Diagnostic Plots for Analysis of Water Production and

i

Diagnostic Plots for Analysis of Water Production and Reservoir Performance

(A Case Study)

By

Echufu-Agbo Ogbene Alexis

RECOMMENDED: ______________________________________ Chair, Professor David Ogbe

______________________________________ Professor Ekwere Peters

______________________________________ Dr Samuel Osisanya

APPROVED: ______________________________________ Chair, Department of Petroleum Engineering

______________________________________ Provost Academic

______________________________________ Date

ii

Diagnostic Plots for Analysis of Water Production and Reservoir

Performance

(A Case Study)

A

Thesis

Presented to the Graduate Faculty

of the African University of Science and Technology

in Partial Fulfilment of the Requirements

for the Degree of

MASTER OF SCIENCE IN PETROLEUM ENGINEERING

By

Echufu-Agbo Ogbene Alexis

Abuja-Nigeria

December 2010.

iii

ABSTRACT

The research is aimed at the understanding of the various diagnostic plots for the

analysis of water production that are available as well as the application of these

methods in a case study. It also aimed at the establishment of a work flow for the

evaluation of water production mechanisms. A workflow was developed that

combines numerical simulation and diagnostic plots to analyze the water production

performance in a reservoir. This workflow was validated using a case study.

The multi-layer reservoir model with varying vertical permeability was constructed

using a numerical simulator with the reservoir properties of the case study. Trends

from the field data were analyzed using the trends observed from the simulated data

as templates.

For the production wells, oil rate and water rate versus time plots as well as the X-

plot were used to evaluate water production characteristics of the case study. The

water-oil ratio (WOR), WOR derivative and X-Plot were used for the field production

diagnosis while the Hall and the Hearn Plots were used for the water injection well

diagnosis. The results of the diagnostic plots showed that multi-layered channelling

was the controlling mechanism and the cause of the water production in the case

study. For the injection wells, the plots indicated that some wells in the case study

had the problem of extensive near wellbore fracturing while other wells had the

problem of wellbore plugging.

The workflow and results of this study can be applied by reservoir and production

engineering teams to other reservoirs to diagnose water production mechanisms;

identify sources of water production, and provide information for planning water

management programmes to mitigate excessive water production problems.

iv

DEDICATION

Trust in the Lord with all your heart and lean not on your own understanding,

in all your ways, acknowledge Him and He shall direct your path

Proverb 3: 4-5

To my God and Saviour- without whom wouldn’t have come this far. You

thought me to trust and hold on.

Thank you

To my Husband and best friend, I couldn’t have asked for a better partner. I

pray I will always be the best for you. Thank you for your prayers and support.

I love you

To my irreplaceable family, you stood by me, cried with me, prayed for me,

You have done so much and I appreciate you.

Thank you and God bless you

To all my friends, you believed in me and encouraged me even when I didn’t

believe in myself.

Thank you

v

ACKNOWLEDGEMENT

I would like to thank the chairman of my committee, Prof (Emeritus) Ogbe for

working tirelessly with me through my research work. His continuous guidance and

understanding made this work possible. I would also like to thank members of my

committee, Prof Ekwere and Prof Osisanya for their contributions and suggestions in

this research work.

I am also grateful to Brian Coats of Coats Engineering, Inc., USA, for promptly

attending to me and making available the simulator for this work.

My appreciation also goes to African University of Science and Technology (AUST)

for availing me this opportunity.

Special thanks to the Faculty and Staff of AUST for making this environment

bearable for me.

Appreciation also goes to Dr () Felicia Chukwu, whose advice and support I never

lacked.

Finally, my appreciation goes to all my colleagues for all the support they rendered.

Without you, I would have stood alone.

vi

TABLE OF CONTENTS

SIGNATURE PAGE ............................................................................................................... i

TITLE PAGE ..........................................................................................................................ii

ABSTRACT .......................................................................................................................... iii

DEDICATION....................................................................................................................... iv

ACKNOWLEDGEMENT ....................................................................................................... v

TABLE OF CONTENTS ....................................................................................................... vi

LIST OF FIGURES ............................................................................................................... ix

LIST OF TABLES ................................................................................................................ xii

LIST OF APPENDICES ...................................................................................................... xiii

CHAPTER 1 ......................................................................................................................... 1

1.0 INTRODUCTION............................................................................................................. 1

1.1 Description of Problem ................................................................................................. 1

1.2 Study Objective ............................................................................................................. 2

1.3 Scope of Work ............................................................................................................... 2

CHAPTER 2 ......................................................................................................................... 3

2.0 LITERATURE REVIEW .................................................................................................. 3

2.1 Source of water ............................................................................................................. 3

2.1.1 Sweep water ......................................................................................................... 4

2.1.2 Good water ........................................................................................................... 5

2.1.3 Bad water .............................................................................................................. 5

2.2 Water Production Mechanism ...................................................................................... 7

2.3 Causes of premature water production. ...................................................................... 7

2.3.1 Channels behind casing ...................................................................................... 8

2.3.2 Barrier breakdowns. ............................................................................................. 8

2.3.3 Completions into or near water. .......................................................................... 8

2.3.4 Coning and cresting. ............................................................................................ 8

2.3.5 Channelling through higher permeability zones or fractures. .......................... 9

2.3.6 Fracturing out of zone. ......................................................................................... 9

2.4 ReservoirPerformancePlots and Analysis for WaterProduction ............................. 10

2.4.1 Decline Curve Analysis ...................................................................................... 11

2.4.2 Log Of Water Cut or Oil Cut Versus Cumulative Production .......................... 13

2.4.3 Fetkovich Type Curves ...................................................................................... 14

2.4.4 Omoregie and Ershaghi (X-Plot) ........................................................................ 15

2.4.5 Hall and Hearn Plot for Injectors ....................................................................... 17

2.4.6 Diagnostic Plot ................................................................................................... 19

vii

CHAPTER 3 ....................................................................................................................... 24

3.0 METHODOLOGY .......................................................................................................... 24

3.1 Flowchart for Evaluation of water production mechanism ............................................ 24

3.1.1 Sonic Tool ........................................................................................................... 27

3.1.2 Treatment ............................................................................................................ 27

3.1.3 Monitoring ........................................................................................................... 27

3.2 Case Study One........................................................................................................... 27

3.2.1 Field Production Performance Evaluation ........................................................ 31

3.2.2 Field Production Data Diagnostic Plots ............................................................ 32

3.2.3 Field Injection Performance Evaluation ............................................................ 32

3.2.4 Injection Well Diagnostic Plots.......................................................................... 32

CHAPTER 4 ....................................................................................................................... 34

4.0 RESULTS AND DISCUSSION OF RESULTS .............................................................. 34

4.1 Evaluation of Reservoir Performance Trends.............................................................34 from Simulated Data

4.1.1 Analysis of Simulated Oil Rate and Water Rate Plots ...................................... 34

4.1.2 Analysis of X-Plot Simulated Data .................................................................... 40

4.2 Evaluation of Reservoir Performance trends from....................................................43 Field Case Study

4.2.1 Analysis of Field Oil Rate and Water Rate Plots .............................................. 43

4.2.2 Analysis of Field X-Plot ...................................................................................... 45

4.3 Diagnosis of Simulated Reservoir Production Performance ................................... 50

4.4 Diagnosis of Reservoir Production Performance ..................................................... 52

4.5 Injection Well Performance ....................................................................................... 54

4.5.1 Simulated Injection Well Performance .............................................................. 55

4.5.2 Field Water Injection Performance ................................................................... 54

4.6 Injection Well Diagnosis ............................................................................................ 57

4.6.1 Simulated Water Injection diagnosis ................................................................ 57

4.6.2 Field Water Injection Diagnosis ........................................................................ 60

4.7 Guidelines.................................................................................................................... 62

CHAPTER 5 ....................................................................................................................... 63

5.1 SUMMARY AND CONCLUSIONS ................................................................................ 63

5.3 RECOMMENDATIONS ................................................................................................. 64

REFERENCES ................................................................................................................... 65

viii

APPENDIX ......................................................................................................................... 67

A. NOMENCLATURE ................................................................................................... 67

B. CASE STUDY ONE OIL RATE AND WATER RATE PLOTS ................................... 68

C. CASE STUDY ONE X-PLOT .................................................................................... 72

D. CASE STUDY ONE DIAGNOSTIC PLOTS .............................................................. 74

E. CASE STUDY ONE INJECTION WELL DIAGNOSTIC PLOTS.................................75

ix

LIST OF FIGURES

Fig 2.1: Water production with time, the case of an advancing water front .............................4

Fig 2.2: A plot showing one quadrant of a uniform five-spot injection......................................5

pattern where the water from the most direct streamline is

the first to break through to the producer.

Fig 2.3: Production plot showing the decline types..................................... .............. ............11

Fig 2.4: Production plot showing the exponential decline type..............................................12

Fig 2.5: Production plot showing the oil/water contact depth with .........................................12

cumulative production.

Fig 2.6: Production plot showing log of water cut versus ......................................................13

cumulative oil production

Fig 2.7: Production plot showing log of oil cut versus cumulative oil ....................................14

Production.

Fig 2.8: Composite of analytical and empirical type curves and the standard.......................15

“empirical” exponential, hyperbolic and harmonic decline curve solution

on a single dimensionless curve.

