A Data-Driven Smart Proxy Model for A Comprehensive Reservoir Simulation

Transcription

1 A Data-Driven Smart Proxy Model for A Comprehensive Reservoir Simulation Faisal Alenezi Department of Petroleum and Natural Gas Engineering West Virginia University falenezi@mix.wvu.edu Shahab Mohaghegh Department of Petroleum and Natural Gas Engineering West Virginia University shahab.mohaghegh@mail.wvu.edu Abstract One of the most important tools for studying fluid flow behavior in oil and gas reservoirs is reservoir simulation. It is constructed based on a comprehensive geological information. A comprehensive numerical reservoir model has tens of millions of grid blocks. Therefore, it becomes computationally expensive and time consuming to run the model for different reservoir simulation scenarios. There are many efforts have been made to reduce the computational size using the proxy models. Proxy models are the substitute to the complex numerical simulation by producing a meaningful representation of the complex system in a very short time. The conventional proxy models are either statistical or mathematical approaches. These conventional approaches are still limited to the complexity of the reservoir and the number of the numerical simulation runs needed to build the proxy model. In this study, a smart proxy model that is based on artificial intelligence and data mining is presented. A grid based smart proxy model is developed to reproduce the dynamic reservoir properties of a full- field numerical simulation in few seconds. A comprehensive spatio-temporal database is built using the conducted numerical simulation run. The data from the database is trained, calibrated, and verified throughout the development of the smart proxy model. Smart proxy model is able to produce pressure and saturation at each reservoir grid block accurately and with a significantly less computational time compared to the numerical reservoir simulation model. Keywords Artificial Intelligence, Data Mining, Proxy Modeling, Reservoir Simulation. I. INTRODUCTION Petroleum industry strives to find oil and gas reserves, developing these resources, meet the world energy demand, and maximize profits. One of the most important tools in oil and gas reservoirs development and management is reservoir simulation. It is a necessary tool for reservoir engineering strategy plans. The key goal of reservoir simulation is to predict future performance of the reservoir and find ways and means of optimizing the recovery of some of the hydrocarbons under different operating conditions. Accurate reservoir simulation involves a comprehensive description of the reservoir properties. To date, the computational science, addressing numerical solution to complex multi-physic, non-linear, and partial differential equations, are at the lead of engineering problem solving and optimization [1]. Due to the complexity of a reservoir, sometimes it is computationally extravagant to develop and run numerical simulation models. Therefore, the petroleum industry investment in reservoir simulation tools is expensive. The rate of return on these investments should be calculated to maximize the benefits from the reservoir simulation. Reservoir simulation proxy models are one way to increase the return on investment in reservoir simulation. Proxy-modeling (also known as surrogate modeling) is a computationally inexpensive alternative to full numerical simulation in assisted history matching, production optimization, and forecasting. A proxy model is defined as a mathematically, statistically, or data driven model defined function that replicates the simulation model output for selected input parameters [2]. The proxy model s results are not to mimic the numerical simulation results with 100% accuracy, but the outputs generated with the amount of time to run these models, give a reasonable range of error. Reducing the computational time to few seconds, make these models significantly competent and attractive to the reservoir engineers [3]. There are several approaches for generating the proxy models. Response surface methodology (RSM), reduced order models (ROD), reduced physics models (RPM) are the first techniques introduced in this field. The most widely used approach is the response surface methodology. Response surface methodology (RSM) consists of a group of mathematical and statistical techniques used in the development of a sufficient functional relationship between a response of interest and a number of associated input variables [4]. In recent years, a newly developed technique for generating proxy modeling has introduced to the reservoir simulation. It is neither statistical nor mathematical; it is a smart approach that is based on data mining and artificial intelligence. II. DATA MINING AND ARTIFICIAL INTTLEGENCE TECHNIQUE The amount of data in the world is increasing dramatically. Data mining is about solving problems by analyzing and discovering the patterns already present in databases [5]. Artificial Intelligence is a powerful technique that teaches the machines how to process data. Data mining and Artificial Intelligent have been applied in petroleum engineering field. In his series of articles in Society of petroleum engineers journal, Shahab D. Mohaghegh presented three types of the virtual intelligence (neural networks, genetic algorithm, and fuzzy logic) and their applications in the oil and gas industry /16/$ IEEE

