]

Figure L-2: Well E-M01P - Analysis 2 of unit-pressure drawdown convolved from deconvolved derivative ..................................................50 Figure L-3: Well E-M01P - Analysis 3 of unit-pressure drawdown convolved from deconvolved derivative ..................................................50 Figure L-4: Well E-M01P - Analysis 4 of unit-pressure drawdown convolved from deconvolved derivative ..................................................51 Figure L-5: Well E-M02Pa - single layer analysis of unit-pressure drawdown convolved from deconvolved derivative .................................51 Figure L-6: Well E-M02Pa - single layer analysis of unit-pressure drawdown convolved from deconvolved derivative .................................52 Figure L-7: Well E-M02Pa - single layer analysis of unit-pressure drawdown convolved from deconvolved derivative .................................52 Figure L-8: Well E-M02Pa - multilayer analysis of unit-pressure drawdown convolved from deconvolved derivative ...................................53 Figure L-9: Well E-M03P - single layer analysis of unit-pressure drawdown convolved from deconvolved derivative ...................................53 Figure L-10: Well E-M03P - single layer analysis of unit-pressure drawdown convolved from deconvolved derivative .................................54 Figure L-11: Well E-M03P - single layer analysis of unit-pressure drawdown convolved from deconvolved derivative .................................54 Figure M-1:Well E-M01P - Analysis M2[101,418] variable skin .....................................................................................................................57 Figure M-2: Well E-M01P - Analysis M2[101,418] constant skin ....................................................................................................................57 Figure M-3: Well E-M01P - Analysis M1[FP 51,68,91,101-878] .....................................................................................................................58 Figure M-4: DST pressure data and entire pressure history matches using model M2[101, 418] with constant and variable skin ...................58 Figure M-5: Well E-M01P (FP 418) - single layer model (open-ended rectangle); kxy=1.7 mD, kz=10 mD, L=556m .....................................59 Figure M-6: Well E-M01P (FP 581) - single layer model (open-ended rectangle); kxy=14.7 mD, kz=4.8 mD, L=919m ..................................59 Figure M-7: Well E-M01P - multilayer model (open-ended rectangle) k2z = 10E-06 mD ..............................................................................60 Figure M-8: Well E-M01P - multilayer model (open-ended rectangle) k2z = 10E-04 mD ..............................................................................61 Figure M-9: Well E-M02Pa - single layer analysis ...........................................................................................................................................61 Figure M-10: Well E-M02Pa - multilayer analysis ...........................................................................................................................................62 Figure M-11: Well E-M03P - analysis of DST build-up 20 ..............................................................................................................................63 Figure M-12: Well E-M03P - application of single layer model to measured pressure data (flow period 457).................................................63 Figure M-13: Well E-M03P - single layer model (FP 290), closed rectangle, variable skin, d4=340m ............................................................64 Figure M-14: Well E-M03P - single layer model (FP290), closed rectangle, variable skin, d4=1651m ...........................................................64 Figure N-1: Well E-M03P - comparison between deconvolved derivatives ......................................................................................................65 Figure O-1: Validation of initial reservoir pressure in well E-M02Pa - DST build-ups are deconvolved using initial pressure value of 3696.75

psia ....................................................................................................................................................................................................................65 Figure O-2: Well E-M02Pa - deconvolved derivative resulted from deconvolution of all flow periods in one sweep in Saphir ......................66 Figure O-3: Validation of initial reservoir pressure in well E-M01P - DST build-ups are deconvolved using initial pressure value of 3798

psia ....................................................................................................................................................................................................................66

LIST OF TABLES Table 1: Stratigraphy of the E-M field [1] .......................................................................................................................................................... 4 Table 2: Time intervals of new acquired data ..................................................................................................................................................... 4 Table 3: Received and reduced pressure data ..................................................................................................................................................... 7 Table 4: Summary of obtained results ...............................................................................................................................................................15 Table D-1: Zones encountered while drilling well E-M01P ..............................................................................................................................30 Table D-2: Zones encountered while drilling well E-M02Pa ............................................................................................................................30 Table D-3: Zones encountered while drilling well E-M03P ..............................................................................................................................30 Table E-1: Additional information provided for each well [15,16,17] ..............................................................................................................31 Table E-2: Reported reservoir and well parameters according to [16] ..............................................................................................................31 Table F-1: Received pressure data for 3 E-M field development wells .............................................................................................................32 Table L-1: Well E-M01P - well test interpretation models resulted from analysis of convolved unit-rate pressure drawdowns ......................55 Table L-2: Well E-M02Pa - well test interpretation models resulted from analysis of convolved unit-rate pressure drawdowns .....................55 Table L-3: Well E-M03P - well test interpretation models resulted from analysis of convolved unit-rate pressure drawdowns ......................56 Table M-1: Well E-M01P - interpretation models resulted from adjustment of model parameters from Table L-1 ..........................................60

Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)

Student name: Eduard Rinas

Imperial College supervisor: Prof. Alain C. Gringarten

Company supervisor: Dr. Thabo Kgogo

Abstract

Ten years ago the first reliable deconvolution algorithm was developed thereby opening a new decade for application of

deconvolution. Deconvolution as well as being a new well test analysis tool, revealed a new way of transient pressure data

analysis. In 2006 Gringarten, A.C. defined deconvolution as the best analysis method to obtain a well test interpretation model.

Identification of the model is carried out through the analysis of unit-rate pressure drawdown convolved from the respective

deconvolved derivative in the final stage of deconvolution process. The duration of unit-rate pressure drawdown can be as long

as the duration of the entire well test. Thus, deconvolution is able to give access to the radius of investigation corresponding to

the entire duration of this test. This allows well test interpreter to obtain additional information about reservoir and its behavior

which cannot be extracted during conventional well test analysis.

This paper illustrates practical use of deconvolution providing a detailed description of its procedure. Deconvolution is

applied to three horizontal lean gas condensate wells. The objective of the analysis is to investigate whether the reservoir zone,

in which horizontal sections of all three wells are placed, is communicating with the lower zone through a shale layer.

Deconvolution is carried out on individual flow periods, series of flow periods, multi-flow periods and all flow periods in one

sweep. Resulting unit-rate pressure drawdowns are analyzed in the conventional way. Identified interpretation models are used

for analysis of the actual pressure data. Deconvolution is performed with a deconvolution algorithm based on the Total Least

Square method proposed by von Schroeter, T., Hoellander, F. and Gringarten, A.C. (2001). The obtained results lead to

conclusion that there is most likely no communication between two layers in wells E-M01P and E-M03P. In contrast,

deconvolution analysis of well test data acquired in well E-M02Pa identifies multilateral reservoir behavior.

Moreover this paper reflects the author’s own experiences in the implementation of deconvolution to real well test data,

and provides recommendations where the application of this well test tool is advisable and where it should be applied with

caution.

Introduction

Conventional well test analysis, in particular the derivative analysis, is limited to the interpretation of single flow periods with

constant rate (e.g. build-up analysis at zero-rate). The investigation radius of such a single flow period is limited. However, the

measured pressure and rate data, acquired during DST or production period, may contain information about reservoir at much

larger distances. Consequently, analysis of a single flow period because of its often short duration may not describe the

reservoir behavior completely. Therefore, to allow the well test interpreter to describe the reservoir entirely, an additional

analysis technique is required. This well test analysis tool is known as deconvolution.

The process of deconvolution consists in transformation of measured multi-rate pressure data into a single unit-rate

pressure drawdown. Duration of the convolved single unit-rate pressure drawdown can be as long as the duration of the entire

well test - a period of time at which all measured pressure and rate data are acquired. The analysis of the unit-pressure

drawdown yields the corresponding derivative which is then analyzed conventionally. The outcome of this analysis is a well

test interpretation model, which is to apply to the measured pressure data - single flow periods such as build-ups.

Consequently, the main objective of deconvolution is to identify the interpretation model, which would indicate flow regimes

and derivative shapes characterizing the behavior of a given reservoir.

In other words, well test interpreter subjects the reservoir to a unit-rate pressure drawdown. Duration of drawdown is

defined by the user himself depending on the number of flow periods selected for deconvolution. This allows one to describe

the reservoir behavior over entire production length and not only over a certain time interval. Therefore, in contrast to

conventional well test analysis, deconvolution analysis makes it possible to extract more information about reservoir from

available well test data. In addition, since the unit-pressure drawdown corresponds to the initial drawdown in the reservoir

field life, the obtained derivative is free from distortions caused by pressure derivative calculation1 and from errors, which

1 Multi-rate generalization of conventional analysis derivative analysis through the radial flow superposition function introduces bias.

Imperial College

London

2 [Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)]

might occur due to truncated or incomplete rate history (Gringarten, 2010) [3]2. In the following paragraphs, the working

principle of deconvolution is explained in detail.

Concept of deconvolution

Duhamel’s principle

Deconvolution is based on Duhamel’s principle, which is defined by the following integral:

∆𝑝(𝑡) = 𝑝𝑖 − 𝑝(𝑡) = ∫ 𝑞(𝜏)𝑔(𝑡 − 𝜏)𝑑𝜏𝑡

0 (1)

∆𝑝(𝑡) - pressure drop over time

𝑝𝑖 - initial reservoir pressure

𝑝(𝑡) - bottomhole pressure

q - production rate

g - reservoir impulse response

t - time

𝜏 - integration variable

Eq. (1) represents the pressure drop over time ∆𝑝(𝑡) with time-varying flow rate 𝑞(𝑡) and is therefore the convolution

product of the production rate and pressure response [4]. This equation is the basis not only of deconvolution, but in general

for conventional well test analysis. The basis of Eq. (1) is the diffusion equation which describes the fluid flow in the

reservoir. Since the diffusion equation is linear in its nature, the Duhamel’s principle requires linearity in the systems where it

is implemented. However, the linearity is not given in the multiphase systems or in the gas flow systems - just those that are

discussed in this paper. In order to be able to use deconvolution Duhamel’s principle must be satisfied and, thus, the linearity.

For this reason, measured pressure data has to be linearized. The linearization (essentially only the approximation of

linearization) of measured pressure data is carried out by calculating the single-phase pseudo pressures (R. Al-Hussainy et al.,

1966; Meunier et al., 1987) [18,12]. In the present thesis single-phase pseudo pressures are not calculated manually, but using

“Paradigm Interpret 2000” well test analysis software.

Back to Eq. (1). Considering a single flow period with a constant rate the relationship between the pressure drop ∆𝑝(𝑡) and

the reservoir response g can be written as:

𝑑∆𝑝(𝑡)

𝑑 ln (𝑡)= 𝑡𝑔(𝑡) for 𝑞(𝜏) = {

0 𝜏 ≤ 01 𝜏 > 0

} [4] (2)

The left-hand side of Eq. (2) represents the pressure derivative - objective quantity of deconvolution problem. To obtain

this quantity one needs to calculate pressure response from Eq. (1) and multiply it by time: In other words to deconvolve the

measured pressure and rate data [4]. In the past many attempts were made to develop a reliable deconvolution algorithm which

would produce correct deconvolution results. To solve the integral (1) two different techniques such as time-domain and

spectral methods were applied with varying degrees of success. But none of them could provide robust results by application

of deconvolution to real pressure and rate data. The breakthrough occurred in 2001 as von Schroeter, Hollaender and

Gringarten proposed a new deconvolution algorithm, which was successfully adopted to simulated and real well test data and

approved to be reliable. Section below gives a brief description of this deconvolution method.

Deconvolution as a nonlinear TLS problem

Deconvolution method proposed by the above-mentioned authors is presented as the logarithm of the reservoir response

function. This approach to deconvolution is a time-domain approach. The formulation is based on nonlinear encoding of

constraints and is known as nonlinear Total Least Squares (TLS) problem in the numerical analysis literature. In contrast to the

previous publications, the encoding is implicit and not explicit Thus, this approach does not use sign constraints and its

optimization is considerably easier than that with sign constraints. Implicit encoding simplified the solution of algorithm (T.

von Schroeter, F. Hollaender, A.C. Gringarten, 2001) [19]. The significant milestone in the deconvolution formulation was the

implementation of an error model which takes into account errors in measured pressure and rate data. In the last 30 years many

attempts were made to analyze well test data using deconvolution. However, until 2001 the common problem of well test

interpreters was the inability to interpret deconvolved data because of noise in the pressure and rate measurements. Especially

noisy are the measured rate data. Von Schroeter, Hollaender and Gringarten introduced errors in both pressure and rate signals

instead of errors only in pressure signal as it was done in previous publications:

2 See “LIST OF REFERENCES”


𝑝 + 𝝐 = (𝑝𝑖 − 𝑦 × 𝑔) = true, but unobserved signal in pressure, where 𝑝 = measured pressure, 𝜖 = pressure

measurement error, 𝑝𝑖= initial reservoir pressure, g = derivative of the pressure with respect to time

𝑞 + 𝜹 = 𝑦 = true, but unobserved signal in rate, where 𝑞 = measured rate and 𝛿 = rate measurement error

The combination of both unobserved signals in one expression yields the following error measurement function:

𝐸 = 𝑣‖ 휀‖ 22 + 𝜐‖ 𝛿‖ 2

2 + 𝜆‖ 𝐷𝑧‖ 22 (3)

Eq. (3) represents a weighted sum of the squared norms of three errors. The last term 𝐷𝑧 represents the smoothness of the

solution (deconvolved derivative). 𝜐 and 𝜆 signify weight and regularization parameters respectively. The error model reflects

the relative size of contribution of each error to overall error what makes sense, since the errors in measured rates usually are

higher than these in measured pressure data.

In 2002 the error measurement function (3) was modified by same authors to Eq. (4):

𝐸 = 𝑣‖ 휀‖ 22 + 𝜐‖ 𝛿‖ 2

2 + 𝜆‖ 𝐷𝑧 − 𝑘‖ 22 (4)

where 𝐷 = constant matrix and 𝑘 = vector [21]. Now the term 𝜆‖ 𝐷𝑧 − 𝑘‖ 22 denotes a measure of the average curvature of the

deconvolved graphed derivative. The objective of this term is to enforce (regularize) derivative smoothness so that occurring

oscillations during deconvolution disappear. The authors found out that the regularization by total curvature of the

deconvolved pressure derivative instead of regularization by its average slope avoids the flattening of slopes3 associated with

derivative regularization process. The user is able to control the degree of smoothness by changing the regularization

parameter 𝜆.

Back to Eq. (4). The objective of deconvolution consists in minimization of this error model and, thus, in minimization of

each error source. The minimization of Eq. (4) is performed in successive occurred iterations and, therewith, denoting

deconvolution as an iteration process. Final deconvolution outputs are 1) 𝑦, which can be also defined as adapted rate 2) initial

reservoir pressure 𝑝𝑖 , which can be an input parameter as well 3) g as the derivative of the pressure with respect to time and 4)

convolved pressure, calculated from 𝑦 and g.

This study presents an example of practical use of deconvolution. Deconvolution is applied to real well test data acquired

in three lean gas condensate wells. The pressure data in all three wells are measured every minute by permanent downhole

pressure gauges, whereas the rates are detected in 24 hours acquisition frequency at the surface. Deconvolution analysis is

performed using “TLSD” deconvolution software which is provided by Imperial College London. The software uses a

deconvolution algorithm described above. The structure of the presented paper is following: To explain the purpose of

deconvolution in this work, first of all E-M field overview and description of three wells, drilled in this structure, are

introduced. The ensuing section “Methodology” guides through the deconvolution process designating its individual step.

Finally, section “Conclusions and recommendations” provides the final interpretation of the achieved outcomes.

E-M field overview

Figure 1 illustrates the geographical location of E-M field which lies offshore South Africa, in water depths of around 100

meters in the northern part of Block 9. The discovery of the field took place in 1984 by Well E-M. The well E-M1 was proven

as a gas condensate well. Between 1984 and 1986 further 5 wells (E-M2, E-M3, E-M4, E-M5 and E-M6) were drilled with the

objective to delimit the E-M structure. Wells E-M2, E-M4 and E-M6 encountered gas, whereas E-M3 tested an eroded reservoir section and E-M5 penetrated down-dip of the E-H accumulation (Figure 1). In 1989 acquired 3D-seismic

significantly improved the reservoir description. 9 years later, in 1998, reprocessing and reinterpretation of original data was

performed, which allowed much better understanding of E-M field and planning the drilling of new wells - E-M01P, E-M02Pa

and E-M03P. The wells are targeting shallow marine and fluvio-deltaic sandstone within an upper shallow marine interval

(USM) - the primary reservoir in this field. The structure of E-M field is very complex due to extensive faulting, trending in

WNW direction. Therefore, the field is suggested to be vertically compartmentalized. Figure 3 illustrates subdivision of the

field in 10 fault bound segments (polygons). The complexity of the E-M structure is additionally characterized by horizontal

compartmentalization of the field stratigraphy described in Table 1. Two wide, laterally continuous shale layers within the

Zone 3 are identified: Upper Shale Layer (USL) and Lower Shale Layer (LSL). The USL is 1-2m thick and separates Zone 2

and Zone 3. The LSL is 6-13m thick and is located within the Zone 3. Its location varies between the wells (Figure 2) [1].

3 Slopes identification on pressure derivatives is fundamental part of identification process of a corresponding well test interpretation model. Thus, one should

avoid the penalization of slopes during deconvolution process.


Statement of paper concern

The concern of this thesis is to identify potential communication

between Zone 2 and Zone 3 separated from each other by

continuous, laterally extended Upper Shallow Layer. In order to

determine the integrity of USL and to clarify the location of

boundaries around the wells deconvolution in combination with

conventional well test analysis is applied to well test data

acquired from 3 E-M development wells: E-M01P, E-M02Pa and

E-M03P. In august 2005, July 2007 and November 2008 on a

consulting basis [5,6,9,10] the well test data of the same wells

were already analyzed. According to performed analysis USL is,

most likely, laterally continuous and sealing in the well E-M01P.

