Developing a Smart Proxy for the SACROC Water-Flooding Numerical Reservoir Simulation Model

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1 SPE MS Developing a Smart Proxy for the SACROC Water-Flooding Numerical Reservoir Simulation Model Faisal Alenezi and Shahab Mohaghegh, West Virginia University Copyright 2017, Society of Petroleum Engineers This paper was prepared for presentation at the 2017 SPE Western Regional Meeting held in Bakersfield, California, USA, 23 April This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. Abstract The preferred common tool to estimate the performance of oil and gas fields under different production scenarios is numerical reservoir simulation. A comprehensive numerical reservoir model has tens of millions of grid blocks. The massive potential of the existing numerical reservoir simulation models go unrealized because they are computationally expensive and time-consuming [1]. Therefore, an effective alternative tool is required for fast and reliable decision making. To reduce the required computational time, proxy models are developed. Traditional proxy models are either statistical or reduced order models (ROM). They are developed to substitute the complex numerical simulation by producing a representation of the system at a lower computational cost. However, there are shortcomings associated with these approaches when applied to complex systems. In this study, a novel proxy model approach is presented. The smart proxy model presented in this article is based on artificial intelligence and data-mining techniques. A numerical simulation run is designed for the smart proxy objectives. The static and dynamic data from the simulation run are extracted. Selected data parameters are used to create a spatial-temporal database for the smart proxy model. The smart proxy is trained, calibrated, and validated using a series of neural networks for the targeted reservoir property. To validate the smart proxy model, it is deployed to replicate a blind numerical simulation run. The developed smart proxy model can replicate the simulation outcomes in a very short time (seconds) with an acceptable range of error. Introduction In the oil and gas industry, reservoir simulation is the standard tool for field developments and strategies. History matching, predicting future performance, and preparing the reservoir management plans are the main tasks of reservoir simulation. With the recent software capabilities, accurate and comprehensive reservoir description models can be developed. On the other hand, it is computationally expensive and timeconsuming to run these models. Therefore, many comprehensive reservoir models remain under-utilized. With the introduced real-time data technologies combined with the challenging reservoir problems, the need to develop highly accurate simplified reservoir simulation tools is increasing [2]. Many efforts have been made to develop alternative approaches to the complex numerical reservoir simulation to

2 2 SPE MS reduce the computational cost. Proxy models (also known as surrogate models) have been recently used in reservoir simulation. Proxy models are defined as mathematical or statistical approaches that replicate the conventional simulation models for field development and uncertainty quantification with less computational size and running time. Based on the evidence currently available, it seems fair to say that proxy models can mimic the output of the conventional reservoir simulation with a reasonable range of error. Yet, there is a possible challenge related to mathematical and statistical approaches with complex reservoirs. To overcome the possible challenges with conventional proxy models, there is rapidly growing literature on a newly developed technique of surrogate models. It is a smart proxy that is based on artificial intelligence and data mining, where the system behavior is observed through data [3]. Smart proxy models (the surrogate reservoir model) can replicate the simulation responses in a very short time (seconds). This technology was first introduced in 2006 [4]. In the early work, the developed smart proxy primarily dealt with the production profile at the well level. Since then, the smart proxy model has been applied to different reservoir simulation studies for obtaining dynamic reservoir properties at the grid block level and to perform history matching [5][6][7][8]. In these studies, it was proven that the artificial intelligence approach can be used as a proxy model for reservoir simulation with acceptable accuracy. The question of whether the physics is ignored has caused much debate in using this technique recently. In the smart proxy model, by studying all the corresponding reservoir data, the network is learning from the data that carry information of the physics of the system. On these grounds, it can be argued that the physics of the system is not disregarded. The smart proxy model is different than the traditional proxy models, and the differences can be summarized with the following points: It can handle complex reservoirs. The reservoir physics are not simplified. Methodology This study is the continuation of a work that has already been published [9]. The previous paper discussed the smart proxy model in a reservoir with only one injection well and several production wells. In current work, the smart proxy is developed with the same reservoir but in a different time range when the reservoir had several injection wells. The selected performance time range is very complex and challenging, where the number of injection/production wells varies yearly. The objective of this work is to develop a smart proxy model to compute the reservoir pressure and saturation at the grid block level. The smart proxy development procedure is the following: 1. Design the full field numerical simulation model. 2. Extract the static and dynamic data from the simulation run to generate a special-temporal database. 3. Select the required parameters from the database based on the objective of the smart proxy. 4. Using the Neural Networks, train and validate data for the targeted reservoir property (the trained and validated Neural Network is the developed smart proxy model). 5. Apply the smart proxy model to blind simulation run which was not included in the training set for verification. Field of Study Geo-cellar Model The Scurry Area Canyon Reef Operators Committee (SACROC), which constitutes a major part of the Kelly-Snyder Field, is in Scurry County, Texas (Figure 1). It is one of the largest unitized fields in the world, covering approximately 50,000 acres and contains 1,259 wells [10]. The Kelly-Snyder Field was discovered in 1948 and is one of the major oil reservoirs in the United States. It has 2.73 billion barrels of oil originally in place.