2 [6][7][8]. The conclusions from these articles show the ability and the potential of the Artificial Intelligence to solve complex problems in reservoir engineering. In reservoir simulation, Artificial Intelligence is used before to generate a proxy model that is able to reproduce the numerical simulation outputs. In 2006, Mohaghegh developed the first SRM (surrogate reservoir model) based on data mining and artificial intelligence (which is later called smart proxy model). The proxy model built was able to solve the time consuming challenge to run uncertainty analysis in one of the giant oil fields [9]. Since then, the smart reservoir model has applied to several studies to replicate the numerical reservoir simulation outputs. Alireza Shahkarami verified the ability of the smart proxy model in performing reservoir simulation history matching [10]. S. Amini developed a smart proxy model that is capable of mimicking a numerical reservoir simulation results in a complex reservoir [11]. The main part of developing the smart proxy model is to build a spatio-temporal database from a number of numerical simulation runs in order to train, validate, and test the data for successful predication. In this paper, the author investigates the ability of the smart proxy model to mimic the numerical simulation results using one numerical simulation run of a complex reservoir. The main advantages of using the smart proxy model against other proxy models in reservoir simulation are; 1. There is no limitation in reservoir complexity; 2. There is no simplification in the reservoir physics; 3. The time to run the smart proxy model is very short. Fig. 1. Porosity-Permeability Histogram of the High Resolution Geo-cellular Model Fig. 2. Porosity-Permeability Histogram of the Up-scaled Geo-cellular Model III. FIELD OF STUDY AND GEOL-CELLULAR MODEL The SACROC unit (Scurry Area Canyon Reef) is part of the Kelly-Snyder Field located northeastern of the Permian Basin in West Texas. The field discovered in 1948 with approximately 2.73 billion barrels oil in place. In 1954, a pressure maintenance program has established in the reservoir by water injection. A geo-cellular model is developed for the SACROC unit with 221 layers and 149X287 cells spatially. The high number of grid blocks (9,450,632) with more than 2000 wells, make conducting study in the field time consuming. Therefore, to serve the objective of this study, the geo-cellular is upscale to 100X142 spatially and to 16 layers. Also, a northern area of up-scaled geo-cellular is picked with dimensions of 39X51 spatially. The final total number of grid blocks for the study is 31,200. It is important to mention that the porosity-permeability heterogeneity is preserved with the up-scaled geo-cellular model. Figure 1 and Figure 2 show the porosity-permeability histograms before and after the upscaling process. Figure 3 shows the porosity 3D model of the study area. Using the scale on the right side of the figure, this figure provides strong evidence of the field heterogeneity. There are 27 production wells and 12 water injection wells in this part of the field. Fig. 3. Porosity Geo-cellular Model of the Study Area IV. SMART PROXY DEVELOPMENT As aforementioned, the smart proxy model is a data mining and artificial intelligence approach. The development procedure fall in four main stages; Design full field reservoir simulation, extract the output data from the reservoir simulation to generate the database, develop the smart proxy model by train and validate data for a targeted output, and verify the smart proxy model performance using blind sets of data (Figure 4). The following sections are discussing these steps in more details. A. Numerical Simulation Design The purpose of designing and running the numerical simulation is using its outputs as inputs to the neural network for training. The key of designing the simulation model is to take into consideration the objective of the smart proxy model. The aim of this study is to replicate and predict the reservoir dynamic properties at grid block level under different water injection flow rates. With this in mind, the simulation run is designed to calculate the well production data at each formation layer (grid block). Certainly, having the production data at every grid block of the wells is generating the required

