artificial neural network for diagnosis & mitigation …

i

ARTIFICIAL NEURAL NETWORK FOR DIAGNOSIS & MITIGATION OF WATER

PRODUCTION

A Thesis presented to the Department of Petroleum Engineering

African University of Science and Technology

In Partial Fulfilment of the Requirements for the Degree of

MASTER OF SCIENCE

By

SUNDAY, ANTHONY CHUKS

Supervised by

Professor David Ogbe

African University of Science and Technology

www.aust.edu.ng

P.M.B 681, Garki, Abuja, F.C.T

Nigeria

June, 2016

http://www.aust.edu.ng/

ii

ABSTRACT

From the inception of the oil and gas industry, water production has always been an aching

problem for various operators. Throughout the productive life of a field, oil production is often

accompanied with some amount of water production, which in most cases, is so significant and

unwanted. Because of the great operating, environmental and economic challenges associated

with excess water production, operators are in search for different methods and tools that could

be used to identify the sources of water and prevent or mitigate early water breakthrough in

producing oil and gas wells.

In this study, artificial neural network (ANN) models were developed and used as reservoir

management tools to proffer solution to mitigate excess water production problems. Two cases

were considered to build and train the network models. In case one, three neural network models

were developed and optimized by training with data from only one producing well. The built

network models are called CASNNET1, CASNNET2, and CASNNET3, respectively. In case

two, a neural network model called CASNNET4 was developed by using combined data from

two producing wells for training, validation and testing.

The neural network models in both cases were developed to predict well water cut with an

appreciable degree of accuracy. The accuracy of the models was generalized by testing the

trained and optimized network models on unseen data from the other four wells in the same

reservoir. The generalization of the network shows that CASNNET1, CASNNET2, CASNNET3,

and CASNNET4 have predictive capacities of approximately 92.2%, 86.42%, 88.18% and

79.29%, respectively. Finally, the neural network model results were used jointly with reservoir

simulation results to suggest possible ways of preventing or mitigating excess water production.

Keywords: Reservoir simulation, water cut, water production, Artificial Neural Networks (ANN),

network training, validation and testing.

iii

DEDICATION

My special thanks to the Almighty God my creator. You have brought me this far, my efforts

would have been fruitless without your mercies, inspiration, blessings and abundant graces. This

work is dedicated to the glory of your name.

Thank You Lord.

My special thanks also go to my mother (Mrs. Alice Mary Sunday) and my siblings for all their

prayers, financial and moral support. You have always been there for me. I am standing very tall

and strong because you have always been a firm foundation. God bless you all.

iv

ACKNOWLEDGEMENT

My special thanks to my amiable Supervisor and Head of Department, Professor David Ogbe, for

working tirelessly with me throughout my course work and research period. Your continuous

fatherly guidance, immense support and an unrivaled level of understanding is profoundly

appreciated. Thank you so much, Prof.

I also acknowledge the use of SENSOR 6K software donated by Coats Engineering, Inc., USA. I

am grateful to Brian Coats of Coats Engineering Inc. for making the software available to me. It

was really helpful in my research.

My profound appreciation also goes to my benefactor, the Pan African Material Institute

(PAMI), AUST, for giving me the opportunity to study at AUST through their prestigious

scholarship. I am very grateful.

My profound gratitude also goes to the Faculty and Staff of the African University of Science &

Technology, for affording me with this priceless opportunity to study in this serene environment.

Special thanks to all the Ph.D. students, Dr. Akeem Arinkoola, Engr. (Mrs.) Yetunde Aladeitan,

Mr. Haruna Onuh and Mrs. Opeyemi, for your immense support and academic guidance

throughout my course work and research period.

To my amiable friends, Precious, Obed, Daniel, MaryAnn, Adebayo, Catherine, the rest of my

classmates and all AUST SPE members, thanks for your understanding, cooperation, support,

and encouragement. I really had a nice and memorable time with you guys.

v

NOMENCLATURE

AE Absolute error, %

Bg Gas formation volume factor, RB/MCF

Bo Oil formation volume factor, RB/STB

Bwi Water formation volume factor, RB/STB

Ct Total rock isothermal compressibility, 1/PSI

EF Error fraction, Fraction

GOC Gas-oil contact, FT

GOR Gas-oil ratio, SCF/STB

HC PAVG Average hydrocarbon pressure in the reservoir , PSI

K1… Kn Index representing layer 1 to layer n

Kx Permeability in the x - direction, MD

Ky Permeability in the y - direction, MD

Kz Permeability in the z - direction, MD

OWC Oil-water contact, FT

PAVG Average reservoir pressure, PSI

PBH Well bottomhole pressure, PSIA

PGRID Grid block pressure, PSIA

PI Productivity index, RB-CP/D-PSI

QGAS Gas flow rate, MCF/D

QOIL Oil flow rate, STB/D

Tx Grid block transmissibility in the x - direction, RB-CP/D-PSI

Ty Grid block transmissibility in the y - direction, RB-CP/D-PSI

vi

Tz Grid block transmissibility in the z - direction, RB-CP/D-PSI

WCUT Water cut, %

vii

Table of Contents ABSTRACT .................................................................................................................................... ii

DEDICATION ............................................................................................................................... iii

ACKNOWLEDGEMENT ............................................................................................................. iv

NOMENCLATURE ....................................................................................................................... v

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

LIST OF TABLES ....................................................................................................................... xiii

LIST OF APPENDICES ............................................................................................................... xv

CHAPTER ONE ............................................................................................................................. 1

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

1.1 Statement of Problem ....................................................................................................... 1

1.2 Objectives of Study .......................................................................................................... 2

1.3 Expected Outcomes .......................................................................................................... 2

1.4 Scope of Work .................................................................................................................. 3

CHAPTER TWO ............................................................................................................................ 4

Literature Review............................................................................................................................ 4

2.1 Diagnosis of Water Production Mechanisms ................................................................... 4

2.2 Mitigation of Excess Water Production ......................................................................... 20

2.3 Application of Artificial Neural Network (ANN) .......................................................... 25

2.3.1 ANN Application in Medicine ................................................................................ 25

2.3.2 ANN Application in Oil & Gas Industry ................................................................ 27

CHAPTER THREE ...................................................................................................................... 29

Methodology ................................................................................................................................. 29

3.1 Study Methodology and Workflow ................................................................................ 29

3.2 Reservoir Simulation ...................................................................................................... 29

3.2.1 Reservoir XY Model Description ........................................................................... 29

3.2.2 SENSOR Simulator ................................................................................................ 32

3.2.3 Simulation Runs ...................................................................................................... 33

3.3 Concept of Artificial Neural Networks (ANNs) ............................................................ 33

3.3.1 Classification of Neural Networks .......................................................................... 34

3.3.2 Methodology for Developing Neural Networks ..................................................... 35

3.3.3 Neural Network Models .......................................................................................... 39

3.3.4 Testing the Neural Network Models on New Data ................................................. 42

viii

CHAPTER FOUR ......................................................................................................................... 44

Results & Discussion .................................................................................................................... 44

4.1 Reservoir Simulation ...................................................................................................... 44

4.1.1 Maps of the Reservoir Model ................................................................................. 44

4.1.2 Production Parameters Plots ................................................................................... 49

4.2 Neural Network Models ................................................................................................. 51

4.2.1 Case One – Results of Training Network with One Well ....................................... 51

4.2.2 Case 2 – Results of Training Network with Two Wells ......................................... 59

4.2.3 Results of Testing Neural Network Models on New Wells .................................... 63

4.3 Observation & Analysis ................................................................................................. 70

4.3.1 Sensitivity Analysis ................................................................................................ 70

CHAPTER FIVE .......................................................................................................................... 79

Conclusions & Recommendations ................................................................................................ 79

5.1 Conclusions .................................................................................................................... 79

5.2 Recommendations .......................................................................................................... 80

REFERENCES ............................................................................................................................. 82

APPENDICES .............................................................................................................................. 85

Appendix I: CASNNET1 Water Cut Prediction & Accuracy on Well P26 ................................. 85

Appendix II: CASNNET2 Water Cut Prediction & Accuracy on Well P17 ................................ 89

Appendix III: CASNNET3 Water Cut Prediction & Accuracy on Well P22 ............................... 93

Appendix IV: CASNNET4 Water Cut Prediction & Accuracy on Well P24............................... 97

ix

LIST OF FIGURES

Figure 2.1: Water coning and channeling comparison WOR (K. S. Chan, 1995)………………...5

Figure 2.2: Multilayer channeling WOR and WOR derivatives (K. S. Chan, 1995)……………..5

Figure 2.3: Bottom water coning WOR and WOR derivatives (K. S. Chan, 1995)………………6

Figure 2.4: Bottom water coning with late time channeling behavior (K. S. Chan, 1995)…….....6

Figure 2.5: Experimental matrix for the coning and dynamic WOC cases (S. Gasbarri et al,

2008)……………………………………………………………………………………………..10

Figure 2.6: Experimental matrix for the channel behind casing case (S. Gasbarri et al, 2008)….11

Figure 2.7: Water cut performance in the water coning case. 25oAPI (S. Gasbarri et al,

2008)……………………………………………………………………………………………..12

Figure 2.8: Water cut performance in the water coning case. 18oAPI (S. Gasbarri et al,

2008)……………………………………………………………………………………………..13

Figure 2.9: Water cut performance in the dynamic WOC case. 25oAPI (S. Gasbarri et al,

2008)……………………………………………………………………………………………..14

Figure 2.10: Water cut performance in the flow behind the casing case. 25oAPI

(S. Gasbarri et al, 2008)………………………………………………………………………….15

Figure 2.11: Sample plots of WOR against oil recovery factor for different simulated reservoir

models (M. Rabiei et al., 2010)…………………………………………………………………..16

Figure 2.12: Schematic illustration of method (C. M. Reyes et al., 2010)………………………18

Figure 3.1: Research methodology workflow……………………………………………………29

Figure 3.2: 2D view of the XY model showing fluid saturation distribution of layer

2…………………………………………………………………………………………………..31

Figure 3.3: Schematic of an artificial neuron…………………………………………………….34

x

Figure 3.4: ANN workflow………………………………………………………………………36

Figure 3.5: NARX network (CASNNET1) view………………………………………………...40

Figure 3.6: NARX network (CASNNET4) view………………………………………………...42

Figure 4.1a: Map showing the distribution of fluid saturation at the start of simulation – slice

K2………………………………………………………………………………………………...44

Figure 4.1b: Map showing the distribution of fluid saturation at the end of simulation – slice

K2………………………………………………………………………………………………...44

Figure 4.2a: Map showing the distribution of pressure at the start of simulation – slice

K2……...........................................................................................................................................45

Figure 4.2b: Map showing the distribution of pressure at the end of simulation – slice

K2……...........................................................................................................................................45

Figure 4.3: Map showing the distribution of permeability, kx at the start of simulation – slice

K3………………………………………………………………………………………………...45

Figure 4.4: Map showing the distribution of fluid saturation at the end of simulation – slice

J11………………………………………………………………………………………………..46

Figure 4.5a: Map showing the distribution of fluid saturation at the start of simulation – slice

K15……………………………………………………………………………………………….47

Figure 4.5b: Map showing the distribution of fluid saturation at the end of simulation – slice

K15……………………………………………………………………………………………….47

Figure 4.6a: Map showing the distribution of pressure at the start of simulation – slice

K15……………………………………………………………………………………………….47

Figure 4.6b: Map showing the distribution of pressure at the end of simulation – slice K15…...47

Figure 4.7: Producer P26’s water cut and cumulative production vs. time plot…………………49

xi

Figure 4.8: Producer P23’s water cut and cumulative production vs. time plot…………………50

Figure 4.9: Producer P17’s water cut and cumulative production vs. time plot……………….50

Figure 4.10: Correlation coefficient values of the CASNNET1 – P26………………………….52

Figure 4.11: CASNNET1 – P26 water cut prediction and target plot…………………………..53

Figure 4.12: Correlation coefficient values of the CASNNET2 – P23………………………….55

Figure 4.13: CASNNET2 – P23 water cut prediction and target plot…………………………...56

Figure 4.14: Correlation coefficient values of the CASNNET3 – P17…………………………..58


Figure 4.16: Correlation coefficient values of the CASNNET4 – P16&P26……………………60




Figure 4.20: CASNNET1 – P23 water cut correlation plot……………………………………...64







Figure 4.27a: Well P26’s water cut at different initial production rates…………………………71

Figure 4.27b: Well P26’s cumulative oil production at different initial production rates……….71



xii







xiii

LIST OF TABLES

Table 2.1: Typical Properties of N® Sodium Silicate (PQ Corporation Bulletin 35-02, 2006)…22

Table 2.2: Typical Properties of Diluted N® Sodium Silicate (PQ Corporation Bulletin 35-02,

2006)……………………………………………………………………………………………..23

Table 3.1: Reservoir model description………………………………………………………….30

Table 3.2: Reservoir rock properties of model…………………………………………………..32

Table 3.3: Equilibration parameters……………………………………………………………...32

Table 3.4: Reservoir model’s initial fluid in place………………………………………………32

Table 3.5: Input – Output Parameters for Cases One and Two ………..………………………..41

Table 3.6: Well data used to validate and verify the capability of the Networks………………..43

Table 4.1: Summary of CASNNET1 – P26’s results…………………………………………....53

Table 4.2: CASNNET1 – P26’s one year prediction results…………………………………….54

Table 4.3: Summary of CASNNET2 – P23’s results……………………………………………57




Table 4.7: Generalization of CASNNET1 on Five Wells………………………………………..65



Table 4.10: Generalization of CASNNET4 on Six Wells……………………………………….66

Table 4.11: Effect of change in initial flow rates on well P26’s water cut and Cumulative

production………………………………………………………………………………………..74

xiv


production………………………………………………………………………………………..75

Table 4.13: Effect of change in initial flow rates on well P22’s water cut and cumulative

production………………………………………………………………………………………..76


production………………………………………………………………………………………..77


production………………………………………………………………………………………..78

xv

LIST OF APPENDICES

Appendix I: CASNNET1 Water Cut Prediction and Accuracy on Well P26……………....…. 85

Appendix II: CASNNET2 Water Cut Prediction and Accuracy on Well P17………..……….. 89

Appendix III: CASNNET3 Water Cut Prediction and Accuracy on Well P22……...………… 93

Appendix IV: CASNNET4 Water Cut Prediction and Accuracy on Well P24………..………. 97

1

CHAPTER ONE

Introduction

1.1 Statement of Problem

During the production of oil and gas from petroleum reservoirs, water production can come from

an adjoining aquifer or from water injection wells in a waterflooding process. When there is

excess water production, there is a cost associated with operating both subsurface and surface

production facilities, scale and corrosion problems. Besides, the recovery factor is decreased due

to the bypass of oil by the displacement water front. These factors pose significant financial and

environmental challenges for the petroleum industry.