3 SPE MS 3 Figure 1 SACROC Field Figure 2 3D Porosity Model The Texas Bureau of Economic Geology has developed a geo-cellar model for the northern platform of SACROC field. It is high- resolution with dimension of 149 X 287 and 221 layers. Because the high level of detail of SACROC geo-cellular model (9,450,623 grid blocks) increases the computational cost of this model, two major modifications were performed on the geo-cellar model for the purpose of this study: The model is up-scaled from 221 layers to 16 layers. The northern part of the field is selected. The selected part dimensions are 51X39X16 which gives 31,824 total grid blocks.

4 4 SPE MS In this selected area, there are 27 production wells, of which 12 were later converted to injection wells. The number of production/injection wells varies throughout the field history. All the production/injection wells are drilled vertically and are completed as open-hole wells across all 16 geological layers. Simulation Run Desgin The purpose of designing and running the numerical simulation model is to provide the sample space of the model input-output relationships for the neural network training. The key of the simulation run design is to consider the objective of the smart proxy model. As mentioned, the aim of this study is to replicate and predict the reservoir dynamic properties at the grid block level. The simulation run is designed to calculate the well production/injection values at each grid block. In other words, instead of having one production/injection data point at each well, there will be 16 production/injection data points corresponding to 16 layers in the reservoir. The calculated grid block production/injection values with the geological reservoir heterogeneity are sufficient information for the smart proxy to learn about the reservoir responses. To summarize, it is only one simulation run designed to develop the smart proxy model. Spatial-Temporal Database Generation The real challenge with the neural network training and validation is how to attain the right data in the right format [11]. Domain-expert knowledge is needed for where and how to collect the required data. For the mentioned smart proxy objective, static and dynamic data are collected. The static data remain constant over time, such as reservoir porosity, reservoir permeability, well distances from boundaries, etc. By contrast, the dynamic data are changing over time. This type of data belongs to the grid block and well domains, such as reservoir pressure, saturation, well production/injection rates, etc. To ensure enough information for smart proxy training, the effect of the surrounding grid blocks is considered. Therefore, a tier system is defined for selected reservoir parameters. The generated tier system consists of four tiers at each grid block as follows: Tier 1: The grid block in the same layer Tier 2: The grid block in the top layer Tier 3: The grid block in bottom layer Tier 4: The average of immediate grid block in the same layer Moreover, the selected parameters and the tier system are illustrated in Figures 3 and 4.

5 SPE MS 5 Figure 3 Smart Proxy Input Parameters Figure 4 Tier System Once the database is generated, it contains a huge amount of data. The study time range is from 1975 to The data are collected annually from 31,824 grid blocks. This yields 954,720 data records and more than 90 parameters (columns). The personal computer used to perform this study was unable to handle this amount of data. Therefore, data sampling was applied, and a portion of the data was selected for the development of the smart proxy model. In the data sampling process, it is important to ensure that the sampled data is representative of the whole data. The sampled data selected for the study is 10% of the whole database (95,000 data records). Smart Proxy Development (Neural Networks Training and Validation) Three reservoir properties targeted for neural network training are grid block pressure, oil saturation, and water saturation. A neural network is designed for each reservoir property. A back- propagation algorithm was used to train the neural networks. The back-propagation goal is to minimize the error between the network output and the actual output by updating the network weights for each iteration [12]. The total data in the neural networks are divided into three datasets: training, validation, and testing. The training set is used to determine the weight updates of each iteration. The validation set is used to prevent over-fitting. The test data are not included in the training process, and the error will indicate how the network

6 6 SPE MS will perform with new datasets [13]. Random data portioning is used in this study, as 70% of data are in the training set, 15%are for the validation set, and 15%are for the testing set. Once the neural network training and validation are achieved, it can be considered a smart proxy model and tested for generalization. Figure 5 Database Generation Figure 6 Numerical simulator versus smart proxy for pressure and oil saturation On 01/01/1980 at the 7th geological layer.

