Application of Well-Based Surrogate Reservoir Models (SRMs) to Two Offshore Fields in Saudi Arabia, Case Study

SPE 153845 Application of Well-Based Surrogate Reservoir Models (SRMs) to Two Offshore Fields in Saudi Arabia, Case Study Shahab D. Mohaghegh, West Virginia University & Intelligent Solutions, Inc., Jim Liu, Saudi Aramco, Razi Gaskari, and Mohammad Maysami, Intelligent Solutions, Inc., and Olugbenga Olukoko, Saudi Aramco Copyright 2012, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Western North American Regional Meeting held in Bakersfield, California, USA, 19 23 March 2012. 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 Well-based Surrogate Reservoir Model (SRM) may be classified as a new technology for building proxy models that represent large, complex numerical reservoir simulation models. The well-based SRM has several advantages over traditional proxy models, such as response surfaces or reduced models. These advantages include (1) to develop an SRM one does not need to approximate the existing simulation model, (2) the number of simulation runs required for the development of an SRM is at least an order of magnitude less than traditional proxy models, and (3) above and beyond representing the pressure and production profiles at each well individually, SRM can replicate, with high accuracy, the pressure and saturation changes at each grid block. Well-based SRM is based on the pattern recognition capabilities of artificial intelligence and data mining (AI&DM) that is also referred to as predictive analytics. During the development process the SRM is trained to learn the principles of fluid flow through porous media as applied to the complexities of the reservoir being modeled. The numerical reservoir simulation model is used for two purposes: (1) to teach the SRM the physics of fluid flow through porous media as applied to the specific reservoir that is being modeled, and (2) to teach the SRM the complexities of the heterogeneous reservoir represented by the geological model and its impact on the fluid production and pressure changes in the reservoir. Application of well-based SRM to two offshore fields in Saudi Arabia is demonstrated. The simulation model of these fields includes millions of grid blocks and tens of producing and injection wells. There are four producing layers in these assets that are contributing to production. In this paper we provide the details that is involved in development of the SRM and show the result of matching the production from the all the wells. We also present the validation of the SRM through matching the results of blind simulation runs. The steps in the development of the SRM includes design of the required simulation runs (usually less than 20 simulation runs are sufficient), identifying the key performance indicators that control the pressure and production in the model, identification of input parameters for the SRM, training and calibration of the SRM and finally validation of the SRM using blind simulation runs. Introduction The two offshore fields that are the subject of this study are field J and field K. Both fields are producing from carbonate reservoirs in anticlinal traps consisting of an upward shoaling sequence of marine carbonate capped by anhydrite. The structure is an oval-shaped and somewhat tilted anticline, most likely formed by diapirism underneath. The formation consists primarily of limestone and dolomites with reservoir heterogeneities characterized by the existence of high permeability zones, faults and fractures. The review of logs suggests that reservoir characteristics can vary significantly over relative short distances. Four geologic horizons were identified based on log characteristics as reservoir A, B, C and D, and they are separated by a relatively thick non-reservoir rock; however, this separation seems to diminish and possibly vanish in uncertain parts of the

2 Well-based SRM for Two Offshore Green Fields in Saudi Arabia SPE 153845 reservoir. Not all reservoirs are fully developed or present in all both fields. Different oil-water content was interpreted for these reservoirs. The API gravity of the oil varies from 22 to 35 in the oil bearing zones and the crude viscosity varies from 1.5 cp to 9 cp. The reservoirs are initially undersaturated and are currently undeveloped. Figures 1 and 2 are shown to demonstrate the heterogeneity of these fields. Fig. 1. Porosity and permeability maps of field J in Saudi Arabia. Fig. 2. Porosity, water saturation and permeability maps of field K in Saudi Arabia. Reservoir simulation models were constructed for each of the two fields, primarily for field development planning purposes using the in-house massively parallel processing simulator. The models are 3-component (oil-water-gas), 3-phase, and singleporosity single-permeability; although no free gas in the reservoir is expected due to planned pressure maintenance by water

