Maximising Oil Production Through Data Modelling, Simulation and Optimisation José Antonio

216 Pages·2017·2.42 MB·English

Maximising Oil Production Through Data
Modelling, Simulation and Optimisation
José Antonio Peñuelas Alvarez
A thesis submitted in partial fulfilment of the
requirements for the degree of Doctor of Philosophy
The University of Sheffield
Department of Automatic Control and Systems
Engineering
March 2017
Acknowledgements
I would like to thank my main supervisor Dr Hua-Liang Wei for his valu-
able guidance and support during my studies.
I feel privileged for joining the Department of Automatic Control and
Systems Engineering. I have learned a lot from all my friends and colleagues
I have met at the department. You have all contributed to the amazing time
I’ve had in Sheffield during the last years.
I express my gratitude to Mexico’s Ministry of Energy for its financial
support, without this help, this work would not have been possible. I would
like to thank Dr Pablo Ibargüengoytia for his comments, ideas and monitor-
ing the progress of my studies.
Finally, I would like to thank my family for giving me their love and
support. Without you, I would not be here. I dedicate this Thesis to you:
Papá, Mamá y Ale.
Abstract
Theresearchworkpresentedonthisthesisprovidesanalternativetoolfor
characterising oil fields under fluid injection by analysing historical produc-
tion/injection rates. In particular polynomial and radial basis Non Linear
Autoregressive with Exogenous Input Model (NARX) models were devel-
oped; these models were capable of capturing the dynamics of an operating
field in the North Sea.
A Greedy Randomised Adaptive Search Procedure (GRASP) heuristic
optimisation method was applied for estimating a future injection strategy.
This approach is combined with a risk analysis methodology, a popular ap-
proach in financial mathematics. As a result, it is possible to estimate how
likely it is to reach a production goal.
According to the simulations, it is possible to increase oil production
by 10% in one year by implementing a smart injection strategy with low
statisticaluncertainty. Resultingfromthisresearchproject,acomputational
tool was developed. It is now possible to estimate NARX models from any
fieldunderfluidinjectionaswellasfindingthebestfutureinjectionscenario.
Contents
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Contributions and Thesis Overview . . . . . . . . . . . . . . . 8
1.3.1 Main Contributions . . . . . . . . . . . . . . . . . . . 8
1.3.2 Chapter Description . . . . . . . . . . . . . . . . . . . 10
1.3.3 Published Articles . . . . . . . . . . . . . . . . . . . . 12
2 State of the Art in Reservoir Simulation 13
2.1 Traditional Methods . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Analysis of Decline Curves . . . . . . . . . . . . . . . . 15
2.1.2 Material Balance Equation . . . . . . . . . . . . . . . 18
2.2 Capacitive Resistive Model . . . . . . . . . . . . . . . . . . . 23
2.3 Statistical Reservoir Analysis . . . . . . . . . . . . . . . . . . 26
2.4 Linear Data-Driven Models . . . . . . . . . . . . . . . . . . . 29
2.5 Multi-Layer Neural Networks . . . . . . . . . . . . . . . . . . 31
2.5.1 Scott Field, a Case Study From the North Sea . . . . 37
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
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3 New Practical Application of the Non Linear Autoregressive
with Exogenous Input Model in Petroleum Engineering 49
3.1 The Non Linear Autoregressive Moving Average with Exoge-
nousInputModel(NARMAX)SystemIdentificationMethod-