3 Data Type Static Data Dynamic Data Grid Location Grid Injection Rate Grid Top Grid Injection Cumulative Grid Thickness Grid Production Rate Grid Porosity Grid Production Cumulative Grid Permeability Grid Pressure Distance to Injection and Boundaries Grid Saturation TABLE I DATA SELECTED TO DEVELOP SMART PROXY MODEL block pressure/saturation values. Data selected to construct the smart proxy are shown in table 1. Fig. 4. Smart Proxy Model Work Flow data heterogeneity for the neural network training (Figure 5). In sum, it is only one simulation run designed to develop the smart proxy model. C. Data Sampling Mining data from grid blocks is generating a huge data set of 1.5 million records. The tools used in this study are not able to handle such an amount of data. Therefore, data sampling is utilized for developing the smart proxy model. Two sampling methods were verified. First, random sampling is used with acceptable training and prediction results. Then, a smart sampling technique designed. In this sampling approach, the histogram of the targeted output is plotted. Then the output distribution is divided based on the values of the targeted output. In this data sampling process, the output value represented by a high number of data will take a lower percentage of data sampling. On the other hand, the values with less number of data will take a higher proportion of the data sampled. This sampling process will give the proxy model the required data heterogeneity for a better training. Figure 6 explains the smart sampling procedure. Fig. 5. Production Data Histogram at Grid Block B. Database Generation The majority of time in developing the smart proxy model is consumed in database generation. The smart proxy model is constructed to represent the principles pf the reservoir physics. Therefore, reservoir engineer knowledge and inputs are essential to achieve the goal of developing the smart proxy model. The data input in the database are coming from two sources; the geo-cellular model (static data) and from the fluid flow model (dynamic data) at each grid block. Also, the static and dynamic data from the neighboring grid blocks are collected to monitor the pressure and saturation movement. The static data include reservoir structure and grid blocks information. The dynamic data are the properties that change with time, such as well production/injection values and the grid Fig. 6. Smart Sampling Technique for Pressure Data D. Neural Networks Development and Training A neural network is designed for each of the three reservoir properties investigated in this paper (pressure, oil saturation, and water saturation). The algorithm used to construct the neural networks is Back Propagation. In this algorithm, the error for each output is back-propagate to the input in order to adjust the weights in each layer of the neural network [12]. The network typically consists of three layers; input layer, hidden layer, and the output layer. Each neural networks developed in this work has 64 inputs (table 1), 90 hidden layers, and

4 1 output. The selection of the inputs is followed by data partitioning. The objective of data partitioning is to divide the input data during the training process into training data-set, validation data-set, and testing data-set. Random partitioning is used in this study (80% of the input data is assigned to training set, 10% is assigned to validation set, and 10% is assigned to testing set). Once the network is constructed, the training process starts and the network performance can be monitored using several visualization plots in the software used [13]. V. RESULTS A. Training Results The static and dynamic input data (table 1) have been gathered for 10 years (from 1953 to 1963). The gathered inputs are used to train the neural networks for the targeted reservoir properties (pressure, oil saturation, and water saturation). For each property, neural network training is performed. For the pressure property, the coefficient of determination (R-squared) for the three data-sets, training, validation, and testing, is 0.99 (figure 7). The same R-squared values are achieved for the training models for oil saturation and water saturation from neural networks (figures 8 and 9). Fig. 8. Training cross plots for the Oil Saturation Fig. 9. Training cross plots for the Water Saturation Fig. 7. Training cross plots for the Pressure B. Validation and Prediction Results In addition to the objective of replicating the numerical simulation results, the smart proxy model is verified by testing its ability to predict the dynamic reservoir properties for the forthcoming time steps under the same operational constraint. The smart proxy model is verified by comparing the smart proxy model prediction results to the numerical reservoir model. The error is then measured between the two models. In this study, the smart proxy model (trained neural networks model) is applied to predict pressure, oil saturation, and water saturation for the years from 1964 to 1968 (which are not included in the training process). The results show that the average error of the three reservoir properties is less than 4%.. Figure 10 shows the distribution maps of pressure values of layer 2 in The top part of the figure shows the pressure map of the numerical simulator. The middle section of the figure shows the pressure map of the smart proxy model. Next to these maps is the pressure scale. At the bottom of the figure is the error map, which measured between the upper and middle pressure maps with the error scale next to it. The same explanation can be written for the figures from 11 to 14 with different reservoir properties, different layers, and different years. VI. CONCLUSION This paper presented an alternative tool for reservoir simulation. The smart proxy model uses data mining and artificial intelligence techniques, and the development procedure of this model is discussed. It is shown that the smart proxy model is