Fig 2.9: The X-plot for a hypothetical three-layer system.......................................................16

Fig 2.10: The Hall Plot ....................................................................................................... ..17

Fig 2.11: The Hearn Plot ..................................................................................................... 18

Fig 2.12: Water coning and channelling WOR comparison...................................................22

Fig 2.13: Multi-layer channelling WOR and WOR derivatives.. ....................... .....................23

Fig 2.14: Bottom-water coning WOR and WOR derivatives. ................................................23

Fig 2.15 : Bottom water coning with late time channelling. .................................................. 24

Fig 3.1 Flow Chart for the Evaluation of water production mechanism. ............................... 25

Fig 3.2: The MBB/W31S structure.........................................................................................28

Fig 4.1: Simulated Field Production rates and water cut versus time (Field) ........................ 35

Fig 4.2: Simulated Well Production rates and water cut versus time (Well P2) .................... 35

Fig 4.3: Simulated Well Production rates and water cut versus time (Well P3) .................... 36

Fig 4.4: Simulated Field Oil cut versus Time (real) .............................................................. 37

Fig 4.5: Simulated Oil cut versus Time (Well P2) ................................................................ 38

Fig 4.6: Simulated Well Oil cut versus Time (Well P3) ......................................................... 38

Fig 4.7: Simulated Field water cut versus cumulative production ........................................ 37

Fig 4.8: Simulated well water cut versus cumulative production (Well P2) ........................... 40

Fig 4.9: Simulated well water cut versus cumulative production (Well P3) ........................... 38

Fig 4.10: Simulated Field X-Plot .......................................................................................... 39

Fig 4.11: Simulated X-Plot (Well P2) ................................................................................... 39

Fig 4.12: Simulated X-Plot (Well P3) ................................................................................... 40

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LIST OF FIGURES (CONT’D)

Fig 4.13: Field production rate versus time .......................................................................... 43

Fig 4.14: Well production rate versus time (Well PR1) ........................................................ 43

Fig 4.15: Field Oil cut versus Time ...................................................................................... 44

Fig 4.16: Well Oil cut versus time (Well PR1) ...................................................................... 45

Fig 4.17: Well Oil cut versus Production time (Well PR2) .................................................... 45

Fig 4.18: Field Water cut versus Cumulative Production ..................................................... 46

Fig 4.19: Well Water cut versus Cumulative Production (Well PR1) .................................... 46

Fig 4.20: Field X-Plot........................................................................................................... 47

Fig 4.21: Well X-Plot (Well PR1) ......................................................................................... 48

Fig 4.22: Simulated Field Diagnostic Plot ............................................................................ 49

Fig 4.23: Simulated Well Diagnostic Plot (Well P2) ............................................................. 49

Fig 4.24: Simulated Well Diagnostic Plot (Well P3) ............................................................. 50

Fig 4.25: Field Diagnostic Plot ............................................................................................. 51

Fig 4.26: Well Diagnostic Plot (Well PR1) ........................................................................... 52

Fig 4.27: Simulated Injection rate and pressure versus time (Injector I1)............................. 53

Fig 4.28: Simulated Injection rate and pressure versus time (Injector I4)............................. 53

Fig 4.29: Well Injection rate and pressure versus time (Injector 1) ...................................... 54



Fig 4.32: Simulated Well Hall Plot (Injector 1) ..................................................................... 56

Fig 4.33: Simulated Well Hall Plot (Injector 4) ..................................................................... 57

Fig 4.34: Well Hall Plot (Injector 1) ...................................................................................... 58



Fig 4.37: Well Hearn Plot (injector 1) ................................................................................... 60

Fig A-1: Well production rate versus time (Well PR2) .......................................................... 65



Fig A-4: Well Oil cut versus Production time (Well PR3) ..................................................... 66

Fig A-5: Well Oil cut versus Production time (Well PR4) ..................................................... 67

Fig A-6: Well Water cut versus Cumulative Production (Well PR3) ..................................... 70



Fig B-1: Well X-Plot (Well PR3) ........................................................................................... 69



Fig C-1: Well Diagnostic Plot (Well PR3)............................................................................. 71

xi

LIST OF FIGURES (CONT’D)



Fig D-2: Hearn Plot (Well injector F2) .................................................................................. 73

Fig D-2: Hearn Plot (Well injector F3) .................................................................................. 73

xii

LIST OF TABLES

TABLE 3.1: SUMMARY OF THE RESERVOIR PROPERTIES FOR THE CASE STUDY. .. 28

TABLE 3.2: RESERVOIR MODEL LAYER AND THICKNESS ............................................ 28

xiii

LIST OF APPENDICES

APPENDIX A: Nomenclature .............................................................................................. 64

APPENDIX B: Case Study One Oil Rate and Water Rate Plots ......................................... .65

APPENDIX C: Case Study One X-Plot ................................................................................ 69

APPENDIX D: Case Study One Diagnostic Plots ................................................................ 71

APPENDIX E: Case Study One Hearn Plots ....................................................................... 73

.

1

CHAPTER 1

1.0 INTRODUCTION

1.1 DESCRIPTION OF PROBLEM

Produced water is any water that is present in a reservoir with the hydrocarbon

resource and is produced to the surface with the crude oil or natural gas. This water

could either come from an aquifer or from injection wells in water flooding process.

The production of this water alongside the oil from any reservoir is a condition that is

natural in all reservoirs. It is expected that water production would increase with the

life of the reservoir. However, a premature increase in the production of water in any

reservoir is an undesirable condition. Excess or premature water production, exists

with associated cost implication on the surface facilities, artificial lift systems,

corrosion and scale problems. Another effect that ensues is a decrease in the

recovery factors as oil is left behind the displacement front, thereby reducing the

performance of the reservoir. All these along with the decrease in the quantity and

quality of the oil imply a reduced profitability.

Globally, as at 2002, analysis showed that three barrels of water is produced to one

barrel of oil and the cost of water handling ranges from 5 to 50 cents, where this cost

is a function of the water cut (Bailey et al, 2000). It is therefore imperative that

actions be taken to reduce this adverse effect, as this will not just lead to potential

savings but its greatest values comes from potential increase in oil production and

recovery. To control the produced water effectively, the source or the mechanism of

the water problem must be identified. Diagnostic plots have been used successfully

to identify the mechanism of water production and that is the focus of this work.

2

1.2 STUDY OBJECTIVES

Reservoir simulation would most likely describe a reservoir adequately but a quicker

and cheaper way to analyse the performance of a reservoir is by the use of analytical

and diagnostic plots, therefore, this research work is aimed at:

Developing a work flow for the evaluation of water production mechanisms.

Presenting the workflow by considering detailed step by step approach on

how water production problems in the reservoir can be diagnosed to support

water management planning for mitigation actions.

The use of a couple of case studies to demonstrate the application of the

workflow and diagnostic plots to identify water production characteristics.

Formulating guidelines on how to mitigate water production and thereby

optimizing well performance and oil recovery.

1.3 SCOPE OF WORK

The work is limited to a number of case studies and is focused on performance

evaluation and diagnostics for water production. The various ways in which water

can encroach the wellbore are reviewed; in addition, the water production

mechanisms and how they can be diagnosed is also discussed. The knowledge of

these ways would provide an effective design, treatment and monitoring.

3

CHAPTER 2

2.0 LITERATURE REVIEW

A review of the literature is presented in this chapter. This presentation includes the

source of water, water production mechanisms, diagnosis of the causes of water

production and ways of mitigating it.

2.1 SOURCE OF WATER

The sources of water include formation water aquifer and injected water

(http://karl.nrcce.wvu.edu/ accessed 25/10/2010).The formation water can originate

from water saturated zone within the reservoirs or zones above or below the pay

zone. A good number of reservoirs are adjacent to an active aquifer and are subject

to bottom or edge water drive. Another source of water is through water injection into

the reservoir for the purpose of pressure maintenance and secondary recovery. This

constitutes a source of water production problem. No matter the source of the water,

one form of produced water is always better than another (Bailey et al 2000).

Therefore in oil production, the water could be described as either sweep, good or

bad.

2.1.1 Sweep water

This water comes from either an injection well or an aquifer that is contributing to the

sweeping of the oil from the reservoir. The management of this water is usually a

vital part of reservoir management. It can also be a determining factor in oil

productivity and ultimate reserves. In the later life of the reservoir, with proper

http://karl.nrcce.wvu.edu/

4

management, a reduction in the production of this kind of water most likely implies a

reduction in the oil production, (Bailey et al 2000).

2.1.2 Good water

This is water that is produced into the wellbore at a rate that is below the water-oil

ratio (WOR) economic limit (Fig 2.1). This flow of water is inevitable and cannot be

shut off without the adverse effect of losing reserves. In this water source, there is

commingling of water and oil through the formation matrix. The water cut is dictated

by the natural mixing behaviour which gradually increases the water-oil ratio.

Fig 2.1: Water production with time, the case of an advancing water front (Bailey et al, 2000)

Also, good water is the water production that is caused by converging flow lines into

the well during water injection. Since this is the shortest line from the injector to the

producer (Fig 2.2), water break through occurs first on this line. This water is

considered as good water since it is impossible to shut off flow lines.

5

Fig 2.2: A plot showing one quadrant of a uniform five-spot injection pattern where the water from the most direct streamline is the first to break through to the producer. (Bailey et al, 2000)

Since good water is produced with oil, water management would seek to maximize

its production and to minimize associated water costs, and the water should be

removed as early as possible.