Gasbarri et al., 2008, classified problems associated with excessive water production into two

broad categories:

1. Problems associated with the reservoir, e.g., water coning, channelization (premature

breakthrough of water in producing wells through channels of high permeability leaving

fluid back in zones of low permeability), and movement of the oil-water contact.

2. Problems associated with near wellbore flow, e.g., flow behind casing.

Very importantly, to accurately predict and mitigate the amount of produced water, the sources

or mechanisms of the water production must be properly identified.

2

1.2 Objectives of Study

The fundamental objective of this study is to develop Artificial Neural Network (ANN) models

that will accurately:

1. Forecast well water cut over the useful life of the field.

2. Identify the mechanisms (sources) of water production.

3. Recommend possible ways of preventing or mitigating excess water production.

The proposed models will be validated and tested on new data to obtain optimized neural

network models that will not only predict water production, but also predict other important

parameters, such as oil and gas production, under the same reservoir and well operating

conditions.

1.3 Expected Outcomes

My expectations in this study are:

1. Understand the practical applications of Artificial Neural Networks (ANNs), especially

as a diagnostic and prediction tool in the petroleum industry.

2. Develop a robust neural network model that could be used to identify the sources of

water production, make a reasonable forecast of water production and other parameters

like oil and gas production.

3. Use neural network as a reservoir management tool to predict and find ways to reduce the

amount of water produced from an oil well/reservoir/field.

4. To be able to justify technically and economically why ANNs could be advantageous to

other conventional analytical and reservoir simulation tools, when used as a diagnostic

and prediction tool.

3

1.4 Scope of Work

This study is limited to the particular reservoir (XY model) described in this work. Every

reservoir model is unique. There are no reservoirs with similar fluid and rock properties; even

reservoirs located in the same field. Therefore, it is pertinent to state here that the neural

network models developed in this study will only do well when fed with data from wells in the

XY reservoir model. However, the same process or similar methodology is used for building

artificial neural networks for other reservoirs. This implies that neural network models can be

developed for any reservoir to solve a well-defined problem. In this study, well water cut is the

problem under investigation. Also, the neural network models built in this study were designed

to predict water cut which is a time dependent variable.

4

CHAPTER TWO

Literature Review

2.1 Diagnosis of Water Production Mechanisms

Several techniques to determine excessive water and gas production mechanisms as seen in oil

and gas producing wells have been developed and verified. Excess water production problems

have been generally classified as: water coning; oil – water contact movement; water channeling

in a multilayered reservoir, and near wellbore problems, among others. However, there are no

effective methods to diagnose these differences. In reality, the problem could be very complex,

and usually is the combination of various mechanisms taking place throughout the useful life of

the production wells and the entire field (K. S. Chan, 1995). Chan presented a methodology

which could be used to quickly diagnose and evaluate the mechanisms of production. This

mainly uses diagnostic plots generated from available production history data. The set of plots

include (1) production history for the natural depletion period or waterflood period for water, oil

and gas, (2) WOR and its derivatives, (3) cumulative oil produced or recovery efficiency, and (4)

oil and gas rate declines. Chan’s plots provide a composite picture of the past and current

production behaviors and the remaining production potential of the well. Chan’s methodology

was applied on wells in several fields in Texas, California, the Gulf Coast and Alaska; and has

been used as one of the effective reservoir management tools for the selection of water control

treatment candidates to improve excess water production treatment success. Figures 2.1 through

to 2.4 (Chan, 1995) illustrate how the diagnostic plots are used to differentiate among the various

water production mechanisms.

5

Figure 2.1: Water coning and channeling comparison WOR (K. S. Chan, 1995)

Figure 2.2: Multilayer channeling WOR and WOR derivatives (K. S. Chan, 1995)

6

Figure 2.3: Bottom water WOR and WOR derivatives (K. S. Chan, 1995)

Figure 2.4: Bottom water coning with late time channeling behavior (K. S. Chan, 1995)

7

Fig. 2.1 shows a comparison of WOR diagnostic plots for coning and channeling. The WOR

behavior for both coning and channeling is divided into three periods: the first period extends

from the start of production to water breakthrough, where the WOR is constant for both

mechanisms. When water production begins, Chan claims that the behavior becomes very

different for coning and channeling. 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 breakthrough is relatively slow and

gradually approaches a constant value. This occurrence is called the transition period. For

channeling, 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 channeling 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 described the WOR increase to be quite rapid for both mechanisms,

which indicates the beginning of the third period. The channeling 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 behavior as channeling.

8

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

excessive water production mechanisms, are shown in Figures 2.2 through to 2.4. Chan (1995)

proposed that the WOR derivatives can distinguish between coning and channeling. Channeling

WOR' curves should show an almost constant positive slope (Fig. 2.2), as opposed to coning

WOR' curves, this should show a changing negative slope (Fig. 2.3). A negative slope turning

positive when “channeling” occurs as shown in Figure 2.4, characterizes a combination of the

two mechanisms. Chan classified this as coning with late channeling behavior. Chan’s WOR

diagnostic plots methodology received significant interest in the oil and gas industry (R. H.

Seright et al., 2003). 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 makes good decision making very difficult.

Previous attempts at diagnosing the problem of water production in oil wells have been carried

out without regard to the random and periodic nature of the problem. By treating the water-oil-

ratio (WOR) as a stationary stochastic time series, a model for diagnosing water production in oil

wells based on Spectral Analysis/Fourier Transformation of the random production data was

presented (Egbe and Appah, 2005). The interest in their research was to transform surface water-

oil rate (WOR) from the time domain to frequency domain in order to gain a clearer

understanding of the mechanism (or source) of the water production. Therefore, the objectives of

their study were: (1) to investigate the spectral properties of surface water production in relation

to the water source, (2) to develop time series/spectral plots for water coning characterization,

and (3) to develop an intelligent software for diagnosing water production using spectral

analysis.

9

Spectral analysis is an aspect of mathematical physics used to analyze systems fluctuating with

time. The two main goals of spectral analysis are: (1) Identification of the nature of the

phenomenon represented by the sequence of observation, and (2) predicting future values of the

time series variables (Egbe and Appah, 2005).

Both of these goals require that the pattern of observed time series data be identified and

formally described. This is accomplished by decomposing the original time series into

underlying sinusoidal functions of different frequencies by direct Fourier transformation of the

input time series. The effect of noise in the transformation is reduced by smoothening the

spectrum, using various moving average windows or smoothing filters. Spectral analysis was

used in diagnosing the different mechanisms causing water production by observing the surface

water-oil ratio. This surface water-oil ratio was the time series of interest. By Fourier

transforming the time series, the water-oil ratio was converted to a spectrum of frequencies with

periods and amplitudes peculiar to the source time series. That spectrum was then used to gain a

clearer insight into the nature and source of the produced water.

In 2008, an interesting method of water production diagnosis using transient test with

multiphase flowmeter was proposed (S. Gasbarri et al., 2008). In their study, they showed how a

multiphase flowmeter (MPFM) may be used as a valuable tool to evaluate water production

problems of a well by imposing transient flowing conditions to the well, and tracking

characteristic parameters such as flow rates, water cut, gas – oil ratio, with the equipment during

the test. Representative curves were shown in their study in order to identify some common

wellbore problems associated with water conformance. The curves, as shown in Figures 2.5–

10

2.10, were obtained through numerical reservoir simulation using a number of cases related to

the most important problems such as: water channeling in stratified formations, mechanical

wellbore integrity, water coning, and movement of oil – water contact.

Figure 2.5: Experimental matrix for the coning and dynamic WOC cases (S. Gasbarri et al,

2008)

11

Figure 2.6: Experimental matrix for the channel behind casing case (S. Gasbarri et al, 2008)

Several simulations were performed in order to determine how sensitive the water cut parameter

is to short term flowrate changes for each water production mechanism. Well production rates

were easily decreased with the use of chokes. The method adopted was to shorten the flowrate to

one – half of what the well had been producing (S. Gasbarri et al., 2008). However, in cases

12

where the well was not at the maximum rate, its production was temporarily increased by

increasing the choke diameter or changing artificial lift settings, such as electric frequency of

ESP, gas lift injection rate, RPM in the sucker rod pump or PCP. Since their methodology was

based on identifying patterns, an actual well will not exactly match with any of the conditions in

their study.

Figure 2.7: Water cut performance in the water coning case. 25oAPI (S. Gasbarri et al, 2008)

13

Figure 2.8: Water cut performance in the water coning case. 18oAPI (S. Gasbarri et al, 2008)

14

Figure 2.9: Water cut performance in the dynamic WOC case. 25oAPI (S. Gasbarri et al, 2008)

15

Figure 2.10: Water cut performance in the flow behind the casing case. 25oAPI

(S. Gasbarri et al, 2008)

Accurate and timely diagnosis of water production mechanism is critical in the success of

applied treatment methodology. While many empirical techniques have been traditionally used in

production data analysis, the significance of the water-oil ratio (WOR) in proper identification of

the type of water production problem in oil wells was critically investigated (M. Rabiei et al.,

2010). They employed Data Mining Techniques to facilitate the extraction of any hidden

predictive information from oil and water production data to be used in water control studies. In

16

their studies, they explored plots of WOR against the oil recovery factor, as shown in Figure

2.11, and used WOR feature subsets to extract predictive data points from those plots to be used

in the classifier along with other reservoir parameters.

Figure 2.11: Sample plots of WOR against oil recovery factor for different simulated reservoir

models (M. Rabiei et al., 2010)

Feature extraction helped in removing irrelevant and redundant information, which adversely

affected the performance of the classifier. Basically, their methodology adopted a meta learning

classification technique called Logistic Model Trees (LMT) to diagnose water production

mechanisms based on WOR data and static reservoir parameters (M. Rabiei et al., 2010). They

built synthetic reservoir models to simulate excess water production due to coning, channeling

and gravity segregated flows. Various cases were then generated by varying some of the input

parameters in each model. A number of key features from the plots of WOR against oil recovery

17

factor were heuristically extracted by segmenting these plots at certain points. LMT classifiers

were then applied to integrate these features with reservoir parameters to build classification

models for predicting the water production mechanism in different scenarios of pre and post

water production stages. Their results revealed that WOR monitoring could also help in

predicting the type of water production mechanisms before the actual problem hit the well,

which means remedial actions could be taken accordingly ahead of time.

A reliability-based systemic method for water production analysis, diagnosis and solution design

was also introduced (C. M. Reyes et al., 2010). They adopted a methodology that integrated

petroleum engineering knowledge, reliability and six sigma tools in a reservoir production

system model representing all potential cause effect relations, and failure modes to identify the

origin of water production and its classification as wanted or unwanted. The method has seven

macro processes: (1) Data gathering and reliability analysis (2) Determination of non-wanted

water production (3) Analysis of causes related to mechanical problems in the well (4) Analysis

of causes related to the well drainage area (5) Analysis of causes related to the reservoir (6)

Definition of corrective and preventive actions (7) Cost, cycle time and resources modeling to

design a solution with the required actions during the life cycle of the field. This method is

schematically shown in Figure 2.12 (C. M. Reyes et al., 2010). Two examples from two fields in

Venezuela were used to describe the application of the method.

18

Figure 2.12: Schematic illustration of method (C. M. Reyes et al., 2010)

Reliability and Six Sigma Tools: Reliability is the probability that a system (integrated by

processes, technologies and personnel) will perform its functions within its design limits for a

given period of time when used under stated conditions. Operational reliability, on the other

hand, is defined as a series of continuous improvement processes that incorporate a systematic,

advanced diagnostic tool, to optimize industrial production, and it is necessary to analyze four

parameters: human reliability, reliability of processes, equipment maintainability and reliability

19

of equipment and individual variation in any, or all of the four parameters affects the overall

performance of reliability of a given system (C. M. Reyes et al., 2010). These tools are: Critical

Analysis (CA), Failure Modes and Effects Analysis (FMEA), Root Cause Analysis (RCA), Risk

Based Inspection (RBI), Benefit Risk Based Inspection (BRBI) and Life Cycle Cost (LCC).

Basically, these tools are used to evaluate the performance of the asset in a systematic way in

order to determine the level of operability, the amount of risk and other mitigation measures

required to ensure its integrity and continuity. In terms of quality, Sigma is a dispersion statistic

which expresses the variability of a set of values about its mean, the smaller the sigma, and the

greater the number of defects. The larger the value of sigma of a process, product or service, the

better is its quality. Six Sigma is a method of management administration and troubleshooting,

framed in the precepts of quality and looking for the lowest ranking of errors in the process

operationally (C. M. Reyes et al., 2010). The analysis of trends in Six Sigma begins with the

formulation of a problem. The tools that can be used to implement the strategy are: 5S, Cause

and Effect, Control and Graphical Analysis Charts, FMEA, Brainstorming, Pareto, Process

Mapping and Simulation (C. M. Reyes et al., 2010). In their study, they identified the source

(origin) of water production by: (1) Reviewing key variables that are used to model typical oil

wells such as – volume of produced fluids, water injection, WOR, water cut, mobility ratio,

reservoir pressure, wellhead pressure, pressure drop at drainage area, injectivity index, remaining

reserves, oil prices, water production cost, reservoir depletion, and water invasion and effect of

specific gravity (2) Modeling cause-and-effect relationships using causal loop diagrams. In

general, their proposed methodology involved gathering information from wells and reservoirs

(history of production, workover, well testing, etc.). This was used to assess the well integrity,

determining which factors were most critical and equipment involved in the production and

20

likely to fail. The next step taken was to perform a Root Cause Analysis of water production

problems, which involved analyzing the well drainage area production system using an FMEA

Analysis sheet and conducting a dynamic simulation using as input, causal diagrams for typical

wells; identifying corrective or preventive actions and the feasibility of implementation, and

finally performing a stochastic simulation to determine the cost of implementing the

methodology and conducting a cost-benefit analysis (C. M. Reyes et al., 2010).

