The Pennsylvania State University. The Graduate School. Department of Energy and Mineral Engineering DEVELOPMENT OF ARTIFICIAL NEURAL NETWORKS

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1 The Pennsylvania State University The Graduate School Department of Energy and Mineral Engineering DEVELOPMENT OF ARTIFICIAL NEURAL NETWORKS FOR STEAM ASSISTED GRAVITY DRAINAGE (SAGD) RECOVERY METHOD IN HEAVY OIL RESERVOIRS A Thesis in Energy and Mineral Engineering by Ayhan Sengel 2013 Ayhan Sengel Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science August 2013

2 The thesis of Ayhan Sengel was reviewed and approved* by the following: Turgay Ertekin Professor of Petroleum and Natural Gas Engineering Thesis Advisor Russell T. Johns Professor of Petroleum and Natural Gas Engineering John Yilin Wang Assistant Professor of Petroleum and Natural Gas Engineering Luis F. Ayala H. Associate Professor of Petroleum and Natural Gas Engineering Associate Department Head for Graduate Education *Signatures are on file in the Graduate School

3 iii ABSTRACT As no alternative energy source has been introduced to efficiently replace fossil fuels yet, the demand for oil and gas is still increasing in the world. Conventional hydrocarbon reservoirs have been depleted rapidly to meet the demand; in doing so, the amount of conventional resources has declined. This has led to the interest of methods to enhance hydrocarbon recovery in unconventional resources such as heavy oil, bitumen and oil shale. As a result of its high viscosity, economic recovery of heavy oil and bitumen is a great challenge. Steam Assisted Gravity Drainage (SAGD) is a commercial in-situ recovery technology used to reduce oil viscosity by increasing the temperature of the reservoir to enhance the recovery of heavy oil and bitumen. Two parallel horizontal wells are employed in the SAGD process. The upper horizontal well is employed for continuous steam injection into the reservoir, while the lower horizontal well is used to produce reservoir fluids. Numerical simulation of SAGD is a complex task. Instead of struggling with high complex problems, simple models are used to substitute reservoir simulations over a given range of input parameters. Usage of neural-network based proxy models for the solution of non-linear relationships has been increasingly popular in recent years in the oil and gas industry. Artificial neural network (ANN) methodology is used to avoid excessive time consumption of computer simulations. The objective of this study is to develop neural-network based proxy models that can provide instant and reasonably accurate preliminary estimations for SAGD applications. The variables used in this study include reservoir rock/fluid properties, such as reservoir thickness, porosity, horizontal permeability, horizontal-vertical permeability ratio, initial reservoir pressure, reservoir temperature, rock thermal conductivity, initial oil saturation and oil density, together with operational variables including vertical spacing, spacing between the producer and the base of the reservoir, inter-well (well pattern) spacing, sub-cooling temperature, steam quality, well length, maximum injector bottom-hole pressure and minimum producer bottom-hole pressure.

4 iv The present study aims at developing neural-network based proxies for SAGD recovery method in heavy oil reservoirs. A two-stage approach was used. In stage I, a total of 904 reservoir specific samples have been trained. The forward-looking artificial neural network is used to predict performance indicators such as cumulative oil production, cumulative steam oil ratio and cumulative water production profiles over a period of 10 years for a given set of operational (design) parameters. On the other hand, the inverse-looking artificial neural network is used to predict operational parameters for a given set of desired 10-year cumulative oil production and cumulative steam-oil ratio profiles. In stage II, reservoir properties are varied as well. ANN methodology is extended to a range of homogeneous reservoirs. A total of 1590 samples were generated. This stage provides a forward-looking artificial neural network that predicts performance indicators over a period of 10 years and two inverse-looking artificial neural networks: one that predicts operational parameters and another that predicts reservoir properties. CMG 1 CMOST Studio automation tool was used to generate SAGD numerical simulation samples over a given input data range. Numerical simulations were performed using the CMG STARS thermal simulator (version ). Numerical simulations were utilized to feed the training of the artificial neural network using MATLAB 2 neural network toolbox (version R2011a). The results of this study show that artificial neural networks are able to recognize complex relationships between input data and corresponding output data for SAGD simulations. Therefore, ANNs are suitable tools for SAGD forecasting and analysis. 1 CMG: Computer Modeling Group 2 MATLAB: MATrix LABoratory

5 v TABLE OF CONTENTS List of Figures... v List of Tables... vi Acknowledgements... vii Chapter 1 Introduction... 1 Chapter 2 Literature Review Steam Assisted Gravity Drainage Horizontal Wellbores Overview of Artificial Neural Networks Chapter 3 Problem Statement Chapter 4 Numerical Simulation of Steam Assisted Gravity Drainage Grid Sensitivity Analysis Numerical Simulation Model Chapter 5 Stage I: Development of Reservoir Specific Proxies Data Gathering and Input Variable Selection Response Surface Methodology Sensitivity Analysis ANN Development Forward Problem Inverse Problem Chapter 6 Stage II: Development of Universal Proxies Data Gathering and Input Variable Selection Sensitivity Analysis ANN Development Forward Problem Inverse Problem I Inverse Problem II Chapter 7 Graphical User Interface (GUI) Chapter 8 Conclusion and Recommendations Conclusion Recommendations... 94

6 Appendix A Grid Sensitivity Analysis Appendix B Example of Steam Chamber Development Appendix C Response Surface Quadratic Proxy Model Equations Appendix D Example of STARS Input File for SAGD Appendix E Parameter Distribution Appendix F MATLAB Script vi

7 vii LIST OF FIGURES Figure 1-1. The average well productivity in 2011 by recovery method for SAGD, CSS, and primary (including enhanced recovery)... 2 Figure 1-2. Annual crude oil production from oil sands by technology... 3 Figure 2-1. Steam assisted gravity drainage schematic... 4 Figure 2-2. Conceptual diagram of the steam assisted gravity drainage process... 5 Figure 2-3. Typical SAGD horizontal well pair configuration Figure 2-4. Single input neuron Figure 2-5. Example of multilayer perceptron (MLP) neural network architecture Figure 3-1. Stage I ANNs Figure 3-2. Stage II ANNs Figure 4-1. Schematic 2D reservoir model (cross section) Figure 4-2. Schematic 2D reservoir model (top view) Figure 4-3. Water Oil relative permeability curves Figure 4-4. Liquid Gas relative permeability curves Figure 5-1. Proxy model verification plot for cumulative oil production (2 nd year) Figure 5-2. Proxy model verification plot for cumulative oil production (10 th year) Figure 5-3. Proxy model verification plot for cumulative steam-oil ratio (2 nd year) Figure 5-4. Proxy model verification plot for cumulative steam-oil ratio (10 th year) Figure 5-5. Proxy model verification plot for cumulative water production (2 nd year) Figure 5-6. Proxy model verification plot for cumulative water production (10 th year) Figure 5-7. Sensitivity analysis on cumulative oil production (2 nd year) Figure 5-8. Sensitivity analysis on cumulative oil production (10 th year) Figure 5-9. Sensitivity analysis on cumulative steam oil ratio (2 nd year) Figure Sensitivity analysis on cumulative steam oil ratio (10 th year)... 28

8 viii Figure Sensitivity analysis on cumulative water production (2 nd year) Figure Sensitivity analysis on cumulative water production (10 th year) Figure Artificial neural network workflow Figure Artificial neural network architecture - Stage I forward problem Figure The testing data regression plots for cumulative oil production Stage I forward problem Figure The testing data regression plots for cumulative steam-oil ratio Stage I forward problem Figure The testing data regression plots for cumulative water production Stage I forward problem Figure Cumulative oil production absolute percentage errors for the testing data Figure Cumulative steam-oil ratio absolute percentage errors for the testing data Figure Cumulative water production absolute percentage errors for the testing data Figure Comparison between ANN and CMG for the sample # Figure Comparison between ANN and CMG for the sample # Figure Comparison between ANN and CMG for the sample # Figure Comparison between ANN and CMG for the sample # Figure Artificial neural network architecture Stage I inverse problem Figure The testing data regression plots for operational parameters Stage 1 inverse problem Figure BHP injector absolute percentage errors for the testing data Figure Steam quality absolute percentage errors for the testing data Figure Sub-cooling temperature absolute percentage errors for the testing data Figure Well length absolute percentage errors for the testing data Figure BHP producer absolute percentage errors for the testing data Figure Inter-well spacing absolute percentage errors for the testing data Figure Vertical spacing absolute percentage errors for the testing data... 50