Zone 3 is therefore not drained significantly by the horizontal

well E-M01P. In well E-M02Pa communication between Zone 2

and Zone 3 through USL is observed, whilst deconvolution and

well test analysis of well E-M03P provided no evidence of

communication with Zone 3 through USL. On its part, this study

incorporates the analysis of data already examined in above-

mentioned consulting reports plus data acquired in the period

from the date, at which the analyses were carried out, till end of

Mai 2011. Table 2 presents time intervals of new acquired data

for each well.

Well Time interval analyzed in consulting

reports and in a MSc thesis [11] Time interval of new acquired data

Additional pressure data

(hours)

E-M01P 29/11/2000 - 28/02/2008 28/02/2008 -30/04/2011 27785

E-M02Pa 05/12/2001 - 28/02/2008 28/02/2008 -06/04/2011 18441

E-M03P 06/06/2000 - 01/06/2008 01/06/2008 -30/04/2011 22839

Table 2: Time intervals of new acquired data

The assessment whether the Upper Shallow Layer is sealing would contribute significantly to decision whether infill

drilling in the reservoir would make sense. Sealing USL would act as a flow barrier between two zones and, thus, not allow the

existing wells to produce gas from separated Zone 3. In this case infill drilling could be taken into account. In the following

paragraphs three analyzed wells are briefly introduced.

Well E-M01P

It is the first deviated, sub-horizontal development well drilled in E-M reservoir structure. Well E-M01P is spudded on 26th

December 1998. The primary objective of this well is to intersect a production interval in the Zone 2 (comprising Zone 2B and

Zone 2A), to access gas in polygons 4 and 5 of the E-M filed structure and to produce at least 271 Bcf of dry gas. Because of

the potential vertical compartmentalization of the filed every development well, including E-M01P, is designed with sub-

horizontal producing section to enable access to gas in individual potentially sealing compartments. In case of E-M01P, the

Figure 1: E-M field location map [17]

Zone

Interval Description

Zone 1 Fluvio-deltaic (non-reservoir), bounded by 1At1

and TUSM

Zone 2

Shallow marine. Main reservoir in the E-M field

consisting of a series of shallow marine sands

beneath TUSM with net to gross in the region of 90

-100% and 15% porosity. The average thickness is

55m.

Zone 3

Fluvio-deltaic/shallow marine. An interbedded

interval of non-glauconitic sandstone and shale with

net to gross in the region of 66% and porosity of

13%. The average thickness is 80m.

Zone 4

Shallow marine. Very similar sandstones to Zone 2

with an average thickness of 85m and a net to gross

of 90% and porosity of 14%. The base of Zone 4 is

marked by BUSM. Zone 4 has never been

intersected above the GWC in the E-M field.

Zone 5 Non reservoir. Fluvial red beds.

Table 1: Stratigraphy of the E-M field [1] Figure 2: Cross section E-M4 to E-M6 [1]

E-M Field


sub-horizontal section is about 1000 m [17]. Figure 3 shows the trajectory of E-M01P. Blue color indicates the entire length of

this well, whereas black color represents the sub-horizontal producing section, which start is located in 770 m from E-M1 and

its end in 320 m from E-M4.

Well E-M02Pa

Well E-M02Pa is a replacement well for the E-M02PZ1 well

which was lost in July 2001 [15]. It is spudded on 29th

September 2001. Well E-M02Pa is designed with sub-

horizontal producing section, drilled in the central part of the

field, parallel to the E-M02PZ1, focusing on the effective

drainage of reservoir hydrocarbons in polygons 5 and 6 and

aiming to produce 312 Bcf of gas. Approximately 800 m of

the producing interval is in polygon 5, and approximately 400

m in polygon 6.

Well E-M03P

Well E-M03P is the third horizontal development well in the

E-M gas field, spudded on 21st April 2000. The primary

objective of this well is to drill production interval in the

Zone 2B and Zone 2A and, thus, to drain effectively the

proven GIIP from polygons 8a and 8b by production of at

least 128 Bcf of gas. The secondary objective is set to

observe late time behavior for possible boundary effects. The around 500 m long sub-horizontal section is drilled in Zone 2 -

target reservoir, which comprises the upper shallow marine (USM) sandstones. About 340 m of this section is in polygon 8a

and about 160 m in polygon 8b. Two polygons are separated by a major fault. Blue color indicates the entire length of the well,

whereas black color represents the sub-horizontal producing section. To note is the workover carried out from 9th

August 2005

to 28th

January 2006. The workover is performed to recover existing well completion and to evaluate the source of water

ingress which affected the first years of production.

Methodology

Data management

As discussed previously in the introduction section, first of all one needs to prepare available pressure and rate data for

deconvolution analysis. Taking into account Levitan’s (2004, 2005, and 2006) instructions, with implementation of “Interpret

2000” as conventional well test analysis software, following data processing is performed:

1. Correction and depth adjustment of available DST and production pressure data. Since DST and production pressure

data is measured at different gauges, one needs either to adjust them or to correct to a reference depth.

2. Elimination of noisy pressure data or pressure data not corresponding to the actual reservoir behavior (for instance, data

with zero-pressure)

3. Reduction of original pressure data using “Winnow”- function in Interpret. The reduction of pressure and rate data is

necessary for data upload into TLSD deconvolution software where the number of pressure data points and rates is limited.

Note that the behavior of the reservoir must remain the same after the pressure data is reduced. For this reason one tries to

preserve, especially build-up pressure data, because these data are most reliable compared to often poor quality drawdown

data. Consequently, build-up data are analyzed thereinafter.

4. Simplification of rate history using “Merge flow periods”- function in Interpret. Simplification is necessary to speed up

calculations and to ensure successful data upload into TLSD. Simplified (analysis) rates are used for deconvolution.

5. Calculation of total rates. Gas, Oil and Water rates are available for analysis. Using the individual rates the total gas

rates are calculated. These rates are used for subsequent deconvolution and conventional well test analysis.

6. Synchronization of the start and the end of each flow period in the test rate with pressure data. Note that deconvolution

only corrects the rates, but does not synchronize the time of each flow period in the rate with pressure signal [20]. Prior to

deconvolution user needs to do that.

7. Approximation of linearization by single-phase pseudo-pressures calculation. As discussed previously it is essential to

linearize measured pressured data acquired in multiphase or gas systems what is the case here. Otherwise Duhamel’s principle

will not be satisfied, and deconvolution will yield unreliable results.

Evaluation of the prepared data prior to deconvolution

One of the reasons to perform this step of analysis is to identify the portions of pressure data that are of a good quality, and

thus, to allow one to decide what pressure data are to use for deconvolution [13]. For instance, the pressure data affected by

phase redistribution in a gas condensate well should not be used, because it falsifies the actual behavior of reservoir.

Figure 3: E-M field polygon map and three located wells [15]


8. Comparison of rate normalized build-ups plotted together on the same log-log plot. Behavior of DST and production

build-ups is evaluated and discussed.

9. Identification of boundaries and depletion from “pressure versus superposition function” plot.

Determination of initial reservoir pressure

10. Deconvolution of DST data to determine the value of initial reservoir pressure is performed. According to Levitan

(2003) the pressure data from a single flow period do not contain enough information to identify initial reservoir pressure.

Thus, comparison of deconvolved responses obtained by deconvolution of pressure data from different flow periods is

necessary to identify its value. In addition, according to Gringarten (2010) [8], such flow periods should be selected that are

infinite acting and not sensitive if boundaries have been reached. In this case deconvolved derivatives of chosen flow periods

behave in a very sensitive way to the initial reservoir pressure. Best candidates for this procedure are deconvolved derivatives

of DST build-ups which often do not show the existence of boundaries and are sensitive to the change of initial reservoir

pressure value.

Deconvolution

11. Deconvolution of individual flow periods, series of build-ups, multi-flow periods and all flow periods in one sweep is

applied to available pressure data. Example of deconvolved derivative (Figure 4) demonstrates and clarifies all with it

associated labels which are used in the “Analysis results” section.

Verification of deconvolution

12. The quality of deconvolution is verified by comparing: 1) the pressures convolved from the deconvolved derivatives

with adapted rates with measured pressure data and 2) adapted rates with measured rates.

Analysis of unit-rate pressure drawdown

13. Analysis of unit-rate pressure drawdown. The next step of deconvolution process is to analyze convolved unit-rate

pressure drawdowns in conventional way. The objective of this analysis is to identify the well test interpretation model, which

would describe the reservoir behavior.

Application of obtained model to measured pressure data

14. Application of obtained model to measured pressure data with adapted rates.

15. Adjustment of model parameters to optimize the match - final step in deconvolution analysis.

Analysis results

In the following, well test data acquired in well E-M02Pa are analyzed and results of this analysis are presented. The analysis

of well E-M02Pa serves as an example how to apply deconvolution. Deconvolution analysis is performed using methodology

described above. The same methodology is carried out to wells E-M01P and E-M03P.

Figure 4: Example of a deconvolved derivative providing explanation for each label


Data management

Table 3 below shows the number of pressure and rate data for each well received for the analysis. During the process of data

preparation (steps 1-7) they are reduced to the number of points and rates presented in the same table. Reduced data are used

for deconvolution analysis.

Well Received Data Data after reduction

Pressure points Measured Rates Pressure points Simplified rates

E-M01P 5.5 Millions 3350 21950 878

E-M02Pa 4.2 Millions 3080 25520 873

E-M03P 5.4 Millions 2020 30300 578

Table 3: Received and reduced pressure data

Evaluation of prepared data prior to deconvolution

Figure 5: Well E-M02Pa - log-log rate validation plot, normalized to flow period 19: useful build-ups up to the last build-up 833 of the production

Figure 5 shows the derivatives behavior of useful build-ups during the production period (including DST build-ups 5,15 and

19). All build-ups exhibit the same initial radial flow stabilization as the DST build-ups. This stabilization is firstly followed

by a half-unit slope straight line and finally by a unit slope straight line - evidence of a closed system. Moreover, it seems that

the potential condensate bank stabilization is diminishing (except FP 589). Decrease in skin values corresponding to pressure

of selected flow periods confirms that. Figure 6 demonstrates the superposition plot which suggests depletion and thus the

existence of boundaries. DST build-ups do not show boundaries.

Figure 6: Well E-M02Pa - superposition plot

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Log-Log Rate Validation - Flow Period 19

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Superposition Function (MMscf/D)

Horner Match - Flow Period 15

Slope 1

Condensate bank

stabilization

Radial flow

stabilization

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Elapsed time (yrs)


nm(p) ChangeDerivativeRate Normalised nm(p) Change Flow Period 5Rate Normalised Derivative Flow Period 5Rate Normalised nm(p) Change Flow Period 15Rate Normalised Derivative Flow Period 15Rate Normalised nm(p) Change Flow Period 318Rate Normalised Derivative Flow Period 318Rate Normalised nm(p) Change Flow Period 546Rate Normalised Derivative Flow Period 546Rate Normalised nm(p) Change Flow Period 833Rate Normalised Derivative Flow Period 833Rate Normalised nm(p) Change Flow Period 785Rate Normalised Derivative Flow Period 785Rate Normalised nm(p) Change Flow Period 754Rate Normalised Derivative Flow Period 754Rate Normalised nm(p) Change Flow Period 747Rate Normalised Derivative Flow Period 747Rate Normalised nm(p) Change Flow Period 589Rate Normalised Derivative Flow Period 589


Figure 7 provides an example which data

should not be used for deconvolution. It

shows a log-log plot with rate-normalized

DST build-ups (Well E-M01P). The

derivatives of FP-51, FP-68, FP-91 and FP-

101 have very similar shapes except that of

FP-27. This build-up suggests phase

redistribution in the wellbore and, thus,

should not be selected for deconvolution

analysis. DST build-up derivatives clearly

show early radial (or cylindrical) flow

stabilization between 0.03 and 0.3 hours

corresponding to√𝑘𝑧𝑘𝑥𝑦L, followed by a

half-unit slope corresponding to a linear

flow in a horizontal well. Derivatives of FP-

101 and FP-91 seem to stabilize at elapsed

time of about 10 hours indicating pseudo-

radial flow stabilization corresponding to

𝑘𝑥𝑦ℎ.

Determination of initial reservoir pressure

In well E-M02Pa initial reservoir pressure is determined to be 3696.75 psia. The deconvolved derivatives of DST build-ups

(FP 15 and FP 19) converge at late times indicating the correctness of identified value of initial pressure (Figure 8). FP 147

and FP 290, which are infinite acting, are deconvolved as well. Their deconvolved derivatives converge with those from DST

build-ups confirming the accuracy of this analysis.

Figure 8: Determination of initial reservoir pressure in well E-M02Pa through comparison of deconvolved derivatives of DST build-ups

Deconvolution of flow periods

Deconvolution of individual build-ups, series of build-ups, multi-flow periods and eventually deconvolution of all flow periods

in one sweep is performed (well E-M02Pa). The final result is illustrated in Figure 9. Deconvolved derivatives of build-ups in

the early stage of production (between 100 and 21200 hours) provide a unit slope log-log straight line at late times - evidence

of a closed rectangular reservoir. Deconvolved derivatives of build-ups corresponding to production period between 21200 and

73100 hours also show a unit slope log-log straight line at late times. However, in comparison to that of previous build-ups this

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Elapsed Time hrs

5151994#(1-873)[147]{2.62045E+05}3696.75#(1-873)[94]{1.09880E+05}3696.75#(1-873)[5]{1.02477E+03}3696.75#(1-873)[15]{4.47372E+02}3696.75#(1-873)[19]{4.29609E+02}3696.75#(1-873)[5,15,19]{6.40522E+03}3696.75#(1-873)[290]{6.71692E+05}3696.75

Figure 7: Well E-M01P - log-log rate validation plot normalized to FP-91


straight line is shifted down. The shift is indicated in Figure 9 by orange dashed circle. Deconvolved derivative corresponding

to pressure data of FP [5,15,19-301] still follows the first obtained unit slope. Indeed, deconvolved derivative corresponding to

pressure data of FP [5,15,19-318] starts to deviate from the original slope. Thus, deviation occurs between flow periods 301

and 318 (16100 - 17350 hrs). Note that this shift cannot be seen on individual build-ups and is only identifiable through

deconvolution process. The behavior of deconvolved derivative resulted from deconvolution of all flow periods in one sweep

denotes the multilateral behavior due to recharge from Zone 3 through USL.

Figure 9: Well EM02Pa - deconvolution of flow periods corresponding to different stages of production

The same procedure to identify the initial reservoir pressure is applied to pressure and rate data acquired in well E-M01P.

The initial reservoir pressure, at which consistent derivatives are identified, is obtained to be 3798 psia. Deconvolved

derivatives of build-ups during production phase 1 (FP 103 - FP 418) suggest early radial flow stabilization followed by a half-

unit slope. Including FP 418 in deconvolved series of previous build-ups results in a deconvolved derivative with a unit slope

at the late time - evidence of a closed system (closed rectangular reservoir) at the late time. Note, that the interpretable time of

FP 418 is about 4100 hrs when analyzing it in conventional way. In contrast, deconvolution increases the interpretable time by

a factor of 8. In addition, deconvolution identifies the unit slope log-log straight line at the late time, whereas the unit slope is

not evident on the conventional derivative. Deconvolved derivatives of build-ups during production phase 2 (FP 419 - FP 878)

follow the behavior of the deconvolved derivatives of previous flow periods. However, at late times, there is a deviation from

unit slope log-log straight line obtained during production phase 1. The unit slope changes to a half-unit slope - indication of

the successive change of late time behavior. Deconvolution of multi-flow periods is performed to identify when the deviation

is started. Figure 10 represents the obtained results. According to results the deviation started between FP 466 and FP 581.

Eventually, entire production pressure history together with DST build-ups is deconvolved. Figure 10 shows the deconvolved

derivative (red dashed line) which confirms the change of the slope at late time.

The initial reservoir pressure in well E-M03P is determined to be 3727 psia. Figure 11 illustrates deconvolved derivatives

of flow periods corresponding to different production periods: pre-workover (0 - 49700 hours), post-workover 1 (49700 -

68000 hours) and post-workover 2 (68000 - 93000 hours). All derivatives provide evidence of boundaries reached during

production. Derivatives corresponding to pre-workover phase exhibit a unit slope log-log straight line at late times - indication

of a closed rectangular reservoir. Derivatives of post-workover phase 1 follow the previously obtained slope at late times -

without any shift. In contrast, deconvolution of subsequent flow periods results in derivatives with a lower slope at late times.

This may be due to drainage of Zone 3 through USL. Figure 11 demonstrates discussed observations as well as the

deconvolved derivatives obtained while deconvolution of all flow periods in one sweep with different λ values.