2.2 Mitigation of Excess Water Production

Polymer gels have been successfully applied to control water production in many oil producing

regions of the world, especially in Poza Rica, Northern Mexico (D. Perez et al., 2001). They

discussed three case studies that used a systematic methodology to correctly diagnose near-

wellbore water channeling behind the casing. They adopted a methodology that used diagnostic

plots based on the historical behavior of the water/oil ratio (WOR) as a function of time and

included information from original cement bond logs (CBL’s), oxygen-activated logs during

production to effectively determine the origin of the water, and saturation logs to determine the

water levels independent of the salinity of the water produced (D. Perez et al., 2001). In addition,

they presented successful applications of polymer gels to re-establish zonal isolations in the three

case studies previously mentioned. Their methodology, which was adopted in northern Mexico

corrected water channeling behind the pipe with chromium cross-linked polymer gels. The

advantages of using gels over cement include their flexibility for pumping without a workover

rig, higher control of setting time, ease of cleaning, lack of milling time, and superior operation

costs without risking effective treatment (D. Perez et al., 2001). The presence of water in a

production interval brings questions about the actual level of the OWC. In many cases, this

uncertainty causes premature abandonment of oil reserves assumed to be water invaded. Near-

21

wellbore flow is one of the most prominent causes of confusion because of several factors like

poor cement bond, caverns formed by sand production, channels in the formation, natural

fissures, hydraulic fractures, reduced oil flow caused by formation damage, and frequent

stimulation in the near wellbore. The results of their studies demonstrated the effectiveness of

polymeric gels in both their results and the simplicity of pumping in the field, for remedial

workover operations to correct fissures and channels behind the pipe. The progressive gel time

has a higher flexibility than cement, allowing longer work periods with lower risks of premature

setting. Compared to conventional interventions with cement, their analysis of all associated

costs incurred with gels showed that they are at least 25% lower. The system is compatible with

most formation minerals and is not sensitive to changes in concentration, making it very useful in

field operations. In fact, acid does not affect the isolation effectiveness of the gel (D. Perez et al.,

2001). In spite of these advantages of using cross-linked polymers, the shutoff of the water zone

is not permanent throughout the productive life of the well/reservoir i.e., the polymer gel may

lose its gelation strength with time.

Importantly, soluble silicates have also been used for water control and lost circulation (PQ

Corporation Bulletin 35-02, 2006). Oil and gas industry surveys have estimated the cost of

unwanted water production to be in excess of 50 billion dollars worldwide. These high costs are

incurred for various reasons, such as water flow through fractures, thief zones, high permeability

streaks and water coning, or lack of integrity in cement; safe environmental disposal is also now

included in these costs. An effective means of reducing the flow of unwanted water is by taking

advantage of the gelation and/or polymerization reactions of sodium silicate (PQ Corporation

Bulletin 35-02, 2006).

22

PQ’s silicates have a long history of being reliably used to lower production costs and help

extend the life of the well. By controlling the type and concentration of setting agent, sodium

silicate can be made to gel and set in minutes to hours. The result is an inorganic high strength

gel plug, which can be placed in harsh reservoir environments and at higher temperatures

(>150ºC) where most organic polymers are not suited. Sodium silicate production begins by

fusing sand (SiO2) and soda ash (Na2CO3) in varying proportions at high temperatures. The

resulting glassy materials are dissolved in steam to produce liquid sodium silicate or “water

glass.” PQ sodium silicates are produced in ratios of SiO2:Na2O ranging from 3.22 to 1.00. It is

N® grade sodium silicate that is predominantly used for water control applications. N® can be

diluted prior to application resulting in reduced viscosity and deeper penetration into the zone of

interest, as shown in Tables 2.1 and 2.2 (PQ Corporation Bulletin 35-02, 2006).

Table 2.1: Typical Properties of N® Sodium Silicate (PQ Corporation Bulletin 35-02, 2006)

Wt. Ratio SiO2/Na2O 3.22

%SiO2 28.7

% Na2O 8.9

Density at 68oF,

oBe 41.0

Density at 68oF, lb/gal 11.6

Density at 68oF, lb/gal 1.38

pH 11.3

Viscosity, cp 180

Characteristics Syrupy liquid

23

Table 2.2: Typical Properties of Diluted N® Sodium Silicate (PQ Corporation Bulletin 35-02,

2006)

Sodium silicates can be involved in four distinct types of chemical reactions: (1) Gelation (2)

Metal Ion reactions / Precipitation (3) Hydration / Dehydration (4) Surface Charge Modification

in water and lost circulation control, the gelation and precipitation reactions are exploited in a

cost-effective way. PQ silicates are very stable and do not cause the adverse environmental

effects associated with most gel-forming chemicals. Sodium silicate reactions can take place via

an externally or internally placed setting agent. Soluble silicates contain three components: silica,

alkali, and water – silica molecules exist as monomeric to polymeric forms in equilibrium. The

silica tetrahedral can link to form chains, cyclic and larger polymeric structures. Dilution is a

significant factor in determining the final strength and setting time of the silicate gel plug (PQ

Corporation Bulletin 35-02, 2006).

Water shutoff involves injecting a plugging agent into a production well to seal or selectively

plug water production from high water production zones. In this application, the sodium silicate

is externally catalyzed with a setting agent (activator). Calcium chloride is a good example of an

activator in the formation of stable silicate plugs (PQ Corporation Bulletin 35-02, 2006). Sodium

24

silicate and an activator may be applied through a single tubular by encapsulating the activator in

a material that is temperature sensitive, thus delaying the timing of the reaction. Other potential

activators include mineral acids, acid salts and some organics. Profile control involves injecting a

plugging agent into an injection well to seal or partially block high permeability oil depleted

zones. This allows flood water to be directed to lower permeability oil rich zones. Sodium

silicate offers many of the necessary characteristics to achieve a successful and low-cost

reduction in permeability. Its vital properties are: (1) Low viscosity (2) High gel strength (3)

Flexibility in set times. Properties of plugs formed by the reaction of silicates with mineral acids

and acid salts are: (1) Hard solid plugs prevent influx of water into the wellbore (2) Plugs can be

formed over a temperature range from low to > 300oC (3) Higher temperature of formation

reduces the incidence of syneresis (4) Long-term stability, low and high-temperature

compatibility (5) Environmentally benign (PQ Corporation Bulletin 35-02, 2006).

In preparation of a gelant solution for making cross-linked polymer gels for water shutoff

applications, unpublished experiments and chemical intuition suggest that, unless hydrolyzed

polyacrylamide (HPAM) polymer is fully hydrated before addition of a cross-linker, the final gel

will have lower than optimum mechanical strength, presumably because polymer chains need to

be fully unfolded before proper crosslinking can occur (Shriwal & Lane, 2012). In their research,

they evaluated the gel strengths of “flowing” gels for water shutoff in natural fractures and other

non-matrix features as a function of the time of addition of the cross-linker, relative to the time

of hydration of the polymer. Gels were prepared from moderately high molecular weight HPAM

cross-linked with chromium (III) acetate (CrAc) or polyethyleneimine (PEI). A cross-linker was

25

added after either (1) initial wetting of solid polymer particles or (2) complete dissolution of the

polymer (Shriwal & Lane, 2012).

There are both mechanical and chemical means of decreasing excess water production. The most

common widely used chemical means are “rigid gels” for total shutoff of flow in the near

wellbore area (usually applied to hydraulically-isolated matrix or very near well non-matrix

water shutoff problems) and “flowing gels” used to extrude into non-matrix flow features,

potentially to many tens or even hundreds of feet from the wellbore through which it is injected

(Seright et al., 2001). Shriwal & Lane’s study concerned the preparation of “flowing gels” (low

concentration of moderately high molecular weight polymer) which are used for treating natural

fractures and similar fractures. Polymers have been very effective approaches for permeability

reduction treatment of excess water production from the matrix (rigid gels), as well as from

fractures, faults and similar non-matrix flow features (flowing gels). The most common polymer

gels are derived from a solid-free solution of a water soluble polymer plus a crosslinker (Shriwal

& Lane, 2012).

2.3 Application of Artificial Neural Network (ANN)

2.3.1 ANN Application in Medicine

Artificial Neural Networks (ANNs) are currently a 'hot' research area in medicine, particularly in

the fields of radiology, urology, cardiology, and oncology among many others. It has a huge

application in many areas such as education, business, medicine, engineering and manufacturing

(Dr. N. Ganesan et al., 2010). Neural Network plays an important role in a decision support

system. In their work, an attempt was made to make use of neural networks in the medical field -

carcinogenesis (pre-clinical study). They reported on a systematic review that was conducted to

26

assess the benefit of Artificial Neural Networks (ANNs) as decision-making tools in the field of

cancer. The aim of their research was to apply neural networks and their associated analysis

techniques to health-care, specifically to the management of lung cancer patients (Dr. N.

Ganesan et al., 2010).

Artificial Neural Networks now are used in many fields. They have become well established as

viable, multipurpose, robust computational methodologies with solid theoretic support and with a

strong potential to be effective in any discipline, especially medicine (Dr. N. Ganesan et al.,

2010). In their ANN model, the input neuron values were the demographic data which included

information such as patient’s age, sex, etc. The hidden neuron values were based on heuristic

diagnostic knowledge represented by experience accumulated through years and concerned the

way an expert uses the patient data to make diagnoses. The data obtained from various hospitals

were used for their study. Initially fifty samples were given in Matlab. Basically, in their study,

the authors showed how neural networks are used in the actual clinical diagnosis of lung cancer.

An Artificial Neural Network model, a diagnostic system that performed at an accuracy level

was constructed developed and the performance of neural network structure was investigated for

lung cancer diagnosis problems (Dr. N. Ganesan et al., 2010).

Artificial Neural Network has also been employed in disease diagnosis, where two cases were

studied. The first one was acute nephritis disease; data was the disease symptoms. The second

was the heart disease; data was on cardiac Single Proton Emission Computed Tomography

(SPECT) images (Qeethara K. Al-Shayea, 2011). In their study, a typical feed-forward back

propagation neural network model was proposed to diagnosis diseases. Their model consists of

27

three layers: the input layer, a hidden layer, and the output layer. A one hidden with 20 hidden

layer neurons was created and trained. Most applications of Artificial Neural Networks to

medicine are classification problems, that is, the task is on the basis of the measured features to

assign the patient to one of a small set of classes.

Symptoms, images or signals are the data used in medical diagnosis. The data set is obtained

from UCI Machine Learning Repository. The data was created by a medical expert as a data set

to test the expert system, which will perform the presumptive diagnosis of one of the urinary

system diseases (Qeethara K. Al-Shayea, 2011). The main idea of this data set was to construct

the neural network model, which would perform the presumptive diagnosis of acute nephritis.

Their Artificial Neural Networks showed significant results in dealing with data represented in

symptoms and images. Results showed that the proposed diagnosis neural network could be

useful in identifying the infected person.

2.3.2 ANN Application in Oil & Gas Industry

Polymers and gels have been used extensively in field applications to suppress excess water

production and improve oil productivity. Using actual field cases, a neural network model was

developed to identify candidate wells and predict well performance for water-shutoff treatments

using polymer gels (A. Saeedi et al., 2006). They used a feedforward-backpropagation algorithm

to develop the neural networks. They collected before and after treatment data for 22 wells

treated with polymer gels in the Arbuckle formation in central Kansas. These data were used to

train and verify the accuracy of their network. With only pretreatment well data as input

parameters, the neural networks developed could accurately predict the cumulative oil

production of the well one month after treatment with an average error of 16%, and the

28

cumulative oil production three months after treatment with an average error of 10% (A. Saeedi

et al., 2006).

Several methods are available to estimate the water saturation in shaly formations but the most

commonly used in the industry are those based on petrophysical models, such as Waxman-Smits

and Simandoux. These models have limitations and their input parameters are often not readily

available. This consequently leads to either underestimated or overestimated fluid saturations

(Al-Bulushi et al., 2007). In their study, a methodology based on ANN models was developed

and tested to predict water saturation using wire-line logs and core Dean-Stark data.

The model used in their study was based on a three-layered neural network with a Resilient

Back-propagation (PROP) learning algorithm. The model was successfully tested on the Haradh

sandstone formation (in Oman), yielding a prediction of water saturation with a root mean square

error (RMSE) of around 2.5 saturation units (saturation measured in percentage) and a

correlation factor of 0.91 on the testing data (Al-Bulushi et al., 2007).

A feed forward neural network approach was also developed to locate the infill production wells

in order to increase the total oil production from that production sector (Ghazwan N S, 2012). In

his study, he presented a methodology for the determination of the optimum number and location

of the new infill production wells under development stage of the Southern Iraqi Oil Field.

Ghazwan used 41 data sets of six variables (no. of injection wells, no. of production wells,

injection-production ratio, oil fraction, cumulative water injected and cumulative water

production) as input parameters in his feedforward neural network. His network was developed

to accurately predict cumulative oil production

29

CHAPTER THREE

Methodology

3.1 Study Methodology and Workflow

In this chapter, a methodology which begins with developing a dynamic reservoir model and

culminating in developing an optimized neural network model is adopted. Figure 3.1 shows the

methodology adopted in the research. It includes the major elements of the work flow.

Figure 3.1: Research methodology workflow

3.2 Reservoir Simulation

3.2.1 Reservoir XY Model Description

In this study, a dynamic reservoir XY model was built using the SENSOR simulator (Coats

Engineering Inc., 2011). The model is used to simulate a black oil reservoir with 24 x 15 x 15

Run

Simulation

Data

Collection

Develop Neural

Network Model

Optimize Neural

Network Model

Test Neural

Network Model

Comparison/Analysis

of Network Accuracy

Simulation

Results

Neural Net

Results

Decision Making

30

cell blocks in the grid system. Figure 3.2 shows a schematic of the 2D dynamic model

illustrating the injection well and some of the producers. Tables 3.1 to 3.4 describe the

equilibration data of the model. Rock and fluid properties of both reservoir and aquifer are also

described. The total number of active blocks in the XY model is 9000, which implies that all

blocks in the model are affected by the flow dynamics in the reservoir.

Table 3.1: Reservoir model description

Reservoir Model Description

Fluid Model Black Oil

Grid: NX 24

NY 15

NZ 15

Total Grid Blocks 9000

No. of Active

Blocks 9000

Simulation Time: Start 1/1/1970

End 1/1/1985

Days 5479

Years 15

Time Steps 115

Avg.