2.1.3 Bad water

Bad water can be any water that negates profit. It could be defined as water that is

produced into the wellbore and produces no oil or insufficient oil to pay for the cost of

handling the water. Basically, this is water that is produced above the water/oil

economic limit. Most water production problems fall into this category and this

classification is discussed below.

2.2 WATER PRODUCTION MECHANISMS

As earlier stated, once the water production mechanism is understood, an effective

strategy can be formulated to control the water production. The flow of water into the

6

well bore can occur through two main paths i.e. flow through a separate path as the

hydrocarbons and flow of water with the hydrocarbons (http://karl.nrcce.wvu.edu/

accessed 25/10/2010).

Flow through a separate path from the hydrocarbon often leads to direct competition

between the water and the hydrocarbon production. This usually constitutes bad

water. Therefore, reducing or controlling this water production would lead to the

increase of oil or gas production rate and recovery efficiencies. The second flow path

usually constitutes good and sweep water. Therefore a reduction or control in the

production of this water would imply a reduction in the production of the hydrocarbon

(Bailey et al 2000). However, no matter the flow path, there are three factors that

must be present, namely the source of water, pressure gradient and a favourable

relative permeability to water (http://karl.nrcce.wvu.edu/ accessed 25/10/2010).

Pressure gradient: Production of oil and gas from the reservoir can only be achieved

by applying a pressure draw-down at the wellbore which creates a pressure gradient

within the formation. Production from a fully penetrating and perforated well results in

a horizontal pressure gradient in the formation. However, flow from a partially

penetrated well will result in not just a horizontal pressure gradient but also a vertical

pressure gradient. This will often lead to an undesirable condition.

Favourable relative permeability to water: Oil, water and gas mainly flow through the

path of least resistance, which is usually the part of the reservoir with higher

permeability. For a reservoir with uniform geometry and permeability, flow will be

along a simple line into the wellbore but this is not the usual case. With water driven

or water flooded reservoirs, this heterogeneity especially in multi-layered cases

http://karl.nrcc.wvu.edu/

http://karl.nrcc.wvu.edu/

7

would result in water channelling through the high permeability streaks. Most

reservoirs consist of layers of different permeability, either immediately adjacent to

each other or separated by impermeable layers. Layering and associated

permeability variations are major causes of channelling in the reservoir. As the water

sweeps the higher permeability intervals, permeability to subsequent flow of the

water becomes even higher in those intervals and the lower permeability intervals

remain unswept. This leads to a premature water breakthrough. Channelling can be

further exacerbated by lower water viscosity as compared to that of oil especially

during water flooding.

2.3 CAUSES OF PREMATURE WATER PRODUCTION.

Excessive water production can result from either a well problem (mechanical

failure/casing integrity) or other reasons related to the reservoir like water

channelling from water table to the well through natural fractures or faults into the

well, water breakthrough in high permeability zones or water coning.

In general, water production problems related to the well integrity are easier to solve.

However, it gets more complicated to control water production if it is related to the

reservoir characteristics. The factors that are reservoir related are discussed below:

2.3.1 Channels behind casing.

Channels behind casing can develop throughout the life of a well, but are most likely

to occur immediately after the well is completed or stimulated. Unexpected water

production at these times strongly indicates a channel may exist. Channels in the

casing-formation annulus result from poor cement/casing bonds, (Reynolds 2003).

8

2.3.2 Barrier breakdowns.

Even if natural barriers, such as dense shale layers, separate the different fluid

zones and a good cement job exists, shale can heave and fracture near the

wellbore. As a result of production, the pressure differential across these layers of

shale allows fluid to migrate through the wellbore. More often, this type of failure is

associated with stimulation attempts. Fractures break through the shale layer, or

acids dissolve channels through it, (Reynolds 2003).

2.3.3 Completions into or near water.

Completion into the unwanted fluid allows the fluid to be produced immediately. Even

if perforations are above the original water-oil contact, proximity allows production of

the unwanted fluid, through coning or cresting, to occur more easily and quickly,

(Reynolds 2003).

2.3.4 Coning and cresting.

According to Reynolds (2003), fluid coning in vertical wells and fluid cresting in

horizontal wells are due to pressure drop near the well completion. This causes

water inflow from an adjacent connected zone toward the completion. Eventually, the

water can break through into the perforated or open hole section, replacing all or part

of the hydrocarbon production. At water breakthrough, higher cuts of the unwanted

fluid are produced. Although reduced production rates can curtail the problem, they

cannot cure it.

9

2.3.5 Channelling through higher permeability zones or fractures.

Higher permeability streaks can allow fluid that is driving hydrocarbon production to

breakthrough prematurely, bypassing potential production by leaving lower

permeability intervals unswept. This is most common in active water-drive reservoirs

and water floods. As the driving fluid sweeps the higher permeability intervals,

permeability to subsequent flow of the fluid becomes even higher, which results in

increasing water-oil ratios throughout the life of the well or project, (Reynolds, 2003).

2.3.6 Fracturing out of zone.

An improperly designed or poorly performed stimulation treatment can allow a

hydraulic fracture to enter a water zone. If the stimulation is performed on a

producing well, an out-of-zone fracture can allow early breakthrough of water,

(Reynolds, 2003).

Water coning, multilayer channelling and near wellbore problems are the main three

contributors to excessive water production, (Chan 1995). Obviously, the

understanding of excessive water production mechanism and identifying the water

entry in the well are the two major factors that make the shut-off job successful.

Over the last 30 years, technical efforts for water control were mainly on the

development and implementation of gels to create flow barriers for suppressing

water production. Various types of gels were applied in different types of formations.

Quite often, excessive water production mechanisms were not clearly understood or

confirmed. Although many successful treatments were reported, the overall

treatment success ratio remains low, (Chan, 1995).

10

2.4: RESERVOIR PERFORMANCE PLOTS AND ANALYSIS FOR WATER PRODUCTION

According to Seright et al (1997), several methods can be useful in the identification

of the source and nature of excess water production. Some of these methods could

include simple injectivity and productivity calculations, inter-well tracer studies,

reservoir simulation, pressure transient analysis, and various logs.

Kikani (2005) itemized the following plots for the analysis of both the producers and

the injection wells. The following plots were identified for producing wells:

Decline Curve Analysis

Log of Water Cut or Oil Cut Versus Cumulative Production

Fetkovich type curves

Omoriegie-Ershaghi Plot (X plot)

Dowell-Schlumberger log(WOR) Diagnostic Plot

While for the injection wells, the plots are

Injectivity curves - pseudo injectivity

Hall Plots

Hearn plot

Some of these plots are discussed in the following section.

2.4.1 DECLINE CURVE ANALYSIS

It is a production data analysis method used to match historical decline trends in

order to forecast future production rates. It works with the premise that, “the factors

that affected production in the past will affect production in the future”. It usually uses

various production and performance plots. Some of these production plots are as

shown below.

11

Fig 2.3: Production plot showing the decline types (Satter and Thakur, 1994)

Fig 2.4: Production plot showing the exponential decline type (Satter and Thakur, 1994)

12

Fig 2.5: Production plot showing the oil/water contact depth versus cumulative production (Satter and Thakur, 1994)

These plots show the performance of the reservoir with production.

2.4.2 LOG OF WATER CUT OR OIL CUT VERSUS CUMULATIVE PRODUCTION

According to Bondar (2002), the logarithm of WOR or water cut (fw) function plotted

against cumulative production is commonly used for evaluation and prediction of

water flood performance. This presumed semi-log plot of fw and oil recovery allows

extrapolation of the straight line to any desired water-cut as a mechanism for

determining the corresponding oil recovery. Straight-line extrapolation method

assumes that the mobility ratio is equal to unity and the plot of the log of relative

permeability ratio of the flowing liquids, (krw/kro), versus water saturation, Sw is a

straight line. According to Omoregie and Ershaghi (1978), this approach is only

13

applicable for fw greater than 0.5 and it should not be used during the early stage of

a water flood.

Fig 2.5: Production plot showing log of water cut versus cumulative oil production (Satter and Thakur, 1994)

Fig 2.7: Production plot showing log of oil cut versus cumulative oil production (Satter and Thakur, 1994)

14

2.4.3 FETKOVICH TYPE CURVES

In 1973, Fetkovich' proposed a dimensionless rate-time type curve for decline curve

analysis of wells producing at constant bottomhole pressure. These type curves,

shown in Fig. 2.8, were developed for slightly compressible liquids. These type

curves combined analytical solutions to the flow equation in the transient region with

empirical decline curve equations in the pseudo-steady state region. The transient

portion of the Fetkovich type curve is based on an analytical solution to the radial

flow equation for slightly compressible liquids with a constant pressure inner

boundary and a no-flow outer boundary.

The following dimensionless equations were used:

The late time portion of Fetkovich’s type curve, describing Pseudo-steady state or

boundary dominated flow is given by

Where the dimensionless variables are:

15

Fig 2.8: Composite of analytical and empirical type curves and the standard “empirical” exponential, hyperbolic and harmonic decline curve solution on a single dimensionless curve (Fetkovich, 1980).

