with high computational cost. In the recent years, many efforts mainly referred as assisted history matching have

Transcription

1 SPE MS Artificial Intelligence (AI) Assisted History Matching Alireza Shahkarami, Shahab D. Mohaghegh, Vida Gholami, Sayed Alireza Haghighat, West Virginia University Copyright 2014, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Western North American and Rocky Mountain Joint Regional Meetingheld in Denver, Colorado, USA, 16 18April 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 History matching is the process of adjusting uncertain reservoir parameters until an acceptable match with the measured production data is obtained. Complexity and insufficient knowledge of reservoir characteristics makes this process timeconsuming with high computational cost. In the recent years, many efforts mainly referred as assisted history matching have attempted to make this process faster; nevertheless, the degree of success of these techniques continues to be a subject for debate. This study aims to examine the application of a unique pattern recognition technology to improve the time and efforts required for completing a successful history matching project. The pattern recognition capabilities of Artificial Intelligence and Data Mining (AI&DM) are used to develop Surrogate Reservoir Model (SRM) for utilization as the engine to drive the history matching process. SRM is an intelligent prototype of the full-field reservoir simulation model that runs in fractions of a second. SRM is built using a handful of geological realizations. In this study, a synthetic reservoir model of a heterogeneous oilfield with 24 production wells and 30 years of production history was used as the ground truth (the subject and the goal of the history match). An SRM was created to accurately represent this reservoir model. The history matching process for this field was performed using the SRM and by tuning static data (Permeability). The result of this study demonstrates the capabilities of SRM for fast track and accurate reproduction of the numerical model results. Speed and accuracy make SRM a fast and effective tool for assisted history matching. Keywords: History Matching, Artificial Intelligence, Surrogate Reservoir Model (SRM), AI Assisted History Matching

2 2 SPE SPE MS 1. Introduction The purpose of reservoir management is to develop strategies to maximize recovery. Reservoir simulation is usually used as a decision making tool in this procedure. The common concern of reservoir simulation and modeling is accuracy. It is generally believed that models with higher resolution (in both time and space) are more accurate. Since increase in resolution (time and space) translates to increase in computational time, a well-known dichotomy arises. On one hand the model must satisfy the accuracy requirements (high resolution), and on the other hand, it needs to be fast enough to become practical. The new advancements in reservoir data acquisition have raised the complexity of the reservoir model and therefore the time required to run it. At the same time typical reservoir modeling tasks such as sensitivity analysis, history matching, field development optimization, and uncertainty assessment require large number of simulation runs. The challenge now is to keep the complexity of the reservoir model while shortening its run-time. The main objective of history matching is to improve and validate the reservoir simulation model by incorporating the observed data into the characterization process, in order to obtain reliable production forecast. A simulation model which has been tuned to match the past performance of a reservoir offers a higher degree of confidence to predict the future. Having a trustworthy prediction of field performance has direct impact on technical and financial performance of operators. History matching, by nature, is an ill-posed inverse problem. Correspondingly, classical history matching where reservoir parameters are adjusted manually by trial-and-error makes this scenario more tedious and time-consuming. Assisted (automated) history matching was proposed to decrease the amount of labor required during the manual history matching. During last two decades there have been efforts to improve assisted history matching in a way that could be applicable in the real world. But despite all the attempts, due to increasing rate of complexity and resolution in the reservoir models, there is still hesitation about the practicality and potential of these methods to handle highly complicated real reservoir models. This makes assisted history matching still a challenging research topic. The novelty of the idea in this study is to examine a new application of pattern recognition technologies to improve the time and efforts required for completing a successful history matching project. The pattern recognition capabilities of Artificial Intelligence and Data Mining (AI&DM) are used to develop a Surrogate Reservoir Model (SRM) and use it as the engine to drive the history matching process. SRM is a prototype of the full-field reservoir simulation model that runs in fraction of a second. SRM is built using a small number of geological realizations. The geological realizations are used to create a spatiotemporal database. The AI&DM techniques are utilized to derive the complicated relationship between different parameters in

3 SPE SPE MS 3 the database. Clearly the relationship originates from the nonlinear behavior of fluid flow thorough the porous media. In this study Artificial Neural Networks (ANNs) are the AI&DM tool in building the SRM. In order to develop the SRM, the spatiotemporal database was used to build ANNs. 2. Literature Review 2.1. History Matching The advancement of computational power pushed reservoir simulation as the main tool to model the behavior of fluid flow in reservoir (Watts 1997). Nowadays, feedbacks from reservoir simulation models are used in almost all reservoir development decisions. Simulating reservoirs easily and realistically makes them a primary and reasonable choice for oil and gas companies in the development of new (green) fields. Similarly, they are used in developed (brown or mature) fields where production forecasts are required to help make future investment decisions. In general, most of the required input data for building a numerical reservoir model comes from samples in wellbore or near wellbore (Fanchi 2006). Compared to the size of a reservoir, these data are inadequate and their sources represent a very limited section of reservoir. Furthermore, the methods applied for preparing these data are treating them in a very local aspect. However, these data and the techniques to attain them are the only options that provide input data for the reservoir simulation model of the field under study. The main point is that a huge part of the reservoir remains unknown to the engineers and geologists working on the simulation model. As a result, the initial data in a simulation model should be adjusted in order to be matched with the available historical data and predict the future performance of reservoir. This tuning procedure is performed during history matching process. History matching is a calibration process that includes adjusting the uncertain parameters of reservoir model until the model reproduces the historical field performance as closely as possible. History matching is an ill-posed inverse problem. The inverse problem is the opposite of forward or direct problem which the model parameters are used to predict the data. While in inverse problem the observed data is used to conclude (adjust) the model parameters. On the other hand, a problem is ill-poised (not well-posed) when there are multiple non-unique solutions for a certain problem. History matching is an ill-posed problem because many possible combinations of reservoir parameters can result in almost the same behavior of reservoir (match the history data). There is no doubt that history matching is a complicated procedure. Many criteria could be named which affect the degree of success in this process: the quality and quantity of available data, the specific characteristics of the reservoir under study, the