Transmissibility: TX 2.3342

(RB-CP/D-PSI) TY 0.84991

TZ 2.1855

Wells: No. of Injector 1

No. of Producer 25

WATER

PROPERTIES: Bwi , RB/STB 1.0034

ɣw, (Water = 1.0) 1.0095

Cw, 1/Psi 0.000001

µw, cp 0.96

Stock Tank Oil: ɣo, 0.7206

ρo, lb/Cuft 44.986

DEG. API 64.864

GAS: ɣg, (AIR = 1.0) 0.92

ρg, lb/SCF 0.07025

31

Figure 3.2: 2D view of the XY model showing fluid saturation distribution of layer 2

In the model, there are 26 wells; one injector (WI) and twenty five producers (P2 – P26). All

producers are completed in layers 2, 3 and 4, while the injector was completed in layers 11, 12,

13, 14 and 15. As will be shown in chapter four, the injector drilled and completed at the flank of

the reservoir (see figure 3.2) was capable of supporting the pressure throughout the simulation

time of 15 years. Besides, the producing wells also had significant water breakthrough for this

depletion time; which is also evident of the water encroachment from the aquifer.

32

Table 3.2: Reservoir rock properties of model

Property Unit value

Rock Compressibility, Cf, 1/Psi (Field) 0.000001

Reservoir Net Pay FT 359

Reservoir Gross Th. FT 359

Avg. Reservoir

Porosity Fraction 0.1262

Avg. Reservoir Kx md 108.1

Avg. Reservoir Ky md 108.1

Avg. Reservoir Kz md 1.081

Table 3.3: Equilibration parameters

Equilibration (Initialization) Region 1

Initial Hydrocarbon - Water Contact, FT 9950

Depth to Center of Shallowest Block, FT 9009.85

Depth to Center of Deepest Block, FT 10502.48

Reference Depth, FT 9035

Table 3.4: Reservoir model’s initial fluid in place

Initial Fluids in Place

Water OIL GAS GOR Bo Bg

HC

PAVG PAVG

MRB MRB MMCF SCF/STB RB/STB RB/MCF PSI PSI

Region

1 211,332 241,712 0 1385 1.1092 0 3,820.10 3,896.30

Region

2 210,696 217,912 301,880 1385 1.1092 0 3,820.10 3,896.30

3.2.2 SENSOR Simulator

SENSOR is a black oil and compositional reservoir simulation software used to optimize oil and

gas recovery from underground reservoirs. It is a trademark of Coats Engineering and was used

extensively in this research to study fluid withdrawal capacity of the reservoir XY model.

33

3.2.3 Simulation Runs

The SENSOR input data file for the XY model was prepared for a simulation run. The initial

production and injection rates in the model were 1500 STB/D and 5000 STB/D, respectively.

With all producers completed in layers K2 to K4 and injector completed in layers K11 to K15,

the simulation was run for 15 years, as shown in Table 3.1.

After 15 years of field depletion, the simulation run was terminated and an output file which

contains the simulation results was created by the simulator. The SENSOR maps which

graphically show the IJK slice of the XY reservoir model were generated. With the aid of the

SENSOR Plot tool, each well and field summary production data for the depletion period were

plotted.

It is important to state here that one of the objectives of this study is to generate an Artificial

Neural Network model that will accurately predict water cut with an appreciable accuracy level.

Neural networks are data driven, therefore, one of the aims of running this simulation was to

generate sufficient and reliable data which is then used to develop the neural network model.

3.3 Concept of Artificial Neural Networks (ANNs)

An Artificial Neural Network (ANN) is a signal-processing system. It processes its signals or

information in such a way that mimics the biological neural network action of the human brain.

ANNs are developed by mathematically modeling the biological neural networks behavior. In

ANNs, signal processing is done in many individual processors known as neurons. Electric

signals are passed between neurons through connecting links. Each connection has an associated

weight. In typical ANNs, the transmitted signal is multiplied by this weight, w. After receiving

34

signals from the proceeding neurons, each neuron applies an activation function (which could be

a linear or a non-linear function) to its net input to produce an output. The net input of a neuron

is the summation of the input signals to that neuron multiplied by the weights associated with the

links which the signal has passed through. Figure 3.3 shows the schematic of an artificial neuron.

Figure 3.3: Schematic of an artificial neuron

The output of each neuron upstream is multiplied by an associated connection weight and then

enters the neuron as an input. As shown in Figure 3.3, an artificial neuron has many inputs but

only one output. Inputs received by the neuron are summed and the summation is applied to the

activation function (AF). The result obtained is the output of the neuron.

3.3.1 Classification of Neural Networks

There are several classifications of neural networks based on various characteristics. One of the

general classifications is based on the type of training algorithm. On this basis, artificial neural

networks could be divided into two main groups, which are the supervised and the unsupervised

neural networks. In unsupervised neural networks, no feedback is provided to the network during

training. On the other hand, in supervised networks, the networks are fed with both inputs and

target values and learn on a feedback basis.

∑Iiwi

I1

I2

IN

Input Layer

Hidden Layer

Output Layer

O

:

w1

w2

wN

AF

35

There are basically two steps in building ANNs: the training step and the testing (verification)

step. In the training process or step, connection weights are technically adjusted to yield the

desired outputs. In the testing process, the trained neural network’s capacity to predict the

desired outputs is evaluated using datasets that were not seen by the neural network during the

training process.

Training is done by technically adjusting the connection weights until convergence between the

network’s prediction (outputs) and desired outputs (targets) is reached. Changing the connection

weights allows the neural network to adjust its behavior in response to the fed inputs. The most

commonly used supervised training algorithm is the backpropagation algorithm. This algorithm

was used to develop the neural network model in this study. When the backpropagation

algorithm is used in training, the neural network’s prediction (output) is compared with the

actual output (target) in the training dataset and the error is transmitted backward to the network.

During backpropagation process, the connection weights are technically adjusted to decrease the

error value. This process is continued iteratively until the network outputs are considerably close

to the target values.

3.3.2 Methodology for Developing Neural Networks

In this study, several processes or steps were taken to build optimized neural network models

which can be used to predict well water cut.

36

Figure 3.4: ANN workflow

This methodology is presented in the ANN workflow shown in Figure 3.4. This workflow

defines all the processes involved in developing the neural network models in this study. The

different processes include, problem definition, data collection, data preprocessing and division,

determination of the network architecture, training and optimizing the network among many

others. Some of the items on the workflow diagram are discussed in detail.

Problem Definition

Data Collection &

Analysis

Data Division

Network Structure

Model Training &

Testing

Model

Optimization

Sensitivity Analysis:

e.g. different learning

algorithms; number of

hidden neurons;

network delay, etc.

Best Model

Selection

Robustness of

Model

Comparison

YES

NO

37

3.3.2.1 Problem Definition

The first step is to define the problem(s) to be investigated. This step includes:

1. Properly defining the parameter to be predicted by the network; this is water cut in this

study.

2. Determination of the data to be used in training, validating and testing the network. The

source and reliability of the data should be taken into consideration. In this study, the

results generated from reservoir simulation were used as neural network training,

validating and testing datasets. Therefore, the water cut generated from reservoir

simulation were used as a base or desired water cut in training the network.

3. Uncertainty analysis is carried out on the data

4. Determination of the ANN input parameters. This is very crucial to the accuracy of the

model. For example, average reservoir pressure, PAVG was used as an input parameter in

the network that predicts field water cut. On the other hand, average grid block pressure,

PGRID was used as an input parameter in the network that predicts the well water cut.

3.3.2.2 Data Collection and Partitioning

As earlier mentioned, reservoir simulation data were collected, carefully analyzed and

adequately screened. The data was then partitioned into three sub sets: training, validation and

testing. In the training of the neural network models developed in this study, the data partitioning

was done as follows:

Training data = 40%

Validation data = 15%

Testing data = 45%

38

3.3.2.3 Network Structure

The neural network architecture or structure involves determining:

1. The number of networks’ hidden layers and the number of hidden neurons. In this work,

only one hidden layer (with ten hidden neurons) was used.

2. The number of network input and output parameters or neurons.

3. The type of activation functions used both in the hidden and output layers.

4. Selecting an optimized training algorithm.

3.3.2.4 Model Training & Testing

When the network architecture has been decided and data to be used has been preprocessed, the

network is set to be trained, validated and tested. In supervised learning, the network training is

done using a selected training function or algorithm.

There are several training functions such as: Levenberg-Marquardt backpropagation; Bayesian

regulation backpropagation; Scaled conjugate gradient backpropagation, and Resilient

backpropagation, among others. The Levenberg-Marquardt backpropagation is the most

commonly used training functions in neural network training. It is a network training function

that updates weight and bias values according to Levenberg-Marquardt optimization. It is often

the fastest backpropagation algorithm in the Matlab toolbox, and is highly recommended as a

first-choice supervised algorithm, although it does require more memory than other algorithms

(MathWorks®, 2016). In this study, the models were tested to examine its generalization and its

ability to predict water cut values.

39

3.3.2.5 Model Optimization

Since trial and error was involved in selecting the network architecture, it was necessary to run

different sensitivity analyses to investigate if the models could be further optimized. Importantly,

this step could be combined with the training and testing step. The sensitivity analyses include

testing the following parameters:

1. The optimum number of hidden neurons. Since there is no rule of thumb for selecting the

optimum number of hidden neurons, during training, this number was continually

changed until an optimum network with appreciable accuracy was obtained.

2. Different learning parameters, e.g. the number of delays, as used in a time series network.

3. Different training algorithms. In this study, the Levenberg-Marquardt backpropagation

algorithm was used for training the models. This was also sensitized on by using the

Bayesian regulation backpropagation algorithm. However, it was observed that the

Levenberg-Marquardt backpropagation algorithm gave more accurate results than the

Bayesian regulation backpropagation algorithm.

3.3.3 Neural Network Models

In this study, two cases were considered in building the neural network model. The network

models developed in both cases are called CASNNET1, CASNNET2, CASNNET3, and

CASNNET4.

3.3.3.1 Case One – Training with Data from One Well

In this case, three non-linear auto regressive time series neural network models with exogenous

input (NARX) were developed by using data sets from a single well. The first network was

trained, validated and tested with data from well P26 (see Figure 3.2). This neural network model

40

is called the CASNNET1. Similarly, the second and third neural network models were trained,

validated and tested with data from wells P23 and P17, respectively (Figure 4.2b). These are

called CASNNET2 and CASNNET3.

The nonlinear autoregressive network with exogenous inputs (NARX) is a recurrent dynamic

network with feedback connections enclosing several layers of the network. The defining

equation for the NARX model is given as:

y(t) = f[y(t−1), y(t−2) ,…, y(t−n), x(t−1), x(t−2) ,…, x(t−n)]………………………… (1)

Where the next value of the dependent output signal y(t) is regressed on previous values of the

output signal and previous values of an independent (exogenous) input signal. In the equation, n

is the maximum number of delay, x is a time dependent input variable, while t, t-1, t-2, etc., are

time steps. The NARX model can be implemented by using a feedforward neural network to

approximate the function f. The network architecture of CASNNET1 is shown in Figure 3.5.

Figure 3.5: NARX network (CASNNET1) view

41

In building the CASNNET1, twenty-seven (27) input parameters and one desired output

parameter were used. The desired parameter is the water cut of the producer P26. These

parameters are depicted in Table 3.5.

Table 3.5: Input – Output Parameters for Cases One & Two

Cases One & Two Training Data

CASNNET1, CASNNET2, CASNNET3 & CASNNET4

S/N Input Parameter Output Parameter

1 QOIL, STB/D

2 QGAS, MCF/D

3 GOR, SCF/STB

4 PBH, PSIA

5 PGRID, PSIA

6 Porosity of K2, Fraction

7 Porosity of K3, Fraction

8 Porosity of K4Fraction

9 PI of K2, RB-CP/D-PSI



Water Cut (%) 12 Kx of Layer 2, MD

13 Kx of Layer 3, MD

14 Kx of Layer 4, MD

15 Ky of Layer 2, MD



18 Kz of Layer 2, MD



21 Net Pay Thickness of Layer K2, FT



24 Res. Ref. Depth (GOC), FT

25 Well Lateral Distance to Aquifer, FT

26 Initial OWC, FT

27 Aquifer Ct, 1/PSI

42

3.3.3.2 Case Two – Training with Data from Two Wells

As in Case one, a NARX time series network called CASNNET4 was developed to predict well

water cut by using data from two producing wells. The architecture of CASNNET4 consists of

thirty-three (33) input parameters and two (2) desired output parameters. The same datasets used

in case one were also used to design the CASNNET4. However, since data from two producing

wells were used for training, validation and testing, the dataset common to the two wells was

taken as one to avoid clumsiness of the data fed into the network. The two output parameters are

the water cuts for two producing wells. The CASNNET4 architecture is shown in Figure 3.6.

Figure 3.6: NARX network (CASNNET4) view

3.3.4 Testing the Neural Network Models on New Data

The accuracy of the developed neural network models was verified on data never seen by the

networks. The well P26 data (Figure 3.2) used in training and validating the CASNNET1 had

eighty-five (85) time steps. To further ascertain the predictive capability of the network, the

CASNNET1 was used for multistep ahead prediction. Thirty (30) time steps ahead input

parameters were fed into the trained network to predict water cut of the well 30 steps ahead. This

was done to check the predictive capability of the built network, CASNNET1 on the well P26

data.

43

Similarly, the CASNNET1 was tested on data from wells P16, P17, P22 and P23 and it gave

appreciably accurate results. The capability of the network is measured using its mean squared

error (mse) and R-Squared values, as well as the predictability (%) on each of the wells.

In the same way, CASNNET2, CASNNET3, and CASNNET4 were tested on unseen data from

other wells. As shown in Table 3.6, CASNNET2 was developed with data from well P23 and its

capability was checked by using data from wells P16, P17, P22, and P26. CASNNET3 was built

with data from well P17 and its capability was verified using data from wells P16, P22, P23, and

P26. Finally, CASNNET4 was trained and validated with combined data from wells P16 and

P26, while its capability was verified using combined data from wells P17 and P24 and wells

P22 and P23 respectively. The results on the four networks are discussed in the following

chapter.

Table 3.6: Well data used to validate and verify the capability of the Networks

Built and validated Capability Verified

Network on data from using data from Well(s)

CASNNET1 well P26 P16, P17, P22 and P23



CASNNET4 wells P16&P26 P17&P24

P22&P23

44

CHAPTER FOUR

Results & Discussion

4.1 Reservoir Simulation

As earlier discussed, reservoir simulation runs were made and results were generated. Maps and

plots of the results were generated to properly visualize and analyze the results discussed in the

following sections.

