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
i
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.
ii
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 Xplot 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.
iii
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
iv
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.
v
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
vi
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
vii
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
viii
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
ix
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 4.30: Well Injection rate and pressure versus time (Injector 2) ...................................... 55
Fig 4.31: Well Injection rate and pressure versus time (Injector 3) ...................................... 55
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 4.35: Well Hall Plot (Injector 2) ...................................................................................... 58
Fig 4.36: Well Hall Plot (Injector 1) ...................................................................................... 59
Fig 4.37: Well Hearn Plot (injector 1)................................................................................... 60
Fig A-1: Well production rate versus time (Well PR2) .......................................................... 65
Fig A-2: Well production rate versus time (Well PR3) .......................................................... 65
Fig A-3: Well production rate versus time (Well PR4) .......................................................... 66
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 A-7: Well Water cut versus Cumulative Production (Well PR4) ..................................... 68
Fig A-8: Well Water cut versus Cumulative Production (Well PR2) ..................................... 68
Fig B-1: Well X-Plot (Well PR3) ........................................................................................... 69
Fig B-2: Well X-Plot (Well PR4) ........................................................................................... 69
Fig B-3: Well X-Plot (Well PR2) ........................................................................................... 70
Fig C-1: Well Diagnostic Plot (Well PR3)............................................................................. 71
x
LIST OF FIGURES (CONT’D)
Fig C-2: Well Diagnostic Plot (Well PR4)............................................................................. 71
Fig C-3: Well Diagnostic Plot (Well PR2)............................................................................. 72
Fig D-2: Hearn Plot (Well injector F2).................................................................................. 73
Fig D-2: Hearn Plot (Well injector F3) .................................................................................. 73
xi
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
xii
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
.
xiii
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.
1
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.
2
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
3
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.
4
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
5
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
6
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).
7
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.
8
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).
9
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.
10
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)
11
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
12
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)
13
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:
14
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
15
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))
16
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, p e 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
17
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)
18
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, highpermeability 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
19
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”
20
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)
21
Fig 2.14: Bottom-water coning WOR and WOR derivatives. Chan (1995)
Fig 2.15: Bottom water coning with late time channelling. Chan (1995)
22
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.
23
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.
24
Start
evaluation
Production data
Performance evaluation
No
Water
production?
Continue
monitoring
Yes
Diagnostic plot
PLT
No
Mechanical
problem?
Yes
3
4
1
Fig 3.1: Flow Chart for the Evaluation of water production.
25
2
4
1
2
3
Further
Diagnostic plot
Sonic tool
No
No
Coning/
channelling
?
Detect
leakage?
Yes
Yes
Treatment/
shutdown
Treatment
No
No
Improve?
Improve?
Yes
Yes
Still
producing?
Yes
No
Stop
evaluation
Fig 3.1(cont’d): Flow Chart for the Evaluation of water production.
26
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
27
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
28
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
6485
45
L2
6525
40
L3
35
L4
6580
20
L5
6660
20
L6
35
L7
35
L8
35
L8
6440
6560
6695
WOC
6730
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
29
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
30
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
31
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
32
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.
33
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
34
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.
FIELD SIMULATED PRODUCTION RATES AND WCUT
300000
100
250000
80
QWAT Impes
70
200000
QOIL Impes
50% water cut
60
WCUT Impes
150000
50
40
100000
30
20
50000
10
0
0
0
1000
2000
3000
4000
TIME (DAYS)
Fig 4.1: Simulated Field Production rates and water cut versus time
35
WCUT (%)
QWAT (STB/D), QOIL (STB/D), QGAS (MCF/D)
90
SIMULATED PRODUCTION RATES AND WCUT (WELL P2 )
100
90
80
15000
70
60
50% water cut
10000
50
QWAT Impes
40
QOIL Impes
30
WCUT Impes
5000
WCUT (%)
QWAT (STB/D), QOIL (STB/D),
20000
20
10
0
0
0
500
1000
1500
2000
2500
3000
3500
4000
TIME (DAYS)
Fig 4.2: Simulated Well Production rates and water cut versus time (Well P2)
SIMULATED PRODUCTION RATES AND WCUT (WELL P3 )
100%
90%
80%
15000
70%
60%
50% water cut
10000
50%
QWAT Impes
QOIL Impes
WCUT Impes
WCUT
QWAT (STB/D), QOIL (STB/D),
20000
40%
30%
5000
20%
10%
0
0%
0
500
1000
1500
2000
2500
3000
3500
4000
TIME (DAYS)
Fig 4.3: Simulated Well Production rates and water cut versus time (Well P3)
36
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.