Though the type curve analysis can be cumbersome in application, Fetkovich (1980)

says that, “type curve approach provides unique solution upon which engineers can

agree or shows when a unique solution is not possible with a type curve only. In the

event of a non unique solution, a most probable solution can be obtained if the

producing mechanism is obtained. This gives the decline curve analysis (type curve)

a good diagnostic power”

2.4.4 OMOREGIE AND ERSHAGHI (X-PLOT)

According to Omoregie and Ershaghi (1978), for a fully developed water flood with

no major operational changes, a plot of fractional water cut versus total recovery is

used often to obtain a quick estimate of the ultimate recovery at given economic

water cut. The extrapolation of the past performance on the “cut-cum” plot is a

complicated task. The difficulty arises mainly because a curve fitting by simple

16

polynomial approximation does not result in satisfactory answers in most cases. The

concept of fractional flow was based on the Buckley-Leverett recovery formula given

by,

where

This method is based purely on the actual performance of a water flood project. It

implicitly considers reservoir configurations, heterogeneity, and displacement

efficiency. One major assumption is that the operating method will remain relatively

unchanged. An interesting application of this plot is that the linear plot of cumulative

production ER versus X, the two constants, m and n, may be used to derive a field

krw/kro.

Fig 2.9: The X-plot for a hypothetical three-layer system (Ershaghi and Abdassah, 1984))

17

2.4.5 HALL AND HEARN PLOT FOR INJECTORS

Hall and Hearn method are applicable to water flooded operations where injection

wells are surface pressure controlled and where bottom hole injection just below

formation parting pressure (FPP) is desired (Jarrel and Stein, 1991). These methods

help in monitoring the acceleration of fill-up and average reservoir pressure growth in

an actual field.

While the Hall plot is the plot of the bottom hole injection pressure versus the

cumulative water injected, Hearn plot is the plot of inverse injection index versus

cumulative water injection. Monitoring these plots as pressure and rate increases

renders qualitative interpretation of whether the rates are being maintained below the

formation parting pressure (FPP).

The assumptions inherent in these plots are piston-like displacement, steady state,

radial single phase and single layer flow with the reservoir pressure, pe being

constant. It is also assumed that there is no residual gas saturation in the water and

oil zones.

The Hall and Hearn plots can be used to determine reservoir properties such as

transmissivity (kh) etc as reservoir condition changes. These plots are based on the

radial, steady state form of Darcy’s law of flow with the relationship,

Where

According to Chan (1995), the above plots could be useful to evaluate production

efficiency, but they do not reveal any detail on reservoir flow behaviours. Although,

some of the plots could show reservoir characteristics, they do not shed any clue on

18

the timing of the layer breakthrough. Therefore the need for the diagnostic plot was

proposed by Chan. It reveals detailed reservoir flow behaviours, the timing of the

layer breakthrough and the relationship between the rates of change of the WOR

with the excessive water production mechanism.

Fig 2.10: The Hall Plot (Jarrel and Stein, 1991)

Fig 2.11: The Hearn Plot (Jarrel and Stein, 1991)

19

2.4.6 DIAGNOSTIC PLOTs

According to Chan (1995), the log-log plots of WOR (Water-Oil Ratio) versus time or

GOR (Gas-Oil Ratio) versus time show different characteristic trends for different

mechanisms. The time derivatives of WOR and GOR were found to be capable of

differentiating whether the well is experiencing water and gas coning, high-

permeability layer breakthrough or near wellbore channelling. Chan identified three

most noticeable water production mechanisms namely water coning, near well-bore

problems and multi-layer channelling.

Log-log plots of the WOR (rather than water cut) versus time were found to be more

effective in identifying the production trends and problem mechanisms. !t was

discovered that derivatives of the WOR versus time can be used for differentiating

whether the excessive water production problem as seen in a well is due to water

coning or multilayer channelling.

Figures 2.12 through 2.15 (Chan, 1995) illustrate how the diagnostic plots used to

differentiate among the various water production mechanisms. Fig. 2.15 shows a

comparison of WOR diagnostic plots for coning and channelling. The WOR

behaviour for both coning and channelling is divided into three periods; the first

period extends from start of production to water breakthrough, where the WOR is

constant for both mechanisms. When water production begins, Chan claims that the

behaviour becomes very different for coning and channelling. This event denotes the

beginning of the second time period.

For coning, the departure time is often short (depending on several variables), and

corresponds to the time when the underlying water has been drawn up to the bottom

of the perforations. According to Chan, the rate of WOR increase after water

20

breakthrough is relatively slow and gradually approaches a constant value. This

occurrence is called the transition period.

For channelling, the departure time corresponds to water breakthrough for the most

water-conductive layer in a multi-layer formation, and usually occurs later than for

coning. Chan (1995) reported that the WOR increases relatively quickly for the

channelling case, but it could slow down and enter a transition period, which is said

to correspond to production depletion of the first layer.

Thereafter, the WOR resumes at the same rate as before the transition period. This

second departure point corresponds to water breakthrough for the layer with the

second highest water conductivity. According to Chan, the transition period between

each layer breakthrough may only occur if the permeability contrast between

adjacent layers is greater than four.

After the transition period(s), Chan describes the WOR increase to be quite rapid for

both mechanisms, which indicates the beginning of the third period. The channelling

WOR resumes its initial rate of increase, since all layers have been depleted. The

rapid WOR increase for the coning case is explained by the well producing mainly

bottom water, causing the cone to become a high-conductivity water channel where

the water moves laterally towards the well. Chan (1995), therefore, classifies this

behaviour as channelling.

Log-log plots of WOR and WOR time derivatives (WOR') versus time for the different

excessive water production mechanisms are shown in Figures 2.13 through 2.15.

Chan (1995) proposed that the WOR derivatives can distinguish between coning and

channelling. Channelling WOR' curves should show an almost constant positive

slope (Fig. 2.13), as opposed to coning WOR' curves, this should show a changing

negative slope (Fig. 2.14). A negative slope turning positive when “channelling”

21

occurs as shown in Figure 2.15, characterizes a combination of the two

mechanisms. Chan classifies this as coning with late channelling behaviour.

Fig 2.12: Water coning and channelling WOR comparison. Chan (1995)

Fig 2.13: Multi-layer channelling WOR and WOR derivatives. Chan (1995)

22

Fig 2.14: Bottom-water coning WOR and WOR derivatives. Chan (1995)

Fig 2.15: Bottom water coning with late time channelling. Chan (1995)

23

Recently, the use of Chan’s WOR diagnostic plots has received significant interest in

the oil and gas industry (Seright, 1997). However, the applications of the diagnostic

plot to field data and results from numerical simulations have indicated their

limitations, especially the use of derivative plots with noisy production data. There is

therefore, a need to determine the validity of using these plots as a diagnostic

method and to see if it can be fine tuned; and that is the focus of this work.

24

CHAPTER 3

3.0 METHODOLOGY

This chapter deals with the methodology and the major directions of this research.

The presentation includes:

1. The flow chart for the evaluation of water production mechanism gives a step

by step procedure on how to evaluate water production mechanism in the

reservoir.

2. The production well performance evaluation and diagnostics deals with

various plots on well evaluation and diagnostics

3. The injection well performance evaluation plots and the diagnostic plots.

The methodology is validated using production and injection data in a case study of

the 31S reservoir, (Stevens Formation), Elk Hills, California.

3.1.1 FLOWCHART FOR EVALUATION OF WATER PRODUCTION MECHANISMS

Fig 3.1 describes a step by step procedure on how to evaluate water production

problem effectively. The procedure is comprehensive. However, it may not apply to

every reservoir since every reservoir may have its own peculiarities.

25

Fig 3.1: Flow Chart for the Evaluation of water production.

4

Start evaluation

Production data

Performance evaluation

Water production?

Continue monitoring

Diagnostic plot

PLT

Mechanical problem?

1 3

2

No

Yes

Yes

No

26

Fig 3.1(cont’d): Flow Chart for the Evaluation of water production.

No

Yes

No No

1

Treatment/ shutdown

Treatment

Improve?

Detect leakage?

Coning/ channelling?

Sonic tool

Stop evaluation

Still producing?

Improve?

2

Further Diagnostic plot

3

Yes

4

Yes

Yes Yes

No

No

27

Some parts of the flowchart are described below

3.1.2 Sonic Tool

These are wire line tools used mainly for evaluation. It is used to evaluate the state

of the set cement. A leaky casing close to a water zone can be detected and an

effective treatment administered (Osisanya 2010).

3.1.3 Treatment

Most mechanical problem are casing related. That is, either a casing with

compromised integrity or a poor cementing job. These usually require a remedial

cement job like squeeze cementing to shut off the zone or a change of the casing in

question. This can serve as treatment of the mechanical problem in question

(Reynolds 2003).

3.1.4 Monitoring

Prior to the necessary treatment and even after the treatment, it is a good

management practice to monitor the reservoir performance. This will help to

determine if the reservoir is producing as required or if a necessary treatment has

improved the reservoir performance (Bailey et al, 2000).

3.2 THE CASE STUDY

The data for The Case Study is taken from the 31S reservoir, Elk Hills, California.

The geology of the 31S reservoir is described by Ezekwe (2010). The largest of the 3

anticlines in the Elk Hills is the 31S. The entire 31S is occupied by the Main Body “B”

(MBB) and the Western 31S (W31S) reservoirs. The 31S structure is 9 miles long

28

and 1.5 miles wide. The MBB/W31S is a turbite sandstone reservoir consisting of

feldspathic, clay rich deposits.