9 ix Figure Cumulative oil production comparison between ANN well configuration and actual for the testing sample # Figure Cumulative steam-oil ratio comparison between ANN well configuration and actual for the testing sample # Figure Cumulative water production comparison between ANN well configuration and actual for the testing sample # Figure Cumulative oil production comparison between ANN well configuration and actual for the testing sample # Figure Cumulative steam-oil ratio comparison between ANN well configuration and actual for the testing sample # Figure Cumulative water production comparison between ANN well configuration and actual for the testing sample # Figure Cumulative oil production comparison between ANN well configuration and actual for the testing sample # Figure Cumulative steam-oil ratio comparison between ANN well configuration and actual for the testing sample # Figure Cumulative water production comparison between ANN well configuration and actual for the testing sample # Figure 6-1. Sensitivity analysis on cumulative oil production (1 st year) Figure 6-2. Sensitivity analysis on cumulative oil production (2 nd year) Figure 6-3. Sensitivity analysis on cumulative oil production (10 th year) Figure 6-4. Sensitivity analysis on cumulative steam-oil ratio (1 st year) Figure 6-5. Sensitivity analysis on cumulative steam-oil ratio (2 nd year) Figure 6-6. Sensitivity analysis on cumulative steam-oil ratio (10 th year) Figure 6-7. Sensitivity analysis on cumulative water production (1 st year) Figure 6-8. Sensitivity analysis on cumulative water production (2 nd year) Figure 6-9. Sensitivity analysis on cumulative water production (10 th year) Figure Artificial neural network architecture Stage II forward problem Figure The testing data regression plots for cumulative oil production Stage II forward problem... 67

10 x Figure The testing data regression plots for cumulative steam-oil Ratio Stage II forward problem Figure The testing data regression plots for cumulative water production Stage II forward problem Figure Artificial neural network architecture Stage II inverse problem I Figure Comparison of the actual injection pressure with the predicted injection pressure values Figure Comparison of the actual BHP producer with the predicted BHP producer values Figure Comparison of the actual steam quality with the predicted steam quality values Figure Comparison of the actual sub-cooling temperature with the predicted subcooling temperature values Figure Comparison of the actual well length with the predicted well length values Figure Comparison of the actual base-producer spacing with the predicted baseproducer spacing values Figure Comparison of the actual vertical spacing with the predicted vertical spacing values Figure Inter-well spacing comparison for the testing data Figure Comparison of the cumulative oil production resulting from ANN well configuration with the actual cumulative oil production for the testing sample # Figure Comparison of the cumulative steam-oil ratio resulting from ANN well configuration with the actual cumulative steam-oil ratio for the testing sample # Figure Comparison of the cumulative oil production resulting from ANN well configuration with the actual cumulative oil production for the testing sample # Figure Comparison of the cumulative steam-oil ratio resulting from ANN well configuration with the actual cumulative steam-oil ratio for the testing sample # Figure Comparison of the cumulative oil production resulting from ANN well configuration with the actual cumulative oil production for the testing sample # Figure Comparison of the cumulative steam-oil ratio resulting from ANN well configuration with the actual cumulative steam-oil ratio for the testing sample # Figure Artificial neural network architecture Stage II inverse problem II... 84

11 xi Figure Comparison of the actual permeability ratio with the predicted permeability ratio values Figure Comparison of the actual permeability with the predicted permeability values Figure Comparison of the actual porosity with the predicted porosity values Figure Comparison of the actual reservoir pressure with the predicted reservoir pressure values Figure Comparison of the actual reservoir temperature with the predicted reservoir temperature values Figure Comparison of the actual reservoir thickness with the predicted reservoir thickness values Figure Comparison of the actual rock thermal conductivity with the predicted rock thermal conductivity values Figure Comparison of the actual oil saturation with the predicted oil saturation values Figure Comparison of the actual oil density with the predicted oil density values Figure 7-1. GUI main screen Figure 7-2. The forward-looking ANN interface Figure 7-3. The inverse ANN-1 interface Figure 7-4. The inverse ANN-2 interface... 92

12 xii LIST OF TABLES Table 4-1. Heat Loss Calculations Table 5-1. Reservoir/Fluid Properties Stage I Table 5-2. Operational Parameters Stage I Table 5-3. Performance Indicators Table 5-4. R 2 and R 2 Adjusted Values for the Quadratic Proxy Model Table 5-5. Division of Database Stage I Table 5-6. Functional Links - Stage I Forward Problem Table 5-7. Operational Parameters for Sample#1, Sample#2, Sample#3 and Sample# Table 5-8. Reservoir Properties for the Validation of the Network Architecture Stage I Table 5-9. Mean Absolute Percentage Errors Stage I Inverse Problem Table 6-1. Reservoir/Fluid Properties Stage II Table 6-2. Operational Parameters Stage II Table 6-3. Division of Database Stage II Table 6-4. Functional Links - Stage II Forward Problem Table 6-5. Mean Absolute Percentage Errors for the Testing Data Stage II Forward Problem Table 6-6. Functional Links - Stage II Inverse Problem I... 74

13 xiii Nomenclature ANN API bbl BHP BTU CMG COP csor CSS CWP k x k y k z LHD MAPE MLP MSE P sat SAGD STB Ø Artificial Neural Network American Petroleum Institute Barrels Bottom-hole Pressure British thermal unit Computer Modeling Group Cumulative Oil Production Cumulative Steam-Oil ratio Cyclic steam stimulation Cumulative Water Production Permeability in the x-direction, md Permeability in the y-direction, md Permeability in the z-direction, md Latin hypercube experimental design Mean absolute percentage error Multilayer perceptron Mean square error Saturation pressure Steam assisted gravity drainage Stock tank barrel Porosity

14 xiv ACKNOWLEDGEMENTS First and foremost, I want to thank my advisor Prof. Dr. Ertekin for his guidance, encouragement and support. I really appreciate that he has always been very helpful during my studies. I am thankful to my family for their support. My family is extremely important to me and I would not be the person I am today without the love and support they have given me. I dedicate this study to my mother Omur Sengel who fought cancer and passed away this year. I wish to thank the members of the examination committee, Prof. Dr. Johns and Prof. Dr. Wang, for their participation and agreeing to review the entire thesis. I also would like to express my appreciation to my company, Turkish Petroleum Corporation (TPAO), for providing me financial support to study Petroleum and Natural Gas Engineering at the Pennsylvania State University. Ayhan Sengel August, 2013

15 1 Chapter 1 Introduction As no alternative energy source has been introduced to efficiently replace fossil fuels yet, the demand for oil and gas is still increasing in the world. Conventional hydrocarbon reservoirs have been depleted rapidly to meet the demand; in doing so, the amount of conventional resources has declined. This has led to the interest of methods to enhance hydrocarbon recovery in unconventional resources such as heavy oil, bitumen and oil shale. Heavy oil and bitumen resources comprise approximately 70% of worldwide oil reserves which means that these reserves appear to be significant players for the future global oil supply (Gossuin et al., 2010). The total oil in place of such reserves is estimated to be about trillion barrels in Canada and Venezuela (Dusseault, 2001). It is believed that the total volume of bitumen in Canada is almost as much as that of conventional crude oil in the Middle East (Butler, 1994). The classification of heavy oil, extra-heavy oil and bitumen is based on API gravity and viscosity. Heavy oil has the API gravity in the range of 10 and 20 whereas it is less than 10 for natural bitumen and extra-heavy oil. Natural bitumen displays a dead oil viscosity which is greater than 10,000 centipoises (cp) at original reservoir temperature while heavy oil and extraheavy oil correspond to the oil with a dead oil viscosity less than 10,000 centipoises (cp) (U.S. Geological Survey, 2006). As a result of its high viscosity, economic recovery of heavy oil and bitumen is a great challenge. Surface mining technique is only applicable for the production from shallow heavy oil and bitumen reservoirs. Many recovery methods have been tried over the past several decades to enhance the bitumen and heavy oil production since the exploration of oil sands. Thermal methods such as steam flooding, cyclic steam stimulation (CSS) and steam assisted gravity drainage (SAGD) have been developed to reduce the high viscosity nature of the crude oil by

16 2 heating it up. One of the most successful and best known methods of tertiary thermal recovery is steam-assisted gravity drainage (SAGD) process, which has returned production efficiencies up to 60% or better in Canadian heavy oil reservoirs (Halliburton, 2013). The UTF (Underground Test Facility) project which started in 1988 in Athabasca was designed to test the application of SAGD (Butler, 1998). This field test started with phase A consisting 50 m long three horizontal well pairs. This successful pilot test was followed by phase B and D with increasing well lengths for each phase. These both phases have been completed successfully and exhibited higher oil recoveries (over 50%) as expected (Butler, 1998). Overall, the project has proven that SAGD recovery method is commercially viable for the recovery of heavy oil and bitumen. Following this encouraging field test results, SAGD has become a wellknown in-situ recovery method over the last ten years in major deposits of Canada such as Athabasca, Cold Lake and Peace River. According to ECRB, the average well productivity by SAGD recovery method is much higher than other methods as seen in Figure 1-1. Therefore, it is projected to be a more widely used process for upcoming projects in Athabasca oil sands reserves (Crowfoot et al., 2012). In 5 years, the number of commercial SAGD projects in operation in Athabasca has been ascended from 4 to 15 since 2001 (Li et al., 2009). Figure 1-2 shows that crude oil production in Canada by SAGD recovery method demonstrates an exponential growth especially after the year of Figure 1-1. The average well productivity in 2011 by recovery method for SAGD, CSS, and primary (including enhanced recovery) (Crowfoot et al., 2012)

17 3 Figure 1-2. Annual crude oil production from oil sands by technology (Holly, et al., 2012) Artificial neural network (ANN) is a predictive tool which is able to model various complex and challenging non-linear relationships between inputs and outputs better than conventional regression techniques (Jahanbakhshi and Keshavarzi, 2012). This is because artificial neural networks have large degrees of freedom that provide a prominent ability for them to map non-linear relationships (Sadiq and Nashawi, 2000). Usage of neural-network based proxy models for the solution of non-linear relationships has been increasingly popular in recent years in the oil and gas industry. Neural networks have been utilized as a proxy model for optimization of SAGD processes (Queipo et al., 2001) and prediction of SAGD performance (Amirian et al., 2013).