Simulated Field Oil Cut with Time (Field)
Oil Cut
100%
10%
1%
0
500
1000
1500
2000
Time, Days
Fig 4.4: Simulated Field Oil cut versus Time
37
2500
3000
3500
4000
Simulated Well Oil Cut with Time(Well P2)
Oil Cut
100%
10%
1%
0
500
1000
1500
2000
2500
3000
3500
4000
Time, Days
Fig 4.5: Simulated Well Oil cut versus Time (Well P2)
Simulated Well Oil cut with production time
(Well P3)
Oil Cut
100%
10%
1%
0
500
1000
1500
2000
2500
Time, Days
Fig 4.6: Simulated Well Oil cut versus Time (Well P3)
38
3000
3500
4000
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 k rw/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.
Simulated Field Water Cut with Cumulative
Production
100.00%
Water Cut
point at which
linear
extrapolation starts
10.00%
1.00%
0
50000
100000
150000
200000
250000
Cumulative Oil Production, MMSTB
Fig 4.7: Simulated Field water cut versus cumulative production
39
300000
Simulated Well Water Cut with Cumulative
Production (Well P2)
100.00%
Water Cut
point at which linear
extrapolation starts
10.00%
1.00%
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
Cumulative Oil Production, MMSTB
Fig 4.8: Simulated well water cut versus cumulative production (Well P2)
Simulated Well Water Cut with Cumulative
Production (Well P3)
100.00%
Water Cut
point at which
linear
extrapolation starts
10.00%
0
2000
4000
6000
8000
10000
12000
14000
16000
Cumulative Oil Production, MMSTB
Fig 4.9: Simulated well water cut versus cumulative production (Well P3)
40
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.
Simulated Field X Plot
2.50
y = 0.004x + 1.4746
2.40
X
2.30
2.20
2.10
2.00
100.0
150.0
200.0
Cumulative Oil Production, MMSTBO
Fig 4.10: Simulated Field X-Plot
41
250.0
300.0
Simulated Well X Plot (Well P2)
2.5000
2.4000
Changing slopes depicting
Layers with varying
permeabiltiy
point at which
extrapolation
starts
X
2.3000
2.2000
2.1000
2.0000
2.0
4.0
6.0
Cumulative Oil Production, MMSTBO
Fig 4.11: Simulated X-Plot (Well P2)
Simulated Well X Plot (Well P3)
2.5
2.4
Changing slopes depicting Layers
with varying permeabiltiy
X
2.3
2.2
point at which
extrapolation
starts
2.1
2.0
6.0
7.0
8.0
9.0
10.0
Cumulative Oil Production, MMSTBO
Fig 4.12: Simulated X-Plot (Well P3)
42
11.0
12.0
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.
43
Field Production Rate with time
35000
Oil and Water Rate, STB/D
30000
25000
oil rate equals
water rate
20000
Water Rate
15000
Oil Rate
10000
5000
0
0
2000
4000
6000
8000
10000
Time, Days
Fig 4.13: Field production rate versus time
Production Rate with Time (Well PR1)
35000
Oil and Water Rate, STB/D
30000
oil rate equals
water rate
25000
20000
Oil Rate
15000
Water Rate
Well shut in
10000
5000
0
0
1000
2000
3000
4000
5000
6000
Time, Days
Fig 4.14: Well production rate versus time (Well PR1)
44
7000
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.