SPE 153845 Mohaghegh, Liu, Gaskari, Maysami and Olukoko 3 injection. Specific features of the simulation models are as follows: a. The field K model consists of 81,000 cells with an areal grid size of 250 m x 250 m. The model consists of 23 vertical production wells and 10 vertical water injection wells. It takes only 2 minutes for a single run of this model on the massively parallel computer clusters. b. The field J model consists of 4.8 million cells with areal grid size of 125 m x 125 m. The model consists of 50 vertical production wells and 36 vertical water injection wells. The run time of this model is 30 minutes on the massively parallel computer clusters. Due to the limited number of wells that have been drilled in these fields, considerable uncertainties exist in reservoir description as well as in engineering data, an uncertainty/risk analysis is necessary to realistically assess the field development potentials. Surrogate Reservoir Models (SRM) Classified as an AI-based Reservoir Model (Mohaghegh, 2011), Surrogate Reservoir Model (SRM) is defined as an accurate replica of a reservoir simulation model that runs in real-time. Developed for the first time to replicate a mature field in the Middle East (Mohaghegh, 2006a, 2006b, 2006c and Mohaghegh, 2009), SRM can be applied to both mature and green fields. SRMs are ensemble of multiple, interconnected neuro-fuzzy systems that are trained to adaptively learn the fluid flow behavior from a multi-well, multilayer reservoir simulation model, such that it can reproduce the results similar to those of the full field reservoir simulation model (with high accuracy) in real-time (a fraction of a second per SRM run). In a recent paper (Mohaghegh, 2012) a reasonably detailed discussion about the specifications of SRM was presented. In this discussion, steps involved in development of a SRM as well as it distinct features, when compared to proxy and reduced models were discussed. In this paper we only present the results of building and validating two SRMs for two offshore green fields in Saudi Arabia. The common features for SRM development in both fields are the number of the simulation runs that were designed and implemented. One of the most attractive and innovative features of SRM is that only a small number of simulation runs is required for its development. A total of nine simulation runs were designed for the development of the SRM for each of the fields. Figure 3 summarizes the operational constraints that were used for each of the nine simulation runs. In this figure it is shown that the bottom-hole pressure (BHP) and maximum liquid rate in each run were varied within the expected operational ranges. These operational constraints were imposed on all the producing wells in the field. While in five of the simulation runs, BHP was kept constant for the entire 20 years of production; in four of the simulation runs the BHP were varied as a function of time. The schemes for the variation of the BHP are shown in Fig. 4. Fig. 3. Nine simulation runs designed for the development of the SRM for fields K and J.