18 4 Chapter 2 Literature Review 2.1. Steam Assisted Gravity Drainage Steam Assisted Gravity Drainage (SAGD) is a commercial in-situ recovery technology used to reduce oil viscosity by increasing the temperature of the reservoir to enhance the recovery of heavy oil and bitumen. Nowadays, it is widely used recovery method to produce from the fields which have a great amount of heavy oil and bitumen sand reserves in the countries like Canada and Venezuela because it is convenient for such unconsolidated reservoirs that shows high vertical permeability (Albahlani and Babadagli, 2008). Figure 2-1. Steam assisted gravity drainage schematic (British Petroleum, 2010)

19 SAGD Concept and Mechanism Roger Butler (1981) and his friends proposed the concept at Imperial Oil in the late 1970s. Two parallel horizontal wells are employed in the SAGD process. The upper horizontal well is employed for continuous steam injection into the reservoir, while the lower horizontal well is used to produce reservoir fluids. The injected steam rises up in the formation and it forms a steam chamber. The steam chamber grows to the top of the reservoir rapidly. After it reaches to the top of the reservoir, it expands sideways beneath the overburden. The steam condenses and moves down with heated oil to the production well under the effect of gravity (Butler, 1991). The viscosity of the oil which is originally in the millions of centipoises can be reduced to single digit centipoise values by using SAGD technique. Thus, heavy oil becomes producible with the help of gravity which is already present in the reservoir. The process in early phase is shown in Figure 2-1. Figure 2-2. Conceptual diagram of the steam assisted gravity drainage process (Butler, 1994) Analytical Models The original equation for the rate of drainage was concluded by Butler (1994) after conducting a number of experiments using Darcy s equation as follows:

20 6 (Eq. 2.1.) (Eq. 2.2.) where, q is the flow rate (m 3.s -1 ), L is the length of the horizontal well (m), k is the effective permeability for the flow of oil (m 2 ), g is the acceleration due to gravity (m.s -2 ), h is the steam chamber height (m), So is the oil saturation, α is the thermal diffusivity of reservoir (m 2.s -1 ), Ø is the porosity, m is the dimensionless parameter (typically 3-4) which depends on viscositytemperature characteristics of the oil, T is the temperature ( C), and v is the kinematic viscosity of oil (g.cm -1.sec -1 ). In addition to the gravity drainage, another main contributor to this theory is the energy flow by thermal conduction. The convection is not considered as a heat transfer factor in Butler s original equation (O Rourke et al., 1997). Because of the assumption that the temperature accounts for the steady state in every location along the steam condensation surface, drainage rate from the original equation is likely to be overestimated. There are two alterations of the original equation called TANDRAIN and LINDRAIN that consider these influences. The constant value under square root which is 2 for the original equation is changed to 1.5 and 1.3 for TANDRAIN and LINDRAIN respectively (O Rourke et al., 1997). The original Butler s theory also focused on only one dimension, the drainage height, to establish a connection with the drainage rate without considering the shape of the interface or its horizontal extension. The shape of the interface and horizontal dimension were included to the theory afterwards. A guideline prepared by Butler is simplified to a flow chart and it can be used to calculate oil production analytically (Albahlani and Babadagli, 2008). Later, Ito came up with a realization that heat transfer by convection is not negligible at all. He states that approximately 56% of total heat transfer in the vicinity of steam chamber accounts for heating by convection (Ito and Suzuki, 1997). Edmunds (1999) disagreed that percentage of total heat transfer would be carried by convection and he explained the actual heat capacity of condensate.

21 SAGD Improvements Some modifications of SAGD have been made by researchers to improve recovery. They can be divided into two categories: geometrical and chemical. Geometrical variations of SAGD process enhancements: Single well SAGD (SW-SAGD): Instead of using two horizontal wells, one horizontal well is employed in this variation for both injection and production (Elliot and Kovscek, 1999). Fast-SAGD: The Fast-SAGD method is the combination of the SAGD well pair and cyclic steam stimulation (CSS) offset wells. CSS contributes to the steam chamber spreading laterally (Shin and Polikar, 2006). Cross SAGD (X-SAGD): Stalder (2007) described an alternative SAGD configuration in which the horizontal injection wells are placed perpendicular to the horizontal production wells rather than parallel as in SAGD. J-SAGD: Gates proposed a J-shaped producer above a horizontal injector. He claims that this design works better than SAGD in terms of csor and oil recovery in a reservoir which has variable viscosity in the vertical direction (Tamer and Gates, 2012). Chemical variations of SAGD process enhancements: Steam and gas push (SAGP): In the SAGP process, non-condensable gas, for example natural gas or nitrogen, is injected with steam (Butler, 1997). Non-condensable gas at the top of the steam chamber improves the efficiency of SAGD by reducing heat loss to the overburden. Expanding solvent SAGD (ES-SAGD): In the ES-SAGD process, a hydrocarbon solvent at low concentration is injected with steam in a vapor phase. At reservoir conditions, condensed solvent around the interface of the steam chamber serves to decrease oil viscosity (Nasr et al., 2002) SAGD Optimization SAGD process is usually initiated with a preheating period. During the preheating period, steam is circulated into both injector and producer wells to establish heat communication. Cumulative steam oil ratio (csor) plays an important role as a performance indicator for the

22 8 optimization of SAGD projects. Cumulative steam oil ratio is the ratio of total amount of steam injected to the total amount of oil produced at standard conditions (Souraki et al., 2013). The higher csor, the greater volume of injected steam, the greater amount of the natural gas required to generate steam and the higher cost of the process. Well configuration and operational conditions are controllable parameters and the optimization can be reached by designing them efficiently. The primary goal of any project is to find the optimum design. There are significant parameters influencing economics strongly in all kinds of projects. Injection constraint and steam trap control are considered as parameters that affect csor significantly because they control the propagation of injected steam (Bao et al., 2010). Maximum Injection Pressure: Steam injection pressure is one of the most important parameters on SAGD performance. Predominantly, higher steam injection pressure supports to sweep fluid from the wellbore to the surface. Therefore, it leads to achieving higher oil production rates and faster oil drainage. On the other hand, in case the overburden is damaged by the higher injection pressure, it may cause using much more steam per unit of oil production (Li et al., 2009). The geo-mechanical competence of the overburden (cap rock) should be taken into consideration; the overburden is impervious so steam will not leak through the upper side. It would have a negative impact on the expansion of the steam chamber and even the environment (Medina, 2010). The motivation should be minimizing heat losses to the overburden. Gates studied on the optimization of SAGD by altering the injection pressure. He concluded that higher injection pressure until the steam chamber reaches the overburden followed by lower injection pressure is the optimum injection strategy (Gates and Chakrabarty, 2005). Steam Trap Control: The prevention of live steam to flow directly into the producer is required to maintain thermal efficiency of a SAGD process. Steam trap control is an operational constraint on the production well. Steam trap control is applied to keep the temperature of produced fluids below the saturation temperature of the steam. Adjusting the producer bottomhole pressure (BHP) is the way to make this possible. CMG STARS User s Manual (2010) describes this constraint with the following equation. BHP Producer = P sat (T (block) + value) (Eq. 2.3.)