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#(1-873)[5,15,19,301]{1.99518E+06}3696.75

#(1-873)[5,15,19,318]{4.06776E+06}3696.75

#(1-873)[5,15,19,546]{2.42354E+06}3696.75

#(1-873)[5,15,19-873]{2.38813E+08}3696.75

#(1-873)[19,785]{3.84821E+06}3696.75

#(1-873)[5,15,19-318]{4.93654E+06}3696.75

#(1-873)[5,15,19-785]{2.06625E+07}3696.75

Shift of the unit slope log-

log straight line


Figure 10: Well E-M01P - deconvolution of multi-flow periods

Figure 11: Well EM03P - deconvolution of flow periods during different stages of production

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91101200418581613709#(1-878)[51,68,91,101-536]{5.69987E+07}3798.00#(1-878)[51,68,91,101-878]{3.55209E+07}3798.00#(1-878)[51,68,91,101-418]{2.12456E+07}3798.00#(1-878)[51,68,91,101-466]{5.29029E+07}3798.00#(1-878)[51,68,91,101-581]{5.72346E+07}3798.00#(1-878)[51,68,91,101-436]{2.19391E+07}3798.00#(1-878)[51,68,91,101-450]{2.21250E+07}3798.00#(1-878)[51,68,91,101-300]{1.63158E+07}3798.00#(1-878)[51,68,91,101,166]{5.47862E+05}3798.00#(1-878)[51,68,91,101,166,200]{2.05458E+06}3798.00#(1-878)[51,68,91,101,200,294,418]{7.16729E+05}3798.00

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224 #(1-578)[16]{4.91348E+03}3727.00

#(1-578)[20]{3.70287E+03}3727.00 #(1-578)[252]{2.22083E+06}3727.00

#(1-578)[224]{1.39649E+04}3727.00 #(1-578)[60]{8.92667E+05}3727.00

#(1-578)[285]{3.07239E+06}3727.00 #(1-578)[414]{3.96719E+06}3727.00

#(1-578)[419]{3.83708E+06}3727.00 #(1-578)[513]{4.41171E+06}3727.00

#(1-578)[11,16,20-578]{2.96979E+07}3727.00 #(1-578)[11,16,20-578]{1.00000E+09}3727.00

#(1-578)[11,16,20-578]{2.96979E+08}3727.00 #(1-578)[11,16,20-578]{3.07884E+06}3727.00

Note: Increasing λ results in smoothing of the derivative (all

flow periods deconvolved) and, thus, in elimination of

oscillations. In grey oval dotted circle, reservoir behaviour is

displaced, which disappears during smoothing process. It may

represent stabilization at late times. Particularly in this well in

the past a leaky fault has been identified. This feature may be

indication of this fault. It is up to well test interpreter to decide

when the smoothing is just enough to stop to increase λ.

35000 hrs 4090 hrs

Increase in

interp

retable tim

e


Verification of deconvolution

Example of percentaged difference between the measured and convolved pressure data is demonstrated for well E-M02Pa in

Figure 12. The pressure difference is within 10% range - indication of a satisfactory pressure match. The comparison between

the measured and adapted rates is shown below (Figure 13). The difference between the rates should be expected, since the

poor acquisition frequency of measured rates (1 rate every 24 hours) implies some degree of uncertainty in correctness of their

measurement. However, the difference should not be more than 15-20%, which is the case in analyzed wells. In summary, the

pressure and rate matches for wells E-M01P and E-M02Pa are good enough to conclude that the performed deconvolutions are

satisfactory to proceed with the further analysis step. In contrast, rates recorded in well E-M03P seem to be erroneous. They

are manually corrected in the course of this study.

Figure 12: Well EM02Pa - difference in % between actual measured pressure data and convolved pressures

Figure 13: Well EM02Pa - rate history match for deconvolved derivative (1-873)[5,15,19-873]{1.00000E+09}3696.75

Analysis of unit-rate pressure drawdown In the following paragraphs final steps of deconvolution analysis applied to well test data recorded in well E-M02Pa are

discussed in detail. Figure 14 illustrates a unit-rate pressure drawdown resulted from deconvolution of DST build-up data

together with all production data. Log-log plot (Figure 15) shows the initial unit slope log-log straight line due to wellbore

storage. Moreover, the early radial flow (cylindrical) stabilization corresponding to √𝑘𝑥𝑦𝑘𝑧𝐿 and the linear flow characterized

by a half-unit slope on the log-log straight line can be identified. There is no clear evidence of a second radial flow

stabilization corresponding to kxyh in the middle time. Instead, channel starts to develop indicating its dominance. Then the

channel changes over to a closed system (rectangle). At the latest time (indicated by yellow circle) deviation from unit slope is

observed. This deviation suggests multilateral behavior due to drainage from Zone 3. In summary, the well test interpretation

model corresponds to a horizontal well with wellbore storage and skin in a reservoir with successively changing boundaries.

Additionally, unit-pressure drawdowns convolved from deconvolved derivatives of FP [19,290], FP [19,546] and FP [19,785]

are analyzed. In all cases single layer model is applied to match the data. There is no indication of multilayer reservoir

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(1-873)[5,15,19-873]{2.37965E+06}3696.75 (1-873)[5,15,19-873]{2.38813E+08}3696.75

(1-873)[5,15,19-873]{1.00000E+09}3696.75

Pressure history from measured data

Convolved pressure (1-878)[51,68,91,101-878] {6.63682E+07}3798


Adapted Rates

Measured Rates

Difference in %

+20%

-20%


behavior when analyzing the drawdowns convolved from deconvolved derivatives of individual flow periods or series of flow

periods.

In contrast, the analysis of unit-

pressure drawdown displaced in

Figure 14 suggests communication

between two layers through USL

(Figure 15). In this case single layer

model cannot match the pressure

and derivative data of the convolved

drawdown. Instead, a multilayer

model is used to match the

convolved pressure data. Figures

16-17 represent both models and the

corresponding pressure simulation

histories of each convolved

drawdown. The vertical

permeability of the shale layer must

be in the order of 10-4

mD to

provide a match. If the kz of shale

layer is less, the USL acts as non

sealing barrier. Using k2(z) = 10-9

mD the multilayer model becomes

almost identical with that of a single

layer. Figures 15-18 summarize

discussed observations.

Application to measured pressure data

Identified models from drawdown analyses are applied to measured pressure data. Deconvolution analysis of welt rest data

recorded in well E-M02Pa is continued. Identified well test interpretation models are applied to measured pressure data in well

E-M02P. Adapted rates are used. Figure 20 illustrates the match resulted in application of the single layer model. It clearly

shows that the single layer well test interpretation model does not match the entire pressure history. The match is only obtained

until and including FP 277. Deviation from the actual pressure history starts during the FP 290. In contrast, multilayer analysis

model matches the entire pressure history very well (Figure 22). The model parameters are adjusted to refine the final match.

Figure 14: Well EM02Pa - drawdown resulted from deconvolution of all flow periods in one sweep

f

Figure 15: Well E-M02Pa - identification of flow regimes

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Wellbore

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Slope 1

nm(p) change and derivative data

corresponding to convolved drawdown

convolved pressure

drawdown data


Figure 16: Well E-M02Pa - multilayer closed reservoir behavior

Figure 17: Well E-M02Pa - single layer closed reservoir behavior

Figure 18: Simulations of unit-rate drawdowns convolved from derivatives of different flow periods

Figure 19: Well E-M02Pa - pressure match of flow period 277

Figure 20: Well E-M02Pa - single layer analysis applied to simulate entire pressure history

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3670

3680

3690

3700

0 10000 20000 30000 40000 50000 60000 70000 80000

Pre

ssure

(psia

)

Elapsed time (hrs)

Simulation (Constant Skin) - Flow Period 2

Pressure DataSimulated PressureSimulated Pressure - Single layer FP [19,290]Simulated Pressure - Single layer FP [19,785]Simulated Pressure - Multilayer k2(z)=k2(xy) = 10^(-9)

0

1000

2000

3000

4000

5000

0 10000 20000 30000 40000

Pre

ssu

re (

psia

)

Elapsed time (hrs)


Simulated Pressure - Multilayer k2(xy)=10-4 & k2(z)=1.5*10-4

(FP [5,15,19-873])

Simulated Pressure - Multilayer k2(z)=k2(xy)=10-9

(FP [5,15,19-873])

Simulated Pressure - Single layer FP [19,290]

Simulated Pressure - Single layer FP [19,785]

FP 277

FP 277 FP 290

Layer 1 = Zone 2

Layer 2 = Upper Shale Layer

Layer 3 = Zone 3

Model Data Data Model

convolved pressure

drawdown data

Data Model


Figure 21: Well E-M02Pa - pressure match of flow period 277

Figure 22: Well E-M02Pa - multilayer analysis applied to simulate entire pressure history

Conclusions and recommendations

Taking into account results obtained from consulting reports prepared by Gringarten, A.C. and comparing them with those

identified in this study following conclusions can be drawn:

Deconvolution of well test data acquired in well E-M02Pa indicates multilateral reservoir behavior. Drawdown analyses,

carried out in this study, suggest the recharge from Zone 3. Single layer model can match pressure data until June 2003

meaning that there is no communication between Zones 2 and 3. After this date single layer model fails to provide the

match - recharge from Zone 3 starts. In contrast, multilayer analysis model provides a good match. The vertical

permeability of the shale layer must be in the order of 10-4

mD to provide the pressure match. Variation of the horizontal

permeability of the USL by preserving the vertical shale layer permeability in the above-mentioned magnitude does not

affect pressure match. The observations made in this study agree with results obtained by Gringarten, A.C. in May 2008.

New acquired pressure and rate data do not show the change in reservoir behavior.

In contrast, deconvolution of well test data acquired in well E-M01P indicates a change of reservoir behavior at late times.

There is a decrease of the final unit slope examined. The deviation from the unit slope log-log straight line in the consulting

report from July 2007 is not present. The deviation may be a sign of drainage of Zone 3. However, this study cannot give

definitive answer whether this change is due to multilateral behavior or not. Both single and multilayer model provide

pressure matches of the same quality. Both models describe open-ended rectangular reservoir. The vertical permeability of

the shale layer must be in the order of 10-6

mD and less in order to obtain a match. That leads to assumption that the USL is

most likely sealing. It should be noted that the new acquired data particularly in this well are of poor quality. The noisy

data and data with zero-pressure values has to be eliminated resulting in gaps of pressure history. Just these data are not

matched satisfactorily in both models.

Deconvolution of well test data acquired in well E-M03P does not signify any changes at late time behavior of the

reservoir. Deconvolved derivatives analyzed in consulting report from November 2008 and those investigated in this paper

show the same unit slope log-log straight line at late times without any shift or deviation. Single layer model is used to

match the entire pressure history data. Attempts are made to apply multilayer model, but no model is found which would

match the pressure data on the log-log, Horner and pressure history plots.

Deconvolution of well test data acquired in all analyzed wells confirms the existence of boundaries obtained in the

previous analyses. Specifically deconvolution validates the existence of the sub-seismic faults. The first boundary is

located between wells E-M01P and E-M02Pa whereas the second one is found to be to the West from the centre of the well

E-M03P. The distances to the boundaries from each well are listed in Table 4 which also specifies vertical and horizontal

permeabilities as well as the effective horizontal lengths resulted from the analysis. Uncertainty in well test analysis results,

according to Azi et al (2008) [2], is incorporated where no range of parameters is provided.

Current study shows that deconvolved derivatives identify features which are not evident on the conventional derivatives.

For instance, in well E-M01P deconvolution of FP 418 can recognize unit slope log-log straight line on the deconvolved

derivative, whilst the slope is not seen on the conventional derivative of the same flow period. Deconvolution increases the

interpretable time for this flow period.

Deconvolution allows determination of initial reservoir pressure. Recommendations by Levitan are considered to identify

the initial pressure values.

0

1000

2000

3000

4000

0 10000 20000 30000 40000 50000 60000 70000 80000

Pre

ssu

re (

psia

)

Elapsed time (hrs)


FP 277 Model Data


Recommendations

According to achieved results and encountered problems while deconvolution analysis following recommendations can be

given:

Synchronization of the start and the end of each flow period is a very important step in data preparation for

deconvolution analysis. This step of analysis has to be carried out carefully. In this study problems are encountered

because of inaccurate adaptation of the start and the end of each flow period. However, to carry out this step of

analysis properly one requires sufficient pressure and rate data quality. The synchronization process performed in this

paper is complicated due to high difference in acquisition frequency of pressure and rate data.

Further simplification of the rate history is advisable to speed up the deconvolution process and at the same time to

reduce the uncertainty during the process of synchronization discussed above. Attempts were made to simplify further

the rate history in all wells. The reduction of flow periods results in better match between convolved and measured

pressure history and between the adapted and measured rates. Especially the match of convolved drawdowns with

actual measured drawdown pressure data was improved. The calculation of derivatives in TLSD software became

faster.

However, major concern in deconvolution applied to well test data from gas or gas condensate wells is the rate

adaptation which is carried out through deconvolution process. Deconvolution does not distinguish between

erroneous rates and changes in skin. The skin might vary due to build-up of gas condensate bank or turbulent flow

caused by high gas flow rates (rate dependent skin). Consequently, adapted rates may reflect changes in skin or

erroneous rates or both at the same time. Thus, one should pay special attention to adaptation of rates in gas and gas

condensate systems. This issue requires further investigation. Attempts were made to deconvolve data without

adaptation of rates. Pressure difference between convolved and measured pressures became very high. The resulted

derivative shapes, however, did not change significantly.

The criterion of selection of regularization parameter λ remains very subjective. This study uses default λ values

while deconvolving individual build-ups. When deconvolution is applied to multi-flow periods default λ values are

multiplied by a factor of 10-1000. It is recommended to perform deconvolution increasing the magnitude of λ stepwise and in doing so to compare the derivatives shapes. Attempts were made to change weight parameter 𝜐 as

well. Decrease of 𝜐 improves the pressure match but impairs the rate match. The user has to aim the equilibrium in

both matches. In this study default 𝜐 are used.

Well Parameter This study Gringarten, A.C. Units

E-M01P

Effective flowing horizontal well length 340 - 900 250 - 920 m

Horizontal permeability kxy 1.8 - 13.8 2 - 13 mD

Vertical permeability kz 1.7 - 15.4 2 -20 mD

Boundary d1 (to the West) 500 - 640 30 - 470 m

Boundary d2 (to the North) 940 - 1200 > 3000 m

Boundary d3 (to the East) 130 - 360 200 ± 50 m

Boundary d4 (to the South) 1850 - 2830 1000 - 2000 m

E-M02Pa

Effective flowing horizontal well length 800 ± 200 900 ± 225 m

Horizontal permeability kxy 22 ± 4.4 30 ± 6 mD

Vertical permeability kz 2 ± 0.4 5 ± 1 mD

Boundary d1 (to the West) 580 ± 145 250 - 460 m

Boundary d2 (to the North) 1090 ± 275 2000 - 2200 m

Boundary d3 (to the East) 560 ± 140 230 - 470 m

Boundary d4 (to the South) 220 ± 55 320 - 700 m

E-M03P

Effective flowing horizontal well length 240 - 320 175 - 240 m

Horizontal permeability kxy 7 - 14 14 ± 2.8 mD

Vertical permeability kz 2.3 - 3.3 2.6 ± 0.5 mD

Boundary d1 (to the West) 140 - 350 230 - 300 m

Boundary d2 (to the North) 1750 - 2100 2000 - 2100 m

Boundary d3 (to the East) 110 - 170 100 - 140 m

Boundary d4 (to the South) 1500 - 1650 1500 - 1600 m

Table 4: Summary of obtained results


NOMENCLATURE

B formation volume factor res vol/norm vol k2(z) Layer 2 vertical permeability mD

kh permeability-thickness product md.ft k3(z) Layer 3 vertical permeability mD Kh horizontal permeability md A drainage area m2

Lw effective horizontal length

of a well

m Dp(S) pressure drop due to wellbore

skin effect

psi

1At1 cretaceous synrift unconformity identified in

the E-M-Field structure

d1(1:3) distance to first boundary in

layers 1 to 3 (crossflow)

m

TUSM GWC

Top Upper Shallow Marine gas water contact

m (Depth)

d2(1:3) distance to second boundary in layers 1 to 3 (crossflow)

m

BUSM FP

Bottom Upper Shallow Marine flow period at constant rate

d3(1:3) distance to third boundary in layers 1 to 3 (crossflow)

m

kz

kxy

vertical permeability

horizontal permeability

md

md

d4(1:3) distance to fourth boundary in

layers 1 to 3 (crossflow)

m

L

(pav)i

horizontal well length

initial average reservoir pressure

m

psia

Type d1

Type d2

Type of first boundary

Type of second boundary

(pav)f

pwf final average reservoir pressure flowing pressure at the start of flow period

psia psia

Type d3 Type d4

Type of third boundary Type of fourth boundary

(kh/u)t

(k/u)t

total mobility thickness

total mobility

mD.ft/cp

mD/cp

P/Z corr. ct correction to ct to honour

material balance

(kxy/u)t total horizontal mobility mD/cp ct total compressibility 1/psi

(kz/u)t total vertical mobility mD/cp D non-darcy flow coefficient D/Mscf

h layer thickness m Zw distance to lower boundary m S(w) wellbore skin factor C wellbore storage coefficient bbl/psi

S(c)

S(t)

completion skin factor

total skin factor

Type top

Type bottom

type of top boundary

type of bottom boundary

d1 distance to first boundary m k1(xy) Layer 1 horizontal permeability mD

d2 distance to second boundary m k2(xy) Layer 2 horizontal permeability mD

d3 distance to third boundary m k3(xy) Layer 3 horizontal permeability mD d4 distance to fourth boundary m k1(z) Layer 1 vertical permeability mD

MPLT memory production logging tool

LIST OF REFERENCES

1. Amudo, C., Turner, J., Frewin, J., Kgogo, T.C., PetroSA, and Gringarten, A.C., Imperial College London: ” Integration of Well Test Deconvolution

Analysis and Detailed Reservoir Modelling in 3D Seismic Data Interpretation: A Case Study”, SPE paper 100250, June 2006

2. Azi, A.C., Gbo, A., Whittle, T., Gringarten A.C.: “Evaluation of Confidence Intervals in Well Test Interpretation Results”, SPE paper 113888, June 2008

3. Gringarten, A.C., Imperial College London: “From Straight Lines to Deconvolution: The Evolution of the State of the Art in Well Test Analysis”, SPE

paper 102079, September 2006 4. Gringarten, A.C., T. von Schroeter, Rolfsvaag, T., Bruner, J.: „Use of Downhole Permanent Pressure Gauge Data to Diagnose Production Problems in a

North Sea Horizontal Well”, SPE paper 84470, October 2003

5. Gringarten, A.C.: “Additional Well Test Analysis of Well E-M01P for PetroSA”, Consulting report for PetroSA, July 2007 6. Gringarten, A.C.: “Additional Well Test Analysis of Well E-M02Pa for PetroSA”, Consulting report for PetroSA, May 2008

7. Gringarten, A.C.: “From straight lines to deconvolution: the evolution of the state-of-the art in well test analysis”, SPE paper 102079-MS, 2006

8. Gringarten, A.C.: “Practical use of well test deconvolution”, SPE paper 134534, September 2010 9. Gringarten, A.C.: “Well Test Analysis of Well E-M01P for PetroSA”, Consulting report for PetroSA, August 2005

10. Gringarten, A.C.: “Well Test Analysis of Well E-M03P for PetroSA”, Consulting report for PetroSA, November 2008

11. Kgogo, T.C., “Deconvolution Analysis of a Horizontal Gas Condensate Well” MSc Thesis, Imperial College London, September 2005 12. Meunier, D.F., Kabir, C.S., and Wittman, M.J.: “Gas Well Test Analysis: Use of Normalized Pressure and Time Functions”, SPEFE 2 (4): 629-636.