ology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.1.1 Polynomial NARX Models . . . . . . . . . . . . . . . . 52
3.2 The FROLS Algorithm for Term Selection . . . . . . . . . . . 54
3.2.1 NARX Model Estimation . . . . . . . . . . . . . . . . 58
3.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4 NovelProbabilisticNARXNeuralNetworkModelApproach 75
4.1 Single Layer Multi-Scale Radial Basis Function Models . . . . 76
4.2 Implementing MSRBF Models for EOR Modelling . . . . . . 80
4.3 Novel Pruning Method for NARX MSRBF Models . . . . . . 86
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
5 Estimating Future Uncertainty 99
5.1 Feature Selection Comparative Study . . . . . . . . . . . . . . 99
5.2 Introduction to Risk Analysis . . . . . . . . . . . . . . . . . . 111
5.2.1 Qualitative Methods . . . . . . . . . . . . . . . . . . . 112
5.2.2 Quantitative Methods . . . . . . . . . . . . . . . . . . 114
5.3 Monte Carlo for NARX Models . . . . . . . . . . . . . . . . . 115
5.3.1 Risk Profile Analysis . . . . . . . . . . . . . . . . . . . 120
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6 Production Optimisation 131
6.1 Problem Definition . . . . . . . . . . . . . . . . . . . . . . . . 131
6.2 Heuristic Optimisation Methods . . . . . . . . . . . . . . . . . 132
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6.3 GRASP Optimisation Using NARX Models . . . . . . . . . . 134
6.3.1 Financial Benefits . . . . . . . . . . . . . . . . . . . . 148
6.4 Forecasting Using Ensemble Modelling . . . . . . . . . . . . . 150
6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
7 Conclusions and Future Work 156
7.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
7.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
Appendices 162
A MSRBF Model Structure 163
A.1 Multi-Layer Neural Network Performance . . . . . . . . . . . 169
B Production Well Models 172
C Future Injection Values 182
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List of Figures
1.1 Energy Sources . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 World Energy Consumption Forecast . . . . . . . . . . . . . . 3
1.3 Simple Field Under Injection Diagram . . . . . . . . . . . . . 7
2.1 Exponential Decline Curve Analysis Example . . . . . . . . . 17
2.2 Oil, Gas and Water Compressibility Ratios. . . . . . . . . . . 19
2.3 Fluid Expansion Diagram . . . . . . . . . . . . . . . . . . . . 22
2.4 Neural Network Structure . . . . . . . . . . . . . . . . . . . . 33
2.5 Multi-Layer Neural Network Structure . . . . . . . . . . . . . 34
2.6 Scott Field Location . . . . . . . . . . . . . . . . . . . . . . . 37
2.7 Raw Oil Production Data . . . . . . . . . . . . . . . . . . . . 38
2.8 Raw Water Injection Data . . . . . . . . . . . . . . . . . . . . 39
2.9 Total Oil Production . . . . . . . . . . . . . . . . . . . . . . . 40
2.10 Total Water Injection. . . . . . . . . . . . . . . . . . . . . . . 41
2.11 Outlier Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.12 Partial Autocorrelation Function . . . . . . . . . . . . . . . . 44
2.13 12-Delays 21-Hidden Neurons NN Model Response . . . . . . 45
2.14 11-Delays 2-Layers NN Model Structure . . . . . . . . . . . . 46
3.1 MISO System Identification Diagram . . . . . . . . . . . . . . 50
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3.2 Third order Polynomial-Model 16 Performance . . . . . . . . 66
3.3 Model 2 Performance . . . . . . . . . . . . . . . . . . . . . . . 67
3.4 Model 3 Performance . . . . . . . . . . . . . . . . . . . . . . . 67
3.5 Model 3 Residuals Histogram . . . . . . . . . . . . . . . . . . 68