23 T (block) is the temperature in the grid block and value corresponds to the sub-cooling temperature which is the difference from the saturation temperature. 9 Steam trap control makes a liquid accumulation between injection well and production well to close the flow path of injected steam and direct it upwards to the oil zone for more efficient heat transfer (Gates, 2007). However, an extensive amount of liquid leg may result in less productivity because its lower temperature and higher viscosity hinder oil flow as well through the wellbore when sub-cooling temperature is high (Valk and Yang, 2005). According to Ito and Suzuki (1999), optimum sub-cooling temperature is between 30 and 40 C to minimize csor in the McMurray formation Horizontal Wellbores Horizontal drilling technology has been shown to improve the ultimate recovery of reserves. It has made SAGD recovery method viable to produce from oil sands reserves. Horizontal well application provides large contact area with the reservoir so that more fluid withdrawal is achieved. Using a horizontal producer not only utilizes removing higher fluid volume from the reservoir but also accelerates the propagation of steam chamber in the cross-well direction. Therefore, a larger steam chamber and also a larger heat transfer area occur. (Tamer and Gates, 2012). A longer well unquestionably offers a greater contact area. However, in addition to higher drilling cost, using a longer well in SAGD may cause steam chamber expanding irregularly as a result of pressure drop in the horizontal well (Parappilly and Zhao, 2007). Producer well drilling takes place first in a SAGD process. The producer well placement as close as possible to the bottom of the pay zone is desired at the planning stage in which geology and the presence of the water aquifer are also considered (Terez et al., 2002). Well placement directly affects the performance of SAGD; therefore, it is important to implement the process in practice accurately. Too short vertical spacing between injector and producer leads to the steam flow suddenly into the producer, while too long vertical spacing leads to unsuccessful gravity drainage (Guinand et al., 2011).

24 10 Figure 2-3. Typical SAGD horizontal well pair configuration (Medina, 2010) 2.3. Overview of Artificial Neural Networks Warren McCulloch and Walter Pitts designed the first neural networks in 1943 (Mohaghegh, 2000). Development of artificial neural networks using neurons grouped in layers was inspired by the capabilities of biological neurons in the human brain (Fausett, 1993). Frank Rosenblatt pioneered the first practical ANN implementation called Mark I Perceptron by applying it on pattern recognition in the late 1950 s (Rosenblatt, 1960). Neural network research was brought into action by Hopfield after his research activities led to new learning algorithms such as back-propagation in the early 1980 s and the neural network research and its applications have been improving rapidly since then (Mohaghegh, 2000). Artificial neural networks can be divided into two main categories based on training methods: unsupervised and supervised. Unsupervised neural networks are principally used for classification. It sorts out the input vectors into groups and clusters. Interpretation of well logs and identification of lithology have been applied by these networks in the oil and gas industry (Mohaghegh, 2000). The actual output is not necessary to be presented to the network during training/learning process. On the other hand, learning performed by supervised training algorithms is based on a feedback principle. Throughout the training period, the network is fed by

25 11 both known input and output data sets (Mohaghegh, 2000). Back-propagation is the most wellknown supervised training algorithm and the most applications in the oil and gas industry are based on it. A feed-forward artificial neural network consists of neurons connected together. They are the simple elements where information processing takes place. Input neuron is multiplied by a value called weight (w). Bias (b) is also added to the weighted value and then the resulting sum of the signals can be transferred in the forward direction by a transfer function. Both weight (w) and bias (b) are scalar parameters that are able to be updated by numerical iterations (Nazzal et al., 2008). Initial weights can be random numbers. Figure 2-4. Single input neuron (Shokir et al, 2002) The designer decides the training algorithm, the number of neurons and hidden layers and the transfer function(s) by trial and error during the training/learning process. Once the network has been educated with training data, one can make rapid calculations. According to Fausett (1993) an artificial neural network is characterized by (1) its architecture, (2) its training algorithm and (3) its activation function Architecture Multilayer perceptron (MLP) is the most common type of artificial neural network architecture that has one input layer, output layer and one or more hidden layers between the input layer and output layer. Input and output data represented to the network determines the number of neurons in the input and output layer respectively. Determination of the number of hidden layers and the number of neurons in each layer is very critical for the performance of the network. Increasing the number of hidden layers and neurons usually enhances prediction

26 12 capability of the network. However, this approach results in a long training time and memorization (over-fitting) of the training data at some point instead of generalization of the problem (Sadiq and Nashawi, 2000). A neural network architecture that is constructed for one problem may not work for another problem. An example of MLP network architecture that has a single hidden layer of 4 neurons is shown in Figure 2-5. Input Layer Hidden Layer Output Layer Figure 2-5. Example of multilayer perceptron (MLP) neural network architecture Training/Learning Algorithm During the training/learning process, the performance of the network is continuously evaluated to see how outputs from the network match targets by calculating errors between them. Until a back-propagation network is able to perform predictions with errors not greater than specified satisfactory goal, the calculated errors at the output layer are propagated backward following one after another to update weights and biases (Silpngarmlers et al., 2001). The relative impact of the weight in each connection on the calculated error at the output layer is taken into consideration while updating (AI-Kaabi and Lee, 1990). There are many types of the backpropagation training algorithm functions available on MATLAB such as bayesian regulation, conjugate gradient back-propagation, gradient descent, Levenberg-Marquardt and scaled conjugate gradient back-propagation.

27 Activation Function Sigmoid functions are the most widely used activation functions. The logistic function and the hyperbolic tangent function are classified as sigmoid functions. They are readily and easily differentiable functions. The derivative of a point is related to its value in an unsophisticated way that does not make calculations too complicated for the training. These characteristics make sigmoid functions very suitable for back-propagation learning (Fausett, 1993). Logistic function maps the output between 0 and 1 and tangent hyperbolic function maps between -1 and 1. The following equations express these functions. Logistic Function: f (x) = < x < (Eq.2.4.) Tangent Hyperbolic Function: f (x) = < x < (Eq.2.5.)

28 14 Chapter 3 Problem Statement Numerical simulation of SAGD is a complex and time-consuming task. Instead of struggling with high complex problems, simple models are used to substitute reservoir simulations over a given range of input parameters. Usage of neural-network based proxy models for the solution of non-linear relationships has been increasingly popular in recent years in the oil and gas industry. Artificial neural network (ANN) methodology is used to avoid excessive time consumption of computer simulations. The objective of this study is to develop artificial neural networks that can provide instant and reasonably accurate preliminary estimations for SAGD applications in heavy oil reservoirs. SAGD performance depends on operating conditions and reservoir properties. These parameters are used as inputs for the numerical simulations. A sequence of SAGD numerical simulations were executed using CMG STARS thermal simulator. Sensitivity analysis is performed to determine the best candidate reservoirs for SAGD and the most influential operational parameters on the SAGD performance. Neural network based proxies were trained to capture the relationship between the input parameters and SAGD performance. Then, they were tested and compared with the results of the thermal simulator. Consequently, they are used to substitute the reservoir simulator over a given range of input parameters. The forward-looking artificial neural network can be used for 10 years of production forecast for a given set of operational parameters and reservoir properties. Using the inverselooking ANN-1, one can design a SAGD process for the desired performance indicators in a heavy oil reservoir. If the SAGD process was designed in the field and the achieved performance indicators are known, the inverse-looking ANN-2 can be used to predict the reservoir properties. It might be helpful to re-evaluate and/or correct the reservoir properties that were considered at the first place.

29 15 FORWARD PROBLEM Operational Parameters Performance Indicators INVERSE PROBLEM Operational Parameters Performance Indicators Figure 3-1. Stage I ANNs FORWARD PROBLEM Operational Parameters Reservoir Properties Performance Indicators INVERSE PROBLEM-1 INVERSE PROBLEM-2 Performance Indicators Reservoir Properties Operational Parameters Performance Indicators Operational Parameters Reservoir Properties Figure 3-2. Stage II ANNs

30 16 Chapter 4 Numerical Simulation of Steam Assisted Gravity Drainage 4.1. Grid Sensitivity Analysis Small enough grid size is essential to provide better results. However, it results in increasing the number of grid blocks and eventually takes longer computational times. An optimal grid size which compromises between simulation runtime and proper resolution of steam chamber growth should be selected by the reservoir engineer. The grid size affects the heat transfer. The heat happens to be transferred faster to the adjacent grid when a smaller grid size is used and it causes high average temperature in a grid block. Therefore, oil recovery and steam chamber shape differs depending on the grid size as the viscosity changes with temperature (Shin et al., 2012). A grid sensitivity analysis was conducted to select an appropriate grid system. Many different grid systems from very fine to very coarse were studied. The oil rate profiles for 10 years using different grid systems are presented in Appendix A. It is understood that changing the grid size in the wellbore direction (y direction) does not change the results significantly but increase the run time. On the other hand, grid size effect in the x-z plane plays an important role for the grid sensitivity analysis. Therefore, after grid sensitivity analysis for the oil field, a grid system of 91x1x30 is considered appropriate to run all the simulations Numerical Simulation Model The simulation model used in this study is a rectangular Cartesian model. The model is two-dimensional and consists of 2730 grid cells (91x1x30). No flow boundary but heat loss is assumed at the overburden and underburden.