SPE-13082-PA. DOI: 10.2118/13082-PA

13. Michael M. Levitan, Gary E. Crawford, Andrew Hardwick: “Practical Considerations for Pressure-Rate Deconvolution of Well Test Data”, SPE paper 90680-MS, September 2004

14. Michael M. Levitan: “Practical Application of Pressure-Rate Deconvolution to Analysis of Real Well Tests”, SPE paper 84290-MS, October 2003

15. Mossgas (Pty) Ltd, “Borehole E-M02Pa Geological Well Completion Report”, December2001 16. Mossgas (Pty) Ltd, “Petroleum Engineering Report Well E-M03P”, July 2000

17. PGS Reservoir Consultants (UK) Limited, “Petroleum Engineering Report Well E-M01P”, January 2000

18. R. Al-Hussainy and H.J. Ramey Jr.: “Application of Real Gas Flow Theory to Well Testing and Deliverability Forecasting”, Journal of Petroleum

Technology: 637-642. SPE 1243-B-PA, Mai 1966

19. T. von Schroeter, F. Hollaender, A.C. Gringarten: „Deconvolution of Well Test Data as a Nonlinear Total Least Squares Problem“, SPE paper 71574, September 2001

20. T. von Schroeter, Hollaender, F., Gringarten, A.C.: „Deconvolution of Well Test Data as a Nonlinear Total Least Squares Problem“, SPE paper 77688-

PA-P, SPE Journal, 2004 21. T.von Schroeter, Hollaender, F., Gringarten, A.C.: “Analysis of Well Test Data From Permanent Downhole Gauges by Deconvolution”, SPE paper

77688, September 2002


APPENDICES


APPENDIX A (Table of milestones in deconvolution of well test data)

SPE paper n° Year Title Authors Contribution

62920-MS 2000 Well Test Analysis in Gas-

Condensate Reservoirs

A.C. Gringarten, A. Al-Lamki, S.

Daungkaew, R. Mott,

T.M. Whittle

- First to use 3-region composite model to analyze gas condensate well tests.

- First well test evidence in the literature of the

existence of the velocity stripping zone. - Identification that phase redistribution during the

build-up’s and drawdown’s in the gas condensate

wells is a significant problem in analyzing the data.

71588-MS 2001

Evaluation of a Horizontal Gas-

Condensate Well Using Numerical

Pressure Transient Analysis

R.A. Harisch, R.C.

Bachman, P.J. Puchyr,

G.W. Strashok

- Analysis of well test in horizontal gas condensate

well using numerical analysis well test software

instead of using analytical techniques because of complex PVT behaviour of gas condensate system.

- For this well test, multiphase effects appeared to

have minimal impact on the pressure response of the system. Instead, horizontal well fluid flow regimes,

driven by reservoir permeability and geometry,

appeared dominant.

71574-MS 2001

Deconvolution of Well Test Data as

a Nonlinear Total Least Squares Problem

Thomas von Schroeter, Florian

Hollaender, Alain C.

Gringarten

- First to introduction a new method which 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-MS 2002

Analysis of Well Test Data From

Permanent Downhole Gauges by Deconvolution

Thomas von Schroeter, Florian

Hollaender, Alain C.

Gringarten

- Improvement of nonlinear TLS method.

Regularization by curvature – technique which allows

the user to control the degree of smoothness while avoiding the flattening of the slopes associated with

derivative regularization.

84290-MS 2003

Practical Application of Pressure-

Rate Deconvolution to Analysis of

Real Well Tests

Michael M. Levitan

- Schroeter’s algorithm fails when used with

inconsistent data. Enhancement of the Schroeter’s deconvolution algorithm that allows it to be used

reliably with real test data.

90680-MS 2004

Practical Considerations for

Pressure-Rate Deconvolution of

Well Test Data

Michael M. Levitan,

Gary E. Crawford,

Andrew Hardwick

- Providing of recommendations how to produce correct deconvolution results.

- Deconvolution requires a good estimate of initial

reservoir pressure. Paper presents how to recover the

initial reservoir pressure from well test data by use of

Deconvolution.

-Application of Deconvolution sequentially to individual build-ups.

89905-MS 2004

Well Test Analysis of Horizontal

wells in Gas-Condensate Reservoirs

Abdolnabi Hashemi,

Laurent M. Nicolas, Alain C. Gringarten

- Leadoff presentation of results detailing near-

wellbore effects in well tests of horizontal wells in gas condensate reservoirs below the dew point.

- Condensate deposition creates composite well test

behaviour similar to that obtained in vertical wells, but superimposed on a horizontal well behaviour.

93988-MS 2005

Analysis of an Extended Well Test

to Assess Connectivity Between

Adjacent Compartments in a North Sea reservoir

A.C. Gringarten

First points out an important issue: Duration of the

extended well test and with it associated costs can be

reduced by analyzing the well test data by deconvolution.

100993-MS 2006 Well Test Analysis in Lean Gas Condensate Reservoirs: Theory and

Practice

A.C. Gringarten, M.

Bozorgzadeh, S.

Daungkaew, and A. Hashemi

- Detailed description of challenges in well test

analysis in gas condensate wells and how to overcome those using tools such as the deconvolution. More

than 20 different gas condensate reservoirs are

analyzed with presented results!

100250 2006

Integration of Well Test Deconvolution Analysis and

Detailed Reservoir Modelling in 3D Seismic Data Interpretation: A

Case Study

C. Amudo, J. Turner,

J. Frewin, T.C. Kgogo, A.C. Gringarten

- Paper demonstrates the result of deconvolution analysis on the wells E-M01P and E-M02Pa of the E-

M field, namely, that all the mapped faults in the field are sealing and that additional two vertical sub-

seismic faults have been found.

102079-MS 2006

From straight lines to

deconvolution: the evolution of the

state-of-the art in well test analysis

A.C. Gringarten

- The detailed evolution review of well test analysis

techniques over the last half-century where the deconvolution as a new tool takes an important part in

extracting the information from well test data.

- Field examples are given when the deconvolved derivative showed reservoir behaviour different to

that indicated by conventional derivative analysis.


134534-MS 2010 Practical Use of Well-Test

Deconvolution A.C. Gringarten

- Variety of practical applications of deconvolution is

presented such as correction of erroneous rates from DST’s, identification of recharge from reservoir

layers and compartmentalization - features which

conventional well test analysis could not provide.


APPENDIX B (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 a deconvolution method in well testing:

New formulation of deconvolution method as the logarithm of the reservoir response function. This formulation is

based on nonlinear encoding and known as nonlinear Total Least Squares (TLS) problem in the numerical analysis

literature.

New error model is presented, which takes into account errors in pressure and rate data

Derivative can be regularized by controlling the weight (ν) and the regularization (λ) parameters

Objective of the paper:

To introduce a new algorithm to deconvolve pressure and flow rate data in well testing; to show its advantages

compared to methods presented in the past and its application.

Methodology used:

Encoding of reservoir response function in a more natural way compared to encoding method, which uses sign

constraints. Consequently, no sign constraints are used, which makes the deconvolution problem nonlinear.

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:

This method allows to deconvolve simulated and field pressure and rate data (chosen in this paper), with errors in rate

measurements up to 10%, resulting in smooth, interpretable derivatives. However, to achieve these results, λ and ν

should be selected carefully.

Moreover, in comparison to conventional well test analysis, the presented deconvolution method, applied to selected

data in this paper, extends the interpretable time by a factor of 2.

Comments:

Significant improvement of an error model, which accounts for uncertainties not only in pressure, but also in rate

data, which is usually much less accurately measured.


SPE: 77688-MS (2002)

“Analysis of well test data from permanent downhole gauges by deconvolution”



This paper is a first paper which presents a method to give estimates for bias and confidence intervals of the

parameters


Demonstration of improvements of deconvolution algorithm presented in SPE paper 71574-MS.

Illustration of its application to simulated data and two large sets of real field data with up to 6000 hours of pressure

data and up to 450 flow periods

To show the direct comparison of deconvolution analysis with derivative analysis

Methodology used:

In contrast to previous SPE paper 71574, assumption is made that the initial reservoir pressure is known

Modification of the original error weight (ν) by its multiplication with factor "𝑁/𝑚" in order to balance the effect of

significant differing sample sizes for pressure drop and derivative

Modification of the error measure model of deconvolution algorithm: now the third term represents a measure of the

average curvature of the graph

Conclusion reached:

Regularization is required to impose conditions on the solution (deconvolved derivative) to make it a physically

meaningful estimate of the response function. Smoothing and positivity are the effects of regularization.

Regularization by curvature allows the user to control the degree of smoothness avoiding the flattening of slopes

associated with derivative regularization.

In contrast to derivative analysis, deconvolution does not suffer from any bias due to implicit model assumptions.

Deconvolution has no restrictions in terms of the choice of pressure data window to be deconvolved.

Errors in rate and pressure measurements are well handled by deconvolution.

The selection criteria of error weight (ν) and regularization parameter (λ) remains as a very subjective one.

Comments:

There is no confidence in selecting the regularization parameter λ, which relates to the smoothness of the

deconvolved derivative. According to this paper, the only way to select λ correctly is given by looking at the result

and increasing λ to a value for which the response is just smooth enough to be interpretable without losing its

dominant features.


SPE: 84290-MS (2003)

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

Authors: Michael M. Levitan


In this paper the evaluation of algorithm, which was presented in SPE paper 71574-MS, shows that this algorithm

works well on consistent sets of pressure and rate data. However, the algorithm does not work well or even fails when

applied on inconsistent data set. Inconsistency is given by skin factor or wellbore storage changing with time.


Performance evaluation and identification of possible limitations of deconvolution logarithm (called Schroeter

algorithm in this paper) using novel ideas of this logarithm, but different code.

Demonstration of Schroeters algorithm enhancements which would allow using it reliably on well test data with

inconsistencies.

Methodology used:

Code validation of deconvolution algorithm on both consistent simulated test data and inconsistent simulated test

data. Deconvolution of individual build-ups and deconvolution of entire test sequence was performed to show the

limitations of this algorithm.

Demonstration of results obtained while application of deconvolution algorithm on several real tests.

Conclusion reached:

Schroeters deconvolution algorithm works well on the test pressure and rate data that are consistent, and fails when

used with inconsistent data.

Schroeters deconvolution algorithm only works well with inconsistent data if it is applied on pressure data from only

one single flow period.

However, the pressure data from a single flow period do not contain enough information to identify initial reservoir

pressure and to correct rates. Comparison of deconvolved responses obtained by deconvolution of pressure data from

several flow periods is necessary to identify initial reservoir pressure and model parameters.

In comparison to conventional well test analysis, deconvolution analysis increases the interpretable time significantly

(in this paper maximum by a factor of 17). Thus, one can extract more information from well test data than it would

be possible by using conventional well test analysis methods.

Particularly in this paper deconvolution analysis detected a closed reservoir behavior.


SPE: 77688-PA-P (SPE Journal, 2004)

„ Deconvolution of well test data as a nonlinear total least squares problem”



Deconvolution method, described in SPE papers 71574-MS and 77688-MS, as the logarithm of the reservoir response

function instead of the rate-normalized pressure derivative itself, is presented in more detail providing additional

explanations and definitions. This method is based on nonlinear encoding and known as nonlinear Total Least

Squares (TLS) problem in the numerical analysis literature.


Presentation of deconvolution as a regularized, nonlinear TLS formulation.

Application of deconvolution algorithm on a simulated data set to demonstrate the effect of varying levels of

regularization on the confidence intervals

Application of deconvolution to a large real field example to show the direct comparison of deconvolution analysis

with derivative analysis.

Methodology used:

Deconvolution is performed using a time-domain approach. Instead of numerically unstable explicit encoding, the

implicit constraint encoding is used. The solution of deconvolution - deconvolved derivative - is forced to be positive.

Error model is used, which takes into account error in measured rates (δ), error in measured pressure (ε) and error in a

measure of the average curvature of the deconvolved graphed derivative (𝐷𝑧 − 𝑘).

The smoothness of deconvolved derivative is controlled by regularization parameter λ

Conclusion reached:

Deconvolution is able to extract the correct late-time behavior already from the earlier build-up data.

In addition to conclusions drawn in the previous two SPE papers the authors point out that deconvolution must be

used with caution in situations when the reservoir behavior undergoes major changes during the test duration. Such

situations are changing skin due to transport of solid particles into or out of the zone around the wellbore, changing

wellbore storage due to phase redistribution in the well, liquid build-up around the wellbore during drawdowns in gas

condensate reservoirs and water invasion.

Derivative regularization, performed by changing regularization parameter λ, introduces bias. According to authors, λ

should be chosen as high as possible without generating visible bias. It means that the increasing of λ should be

stopped once the deconvolved derivative looks smooth enough to be interpretable, and before its dominant features

begin to flatten out.

Comments:

Selection of error weight ν and especially of regularization parameter λ remains subjective.


SPE 90680-MS (2004)

“Practical considerations for pressure-rate deconvolution of well test data”

Authors: Michael M. Levitan, Gary E. Crawford, Andrew Hardwick


Deconvolution method discussed by von Schroeter, Hollaender and Gringarten is a base of deconvolution algorithm

used by Levitan.

The deconvolution algorithm in the form described by Levitan in SPE paper 84290 in 2003 has been implemented in

the well test analysis software

Reliability of deconvolution is underlined by application of deconvolution on real test data and showing consistent

results


To identify and to discuss specific issues one has to be aware of when using deconvolution of pressure and rate data

in well testing; to provide practical considerations and recommendations on how to produce correct deconvolution

results.

Demonstration of reliable use of deconvolution applied on several pressure and rate test data.

Methodology used:

In this paper deconvolution algorithm is used which reconstructs the pressure response to constant rate production

along with its log-derivative. In contrast, the original algorithm by von Schroeter, Hollaender and Gringarten

reconstructs only the logarithm of log-derivative of the pressure response to constant rate production.

Deconvolution algorithm is applied on simulated oil well test data and on real gas well test data.

Conclusion reached:

The pressure-rate deconvolution is not replacement of conventional well test techniques but a useful addition to the

suite of tools used in well test analysis.

Before application of deconvolution on well test data following has to be considered:

- The start and the end of a flow period in the test rate data should be synchronized with pressure data

- Pressure data affected by phenomena other than fluid flow in the reservoir (e.g. fluid segregation in the wellbore)

must be removed

- Only consistent and of good quality pressure data should be used for deconvolution

Deconvolved derivative is sensitive to the value of initial reservoir pressure. A wrong value of initial pressure used in

deconvolution would cause distortions in the deconvolved derivative at late time and falsify the actual reservoir

behavior

Initial reservoir pressure can be estimated by comparison of deconvolved derivatives of several build-ups which

should merge at late times.

The duration of pressure build-up does have an effect on the accuracy of a constant rate drawdown response

reconstruction when deconvolution is applied to individual build-up data. The accuracy of reconstruction is much

better for longer pressure build-up periods.

Correct reconstruction of constant-rate drawdown pressure response requires accurate representation of the well rate

history or correct simplification of rate history in pressure-rate deconvolution.


SPE 100250 (2006)

“Integration of well test deconvolution analysis and detailed reservoir modelling in 3D seismic data interpretation: a

case study”

Authors: C. Amudo, J. Turner, J. Frewin, T.C. Kgogo, A.C. Gringarten

Contribution to the understanding of a deconvolution method in well testing (in particular with respect to E-M field located

offshore in South Africa):

Deconvolution as an advanced well test analysis tool is successfully applied in oil and gas industry. It is used in

combination with seismic data interpretation and reservoir modeling to solve existing problems.


One of the objective of this paper is to demonstrate how deconvolution analysis can contribute to a solution of a given

problem, namely to describe the reservoir compartmentalization in the E-M filed.

Another objective of this paper is to present the process of deconvolution analysis and to demonstrate this process by

application of deconvolution on real test data.

Methodology used:

Deconvolution was applied on well test data from two gas condensate wells EM-01P and E-M02Pa

Using different initial pressures individual build-up data as well as all flow periods were deconvolved

Verification of deconvolution by comparing adapted rates with measured rates, and pseudo-pressures convolved from

the deconvolved derivatives with adapted rates with those derived from actual data

Unit-rate pressure drawdowns for different initial reservoir pressures were analyzed and corresponding well test

interpretation models from characteristic flow regimes identified

The determined model was applied to the measured pressure data with adapted rates - rates, which have been

corrected while deconvolution process

Conclusion reached:

Deconvolution analysis identified a sub-seismic boundary between wells E-M01P and E-M02Pa. This sub-seismic

fault was not evident on the seismic data.

Together with an integrated petroleum engineering study deconvolution helped to propose a new structural and

stratigraphic model of the field and, thus, to explain the historical production performance of the E-M reservoir

structure.

Comments:

In presented deconvolution analysis there is an uncertainty on the determination of the initial reservoir pressure.

Apparently, deconvolution could not provide the confidence in the initial reservoir pressure value. In addition, there is

no information given, how the author chose two values of initial reservoir pressure.


SPE 102079-MS (2006)

“From straight lines to deconvolution: the evolution of the state-of-the art in well test analysis”

Authors: A.C. Gringarten


In comparison to existing well test analysis methods deconvolution is presented as the best method to identify a well

test interpretation method. Its verification is as good as that of pressure derivative analysis method.