3.6 Model 3 Residuals Confidence Limits . . . . . . . . . . . . . . 69
4.1 Output Lag Estimation . . . . . . . . . . . . . . . . . . . . . 82
4.2 Input Lag Estimation . . . . . . . . . . . . . . . . . . . . . . 83
4.3 MSRBF Model ny=5 nu=4 . . . . . . . . . . . . . . . . . . . 84
4.4 Drop-out Diagram . . . . . . . . . . . . . . . . . . . . . . . . 89
4.5 MSRBF Dropout Diagram . . . . . . . . . . . . . . . . . . . . 90
4.6 No of Models vs MSE OSA . . . . . . . . . . . . . . . . . . . 93
4.7 No of Models vs MSE MPO . . . . . . . . . . . . . . . . . . . 93
4.8 Ensemble OSA Predictions . . . . . . . . . . . . . . . . . . . 95
4.9 Ensemble MPO Predictions . . . . . . . . . . . . . . . . . . . 95
4.10 Ensemble Prediction Performance . . . . . . . . . . . . . . . . 96
5.1 Flow Chart For Sequential Feature Selection Algorithm. . . . 103
5.2 Moving Average Ranking For Input 3 . . . . . . . . . . . . . . 104
5.3 MSE vs Added Feature . . . . . . . . . . . . . . . . . . . . . . 110
5.4 Fishbone Diagram . . . . . . . . . . . . . . . . . . . . . . . . 114
5.5 Polynomial model predicted scenarios. . . . . . . . . . . . . . 119
5.6 MSRBF model predicted scenarios . . . . . . . . . . . . . . . 120
5.7 Changes in Std Polynomial Model . . . . . . . . . . . . . . . 121
5.8 Changes in Std MSRBF Model . . . . . . . . . . . . . . . . . 122
5.9 Histogram From Polynomial Model . . . . . . . . . . . . . . . 124
5.10 Histogram From MSRBF Model . . . . . . . . . . . . . . . . . 125
5.11 Risk Profiles From Polynomial Model . . . . . . . . . . . . . . 126
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5.12 Risk Profiles From MSRBF Model . . . . . . . . . . . . . . . 127
6.1 Optimised Oil Production-Polynomial Model . . . . . . . . . 143
6.2 Optimised Oil Production-MSRBF Model . . . . . . . . . . . 143
6.3 30% Production Increase Polynomial Model . . . . . . . . . . 147
6.4 30% Production Increase MSRBF Model . . . . . . . . . . . . 147
6.5 Ensemble Diagram . . . . . . . . . . . . . . . . . . . . . . . . 151
6.6 Ensemble Forecast Polynomial & MSRBF Model . . . . . . . 152
6.7 Ensemble Residual Limits Polynomial & MSRBF Model . . . 152
6.8 Ensemble Prediction Distribution Polynomial & MSRBF Model153
6.9 Ensemble Modelling Optimisation . . . . . . . . . . . . . . . . 154
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List of Tables
2.1 Best Multi-Layer Models . . . . . . . . . . . . . . . . . . . . . 45
3.1 Polynomial NARX Models . . . . . . . . . . . . . . . . . . . . 64
3.2 Polynomial NARX Model 3 . . . . . . . . . . . . . . . . . . . 70
3.3 Injection Well Frequency-Model 3 . . . . . . . . . . . . . . . . 72
4.1 MSRBF Model Performance Comparison . . . . . . . . . . . . 96
4.2 Model Performance Comparission . . . . . . . . . . . . . . . . 97
5.1 Number of Estimated Models . . . . . . . . . . . . . . . . . . 105
5.2 Feature Selection Time Comparison . . . . . . . . . . . . . . . 106
5.3 Input Variable Ranking . . . . . . . . . . . . . . . . . . . . . 107
5.4 Injection Well Ranking . . . . . . . . . . . . . . . . . . . . . . 109
5.5 Monte Carlo Iterations for Polynomial Model . . . . . . . . . 117
5.6 Monte Carlo Iterations for MSRBF Model . . . . . . . . . . . 118
6.1 Number of iterations for local search-Polynomial Model . . . 141
6.2 No of iterations for local search-MSRBF Model . . . . . . . . 142
6.3 Probability of Reaching Production Levels-Polynomial Model 144
6.4 Probability of Reaching Production Levels-MSRBF Model . . 145
6.5 Financial Increase in Sales . . . . . . . . . . . . . . . . . . . . 149
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