31 17 Table 4-1. Heat Loss Calculations Minimum Volumetric Heat Capacity Thermal Conductivity Temperature Differenced to Start Heat Loss Calculation Overburden 35 BTU/(ft3* F) 24 BTU/(ft*day* F) 10 F Underburden 35 BTU/(ft3* F) 24 BTU/(ft*day* F) 10 F No capillary pressure is assumed in the model. Reservoir has no gas cap and aquifer. No pre-heating period was modeled at the beginning of the process. Wellbore is modeled as source/sink terms. A well pair is placed in the center with the assumption of symmetry between well pairs (Figure 4-1). Constant well radius of 0.28 ft is used. The simulation uses a three-phase (water, heavy oil and steam) model. The heavy oil has no solution gas. The water component is allowed to exist in both gas and aqueous phases. Relative permeability curves used in this study are given in Figure 4-2 and 4-3. Steam temperature is the corresponding saturation temperature of the injection pressure in the numerical simulations. The viscosity can be determined from the composition of the fluid. Viscosity correlations which use API gravity and reservoir temperature as input variables are also used to make estimations. In this study, a new dead oil viscosity correlation from the literature is selected to predict the oil viscosity as a function of the temperature and the API gravity. Based on the study on the various fluid databanks, the new dead oil correlation is developed and it indicates 3% to 50% enhancement over the Bennison correlation which was considered as the best correlation in the past (Hossain et al., 2005). μ od = 10 ( API ) x T ( API ) (Eq. 4.1.)

32 -1,900-1,700-1,500-1,300-1,100 1, Grid Top (ft) J layer: File: 91x1x30.dat User: aus310 Date: 7/18/2013 Scale: 1:630 Z/X: 1.00:1 Axis Units: ft 1, ,000 Well-1 Well-2 Injector Producer 1, feet meters Figure 4-1. Schematic 2D reservoir model (cross section) Grid Top (ft) K layer: 1-1, File: 91x1x30.dat User: aus310 Date: 7/26/2013 Scale: 1:2146 Y/X: 1.00:1 Axis Units: ft 1,016-1,300 1, , , , feet meters Figure 4-2. Schematic 2D reservoir model (top view)

33 kr - relative permeability kr - relative permeability Sw Figure 4-3. Water Oil relative permeability curves Sl Figure 4-4. Liquid Gas relative permeability curves

34 20 Chapter 5 Stage I: Development of Reservoir Specific Proxies of the SAGD Process 5.1. Data Gathering and Input Variable Selection Input data and corresponding targets are required to train the neural networks. The first stage in this study is to develop reservoir specific proxy model for specially one reservoir. Reservoir/fluid properties are given in Table 5-1. Table 5-1. Reservoir/Fluid Properties Stage I Reservoir Properties Depth (ft) 900 Permeability Ratio 0.6 Horizontal Permeability (md) 2000 Porosity 0.3 Initial Reservoir Pressure (psia) 580 Initial Reservoir Temperature ( F) 65 Rock Thermal Conductivity (Btu/(ft*day* F)) 96 Oil Saturation 0.7 Thickness (ft) 120 Oil Density ( API) 15 Relative Permeability Model Water Wet, Stone s 2 Formation Compressibility (1/psi) 5e-04 Volumetric Heat Capacity (Btu/(ft 3 * F)) 35 Oil Thermal Conductivity (Btu/(ft*day* F)) 2 Water Thermal Conductivity (Btu/(ft*day* F)) 8.6 Gas Thermal Conductivity (Btu/(ft*day* F)) Oil Compressibility (1/psi) 4e st Thermal Expansion Coefficient (1/ F) 4.4e-004

35 21 A model which requires a minimum number of simulations to satisfy accuracy of the network is generated with an efficient sampling algorithm. Experimental design techniques are used to reduce redundancy of samples. Latin hypercube experimental design (LHD) was adopted in this study. Candidate values were inserted for each operational parameter based on arithmetic sequence and numerous samples were generated based on LHD. This sampling design is used to establish an effective distribution of input variables. Table 5-2 shows minimum and maximum limits of varying operational parameters. Injector well placement is allowed to move in the vertical direction. Minimum bottom-hole pressure is taken as primary constraint on the producer well. The spacing between the producer well and the base of the reservoir is kept fixed to 10 ft for this stage. Table 5-2. Operational Parameters Stage I Operational Parameters MIN MAX Injector BHP (psia) Steam Quality Sub-cooling Temperature ( F) 5 40 Well Length (ft) Producer BHP (psia) Inter-well Spacing (ft) Vertical Spacing (ft) Table 5-3. Performance Indicators Performance Indicators Yearly Cumulative Oil Production (for 10 years) Yearly Cumulative Steam-Oil Ratio (for 10 years) Yearly Cumulative Water Production (for 10 years)

36 22 Inappropriate runs were excluded from the study before developing the artificial neural networks. A total of 904 reservoir specific samples were generated. These samples were simulated using CMG s Thermal Reservoir Simulator STARS for a period of 10 years Response Surface Methodology Response surface methodology (RSM) is a simple polynomial model of first or second order (linear or quadratic models, respectively) determined by a least-square fit between the polynomial response and the supplied training data (Akram, 2011). It was applied using CMOST to construct linear and quadratic proxy models to substitute complex reservoir simulations over a region of interest. Due to high coefficient of determination (R 2 ), the quadratic proxy model fits the data better compared to the linear model. The predicted data is in a good agreement with the actual data. Equations in terms of varied operational parameters were obtained to calculate cumulative oil production, cumulative steam-oil ratio and cumulative water production over a period of 10 years; this is done using three equations for each year, resulting in 30 equations in total. The proxy model predicts the performance indicator better with increasing project time. The verification plots for only the 2 nd year and 10 th year are shown in Figures 5-7 and 5-8. Cumulative oil production equations for each year can be found in Appendix C. Figure 5-1. Proxy model verification plot for cumulative oil production (2 nd year)

37 23 Figure 5-2. Proxy model verification plot for cumulative oil production (10 th year) Figure 5-3. Proxy model verification plot for cumulative steam-oil ratio (2 nd year)

38 24 Figure 5-4. Proxy model verification plot for cumulative steam-oil ratio (10 th year) Figure 5-5. Proxy model verification plot for cumulative water production (2 nd year)

39 25 Figure 5-6. Proxy model verification plot for cumulative water production (10 th year) The prediction capability of the model was evaluated through statistics such as R 2 and R 2 adjusted. R 2 and R 2 adjusted close to 1 show that the regression line fits the actual data. Table 5-4. R 2 and R 2 Adjusted Values for the Quadratic Proxy Model R-square Performance R-square adjusted Cumulative Oil Production (2 nd year) Cumulative Oil Production (10 th year) Cumulative Steam-Oil Ratio (2 nd year) Cumulative Steam-Oil Ratio (10 th year) Cumulative Water Production (2 nd year) Cumulative Water Production (10 th year)

40 Sensitivity Analysis A sensitivity analysis was conducted to identify which operational parameters are the most influential parameters on cumulative oil production, cumulative steam oil ratio and cumulative water production using the linear model of the response surface methodology. For example, the effect of varying these parameters over a given range on cumulative oil production at the end of the second year is shown in Figure 5-1. Figure 5-2 shows the same variation effect on cumulative oil production at the end of 10th year. GRIDSIZE_X and POS_INJECTOR represent the grid size in the x-direction to adjust inter-well spacing and the layer in which the injector well is placed respectively. The parameter higher up is the most influential. Well length has the highest impact on cumulative oil and water production profiles. It is varying the cumulative oil production over a period of 10 years over a range of x10 6 STB between minimum and maximum. Steam quality has the least impact on cumulative oil production for the 10 th year. However, the sensitivity analysis of the same parameters on cumulative steam-oil ratio (csor) shows that steam quality is the most influential parameter at the end of 10 years; the lower steam quality, the better csor and vice versa as seen in Figures 5-3 and 5-4. Figure 5-5 and 5-6 show that vertical spacing has the least impact on cumulative water production. Figure 5-7. Sensitivity analysis on cumulative oil production (2 nd year)

41 27 Figure 5-8. Sensitivity analysis on cumulative oil production (10 th year) Figure 5-9. Sensitivity analysis on cumulative steam oil ratio (2 nd year)

42 28 Figure Sensitivity analysis on cumulative steam oil ratio (10 th year) Figure Sensitivity analysis on cumulative water production (2 nd year)

43 29 Figure Sensitivity analysis on cumulative water production (10 th year) 5.4. ANN Development The dataset was represented to the neural network toolbox on MATLAB. The dataset was divided into three categories, labeled as training, validation and testing. Training data was used for the training process. The network performance on the validation data is checked during the training process to avoid over-fitting. Data Division Pre- Processing Network Structure Training & Testing Optimization Figure Artificial neural network workflow