4 4 SPE SPE MS time and resources allocated to the study, and finally the experience and knowledge of the research group working on the model. Consequently, each one of these criteria gives the history matching problem its most important characteristic which is the non-uniqueness character of the results. There is no specific and unique method for history matching process. Each reservoir has the particular specification and behavior. Many efforts to improve manual history matching techniques have been made since the mid 1960 s to both speed up and automate history match process (Kruger 1961) (Jacquard and Jain 1965) (Jahns 1966). Gradient optimization methods were used for history matching in late 1960 s (Coats, Dempsey and Henderson 1968)(Slater and Durrer 1970). Chen et al. (1974) tried to formulate history matching as an optimal control problem. Williams et al (1998) offered a structured approach to perform history matching on a complex reservoir and based on their experience proposed multiple recommendations which make the manual history matching easier. Bush and Carter (1996) showed that simple optimization techniques are not good enough to address complex history matching problems. He and Chamber (1999) claimed that automatic history matching using an object-based approach could provide acceptable results without the need to manually adjust the model. In the early 90 s, using stochastic modeling to generate multiple realizations were started (Tyler, Svanes and Omdal 1993) (Palatnic, et al. 1993). Stochastic modeling, which provides many different geological realizations, increases the variation of the most important input parameters, e.g. the geological properties influencing fluid flow. Sultan et al. (1994) and Ouenes et al. (1993) used the Simulated Annealing Method (SAM) to automate history matching process. SAM was a non-gradient optimization method capable of handling large number of parameters. Gao et al. (2004) for the first time suggested the idea of combining the simultaneous perturbation stochastic approximation (SPSA) method with a simulator to perform automatic history match of multiphase flow production data. Hajizadeh et al. (2009) (2010) introduced a stochastic approach for automatic history matching based on a continuous Ant Colony Optimization (ACO) algorithm. Other stochastic algorithms have been examined in this area. Evolutionary algorithms have gained popularity as a standard optimization approach in history matching. These algorithms are generally inspired by the evolution theory. There have been may examples of application of these algorithms in history matching (Schulze-Riegert et al. 2002) (Cheng et al. 2008)(Ferraro and Verga 2009) (Abdollahzadeh et al. 2012) (Christie et al. 2013). However, high nonlinear behavior of the problem, large computational expenses and huge dimension of a real size field make the history match process more difficult. Although significant computational and solver efficiencies have been gained over the past four decades, ever-increasing size of geo-statistical earth models has continued to challenge the computational speed issue (Kabir, Chien and Landa 2003).

5 SPE SPE MS Artificial Neural Networks Artificial neural network (ANN), usually called Neural Network (NN), is an algorithm that was originally motivated by the goal of having machines that can mimic the brain. A neural network consists of an interconnected group of artificial neurons. They are physical cellular systems capable of obtaining, storing information, and using experiential knowledge. Like human brain, the ANN s knowledge comes from examples that they encounter. In human neural system, learning process includes the modifications to the synaptic connections between the neurons. In a similar way, ANNs adjust their structure based on output and input information that flows through the network during the learning phase. Data processing procedure in any typical neural network has two major steps: the learning and application step. At the first step, a training database is needed to train the networks. This dataset includes an input vector and a known output vector. Each one of the inputs and outputs are representing a node or neuron. In addition, there are one or more hidden layers. The objective of the learning phase is to adjust the weights of the connections between different layers or nodes. After setting up the learning samples, in an iterative approach a sample will be fed into the network and the resulting outputs will be compared with the known outputs. If the result and the unknown output are not equal, changing the weights of the connections will be continued until the difference is minimized. After acquiring the desired convergence for the networks in the learning process, the validation dataset is applied to the network for the validating step (Hagan, Demuth and Beale 2002)(Haykin 1998). Figure 1 depicts the input, hidden and output layers and their connections. Since the advent of ANNs (McCulloch and Pitts 1943), they have seen different stages of rise and fall; however nowadays ANNs enjoy huge popularity and interests in different fields. Some applied applications of ANNs are listed in Table 1. Shahab Mohaghegh is one of the pioneers in applying AI in petroleum engineering. He (Mohaghegh 1995) refers the main advantage of ANN to the type of recognition ability and the difference of the mechanism that human brain processes information compared to conventional digital computers. Computers are fast and accurate tools in performing prepared instructions. On the other hand, human brain performance is tremendously slower but more efficient than computers at computationally complicated jobs such as speech and other pattern recognition problems. ANNs can be helpful tool to solve many conventional and unconventional problems in petroleum engineering. Although they have a long history, their popularity in petroleum engineering started two decades ago (Ali 1994). Since this time, the applications of ANNs in addressing conventional problems of petroleum industry have been widely studied. Table 2 concisely lists different applications of ANNs in petroleum engineering.