To position deconvolution within the existing well test analysis techniques and emphasize its recent breakthrough.

To demonstrate the results obtained during application of deconvolution on real well test data

Methodology used:

(1)Deconvolution is applied to a single exploration and to a single production build-up between those no further

pressure data is measured, but rates are available.

(2)Deconvolution is applied to an extended test, which includes a series of drawdowns and build-ups

(3) Deconvolution is applied on gas well test data

Conclusion reached:

(1)Deconvolution allows to close the gap between two build-ups and represent the reservoir behavior

(2) In comparison to conventional well test analysis deconvolution shows the complete reservoir behavior with only

first 5 weeks of data instead of 10 ½ months of data.

(3) Deconvolution helps to identify the actual reservoir behavior contradictory to that suggested during conventional

well test analysis.

Comments:

The author underlines that deconvolution has to be used carefully, with understanding. Deconvolution control

parameters must be adjusted by the user. For example, smoothing of derivative requires to change regularization

parameter λ in order to eliminate small-scale oscillations, but at the same time the actual reservoir features should not

be falsified. Thus, deconvolution requires necessary knowledge from the user.


SPE 134534-MS (2010)

“Practical use of well-test deconvolution”

Authors: A.C. Gringarten


Deconvolution as a powerful tool in well test analysis has approved to have advantages over conventional well test

analysis in identification of boundaries and connectivities. In this paper, through deconvolution analysis, a multilayer

behavior in a gas condensate well was identified. In addition, deconvolution allows correction of the errors in rate

measurements rates and determination of missing rates.


To encourage well test interpreters to use deconvolution confidently as a well test analysis tool

To give recommendations on how to perform deconvolution and how to verify deconvolution results

Illustration of various deconvolution applications in well tests of short and long durations

Methodology used:

Deconvolution of well test data from a gas condensate reservoir is applied to individual DST build-ups, build-ups

during production phase, groups of build-ups and continuous multi-flow periods & final unit-rate pressure drawdown

analysis.

Deconvolution of oil well test data with erroneous rates. Deconvolution is applied on two main build-ups and on

entire pressure history.

Deconvolution of DST data in an oil well. Comparison of pressure histories calculated from the deconvolved

derivatives, with and without rate adaptation, with actual pressure history.

Conclusion reached:

Two major benefits of deconvolution presented in this paper are: 1) Deconvolution increases the radius of

investigation, which allows seeing boundaries and connectivities not visible in individual flow periods and 2)

Deconvolution corrects erroneous rates and determines missing rates. Both benefits require application of

deconvolution to entire pressure history sequences - including build-up and drawdown data.

Deconvolution cannot distinguish an error in rate from a change in skin factor

In addition to linear systems deconvolution can be applied to pseudo-linear systems such as with gas and multiphase

flow.

Deconvolution must be validated by verifying that the pressure history calculated from the deconvolved derivative

can closely reproduce the actual pressure data.


APPENDIX C (Practical application of deconvolution in the past)

This section concerns the application of deconvolution especially in the early stage of its development when new

deconvolution algorithm was developed and could already provide noticeable results.

In 2001 von Schroeter, Hollaender and Gringarten adopted the novel deconvolution algorithm on simulated and real well

test data. Data with errors in rate measurements up to 10% was deconvolved successfully resulting in smooth, interpretable

derivatives. In 2002 deconvolution algorithm was modified and again tested on simulated and field data. In both published

papers the authors used initial reservoir pressure as a well known input value. In contrast, in this study deconvolution considers

initial reservoir pressure as an unknown parameter, which is to identify through the deconvolution process. In addition, the

authors pointed out that the selection of error weight ν and regularization parameter λ is very subjective4. Specifically, there is

no criterion given for selection of λ, which relates to smoothness of the deconvolved derivative. The only way to select λ

correctly is given by looking at the result and increasing λ to a value for which the response is just smooth enough to be

interpretable without losing its dominant features. On the other hand, when λ is selected too high, the deconvolved derivative

becomes too stiff, thereby altering one or another reservoir feature. In the present study this issue is noted as well and, thus,

concerned carefully.

In December 2004 von Schroeter, Hollaender and Gringarten published an updated version of deconvolution algorithm as a

nonlinear TLS problem in SPE Journal [20]. They applied deconvolution to simulated and real well test data. Deconvolved

derivatives were compared with derivatives obtained by conventional well test analysis. Both analyses provided very similar

derivative shapes. In addition, one has identified that deconvolution could extract the correct late-time behavior already from

the earlier build-up data. Additionally they indicated that deconvolution should be used with particular caution in situations

when the reservoir behavior undergoes major changes over the duration of the test. Such situations can be the changing skin

due to transport of solid particles into or out of the zone or changing wellbore storage due to phase redistribution in the well.

At the same time the authors refer to Michael M. Levitan - another contributor to deconvolution problem in well test analysis,

who suggested different strategies to deal with these situations.

In 2003 Levitan evaluated deconvolution algorithm proposed by von Schroeter at al [14]. He identified its shortcomings

and suggested modifications. Levitan observed that the algorithm worked well only with consistent sets of pressure and rate

data. However, the algorithm did not work well or even failed when applied to inconsistent data set. Inconsistency is given by

a skin factor or wellbore storage changing with time. Levitan states that von Schroeter’s algorithm is developed for Eq. (1).

This equation is only valid for consistent data sets - for instance, data with constant wellbore storage coefficient and constant

pressure drop due to skin. If wellbore storage coefficient and/or pressure drop due to skin change during the well test period,

then the data becomes inconsistent for (1). Therefore, an identified interpretation model would be a false model for the

analyzed well test data in this case. He tested the algorithm on stimulated data by deconvolving all flow periods in one sweep

1) for pressure data with constant wellbore storage coefficient and 2) for pressure data with different values of wellbore

storage coefficient. The latter deconvolution failed to reproduce correct deconvolved derivative, especially at late times

inconsistencies with the actual model have been observed. Nevertheless, Schroeter’s deconvolution algorithm can work well

with inconsistent data if it is applied to pressure data only from one single flow period, since it will consider only one value of

wellbore storage or skin pressure drop. Alternatively the logarithm can also be adapted to successively increasing portions of

the data. However, in doing so the pressure match between the convolved and measured pressure as well as the rate match

between the adapted and measured rates should be monitored.

In contrast to previously discussed publications, Levitan pursues the question of how to extract initial reservoir pressure

from deconvolution analysis. He underlines that the pressure data from a single flow period does not contain enough

information to identify initial reservoir pressure and to correct the measured rates. Comparison of deconvolved responses

obtained by deconvolution of pressure data from individual flow periods is necessary to identify initial reservoir pressure and

model parameters. In his further publication [13] he states that initial reservoir pressure can be estimated by comparison of

deconvolved derivatives of individual build-ups which should merge at late times.

In 2004 Michael M. Levitan, Gary E. Crawford and Andrew Hardwick published a SPE paper [13] which concerns

practical consideration of pressure-rate deconvolution of well test data. This work significantly contributes to the

understanding of practical aspects associated with deconvolution. Whilst previous publications focused mainly on derivation

of deconvolution formulation, its foundation and counterstatement to conventional well test analysis, this paper identifies and

discusses specific issues one has to be aware of when using deconvolution of pressure and rate data in well testing. The

authors also indicate what to consider prior to starting to deconvolve the available data. In conclusion, Levitan describes

deconvolution as a very useful addition to the suite of tools used in well test analysis, but not a replacement of conventional

well test techniques.

4 The exception is the use of default λ values which are working well while deconvolution of individual flow periods.


A number of practical applications of deconvolution followed the above described publications. In 2006 C. Amudo, J.

Turner, J. Frewin, T.C. Kgogo, and A.C. Gringarten [1] applied deconvolution to pressure and rate data acquired in lean gas

condensate wells and identified a sub-seismic boundary between two wells which was not evident on the seismic data.

In the same year A.C. Gringarten [7] positioned deconvolution within the existing well test analysis techniques as the best

method to identify a well test interpretation method, and, therewith emphasized its recent breakthrough.

Recently, in 2010, A.C. Gringarten in his publication “Practical use of well test deconvolution” [8] encourages the well test

interpreters to use deconvolution as a powerful tool in well test analysis which approved to have advantages over conventional

well test analysis in identification of reservoir boundaries and connectivities.


APPENDIX D (Zones encountered while drilling the wells)

Zone Top

(mTVDSS)

Bottom

(mTVDSS)

Net pay

thickness (m) Description

Zone 1 2458 2487.7 13.9 This interval is characterized by sandstone and argillaceous interbeds.

Bounded by 1At1.

Zone

2B 2487.7 2521 26

Upper Shallow Marine (USM) sandstone with thin claystone and siltstone

interbeds occurring intermittently throughout and with significant pebbly

intervals. The sandstones are tight to moderately porous, sorted, slightly

glauconitic to glauconitic in places. Zone

2A 2521 2562.2 37

Zone 3

Fluvio-deltaic/shallow marine. An interbedded interval of non-glauconitic

sandstone and shale with net to gross in the region of 66% and porosity of

13%.

Zone 4

Shallow marine. Very similar sandstones to Zone 2 with a net to gross of

90% and porosity of 14 %. The base of Zone 4 is marked by BUSM. Zone

4 has never been intersected above the GWC (gas water contact) in the E-

M field.


Table D-1: Zones encountered while drilling well E-M01P

Zone Top

(mTVDSS)

Bottom

(mTVDSS)

Average

thickness (m) Description

Zone 1 2386.5 2408.2 31 Non-reservoir. Claystone with minor interbedded siltstone and sandstone.

Bounded by 13At1 and 1At1 horizons.

Zone

2B 2408.2 2462 43

Upper Shallow Marine (USM) sandstone with significant pebbly intervals

and very minor shale interbeds and drapes. Main reservoir in the E-M field.

Zone

2A 2462 2552.7 64

Upper Shallow Marine (USM) sandstone. Targeting Zone: highest quality,

potentially most productive reservoir interval.

Zone 3 80



13%.

Zone 4 85



4 has never been intersected above the GWC in the E-M field.


Table D-2: Zones encountered while drilling well E-M02Pa

Zone Top

(mTVDSS)

Bottom

(mTVDSS)

Thickness

(m) Description

Zone 1 2492 2521 29 Non-reservoir. Claystone with minor interbedded siltstone and sandstone.

Bounded by 1At1.

Zone

2B 2521 2570 49

Early Cretaceous Shallow Marine sandstones with very rare claystone

partings. The sandstones are generally tight to porous, very fine to medium

grained, and occasionally extremely pebbly. Zone

2A 2570

Zone 3



13%.

Zone 4



4 has never been intersected above the GWC in the E-M field.


Table D-3: Zones encountered while drilling well E-M03P


APPENDIX E (Reported reservoir and well parameters)

Well E-M01P

The completed reservoir section indicates the presence of good porosity, high net to gross and clean sand. According to [17]

the gross wellbore length available to contribute to flow is 904 m of which around 800 m is estimated to be net sand. Over

this interval, the average porosity and net to gross ratio was estimated to be 13.4% and 88.1% respectively. Well test and

core data from the closest offset appraisal wells, give an estimate of average horizontal permeability in the range of 10 to 30

md. Initial reservoir pressure is reported to be 3723 psia at 2595 mTVDSS.

Well E-M02Pa

Well E-M02Pa penetrates both Zones 2A and 2B. According to petrophysical interpretation of the logged interval the gross

wellbore length available to contribute to flow is 1,265 m. According to well test interpretation results, presented in [15],

there is a low vertical transmissibility given. Since the sand quality within the zones and net to gross are very good, the

reason of poor transmissibility between Zones 2A and 2B might be the lower vertical permeability of shale interbeds.

Well E-M03P

The completed reservoir section indicates the presence of good quality gas bearing reservoir. According to [9] the average

porosity and net to gross ratio was estimated to be 14.3% and 82% respectively. Net water saturation is 20.5%. Initial

reservoir pressure is reported to be 3708.4 psia at 2595 mTVDSS. In another report, reservoir pressure is given as 3843 psia

at 2605 TVDSS. One of the main problems in early phase of this development well was unexpectedly high water rate (2500

bbl/day) during the initial clean-up and production test in Q2/2000. According to [16] the source of the produced water was

identified to be from a shallow horizon (13AT1 sands) that was produced via a poorly cemented 9 5/8’’ casing annulus. The

well was subsequently produced at a minimal rate during 2001 due to hydrate formation in the pipeline slug catcher, and salt

contamination in the MEG regenerator, which were attributed to the water production from well E-M03P. Finally, to recover

the existing completion and to evaluate the source of the water ingress, a workover from 9th August 2005 to 28th January

2006 was performed.

Table E-1: Additional information provided for each well [15,16,17]

Well Kh (md) Lw (m) �̅�Lw Entire horizontal length (m)

E-M01P 15 366-457 9300 904

E-M02PZ1 14-25 610-914 22000 1030

E-M03P 11 440 4800 490

Table E-2: Reported reservoir and well parameters according to [16]


APPENDIX F (Received pressure data for 3 E-M field development wells)

Well DST data Production data from until Gauge Depth

(mTVDSS)

from until Gauge Depth

(mTVDSS) E-M01P 06/11/99

14:00:00

12/11/99

01:00:00

2244

22/09/2000

00:00

30/04/2011

23:32

2244

E-M02Pa 05/12/20015

07:30:00

09/12/2001

03:59:55

2324

10/12/2001

00:00

06/04/2010

08:40

2398

E-M03P 02/06/2000

13:45:59

09/06/2000

02:45:00

2423.8

13/10/2000

00:00

30/04/2011

23:59

2425

and

2375 Table F-1: Received pressure data for 3 E-M field development wells

Pressure data correction and depth adjustment

Well E-M01P

DST and production pressure data is measured at different gauges. Production pressure data exhibit pressures higher than these

from DST. Consequently, DST data is adjusted to production data (Figure F-1).

Figure F-1: DST pressure data adjustment: green - first build-up in the production; red - original DST data; purple - adjusted DST data

Well E-M02Pa

DST and production pressure data is measured at different gauges. Both data is corrected to a mid-perforation depth of 2550

mTVDSS.

Well E-M03P

The DST pressure was measured at a depth of 2423.8 mTVDSS. In contrast, the pressure during production was measured at

2425m TVDSS in the pre-workover period and at 2375 mTVDSS in the post-workover period. Consequently, both DST and

production pressure data was corrected to a mid-perforation depth of 2550 mTVDSS. Correction of DST pressure data was +

41.4 psia, that of pre-workover data + 41.01 psia and that of post-workover data + 57.41 psia. Gradient of 0.1 psi/ft was

employed.

5 Note, at this time well E-M01P was on production at high rates for the duration of the test. Thus, the quality of the DST build-ups (as obtained later) was

interfered with production of well E-M01P.

3300

3400

3500

3600

3700

3800

3900

8000 9000 10000 11000

Pre

ssure

(psia

)

Elapsed time (hrs)

Pressure History Comparison


APPENDIX G (Pressure and rate histories for three E-M-Field development wells)

Figure G-1: Well E-M01P - pressure and rate history

Figure G-2: Well E-M01P - DST Data


Figure G-3: Well E-M02Pa - pressure and rate history

Figure G-4: Well E-M02Pa - DST Data


Figure G-5: Well E-M03P - pressure and rate history

Figure G-6: Well E-M03Pa - DST Data


APPENDIX H (Log-log rate validation & superposition plots)

Figure H-1: Well E-M01P - log-log rate validation plot

Figure H-2 represents a superposition plot for the entire pressure and rate history. No boundaries are identified during DST

build-ups as well as during the first build-up (FP 117) of the production period. In contrast, all subsequent flow periods clearly

indicate depletion and existence of boundaries. The flow period annotation is the same as in the Figure H-1 above.

Figure H-2: Well E-M01P - superposition plot


Figure H-3: Well E-M02Pa - log-log rate validation plot, normalized to flow period 19: DST build-ups 5, 15 and 19

Derivatives of DST build-ups exhibit initial unit slope straight line indicating wellbore storage and early radial flow

stabilization corresponding to √𝑘𝑥𝑦𝑘𝑧𝐿 in a horizontal well. Instead of a half-unit slope, which would follow the first

stabilization in a horizontal well, the derivatives show downward trend. That trend could be due to partial penetration of the

reservoir, interference due to production of well E-M01P or insufficient effective wellbore length (less than the length of the

formation). In addition, the derivatives of build-ups 15 and 19 show an indication of condensate bank stabilization. However,

in contrast to well E-M03P (see further content of Appendix H), there is no justification for condensate bank build-up. First of

all there is no consistency with the higher skin value of pressure corresponding to build-up 5. Furthermore, the pressure during

DST is higher than the reported dew point pressure of 3465 psia (measured in well E-M02PZ1).

Figure H-4: Well EM02Pa - log-log rate validation plot, normalized to flow period 19: useful build-ups up to build-up 290

Figure H-4 indicates higher radial flow stabilization (in comparison to that obtained during DST build-ups) for build-ups in the

first two years of production. In addition, increasing condensate bank stabilization is observed. The increasing skin values of

pressures corresponding to different flow periods confirm this. Consequently, FP 290 exhibits the highest condensate bank

stabilization with the highest skin value. Furthermore, derivative of FP 290 shows a half-unit slope straight line indicating

linear flow in a horizontal flow.