4 Well-based SRM for Two Offshore Green Fields in Saudi Arabia SPE 153845 Fig. 4. Variable BHP constraints in step and continuous decrease used in the simulation runs. Characteristics of SRMs Building proxy models have a long history in our industry. Proxy models are needed for fast track analysis of the complex reservoir simulation models. Their use in reservoir management, field development planning and optimization and history matching has been well documented. Given the fact that SRM reproduces the results of numerical simulation models in a fraction of a second and quite accurately, it is natural to see interest and curiosity in how SRMs work and how they are built. Results cited in the literature (Mohaghegh, 2006a, 2006b, 2006c, 2009, 2011, 2012) that are mainly actual field applications of SRM and demonstrate its accuracy and effectiveness come to sharp contrast with conclusions reached by others (Zubarev, 2009) that have found the use of Neural Network in building proxy models a disappointing exercise. This is not the first time that a technology has been misused and consequently misjudged and prematurely dismissed. The brief explanation provided in Zubarev s study on how the Neural Network has been used to build the proxy model presents ample reasoning on why it did not work. Without going into the details of what was wrong with the way the Neural Network was used in the aforementioned study, it suffices to say that whenever Neural Networks have been used purely as a regression tool it has resulted in disappointing outcomes. Neural Networks should not be used merely as a regression tool, without paying attention that as part of a larger toolset, it attempts to observe, learn and generalize. This is due to the fact that artificial intelligence and data mining (AI&DM) (as an overarching discipline) are far more than regression tools and certain understanding of machine learning activities are required for their effective use and deployment. Effective use of AI&DM requires the realization that by using them we are embarking upon a new way of thinking and a new paradigm for problem solving. Therefore, our current intuition on how things work, for example in reservoir simulation and modeling, may not necessarily apply when using AI&DM in reservoir modeling. In other words, some aspects of SRM may even be counter-intuitive. Let us clarify this with an example. We have developed the intuition that as reservoirs become simpler (i.e., homogeneous and small number of wells, small number of grid blocks, etc., a.k.a. toy problems or academic problems) it becomes easier to solve and analyze them and consequently it is easier to build proxy models that accurately represent them. This is true as long as we are using non-ai based techniques, such as parametric statistical tools or analytical solutions to build the proxy models; however, we have learned that building a SRM for such simplified (and unrealistic) problems is a very hard task and essentially worthless. In other words, (and this may sound counter-intuitive) the harder the problem gets (as the reservoir gets closer to real cases with plenty of heterogeneity and large number of wells) the more realistic it becomes to build a successful SRM. Let us try to explain why SRM works in this counter-intuitive fashion. Since SRM is based on data-driven technologies and uses machine learning, it is built using observations of the phenomena being modeled. These observations are represented in the form of data. Data is organized in the form of records, where each record represents a pair of input and output vectors. Given the dynamic nature of the fluid flow in the porous media, the input vector must include static and dynamic characteristics of the reservoir while the output vector includes pressure and/or production rates (including water cut and gas-oil ratio) at the wells. Each record in the data set must provide an instance or an example of dynamic nature of the problem that we are trying to model. Everything and anything that we wish for the SRM to learn (and then be able to generalize and replicate) must be included in this data set. It would be ludicrous to expect SRM to learn, generalize and reproduce something it has never been taught (please note we are not saying something it has never seen). On the other hand, it must be noted that we are using terms, such as teaching and learning and generalization. This is due to the fact that SRM can learn concepts, such as higher transmissibilities, resulting in a higher flow or proximity to the wells that can cause interference. Therefore, as long as we are using the right toolset, we need to just make sure that examples of the concepts that we are interested in (in a given reservoir modeling example) are represented in the data set that is used to train, calibrate and validate the SRM. As mentioned before and documented in previous publications, one of the most attractive attributes of SRM is that unlike other proxy models that require several hundreds of simulation runs for their development, SRM requires only a small number of simulation runs (Usually 10 to 20 runs, at the most). One might ask How is it possible for SRM that has been developed with only a small number of runs to be generalized enough to reproduce accurate simulation model responses for completely blind runs? The answer lies within the innovative way of using the results of the simulation runs to build a

SPE 153845 Mohaghegh, Liu, Gaskari, Maysami and Olukoko 5 representative spatio-temporal database. This database that forms the foundation of the SRM must include all that one wishes to teach the SRM. In other words, all that you want the SRM to learn (and therefore be able to accurately reproduce) must be included in this spatio-temporal database. The spatio-temporal database is uniquely built for each problem based on reservoir simulation runs. For a given reservoir, it may be important for us to teach fluid flow through porous media to SRM such that it can understand the impact of changes in porosity, permeability (within the ranges that are represented in the given reservoir), rock types and facies on fluid production in any given well. Furthermore, it should learn the impact of offset well productions and injections as well as operational constraints on the well. Given the fact that conceptually similar interactions take place throughout the reservoir between the reservoir rock, the reservoir fluid and the injection and production wells, a single simulation run has so much to teach to an SRM. It all comes down to the way these observations are isolated, extracted and represented in the spatio-temporal database. SRM for the Field K Here we will present the results of SRM for field K. As it has been previously discussed (Mohaghegh, 2012) the results from the nine simulation runs are used to develop a representative spatio-temporal database that is used as the foundation of the SRM. The spatio-temporal database is then used to train and calibrate the SRM. Upon completion of the training and calibration, the SRM has learned the intricate details of fluid flow in this reservoir and is capable of generalizing the simulation model s behavior and accurately replicating its results. The generalization capabilities of the SRM are validated through the use of a new and completely blind simulation run. Fig. 5. Comparison of SRM results with the in-house simulator: Oil and gas rates for the entire asset as BHPs change according to time variations shown in Fig. 4. Figures 5 through 8 show examples of SRM performance vs. the simulation runs for the nine runs that were used for training and calibration purposes. In these figures, production rates (bbls/yr) and cumulative production are shown for both oil and gas. Figures 5 and 6 show the results of SRM as it compares to the in-house simulator for the entire field for two of the runs. In Fig. 5, the BHP for all wells was modified as a function of time (shown in Fig. 4 - left) while the maximum fluid rate was set at 10,000 barrels. In Fig. 6, the BHP pressure for all wells was set at 500 psi while the maximum fluid rate was set at 10,000 barrels. Figures 7 and 8 include similar graphs for two of the wells in field K, belonging to two of the simulation runs. The accuracy of SRM results in replicating the results of the simulation runs are clearly demonstrated in these figures.