Field Oil Cut with Production Days
Oil Cut
100%
10%
1%
0
1000
2000
3000
4000
5000
Time, Days
Fig 4.15: Field Oil cut versus Time
45
6000
7000
8000
9000
10000
Oil Cut with Production time (Well PR1)
Oil Cut
100%
10%
1%
0
1000
2000
3000
4000
5000
6000
7000
8000
Time, Days
Fig 4.16: Well Oil cut versus time (Well PR1)
Well Oil Cut with Production time (Well PR2)
Oil Cut
100%
10%
1%
0
1000
2000
3000
4000
5000
6000
Time, Days
Fig 4.17: Well Oil cut versus Production time (Well PR2)
46
7000
8000
9000
Water Cut with Cumulative Production
100.00%
Water cut, fraction
High water cut
linear trend
General water cut
linear trend
10.00%
1.00%
0
20
40
60
80
100
120
140
160
180
200
Cumulative production, MMSTBO
Fig 4.18: Field Water cut versus Cumulative Production
Water Cut with Cumulative Production (Well PR1)
Water Cut
100.00%
High water cut linear
trend
10.00%
General water cut
linear trend
1.00%
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
Cumulative Oil Production, MMSTBO
Fig 4.19: Well Water cut versus Cumulative Production (Well PR1)
47
55.0
60.0
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.
48
X-PLOT
2.05
y = 0.004x + 1.378
2.04
X
2.03
2.02
2.01
2
100
150
200
250
300
Cumulative Oil production, MMSTBO
Fig 4.20: Field X-Plot
X PLOT, Well PR1
3.50
y = 0.1207x - 3.4534
X
3.00
2.50
2.00
40.0
45.0
50.0
Cumulative Oil Production, MMSTBO
Fig 4.21: Well X-Plot (Well PR1)
49
55.0
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.
Simulated Field Diagnostic Plot
100
WOR and WOR'
10
1
0.1
WOR
0.01
WOR'
0.001
0.0001
100
1000
10000
Time, Days
Fig 4.22: Simulated Field Diagnostic Plot
50
Simulated Diagnostic Plot (Well P2)
100
Changing slopes depicting Layers
with varying permeabiltiy
WOR and WOR'
10
1
0.1
WOR
WOR'
0.01
0.001
0.0001
100
1000
10000
Time, Days
Fig 4.23: Simulated Well Diagnostic Plot (Well P2)
Simulated Diagnostic Plot (Well P3)
100
Changing slopes depicting Layers
with varying permeabiltiy
WOR and WOR'
10
1
0.1
WOR
WOR'
0.01
0.001
0.0001
100
1000
10000
Time, Days
Fig 4.24: Simulated Well Diagnostic Plot (Well P3)
51
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)
52
Field Diagnostic Plot
100
WOR and WOR'
10
1
0.1
WOR
WOR'
0.01
0.001
0.0001
1000
10000
Time, Days
Fig 4.25: Field Diagnostic Plot
Diagnostic Plot (Well PR1)
1.00E+02
Changing slopes
depicting layers of
varying permeabilty
WOR and WOR'
1.00E+01
1.00E+00
1.00E-01
wor
wor'
1.00E-02
1.00E-03
1.00E-04
100
1000
10000
Time, Days
Fig 4.26: Well Diagnostic Plot (Well PR1)
53
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.
SIMULATED INJECTION RATE VERSUS TIME
60000
QWI (STB/D)
50000
40000
30000
20000
Pressure maintenance, therefore
constant rate
10000
0
0
500
1000
1500
2000
2500
3000
3500
4000
TIME (DAYS)
Fig 4.27: Simulated Injection rate and pressure versus time (Injector SI1)
54
SIMULATED INJECTION RATE VERSUS TIME
60000
QWI (STB/D)
50000
40000
30000
20000
10000
0
0
500
1000
1500
2000
2500
3000
3500
4000
TIME (DAYS)
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.
55
Injection Pressure and Rate with time
3000
4000
3000
2000
2500
1500
2000
1500
1000
Pressure, psi
injection rate, STB/D
3500
(C) decrease in injection rate and
pressure
2500
inj rate
inj press
1000
500
500
2500
2000
1500
1000
500
0
0
0
Time, Days
Fig 4.29: Well Injection rate and pressure versus time (Injector F1)
Injection Pressure and Rate with time
(E)increase in injection rate with
constant injection pressure
3000
4000
Injection rate, STB/D
3000
2000
2500
1500
2000
1500
1000
1000
500
Injection Pressure, psi
3500
2500
500
3000
2500
2000
1500
1000
500
0
0
0
Time, Days
Fig 4.30: Well Injection rate and pressure versus time (Injector F2)
56
inj rate
inj press
Injection Pressure and Rate with time
4000
3500
2500
3000
2000
2500
1500
2000
(E)Increase in injection rate with
constant injection pressure
1500
1000
1000
500
Inlection Pressure, psi
Injection Rate, STB/D
3000
inj rate
inj press
500
3000
2500
2000
1500
1000
500
0
0
0
Time, Days
Fig 4.31: Well Injection rate and pressure versus time (Injector F3)
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).