7 SPE MS 7 Figure 7 Numerical simulator versus smart proxy for pressure and oil saturation on 01/01/1992 at the first layer. Figure 8 Numerical simulator versus smart proxy for pressure and oil saturation on 01/01/2000 at the 15th geological layer.

8 8 SPE MS Results The developed proxy model is successfully trained to mimic the numerical reservoir simulation for the targeted reservoir properties. The generated smart proxy can replicate the numerical simulator outputs with acceptable accuracy not only at each grid block but also for 30 years of reservoir performance. As noted earlier, only 10% of the data were used for the training, and 90% of the data have not been used in this process. Selected examples of the training results are shown in this paper. The selected results are representing different field performances for the period of 1975 to The following data maps show the numerical simulator results versus the smart proxy results and the absolute error for the targeted reservoir properties. The numerical simulation software used is Computer Modeling Group (CMG) [14] Validation with Blind Simulation Run To verify the ability of the developed smart proxy model in predicting pressure and saturation under different geological realizations, it should be applied to a completely blind injection scenario that was not included in the training set. The porosity of the geological model is modified within the range of the original model permeability. An example of the permeability realization is shown in Figure 9. Once this process is completed, the newly designed numerical simulation run is executed, and the required data are extracted for the smart proxy application. Figure 9 The permeability realization performed on layer 10. (a) is the trained model where (b) is the blind scenario model The results of applying the developed smart proxy model to the designed blind run is showing the ability of this developed technique to predict the targeted reservoir properties at the grid level with acceptable accuracy. Figure 10 shows the pressure histogram of the smart proxy model compared to the numerical simulation. 90,000 pressure data points randomly selected from time ( ) and space (31,200 grid blocks) for this comparison. The histograms are near-equal with an average absolute error of 2%.

9 SPE MS 9 Figure 10 Pressure histograms of the smart proxy model and the blind numerical simulation. Figure 11 The applied smart proxy to the blind numerical simulation run at layer 8 on 01/01/1980.

10 10 SPE MS Figure 12 The applied smart proxy to the blind numerical simulation layer 13 on 01/01/1980. Figure 13 The applied smart proxy to the blind numerical simulation at layer 4 on 01/01/2000.

11 SPE MS 11 Figure 14 The applied smart proxy to the blind numerical simulation run at layer 8 on 01/01/2000. Conclusion In this work, it has been proven that the smart proxy model is a reliable tool for reservoir simulation with complex reservoirs. The developed proxy model can generate the pressure and saturation values with acceptable accuracy compared to the numerical simulator at each grid block. References 1. Shahab Mohaghegh. Surrogate reservoir model. In EGU General Assembly Conference Abstracts, volume 12, page 234, Hector Klie et al Physics-based and data-driven surrogates for production forecasting. In SPE Reservoir Simulation Symposium. Society of Petroleum Engineers, Shahab Mohaghegh. Smart Proxy Modeling for Numerical Reservoir Simulations Big Data Analytics in E&P. SPE Live webinars, Shahab D Mohaghegh et al Quantifying uncertainties associated with reservoir simulation studies using a surrogate reservoir model. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers, Shahab D Mohaghegh, Shohreh Amini, Vida Gholami, Razi Gaskari, Grant S Bromhal, et al Grid-based surrogate reservoir modeling (srm) for fast track analysis of numerical reservoir simulation models at the gridblock level. In SPE Western Regional Meeting. Society of Petroleum Engineers, Shohreh Amini, Shahab D Mohaghegh, Razi Gaskari, Grant Bromhal, et al Uncertainty analysis of a co2 sequestration project using surrogate reservoir modeling technique. In SPE Western Regional Meeting. Society of Petroleum Engineers, 2012.

12 12 SPE MS 7. 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, Qin He, Shahab D Mohaghegh, Zhikun Liu, et al Reservoir simulation using smart proxy in sacroc unit-case study. In SPE Eastern Regional Meeting. Society of Petroleum Engineers, Faisal Alenezi and Shahab Mohaghegh. A data-driven smart proxy model for a comprehensive reservoir simulation. In Information Technology (Big Data Analysis)(KACSTIT), Saudi International Conference on, pages 1 6. IEEE, Batur Isdiken. Integrated geological and petrophysical investigation on carbonate rocks of the middle early to late early canyon high frequency sequence in the northern platform area of the sacroc unit Deep Learning Organization. Data sets and machine learning. Technical report, Deep Learning Organization, RC Chakraborty. Back propagation network, Martin T Hagan, Howard B Demuth, and MH Beale. Neural network design, Boston, PWS Pub, Computer Modeling Group. Cmg.