6 Well-based SRM for Two Offshore Green Fields in Saudi Arabia SPE 153845 Fig. 6. Comparison of SRM results with the in-house simulator. Oil and gas rates for the entire asset. Fig. 7. Comparison of SRM results with the in-house simulator. Oil and gas rates for one of the wells in the asset. Fig. 8. Comparison of SRM results with the in-house simulator. Oil and gas rates for one of the wells in the asset.

SPE 153845 Mohaghegh, Liu, Gaskari, Maysami and Olukoko 7 Fig. 9. SRM comparison of SRM results with the in-house simulator: Oil and gas rates for the entire asset as BHPs change according to time variations shown in Fig. 4. Fig. 10. SRM validation using a blind run. Comparison of SRM with the in-house simulator. Oil and gas rates for one of the wells. Fig. 11. SRM validation using a blind run. Comparison of SRM with the in-house simulator. Oil and gas rates for one of the wells.

8 Well-based SRM for Two Offshore Green Fields in Saudi Arabia SPE 153845 Fig. 12. Quantification of uncertainties associated with permeability using SRM and Monte Carlo simulation. Fig. 13. Quantification of uncertainties associated with permeability using SRM and Monte Carlo simulation.

SPE 153845 Mohaghegh, Liu, Gaskari, Maysami and Olukoko 9 Figures 9, 10 and 11 show examples of SRM performance vs. blind simulation runs. None of the nine runs that were used for training and calibration purposes were constrained with this combination (BHP of 1,000 psi and maximum rate of 15,000 bbls). In these figures production rates (bbls/yr) and cumulative production are shown for both oil and gas. In Fig. 9, the results of SRM are shown as it compares to the in-house simulator for the entire field, while Figs. 10 and 11 show the results of the blind validation test on two individual wells. SRM (together with Monte Carlo simulation) can be effectively used as a tool for uncertainty quantification since thousands of SRM runs can be made in a few seconds. In Figs. 12 and 13, two such examples are presented. In these figures uncertainties associated with permeability values (vertically, in all reservoir layers and spatially, in an area of several tens of acres) are quantified for the first year oil production. P10, P50 and P90 can be quickly identified as permeability values are examined at any given range and distribution. SRM for Field J Field J is a larger field with a considerably larger simulation model. As mentioned before, this field includes nearly 5 million grid blocks. At 30 minutes per run, an uncertainty analysis or field development analysis study that may require 10,000 simulations per run will take about 7 months of continuous computational time on a massive cluster of computers. Similar analysis would need minutes of computational time on a desktop PC using SRM. Next, the results of SRM for field J are presented. As previously discussed, results from nine simulation runs are used to train and calibrate the SRM. Fig. 14. Comparison of SRM results with the in-house simulator: Oil and gas rates for the entire asset as BHPs change according to time variations shown in Fig. 4. Fig. 15. Comparison of SRM results with the in-house simulator. Oil and gas rates for the entire asset.

10 Well-based SRM for Two Offshore Green Fields in Saudi Arabia SPE 153845 Fig. 16. Comparison of SRM results with the in-house simulator. Oil and gas rates for one of the wells in the asset. Fig. 17. Comparison of SRM results with the in-house simulator. Oil and gas rates for one of the wells in the asset. Figures 18, 19 and 20 show examples of SRM performance vs. a blind simulation run for field J. Same as before, none of the nine runs that were used for training and calibration purposes were constrained with the combination (BHP of 1,000 psi and maximum rate of 15,000 bbls) that is used for this blind run. In these figures, production rates (bbls/yr) and cumulative production are shown for both oil and gas. Fig. 18. SRM validation using a blind simulation run. Comparison of SRM results with the in-house simulator. Oil and gas rates for the entire asset.