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000 10000

Rate

No

rma

lised

nm

(p)

Ch

ang

e a

nd D

eriva

tive (

psi)

Elapsed time (hrs)


nm(p) ChangeDerivativeRate Normalised nm(p) Change Flow Period 5Rate Normalised Derivative Flow Period 5Rate Normalised nm(p) Change Flow Period 15Rate Normalised Derivative Flow Period 15Rate Normalised nm(p) Change Flow Period 47Rate Normalised Derivative Flow Period 47Rate Normalised nm(p) Change Flow Period 147Rate Normalised Derivative Flow Period 147Rate Normalised nm(p) Change Flow Period 268Rate Normalised Derivative Flow Period 268Rate Normalised nm(p) Change Flow Period 290Rate Normalised Derivative Flow Period 290

Radial flow

stabilization

Slope 1/2

Changing condensate

bank stabilization


Figure H-5: Well EM03P - log-log rate validation plot, normalized to FP 224

Derivatives of DST build-ups (FP 11, 16, 18, 20) exhibit three successive flow regimes: 1) the first early radial

(cylindrical) flow stabilization corresponding to √𝑘𝑥𝑦𝑘𝑧𝐿, 2) linear flow in a horizontal flow and 3) pseudo-radial flow

stabiliation corresponding to 𝑘𝑥𝑦ℎ. In addition, since this is a gas condensate well, there is indication of potential condensate

bank stabilization between 0.3 and 1 hour. Two facts support that: higher skin value noted on pressure of flow period 20, and

the pressure during DST is below the reported dew point pressure of 3560 psia.

Figure H-6: Well EM03P (pre-workover)- log-log rate validation plot, normalized to FP 224

0.001

0.01

0.1

1

10

100

1000

0.01 0.1 1 10 100 1000 10000

Ra

te N

orm

alis

ed

nm

(p)

Ch

an

ge

and

Deriva

tive

(p

si)

Elapsed time (hrs)



0.001

0.01

0.1

1

10

100

1000

0.01 0.1 1 10 100 1000 10000

Rate

Norm

alis

ed n

m(p

) C

hange a

nd D

erivative (

psi)

Elapsed time (hrs)



FP 224

DST build-ups BU 47 - first build-up of the

production period


Figure H-7: Well EM03P (post-workover) - log-log rate validation plot, normalized to FP 224

Both plots show inconsistencies in rates: Derivatives of individual flow periods are not on top of each other as it would be

the case for consistent rates. Also note that pre-workover period is influenced by water loading as discussed in the beginning

of this work. It makes the interpretation and analysis of data corresponding to this period of time more difficult.

Figure H-8: Well E-M03P - superposition plot

Inspection of Figure H-8 suggests no boundaries are observed during DST build-ups on the superposition plot. In contrast, all

subsequent build-ups show evidence of depletion and thus the existence of boundaries.

1

10

100

1000

10000

0.01 0.1 1 10 100 1000 10000

Ra

te N

orm

alise

d n

m(p

) C

ha

ng

e a

nd

De

riva

tive

(p

si)

Elapsed time (hrs)


1

10

100

1000

10000

0.01 0.1 1 10 100 1000 10000

Rate

No

rma

lised

nm

(p)

Ch

ang

e a

nd D

eriva

tive (

psi)

Elapsed time (hrs)


DerivativeRate Normalised Derivative Flow Period 246Rate Normalised Derivative Flow Period 252Rate Normalised Derivative Flow Period 260Rate Normalised Derivative Flow Period 414nm(p) ChangeRate Normalised nm(p) Change Flow Period 246Rate Normalised nm(p) Change Flow Period 252Rate Normalised nm(p) Change Flow Period 260Rate Normalised nm(p) Change Flow Period 414Rate Normalised nm(p) Change Flow Period 419Rate Normalised Derivative Flow Period 419Rate Normalised nm(p) Change Flow Period 457Rate Normalised Derivative Flow Period 457Rate Normalised nm(p) Change Flow Period 201Rate Normalised Derivative Flow Period 201Rate Normalised nm(p) Change Flow Period 192Rate Normalised Derivative Flow Period 192Rate Normalised nm(p) Change Flow Period 186Rate Normalised Derivative Flow Period 186

0

1000

2000

3000

4000

20 30 40 50 60 70 80 90 100 110 120

Pre

ssure

(psia

)



DST build-ups


0.01

0.1

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100

0.001 0.01 0.1 1 10 100 1000 10000 100000

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ali

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decon

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n(p

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/MM

scf/

D

Elapsed Time hrs

#(1-878)[101]{1.67087E+04}3798.00#(1-878)[91]{2.25234E+04}3798.00#(1-878)[68]{9.05391E+03}3798.00#(1-878)[51]{6.44822E+03}3798.00516891101#(1-878)[418]{2.13106E+06}3798.00

APPENDIX I (Deconvolution of well test data from each well)

Figure I-1: Determination of initial reservoir pressure in well E-M01P through comparison of deconvolved derivatives of DST build-ups

Figure I-2: Well E-M01P - deconvolution of FP 166

0.05

0.5

5

0.001 0.01 0.1 1 10 100 1000 10000 100000Norm

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Elapsed Time hrs

5191101166#(1-878)[51,68,91,101]{1.54751E+06}3798.00#(1-878)[51,68,91,101,166]{5.47862E+05}3798.00

Slope 1/2


Increa

se in

interp

retab

le time


0.05

0.5

5

50

0.001 0.01 0.1 1 10 100 1000 10000 100000

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Elapsed Time hrs

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91

101

166

200

#(1-878)[51,68,91,101]{1.54751E+06}3798.00

#(1-878)[51,68,91,101,166,200]{2.05458E+06}3798.00


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50

0.001 0.01 0.1 1 10 100 1000 10000 100000

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418

51

#(1-878)[51,68,91,101,200,294,418]{7.16729E+05}3798.0035000 hrs

4090 hrs

Slope 1

Slope 1/2

Slope 1/2

Transition between

Slope 1/2 and Slope 1


Figure I-6: Well E-M02P - deconvolution of flow periods corresponding to production time period between 100 and 21200 hours

0.001

0.01

0.1

1

10

100

0.001 0.01 0.1 1 10 100 1000 10000 100000

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5 1994 #(1-873)[147]{2.62045E+05}3696.75#(1-873)[5,15,19]{6.40522E+03}3696.75 147#(1-873)[15,19,94,147,277,290]{4.44809E+06}3696.75 #(1-873)[5,15,19-290]{7.40872E+06}3696.75#(1-873)[15,19,94,147,290,301]{3.69600E+06}3696.75 #(1-873)[15,19,94,147,290,318]{8.06312E+06}3696.75#(1-873)[15,19,94,147,290,351]{3.69526E+06}3696.75 #(1-873)[15,19,94,147,290,330]{3.70269E+06}3696.75

Figure I-5: Well E-M01P - deconvolution of flow periods during production phase 2

0.005

0.05

0.5

5

50

500

5000

0.001 0.01 0.1 1 10 100 1000 10000 100000

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#(1-878)[51,68,91,101,200,418,581,613]{1.58839E+07}3798.00

#(1-878)[51,68,91,101,200,418,581,709]{1.65092E+07}3798.00

#(1-878)[51,68,91,101,200,418,581,709,813]{8.75717E+06}3798.00

#(1-878)[51,68,91,101,200,418,581,826]{7.61693E+06}3798.00

#(1-878)[51,68,91,101,200,294,418]{7.16729E+05}3798.00

Slope 1

Change of

slope


Figure I-7: Well E-M02P - deconvolution of flow periods (mostly series of build-ups) corresponding to production time period between 100 and 73100 hours

Figure I-8: Well E-M02Pa - deconvolution of flow periods (mostly DST’s with individual build-up) corresponding to production time period between 100 and 73100 hrs

0.001

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000 10000 100000

Norm

ali

zed

decon

volv

ed m

n(p

) d

eriv

ati

ve,

psi

/MM

scf/

D

Elapsed Time hrs

5 1994 #(1-873)[147]{2.62045E+05}3696.75#(1-873)[5,15,19]{6.40522E+03}3696.75 147#(1-873)[15,19,94,147,277,290]{4.44809E+06}3696.75 #(1-873)[5,15,19-290]{7.40872E+06}3696.75#(1-873)[15,19,94,147,290,318]{8.06312E+06}3696.75 #(1-873)[15,19,94,147,290,318,546]{1.16694E+06}3696.75#(1-873)[15,19,147,290,747]{1.29883E+06}3696.75 #(1-873)[5,15,19-546]{1.70216E+07}3696.75#(1-873)[15,19,147,290,754]{1.21444E+06}3696.75 #(1-873)[15,19,147,290,785]{2.04063E+06}3696.75#(1-873)[15,19,147,290,833]{2.06759E+06}3696.75

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000 10000 100000

Norm

ali

zed

decon

volv

ed m

n(p

) d

eriv

ati

ve,

psi

/MM

scf/

D

Elapsed Time hrs

#(1-873)[5,15,19]{6.40522E+03}3696.75 #(1-873)[15,19,94]{8.97555E+05}3696.75#(1-873)[15,19,147]{1.31370E+06}3696.75 #(1-873)[5,15,19,301]{1.99518E+06}3696.75#(1-873)[5,15,19,318]{4.06776E+06}3696.75 #(1-873)[5,15,19,747]{2.28081E+06}3696.75#(1-873)[5,15,19,546]{2.42354E+06}3696.75 #(1-873)[5,15,19,754]{2.12876E+06}3696.75#(1-873)[5,15,19,776]{9.48392E+05}3696.75 #(1-873)[5,15,19,785]{3.18830E+06}3696.75#(1-873)[5,15,19,833]{3.23412E+06}3696.75 #(1-873)[5,15,19,290]{5.07269E+05}3696.75#(1-873)[5,15,19,277]{5.10320E+05}3696.75 #(1-873)[5,15,19-873]{2.37965E+07}3696.75#(1-873)[5,15,19-873]{2.38813E+08}3696.75 #(1-873)[19,785]{3.84821E+06}3696.75#(1-873)[19,747]{3.34043E+06}3696.75


Figure I-9: Well E-M03P - determination of initial reservoir pressure (3727 psia)

Figure I-9 shows derivatives deconvolved with different initial reservoir pressure values. Derivatives deconvolved with

incorrect initial pressure do not merge at late times.

Figure I-10: Well E-M03P - deconvolution of flow periods corresponding to pre-workover production period between 0 and 49700 hours (except flow period 224)

0.01

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000 10000 100000

Norm

ali

zed

decon

volv

ed m

n(p

) d

eriv

ati

ve,

psi

/MM

scf/

D

Elapsed Time hrs

#(1-578)[16]{4.91348E+03}3727.00 #(1-578)[20]{3.70287E+03}3727.00

#(1-578)[224]{1.38590E+06}3727.00 #(1-578)[186]{7.85268E+05}3727.00

#(1-578)[252]{2.22083E+06}3727.00 16

20 #(1-578)[16]{2.14889E+03}3700.00

#(1-578)[20]{1.57821E+03}3700.00 #(1-578)[16]{4.05674E+03}3720.00

#(1-578)[20]{3.01203E+03}3720.00 #(1-578)[224]{1.31841E+06}3700.00

#(1-578)[224]{1.39178E+06}3720.00

0.001

0.01

0.1

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000

Norm

ali

zed

decon

volv

ed m

n(p

) d

eriv

ati

ve,

psi

/MM

scf/

D

Elapsed Time hrs

16 20224 11#(1-578)[16]{4.91348E+03}3727.00 #(1-578)[20]{3.70287E+03}3727.00#(1-578)[224]{1.39649E+04}3727.00 #(1-578)[144]{4.20589E+05}3727.00#(1-578)[139]{5.98453E+05}3727.00 #(1-578)[16,20,80]{7.70741E+05}3727.00#(1-578)[16,20,94]{4.80577E+04}3727.00 #(1-578)[16,20,123]{4.59375E+06}3727.00#(1-578)[60]{8.92667E+05}3727.00


Figure I-11: Well E-M03P - deconvolution of flow periods corresponding to post-workover production period 1 between 49700 and 68000 hours

Figure I-12: Well E-M03P - deconvolution of flow periods corresponding to post-workover production period 2 between 68000 and 93000 hours

0.01

0.1

1

10

100

1000

10000

0.001 0.01 0.1 1 10 100 1000 10000 100000

Norm

ali

zed

decon

volv

ed m

n(p

) d

eriv

ati

ve,

psi

/MM

scf/

D

Elapsed Time hrs

16 20

224 #(1-578)[16]{4.91348E+03}3727.00

#(1-578)[20]{3.70287E+03}3727.00 #(1-578)[186]{7.85268E+05}3727.00

#(1-578)[252]{2.22083E+06}3727.00 #(1-578)[16,20,144]{2.42973E+05}3727.00

#(1-578)[16,20,201]{2.03332E+06}3727.00 #(1-578)[16,20,224]{5.04331E+05}3727.00

#(1-578)[260]{2.58609E+06}3727.00 #(1-578)[252]{2.22083E+06}3727.00

#(1-578)[11,16,20-252]{1.21874E+08}3727.00 #(1-578)[11,16,20-285]{1.05129E+08}3727.00

0.001

0.01

0.1

1

10

100

1000

10000

100000

0.001 0.01 0.1 1 10 100 1000 10000 100000

Norm

ali

zed

decon

volv

ed m

n(p

) d

eriv

ati

ve,

psi

/MM

scf/

D

Elapsed Time hrs

#(1-578)[16]{4.91348E+03}3727.00 #(1-578)[20]{3.70287E+03}3727.00

#(1-578)[186]{7.85268E+05}3727.00 #(1-578)[252]{2.22083E+06}3727.00

#(1-578)[16,20,144]{2.42973E+05}3727.00 #(1-578)[16,20,224]{5.04331E+05}3727.00

#(1-578)[252]{2.22083E+06}3727.00 #(1-578)[285]{3.07239E+06}3727.00

#(1-578)[16,20,224]{4.74498E+06}3727.00 #(1-578)[419]{3.83708E+06}3727.00

#(1-578)[513]{4.41171E+06}3727.00 #(1-578)[11,16,20-252]{1.21874E+08}3727.00

#(1-578)[414]{3.96719E+06}3727.00


Figure I-13: Well E-M03P - deconvolution of multi-flow periods

APPENDIX J (Pressure history matches)

Figure J-1: Well EM01P - pressure history match

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000 10000 100000

Norm

ali

zed

decon

volv

ed m

n(p

) d

eriv

ati

ve,

psi

/MM

scf/

D

Elapsed Time hrs

#(1-578)[11,16,20-252]{1.21874E+08}3727.00 #(1-578)[11,16,20-285]{1.05129E+08}3727.00

#(1-578)[11,16,20-414]{1.05376E+08}3727.00 #(1-578)[252-414]{7.96084E+07}3727.00

#(1-578)[11,16,20-578]{2.96979E+08}3727.00 #(1-578)[11,16,20-457]{8.72163E+07}3727.00

#(1-578)[252-419]{7.95907E+07}3727.00 #(1-578)[11,16,20-513]{2.81761E+08}3727.00

#(1-578)[419-513]{8.38767E+07}3727.00

0

1000

2000

3000

4000

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 110000

Pre

ssure

(psia

)

Elapsed time (hrs)






Figure J-2: Well EM02Pa - pressure history match

Figure J-3: Well EM03P - pressure history comparison

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

3400

3600

3800

0 10000 20000 30000 40000 50000 60000 70000 80000

Pre

ssure

(psia

)

Elapsed time (hrs)


0

1000

2000

3000

4000

0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000

Pre

ssu

re (

psia

)

Elapsed time (hrs)



Convolved pressure (1-873)[5,15,19-873]{1.00000E+09}3696.75






Figure J-4: Well EM-01P - difference in % between actual measured pressure data and convolved pressures

The difference for well EM01P is within 10% range (Figure J-4). Only at the end of production period there are higher

deviations observed. That is most highly due to inconsistencies in measured rates.