6 6 SPE SPE MS Table 1- Application of ANNs in different fields. The popularity of ANNs has seen rise and fall since their advent. Applications of ANNs in different fields Sales forecasting (Yip, Hines and Yu 1997) Industrial process control (Devadhas, Pushpakumar and Mary 2012) Customer research (Chattopadhyay, et al. 2012) Risk management (Sarcià, Cantone and Basili 2007) Credit evaluation (Baesens, et al. 2003) Energy cost prediction (Yalcintas and Akkurt 2005) Medical diagnosis (Amato, et al. 2013)(Lei and Xing-cheng 2010) Business applications (Li 1994) Financial applications (Tan 2004) Stock market prediction (Adebiyi, et al. 2012) Table 2- A brief list of ANN applications in petroleum engineering. A brief list of ANN application in petroleum engineering Well log interpretation (Baldwin, Otte and Whealtley 1989)(Jong-Se and Jungwhan 2004)(Masoud 1998) Well test data analysis (Al-Kaabi and Lee 1990)(Ershaghi, et al. 1993)(Athichanagorn and Horne 1995)(Sultanp and Al-Kaabi 2002) Reservoir characterization (Mohaghegh., et al. 1995)(Ahmed, et al. 1997)(Singh, et al. 2008) Seismic attributes calibration Seismic pattern recognition Inversion of seismic waveforms Prediction of PVT data Identifying fractures and faults Detecting hydrocarbons and forecast formation damage (David 1993)(Yang and Huang 1991) (Roth and Tarantoia 1992) (Briones, et al. 1994)(Gharbi and Elsharkawy 1997)(Osman, Abdel- Wahhab and Al-Marhoun 2001)(Oloso, et al. 2009) (Key, et al. 1997)(Sadiq and Nashawi 2000)(Aminzadeh and degroot 2005) (Cheng-Dang, et al. 1994)(Aminzadeh and degroot 2005)(Nikravesh, et al. 1996)(Kalam, Al-Alawi and Al-Mukheini 1996) 2.3. Artificial Intelligence (AI) Assisted History Matching During the last decade, there have been attempts to find alternative methods to reduce the amount of CPU time needed to execute a numerical full field model. AI methods are one of the most famous and efficient examples of these kinds of techniques. Zangl et al. (2006) trained an ANN as a proxy model by using a limited number of simulation runs of a gas storage model. Then they applied this proxy model to replace the numerical model in order to make hundreds and thousands of runs in a very short time in an optimization loop. One of the objectives was to perform the history matching. The results were acceptable and had considerably less computational expenses compared with numerical reservoir simulation outcomes. Cullick

7 SPE SPE MS 7 et al. (2006) compared the performance of proxy models based on ANNs with reservoir simulator to perform history matching. Their results support using ANNs as a substitute for numerical simulator over the trained parameter space. They tried to challenge the limitation of proxy model in their work by decreasing the number of training realizations and increasing the uncertain parameters. The objective of Rodriguez et al. (2007) work was accelerating the history matching process by applying singular value decomposition method. This method helped them to save 75 % of total CPU time. At the same time, they used an ANN in order to reduce number of simulation runs and help to increase the accuracy of solution. Silva et al. (2006)(2008) presented the application of global optimizers combined with ANNs to address the history matching problem. Their results supported the potential of ANNs to reduce the computational effort in history matching process. Sampaio et al. (2009) used feed-forward neural networks as nonlinear proxies of reservoir simulation to speed up history matching. The focus of their work was to discuss the technical criteria that will lead implementation of ANN to be a successful experience. The points that they have mentioned in their paper are crucial for the researchers who are interested in applying ANN in petroleum engineering problems. The aforementioned cases are some examples of ANN application. However what is worth mentioning is the approach used in these examples through development and implementation of AI models, which is the same as the statistical methods. The degree of success of using AI models based on this approach is highly uncertain and it could be as successful or disappointing as the statistical techniques (Cullick, Johnson and Shi 2006)(Zubarev 2009). Particularly addressing application of AI in petroleum engineering problems (such as history matching), it requires a comprehensive knowledge in both areas of petroleum engineering and AI and DM to achieve success. This knowledge plays an important role in keeping the physics to solve the problem. The fact of using physics is something that has been neglected in statistical methods (or applying AI techniques using the same approach) Surrogate Reservoir Models The main objective of this study is to speed up the history matching process. The focus of our work is based on a relatively new technology known as Surrogate Reservoir Model (SRM). SRM has been introduced as a tool for addressing many timeconsuming operations performed with reservoir simulation models (Mohaghegh 2006). SRM is a replica of numerical reservoir simulation model which is able to reproduce the results of simulation model with a high accuracy in real-time. Basically SRMs are a collection of (at least) one or multiple neuro-fuzzy systems that are trained and validated using the information from numerical simulation models. The required information to train the SRM is assimilated in the form of a