57
Hall Plot, Injector SI1
Cumulative (∆P)(∆t), Psi-Day
2.50E+06
2.00E+06
Pressure
maintenance
1.50E+06
Fill up
1.00E+06
5.00E+05
0.00E+00
0
5000
10000
15000
20000
25000
Cumulative Water Injected, MSTB
Fig 4.32: Simulated Well Hall Plot (Injector SI1)
Hall Plot, Injector SI4
Cumulative (∆P)(∆t), Psi-Day
2.50E+06
Pressure
maintenance
2.00E+06
1.50E+06
Fill up
1.00E+06
5.00E+05
0.00E+00
0
5000
10000
15000
20000
Cumulative Water Injected, MSTB
Fig 4.33: Simulated Well Hall Plot (Injector S4)
58
25000
30000
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).
Hall Plot
Cumulative (∆P)(∆t), Psi-Days
5.00E+07
(C)Change in slope due
to Extensive fracture
4.00E+07
3.00E+07
(B)Pressure
maintenance
2.00E+07
1.00E+07
(A)Fill up
0.00E+00
0.00E+00
5.00E+05
1.00E+06
1.50E+06
Cumulative Water Injected, STB
Fig 4.34: Well Hall Plot (Injector F1)
59
2.00E+06
2.50E+06
Hall Plot
3.00E+07
Cumulatve (∆P)(∆t), Psi-Days
2.50E+07
(D)Change in slope
due to wellbore
plugging
2.00E+07
(B)Pressure
maintenance
1.50E+07
1.00E+07
(A)Fill up
5.00E+06
0.00E+00
0.0E+00
1.0E+06
2.0E+06
3.0E+06
4.0E+06
Cumulative Water injected, STB
Fig 4.35: Well Hall Plot (Injector F2)
Hall Plot
Cumulative (∆P)(∆t), Psi-Days
3.50E+07
(D)Change in slope due
to wellbore plugging
3.00E+07
2.50E+07
(B)Pressure
maintenance
2.00E+07
1.50E+07
1.00E+07
(A)Fill up
5.00E+06
0.00E+00
0.E+00
2.E+05
4.E+05
6.E+05
8.E+05
Cumulative Water injected, STB
Fig 4.36: Well Hall Plot (Injector F1)
60
1.E+06
1.E+06
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.
Hearn Plot
Inverse Injectivity, ∆P/qw, Psi/BBL/D
0.5
0
-0.5
(F) Change in slope due to
secondary permeability (fracture)
-1
-1.5
-2
-2.5
-3
10000
100000
1000000
Cumulative Water injected, STB
Fig 4.37: Well Hearn Plot (Injector F1)
61
10000000
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
62
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.
63
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 GasOil 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.
64
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 (10671077)
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 31 st Nigeria
Annual International Conference, Abuja, Nigeria August 6-8
12. Reynolds R. R, “Produced water and associated Issue”, Petroleum Technology
Transfer Council, 2003.
65
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.