4.1.1 Maps of the Reservoir Model

With the aid of the SENSOR Map tool, maps which show the distribution of the XY model’s

fluid and rock properties were created. Since all the producers were completed in layers K2, K3

and K4 and the injector in layers K11, K12, K13, K14 and K15, only the maps for these layers

were generated, as shown in Figure 4.1 - 4.10.

Figure 4.1: (a) Map showing the distribution of fluid saturation at the start of simulation – slice

K2 (b) Map showing the distribution of fluid saturation at the end of simulation – slice K2

(a) (b)

45

Figure 4.2: (a) Map showing the distribution of pressure at the start of simulation – slice K2

(b) Map showing the distribution of pressure at the end of simulation – slice K2

Figure 4.3: Map showing the distribution of permeability, kx at the start of simulation – slice K3

(a) (b)

46

Figure 4.4: Map showing the distribution of fluid saturation at the end of simulation – slice J11

47

Figure 4.5: (a) Map showing the distribution of fluid saturation at the start of simulation – slice

K15 (b) Map showing the distribution of fluid saturation at the end of simulation – slice K15

Figure 4.6: (a) Map showing the distribution of pressure at the start of simulation – slice K15

(b) Map showing the distribution of pressure at the end of simulation – slice K15

(a) (b)

(a) (b)

48

Figure 4.1 is the slice of layer 2 of the XY model. Figure 4.1a shows the distribution of fluid

saturation in the layer at the beginning of the simulation. As given in the ternary diagram, the

blue region indicates high water saturation, which is also an indication of the aquifer region. The

green region indicates high oil saturation, red indicates high gas saturation. However, since the

reservoir model was an undersaturated black oil reservoir at its initial state, there is no indication

of gas on the map. Figure 4.1b also visualizes fluid saturation distribution of layer 2, but this

time, at the end of the simulation. There is an indication of gas in the reservoir at this state,

which implies that the reservoir depleted below its bubble point pressure after 15 years of

continuous production.

Figure 4.2 shows the distribution of pressure in the layer 2. The red region indicates very high

pressure, while blue indicates very low pressure. Figure 4.2a shows the pressure distribution in

the system at the beginning of the simulation, while figure 4.2b shows the depletion of pressure

in the system after 15 years of production. As evident in both maps, the high-pressure regions are

the aquifer regions and those hydrocarbon regions very close to the aquifer.

Figures 4.5 and 4.6 show the slice of layer 15, which is one of the layers the injector was

completed. Figure 4.5a shows the fluid saturation distribution in this layer at the beginning of the

simulation, while figure 4.5b illustrates fluid distribution at the end of the simulation. The

aquifer which is the blue region is obviously on one side of the system, which is an indication of

an edge – water driven system. Figure 4.5a shows the initial position of the oil–water contact,

while Figure 4.5b shows water encroachment into the hydrocarbon zone after 15 years of

depletion. The importance of the Sensor generated maps is to help visualize the distribution of

49

reservoir fluid and rock properties when different portions of the model are sliced in the I, J, and

K directions.

4.1.2 Production Parameters Plots

The simulation results were also used to generate some plots. These plots were produced to help

visualize production data trend with time. One of the aims of this study is to evaluate water cut

trends in producing wells. In the XY reservoir model under investigation, there are 25 producers

(P2 – P26) and 1 injector (WI). From the reservoir simulation results, only fifteen of the

producers produced water during the depletion period. However, only seven had significant

water cut (above 50%) after 15 years of depletion. The production plots of the wells that had

water cut values above 90% are shown in Figures 4.7 – 4.9.

Figure 4.7: Producer P26’s water cut and cumulative production vs. time plot

50



51

Figures 4.7 – 4.9 show that all three producers had early water breakthrough after 10 days of

production (Well P26 = 1.3%, Well P23 = 0.5%, Well P17 = 0.5%). At the end of 5479 days (15

years) of production, the water cut values were: Well P26 = 93.77%, Well P23 = 90.4%, Well

P17 = 92.96%.

4.2 Neural Network Models

Recall that in this study, two cases were considered to develop four (4) neural network models.

In case one, the CASNNET1, CASNNET2 and CASNNET3 time series non-linear

autoregressive networks with exogenous inputs (NARX) were developed to predict well water

cut. The neural network models were developed by using data from a single producing well. In

case two, the CASNNET4 was developed to also predict well water cut. Unlike the network

models in case one, the neural network model in case two was trained, validated and tested with

combined data from two producing wells.

4.2.1 Case One – Results of Training Network with One Well

4.2.1.1 CASNNET1

The CASNNET1 is an NARX time series network built by using data from well P26. This

network was trained, validated and tested to predict well P26’s water cut. For well P26, there

were 115 simulation time steps. The data for the first 85 time steps (10 years) were used for

training and validating the network, while the data for time steps 86 – 115 (5 years) were used to

make multistep ahead prediction. The well data were partitioned as: Training data = 40%;

Validation data = 15%; and Testing data = 45%. The training algorithm used was the

Levenberg-Marquardt backpropagation. Other training parameters are: Number of delay = 2;

number of hidden neurons = 10; number of input neurons = 27; number of output neurons = 1

52

(well water cut). The results generated by the CASNNET1 on well P26 are shown in Figures

4.10 – 4.11.

Figure 4.10: Correlation coefficient values of the CASNNET1 – P26

In Figure 4.14, the network’s overall correlation coefficient, R value of 0.99426 is an indication

of a good prediction ability of CASNNET1 on well P26’s data. This is reflected in the accuracy

20 40 60 80

10

20

30

40

50

60

70

80

90

Target (Actual WCUT)

CA

SN

NE

T W

CU

T P

red

icti

on

Training: R=0.99998

Data

Fit

Y = T

20 40 60 80

10

20

30

40

50

60

70

80

90


CA

SN

NE

T W

CU

T P

red

icti

on

Validation: R=0.97431

Data

Fit

Y = T

20 40 60 80

10

20

30

40

50

60

70

80

90


CA

SN

NE

T W

CU

T P

red

icti

on

Test: R=0.99327

Data

Fit

Y = T

20 40 60 80

10

20

30

40

50

60

70

80

90


CA

SN

NE

T W

CU

T P

red

icti

on

All: R=0.99426

Data

Fit

Y = T

53

value of approximately 98% and mean squared error (mse) value of 5.48 as shown in Table 4.1.

In Figure 4.15, the black line is the P26’s observed or desired water cut for 115-time steps. The

blue line is CASNNET1 water cut match during training for 85-time steps, while the red line is

the 30-time steps ahead (86 -115) prediction of water cut by the network. Table 4.2 shows the

summary of the network’s prediction of well P26’s water cut values for 1 year (20 simulation

time steps).

Table 4.1: Summary of CASNNET1 – P26’s results

CASNNET1 Summary for the Prediction of Well P26's Water Cut

Correlation Coefficient (R.) 0.9943

Mean Squared Error (MSE) 5.4841

Average Error Fraction 0.0189

Accuracy of Network (%) 98.11

Figure 4.11: CASNNET1 – P26 water cut prediction and target plot

0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100

Time (Days)

Well

Wate

r C

ut

(%)

CASNNET-Producer26 Water Cut Prediction


NN Prediction

NN Training

54

Table 4.2: CASNNET1 – P26’s one year prediction results

TIME

ACTUAL

WCUT

NEURAL

NETWORK

PREDICTION

ABSOLUTE

ERROR (AE)

ERROR

FRACTION

(AE)^

2 MSE

NETWORK

ACCURACY

DAYS % % % Fraction %

10.000 1.297 1.297 0.000 0.000 0.000

22.044 1.311 1.311 0.000 0.000 0.000

31.000 1.383 1.327 0.056 0.040 0.003

44.435 1.583 1.692 0.110 0.069 0.012

64.586 2.114 1.789 0.325 0.154 0.106

90.668 3.171 3.169 0.002 0.001 0.000

104.71

5 4.064 3.910 0.153 0.038 0.024

117.44

4 5.027 4.282 0.745 0.148 0.555

128.00

8 5.968 5.790 0.178 0.030 0.032

143.85

3 7.675 7.355 0.320 0.042 0.102

162.08

4 9.954 9.163 0.791 0.079 0.625 5.484 98.106

178.57

7 12.220 12.137 0.083 0.007 0.007

197.86

0 15.383 15.341 0.043 0.003 0.002

219.19

6 18.987 18.843 0.143 0.008 0.021

240.85

5 22.585 22.562 0.023 0.001 0.001

260.76

1 25.923 26.039 0.116 0.004 0.013

285.46

1 30.156 28.946 1.210 0.040 1.464

309.95

6 33.478 33.322 0.156 0.005 0.024

335.95

5 36.727 36.314 0.414 0.011 0.171

365.00

0 39.827 39.266 0.561 0.014 0.315

55

4.2.1.2 CASNNET2

The CASNNET2 is also a NARX time series network built by using data from well P23. This

network was trained, validated and tested to predict well P23’s water cut. The training algorithm

used was also the Levenberg-Marquardt backpropagation (trainlm). Other training parameters

are: Number of delay = 2; number of hidden neurons = 10; number of input neurons = 27;

number of output neurons = 1 (well water cut). The results generated by the CASNNET2 on well

P23 are shown in Figures 4.12 – 4.13.


0 20 40 60 80

0

10

20

30

40

50

60

70

80


CA

SN

NE

T2

WC

UT

Pre

dic

tio

n

Training: R=0.99999

Data

Fit

Y = T

0 20 40 60 80

0

10

20

30

40

50

60

70

80


CA

SN

NE

T2

WC

UT

Pre

dic

tio

n


Data

Fit

Y = T

0 20 40 60 80

0

10

20

30

40

50

60

70

80


CA

SN

NE

T2

WC

UT

Pre

dic

tio

n

Test: R=0.99882

Data

Fit

Y = T

0 20 40 60 80

0

10

20

30

40

50

60

70

80


CA

SN

NE

T2

WC

UT

Pre

dic

tio

n

All: R=0.99923

Data

Fit

Y = T

56


Figure 4.12 shows that CASNNET2 has a correlation coefficient (R) value of 0.99923, which

indicates the good performance of CASNNET2 when fed with data from well P23. This

performance is also reflected in the network’s accuracy of approximately 96.5%, and a mean

squared error (mse) value of 0.6037, as shown in Table 4.3. The black line in Figure 4.13 is the

desired P23 water cut for 115-time steps. The blue line is CASNNET2 water cut match during

training for 85-time steps, while the red line is the 30 steps ahead (86 -115 time steps) prediction

of water cut by the network.

0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100

Time (Days)

Well

Wate

r C

ut

(%)

CASNNET2 - Producer23 Water Cut Prediction


NN Prediction

NN Training

57







4.2.1.3 CASNNET3

In the same way, the CASNNET3 neural network model was trained, validated and tested to

predict well P17’s water cut. The training algorithm used was also the Levenberg-Marquardt

backpropagation. Other training parameters are: Number of delay = 2; number of hidden neurons

= 10; number of input neurons = 27; number of output neurons = 1 (well water cut). The results

generated by the CASNNET3 on well P17 are shown in Figures 4.14 – 4.15. The summary of

CASNNET3 prediction ability on well P17 is given in Table 4.4.







58


0 20 40 60 80

0

20

40

60

80


CA

SN

NE

T3

WC

UT

Pre

dic

tio

n

Training: R=0.99889

Data

Fit

Y = T

0 20 40 60 80

0

20

40

60

80


CA

SN

NE

T3

WC

UT

Pre

dic

tio

n


Data

Fit

Y = T

0 20 40 60 80

0

20

40

60

80


CA

SN

NE

T3

WC

UT

Pre

dic

tio

n

Test: R=0.96164

Data

Fit

Y = T

0 20 40 60 80

0

20

40

60

80


CA

SN

NE

T3

WC

UT

Pre

dic

tio

nAll: R=0.98905

Data

Fit

Y = T

59


4.2.2 Case 2 – Results of Training Network with Two Wells

4.2.2.1 CASNNET4

CASNNET4 neural network model was also built to predict well water cut. However, the

network was trained, validated and tested with data from two producers. Wells P16 and P26 were

used for training this network. The training algorithm used was also the Levenberg-Marquardt

backpropagation. Other training parameters are: Number of delay = 2; number of hidden neurons

= 10; number of input neurons = 33; number of output neurons = 2 (water cut for two wells). The

0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100

Time (Days)

Well

Wate

r C

ut

(%)



NN Prediction

NN Training

60

results generated by the CASNNET4 on wells P16 and P26 are shown in Figures 4.16 – 4.18.

The summary of CASNNET4 prediction ability on wells P16 and P26 is given in the Tables 4.5

and 4.6.

Figure 4.16: Correlation coefficient values of the CASNNET4 – P16&P26

0 20 40 60 80

0

20

40

60

80


CA

SN

NE

T4

WC

UT

Pre

dic

tio

n

Training: R=0.99891

Data

Fit

Y = T

0 20 40 60 80

0

20

40

60

80


CA

SN

NE

T4

WC

UT

Pre

dic

tio

n


Data

Fit

Y = T

0 20 40 60 80

0

20

40

60

80


CA

SN

NE

T4

WC

UT

Pre

dic

tio

n

Test: R=0.9955

Data

Fit

Y = T

0 20 40 60 80

0

20

40

60

80


CA

SN

NE

T4

WC

UT

Pre

dic

tio

n

All: R=0.99048

Data

Fit

Y = T

61


0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

Time (Days)

Well

Wate

r C

ut

(%)



NN Prediction

NN Training

62








0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100

Time (Days)

Well

Wate

r C

ut

(%)



NN Prediction

NN Training

63







4.2.3 Results of Testing Neural Network Models on New Wells

CASNNET1 was originally developed by using well P26’s data. To check for network

generalization, unseen data from other producing wells in the same reservoir were fed into the

network. Wells P23, P22, P17 and P16 data were used for this generalization. In the same way,

CASNNET2 was generalized on wells P16, P17, P22, and P26 individually; CASNNET3 on

wells P16, P22, P23, and P26; while CASNNET4 was generalized using combined data from

wells P17 and P24 and P22 and P23 respectively. Tables 4.7 – 4.10 show the generalizations of

all the neural network models, while Figures 4.19 – 4.26 show the water cut and correlation plots

of each of the networks on a particular well.