Fig 3.1: The MBB/W31S Structure (Ezekwe, 2010)

Table 3.1 lists the fluid properties used in The Case Study.

Table 3.1: Summary of the Reservoir properties for the Case Study (Ezekwe,2010).

Porosity range 11-26%

Air permeability range 10-250 md

Initial water saturation range 30-45%

Initial average reservoir pressure 3150 psia

Initial bubble point pressure 2965 psia

Reservoir temperature 210 oF

Reservoir oil viscosity 0.40 cp

Oil gravity 36 oAPI

Mobility ratio 0.6

Residual oil saturation to water 25%

Estimated original oil-in-place 610 MMBO

29

For the reservoir study of The Case Study, a 50 x 15 x 8 grid was used to establish

an 8 layer model characteristic of the reservoir (Ezekwe 2010), Each grid block had

an areal dimension of 300ft x 500ft. The model had a variable thickness as shown in

Table 3.2. An average porosity of 20% and permeability of 750md was used with the

vertical permeability, kv, varying according to the layers. These values were input into

the black oil simulator, (SENSOR, 2009).

Table 3.2: Reservoir thickness distribution for each layer in the model

Top 6400

40 L1

6440

45 L2 6485

40 L3 6525

35 L4

6560

20 L5

6580

20 L6

6660

35 L7

35 L8

6695

WOC 6730 35 L8

The summary of some of the reservoir properties used is as shown in Table 3.1.

Production and injection perforations are through all the layers. There were 44 wells

with 26 injectors and 18 producers in the model. Initial reservoir pressure is 3150psi

at 6400ft depth with bubble point pressure at 2950 psi. Rock compressibility was

taken to be 5x10ˉ6 per psi. The simulations were run for 10 years to provide data for

30

evaluating field performance and determination of water production mechanisms

using diagnostic plots. The trends of the diagnostic plots from the simulated data

were compared with those from the actual field data for The Case Study.

3.2.1 FIELD PRODUCTION PERFORMANCE EVALUATION

This entails the plots of the field data to determine how well the field is producing

based on the oil and water production rates, pressure and water cut with cumulative

production and time.

The plots considered here are:

- Oil and water production rates with time

- Oil cut with time

- Water cut with cumulative production

- X-Plot

Where,

water oil ratio (WOR) is given as

water cut is

31

For the X-Plot, the plot of the X function against cumulative production is carried out

such that the x function is given by

3.2.2 FIELD PRODUCTION DATA DIAGNOSTIC PLOT

The diagnostic plots for the field and well production are described for identifying the

nature and the cause of the water production problems; that is, the water production

mechanisms in the reservoir. The plots considered for the diagnosis are

- X-Plot

- The Log-Log plot of Water Oil Ratio with time

- The Log- Log Plot of Water Oil Ratio derivative with time

The X-Plot can be used to evaluate the performance of water flooding via a straight

line extrapolation which gives the corresponding recovery for given water cut. For

this reason, water cuts greater than 0.5 is used for this analysis.

Another application of the plots is the ability to diagnose layering in a multi layered

system. The assumption inherent in this plot is that the operating conditions in the

reservoir remain relatively unchanged.

The WOR and the WOR derivative (WOR′) plots are used in combination to

diagnose the reservoir related water production mechanism prevailing in the

reservoir. It takes into cognisance that an upward sloping of the WOR plot with time

indicates increased water production. It also considers that the upward sloping of the

WOR derivative indicates multilayer channelling while the downward sloping

indicates water coning. For the purpose of this work, the centre difference first order

derivative approach is used to determine the WOR′. Where WOR′ is given by

32

3.2.3 FIELD INJECTION PERFORMANCE EVALUATION

Analysis of field injection was carried out using data from The Case Study to

evaluate injectivity and performance. The plots considered for the evaluation are the

injection rate and injection pressure plots versus time and cumulative water injected.

The plot of injection pressure and rate versus time are used to determine how well

the pressure of the reservoir is being maintained in order not to exceed the

Formation Parting Pressure and the rates for achieving this.

3.2.4 INJECTION WELL DIAGNOSTIC PLOTS

The main plots considered for the diagnosis of water injection behaviour at the

injection wells are the Hall plot and the Hearn Plot. Injection data from both

simulations and actual field data were plotted for The Case Study.

The Hall plot is the plot of the Bottom hole injection pressure with time while the

Hearn plot is the plot of inverse injectivity index, Jˉ1, with time. These plots are used

to diagnose cases like near wellbore fracture, fracture extension and wellbore

plugging which are used to evaluate. All these cases would tell how well the water

flooding project is doing.

The inverse injectivity index, Jˉ1 is defined as

33

The assumptions inherent in the Hall and Hearn plots are

- Piston Displacement

- Steady State behaviour of the reservoir

- Radial single phase flow

- Single layer flow

- Average reservoir pressure

It is important to recall the rationale behind the methodology of this work. The ideal

trends of WOR, WOR’, X-Plot etc are generated from the simulations and used for

the basis (templates) for comparison with actual trends obtained from the plots of

field data.

34

CHAPTER 4

4.0 RESULTS AND DISCUSSION OF RESULTS

The results obtained from The Case Study are presented and discussed in this

section. The order of the discussion is thus;

The reservoir simulation performance evaluation and diagnostics are

discussed.

The field performance and diagnostics with the field data from The Case

Study are presented.

The performance evaluation and diagnostics of the injection wells from the

simulation as well as that of the Case study are presented.

4.1 EVALUATION OF RESERVOIR PERFORMANCE TRENDS FROM SIMULATED DATA Oil rate and water rate as well as water cut and oil cut data are compared to the ideal

trends obtained from simulation

4.1.1 ANALYSIS OF SIMULATED OIL RATE AND WATER RATE PLOTS

The simulated field and wells production rates and water cut versus time are shown

in Fig 4.1 and Fig 4.2 and Fig 4.3respectively, it can be seen that as water

production increased, oil production starts to decrease with time. From the material

balance premise for water flooding, the rate of water injected is equal to the oil

produced and water produced in reservoir barrels/day. Therefore, an increase in

water rate would imply a decrease in oil rate since the injection rate is taken to be

constant during pressure maintenance. It is also observed that if water rate equals oil

35

rate, then water cut is 50%, and therefore at this point and beyond, the X-plot can be

effective for performance evaluation and diagnoses of water production

mechanisms. The point beyond which the X-Plot analysis is valid is shown in Figures

4.1 through 4.3.

Fig 4.1: Simulated Field Production rates and water cut versus time

0

10

20

30

40

50

60

70

80

90

100

0

50000

100000

150000

200000

250000

300000

0 1000 2000 3000 4000

WC

UT

(%

)

QW

AT

(S

TB

/D),

QO

IL (

ST

B/D

), Q

GA

S (

MC

F/D

)

TIME (DAYS)

FIELD SIMULATED PRODUCTION RATES AND WCUT

QWAT Impes

QOIL Impes

WCUT Impes50% water cut

36

Fig 4.2: Simulated Well Production rates and water cut versus time (Well P2)

Fig 4.3: Simulated Well Production rates and water cut versus time (Well P3)

0

10

20

30

40

50

60

70

80

90

100

0

5000

10000

15000

20000

0 500 1000 1500 2000 2500 3000 3500 4000

WC

UT

(%

)

QW

AT

(S

TB

/D),

QO

IL (

ST

B/D

),

TIME (DAYS)

SIMULATED PRODUCTION RATES AND WCUT (WELL P2 )

QWAT Impes

QOIL Impes

WCUT Impes

50% water cut

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0

5000

10000

15000

20000

0 500 1000 1500 2000 2500 3000 3500 4000

WC

UT

QW

AT

(S

TB

/D),

QO

IL (

ST

B/D

),

TIME (DAYS)

SIMULATED PRODUCTION RATES AND WCUT (WELL P3 )

QWAT Impes

QOIL Impes

WCUT Impes

50% water cut

37

The plot of the oil rate versus time in figures 4.1, 4.2 and 4.3 shows an exponential

decline trend. Therefore, making it possible to fit in the proposed model by Lawal

and Utin (2007). The trends of the plots of oil cut versus time are analysed for the

simulated data in Fig 4.4, Fig 4.5 and Fig 4.6. Fig 4.4 shows the trends for the field,

while Fig 4.5 and Fig 4.6 show the trend for producer well P2 and producer P3,

respectively. These curves show a linear trend and therefore, can be extrapolated at

a given economic limit of oil cut to project future oil production and reserves for the

water flooding process.

Fig 4.4: Simulated Field Oil cut versus Time

1%

10%

100%

0 500 1000 1500 2000 2500 3000 3500 4000

Oil

Cu

t

Time, Days

Simulated Field Oil Cut with Time (Field)

38

Fig 4.5: Simulated Well Oil cut versus Time (Well P2)

Fig 4.6: Simulated Well Oil cut versus Time (Well P3)

1%

10%

100%

0 500 1000 1500 2000 2500 3000 3500 4000

Oil

Cu

t

Time, Days

Simulated Well Oil Cut with Time(Well P2)

1%

10%

100%

0 500 1000 1500 2000 2500 3000 3500 4000

Oil

Cu

t

Time, Days

Simulated Well Oil cut with production time (Well P3)

39

From the plot of water cut with cumulative oil production, a linear extrapolation can

be established for high tension water flooding, where the log plot of krw/kro with

saturation is linear (Ershaghi and Abdassah, 1984). The plots of log of water cut

versus cumulative oil production are shown in Figures 4.7 through 4.9. However,

Figures 4.7 through 4.9 do not show a linear fit from the beginning of oil production.