8 8 SPE SPE MS spatio-temporal database. Design of spatio-temporal database is a function of the objective of SRM. The examples of Surrogate Reservoir Models in the industry to address time-consuming reservoir modeling are available in the literature. Mohaghegh introduced this tool for the first time in 2006 to perform uncertainty analysis of a giant oilfield with 165 horizontal wells in the Middle East (Mohaghegh 2006). The efficiency of SRMs to reproduce the results of reservoir simulators has been proved in several case studies (Mohaghegh et al. 2009)(Mohaghegh 2009)(Mohaghegh 2010)(Mohaghegh et al. 2012b)(Mohaghegh et al. 2012)(Amini et al. 2012). In this study, SRM is being used, for the first time as a tool for assisted history matching. 3. Methodology SRMs are developed based on representative spatio-temporal databases. Building this database is the first step of developing AI-based reservoir models. The main objective of the database is to teach the ANN model the whole process of fluid flow phenomena in the reservoir. In general, this database should meticulously provide static and dynamic information of the reservoir. The quality and quantity of this database determines degree of success to develop a successful AI-based reservoir model including an SRM (Mohaghegh 2011). Compared to the other steps of SRM development, preparing the database is relatively the most tedious part, which needs a lot of thought process. However a good database guarantees the success of the modeling. In order to build this SRM different steps were required. Followings are steps involved to develop the SRM: 1) Pre-processing step includes model development and dataset generation: a. Development of a heterogeneous reservoir model using a commercial simulator. Starting with the base case of reservoir model a small number of informative realizations were created. These informative realizations represent the geological uncertainties involved in the reservoir model. b. Depending on the objective of developing SRM, the reservoir could be divided into different segments and tiers. Segmenting the reservoir helps to emphasize on the sections which are more important, such as well block and the grid blocks around the well. c. Extracting different static and dynamic data from the numerical simulation models in order to build the spatio-temporal database. 2) SRM Development:

9 SPE SPE MS 9 a. Performing Key Performance Indicators (KPIs) to identify and rank the influence of different reservoir characteristics on the reservoir performance. The ranked KPIs will be a guide to select ANN inputs. b. Partitioning the spatio-temporal database into training, calibration and validation sets. c. Designing Artificial Neural Network (ANN) architecture. d. Training, calibrating and validating the ANNs. e. Testing the created ANNs using a complete blind realization of the reservoir. Figure 2 summarizes the steps to develop the SRM. 4. The Reservoir Model The reservoir model used in this study is a synthetic replica of a highly heterogeneous oil field, with 24 production wells and 30 years of production history. The base simulation model is a single porosity oil reservoir, which was constructed in CMG- IMEX TM1. The reservoir has been divided to 4800 Non-Orthogonal grid blocks, 80 in X direction and 60 in Y direction. The reservoir has a single layer and thickness values are variable in different gird blocks. The field is producing oil at initial pressure of 13,789.5 kilopascals (2,000 psi) and bubble point pressure of 2,068.4 kilopascals (300 psi), therefore it is expected that the candidate reservoir will be producing oil for a long time in an under-saturated condition. The model is synthetic and does not represent a real field. Figure 3 shows three and two dimensional views of the reservoir structure. Figure 4 and 5 illustrate three and two dimensional views of porosity and grid thickness distributions. The given permeability range for the base model is from 10 to 75 md (Figure 6). In addition, the geological information from the field identifies a high permeable zone. 24 production wells have been drilled in the field and they produce oil for 30 years. Minimum bottom-hole pressure (BHP) is set as the production constraint which varies through time. The wells produce for 30 years, starting in 2000/01/01. The available historical data include oil rate production for all the wells. 5. Training Realizations In order to introduce the uncertainties involved in the reservoir simulation model to the SRM, a small number of simulation runs should be made. In this study, ten different realizations of the base model were designed to develop the SRM. Using the permeability map from base reservoir model, ten different permeability maps were generated. The range of permeability for 1 Computer Modeling Group

10 10 SPE SPE MS the base model is from 10 to 70 md. Due to the uncertainty involved in reservoir properties, a range from 10 to 200 md was considered to create the permeability distributions. Afterward, to create ten different cases of permeability values at well location, an experimental method (Latin Hypercube) was used. Table 3 summarizes generated permeability values at the wells location. Table 3- Permeability (md) values designed at well locations for generating permeability maps. The permeability values for each well have been ranged by color, which red and blue represent minimum and maximum value respectively. Well Wells' Location for 10 Runs applied in Training part Run 1 Run 2 Run 3 Run 4 Run 5 Run 6 Run 7 Run 8 Run 9 Run 10 Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Well Reservoir Segmentation- Tiering System and offset wells In order to include the static data of adjacent grid blocks of a well in the spatio-temporal database, a tiering system was generated. Another objective of this part is to summarize the information based on their influences on the wells production. Obviously, if the Euclidian distance of grid blocks from the production well is considered, different grid blocks show different behavior in terms of fluid flow. For example, the well grid block has the maximum influence on the production of a well. Hence, this influence should be considered during developing the database. Furthermore, considering the impact of the neighborhood wells production was interested (offset wells effects). 7. SRM Development