64


Figure 4.20: CASNNET1 – P23 water cut correlation plot

0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100

Time (Days)

Well

Wate

r C

ut

(%)

CASNNET-Producer23 Water Cut Prediction


NN Prediction

65

Table 4.7: Generalization of CASNNET1 on Five Wells

Network Design Well R-Squared MSE

Accuracy

(%)

Training, validation & testing

of network with data from

P26 P26

Training

Data 0.9896 9.8792 97.7727

Prediction

Data 0.5075 1.0890 99.0495

Further testing of network

with unseen data

P16

Further

testing 0.9638 51.8767 81.1285

P17

Further

testing 0.9786 17.4785 96.0344

P22

Further

testing 0.9813 15.5901 93.0576

P23

Further

testing 0.9900 11.5106 91.7231

Overall Accuracy of CASNNET1 92.20



Accuracy

(%)



P23 P23

Training

Data 0.9988 1.1134 95.3920

Prediction

Data 0.9552 0.0939 99.6714


with unseen data

P16

Further

testing 0.9773 180.5368 74.5705

P17

Further

testing 0.8814 114.2432 86.3160

P22

Further

testing 0.9742 122.2744 81.6800

P26

Further

testing 0.9630 68.4912 89.8529


66



Accuracy

(%)



P17 P17

Training

Data 0.9827 12.1580 96.6783

Prediction

Data 0.9619 0.6517 99.2343


with unseen data

P16

Further

testing 0.9811 100.0248 79.9451

P22

Further

testing 0.9872 91.6948 84.3607

P23

Further

testing 0.9805 32.0812 92.0317

P26

Further

testing 0.9709 126.3451 85.3526


Table 4.10: Generalization of CASNNET4 on Six Wells


Accuracy

(%)


of network with combined

data from wells 16 and 26

P26

Training

Data 0.9734 34.9042 86.1651

Prediction

Data 0.8524 8.0020 96.9697

P16

Training

Data 0.9921 7.4218 88.2442

Prediction

Data 0.7538 61.3326 88.3078


with unseen data

P17

Further

testing 0.9183 134.4877 85.1651

P22

Further

testing 0.9701 436.7869 68.2290

P23

Further

testing 0.9888 20.3030 92.4036

P24

Further

testing 0.9839 35.7579 62.3353


67



0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100

Time (Days)

Well

Wate

r C

ut

(%)



NN Prediction

68



0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

Time (Days)

Well

Wate

r C

ut

(%)



NN Prediction

69



0 1000 2000 3000 4000 5000 60000

10

20

30

40

50

60

70

80

90

100

Time (Days)

Well

Wate

r C

ut

(%)



NN Prediction

70

As shown in the generalizations of Tables 4.7 – 4.10, CASNNET1 shows an overall accuracy of

92.2% in predicting well water cut of the five wells, while the overall accuracy of CASNNET2,

CASNNET3 and CASNNET4 are 86.42%, 88.18% and 79.29% respectively.

4.3 Observation & Analysis

The developed neural net model shows that wells P26, P23, and P17 had early water

breakthrough after 10 days of production, with the initial flow rate of 1500 STB/D. This could be

the result of one or more of the following factors:

1. High initial flow rate;

2. Closeness to the aquifer (edge water drive system) as shown on the simulation map;

3. Near wellbore damage (poor cementing, leaking casing, etc.);

4. Channelization (flow through high permeability streaks);

5. Cross communication between layers.

4.3.1 Sensitivity Analysis

Of all the highlighted factors causing early water breakthrough, the initial well production rate is

the only factor that is cost effective in sensitizing. Therefore, in this study, the initial rates of the

producers were reduced from the initial 1500 STB/D to 750 STB/D, and to 500 STB/D. This was

done to study the effect of well initial flow rates on early water production. Hence, two other

simulation runs were made and results were generated for the cases. Figures 4.27 – 4.31

illustrate the water cut and cumulative oil production for wells P26, P23, P22, P17, and P16,

respectively, while Tables 4.11 – 4.15 show the water cut and cumulative oil production for

wells P26, P23, P22, P17, and P16, respectively, for the first one year of production.

71

Figure 4.27: (a) Well P26’s water cut at different initial production rates (b) Well P26’s

cumulative oil production at different initial production rates.



(a) (b)

(a) (b)

72





(a) (b)

(a) (b)

73



As shown in Figures 4.27, 4.28 and 4.30 and Tables 4.11, 4.12 and 4.14, wells P26, P23 and P17

had early water breakthrough after 10 days of production, even with the reduced initial flow

rates. This could be the results of closeness to the aquifer, channelization or flow behind casing.

Therefore, an initial flow rate of 500 STB/D is recommended for wells P26, P23 and P17. A

workover operation to check the integrity of the casing is also suggested.

In Figures 4.29 and 4.31 and Tables 4.13 and 4.15, wells P22 and P16 had early water

breakthrough after 10 days of production with an initial flow rate of 1500 STB/D, though not

significant. However, with initial flow rates reduced to 750 STB/D and 500 STB/D, there was no

early water breakthrough for both wells. Therefore, an optimum initial rate of 750 STB/D is

recommended for both wells.

(a) (b)

74


production

75


production

76


production

77


production

78


production

79

CHAPTER FIVE

Conclusions & Recommendations

5.1 Conclusions

In this study, four optimized neural network models were developed to predict well water cut

with an appreciable degree of accuracy. CASNNET1, CASNNET2, and CASNNET3 were built

by using data from one producer for training, validation and testing, while CASNNET4 was built

with data from two producers.

The four neural network models were tested on unseen data from other wells in the same

reservoir to evaluate their predictive capacities. Performing network generalization is key to the

success of this study because it gives us a good understanding of the models’ response to new

data from the same reservoir. The water cut prediction of these neural network models on new

data shows that CASNNET1, CASNNET2, CASNNET3 and CASNNET4 have good predictive

capacities of approximately 92.2%, 86.42%, 88.18% and 79.29%, respectively.

Therefore, these neural network models could be used as a reservoir management tool to make

forecast on water cut for any of the wells in the XY Reservoir Model. With a good knowledge of

the amount of water a well or group of wells will produce in the future, possible precautionary

measures could be taken to prevent or mitigate excess water production. Such important

decisions could be:

1. Setting the well flow rates at optimum values, where little or no water is produced but

with optimum hydrocarbon production;

80

2. Performing workover operations to: check casing and cement integrity; re-perforate

existing wells in new (upper) layers and seal off lower perforations, etc.;

3. Shut-in all the producers whose upper perforations are at or below the oil-water contact

(OWC) and if possible, drill either infill or step-out wells and complete in layers or

locations away from the OWC. However, the STOIIP, reserves and other economic

indicators must justify the reason for well shut-in and/or infill drilling.

In this study, the predictions of the neural network models show that wells P17, P23 and P26 had

early water breakthrough after 10 days of production, even with the reduced initial flow rates of

500 STB/D. This could be as a result of closeness to the aquifer, channelization or flow behind

the casing. Therefore, a workover operation to check the integrity of the casing and cement bond

has been suggested for wells P17, P23 and P26.

Similarly, wells P16 and P22 had early water breakthrough, though not significant, after 10 days

of production with an initial flow rate of 1500 STB/D. However, with initial flow rates reduced

to 750 STB/D and to 500 STB/D, there was no early water breakthrough for both wells.

Therefore, an optimum initial rate of 750 STB/D has been recommended for both wells P16 and

P22.

5.2 Recommendations

It is important to state here that Artificial Neural Network applications are gaining more grounds

in the oil and gas industry. Although the accuracy of most networks is questionable (produces

less accurate results than reservoir simulation and other statistical methods), the process of

81

developing the network is cheap and fast unlike reservoir simulation process. Where reservoir

simulation processes are affordable, it should be taken to advantage instead of applying artificial

neural networks. However, because the neural network building process is cheap, fast and has

vast applications in diverse areas of life, more areas where it could be applied in oil and gas field

optimization should be sought; such as using neural networks to predict the oil recovery factor,

gas recovery, permeability and saturation change with time in a given location in a reservoir.

82

REFERENCES

1. A. Saeedi et al., 2006, Using Neural Networks for Candidate Selection & Well Performance

Prediction in Water-Shutoff Treatments Using Polymer Gels, SPE 101028. A Paper Presented at

the Asia Pacific Oil & Gas Conference & Exhibition held in Adelaide, Australia, 11-13

September.

2. C. M. Reyes et al., 2010, A Reliability-Based Systemic Method for Water Production

Analysis, Diagnosis and Solution Design, SPE138935. A Paper Presented at the SPE Latin

American and Caribbean Petroleum Engineering Conference, Lima, Peru, December 1-3.

3. Coats Engineering Inc., 2011, SENSOR Compositional and Black Oil Simulation Software

Manual, April 1, 2011.

4. D. Perez et al., 2001, Applications of Polymer Gel for Establishing Zonal Isolations & Water

Shutoff in Carbonate Formations, SPE 73196. A Paper Presented at the 1997 SPE/IADC Drilling

Conference, Amsterdam, March 4 - 6; revised for publication in 1997 as SPE 37622 and in 2001.

5. Dr. N. Ganesan et al., 2010, Application of Neural networks in Diagnosing Cancer Disease

using Demographic Data, International Journal of Computer Applications (0975-8887), Volume

1 – No. 26.

83

6. Gasbarri et al., 2008, Water Production Diagnosis using Transient Test with Multiphase

Flowmeter, SPE-117236. A Paper presented at the SPE Eastern Regional/AAPG Eastern Section

Joint Meeting held in Pittsburgh, Pennsylvania, USA, October 11-15.

7. Jreou Ghazwan N S, 2012, Application of neural network to optimize oil field production,

Asian Transactions on Engineering (ATE ISSN: 2221-4267), Volume 02, Issue 03.

8. K. S. Chan, 1995, Water Coning Diagnostic Plots, SPE 30775. A Paper Presented at the SPE

Annual Technical Conference & Exhibition, Dallas, October 22 – 25.

9. MathWorks®, 2016, MATLAB R2016a Documentation,

www.mathworks.com/help/nnet/ref/trainlm.html, 2016.

10. M. Rabiei et al., 2010, Transforming Data into Knowledge Data Mining Techniques:

Application in Water Production Diagnosis in Oil Wells, SPE 133929. A Paper Presented at the

SPE Asia Pacific Oil & Gas Conference and Exhibition held in Brisbane, Queensland, Australia,

October 18-20.

11. N.Al-Bulushi et al., 2007: Predicting Water Saturation Using Artificial neural Networks. A

Paper Presented at the First Annual Middle East Regional SPWLA Symposium, April, 2007.

12. PQ Corporation Bulletin 35-02, 2006, Soluble Silicates for Water Control & Lost

Circulation, www.pqcorp.com/portals/1/lit/bulletin_35-02.pdf.

http://www.mathworks.com/help/nnet/ref/trainlm.html

84

13. Prashant Shriwal & Robert H. Lane, 2012, Impacts of Timing of Crosslinker Addition on

Water Shutoff Polymer Gel Properties, SPE 153241. A Paper Presented at the 18th SPE

Improved Oil Recovery Symposium held in Tulsa, Oklahoma, USA, April 14-18.

14. Qeethara K. Al-Shayea, 2011, Artificial Neural Networks in Medical Diagnosis, IJCSI

International Journal of Computer Science Issues, Vol. 8, Issue 2, March, 2011.

15. R. S. Seright and R. H. Lane, 2003, A Strategy for Attacking Excess Water Production, SPE

84966. A Paper Presented at the SPE Annual Technical Conference & Exhibition, Denver, USA,

October 5 – 8.

16. ThankGod Egbe and Dulu Appah, 2005, Water Coning Diagnosis using Spectral Analysis,

SPE 98816. A Paper Presented at the SPE Nigerian Annual International Conference &

Exhibition in Abuja, Nigeria, August 1-3.

85

APPENDICES

Appendix I: CASNNET1 Water Cut Prediction & Accuracy on Well P26

TIME STEP TIME ACTUAL WCUT

NEURAL NETWORK PREDICTION

ABSOLUTE ERROR (AE)

ERROR FRACTION

S/N DAYS % % % Fraction

1 10.000 1.297 1.297 0.000 0.000

2 22.044 1.311 1.311 0.000 0.000

3 31.000 1.383 1.327 0.056 0.040

4 44.435 1.583 1.692 0.110 0.069

5 64.586 2.114 1.789 0.325 0.154

6 90.668 3.171 3.169 0.002 0.001

7 104.715 4.064 3.910 0.153 0.038

8 117.444 5.027 4.282 0.745 0.148

9 128.008 5.968 5.790 0.178 0.030

10 143.853 7.675 7.355 0.320 0.042

11 162.084 9.954 9.163 0.791 0.079

12 178.577 12.220 12.137 0.083 0.007

13 197.860 15.383 15.341 0.043 0.003

14 219.196 18.987 18.843 0.143 0.008

15 240.855 22.585 22.562 0.023 0.001

16 260.761 25.923 26.039 0.116 0.004

17 285.461 30.156 28.946 1.210 0.040

18 309.956 33.478 33.322 0.156 0.005

19 335.955 36.727 36.314 0.414 0.011

20 365.000 39.827 39.266 0.561 0.014

21 394.373 41.972 42.188 0.216 0.005

22 411.844 42.510 42.480 0.030 0.001

23 424.000 42.743 63.520 20.777 0.486

24 442.235 43.239 63.150 19.911 0.460

25 454.949 43.741 44.813 1.073 0.025

26 470.330 44.597 44.609 0.012 0.000

27 493.402 46.202 45.446 0.756 0.016

28 522.121 48.408 47.276 1.132 0.023

29 551.976 50.767 50.039 0.728 0.014

86



ABSOLUTE ERROR (AE)