44 30 Table 5-5. Division of Database Stage I Total Dataset = 904 Partition of Total Number of Samples Training 5:7 645 Validation 1:7 129 Testing 1:7 130 The network inputs and targets were pre-processed by normalization between -1 and 1. It is useful for simplifying the network. The data is conformed to the same range by normalization before the training process to improve the fairness of training and minimize bias within the neural network. In this stage, cascade-forward (newcf) network with Levenberg Marquardt (trainlm) back-propagation training function was selected by comparing the error in network prediction between different types of back-propagation. Gradient descent with momentum weight and bias learning function (learngdm) was employed. Mean squared error (MSE) was used for qualifying the network performance. It calculates the average of the squares of differences between actual and predicted values Forward Problem This forward-looking artificial neural network was constructed to predict reservoir performance without the expense of using the reservoir simulator over given ranges of operational parameters. The artificial neural network developed for the forward problem is able to predict cumulative oil production, cumulative steam oil ratio and cumulative water production profiles over a period of 10 years for a specific reservoir. Functional links that are mathematical relationships of the most influential input parameters from the sensitivity analysis were added to improve effectiveness of the network. It was observed that transforming the output to the logarithm of the output improved the

45 performance. The performance of the network was measured with the testing data which was not included in the training process. 31 Table 5-6. Functional Links - Stage I Forward Problem Input Functional Links BHP Injector x Well Length, (Vertical Spacing) 2, (BHP Injector) 2, BHP Injector x Inter-well Spacing, (Inter-well Spacing) 2, Well Length x Inter-well Spacing, BHP Injector x BHP Producer, BHP Injector x Vertical Spacing Output Functional Links Cumulative Oil Production x Cumulative Steam-Oil Ratio (10) The architecture consists of a single hidden layer of 20 neurons using hyperbolic tangent activation function. A linear activation function was used in the output layer. The final ANN architecture is shown in Figure neurons BHP Injector BHP Producer Steam Quality Sub-cooling Temperature Vertical Spacing Inter-well Spacing Well Length BHP Injector x Well Length (Vertical Spacing) 2 (BHP Injector) 2 BHP Injector x Inter-well Spacing (Inter-well Spacing) 2 Inter-well Spacing x Well Length BHP Injector x BHP Producer BHP Injector x Vertical Spacing Cumulative Oil Production (10) Cumulative Steam-Oil Ratio (10) Cumulative Water Production (10) Cumulative Oil Production x Cumulative Steam-Oil Ratio Figure Artificial neural network architecture - Stage I forward problem

46 32 Regression plots for the testing data given in Figure 5-15, 5-16, and 5-17 show a high accuracy with the correlation coefficients between 0.99 and 1. Based on the correlation coefficient comparison, neural network based proxy model gives more accurate results than the response surface quadratic proxy model. Cumulative Oil Production (1 st year) Cumulative Oil Production (2 nd year) Cumulative Oil Production (3 rd year) Cumulative Oil Production (4 th year)

47 33 Cumulative Oil Production (5 th year) Cumulative Oil Production (6 th year) Cumulative Oil Production (7 th year) Cumulative Oil Production (8 th year) Cumulative Oil Production (9 th year) Cumulative Oil Production (10 th year) Figure The testing data regression plots for cumulative oil production Stage I forward problem

48 34 Cumulative Steam-Oil Ratio (1 st year) Cumulative Steam-Oil Ratio (2 nd year) Cumulative Steam-Oil Ratio (3 rd year) Cumulative Steam-Oil Ratio (4 th year) Cumulative Steam-Oil Ratio (5 th year) Cumulative Steam-Oil Ratio (6 th year)

49 35 Cumulative Steam-Oil Ratio (7 th year) Cumulative Steam-Oil Ratio (8 th year) Cumulative Steam-Oil Ratio (9 th year) Cumulative Steam-Oil Ratio (10 th year) Figure The testing data regression plots for cumulative steam-oil ratio Stage I forward problem

50 36 Cumulative Water Production (1 st year) Cumulative Water Production (2 nd year) Cumulative Water Production (3 rd year) Cumulative Water Production (4 th year)

51 37 Cumulative Water Production (5 th year) Cumulative Water Production (6 th year) Cumulative Water Production (7 th year) Cumulative Water Production (8 th year)

52 38 Cumulative Water Production (9 th year) Cumulative Water Production (10 th year) Figure The testing data regression plots for cumulative water production Stage I forward problem Absolute percentage error for the testing data was calculated based on the following formula. Actual value represents the value obtained from the thermal reservoir simulator and predicted value represents the value obtained from the ANN. Absolute Percentage Error (%) = (Eq. 5-1) Calculated absolute percentage errors at the end of 10 years for the testing samples are illustrated in Figure 5-18, 5-19 and 5-20.

53 Error % Error % 39 Cumulative Oil Production (10th year) Testing Sample No. Figure Cumulative oil production absolute percentage errors for the testing data Cumulative Steam-Oil Ratio (10th year) Testing Sample No. Figure Cumulative steam-oil ratio absolute percentage errors for the testing data

54 Error % 40 Cumulative Water Production (10th year) Testing Sample No. Figure Cumulative water production absolute percentage errors for the testing data Mean absolute percentage errors (MAPE) for cumulative oil production, cumulative steam-oil ratio and cumulative water production profiles over a period of 10 years are 1.40%, 0.90% and 0.97% respectively. Several additional samples were simulated using CMG STARS and ANN to examine prediction capabilities of ANN beyond the ranges. Operational parameters for sample #3 and sample #4 are out of the ranges used for the training process while operational parameters for sample #1 and sample #2 are in that ranges. ANN was not able to match CMG results for those runs which are out of the ranges.

55 Cumulative Oil Production (bbl) 41 Table 5-7. Operational Parameters for Sample#1, Sample#2, Sample#3 and Sample#4 Operational Parameters Sample #1 Sample #2 Sample #3 Sample #4 BHP Injector Steam Quality Sub-cooling Temperature Well Length BHP Producer Inter-well Spacing Vertical Spacing Sample # Time, year CMG ANN Figure Comparison between ANN and CMG for the sample #1

56 Cumulative Oil Production (bbl) Cumulative Oil Production (bbl) 42 Sample # CMG ANN Time, year Figure Comparison between ANN and CMG for the sample #2 Sample # CMG ANN Time, year Figure Comparison between ANN and CMG for the sample #3

57 Cumulative Oil Production (bbl) Sample # Time, year CMG ANN Figure Comparison between ANN and CMG for the sample #4 To validate the qualification of the artificial neural network architecture, a different reservoir case was taken into consideration. The reservoir properties given in Table 5-8 were used to generate samples. The number of samples was increased to 975 for this reservoir. Consequently, mean absolute percentage errors for cumulative oil production, cumulative steamoil ratio and cumulative water production profiles over a period of 10 years decreased to 1.13%, 0.59% and 1.06% respectively. The same artificial neural network structure that has a single hidden layer of 20 neurons is still able to forecast SAGD performance although reservoir properties were changed.

58 44 Table 5-8. Reservoir Properties for the Validation of the Network Architecture Stage I Reservoir Properties Permeability Ratio 0.5 Horizontal Permeability (md) 1500 Porosity 0.2 Initial Reservoir Pressure (psia) 500 Initial Reservoir Temperature ( F) 80 Oil Saturation 0.6 Thickness (ft) Inverse Problem In an inverse problem, the cause is estimated for a given effect. Inverse problems are challenging to be solved because of their variable and ill-posed nature (Dadvand et al., 2006). In this problem, operational parameters were predicted using cumulative oil production and cumulative steam-oil ratio profiles over a period of 10 years as inputs. The artificial neural network has three hidden layers using tangent hyperbolic, tangent hyperbolic and logistic activation functions respectively. Linear activation function was used in the output layer. The final ANN architecture is illustrated in Figure 5-25.

59 45 50 neurons 30 neurons 15 neurons Cumulative Oil Production (10) Cumulative Steam-Oil Ratio (10) BHP Injector BHP Producer Steam Quality Sub-cooling Temperature Vertical Spacing Inter-well Spacing Well Length Figure Artificial neural network architecture Stage I inverse problem BHP Injector Steam Quality

60 46 Sub-cooling Temperature Well Length BHP Producer Inter-well Spacing Vertical Spacing Figure The testing data regression plots for operational parameters Stage 1 inverse problem

61 Error % Error % 47 BHP Injector Testing Sample No. Figure BHP injector absolute percentage errors for the testing data Steam Quality Testing Sample No. Figure Steam quality absolute percentage errors for the testing data

62 Error % Error % 48 Sub-cooling Temperature Testing Sample No. Figure Sub-cooling temperature absolute percentage errors for the testing data Well Length Testing Sample No. Figure Well length absolute percentage errors for the testing data

63 Error % Error % 49 BHP Producer Testing Sample No. Figure BHP producer absolute percentage errors for the testing data Inter-well Spacing Testing Sample No. Figure Inter-well spacing absolute percentage errors for the testing data

64 Error % 50 Vertical Spacing Testing Sample No. Figure Vertical spacing absolute percentage errors for the testing data Table 5-9. Mean Absolute Percentage Errors Stage I Inverse Problem Mean Absolute Percentage Errors (%) of Operational Parameter Predictions BHP Steam Sub-cooling Well BHP Inter-well Vertical Injector Quality Temperature Length Producer Spacing Spacing The artificial neural network is not able to predict sub-cooling temperature and minimum bottom-hole pressure of producer well with a reasonable accuracy. The main reason is that the producer well has both these two constraints. The primary constraint is initially minimum bottomhole pressure. It is observed that after steam reaches the producer well, steam trap constraint takes over the control of the producer well to prevent steam breakthrough. Steam breakthrough time depends on injection pressure and vertical spacing. As the producer well experiences the steam injection pressure, bottom-hole pressure of producer well changes with time to satisfy steam trap control.