11 SPE SPE MS Input Selection At this step, the inputs to develop the spatio-temporal database are selected. As it was mentioned, building this database is the most important step of developing an SRM. In building of this database, the objective of the reservoir modeling should be considered (Amini et al. 2012)(Mohaghegh et al. 2012a). For instance, the objective of this study is using the SRM to estimate the well parameters such as oil production. Therefore, the reservoir properties, which are affecting the objective of study, have higher degree of importance. The spatio-temporal database includes different types of data such as static and dynamic reservoir characteristics, operational constraints, etc. Static data refer to the properties of reservoir that are not changing through the time such as permeability, porosity, top and thickness. Similarly, the dynamic data address variable parameters that are altering over the time, such as oil production rate, bottom-hole pressure, and production time. For the tiers which have more than one grid block, the average of the property was calculated. This calculation was done just for static properties. Figure 7 summarizes different types of data in the spatio-temporal database Building the Artificial Neural Networks After having the database ready, the next step is to create the ANNs. In order to generate ANNs, software called IDEA TM2 was used (Intelligent Solutions Inc. 2012). The inputs of ANNs are displayed in figure 7 and the output of the networks is annual oil rate production. The training algorithm was Back Propagation (BP). BP is one of the most common training methods to train the ANN and the time-based model development feature of this paradigm was appropriate for our study. One novel pre-modeling analysis in SRM development is performing Key Performance Indicators (KPIs) analysis. This feature provided in IDEA TM identifies the most influential parameters in any given process prior to modeling. This feature operates based on a pattern recognition and fuzzy logic engine. Figure 8 displays the results of KPI analysis in this study. Training the ANNs is the following step. The training process includes three different processes: Training (learning), Calibration and Validation (testing). Therefore, the database is partitioned into three categories: training or learning set, calibration set and validation or verification set. The training set is part of data shown to the ANNs during the training process. The ANNs are adapted to this set to match the provided outputs (reservoir simulation results). On the other hand, the calibration set is not used to adjust the outputs. This set is utilized to assure that any increase in accuracy over the training data 2 IDEA TM is a data-driving and AI modeling software developed by Intelligent Solutions Inc. (ISI).

12 12 SPE SPE MS set will lead to an increase in accuracy over a data set that has not been shown to the ANNs before. This set of data is helpful to find out when the training should be stopped. If the error trend over the training data set has a decreasing trend, but the same error for the calibration set has different trend, the ANN is over-fitting and it is time to stop the training process. Finally, the verification set is a part of database to verify the validity of the trained ANN. Obviously this data set has not been used to train the ANN. It is worth mentioning that the elapsed time to perform the training process (learning, calibration and verification) is negligible compared to the reservoir simulation run-time. The training, calibration and verification included 80%, 10% and 10% of the data in the database Validation the SRM by a Blind Realization The trained SRM is validated against a complete blind realization of the reservoir. Therefore, a new simulation run was made. This realization has a permeability distribution which is completely different from the ten realizations used in training process. However it should be noted that the permeability range should be in the range of values used in the training runs. Finally, the trained SRM was applied to predict the oil rate from the blind realization inputs History Matching The trained and validated SRM is ready to be used in the process of history matching. In order to accomplish the history matching, permeability values at each defined tier have been adjusted. The oil rates predicted by the SRM are compared against the real production rates. This procedure must be repeated until an acceptable match in each well is obtained. The objective functions to compare the results are presented in Equation 1 and Equation 2. Equation 1 calculates the difference between measured and actual data at the well level and Equation 2 includes the well level objective function in a global objective function at the field level. In Equation 1, the subscripts and represent well and time respectively. is the total number of measured data points (In this study is 30 corresponding to 30 years of annual oil rate existing for each well). is the predicted production by SRM and is measured production data. is the scale calculated by subtracting the maximum and minimum of measured production data for well. In the global objective function, is the objective function for well, and is the total number of wells (24 wells in this study). In practice, it is also common to consider that the quality and importance of measured data may be different for some specific wells. is the defined weight for well. In this work, all the wells were considered equally important and the weight coefficient is one for all of them.

13 SPE SPE MS 13 Equation 1: Individual well objective function Equation 2: Global (Field) objective function 8. Results This section intends to present the results for one of the wells (well # 20) for different steps of developing and applying the SRM. The results for all wells can be found in somewhere else (Shahkarami 2012). Figure 9 displays the results after the training process; the chart portrays the oil rate profile for 30 years of production comparing SRM results with the simulator outputs. The blue squares represent the SRM and the red line with stars shows the numerical simulator results. It is evident that SRM can reproduce the simulator results accurately. Figure 10 shows the results of blind verification realization. As was mentioned earlier, a blind realization was used for testing the SRM. The blind set consists of a realization, which has not been seen by SRM in the training process. Therefore, this graph validates the potential of SRM to predict a realization performance out of the training dataset and displays the robustness of the technique. Finally figure 11 is a snapshot of the history matching (HM) results for this well. This graph is the comparison of the SRM outcome with the measured production data. The distribution of matched values of permeability is shown in figure 12. The right side of this figure pictures some shots of the matched permeability map, while the left side shots are the actual permeability distribution. Figure 13 demonstrates the error distribution of the results after history matching process. Figure 14 is an error frequency distribution of these results, as well. 9. Summary and Concluding Remarks An SRM was created for a synthetic but highly heterogeneous oil field, with 24 production wells and 30 years of production history. The goal was achieving a match of the production history by tuning permeability distribution. SRM was trained using ten heterogeneous realizations and then validated by a blind simulation run. Finally, the full field model was substituted by the trained SRM to perform the history match process.