ERROR FRACTION


30 580.634 53.060 52.913 0.147 0.003

31 602.261 54.745 55.495 0.750 0.014

32 622.783 56.396 57.091 0.695 0.012

33 647.624 58.421 58.740 0.318 0.005

34 684.886 61.225 60.743 0.482 0.008

35 732.934 64.094 63.460 0.634 0.010

36 766.850 65.657 65.959 0.302 0.005

37 791.564 66.777 67.240 0.463 0.007

38 828.636 68.270 68.224 0.046 0.001

39 865.693 69.611 69.714 0.103 0.001

40 921.279 71.532 71.021 0.511 0.007

41 981.279 73.246 73.020 0.226 0.003

42 1041.279 74.760 74.479 0.282 0.004

43 1096.000 76.013 75.866 0.146 0.002

44 1156.000 77.193 77.060 0.133 0.002

45 1216.000 78.253 78.062 0.191 0.002

46 1276.000 79.108 79.039 0.069 0.001

47 1336.000 79.953 79.897 0.057 0.001

48 1396.000 80.743 80.656 0.088 0.001

49 1461.000 81.535 81.369 0.166 0.002

50 1521.000 82.223 82.131 0.092 0.001

51 1581.000 82.869 82.674 0.196 0.002

52 1641.000 83.463 83.233 0.230 0.003

53 1701.000 83.973 83.784 0.189 0.002

54 1761.000 84.456 84.300 0.156 0.002

55 1826.000 84.884 84.777 0.107 0.001

56 1884.329 85.276 85.113 0.163 0.002

57 1944.329 85.666 85.501 0.165 0.002

58 2004.329 86.041 85.878 0.164 0.002

59 2064.329 86.402 86.215 0.186 0.002

87



ABSOLUTE ERROR (AE)

ERROR FRACTION


60 2124.329 86.747 86.552 0.195 0.002

61 2191.000 87.114 86.882 0.232 0.003

62 2251.000 87.428 87.221 0.207 0.002

63 2311.000 87.739 87.536 0.203 0.002

64 2371.000 88.036 87.866 0.170 0.002

65 2431.000 88.319 88.122 0.197 0.002

66 2491.000 88.589 88.411 0.178 0.002

67 2557.000 88.888 88.681 0.207 0.002

68 2613.061 89.109 88.971 0.138 0.002

69 2673.061 89.332 89.246 0.085 0.001

70 2733.061 89.546 89.467 0.079 0.001

71 2793.061 89.754 89.617 0.137 0.002

72 2853.061 89.957 89.753 0.204 0.002

73 2922.000 90.183 89.907 0.276 0.003

74 2982.000 90.371 90.097 0.274 0.003

75 3042.000 90.553 90.304 0.249 0.003

76 3102.000 90.728 90.510 0.217 0.002

77 3162.000 90.896 90.719 0.177 0.002

78 3222.000 91.058 90.917 0.142 0.002

79 3287.000 91.228 91.115 0.114 0.001

80 3347.000 91.330 91.319 0.010 0.000

81 3407.000 91.404 91.382 0.022 0.000

82 3467.000 91.483 91.129 0.354 0.004

83 3527.000 91.576 91.391 0.185 0.002

84 3587.000 91.688 91.565 0.123 0.001

85 3652.000 91.821 90.964 0.857 0.009

86 3712.000 91.945 90.101 1.845 0.020

87 3772.000 92.070 90.278 1.792 0.019

88 3832.000 92.191 90.769 1.421 0.015

88



ABSOLUTE ERROR (AE)

ERROR FRACTION


89 3892.000 92.306 91.345 0.961 0.010

90 3952.000 92.421 91.997 0.423 0.005

91 4018.000 92.526 92.666 0.140 0.002

92 4078.000 92.622 93.203 0.581 0.006

93 4138.000 92.715 93.517 0.802 0.009

94 4198.000 92.796 93.691 0.895 0.010

95 4258.000 92.874 93.787 0.913 0.010

96 4318.000 92.949 93.848 0.899 0.010

97 4383.000 93.026 93.912 0.886 0.010

98 4443.000 93.085 93.984 0.899 0.010

99 4503.000 93.128 94.038 0.910 0.010

100 4563.000 93.162 94.162 1.000 0.011

101 4623.000 93.198 94.243 1.045 0.011

102 4683.000 93.237 94.074 0.837 0.009

103 4748.000 93.286 93.675 0.390 0.004

104 4808.000 93.336 93.363 0.028 0.000

105 4868.000 93.389 93.296 0.093 0.001

106 4928.000 93.446 93.480 0.035 0.000

107 4988.000 93.504 93.848 0.344 0.004

108 5048.000 93.562 94.273 0.711 0.008

109 5113.000 93.622 94.628 1.006 0.011

110 5173.000 93.673 94.916 1.243 0.013

111 5233.000 93.706 95.024 1.318 0.014

112 5293.000 93.726 94.877 1.151 0.012

113 5353.000 93.739 94.236 0.497 0.005

114 5413.000 93.751 92.916 0.835 0.009

115 5479.000 93.768 91.137 2.631 0.028

89

Appendix II: CASNNET2 Water Cut Prediction & Accuracy on Well P17



ABSOLUTE ERROR (AE)

ERROR FRACTION


1 10.0000 0.4646 0.4646 0.0000 0.0000

2 22.0437 0.8091 0.8091 0.0000 0.0000

3 31.0000 1.4226 2.8873 1.4647 1.0296

4 44.4345 3.2954 2.9100 0.3854 0.1170

5 64.5861 8.4623 2.9982 5.4641 0.6457

6 90.6684 16.4960 3.6755 12.8205 0.7772

7 104.7154 20.3143 10.1720 10.1423 0.4993

8 117.4438 24.3423 13.0407 11.3016 0.4643

9 128.0075 27.0070 15.4632 11.5438 0.4274

10 143.8530 31.4458 16.8491 14.5967 0.4642

11 162.0841 35.5486 18.1514 17.3972 0.4894

12 178.5766 39.3164 19.5697 19.7467 0.5023

13 197.8604 42.6891 21.5196 21.1695 0.4959

14 219.1955 45.3337 28.6548 16.6789 0.3679

15 240.8549 47.7309 35.3516 12.3793 0.2594

16 260.7609 49.5699 36.3382 13.2317 0.2669

17 285.4612 51.5119 37.1991 14.3128 0.2779

18 309.9560 53.2120 39.6076 13.6044 0.2557

19 335.9551 54.7577 41.5233 13.2344 0.2417

20 365.0000 56.0262 46.1392 9.8870 0.1765

21 394.3732 71.4012 46.1609 25.2403 0.3535

22 411.8436 73.9710 98.2162 24.2452 0.3278

23 424.0000 74.3918 49.4358 24.9560 0.3355

24 442.2346 58.7925 47.9054 10.8871 0.1852

25 454.9491 54.8563 24.4086 30.4477 0.5550

26 470.3303 54.2129 89.2785 35.0656 0.6468

27 493.4021 56.6243 79.2213 22.5970 0.3991

28 522.1210 58.5211 67.3932 8.8721 0.1516

29 551.9757 61.6203 70.0504 8.4301 0.1368

90



ABSOLUTE ERROR (AE)

ERROR FRACTION


30 580.6344 63.1061 33.8339 29.2722 0.4639

31 602.2611 64.0517 40.1650 23.8867 0.3729

32 622.7828 64.8809 47.6425 17.2384 0.2657

33 647.6240 65.8501 55.9309 9.9192 0.1506

34 684.8858 67.2134 65.5766 1.6368 0.0244

35 732.9335 68.8456 74.7236 5.8780 0.0854

36 766.8496 69.6218 78.2385 8.6167 0.1238

37 791.5642 70.3319 82.4717 12.1398 0.1726

38 828.6360 71.3939 81.3099 9.9160 0.1389

39 865.6932 72.3543 74.6327 2.2784 0.0315

40 921.2790 73.7970 65.9687 7.8283 0.1061

41 981.2790 75.2032 56.1278 19.0754 0.2537

42 1041.2790 76.5045 51.4330 25.0715 0.3277

43 1096.0000 77.5874 53.5423 24.0451 0.3099

44 1156.0000 78.3598 58.0924 20.2674 0.2586

45 1216.0000 79.0513 62.2441 16.8072 0.2126

46 1276.0000 79.6813 65.7862 13.8951 0.1744

47 1336.0000 80.3050 68.9408 11.3642 0.1415

48 1396.0000 80.9446 71.6738 9.2708 0.1145

49 1461.0000 81.6463 73.9881 7.6582 0.0938

50 1521.0000 82.0440 76.0000 6.0440 0.0737

51 1581.0000 82.4545 77.6511 4.8034 0.0583

52 1641.0000 82.9266 78.6630 4.2636 0.0514

53 1701.0000 83.4446 79.6970 3.7476 0.0449

54 1761.0000 83.9839 80.7557 3.2282 0.0384

55 1826.0000 84.5674 81.8134 2.7540 0.0326

56 1884.3292 85.1446 82.8151 2.3295 0.0274

57 1944.3292 85.4481 83.9171 1.5310 0.0179

58 2004.3292 85.7441 83.8902 1.8539 0.0216

59 2064.3292 86.0556 84.3372 1.7184 0.0200

91



ABSOLUTE ERROR (AE)

ERROR FRACTION


60 2124.3292 86.4116 84.7384 1.6732 0.0194

61 2191.0000 86.8398 85.1187 1.7211 0.0198

62 2251.0000 87.0631 85.4871 1.5760 0.0181

63 2311.0000 87.3471 85.9100 1.4371 0.0165

64 2371.0000 87.6639 86.2678 1.3961 0.0159

65 2431.0000 87.9926 86.6382 1.3544 0.0154

66 2491.0000 88.3256 86.9934 1.3322 0.0151

67 2557.0000 88.7043 87.3428 1.3615 0.0153

68 2613.0608 88.8512 87.6703 1.1809 0.0133

69 2673.0608 89.0396 88.0195 1.0201 0.0115

70 2733.0608 89.2823 88.2683 1.0140 0.0114

71 2793.0608 89.5668 88.5302 1.0366 0.0116

72 2853.0608 89.8756 88.7790 1.0966 0.0122

73 2922.0000 90.1603 89.0115 1.1488 0.0127

74 2982.0000 90.3245 89.2086 1.1159 0.0124

75 3042.0000 90.4172 89.4228 0.9944 0.0110

76 3102.0000 90.5330 89.5670 0.9660 0.0107

77 3162.0000 90.6935 89.6971 0.9964 0.0110

78 3222.0000 90.8808 89.8325 1.0483 0.0115

79 3287.0000 91.0641 89.9765 1.0876 0.0119

80 3347.0000 91.1271 90.1113 1.0158 0.0111

81 3407.0000 91.1931 90.2436 0.9495 0.0104

82 3467.0000 91.2753 90.3413 0.9340 0.0102

83 3527.0000 91.3524 90.4288 0.9236 0.0101

84 3587.0000 91.3924 90.4875 0.9049 0.0099

85 3652.0000 91.4030 90.5028 0.9002 0.0098

86 3712.0000 91.3307 90.4720 0.8587 0.0094

87 3772.0000 91.2498 90.4317 0.8181 0.0090

88 3832.0000 91.1940 90.3692 0.8248 0.0090

92



ABSOLUTE ERROR (AE)

ERROR FRACTION


89 3892.0000 91.1713 90.3183 0.8530 0.0094

90 3952.0000 91.1788 90.2916 0.8872 0.0097

91 4018.0000 91.2166 90.2944 0.9222 0.0101

92 4078.0000 91.2822 90.3183 0.9639 0.0106

93 4138.0000 91.3569 90.3919 0.9650 0.0106

94 4198.0000 91.4493 90.4771 0.9722 0.0106

95 4258.0000 91.5416 90.5741 0.9675 0.0106

96 4318.0000 91.6449 90.6870 0.9579 0.0105

97 4383.0000 91.7869 90.7987 0.9882 0.0108

98 4443.0000 91.9123 90.9145 0.9978 0.0109

99 4503.0000 92.0622 91.0435 1.0187 0.0111

100 4563.0000 92.2464 91.1566 1.0898 0.0118

101 4623.0000 92.4628 91.2716 1.1912 0.0129

102 4683.0000 92.5819 91.3908 1.1911 0.0129

103 4748.0000 92.6774 91.4926 1.1848 0.0128

104 4808.0000 92.7337 91.5604 1.1733 0.0127

105 4868.0000 92.7731 91.6184 1.1547 0.0124

106 4928.0000 92.8046 91.6549 1.1497 0.0124

107 4988.0000 92.8340 91.6839 1.1501 0.0124

108 5048.0000 92.8633 91.7104 1.1529 0.0124

109 5113.0000 92.8932 91.7354 1.1578 0.0125

110 5173.0000 92.9088 91.7571 1.1517 0.0124

111 5233.0000 92.9159 91.7821 1.1338 0.0122

112 5293.0000 92.9221 91.7947 1.1274 0.0121

113 5353.0000 92.9321 91.8037 1.1284 0.0121

114 5413.0000 92.9464 91.8124 1.1340 0.0122

115 5479.0000 92.9663 91.8217 1.1446 0.0123

93

Appendix III: CASNNET3 Water Cut Prediction & Accuracy on Well P22



ABSOLUTE ERROR (AE)

ERROR FRACTION


1 10.0000 0.0036 0.0036 0.0000 0.0000

2 22.0437 0.0039 0.0039 0.0000 0.0000

3 31.0000 0.0039 0.0045 0.0006 0.1538

4 44.4345 0.0039 0.0051 0.0012 0.3077

5 64.5861 0.0042 0.0055 0.0013 0.3095

6 90.6684 0.0047 0.0057 0.0010 0.2128

7 104.7154 0.0107 0.0204 0.0097 0.9065

8 117.4438 0.0795 0.0889 0.0094 0.1182

9 128.0075 10.3764 8.8094 1.5670 0.1510

10 143.8530 12.5641 10.0983 2.4658 0.1963

11 162.0841 14.2325 11.9743 2.2582 0.1587

12 178.5766 15.9026 13.8943 2.0083 0.1263

13 197.8604 17.4438 15.7629 1.6809 0.0964

14 219.1955 19.6058 17.7843 1.8215 0.0929

15 240.8549 21.8137 19.9084 1.9053 0.0873

16 260.7609 23.7028 21.5429 2.1599 0.0911

17 285.4612 25.9512 23.6888 2.2624 0.0872

18 309.9560 27.7184 25.6535 2.0649 0.0745

19 335.9551 29.3247 27.5378 1.7869 0.0609

20 365.0000 31.0110 29.0987 1.9123 0.0617

21 394.3732 33.8564 31.6758 2.1806 0.0644

22 411.8436 33.8604 33.7934 0.0670 0.0020

23 424.0000 33.5765 33.8850 0.3085 0.0092

24 442.2346 30.0852 33.9898 3.9046 0.1298

25 454.9491 24.6396 30.7435 6.1039 0.2477

26 470.3303 27.4531 29.6748 2.2217 0.0809

27 493.4021 30.3094 31.0956 0.7862 0.0259

28 522.1210 33.2509 35.8953 2.6444 0.0795

29 551.9757 35.6903 37.9842 2.2939 0.0643

94



ABSOLUTE ERROR (AE)