However, these plots can still be extrapolated if linear trends are observed at higher

water cuts. From the plots below, linear trends at higher water cuts are extrapolated

and the corresponding recovery can be deduced from an economic water cut.

Fig 4.7: Simulated Field water cut versus cumulative production

1.00%

10.00%

100.00%

0 50000 100000 150000 200000 250000 300000

Wat

er

Cu

t

Cumulative Oil Production, MMSTB

Simulated Field Water Cut with Cumulative Production

point at whichlinearextrapolation starts

40

Fig 4.8: Simulated well water cut versus cumulative production (Well P2)

Fig 4.9: Simulated well water cut versus cumulative production (Well P3)

1.00%

10.00%

100.00%

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Wat

er

Cu

t


Simulated Well Water Cut with Cumulative Production (Well P2)

point at which linearextrapolation starts

10.00%

100.00%

0 2000 4000 6000 8000 10000 12000 14000 16000

Wat

er

Cu

t


Simulated Well Water Cut with Cumulative Production (Well P3)

point at which linearextrapolation starts

41

4.1.2 ANALYSIS OF X-PLOT SIMULATED DATA

The X-plot which gives more precise diagnostics than the regular semi log plot of

water cut versus cumulative production is shown in Fig 4.10 through Fig 4.12. The

simulated field plot, Fig 4.10 shows a more linear trend after a production of

150MMSTBO. However, as shown in Fig 4.11 and Fig 4.12, no linear trends were

observed for simulated well X-Plot. Another trend observed in Fig 4.11 and Fig 4.12

are the changing slope which depicts the existence of layers with varying

permeabilities. Because X is a function of water cut (which is dependent on water

rate), therefore, as permeability changes with layers, then water cut changes,

likewise X. This implies a changing slope for the X-Plot. For the performance

evaluation of these wells, like the plot of water cut with production, the X-Plot trends

can be extrapolated at regions where it is most linear (at higher water cuts) and

therefore give the corresponding cumulative production for a given water cut.

Fig 4.10: Simulated Field X-Plot

y = 0.004x + 1.4746

2.00

2.10

2.20

2.30

2.40

2.50

100.0 150.0 200.0 250.0 300.0

X

Cumulative Oil Production, MMSTBO

Simulated Field X Plot

42

Fig 4.11: Simulated X-Plot (Well P2)

Fig 4.12: Simulated X-Plot (Well P3)

2.0000

2.1000

2.2000

2.3000

2.4000

2.5000

2.0 4.0 6.0

X


Simulated Well X Plot (Well P2)

point at whichextrapolationstarts

Changing slopes depicting Layers with varying permeabiltiy

2.0

2.1

2.2

2.3

2.4

2.5

6.0 7.0 8.0 9.0 10.0 11.0 12.0

X


Simulated Well X Plot (Well P3)

point at whichextrapolationstarts


43

4.2 EVALUATION OF RESERVOIR PERFORMANCE TRENDS FROM FIELD CASE STUDY

Oil rate and water rate as well as water cut and oil cut data for the field Case Study

One are compared to the ideal trends obtained from simulation.

4.2.1 ANALYSIS OF FIELD OIL RATE AND WATER RATE PLOTS Oil rate and water rate versus time plots of the field data for The Case Study are

analyzed in the following section. Figures 4.13 and 4.14 shows the graph of the field

and well production rates, respectively. Similar plots for additional wells are shown in

Appendix A. As deduced from the simulated results, oil rate would decline with

increase in water production. These can be seen in the field plots (Fig 4.13) and the

individual well plots (Fig 4.14). The plot of oil and water rate with time shows the

point of equal oil rate and water rate and beyond, therefore making the plots of water

cut with cumulative production and the X-plot applicable. It is noted that individual

well plots (e.g., Fig. 4.14) show the sequence of events (like well shut-ins) during the

production of the wells.

44

Fig 4.13: Field production rate versus time

Fig 4.14: Well production rate versus time (Well PR1)

0

5000

10000

15000

20000

25000

30000

35000

0 2000 4000 6000 8000 10000

Oil

and

Wat

er

Rat

e, S

TB/D

Time, Days

Field Production Rate with time

Water Rate

Oil Rate

oil rate equalswater rate

0

5000

10000

15000

20000

25000

30000

35000

0 1000 2000 3000 4000 5000 6000 7000

Oil

and

Wat

er

Rat

e, S

TB/D

Time, Days

Production Rate with Time (Well PR1)

Oil Rate

Water Rate


Well shut in

45

Fig 4.15, Fig 4.16 and Fig 4.17 are the semi-log plots of oil cut with cumulative oil

production for The Case Study. Fig 4.15 (Field data) shows a linear trend which can

be extrapolated to an economic limit for oil cut. However, the data from the wells

PR1 and PR2 shown in Fig 4.16 and Fig 4.17 does not show this linear trend and

this can be explained by the peculiarities of the individual well exhibit such as,

periodic shut ins and possible work over, during well production. Similar plots with

this trend are shown in Appendix B. Although the field shows a trend, this would not

be very effective in telling the performance of individual wells.

Fig 4.15: Field Oil cut versus Time

1%

10%

100%

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

Oil

Cu

t

Time, Days

Field Oil Cut with Production Days

46

Fig 4.16: Well Oil cut versus time (Well PR1)

Fig 4.17: Well Oil cut versus Production time (Well PR2)

1%

10%

100%

0 1000 2000 3000 4000 5000 6000 7000 8000

Oil

Cu

t

Time, Days

Oil Cut with Production time (Well PR1)

1%

10%

100%

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Oil

Cu

t

Time, Days

Well Oil Cut with Production time (Well PR2)

47

Fig 4.18: Field Water cut versus Cumulative Production

Fig 4.19: Well Water cut versus Cumulative Production (Well PR1)

1.00%

10.00%

100.00%

0 20 40 60 80 100 120 140 160 180 200

Wat

er

cut,

fra

ctio

n

Cumulative production, MMSTBO

Water Cut with Cumulative Production

General water cut linear trend

High water cut linear trend

1.00%

10.00%

100.00%

10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0

Wat

er

Cu

t


Water Cut with Cumulative Production (Well PR1)


General water cut linear trend

48

Fig 4.18 and Fig 4.19 above shows the log of water cut versus cumulative production

for the field and well. Plots of other wells are shown in Appendix B. As was observed

for the simulated plots, linear trends were established at higher water cuts and the

extrapolation of this linear trend to a given economic limit water cut will give the

cumulative oil production for that water cut. Ultimately, the recovery with the water

flooding can be determined and therefore the effectiveness of the operative drive

mechanism.

4.2.2 ANALYSIS OF FIELD X-PLOT

Fig 4.20 and Fig 4.21 show the field X-Plot for The Case Study. The X-plots of water

cut above 50% showed linear trends which can be extrapolated to the cumulative

production to estimate the recovery. However, the diagnostic trend that was

established for the simulated data could not be observed. Similar plots are shown in

Appendix C.

49

Fig 4.20: Field X-Plot

Fig 4.21: Well X-Plot (Well PR1)

y = 0.004x + 1.378

2

2.01

2.02

2.03

2.04

2.05

100 150 200 250 300

X

Cumulative Oil production, MMSTBO

X-PLOT

y = 0.1207x - 3.4534

2.00

2.50

3.00

3.50

40.0 45.0 50.0 55.0

X


X PLOT, Well PR1

50

4.3 DIAGNOSIS OF SIMULATED RESERVOIR PRODUCTION PERFORMANCE

Figures 4.22 through 4.24 shows the trend of the simulated log-log plots of WOR and

WOR’ with time. Fig. 4.22 which is a field simulated plot, shows a positive slope for

WOR but the WOR’ plot is inconclusive. From Fig 4.23 and Fig 4.24, there is an

increasing trend for both WOR and WOR’. Chan (1995) shows the diagnostic trends

of reservoir related problems to have positive slopes for both WOR and WOR’ for

channelling and a positive and negative slope for WOR and WOR’ respectively for

coning. Fig 4.22 does not indicate the trends to conclude whether the water

production is due to channelling or coning. Fig 4.23 and Fig 4.24, exhibits the trend

of water channelling. In addition, there are changing slopes which is observed both

in the WOR and WOR’ plots. This is an indication of the different layers that exist in

the reservoir model.