14 14 SPE SPE MS SRM was able to accurately match the results of training realizations. Robustness of SRM to predict the behavior of a realization which has not been seen by SRM during learning process (blind case) was further verified. Matching the actual data was perfect and comparison between the variable history matched property and actual distribution supports the claim. The pattern recognition characteristics of SRM make it possible to achieve the results in a fraction of second. Although the running time for the case study of reservoir model used in this study is not the concern, the number of simulation runs to attain a desired match is time and power consuming. In numerical reservoir simulator, by increasing the size and complexity of the components the run-time can increase in orders of magnitude. Nevertheless due to pattern recognition capability of SRM this technology, it will not be an issue for SRM. The results of this study could be counted as a proof of concept for showing the potential of this novel technology (SRM) to assist history matching process. Increasing the uncertain variables and implementing the technology on a more sophisticated (and real life) case study is the goal of the authors to achieve in future.

15 SPE SPE MS 15 Figure 1- An artificial neural network is an interconnected group of nodes. Figure 2- Steps to develop an SRM.

16 16 SPE SPE MS Figure 3-Three and two dimensional top views of simulation model. Figure 4- Three and two dimensional views of porosity distribution. Figure 5- Three and two dimensional views of thickness map.

17 SPE SPE MS 17 Figure 6- Given permeability map for the base case. Static Data Dynamic Data Identifier Well Location Static Reservoir Property (at 4 tiers and offset wells) Time Operational Constraint Production Rate Index Well Name Run Number i j k X Y Z Top Porosity Permeability Grid Thickness Bottom-hole pressure Oil Rate at t Oil Rate at a time step behind (t-1) Figure 7- Different types of data in the spatio-temporal database.

18 18 SPE SPE MS Figure 8- The results of KPI analysis. Pre-modeling analysis of KPI is an appropriate guide to select the inputs of ANNs. Figure 9- Training results for well # 20.

19 SPE SPE MS 19 Figure 10- Blind run results for well # 20. Figure 11- Comparison of the matched results coming from SRM with actual outputs (simulator) for well # 20.

20 20 SPE SPE MS Figure 12- Comparison of matched and actual Permeability distributions. Figure 13- Error distribution for the history matched results.

21 SPE SPE MS 21 Figure 14- Error frequency distribution for the history match results.

22 22 SPE SPE MS Bibliography Abdollahzadeh, A. et al On Population Diversity Measures of the Evolutionary Algorithms Used in History Matching. SPE Europec/EAGE Annual Conference, 4-7 June, Copenhagen, Denmark Adebiyi, A.A., C.K. Ayo, M.O Adebiyi, and O.S Otokiti Stock Price Prediction using Neural Network with Hybridized Market Indicators. Journal of Emerging Trends in Computing and Information Sciences. Ahmed, T., C.A. Link, K.W. Porter, C.J. Wideman, P. Himmer, and J. Braun Application of Neural Network Parameter Prediction in Reservoir Characterization and Simulation - A Case History: The Rabbit Hills Field. Latin American and Caribbean Petroleum Engineering Conference. Rio de Janeiro, Brazil. Ali, J K. Neural Networks: A New Tool for the Petroleum Industry? European Petroleum Computer Conference. Aberdeen, United Kingdom. Al-Kaabi, A U, and W J Lee An Artificial Neural Network Approach To Identify the Well Test Interpretation Model: Applications. SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana. Amato, F., A. López, E María, P. Vaňhara, and A. Hampl Artificial neural networks in medical diagnosis. Journal of Applied Biomedicine: Amini, S. et al Uncertainty Analysis of a CO2 Sequestration Project Using Surrogate Reservoir Modeling Technique. SPE Western Regional Meeting. Bakersfield, California, USA. Aminzadeh, F., and P. degroot A Neural Networks Based Seismic Object Detection Technique. SEG Annual Meeting. Houston, Texas. Athichanagorn, S, and Horne, R N Automatic Parameter Estimation From Well Test Data Using Artificial Neural Network. SPE Annual Technical Conference and Exhibition. Dallas, Texas. Baesens, B., Setiono, R., Mues, C., and Vanthienen,J Using Neural Network Rule Extraction and Decision Tables for Credit-Risk Evaluation. Management Science: Baldwin, J. L., Otte, D.N. and Whealtley, C. L Computer Emulation of Human Mental Processes: Application of Neural Network Simulators to Problems in Well Log Interpretation. SPE Annual Technical Conference and Exhibition. San Antonio, Texas, USA. Briones, M F, G.A. Rojas, J.A. Moreno, and E R Martinez. "Application of Neural Networks in the Prediction of Reservoir Hydrocarbon Mixture Composition From Production Data." SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana: Society of Petroleum Engineers, Bush, M.D., and Carter, J.N Application of a Modified Genetic Algorithm to Parameter Estimation in Petroleum Industry.Intelligent Engineering Systems through Artificial Neural Networks(6): 397. Chattopadhyay, M. et al Application of artificial neural network in market segmentation: A review on recent trends. Management Science Letters: Chen, W.H., Gavalas, G.cR., Seinfeld, J. H. and Wasserman, M. L A New Algorithm for Automatic History Matching. SPE-AIME 48th Annual Fall Meeting. Las Vegas, USA.