ERROR FRACTION


30 580.6344 36.6500 39.5312 2.8812 0.0786

31 602.2611 38.0283 39.6651 1.6368 0.0430

32 622.7828 39.2776 40.1009 0.8233 0.0210

33 647.6240 40.6771 40.6739 0.0032 0.0001

34 684.8858 42.6263 43.7842 1.1579 0.0272

35 732.9335 44.8330 48.9983 4.1653 0.0929

36 766.8496 46.2672 54.6794 8.4122 0.1818

37 791.5642 47.1742 59.1264 11.9522 0.2534

38 828.6360 48.3354 60.0493 11.7139 0.2423

39 865.6932 49.3514 60.7625 11.4111 0.2312

40 921.2790 50.5958 61.7448 11.1490 0.2204

41 981.2790 51.6466 62.6398 10.9932 0.2129

42 1041.2790 52.3473 64.0227 11.6754 0.2230

43 1096.0000 52.8049 65.3859 12.5810 0.2383

44 1156.0000 53.0874 66.0501 12.9627 0.2442

45 1216.0000 53.3572 66.6147 13.2575 0.2485

46 1276.0000 53.7297 66.8126 13.0829 0.2435

47 1336.0000 54.1483 67.0947 12.9464 0.2391

48 1396.0000 54.6010 67.5047 12.9037 0.2363

49 1461.0000 55.1808 67.8405 12.6597 0.2294

50 1521.0000 55.6020 68.2245 12.6225 0.2270

51 1581.0000 56.0389 68.6165 12.5776 0.2244

52 1641.0000 56.5916 68.8344 12.2428 0.2163

53 1701.0000 57.2334 69.2549 12.0215 0.2100

54 1761.0000 57.9241 69.8401 11.9160 0.2057

55 1826.0000 58.6192 70.5596 11.9404 0.2037

56 1884.3292 59.1816 71.3286 12.1470 0.2052

57 1944.3292 59.7674 71.9559 12.1885 0.2039

58 2004.3292 60.3264 72.6214 12.2950 0.2038

59 2064.3292 60.8165 73.2561 12.4396 0.2045

95



ABSOLUTE ERROR (AE)

ERROR FRACTION


60 2124.3292 61.2977 73.9501 12.6524 0.2064

61 2191.0000 61.7986 74.6595 12.8609 0.2081

62 2251.0000 62.2227 75.2301 13.0074 0.2090

63 2311.0000 62.8935 75.8932 12.9997 0.2067

64 2371.0000 63.4106 76.5181 13.1075 0.2067

65 2431.0000 63.9228 77.2091 13.2863 0.2078

66 2491.0000 64.4427 77.8643 13.4216 0.2083

67 2557.0000 65.0300 78.5339 13.5039 0.2077

68 2613.0608 65.5286 79.2453 13.7167 0.2093

69 2673.0608 66.0295 79.9222 13.8927 0.2104

70 2733.0608 66.5271 80.5355 14.0084 0.2106

71 2793.0608 67.0429 81.0964 14.0535 0.2096

72 2853.0608 69.1772 81.6037 12.4265 0.1796

73 2922.0000 70.8145 81.9820 11.1675 0.1577

74 2982.0000 71.9892 82.9688 10.9796 0.1525

75 3042.0000 73.0451 83.7868 10.7417 0.1471

76 3102.0000 73.9884 84.4496 10.4612 0.1414

77 3162.0000 74.8418 85.0804 10.2386 0.1368

78 3222.0000 75.6351 85.6756 10.0405 0.1327

79 3287.0000 76.4204 86.2386 9.8182 0.1285

80 3347.0000 77.7261 86.7840 9.0579 0.1165

81 3407.0000 78.5357 87.2797 8.7440 0.1113

82 3467.0000 79.1192 87.6764 8.5572 0.1082

83 3527.0000 79.4524 87.7915 8.3391 0.1050

84 3587.0000 79.7030 87.8651 8.1621 0.1024

85 3652.0000 79.8403 87.8823 8.0420 0.1007

86 3712.0000 79.8578 88.0422 8.1844 0.1025

87 3772.0000 79.7538 88.2706 8.5168 0.1068

88 3832.0000 79.5655 88.4805 8.9150 0.1120

96



ABSOLUTE ERROR (AE)

ERROR FRACTION


89 3892.0000 79.3248 88.5312 9.2064 0.1161

90 3952.0000 79.0655 88.5450 9.4795 0.1199

91 4018.0000 78.7611 88.5339 9.7728 0.1241

92 4078.0000 78.4852 88.5186 10.0334 0.1278

93 4138.0000 78.1396 88.5138 10.3742 0.1328

94 4198.0000 77.8435 88.4124 10.5689 0.1358

95 4258.0000 77.5868 88.2912 10.7044 0.1380

96 4318.0000 77.3847 88.2296 10.8449 0.1401

97 4383.0000 77.2508 88.1590 10.9082 0.1412

98 4443.0000 77.1893 88.1455 10.9562 0.1419

99 4503.0000 77.1913 88.1216 10.9303 0.1416

100 4563.0000 77.2525 88.1530 10.9005 0.1411

101 4623.0000 77.3603 88.1856 10.8253 0.1399

102 4683.0000 77.5115 88.2574 10.7459 0.1386

103 4748.0000 77.6640 88.3551 10.6911 0.1377

104 4808.0000 77.7798 88.4558 10.6760 0.1373

105 4868.0000 77.8582 88.5958 10.7376 0.1379

106 4928.0000 77.8998 88.7116 10.8118 0.1388

107 4988.0000 77.9143 88.8042 10.8899 0.1398

108 5048.0000 77.9096 88.8916 10.9820 0.1410

109 5113.0000 77.8890 88.9700 11.0810 0.1423

110 5173.0000 77.8570 89.0327 11.1757 0.1435

111 5233.0000 77.8030 89.0798 11.2768 0.1449

112 5293.0000 77.7326 89.1112 11.3786 0.1464

113 5353.0000 77.6524 89.0903 11.4379 0.1473

114 5413.0000 77.5550 89.0734 11.5184 0.1485

115 5479.0000 77.4299 89.0547 11.6248 0.1501

97

Appendix IV: CASNNET4 Water Cut Prediction & Accuracy on Well P24



ABSOLUTE ERROR (AE)

ERROR FRACTION


1 10.0000 0.0086 0.0086 0.0000 0.0000

2 22.0437 0.01 0.0100 0.0000 0.0000

3 31.0000 0.0116 0.0215 0.0099 0.8534

4 44.4345 0.0138 0.0276 0.0138 1.0000

5 64.5861 0.0147 0.0286 0.0139 0.9456

6 90.6684 0.0158 0.0299 0.0141 0.8924

7 104.7154 0.0164 0.0389 0.0225 1.3720

8 117.4438 0.0169 0.0391 0.0222 1.3136

9 128.0075 0.0172 0.0396 0.0224 1.3023

10 143.8530 0.0178 0.0402 0.0224 1.2584

11 162.0841 0.0183 0.0388 0.0205 1.1213

12 178.5766 0.0188 0.0389 0.0201 1.0686

13 197.8604 0.0192 0.0408 0.0216 1.1250

14 219.1955 0.0196 0.0432 0.0236 1.2041

15 240.8549 0.0204 0.0445 0.0241 1.1814

16 260.7609 0.0213 0.0512 0.0299 1.4038

17 285.4612 0.0225 0.0554 0.0329 1.4622

18 309.9560 0.0235 0.0581 0.0346 1.4723

19 335.9551 0.0246 0.0588 0.0342 1.3902

20 365.0000 0.027 0.0598 0.0328 1.2148

21 394.3732 0.0422 0.0599 0.0177 0.4194

22 411.8436 0.031 0.0602 0.0292 0.9419

23 424.0000 0.0355 0.0607 0.0252 0.7099

24 442.2346 0.0329 0.0643 0.0314 0.9544

25 454.9491 0.0383 0.0814 0.0431 1.1253

26 470.3303 0.0453 0.0856 0.0403 0.8896

27 493.4021 0.0587 0.0889 0.0302 0.5145

28 522.1210 0.0806 0.0586 0.0220 0.2730

29 551.9757 2.1607 3.2543 1.0936 0.5061

98



ABSOLUTE ERROR (AE)

ERROR FRACTION


30 580.6344 2.5596 3.5638 1.0042 0.3923

31 602.2611 2.8613 5.1008 2.2395 0.7827

32 622.7828 3.1139 5.2251 2.1112 0.6780

33 647.6240 3.4152 5.5632 2.1480 0.6290

34 684.8858 4.4279 5.5676 1.1397 0.2574

35 732.9335 7.4569 7.5643 0.1074 0.0144

36 766.8496 8.3738 7.8989 0.4749 0.0567

37 791.5642 9.0287 8.5670 0.4617 0.0511

38 828.6360 9.8463 8.5670 1.2793 0.1299

39 865.6932 10.5912 10.9856 0.3944 0.0372

40 921.2790 11.5603 9.5678 1.9925 0.1724

41 981.2790 12.6171 11.1009 1.5162 0.1202

42 1041.2790 15.2389 11.4567 3.7822 0.2482

43 1096.0000 15.8511 12.4566 3.3945 0.2141

44 1156.0000 16.5452 14.8897 1.6555 0.1001

45 1216.0000 17.2557 14.9984 2.2573 0.1308

46 1276.0000 18.0194 15.5679 2.4515 0.1360

47 1336.0000 18.9019 14.6799 4.2220 0.2234

48 1396.0000 19.8483 15.5698 4.2785 0.2156

49 1461.0000 20.9188 16.8975 4.0213 0.1922

50 1521.0000 22.1026 17.6753 4.4273 0.2003

51 1581.0000 22.7194 17.8897 4.8297 0.2126

52 1641.0000 23.4969 18.0986 5.3983 0.2297

53 1701.0000 24.2211 22.7854 1.4357 0.0593

54 1761.0000 24.9359 25.4578 0.5219 0.0209

55 1826.0000 25.9611 25.7864 0.1747 0.0067

56 1884.3292 26.8261 26.9262 0.1001 0.0037

57 1944.3292 28.3888 25.5780 2.8108 0.0990

58 2004.3292 29.5027 24.1342 5.3685 0.1820

59 2064.3292 30.5286 23.1030 7.4256 0.2432

99



ABSOLUTE ERROR (AE)

ERROR FRACTION


60 2124.3292 31.517 24.7014 6.8156 0.2163

61 2191.0000 32.5608 26.0479 6.5129 0.2000

62 2251.0000 33.4399 27.6696 5.7703 0.1726

63 2311.0000 34.5297 28.5612 5.9685 0.1729

64 2371.0000 35.512 29.6640 5.8480 0.1647

65 2431.0000 36.4892 30.5395 5.9497 0.1631

66 2491.0000 37.3788 31.2794 6.0994 0.1632

67 2557.0000 38.2215 31.9311 6.2904 0.1646

68 2613.0608 38.929 32.6457 6.2833 0.1614

69 2673.0608 39.679 33.0928 6.5862 0.1660

70 2733.0608 40.4195 33.6598 6.7597 0.1672

71 2793.0608 41.1682 34.0427 7.1255 0.1731

72 2853.0608 41.9678 34.3766 7.5912 0.1809

73 2922.0000 42.8742 34.6896 8.1846 0.1909

74 2982.0000 43.5657 35.2496 8.3161 0.1909

75 3042.0000 44.3229 35.6044 8.7185 0.1967

76 3102.0000 45.0438 36.1089 8.9349 0.1984

77 3162.0000 45.755 36.5888 9.1662 0.2003

78 3222.0000 46.4557 37.0237 9.4320 0.2030

79 3287.0000 47.1994 37.4399 9.7595 0.2068

80 3347.0000 47.9666 37.9676 9.9990 0.2085

81 3407.0000 48.6356 38.5864 10.0492 0.2066

82 3467.0000 49.2266 39.0986 10.1280 0.2057

83 3527.0000 49.3996 39.3544 10.0452 0.2033

84 3587.0000 49.761 39.2156 10.5454 0.2119

85 3652.0000 49.9497 38.9642 10.9855 0.2199

86 3712.0000 50.0146 38.6095 11.4051 0.2280

87 3772.0000 50.0357 38.3707 11.6650 0.2331

88 3832.0000 50.0551 38.1801 11.8750 0.2372

100



ABSOLUTE ERROR (AE)

ERROR FRACTION


89 3892.0000 50.0896 38.0711 12.0185 0.2399

90 3952.0000 50.1887 38.0660 12.1227 0.2415

91 4018.0000 50.3178 38.2113 12.1065 0.2406

92 4078.0000 50.4739 38.5765 11.8974 0.2357

93 4138.0000 50.5469 39.0596 11.4873 0.2273

94 4198.0000 50.7363 39.7371 10.9992 0.2168

95 4258.0000 50.842 40.6254 10.2166 0.2009

96 4318.0000 51.0561 41.0799 9.9762 0.1954

97 4383.0000 51.2901 41.8221 9.4680 0.1846

98 4443.0000 50.6928 42.6850 8.0078 0.1580

99 4503.0000 50.2839 43.1306 7.1533 0.1423

100 4563.0000 50.0863 43.4770 6.6093 0.1320

101 4623.0000 50.0921 43.8379 6.2542 0.1249

102 4683.0000 52.2354 44.2108 8.0246 0.1536

103 4748.0000 53.5268 45.7644 7.7624 0.1450

104 4808.0000 54.2927 47.3304 6.9623 0.1282

105 4868.0000 54.5878 48.4211 6.1667 0.1130

106 4928.0000 54.7766 49.1499 5.6267 0.1027

107 4988.0000 54.7179 49.7005 5.0174 0.0917

108 5048.0000 54.5708 50.1124 4.4584 0.0817

109 5113.0000 54.5125 50.4423 4.0702 0.0747

110 5173.0000 54.5313 50.8088 3.7225 0.0683

111 5233.0000 54.6957 51.2451 3.4506 0.0631

112 5293.0000 54.9799 51.7897 3.1902 0.0580

113 5353.0000 55.2922 52.4041 2.8881 0.0522

114 5413.0000 55.5635 53.0429 2.5206 0.0454

115 5479.0000 55.5943 53.6514 1.9429 0.0349

artificial neural network for diagnosis & mitigation …

Documents