Fig 4.22: Simulated Field Diagnostic Plot

0.0001

0.001

0.01

0.1

1

10

100

100 1000 10000

WO

R a

nd

WO

R'

Time, Days

Simulated Field Diagnostic Plot

WOR

WOR'

51

Fig 4.23: Simulated Well Diagnostic Plot (Well P2)

Fig 4.24: Simulated Well Diagnostic Plot (Well P3)

0.0001

0.001

0.01

0.1

1

10

100

100 1000 10000

WO

R a

nd

WO

R'

Time, Days

Simulated Diagnostic Plot (Well P2)

WOR

WOR'


0.0001

0.001

0.01

0.1

1

10

100

100 1000 10000

WO

R a

nd

WO

R'

Time, Days

Simulated Diagnostic Plot (Well P3)

WOR

WOR'


52

4.4 DIAGNOSIS OF RESERVOIR PRODUCTION PERFORMANCE

Since the simulated model which fairly characterizes The Case Study shows some

diagnostic features of channelling, it can be inferred, that the case study can equally

be diagnosed using the Chan’s log-log plot of WOR and WOR’ with time. Fig 4.25

shows the log-log plot of WOR and WOR’ (diagnostic plot) of the field. This plot

shows increasing slope for both WOR and WOR’. This is an indication that

channelling might be the cause of the water production. However, a look at some of

the wells shows this trend better. Fig 4.26 (Producing well PR1) equally shows an

increasing positive slope of both WOR and WOR’. This indicates that channelling is

the cause of the water production. The changing slopes are however not as clear

with the other wells (see Appendix D). This could be partially due to the number of

shut-ins that existed after the water production had commenced (see Fig 4.14).

These shut-ins as well as other irregularities in production smear the WOR, and the

WOR’ resulting in a lot of noise which would be difficult to diagnose (see Appendix

B).

The diagnosed channelling would seem to be the true diagnosis since, The Case

Study seems to exhibit a layering system with the upper Main Body having higher

permeability and therefore water is being channelled through the upper layers,

Ezekwe (2010)

53

Fig 4.25: Field Diagnostic Plot

Fig 4.26: Well Diagnostic Plot (Well PR1)

0.0001

0.001

0.01

0.1

1

10

100

1000 10000

WO

R a

nd

WO

R'

Time, Days

Field Diagnostic Plot

WOR

WOR'

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1.00E+01

1.00E+02

100 1000 10000

WO

R a

nd

WO

R'

Time, Days

Diagnostic Plot (Well PR1)

wor

wor'

Changing slopes depicting layers of varying permeabilty

54

4.5 INJECTION WELL PERFORMANCE

For successful water flooding to occur, the simple premise is that the rate at which

water is injected is equal to the sum of the rate of oil displaced and water produced

in reservoir barrels, Dake (1978). This implies that a premature water break through

implies a reduced oil recovery. Therefore, there is a need to evaluate the

performance of the injectors.

4.5.1 SIMULATED INJECTION WELL PERFORMANCE

Fig 4.27 and Fig 4.28 shows the simulated injection water rate with time. The

pressure was kept constant and the injection rate regulated till the fill up point.

Beyond the liquid fill-up, the injection rate was fairly constant. this implies that the

reservoir pressure has been maintained.

Fig 4.27: Simulated Injection rate and pressure versus time (Injector SI1)

0

10000

20000

30000

40000

50000

60000

0 500 1000 1500 2000 2500 3000 3500 4000

QW

I (S

TB

/D)

TIME (DAYS)

SIMULATED INJECTION RATE VERSUS TIME

Pressure maintenance, therefore constant rate

55

Fig 4.28: Simulated Injection rate and pressure versus time (Injector SI4)

4.5.2 FIELD WATER INJECTION PERFORMANCE

Three injectors were analysed for performance. The injection pressure and rate with

time are shown on Fig 4.29 through Fig 4.31. From Fig 4.29, initially, injection rate

was kept fairly constant thereby increasing pressure; however, with time, injection

pressure water rate such that a fill up point was not observed. Fig 4.30 shows a fairly

constant pressure with time; however, there were some increases in the rate as

against the decrease that is expected for constant pressure injection. Fill up was not

observed. Fig 4.31 shows another constant pressure with declining injection rate but

at approximately 2250 days, there was an increase in injection rate. This increase in

rate with constant pressure is a pointer at fracturing. Therefore, these wells would be

good candidates for diagnosis. The Hall and Hearn plots were used to diagnose

these wells.

0

10000

20000

30000

40000

50000

60000

0 500 1000 1500 2000 2500 3000 3500 4000

QW

I (S

TB

/D)

TIME (DAYS)

SIMULATED INJECTION RATE VERSUS TIME

56

Fig 4.29: Well Injection rate and pressure versus time (Injector F1)


0

500

1000

1500

2000

2500

3000

3500

4000

0

500

1000

1500

2000

2500

3000

0

50

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00

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00

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00

25

00

Pre

ssu

re, p

si

inje

ctio

n r

ate

, STB

/D

Time, Days

Injection Pressure and Rate with time

inj rate

inj press

(C) decrease in injection rate andpressure

0

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1000

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3500

4000

0

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1000

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0

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00

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00

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00

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00

Inje

ctio

n P

ress

ure

, psi

Inje

ctio

n r

ate

, STB

/D

Time, Days


inj rate

inj press

(E)increase in injection rate with constant injection pressure

57


4.6 INJECTION WELL DIAGNOSIS

The diagnostic plots for the simulated wells are illustrated and the observed trends

are used to diagnose the field data. The Hall’s method and the Hearn’s method are

used to achieve this.

4.6.1 SIMULATED WATER INJECTION DIAGNOSIS

From Fig 4.32 and Fig 4.33, the simulated injectors SI1 and SI4 was diagnosed with

the Hall’s method which is the plot of cumulative (∆P)(∆t) with cumulative water

injected. Both plots show a change in slope after an initial period. Apparently the

initial slope moves to the fill up, after which pressure maintenance starts. This results

in a change of the slope. These points are indicated in Fig 4.32 and Fig 4. 33. After

pressure maintenance, a change in the slope would indicate either wellbore plugging

(increase in slope) or fracture (decrease in slope).

0

500

1000

1500

2000

2500

3000

3500

4000

0

500

1000

1500

2000

2500

3000

0

50

0

10

00

15

00

20

00

25

00

30

00

Inle

ctio

n P

ress

ure

, psi

Inje

ctio

n R

ate

, STB

/D

Time, Days


inj rate

inj press(E)Increase in injection rate with constant injection pressure

58

Fig 4.32: Simulated Well Hall Plot (Injector SI1)

Fig 4.33: Simulated Well Hall Plot (Injector S4)

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

0 5000 10000 15000 20000 25000

Cu

mu

lati

ve (

∆P

)(∆

t), P

si-D

ay

Cumulative Water Injected, MSTB

Hall Plot, Injector SI1

Fill upFill up

Pressuremaintenance

0.00E+00

5.00E+05

1.00E+06

1.50E+06

2.00E+06

2.50E+06

0 5000 10000 15000 20000 25000 30000

Cu

mu

lati

ve (

∆P

)(∆

t), P

si-D

ay

Cumulative Water Injected, MSTB

Hall Plot, Injector SI4

Pressuremaintenance

Fill up

59

4.6.2 FIELD WATER INJECTION DIAGNOSIS

Figs 4.34 through Fig 4.36 show the Hall plot for injectors F1, F2 and F3. The Hall

plot for the selected injection wells show different diagnostic trends that would affect

the performance of the water flooding. Fig 4.34 shows the Hall Plot for injector well

F1. In this plot, after the initial fill up (A), and pressure maintenance (B) for a period,

there was a reduction in the slope which indicates extensive fracture. This could

explain why there was reduction in both pressure and rate (C) for injector F1 in

Fig4.29, shown earlier. A case where water injected is lost into the formation and

pressure cannot be maintained. Both injector well F2 and F3, (Fig 4.35 and Fig 4.36

respectively) show an increase in the slope after the fill up (A) and pressure

maintenance (B). This may indicate near wellbore plugging (D). This would explain

why an increase in rate (E) observed earlier in rate and pressure-time plot (Fig 4.30)

did not affect the constant pressure behaviour (Fig 4.31).

Fig 4.34: Well Hall Plot (Injector F1)

0.00E+00

1.00E+07

2.00E+07

3.00E+07

4.00E+07

5.00E+07

0.00E+00 5.00E+05 1.00E+06 1.50E+06 2.00E+06 2.50E+06

Cu

mu

lati

ve (

∆P

)(∆

t), P

si-D

ays

Cumulative Water Injected, STB

Hall Plot

(A)Fill up

(B)Pressuremaintenance

(C)Change in slope due to Extensive fracture

60



0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

3.00E+07

0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06

Cu

mu

latv

e (

∆P

)(∆

t), P

si-D

ays

Cumulative Water injected, STB

Hall Plot

(A)Fill up


(D)Change in slope due to wellboreplugging

0.00E+00

5.00E+06

1.00E+07

1.50E+07

2.00E+07

2.50E+07

3.00E+07

3.50E+07

0.E+00 2.E+05 4.E+05 6.E+05 8.E+05 1.E+06 1.E+06

Cu

mu

lati

ve (

∆P

)(∆

t), P

si-D

ays


Hall Plot

(A)Fill up


(D)Change in slope due to wellbore plugging

61

Fig 4.37 shows the use of the Hearn plot to diagnose the injection well performance.

Although, Fig 4.37 shows some trend, Fig E-1 and Fig E-2 (Appendix E) does not

show any definite trend that can be diagnosed. At point F on Fig 4.37 there is an

increase in slope which implies an increase in transmissibility possibly due to near

wellbore fracturing. Thus, the Hearn plot is confirming the fracture observed earlier

with the Hall plot.