23 SPE SPE MS 23 Cheng, H. et al A Structured Approach for Probabilistic-Assisted History Matching Using Evolutionary Algorithms: Tengiz Field Applications. SPE Annual Technical Conference and Exhibition, September, Denver, Colorado, USA. Cheng-Dang, Z. et al Direct Identification of Hydrocarbon From Well Logs: A Neural Network Interpretation Approach.Petroleum Society of Canada, Annual Technical Meeting. Calgary, Alberta, Canada. Christie, M. et al An Adaptive Evolutionary Algorithm for History-Matching. EAGE Annual Conference & Exhibition incorporating SPE Europec, June, London, UK CMG, Computer Modelling Group Computer Modelling Group Manual. Coats, K., Dempsey, J. and Henderson, J A New Technique for Determining Reservoir Description from Field Performance Data. 43rd SPE Annual Fall Meeting. Houston, Texas, USA. Cullick, A.S., Johnson, D.and Shi, G Improved and More-Rapid History Matching With a Nonlinear Proxy and Global Optimization. SPE Annual Technical Conference and Exhibition. San Antonio, Texas, USA. David, H. J Seismic Attribute Calibration Using Neural Networks. SEG Annual Meeting. Washington, DC, USA. Devadhas, G., Pushpakumar, S. and Mary, D.M ANN Based MARC Controller Design for an Industrial Chemical Process. International Conference on Computing, Electronics and Electrical Technologies. Ershaghi, I. et al A Robust Neural Network Model for Pattern Recognition of Pressure Transient Test Data. SPE Annual Technical Conference and Exhibition. Houston, Texas, USA. Fanchi, John R Principles of Applied Reservoir Simulation. Elsevier Science and Technology Books, Inc. Ferraro, P. and Verga, F Use Of Evolutionary Algorithms In Single And Multi- Objective Optimization Techniques For Assisted History Matching. Offshore Mediterranean Conference and Exhibition, March, Ravenna, Italy. Gao, G., Li, G. and Reynolds, A.C A Stochastic Optimization Algorithm for Automatic History Matching.Society of Petroleum Engineers. Gharbi, R.B., and Elsharkawy, A.M Neural Network Model for Estimating The PVT Properties of Middle East Crude Oils. Middle East Oil Show and Conference. Bahrain. Hagan, M. T., Demuth, H.B. and Beale, M. H Neural Network Design. Hagan Publishing. Hajizadeh, Y Ants Can Do History Matching.SPE Annual Technical Conference and Exhibition. Florence, Italy. Hajizadeh, Y., Christie, M. and Demyanov, V Ant Colony Optimization for History Matching.SPE EUROPEC/EAGE Annual Conference and Exhibition. Amsterdam, The Netherlands. Haykin, S Neural Networks: A Comprehensive Foundation. Prentice Hall. He, N., and Chambers, K.T Calibrate Flow Simulation Models With Well-Test Data to Improve History Matching. SPE Annual Technical Conference and Exhibition. Intelligent Solutions Inc (accessed 2011). Jacquard, P., and Jain, C Permeability Distribution From Field Pressure Data.SPE: 281. Jahns, H.O A Rapid Method for Obtaining a Two-Dimensional Reservoir Description From Well Pressure Response Data.SPE: 315.