66
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
67
APPENDIX-B: CASE STUDY ONE OIL RATE AND WATER RATE PLOTS
Production Rate with time (Well PR2)
14000
Oil and Water rate, STB/D
12000
10000
Shut-in
8000
oilrate
6000
oil rate equals
water rate
4000
water rate
2000
0
0
2000
4000
6000
8000
10000
12000
Time, MMYY
Fig B-1: Well production rate versus time (Well PR2)
Production Rate with Time (Well PR3)
14000
Oil and Water Rate, STB/D
12000
10000
8000
6000
oil rate
Shut-in
water rate
4000
2000
0
0
2000
4000
6000
8000
Time, Days
Fig B-2: Well production rate versus time (Well PR3)
68
10000
Production Rate with Time (Well PR4)
14000
Oil and Water Rate , STB/D
12000
10000
8000
oil rate equals
water rate
WATER RATE
6000
Shut-in
OIL RATE
4000
2000
0
0
1000
2000
3000
4000
5000
6000
7000
Time, Days
Fig B-3: Well production rate versus time (Well PR4)
Oil Cut with Production time (Well PR3)
Oil Cut
100%
10%
1%
0
1000
2000
3000
4000
5000
6000
7000
Time, Days
Fig B-4: Well Oil cut versus Production time (Well PR3)
69
8000
9000
Oil Cut with Production time (Well PR4)
Oil Cut
100%
10%
1%
0
1000
2000
3000
4000
5000
6000
7000
Time, Days
Fig B-5: Well Oil cut versus Production time (Well PR4)
Water Cut with Cumulative Production
(Well PR3)
100.00%
Water Cut
High water cut
linear trend
10.00%
General water
cut trend
1.00%
20.000
25.000
30.000
35.000
Cumulative Oil Production, MMSTBO
Fig B-6: Well Water cut versus Cumulative Production (Well PR3)
70
40.000
Water Cut with Cumulative Production
(Well PR4)
100.00%
Water Cut
High water cut
linear trend
10.00%
General water
cut trend
1.00%
10.000
15.000
20.000
25.000
30.000
Cumulative Oil Production, MMSTBO
Fig B-7: Well Water cut versus Cumulative Production (Well PR4)
Water Cut with Cumulative Production
(Well PR2)
Water Cut
100.00%
10.00%
1.00%
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
55.0
Cumulative Oil Production, MMSTBO
Fig B-8: Well Water cut versus Cumulative Production (Well PR2)
71
60.0
APPENDIX C– CASE STUDY ONE X-PLOT
X PLOT, Well PR3
3.5000
y = 0.4693x - 14.404
X
3.0000
2.5000
2.0000
34.000
36.000
38.000
Cumulative Oil Production, MMSTBO
Fig C-1: Well X-Plot (Well PR3)
X PLOT Well PR4
4.0000
y = 0.303x - 4.2872
X
3.5000
3.0000
2.5000
2.0000
20.000
22.000
24.000
CUMULATIVE PRODUCTION, MMSTBO
Fig C-2: Well X-Plot (Well PR4)
72
26.000
X PLOT, Well PR2
2.5000
y = 0.8923x - 30.864
2.4000
X
2.3000
2.2000
2.1000
2.0000
36.500
37.000
Cumulative Oil Production
, MMSTBO
Fig C-3: Well X-Plot (Well PR2)
73
37.500
APPENDIX D– CASE STUDY ONE DIAGNOSTIC PLOTS
Diagnostic Plot (Well PR3)
100
WOR and WOR'
10
1
0.1
wor
wor'
0.01
0.001
0.0001
1000
10000
Time, Days
Fig D-1: Well Diagnostic Plot (Well PR3)
Diagnostic Plot (Well PR4)
100
WOR AND WOR'
10
1
0.1
WOR
WOR'
0.01
0.001
0.0001
1000
10000
TIME, DAYS
Fig D-2: Well Diagnostic Plot (Well PR4)
74
DIAGNOSTIC PLOT (Well PR2)
100
WOR and WOR'
10
1
0.1
wor
wor'
0.01
0.001
0.0001
1000
10000
Time, Days
Fig D-3: Well Diagnostic Plot (Well PR2)
75
APPENDIX E – CASE STUDY ONE INJECTION WELL DIAGNOSTIC
PLOTS
Hearn Plot
Inverse Injectivity, ∆P/qw, PSI/STB/D
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
100000
1000000
10000000
Cumulatve water injected, STB
Fig E-1: Hearn Plot (Well Injector F2)
Hearn Plot
Inverse injectivity, ∆P/qw, Psi/STB/D
1.2
1
0.8
0.6
0.4
0.2
0
10000
100000
Cumulative Water Injected, STB
Fig E-2: Hearn Plot (Well injector F3)
76
1000000