SPE 153845 Mohaghegh, Liu, Gaskari, Maysami and Olukoko 11 Fig. 19. SRM validation using a blind run. Comparison of SRM with the in-house simulator. Oil and gas rates for one of the wells. Fig. 20. SRM validation using a blind run. Comparison of SRM with the in-house simulator. Oil and gas rates for one of the wells. Figure 18 shows the results of SRM as it compares to the in-house simulator for the entire field while Figs. 19 and 20 show the results of the blind validation test on two individual wells. Effective use of SRM in conjunction with Monte Carlo simulation can provide uncertainty quantification analysis as shown in Figs. 21 and 22. Thousands of SRM runs can be generated in a few seconds to fulfill the requirement of the Monte Carlo simulation for uncertainty analysis. In Figs. 21 and 22, two such examples are presented for two wells in field J. In these figures, uncertainties associated with permeability values (vertically, in all reservoir layers and spatially, in an area of several tens of acres) are quantified for the first year of oil production. P10, P50 and P90 are identified as permeability values are examined for any given range and distributions.

12 Well-based SRM for Two Offshore Green Fields in Saudi Arabia SPE 153845 Fig. 21. Quantification of uncertainties associated with permeability using SRM and Monte Carlo simulation. Fig. 22. Quantification of uncertainties associated with permeability using SRM and Monte Carlo simulation.

SPE 153845 Mohaghegh, Liu, Gaskari, Maysami and Olukoko 13 Conclusions Results of training, calibration and validation of well-based SRMs for two offshore green fields in Saudi Arabia were presented. Use of SRM in quantification of uncertainties associated with the static model using Monte Carlo simulation was demonstrated. SRMs are accurate replicas of reservoir simulation models that run in fraction of a second and can serve as effective reservoir management tools. References Mohaghegh, S.D., Modavi, A., Hafez, H., Haajizadeh, M., Kenawy, M. and Guruswamy, S., (2006a) Development of Surrogate Reservoir Models (SRM) for Fast Track Analysis of Complex Reservoirs. SPE 99667, Proceedings, 2006 SPE Intelligent Energy Conference and Exhibition. 11-13 April 2006, Amsterdam, The Netherlands. Mohaghegh, S.D., Hafez, H., Gaskari, R., Haajizadeh, M. and Kenawy, M., (2006b) Uncertainty Analysis of a Giant Oil Field in the Middle East Using Surrogate Reservoir Model. SPE 101474, Proceedings, 2006 Abu Dhabi International Petroleum Exhibition and Conference. Abu Dhabi, U.A.E., 5-8 November 2006. Mohaghegh, S.D., (2006) Quantifying Uncertainties Associated with Reservoir Simulation Studies Using Surrogate Reservoir Models. SPE 102492, Proceedings, 2006 SPE Annual Conference & Exhibition. 24-27 September 2006, San Antonio, Texas. Mohaghegh, S.D., (2009) Development of Surrogate Reservoir Model (SRM) for Fast Track Analysis of a Complex Reservoir. International Journal of Oil, Gas and Coal Technology, February 2009, Vol. 2, No. 1, pp. 2-23. Mohaghegh, S.D., (2011) Reservoir Simulation and Modeling Based on Pattern Recognition. SPE 143179, SPE Digital Energy Conference. The Woodlands, Texas, 19-21 April 2011. Mohaghegh, S.D., (2012) Application of Surrogate Reservoir Model (SRM) to an Onshore Green Field in Saudi Arabia; Case Study. SPE 151994, the North Africa Technical Conference and Exhibition, Cairo, Egypt, 20-22 February 2012. Zubarev, D.I. (2009), Pros and Cons of Applying Proxy Models as a Substitute for Full Reservoir Simulations, SPE 124815, SPE Annual Technical Conference and Exhibition, 4-7 October 2009, New Orleans, Louisiana.