24 24 SPE SPE MS Jong-Se, L., and Jungwhan,K Reservoir Porosity and Permeability Estimation from Well Logs using Fuzzy Logic and Neural Networks. SPE Asia Pacific Oil and Gas Conference and Exhibition. Perth, Australia. Kabir, C.S., Chien, M.C.H. and Landa, J.L Experiences with automated history matching. SPE. Kalam, M.Z., Al-Alawi, S.M and Al-Mukheini, M Assessment of Formation Damage Using Artificial Neural Networks.SPE Formation Damage Control Symposium. Lafayette, Louisiana, USA. Key, S.C. et al Fault And Fracture Classification Using Artifical Neural Networks - Case Study From the Ekofisk Field. SEG Annual Meeting. Dallas, Texas, USA. Kruger, W. D Determining Areal Permeability Distribution by Calculations.J. Pet. Tech.:691. Lei, S., and Xing-cheng, W Artificial Neural Networks:Current Applications in Modern Medicine. International Conference on Computer and Communication Technologies in Agriculture Engineering. Li, E Artificial neural networks and their business applications. Information & Management: Masoud, N Neural Network Knowledge-Based Modeling of Rock Properties Based on Well Log Databases. SPE Western Regional Meeting. Bakersfield, California, USA. McCulloch, W.S., and Pitts, W.H A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics Vol. 5 : Mohaghegh, S D Neural Network: What It Can Do for Petroleum Engineers. Journal of Petroleum Technology. Mohaghegh., S D., Arefi, R., Ameri, S., and Rose, D Design and Development of An Artificial Neural Network for Estimation of Formation Permeability. SPE Computer Applications. Mohaghegh, S D Quantifying Uncertainties Associated With Reservoir Simulation Studies Using a Surrogate Reservoir Model. SPE Annual Technical Conference and Exhibition. San Antonio, Texas, USA Mohaghegh, S D Artificial Intelligence and Data Mining: Enabling Technology for Smart Fields. SPE's The Way Ahead Journal : Mohaghegh, S D., A. Modavi, H. Hafez, and M. Haajizadeh Development of Surrogate Reservoir Model (SRM) for Fast Track Analysis of a Complex Reservoir. International Journal of Oil, Gas and Coal Technology : Mohaghegh, S D Surrogate Reservoir Model. European Geological Union General Assembly. EGU Vienna, Austria. Mohaghegh, S D Reservoir Simulation and Modeling Based on Pattern Recognition. SPE Digital Energy Conference and Exhibition. Woodlands, Texas, USA. Mohaghegh, S D. et al. 2012a. Application of Surrogate Reservoir Models (SRM) to an Onshore Green Field in Saudi Arabia; Case Study. North Africa Technical Conference and Exhibition. Cairo, Egypt. Mohaghegh, S D. et al. 2012b. Application of Well-Base Surrogate Reservoir Models (SRMs) to Two Offshore Fields in Saudi Arabia, Case Study. SPE Western Regional Meeting. Bakersfield, California, USA. Mohaghegh, S D., Amini, S., Gholami, V., Gaskari, R. and Bromhal, G Grid-Based Surrogate Reservoir Modeling (SRM) for Fast Track Analysis of Numerical Reservoir Simulation Models at the Gridblock Level. SPE Western Regional Meeting. Bakersfield, California, USA.

25 SPE SPE MS 25 Nikravesh, M., A.R. Kovscek, R.M. Johnston, and T.W. Patzek Prediction of Formation Damage During Fluid Injection into Fractured, Low Permeability Reservoirs via Neural Networks. SPE Formation Damage Control Symposium. Lafayette, Louisiana, USA. Oloso, Munirudeen A. et al Prediction of Crude Oil Viscosity and Gas/Oil Ratio Curves Using Recent Advances to Neural Networks. SPE/EAGE Reservoir Characterization and Simulation Conference. Abu Dhabi, UAE. Osman, E. A, Abdel-Wahhab, O. A. and A Al-Marhoun, M Prediction of Oil PVT Properties Using Neural Networks. SPE Middle East Oil Show. Bahrain. Ouenes, A., et al A New Algorithm for Automatic History Matching: Application of Simulated Annealing Method (SAM) to Reservoir Inverse Modeling. Society of Petroleum Engineers. Palatnic, B., L. Zakirov, S. Haugen, and J. van Roosmalen New Approaches to Multiple History Matching. Seventh European Symposium on Improved Oil Recovery. Moscow, Russia. Rodriguez, Adolfo A., Hector Klie, Mary F. Wheeler, and Rafael Banchs Assessing Multiple Resolution Scales in History Matching With Metamodels. SPE Reservoir Simulation Symposium. Houston, Texas, USA. Roth, Gunter, and Albert Tarantoia Inversion of Seismic Waveforms Using Neural Networks. SEG Annual Meeting. New Orleans, Louisiana, USA. Sadiq, T., and I.S. Nashawi Using Neural Networks for Prediction of Formation Fracture Gradie. SPE/CIM International Conference on Horizontal Well Technology. Calgary, Alberta, Canada. Sampaio, T.P., V.J. Filho, M. Ferreira, and A. de Sa Neto An Application of Feed Forward Neural Network as Nonlinear Proxies for Use During the History Matching Phase.Latin American and Caribbean Petroleum Engineering Conference. Cartagena de Indias, Colombia. Sarcià, S., G. Cantone, and V. Basili A Statistical Neural Network Framework for Risk Management Process - From the Proposal to its Preliminary Validation for Efficiency. Second International Conference on Software and Data Technologies. Barcelona, Spain. Schulze-Riegert, et al Evolutionary algorithms applied to historymatching of complex reservoirs. SPE Reserv. Evalu. Eng.5(2), Silva, P. C., C. Maschio, and D. J. Schiozer Application of Neural Network and Global Optimization in History Matching.Journal of Canadian Petroleum Technology. Silva, P. C., C. Maschio, and D. J. Schiozer Applications of the Soft Computing in the Automated History Matching. Canadian International Petroleum Conference. Calgary, Alberta, Canada. Singh, Virendra et al Neural Networks And Their Applications In Lithostratigraphic Interpretation of Seismic Data For Reservoir Characterization. World Petroleum Congress. Madrid, Spain. Slater, G., and E. Durrer Adjustment of Reservoir Simulation Models to Match Field Performance. SPE 45th Annul Fall Meeting. Houston, Texas, USA. Shahkarami, A Artificial intelligence assisted history matching: proof of concept. Thesis (M.S.)-West Virginia University. Sultan, A.J., A. Ouenes, and W.W. Weiss Automatic History Matching for an Integrated Reservoir Description and Improving Oil Recovery. SPE Permian Basin Oil and Gas Recovery Conference. Midland, Texas, USA.