APPENDIX K (Rate history matches)

Figure K-1: Well EM01P - rate history match for deconvolved derivative (1-878)[51,68,91,101-878] {2.5E+08}3798.00

-20

-10

0

10

20

0.00 10000.00 20000.00 30000.00 40000.00 50000.00 60000.00 70000.00 80000.00 90000.00 100000.00

Dif

feren

ce in

%

Elapsed time, hrs

(1-878)[51,68,91,101-878] {2.50000E+08}3798(1-878)[51,68,91,101-878] {6.63682E+07}3798(1-596)[51,68,91,101-596]{2.50000E+08}3798

Adapted Rates

Measured Rates

Difference in %


Figure K-2: Well EM03P - Rate history match for deconvolved derivative (1-578)[11,16,20-578]{3.17653E+08}3727.00

APPENDIX L (Unit-rate pressure drawdown analysis results)

Figure L-1: Well E-M01P - Analysis 1 of unit-pressure drawdown convolved from deconvolved derivative

(1-878)[51,68,91,101-878]{2.5E+08}3798

0.001

0.01

0.1

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 1000000

nm

(p)

Change a

nd D

erivative (

psi)

Elapsed time (hrs)


0.001

0.01

0.1

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100 1000 10000 100000 1000000

nm

(p)

Change a

nd D

eri

vative (

psi)

Elapsed time (hrs)


2510

2520

2530

2540

2550

2560

2570

2580

2590

2600

2610

2620

2630

2640

-4 -3 -2 -1 0 1 2 3 4 5 6

Norm

alis

ed P

seudo P

ressure

(psia

)


Horner Analysis - Flow Period 2

2510

2520

2530

2540

2550

2560

2570

2580

2590

2600

2610

2620

2630

2640

-4 -3 -2 -1 0 1 2 3 4 5 6

Norm

alis

ed P

seudo P

ressure

(psia

)



3660

3670

3680

3690

3700

3710

3720

3730

3740

3750

3760

3770

3780

3790

3800

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

Pre

ssure

(psia

)

Elapsed time (Date)


Model

Uniform Flux Horizontal Well with C and S Homogeneous Rectangle

Results

(pav)i 3797.727 psia (pav)f 3688.367 psia pwf 3671.496 psia kh 418.2 mD.ft k(xy) 1.656 mD k(z) 5.346 mD L 650.53 m S(w) -2.15 S(c) -6.68 S(t) -6.81 Zw 13.51 m C 0.3422 bbl/psi Type top No Flow Type bot No Flow d1 503.945 m d2 1178.37 m d3 363.442 m d4 2083.08 m A 2.829 km2 Type d1 No Flow Type d2 No Flow Type d3 No Flow Type d4 No Flow Dp(S) -0.9155 psi



(1-878)[101,418]{1.63788E+06}3798


(1-878)[101,581]{2.11564E+06}3798

0.001

0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eriva

tive

(p

si)

Elapsed time (hrs)


0.001

0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eriva

tive

(p

si)

Elapsed time (hrs)


2570

2580

2590

2600

2610

2620

2630

2640

-4 -3 -2 -1 0 1 2 3 4 5

No

rma

lise

d P

se

ud

o P

ressu

re (

psia

)



2570

2580

2590

2600

2610

2620

2630

2640

-4 -3 -2 -1 0 1 2 3 4 5

No

rma

lise

d P

se

ud

o P

ressu

re (

psia

)



3730

3740

3750

3760

3770

3780

3790

3800

2000 2001 2002 2003

Pre

ssu

re (

psia

)

Elapsed time (Date)


Model


Results


0.001

0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Change a

nd D

erivative (

psi)

Elapsed time (hrs)


0.01

0.1

1

10

100

0.0001 0.01 1 100 10000 1000000

nm

(p)

Change a

nd D

erivative (

psi)

Elapsed time (hrs)


2560

2570

2580

2590

2600

2610

2620

2630

2640

-4 -3 -2 -1 0 1 2 3 4 5

Norm

alis

ed P

seudo P

ressure

(psia

)



2560

2570

2580

2590

2600

2610

2620

2630

2640

-4 -3 -2 -1 0 1 2 3 4 5

Norm

alis

ed P

seudo P

ressure

(psia

)



3710

3720

3730

3740

3750

3760

3770

3780

3790

3800

2000 2001 2002 2003 2004 2005 2006

Pre

ssure

(psia

)

Elapsed time (Date)


Model


Results




(1-878)[51,68,91,101-878]{2.5E+08}3798

Figure L-5: Well E-M02Pa - single layer analysis of unit-pressure drawdown convolved from deconvolved derivative

(1-873)[19,290]{6.07580E+05}3696.75

0.001

0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Change a

nd D

erivative (

psi)

Elapsed time (hrs)


0.001

0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Change a

nd D

erivative (

psi)

Elapsed time (hrs)


2500

2520

2540

2560

2580

2600

2620

2640

-4 -3 -2 -1 0 1 2 3 4 5 6

Norm

alis

ed P

seudo P

ressure

(psia

)



2500

2520

2540

2560

2580

2600

2620

2640

-4 -3 -2 -1 0 1 2 3 4 5 6

Norm

alis

ed P

seudo P

ressure

(psia

)



3660

3680

3700

3720

3740

3760

3780

3800

2001 2003 2005 2007 2009 2011

Pre

ssure

(psia

)

Elapsed time (Date)


Model


Results


0.01

0.1

1

10

100

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eri

va

tive

(p

si)

Elapsed time (hrs)


0.01

0.1

1

10

100

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eri

va

tive

(p

si)

Elapsed time (hrs)


2325

2330

2335

2340

2345

2350

-4 -3 -2 -1 0 1 2 3 4 5

No

rma

lise

d P

se

ud

o P

ressu

re (

psia

)



3675

3680

3685

3690

3695

3700

-4 -3 -2 -1 0 1 2 3 4 5

Pre

ssu

re (

psia

)



3675

3680

3685

3690

3695

3700

0 2000 4000 6000 8000 10000 12000 14000 16000

Pre

ssu

re (

psia

)

Elapsed time (hrs)


Model


Results




(1-873)[19,546]{2.93845E+06}3696.75


(1-873)[19,785]{3.84821E+06}3696.75

0.001

0.01

0.1

1

10

100

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eri

va

tive

(p

si)

Elapsed time (hrs)


0.001

0.01

0.1

1

10

100

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eri

va

tive

(p

si)

Elapsed time (hrs)


2310

2320

2330

2340

2350

-4 -3 -2 -1 0 1 2 3 4 5

No

rma

lise

d P

se

ud

o P

ressu

re (

psia

)



3660

3670

3680

3690

3700

-4 -3 -2 -1 0 1 2 3 4 5P

ressu

re (

psia

)



3660

3670

3680

3690

3700

0 10000 20000 30000 40000 50000

Pre

ssu

re (

psia

)

Elapsed time (hrs)


Model


Results

(pav)i 3696.553 psia (pav)f 3665.646 psia pwf 3683.948 psia kh 10010 mD.ft k(xy) 30.51 mD k(z) 2.866 mD L 687.81 m S(w) -1.86 S(c) -4.12 S(t) -5.37 Zw 45.00 m C 1.109 bbl/psi Type top No Flow Type bot No Flow d1 634.464 m d2 2573.43 m d3 492.688 m d4 378.896 m A 3.328 km2 Type d1 No Flow Type d2 No Flow Type d3 No Flow Type d4 No Flow Dp(S) -0.2385 psi

0.001

0.01

0.1

1

10

100

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eri

va

tive

(p

si)

Elapsed time (hrs)


0.001

0.01

0.1

1

10

100

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eri

va

tive

(p

si)

Elapsed time (hrs)


2300

2310

2320

2330

2340

2350

-4 -3 -2 -1 0 1 2 3 4 5

No

rma

lise

d P

se

ud

o P

ressu

re (

psia

)



3650

3660

3670

3680

3690

3700

-4 -3 -2 -1 0 1 2 3 4 5

Pre

ssu

re (

psia

)



3650

3660

3670

3680

3690

3700

0 10000 20000 30000 40000 50000 60000 70000

Pre

ssu

re (

psia

)

Elapsed time (hrs)


Model


Results



Figure L-8: Well E-M02Pa - multilayer analysis of unit-pressure drawdown convolved from deconvolved derivative

(1-873)[5,15,19- 873]{1.00000E+09}3696.75

Figure L-9: Well E-M03P - single layer analysis of unit-pressure drawdown convolved from deconvolved derivative

(1-578)[20,224]{7.16293E+05}3727.00

0.001

0.01

0.1

1

10

100

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eri

va

tive

(p

si)

Elapsed time (hrs)


0.001

0.01

0.1

1

10

100

0.0001 0.01 1 100 10000 1000000

nm

(p)

Ch

an

ge

an

d D

eri

va

tive

(p

si)

Elapsed time (hrs)


2290

2300

2310

2320

2330

2340

2350

-4 -3 -2 -1 0 1 2 3 4 5

No

rma

lise

d P

se

ud

o P

ressu

re (

psia

)



3640

3650

3660

3670

3680

3690

3700

-4 -3 -2 -1 0 1 2 3 4 5P

ressu

re (

psia

)



3600

3620

3640

3660

3680

3700

0 10000 20000 30000 40000 50000 60000 70000 80000

Pre

ssu

re (

psia

)

Elapsed time (hrs)


Model

Uniform Flux Horizontal Well with C and S Multi-layer (with cross-flow) Rectangle

Results

(pav)i 3696.701 psia (pav)f 3666.390 psia pwf 3647.344 psia (kh)t 13587 mD.ft k (av) 13.27 mD L 765.03 m S(t) -1.95 S(w) -2.97 S(c) 1.08 Zw 21.03 m C 1.350 bbl/psi k1 (xy) 20.37 mD k2 (xy) 0.0001 mD k3 (xy) 10.02 mD k1 (z) 3.253 mD k2 (z) 0.00014908 mD k3 (z) 0.04671 mD S(1) -6.23 S(2) Non Perf. S(3) Non Perf. d1(1:3) 593 m d2(1:3) 1396 m d3(1:3) 568 m d4(1:3) 179 m Type d1(1:3) No Flow Type d2(1:3) No Flow Type d3(1:3) No Flow Type d4(1:3) No Flow Dp(S) -1.206 psi

0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


2200

2250

2300

2350

2400

-4 -3 -2 -1 0 1 2 3 4 5

Norm

alis

ed

Pseu

do

Pre

ssure

(p

sia

)



2200

2250

2300

2350

2400

-4 -3 -2 -1 0 1 2 3 4 5

Norm

alis

ed

Pseu

do

Pre

ssure

(p

sia

)



3550

3600

3650

3700

3750

2001 2004 2005

Pre

ssure

(p

sia

)

Elapsed time (Date)


Model


Results

(pav)i 3726.572 psia (pav)f 3602.570 psia pwf 3602.007 psia kh 3425.7 mD.ft k(xy) 14.11 mD k(z) 2.451 mD L 242.70 m S(w) 0.02 S(c) -1.94 S(t) -2.31 Zw 42.40 m C 0.2858 bbl/psi Type top No Flow Type bot No Flow d1 270.334 m d2 2235.81 m d3 68.5673 m d4 2445 m A 1.586 km2 Type d1 No Flow Type d2 No Flow Type d3 No Flow Type d4 No Flow Dp(S) 0.01196 psi



(1-578)[20,457]{3.34908E+06}3727.00


(1-578)[11,16,20-578]{1.00000E+09}3727

0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Cha

ng

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nd D

eri

vative (

psi)

Elapsed time (hrs)


2200

2250

2300

2350

2400

-4 -3 -2 -1 0 1 2 3 4 5

Norm

alis

ed

Pseu

do

Pre

ssure

(p

sia

)



2200

2250

2300

2350

2400

-4 -3 -2 -1 0 1 2 3 4 5N

orm

alis

ed

Pseu

do

Pre

ssure

(p

sia

)



3550

3600

3650

3700

3750

2001 2004 2005 2008

Pre

ssure

(p

sia

)

Elapsed time (Date)


Model


Results


0.01

0.1

1

10

100

1000

0.0001 0.01 1 100 10000 1000000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

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Elapsed time (hrs)


0.01

0.1

1

10

100

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0.0001 0.01 1 100 10000 1000000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


2150

2200

2250

2300

2350

2400

-4 -3 -2 -1 0 1 2 3 4 5

Norm

alis

ed

Pseu

do

Pre

ssure

(p

sia

)



2150

2200

2250

2300

2350

2400

-4 -3 -2 -1 0 1 2 3 4 5

Norm

alis

ed

Pseu

do

Pre

ssure

(p

sia

)



3500

3550

3600

3650

3700

3750

2001 2004 2005 2008 2009

Pre

ssure

(p

sia

)

Elapsed time (Date)


Model


Results

(pav)i 3726.572 psia (pav)f 3578.731 psia pwf 3586.968 psia kh 2029.9 mD.ft k(xy) 8.361 mD k(z) 1.411 mD L 231.16 m S(w) -1.90 S(c) -1.63 S(t) -3.53 Zw 35.22 m C 0.1258 bbl/psi Type top No Flow Type bot No Flow d1 105.111 m d2 3108.82 m d3 246.708 m d4 3100 m A 2.184 km2 Type d1 No Flow Type d2 No Flow Type d3 No Flow Type d4 No Flow Dp(S) -2.077 psi


Model Analysis 1 Analysis 2

[FP 101,418]

Analysis 3

[FP101,581]

Analysis 4

[FP 51,68,91,101-878]

A.C. Gringarten,

(most likely)

A.C. Gringarten,

(most likely)

Units

FP rate 1-878 1-987 measured data analysis

Layer Single layer Single layer Single layer Single layer Single layer Single layer

Study This study This study This study This study August 2005 July 2005

(pav)i 3798 3798 3798 3798 3760 3767 psia

(pav)f 3688.4 3681.6 3730 3687 psia

pwf 3671.5 3671.5 3720.4 3711.9 psia

kh 418.2 457.6 1107 2728 480 mD.ft

k(xy) 1.7 1.8 4.4 10.8 2 10 mD

k(z) 5.3 8.9 8 2 5 4 mD

L 650 601 340 421 900 900 m

S(w) -2.2 -0.8 -1.8 -2.1 1

S(c) -6.7 -6.7 -5.6 -4.1 -7

S(t) -6.8 -6.7 -5.8 -5.2 -7

Zw 13.5 23.8 56 18 m

C 0.3 0.3 0.2 0.9 bbl/psi

Type top No Flow No Flow No Flow No Flow No Flow No Flow

Type bot No Flow No Flow No Flow No Flow No Flow No Flow

d1 504 622 592 4427 450 140 m

d2 1178 1076 944 86 1000 1770 m

d3 363 257 291 133 200 200 m

d4 2083 1960 2239 524 > 3000 > 3000 m

A 2.8 2.7 2.8 2.8 > 3.1 > 3.1 km2

Type d1 No Flow No Flow No Flow No Flow No Flow No Flow




Dp(S) -0.9 -0.3 -0.7 -0.9 psi

Table L-1: Well E-M01P - well test interpretation models resulted from analysis of convolved unit-rate pressure drawdowns

Model Analysis 1

[FP 19,290] Analysis 2

[FP 19,546] Analysis 3

[FP 19,785] A.C. Gringarten

FP[19,203(=290)] A.C. Gringarten

Units

FP rate 1-873 1-481

Layer Single layer Single layer Single layer Single layer

Study This study This study This study November 2008

(pav)i 3696.4 3696.6 3696.7 3695.7 psia

(pav)f 3679.2 3666 3654 3633.5 psia

pwf 3679 3684 3670.2 3679 psia

kh 9782 10010 9085 8858 mD.ft

k(xy) 29.8 30.5 27.7 27 mD

k(z) 4 2.9 3 5 mD

L 611.2 688 798.6 900 m

S(w) -0.4 -1.9 -2.1 3.31

S(c) -4.3 -4.1 -4.7 -5.8

S(t) -4.7 -5.4 -5.8 -5.1

Zw 50 45 22 51 m

C 0.6 1.1 1.2 0.9 bbl/psi

Type top No Flow No Flow No Flow No Flow

Type bot No Flow No Flow No Flow No Flow

d1 282 635 589 289 m

d2 2538 2573 2767 2174 m

d3 417 493 668 400 m

d4 550 379 307 800 m

A 2.2 3.3 3.9 2.2 km2

Type d1 No Flow No Flow No Flow No Flow




Dp(S) 0 -0.2 -0.2 0.3 psi

Table L-2: Well E-M02Pa - well test interpretation models resulted from analysis of convolved unit-rate pressure drawdowns


APPENDIX M (Analysis of measured pressure data in three wells)

Well E-M01P

Each model listed in Table L-1 is applied primarily to two main build-ups (FP 481 and FP 581) of the production history

recorded in well E-M0P1. At this point it should be noted that the new acquired data particularly in this well are of poor

quality. The noisy data and data with zero-pressure values has to be eliminated resulting in gaps of pressure history. Moreover,

in the new acquired production data there are no useful build-ups obtained.

Table M-1 presents different models with corresponding parameters obtained during application of well test interpretation

models resulted from drawdown analyses. Adapted rates are used. Model M2[101,418] applied to FP 481 matches the

measured pressure data (blue color) only till 9th

of February 2005. Then it does not provide the match (Figure M-4).

Deconvolution models “Analysis 1” and “Analysis 3” do not provide the match for the entire pressure history as well, even

after adjustment (regression) of all model parameters. It seems that the single layer models with permeabilities kxy < kz only

match the pressure history till 9th

of February 2005, but do not match the rest of the production period. Thus, several attempts

are made to observe the match of the last 6 years of production:

1) Permeabilities kxy = 10 mD and kz = 4 md are used. These values come from the core analyses in well EM-1. Model M1[FP

51,68,91,101-878] is applied to measured pressure data. However, despite of good matches on the log-log and Horner plots, it

does not match the entire pressure history.

2) Application of a model describing the reservoir as an open-ended rectangle. At the same time vertical and horizontal

permeabilities are varied. The match is improving significantly.

3) Simplification of rate history from 878 to 534 rates.

4) Multilayer analysis. Since all single layer models cannot provide clear and definite match it is tried to apply a multilayer

model. The obtained results are displaced below.