5 able to replicate the complex numerical simulation results at grid block level in a very short time (seconds). REFERENCES [1] Shahab Dean Mohaghegh. Reservoir simulation and modeling based on artificial intelligence and data mining (ai&dm). Journal of Natural Gas Science and Engineering, 3(6): , [2] Denis Igorevich Zubarev et al. Pros and cons of applying proxy-models as a substitute for full reservoir simulations. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, [3] S Amini, SD Mohaghegh, R Gaskari, GS Bromhal, et al. Pattern recognition and data-driven analytics for fast and accurate replication of complex numerical reservoir models at the grid block level. In SPE Intelligent Energy Conference & Exhibition. Society of Petroleum Engineers, [4] André I Khuri and Siuli Mukhopadhyay. Response surface methodology. Wiley Interdisciplinary Reviews: Computational Statistics, 2(2): , [5] Terry Ngo. Data mining: practical machine learning tools and technique, by ian h. witten, eibe frank, mark a. hell. ACM Sigsoft Software Engineering Notes, 36(5):51 52, [6] Shahab Mohaghegh et al. Virtual-intelligence applications in petroleum engineering: Part 1artificial neural networks. Journal of Petroleum Technology, 52(09):64 73, [7] Shahab Mohaghegh et al. Virtual-intelligence applications in petroleum engineering: Part 2evolutionary computing. Journal of Petroleum Technology, 52(10):40 46, [8] Shahab Mohaghegh et al. Virtual-intelligence applications in petroleum engineering: Part 3fuzzy logic. Journal of petroleum technology, 52(11):82 87, [9] Shahab D Mohaghegh, Hafez H Hafez, Razi Gaskari, Masoud Haajizadeh, Maher Kenawy, et al. Uncertainty analysis of a giant oil field in the middle east using surrogate reservoir model. In Abu Dhabi International Petroleum Exhibition and Conference. Society of Petroleum Engineers, [10] Alireza Shahkarami, Shahab Mohaghegh, Vida Gholami, Alireza Haghighat, and Daniel Moreno. Modeling pressure and saturation distribution in a co2 storage project using a surrogate reservoir model (srm). Greenhouse Gases: Science and Technology, 4(3): , [11] Shohreh Amini. Developing a Grid-Based Surrogate Reservoir Model Using Artificial Intelligence. WEST VIRGINIA UNIVERSITY, [12] RC Chakraborty. Back propagation network, [13] The Mathworks, Inc., Natick, Massachusetts. MATLAB version (R2015a), Fig. 10. Distribution map of Layer 2 pressure in 1964 (Numerical Simulator Output, Smart proxy Output, and Error) Fig. 11. Distribution map of Layer 13 pressure in 1965 (Numerical Simulator Output, Smart proxy Output, and Error)

6 Fig. 12. Distribution map of Layer 5 pressure in 1968 (Numerical Simulator Output, Smart proxy Output, and Error) Fig. 14. Distribution map of Layer 10 Oil Saturation in 1965 (Numerical Simulator Output, Smart proxy Output, and Error) Fig. 13. Distribution map of Layer 3 Oil Saturation in 1964 (Numerical Simulator Output, Smart proxy Output, and Error) Fig. 15. Distribution map of Layer 12 Oil Saturation in 1968 (Numerical Simulator Output, Smart proxy Output, and Error)