Fig 4.37: Well Hearn Plot (Injector F1)

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

10000 100000 1000000 10000000

Inve

rse

Inje

ctiv

ity,

∆P

/qw

, Psi

/BB

L/D


Hearn Plot

(F) Change in slope due to secondary permeability (fracture)

62

4.7 GUIDELINES

The following steps of guidelines are therefore suggested for the evaluation of water

production mechanism.

1. Collect data frequently

2. Establish the workflow for the analysis of the data

3. Carry out the reservoir performance evaluation

4. Check for applicability of available methods

5. Carry out diagnoses (If there is reduced performance)

6. Combine diagnosis with logging

7. Treat the problem

8. Re-evaluate for the improvement of reservoir performance

9. Continue steps 1-8 till the end of production

63

CHAPTER 5

5.0 CONCLUSIONS AND RECOMMENDATIONS

5.1 SUMMARY AND CONCLUSIONS

The objectives of this work are to understand the application of various diagnostic

plots to analyse water production problems and to identify water production

mechanisms. The research is also aimed at developing a detailed workflow for water

production evaluation to support reservoir management.. The workflow which uses

numerical simulation and diagnostic plots was applied to analyse the water

production and injection performance of an actual field case study.

Based on the work presented in this study, the following conclusions were arrived at:

Water production and injection characteristics of Case Study (MBB/W31S)

were adequately diagnosed for both the production wells and the injection

wells.

For the producers in Case Study, a problem of multi-layered channelling was

diagnosed. Some injection wells show near wellbore plugging while others

show extensive near wellbore fracturing.

The results of the Case Study validates the workflow proposed for diagnosing

reservoir and near wellbore mechanisms controlling water production and

injection characteristics in the field.

For effective evaluation of water production and injection behaviour of wells in

a reservoir, there is need to verify the applicability of any of the available

diagnostic methods to the particular field of interest. This would ensure that

accurate diagnoses are derived to provide the necessary information for

planning water management programmes in the field.

64

5.3 RECOMMENDATIONS

The following recommendations are presented for future research work to improve

the proposed methodology and results obtained in this study:

A performance evaluation and diagnosis be carried out for the case study of

gas production and guidelines be established for the mitigation of high Gas-

Oil ratios

A fine grid scale and more representative reservoir model should be built of

the Case Study to conduct a history match of the production and injection

data to improve the diagnostic procedure developed in this study.

There is a need to quantify the uncertainty and risk associated with the use of

diagnostic plots, and this topic is proposed for further research.

65

REFERENCES

1. Bailey B, Crabtree M, Tyrie J, Elphick J, Kuchuk F, Romano C, Roodhart L, Water Control, Oilfield Review 12 (Spring 2000) 30-51.

2. Bondar Valentina, 1997, The Analysis and Interpretation of Water- Oil Ratio Performance in Petroleum Reservoir, Moscow State Academy of Oil and Gas, Russia

3. Chan, K.S.: Water Control Diagnostic Plots, paper SPE 30775, SPE Annual

Technical Conference and Exhibition, Dallas, October 22-25

4. Dake L. P 1978 Fundamentals of Reservoir Engineering Elsevier Publishing, Amsterdan, Netherlands, pp 345-348

5. Ershaghi, I. And Omoregie, O. A method for Extrapolation of water cut versus

recovery plots”, JPT (February 1978), 203-204

6. Ershaghi, I. and Abdassah, D. A Prediction Technique for Immiscible Processes Using Field Performance Data, JPT (April 1984), 664-670

7. Ezekwe Nnaemeka, 2010 Petroleum Reservoir Engineering Practice,

Prentice Hall Publishing Company, pp 728-734

8. Fetkovich M. J. ”Decline Curve Analysis using Type Curve” SPE 04629 (1067-1077)

9. http://karl.nrcce.wvu.edu/ (downloaded 25/10/2010).

10. Jarrel P. M. and Stein M. H. 1991 Maximizing Injection Rates in Wells Recently

Converted to Injection Using Hearn and Hall Plots. Paper SPE 21724 presented at the SPE Petroleum Operations Symposium, Oklahoma City, Oklahoma April 7-9

11. Lawal K. A. And Utin E. 2007, A didactic analysis of water cut trend during

exponential Oil decline. Paper SPE 111920 Presented at the 31st Nigeria Annual International Conference, Abuja, Nigeria August 6-8

12. Reynolds R. R, “Produced water and associated Issue”, Petroleum Technology Transfer Council, 2003.

http://karl.nrcce.wvu.edu/

66

13. Satter A. and Thakur G.C., 1994 Integrated Petroleum Reservoir Management, A team approach, PennWell Publishing Company

14. SENSOR Compositional and Black Oil Simulation Software, 2009, Coats Engineering. http://www.CoatsEngineering.com

15. Seright, R.S.: “Improved Methods for Water Shutoff,” Annual Technical Progress Report (U.S. DOE Report DOE/PC/91008-4), U.S. DOE Contract DE-AC22-94PC91008, BDM-Oklahoma Subcontract G4S60330 (Nov. 1997)

. 16. Spivey J.P, Gatens J.M, Semmelbeck M.E and Lee W.J. 1992 Integral Type

Curves for Advanced Decline Curve Analysis” Paper 24301 presented at the SPE Annual Technical Conference, Mid-Amarillo, Texas, DOI, 1992.

http://www.coats/

67

APPENDIX-A: NOMENCLATURE

ᶲ = Porosity, fraction

µ =viscosity, cp

µw = viscosity of water, cp

qi = Initial rate, STB/D

q = rate, STB/D

B = Formation Volume Factor, rb/STB

t = time, days

h = Reservoir thickness

fw = water cut, fraction

ER = Recovery

K = permeability, mD

tD = Dimensionless time

qD = Dimensionless rate

RD = Dimensionless radius

Ct = total compressibility, 1/psi

PI = Initial Reservoir pressure, psi

Pwf = Bottom hole Flowing Pressure

68

APPENDIX-B: CASE STUDY ONE OIL RATE AND WATER RATE PLOTS

Fig B-1: Well production rate versus time (Well PR2)


0

2000

4000

6000

8000

10000

12000

14000

0 2000 4000 6000 8000 10000 12000

Oil

and

Wat

er

rate

, STB

/D

Time, MMYY

Production Rate with time (Well PR2)

oilrate

water rate

Shut-in


0

2000

4000

6000

8000

10000

12000

14000

0 2000 4000 6000 8000 10000

Oil

and

Wat

er

Rat

e, S

TB/D

Time, Days


oil rate

water rate

Shut-in

69


Fig B-4: Well Oil cut versus Production time (Well PR3)

0

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4000

6000

8000

10000

12000

14000

0 1000 2000 3000 4000 5000 6000 7000

Oil

and

Wat

er

Rat

e ,

STB

/D

Time, Days


WATER RATE

OIL RATEShut-in


1%

10%

100%

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Oil

Cu

t

Time, Days


70

Fig B-5: Well Oil cut versus Production time (Well PR4)

Fig B-6: Well Water cut versus Cumulative Production (Well PR3)

1%

10%

100%

0 1000 2000 3000 4000 5000 6000 7000

Oil

Cu

t

Time, Days


1.00%

10.00%

100.00%

20.000 25.000 30.000 35.000 40.000

Wat

er

Cu

t




General water cut trend

71



1.00%

10.00%

100.00%

10.000 15.000 20.000 25.000 30.000

Wat

er

Cu

t




General water cut trend

1.00%

10.00%

100.00%

10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0

Wat

er

Cu

t



72

APPENDIX C– CASE STUDY ONE X-PLOT

Fig C-1: Well X-Plot (Well PR3)


y = 0.4693x - 14.404

2.0000

2.5000

3.0000

3.5000

34.000 36.000 38.000

X


X PLOT, Well PR3

y = 0.303x - 4.2872

2.0000

2.5000

3.0000

3.5000

4.0000

20.000 22.000 24.000 26.000

X

CUMULATIVE PRODUCTION, MMSTBO

X PLOT Well PR4

73


y = 0.8923x - 30.864

2.0000

2.1000

2.2000

2.3000

2.4000

2.5000

36.500 37.000 37.500

X

Cumulative Oil Production , MMSTBO

X PLOT, Well PR2

74

APPENDIX D– CASE STUDY ONE DIAGNOSTIC PLOTS

Fig D-1: Well Diagnostic Plot (Well PR3)


0.0001

0.001

0.01

0.1

1

10

100

1000 10000

WO

R a

nd

WO

R'

Time, Days


wor

wor'

0.0001

0.001

0.01

0.1

1

10

100

1000 10000

WO

R A

ND

WO

R'

TIME, DAYS


WOR

WOR'

75


0.0001

0.001

0.01

0.1

1

10

100

1000 10000

WO

R a

nd

WO

R'

Time, Days

DIAGNOSTIC PLOT (Well PR2)

wor

wor'

76

APPENDIX E – CASE STUDY ONE INJECTION WELL DIAGNOSTIC

PLOTS

Fig E-1: Hearn Plot (Well Injector F2)

Fig E-2: Hearn Plot (Well injector F3)

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

100000 1000000 10000000

Inve

rse

Inje

ctiv

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/qw

, PSI

/STB

/D

Cumulatve water injected, STB

Hearn Plot

0

0.2

0.4

0.6

0.8

1

1.2

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Inve

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inje

ctiv

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∆P

/qw

, Psi

/STB

/D

Cumulative Water Injected, STB

Hearn Plot

Documents

Diagnostic Plots for Analysis of Water Production and