Model Original DST

analysis FP 20

Analysis 1

[FP 20,224]

Analysis 2

[FP 20,457]

Analysis 3

[FP 11,16,20-578] A.C. Gringarten

Units

FP rate - 1-578 1-518

Layer Single layer Single layer Single layer Single layer Single layer

Study This study This study This study This study November 2008

(pav)i 3727 3726.6 3726.63727 3726.6 3708 psia

(pav)f 3602.6 3576 3579 3595 psia

pwf 3509.4 3602 3581 3587 3584 psia

kh 3426 3227 2030 3402 mD.ft

k(xy) 14.1 14.1 13.3 8.4 14 mD

k(z) 2.4 2.5 3.1 1.4 2.4 mD

L 242 243 196 231 239 m

S(w) 1.9 0 -0.9 -1.9 0

S(c) -1.7 -1.9 -1.6 -1.6 -1.8

S(t) -0.7 -2.3 -2.6 -3.5 -2.2

Zw 52 42 32 35 50 m

C 0.4 0.3 0.2 0.1 01 bbl/psi

Type top No Flow No Flow No Flow No Flow No Flow

Type bot No Flow No Flow No Flow No Flow No Flow

d1 146 270 307 105 328 m

d2 2236 1915 3109 2954 m

d3 170 69 147 247 60.2 m

d4 2445 2288 3100 1342 m

A 1.6 1.9 2.2 1.7 km2

Type d1 No Flow No Flow No Flow No Flow No Flow




Dp(S) 45.5 0 -0.6 -2.1 0 psi

Table L-3: Well E-M03P - well test interpretation models resulted from analysis of convolved unit-rate pressure drawdowns


Figure M-1:Well E-M01P - Analysis M2[101,418] variable skin

Figure M-2: Well E-M01P - Analysis M2[101,418] constant skin

1

10

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Skin

Gas Rate (MMscf/D)

Skin Vs. Rate

-1000

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2001 2003 2005

Pre

ssu

re (

psia

)

Elapsed time (Date)

Simulation (Variable Skin) - Flow Period 418

Model


Results

(pav)i 3797.608 psia (pav)f 2466.666 psia pwf 2012.399 psia kh 457.5 mD.ft k(xy) 1.811 mD k(z) 8.869 mD L 601.43 m S(w) -0.83 S(c) -6.68 S(t) -6.71 Zw 23.77 m C 0.2828 bbl/psi Type top No Flow Type bot No Flow d1 628.617 m d2 769.952 m d3 241.007 m d4 1859.18 m A 2.286 km2 Type d1 No Flow Type d2 No Flow Type d3 No Flow Type d4 No Flow Dp(S) 0.00 psi

1

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(p)

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2001 2003 2005 2007 2009 2011

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)

Elapsed time (Date)


Model


Results



Figure M-3: Well E-M01P - Analysis M1[FP 51,68,91,101-878]

Figure M-4: DST pressure data and entire pressure history matches using model M2[101, 418] with constant and variable skin

0.01

0.1

1

10

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1000

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0.01 1 100 10000

nm

(p)

Change (

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Elapsed time (hrs)


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Elapsed time (hrs)


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40 50 60 70 80 90 100 110 120

No

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)



Results

(pav)i 3797.727 psia (pav)f 1605.883 psia pwf 1092.515 psia kh 3480.1 mD.ft k(xy) 13.78 mD k(z) 1.725 mD L 566.16 m S(w) -1.62 S(c) -4.48 S(t) -5.35 Zw 17.40 m C 0.7321 bbl/psi Type top No Flow Type bot No Flow d1 4677.31 m d2 96.6188 m d3 247.229 m d4 403.614 m A 2.463 km2 Type d1 No Flow Type d2 No Flow Type d3 No Flow Type d4 No Flow Dp(S) 0.00 psi

Model


3500

3600

3700

3800

3900

07-Nov 08-Nov 09-Nov 10-Nov 11-Nov 12-Nov

Pre

ssure

(psia

)

Elapsed time (Date)


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2000 2001 2002 2003 2004 2005 2006

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Elapsed time (Date)


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06-Nov 07-Nov 08-Nov 09-Nov 10-Nov 11-Nov 12-Nov

Pre

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re (

psia

)

Elapsed time (Date)


-1000

0

1000

2000

3000

4000

5000

6000

2000 2001 2002 2003 2004 2005 2006

Pre

ssure

(psia

)

Elapsed time (Date)


FP 418

FP 418

DST

DST


Figure M-5: Well E-M01P (FP 418) - single layer model (open-ended rectangle); kxy=1.7 mD, kz=10 mD, L=556m

Figure M-6: Well E-M01P (FP 581) - single layer model (open-ended rectangle); kxy=14.7 mD, kz=4.8 mD, L=919m

0.1

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0.1 1 10 100 1000 10000 100000

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(p)

Cha

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vative (

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Elapsed time (hrs)


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nm

(p)

Cha

ng

e (

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Elapsed time (hrs)


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Norm

alis

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do

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)



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Pre

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(p

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Elapsed time (hrs)


Model

Uniform Flux Horizontal Well with C and S Homogeneous Open Ended Rectangle

Results

(pav)i 3798.000 psia pwf 2012.399 psia kh 428.0 mD.ft k(xy) 1.694 mD k(z) 10.09 mD L 555.63 m S(w) -0.88 S(c) -6.61 S(t) -6.64 Zw 21.69 m C 0.3039 bbl/psi Type top No Flow Type bot No Flow d1 414.618 m d2 937.718 m d3 360.449 m Type d1 No Flow Type d2 No Flow Type d3 No Flow Dinv 2771 ft Dp(S) -0.7776 psi

0.01

0.1

1

10

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0.1 1 10 100 1000 10000

nm

(p)

Ch

an

ge

(psi)

Elapsed time (hrs)


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1500

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3000

3500

0 20 40 60 80 100 120 140 160

Pre

ssure

(psia

)



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0 20000 40000 60000 80000 100000

Pre

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(p

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)

Elapsed time (hrs)


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0.01

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0.001 1 1000 1000000

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(p)

Ch

an

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an

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eriva

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(psi)

Elapsed time (hrs)


300

350

400

450

40 50 60 70 80 90 100 110 120

Norm

alis

ed P

seudo P

ressure

(psia

)



Results

(pav)i 3797.435 psia pwf 1092.515 psia kh 3702.9 mD.ft k(xy) 14.66 mD k(z) 4.715 mD L 918.16 m S(w) -0.30 S(c) -6.54 S(t) -6.63 Zw 50.92 m C 0.6081 bbl/psi Type top No Flow Type bot No Flow d1 153.164 m d2 1199.95 m d3 158.198 m Type d1 No Flow Type d2 No Flow Type d3 No Flow Dinv 4095 ft Dp(S) -1.036 psi

Model

Uniform Flux Horizontal Well with C and S Homogeneous Open Ended Rectangle


Model M2[101,418] M3[101,418] M4[101,581] M1[FP 51,68,91,101-878] A.C. Gringarten,

(most likely)

Units

Layer Single layer Single layer Single layer Single layer Single layer

Skin Constant Variable Constant Constant

Rates Adapted Adapted Adapted Adapted

Based on: Analysis 2 Analysis 2 Analysis 3 Analysis 4

Study This study This study This study This study July 2007

(pav)i 3798 3798 3798 3798 3767 psia

(pav)f 2473 2467 1867 1606 psia

pwf 2012 2012 1093 1093 1077.8 psia

kh 457.5 457.5 692 3480 mD.ft

k(xy) 1.8 1.8 2.7 13.8 10 mD

k(z) 8.9 8.9 15.4 1.7 4 mD

L 601 601 776 566 920 m

S(w) -0.8 -0.8 0.5 -1.6 9.3

S(c) -6.7 -6.7 -7 -4.5 -6.7

S(t) -6.7 -6.7 -5.5 -5.4 -5.5

Zw 23.8 23.8 34.8 17.4 38.5 m

C 0.3 0.3 0.2 0.7 0.4 bbl/psi

Type top No Flow No Flow No Flow No Flow No Flow

Type bot No Flow No Flow No Flow No Flow No Flow

d1 623 628 543 4677 152 m

d2 7621.8 770 358 97 1638 m

d3 254 241 315 247 201 m

d4 1857 1859 2827 403 m

A 2.3 2.9 2.7 2.6 km2





Dp(S) -0.7 0 2.8 0 26.3 psi

Table M-1: Well E-M01P - interpretation models resulted from adjustment of model parameters from Table L-1

Figure M-7: Well E-M01P - multilayer model (open-ended rectangle) k2z = 10E-06 mD

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (days)


0.1

1

10

100

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0.001 0.01 0.1 1 10 100

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (days)


300

320

340

360

380

400

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440

40 50 60 70 80 90 100 110 120

Norm

alis

ed

Pseu

do

Pre

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(p

sia

)



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0 10 20 30 40 50 60 70 80 90 100 110 120

Pre

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(p

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Pre

ssure

(p

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)

Elapsed time (Date)


Model

Uniform Flux Horizontal Well with C and S Multi-layer (with cross-flow) Open Ended Rectangle

Results

(pav)i 3798.000 psia pwf 1092.515 psia (kh)t 4675.9 mD.ft k (av) 9.762 mD L 850.00 m S(t) -1.11 S(w) 0.87 S(c) -1.32 Zw 37.00 m C 1.173 bbl/psi k1 (xy) 9.800 mD k2 (xy) 1E-006 mD k3 (xy) 10.000 mD k1 (z) 4.778 mD k2 (z) 1E-006 mD k3 (z) 1.390 mD S(1) -6.55 S(2) Non Perf. S(3) Non Perf. d1(1:3) 152 m d2(1:3) 2963 m d3(1:3) 141 m Type d1(1:3) No Flow Type d2(1:3) No Flow Type d3(1:3) No Flow Dinv 3343 ft Dp(S) 33.97 psi


Figure M-8: Well E-M01P - multilayer model (open-ended rectangle) k2z = 10E-04 mD

Figure M-9: Well E-M02Pa - single layer analysis

0.1

1

10

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1000

0.001 0.01 0.1 1 10 100

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (days)


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1

10

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0.001 0.01 0.1 1 10 100

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (days)


300

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40 50 60 70 80 90 100 110 120

Norm

alis

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Pseu

do

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(p

sia

)



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0 10 20 30 40 50 60 70 80 90 100 110 120P

ressure

(p

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Pre

ssure

(p

sia

)

Elapsed time (Date)


Model

Uniform Flux Horizontal Well with C and S Multi-layer (with cross-flow) Open Ended Rectangle

Results

(pav)i 3798.000 psia pwf 1092.515 psia (kh)t 4675.9 mD.ft k (av) 9.762 mD L 850.00 m S(t) -3.32 S(w) 0.87 S(c) -3.53 Zw 37.00 m C 1.173 bbl/psi k1 (xy) 9.800 mD k2 (xy) 1E-006 mD k3 (xy) 10.000 mD k1 (z) 4.778 mD k2 (z) 0.00010008 mD k3 (z) 1.063 mD S(1) -6.55 S(2) Non Perf. S(3) Non Perf. d1(1:3) 152 m d2(1:3) 2963 m d3(1:3) 141 m Type d1(1:3) No Flow Type d2(1:3) No Flow Type d3(1:3) No Flow Dinv 3343 ft Dp(S) 33.97 psi

1

10

100

0.000001 0.0001 0.01 1 100 10000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


1

10

100

1000

0.000001 0.0001 0.01 1 100 10000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


1440

1460

1480

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1540

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Norm

alis

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Elapsed time (hrs)


Model


Results



Figure M-10: Well E-M02Pa - multilayer analysis

Well E-M03P

Table L-3 lists the obtained models from drawdown analyses which are applied to measured pressure data. Adapted rates are

used. Model parameters are adjusted to match the pressure data on the log-log and Horner plots. The simulation of the

pressure data (red curve) follows the build-up’s trend, but does not provide match for drawdowns. The problem of not

matching the drawdowns may be because of erroneous rates as already obtained in deconvolution verification step at which

high differences in measured and adapted rates are obtained. Gringarten, A.C. in “Well Test Analysis of Well E-M03Pa”-

report also encountered the problem with erroneous rates. Decision was made to simplify the rate history and to adjust the

rates manually as it was done by A.C. Gringarten. Using the adapted rates do not provide drawdown match.

1

10

100

0.000001 0.0001 0.01 1 100

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (days)


1

10

100

1000

1 10 100 1000 10000 100000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


1440

1460

1480

1500

1520

1540

0 100 200 300 400 500

Norm

alis

ed

Pseu

do

Pre

ssure

(p

sia

)



2700

2800

2900

3000

0 100 200 300 400P

ressure

(p

sia

)



0

1000

2000

3000

0 10000 20000 30000 40000 50000 60000 70000 80000

Pre

ssure

(p

sia

)

Elapsed time (hrs)


Model

Uniform Flux Horizontal Well with C and S Multi-layer (with cross-flow) Rectangle

Results

(pav)i 3696.750 psia (pav)f 3252.688 psia pwf 2752.486 psia (kh)t 12653 mD.ft k (av) 15.24 mD L 803.02 m S(t) -2.96 S(w) -2.50 S(c) -0.32 Zw 50.00 m C 0.1556 bbl/psi k1 (xy) 21.97 mD k2 (xy) 0.00013687 mD k3 (xy) 10.99 mD k1 (z) 1.956 mD k2 (z) 0.00030069 mD k3 (z) 0.05394 mD S(1) -5.99 S(2) Non Perf. S(3) Non Perf. d1(1:3) 583 m d2(1:3) 1092 m d3(1:3) 559 m d4(1:3) 217 m Type d1(1:3) No Flow Type d2(1:3) No Flow Type d3(1:3) No Flow Type d4(1:3) No Flow Dp(S) -50.66 psi


Figure M-11: Well E-M03P - analysis of DST build-up 20

Figure M-12: Well E-M03P - application of single layer model to measured pressure data (flow period 457)

0.1

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100

nm

(p)

Change a

nd D

erivative (

psi)

Elapsed time (hrs)


0.1

1

10

100

1000

0.0001 0.001 0.01 0.1 1 10 100

nm

(p)

Change a

nd D

eri

vative (

psi)

Elapsed time (hrs)


2140

2160

2180

2200

2220

2240

2260

2280

2300

2320

2340

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190

Norm

alis

ed P

seudo P

ressure

(p

sia

)



3500

3520

3540

3560

3580

3600

3620

3640

3660

3680

3700

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190P

ressure

(p

sia

)



3400

3500

3600

3700

40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

Pre

ssure

(p

sia

)

Elapsed time (hrs)


Model

Uniform Flux Horizontal Well with C and S Homogeneous Channel Boundaries

Results

(pav)i 3727.000 psia pwf 3509.382 psia (kh/u)t 1.6022E+005 mD.ft/cp (kxy/u)t 659.3 mD/cp (kz/u)t 109.9 mD/cp k(xy)gas 14.11 mD k(z) gas 2.352 mD L 242.00 m S(w) 1.90 S(c) -1.70 S(t) -0.68 Zw 52.00 m C 0.3900 bbl/psi Type top No Flow Type bot No Flow d1 146.135 m d3 170.37 m Type d1 No Flow Type d3 No Flow Dinv 472 ft Dp(S) 45.45 psi

Infinite extent

Channel boundaries


Figure M-13: Well E-M03P - single layer model (FP 290), closed rectangle, variable skin, d4=340m

Figure M-14: Well E-M03P - single layer model (FP290), closed rectangle, variable skin, d4=1651m

1

10

100

1000

0.1 1 10 100 1000 10000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


1

10

100

1000

0.1 1 10 100 1000 10000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


900

1000

1100

1200

1300

1400

1500

0 10 20 30 40 50 60 70 80 90 100

Pre

ssure

(psia

)



-100

0

100

200

300

0 10 20 30 40 50 60 70

Skin

Gas Rate (MMscf/D)

Skin Vs. Rate

0

1000

2000

3000

4000

0 20000 40000 60000 80000 100000P

ressure

(p

sia

)Elapsed time (hrs)


-200

-100

0

100

200

300

400

0 20000 40000 60000 80000 100000

Skin

Elapsed time (hrs)

Skin vs. Time

Model


Results

(pav)i 3727.000 psia (pav)f 1387.561 psia pwf 1102.312 psia kh 1519.8 mD.ft k(xy) 6.260 mD k(z) 3.585 mD L 348.90 m S(w) 1.13 S(c) -4.92 S(t) -4.65 Zw 51.94 m C 1.196 bbl/psi Type top No Flow Type bot No Flow d1 700.547 m d2 1747.51 m d3 130.685 m d4 340.271 m A 1.735 km2 Type d1 No Flow Type d2 No Flow Type d3 No Flow Type d4 No Flow Dp(S) 15.53 psi

1

10

100

1000

0.1 1 10 100 1000 10000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


1

10

100

1000

0.1 1 10 100 1000 10000

nm

(p)

Cha

ng

e a

nd D

eri

vative (

psi)

Elapsed time (hrs)


1000

1100

1200

1300

1400

1500

20 30 40 50 60 70 80

Pre

ssure

(psia

)



-100

0

100

200

300

0 10 20 30 40 50 60 70

Skin

Gas Rate (MMscf/D)

Skin Vs. Rate

0

1000

2000

3000

4000

0 20000 40000 60000 80000 100000

Pre

ssure

(p

sia

)

Elapsed time (hrs)


-200

-100

0

100

200

300

400

0 20000 40000 60000 80000 100000

Skin

Elapsed time (hrs)

Skin vs. Time

Model


Results

(pav)i 3727.000 psia (pav)f 1386.439 psia pwf 1102.312 psia kh 1687.8 mD.ft k(xy) 6.952 mD k(z) 3.376 mD L 316.44 m S(w) 0.55 S(c) -4.58 S(t) -4.46 Zw 41.53 m C 1.374 bbl/psi Type top No Flow Type bot No Flow d1 349.359 m d2 2105.7 m d3 111.363 m d4 1651.26 m A 1.731 km2 Type d1 No Flow Type d2 No Flow Type d3 No Flow Type d4 No Flow Dp(S) 8.247 psi


APPENDIX N (Comparison between the deconvolved derivatives in well E-M03P)

Figure N-1: Well E-M03P - comparison between deconvolved derivatives

APPENDIX O (Determination of initial reservoir pressure using Kappa engineering software Saphir)

Figure O-1: Validation of initial reservoir pressure in well E-M02Pa - DST build-ups are deconvolved using initial pressure value of 3696.75 psia

0.1

1

10

100

1000

0.001 0.01 0.1 1 10 100 1000 10000 100000

No

rm

ali

zed

deco

nvo

lved

mn

(p)

deriv

ati

ve,

psi

/MM

scf/

D

Elapsed Time hrs

#(1-344)[1-344]{2.26671E+08}3710.00 from

November 2008, Gringarten, A.C.

#(1-304)[1-304]{3.04787E+08}3727.00 from

August 2011, Rinas, E.

1E-4 1E-3 0.01 0.1 1 10 100 1000 10000 1E+5

Time [hr]

1E+5

1E+6

1E+7

1E+8

1E+9

Ga

s p

ote

ntia

l [p

si2

/cp

]

Log-Log deconvolution plot: m(p)-m(p@dt=0) and derivative [psi2/cp] vs dt [hr]

Slope 1


Figure O-2: Well E-M02Pa - deconvolved derivative resulted from deconvolution of all flow periods in one sweep in Saphir

Figure O-3: Validation of initial reservoir pressure in well E-M01P - DST build-ups are deconvolved using initial pressure value of 3798 psia

0.01 0.1 1 10 100 1000 10000 1E+5

Time [hr]

1E+6

1E+7

1E+8

Ga

s p

ote

ntia

l [p

si2

/cp

]


1E-5 1E-4 1E-3 0.01 0.1 1 10 100 1000 10000 1E+5

Time [hr]

1E+6

1E+7

1E+8

1E+9

1E+10

Ga

s p

ote

ntia

l [p

si2

/cp

]


Documents

Deconvolution of Well Test Data from the E-M Gas ... · iii [Deconvolution of Well Test Data from the E-M Gas Condensate Field (South Africa)]