65 51 The operational parameters predicted by ANN were used as inputs to be simulated using CMG STARS thermal reservoir simulator. The comparisons for the first three testing samples are shown in Figures 5-34, 5-35, 5-36, 5-37, 5-38, 5-39, 5-40, 5-41, and Although the network is not able to predict the producer well constraints accurately, the resulting performance indicators are still satisfied. TESTING SAMPLE #1 ANN Well Configuration Actual %Error BHP Injector Steam Quality Sub-cooling Temperature Well Length BHP Producer Inter-well Spacing Vertical Spacing Figure Cumulative oil production comparison between ANN well configuration and actual for the testing sample #1

66 52 Figure Cumulative steam-oil ratio comparison between ANN well configuration and actual for the testing sample #1 Figure Cumulative water production comparison between ANN well configuration and actual for the testing sample #1

67 53 TESTING SAMPLE #2 ANN Well Configuration Actual %Error BHP Injector Steam Quality Sub-cooling Temperature Well Length BHP Producer Inter-well Spacing Vertical Spacing Figure Cumulative oil production comparison between ANN well configuration and actual for the testing sample #2

68 54 Figure Cumulative steam-oil ratio comparison between ANN well configuration and actual for the testing sample #2 Figure Cumulative water production comparison between ANN well configuration and actual for the testing sample #2

69 55 TESTING SAMPLE #3 ANN Well Configuration Actual %Error BHP Injector Steam Quality Sub-cooling Temperature Well Length BHP Producer Inter-well Spacing Vertical Spacing Figure Cumulative oil production comparison between ANN well configuration and actual for the testing sample #3

70 56 Figure Cumulative steam-oil ratio comparison between ANN well configuration and actual for the testing sample #3 Figure Cumulative water production comparison between ANN well configuration and actual for the testing sample #3

71 57 Chapter 6 Stage II: Development of Universal Proxies of the SAGD Process 6.1. Data Gathering and Input Variable Selection In stage II, reservoir/fluid properties are varied as well and a total of 1590 cases were generated. Variable reservoir/fluid properties and variable operational parameters are given in Table 6-1 and 6-2. Table 6-1. Reservoir/Fluid Properties Stage II Reservoir/Fluid Properties MIN MAX Permeability Ratio (k z / k x ) Horizontal Permeability (md) (k x = k y ) Porosity Initial Reservoir Pressure (psia) Initial Reservoir Temperature ( F) Rock Thermal Conductivity (Btu/(ft*day* F)) Oil Saturation Thickness (ft) Oil Density ( API) The spacing between the producer well and base of the reservoir was also included among the variable operational parameters. Both horizontal well positions are allowed to move in the vertical direction. The injector well is always positioned above the producer well.

72 58 Table 6-2. Operational Parameters Stage II Operational Parameters MIN MAX Injector BHP (psia) Steam Quality Sub-cooling Temperature ( F) 2 42 Well Length (ft) Producer BHP (psia) Producer-Base Spacing (ft) Inter-well Spacing (ft) Vertical Spacing (ft) Sensitivity Analysis The sensitivity analysis was performed on input parameters. Figure 6.1, 6.2, and 6-3 show that the increase in reservoir thickness and oil saturation significantly accelerate the oil production. Oil density, horizontal permeability and permeability ratio of vertical to horizontal permeability are influential parameters on cumulative oil production and cumulative steam-oil ratio at early times.

73 59 Figure 6-1. Sensitivity analysis on cumulative oil production (1 st year) Figure 6-2. Sensitivity analysis on cumulative oil production (2 nd year)

74 60 Figure 6-3. Sensitivity analysis on cumulative oil production (10 th year) Figure 6-4. Sensitivity analysis on cumulative steam-oil ratio (1 st year)

75 61 Figure 6-5. Sensitivity analysis on cumulative steam-oil ratio (2 nd year) Figure 6-6. Sensitivity analysis on cumulative steam-oil ratio (10 th year)

76 62 Figure 6-7. Sensitivity analysis on cumulative water production (1 st year) Figure 6-8. Sensitivity analysis on cumulative water production (2 nd year)

77 63 Figure 6-9. Sensitivity analysis on cumulative water production (10 th year) 6.3. ANN Development A total of 1590 samples were represented to the neural network toolbox on MATLAB. The division of database is shown in Table 6-3. The network inputs and targets were pre-processed by normalization between -1 and 1. It is useful for simplifying the network. The data is conformed to the same range by normalization before the training process to improve the fairness of training and minimize bias within the neural network. In all of the artificial neural networks designed in this stage, cascade-forward (newcf) network with Levenberg Marquardt (trainlm) back-propagation training function was selected by comparing the error in network prediction between different types of back-propagation.

78 64 Table 6-3. Division of Database Stage II Total Dataset = 1590 Partition of Total Number of Samples Training 6: Validation 1:8 199 Testing 1: Forward Problem The forward-looking artificial neural network was constructed to predict cumulative oil production, cumulative steam oil ratio and cumulative water production profiles over a period of 10 years using various reservoir properties and operational parameters as input variables. Functional links given in Table 6-4 were used to improve the performance. Table 6-4. Functional Links - Stage II Forward Problem Input Functional Links Oil Saturation x Oil Density Horizontal Permeability x Thickness Injector BHP x Well Length Injector BHP x Vertical Spacing Oil Saturation x Horizontal Permeability Porosity / Horizontal Permeability Output Functional Links None The artificial neural network has a single hidden layer of 40 neurons using tangent hyperbolic activation function. Linear activation function was used in the output layer. The final ANN architecture is illustrated in Figure 6-10.

79 65 40 neurons BHP Injector BHP Producer Steam Quality Sub-cooling Temperature Vertical Spacing Inter-well Spacing Well Length Horizontal Permeability Permeability Ratio Porosity Oil Saturation Oil Density Rock Thermal Conductivity Initial Reservoir Pressure Initial Reservoir Temperature Thickness Oil Saturation x Oil Density Horizontal Permeability x Thickness Injector BHP x Well Length Injector BHP x Vertical Spacing Oil Saturation x Horizontal Permeability Porosity / Horizontal Permeability Cumulative Oil Production (10) Cumulative Steam-Oil Ratio (10) Cumulative Water Production (10) Figure Artificial neural network architecture Stage II forward problem Regression plots for the testing data given in Figures 6-2, 6-3, and 6-4 show a high accuracy with the correlation coefficients between 0.93 and 1. Cumulative Oil Production (1 st year) Cumulative Oil Production (2 nd year)

80 66 Cumulative Oil Production (3 rd year) Cumulative Oil Production (4 th year) Cumulative Oil Production (5 th year) Cumulative Oil Production (6 th year)

81 67 Cumulative Oil Production (7 th year) Cumulative Oil Production (8 th year) Cumulative Oil Production (9 th year) Cumulative Oil Production (10 th year) Figure The testing data regression plots for cumulative oil production Stage II forward problem

82 68 Cumulative Steam-Oil Ratio (1 st year) Cumulative Steam-Oil Ratio (2 nd year) Cumulative Steam-Oil Ratio (3 rd year) Cumulative Steam-Oil Ratio (4 th year)

83 69 Cumulative Steam-Oil Ratio (5 th year) Cumulative Steam-Oil Ratio (6 th year) Cumulative Steam-Oil Ratio (7 th year) Cumulative Steam-Oil Ratio (8 th year)

84 70 Cumulative Steam-Oil Ratio (9 th year) Cumulative Steam-Oil Ratio (10 th year) Figure The testing data regression plots for cumulative steam-oil Ratio Stage II forward problem Cumulative Water Production (1 st year) Cumulative Water Production (2 nd year)

85 71 Cumulative Water Production (3 rd year) Cumulative Water Production (4 th year) Cumulative Water Production (5 th year) Cumulative Water Production (6 th year)

86 72 Cumulative Water Production (7 th year) Cumulative Water Production (8 th year) Cumulative Water Production (9 th year) Cumulative Water Production (10 th year) Figure The testing data regression plots for cumulative water production Stage II forward problem

87 73 Mean absolute percentage error of the all predictions is found to be 5.24%. The artificial neural network is considered as successful expert system and the final values of the weights are stored. Table 6-5. Mean Absolute Percentage Errors for the Testing Data Stage II Forward Problem Mean absolute percentage error (%) 1 st year 2 nd year 3 rd year 4 th year 5 th year 6 th year 7 th year 8 th year 9 th year 10 th year Cumulative Oil Production Cumulative Steam-Oil Ratio Cumulative Water Production Inverse Problem I The development of inverse models for universal proxies is a challenging task as there is no unique solution for the desired output. In this problem, the inverse-looking artificial neural network was developed to predict operational parameters. The artificial neural network has three hidden layers using logistic, tangent hyperbolic and tangent hyperbolic activation functions respectively. Linear activation function was used in the output layer. The final ANN architecture

88 is illustrated in Figure Logarithmic transformation of the inputs and targets before training the data improved the performance of the ANN neurons 30 neurons 30 neurons Cumulative Oil Production (10) Cumulative Steam-Oil Ratio (10) Horizontal Permeability Permeability Ratio Porosity Oil Saturation Oil Density Rock Thermal Conductivity Initial Reservoir Pressure Initial Reservoir Temperature Thickness Oil Density x Oil Saturation Horizontal Permeability x Thickness Oil Saturation x Horizontal Permeability Porosity / Horizontal Permeability BHP Injector BHP Producer Steam Quality Sub-cooling Temperature Vertical Spacing Inter-well Spacing Well Length Figure Artificial neural network architecture Stage II inverse problem I Table 6-6. Functional Links - Stage II Inverse Problem I Input Functional Links Oil Saturation x Oil Density Horizontal Permeability x Thickness Oil Saturation x Horizontal Permeability Porosity / Horizontal Permeability Output Functional Links - Mean absolute percentage error for the all testing samples is 45.14%. For the first 30 testing samples, the comparisons between the actual and predicted values of operational parameters are illustrated in Figures 6-15, 6-16, 6-17, 6-18, 6-19, 6-20, 6-21, and The artificial neural network is still not able to predict two constraints on the producer well. The

89 Max. Injection Pressure 75 predicted values of operational parameters were represented as inputs to the constructed forwardlooking ANN in Stage II. Cumulative oil production and cumulative steam-oil ratio profiles for the predicted operational parameters were obtained from the forward-looking ANN. These profiles were compared with the actual cumulative oil production and cumulative steam-oil ratio profiles. For the first three testing samples, comparisons are given in Figures 6-23, 6-24, 6-25, 6-26, 6-27, and Mean absolute percentage error between the actual and predicted performance indicators for the all testing samples is only 12.00%. This implies that even though the inverselooking ANN does not predict the actual operational parameters with a good accuracy, the resulting performance indicators are fairly in a good agreement with the actual performance indicators Actual ANN Testing Sample No. Figure Comparison of the actual injection pressure with the predicted injection pressure values

90 Steam Quality Min. BHP Producer Actual ANN Testing Sample No. Figure Comparison of the actual BHP producer with the predicted BHP producer values Actual ANN Testing Sample No. Figure Comparison of the actual steam quality with the predicted steam quality values

91 Well Length Sub-cooling Temperature Actual ANN Testing Sample No. Figure Comparison of the actual sub-cooling temperature with the predicted sub-cooling temperature values Actual ANN Testing Sample No. Figure Comparison of the actual well length with the predicted well length values

92 Vertical Spacing Base-Producer Spacing Actual ANN Testing Sample No. Figure Comparison of the actual base-producer spacing with the predicted baseproducer spacing values Actual ANN Testing Sample No. Figure Comparison of the actual vertical spacing with the predicted vertical spacing values

93 Inter-well Spacing Actual ANN Testing Sample No. Figure Inter-well spacing comparison for the testing data TESTING SAMPLE #1 ANN Actual Error % BHP Injector Steam Quality Sub-cooling Temperature Well Length BHP Producer Inter-well Spacing Vertical Spacing Base Producer Spacing

94 Cumulative Steam-Oil Ratio (bbl/bbl) Cumulative Oil Production (bbl) Actual ANN Time (years) Error = 20.35% Figure Comparison of the cumulative oil production resulting from ANN well configuration with the actual cumulative oil production for the testing sample # Actual ANN Time (years) Error = 13.55% Figure Comparison of the cumulative steam-oil ratio resulting from ANN well configuration with the actual cumulative steam-oil ratio for the testing sample #1

95 Cumulative Oil Production (bbl) 81 TESTING SAMPLE #2 ANN Actual Error % BHP Injector Steam Quality Sub-cooling Temperature Well Length BHP Producer Inter-well Spacing Vertical Spacing Base Producer Spacing Actual ANN Time (years) Error = 7.96% Figure Comparison of the cumulative oil production resulting from ANN well configuration with the actual cumulative oil production for the testing sample #2

96 Cumulative Steam-Oil Ratio (bbl/bbl) Actual ANN Tme (years) Error = 3.08% Figure Comparison of the cumulative steam-oil ratio resulting from ANN well configuration with the actual cumulative steam-oil ratio for the testing sample #2 TESTING SAMPLE #3 ANN Actual Error % BHP Injector Steam Quality Sub-cooling Temperature Well Length BHP Producer Inter-well Spacing Vertical Spacing Base Producer Spacing

97 Cumulative Steam-Oil Ratio (bbl/bbl) Cumulative Oil Production (bbl) Actual ANN Time (years) Error = 7.07% Figure Comparison of the cumulative oil production resulting from ANN well configuration with the actual cumulative oil production for the testing sample # Actual ANN Time (years) Error = 10.91% Figure Comparison of the cumulative steam-oil ratio resulting from ANN well configuration with the actual cumulative steam-oil ratio for the testing sample #3

98 Inverse Problem II The purpose of this inverse-looking artificial neural network is to predict reservoir properties including permeability ratio, horizontal permeability, porosity, initial reservoir pressure, initial reservoir temperature, reservoir thickness, rock thermal conductivity, oil saturation and oil density. The artificial neural network has three hidden layers using logistic, tangent hyperbolic and tangent hyperbolic activation functions respectively. Linear activation function was used in the output layer. Logarithmic transformation was applied on the input and output data before the training process. The final ANN architecture is shown in Figure neurons 25 neurons 14 neurons Cumulative Oil Production (10) Cumulative Steam-Oil Ratio (10) Cumulative Water Production (10) BHP Injector BHP Producer Steam Quality Sub-cooling Temperature Vertical Spacing Inter-well Spacing Well Length Permeability Ratio Horizontal Permeability Porosity Initial Reservoir Pressure Initial Reservoir Temperature Rock Thermal Conductivity Thickness Oil Saturation Oil Density Figure Artificial neural network architecture Stage II inverse problem II Mean absolute percentage error for the all testing samples is 26.09%. For the first 30 testing samples, the comparisons between the actual and predicted values of reservoir properties are drawn in Figures 6-30, 6-31, 6-32, 6-33, 6-34, 6-35, 6-36, 6-37, and 6-38.

99 Horizontal Permeability (kx) Permeability Ratio (kz/kx) Actual ANN Testing Sample No. Figure Comparison of the actual permeability ratio with the predicted permeability ratio values Actual ANN Testing Sample No. Figure Comparison of the actual permeability with the predicted permeability values

100 Initial Reservoir Pressure Porosity Actual ANN Testing Sample No. Figure Comparison of the actual porosity with the predicted porosity values Actual ANN Testing Sample No. Figure Comparison of the actual reservoir pressure with the predicted reservoir pressure values

101 Thickness Initial Reservoir Temperature Actual ANN Testing Sample No. Figure Comparison of the actual reservoir temperature with the predicted reservoir temperature values Actual ANN Testing Sample No. Figure Comparison of the actual reservoir thickness with the predicted reservoir thickness values

102 Oil Saturation Rock Thermal Conductivity Actual ANN Testing Sample No. Figure Comparison of the actual rock thermal conductivity with the predicted rock thermal conductivity values Testing Sample No. Actual ANN Figure Comparison of the actual oil saturation with the predicted oil saturation values

103 Oil Density Actual ANN Testing Sample No. Figure Comparison of the actual oil density with the predicted oil density values

104 90 Chapter 7 Graphical User Interface (GUI) Neural network based proxy models were integrated with a graphical user interface (GUI) that was created using MATLAB. This user-friendly interface enables the user to perform SAGD forecasts in heavy oil reservoirs in a simple way. It was developed for universal proxies. Screenshots of the GUI are shown in Figure 7-1, 7-2 and 7-3. Figure 7-1. GUI main screen

105 91 Figure 7-2. The forward-looking ANN interface Figure 7-3. The inverse ANN-1 interface

106 Figure 7-4. The inverse ANN-2 interface 92