Summary Conventional direct optimization methods and evolutionary algorithms are applied to the problem of history matching in reservoir engineering. The advantage of parallel computing for the optimization of complex reservoir models is investigated. Methods to improve the convergence of evolutionary algorithms by introducing prior information are applied. The potential of using optimization methods for the problem of reservoir modeling in various modeling phases is discussed. The methodology is illustrated on realistic simulation cases. In conclusion, results suggest that evolution strategies can be applied successfully to generate possible solutions in the early modeling phase. Introduction Reservoir modeling becomes more difficult as reservoirs become more complex, and requirements for future production estimations need to be more accurate. To obtain an acceptable description of a reservoir, many different simulation runs in completely different regions of the search space must be performed. Owing to a lack of time and increasing pressure to produce results, test runs are often limited to a few "most plausible" sets of model parameters. This is the starting point of the concept followed in this paper, which is to define a methodology capable of supporting reservoir engineers in identifying different starting points in a multidimensional search space, with a high potential to generate calculated well production data that matches the measured data. Usually, limited information on the geological and geophysical backgrounds of the reservoir is available from well tests, seismic surveys, and logs. Applications of reservoir simulations that intend to reproduce measured well-production data on the basis of unknown model parameters define a procedure to solve the inverse problem of reservoir modeling. This procedure is often called history matching. History matching is defined by finding a set of model parameters that minimize the difference between calculated and observed measurement values like pressure and fluid-production rates. In the special case of a gas storage for which seasonal cycling gas injection and production are known, this might simply reduce to the pressure. More generally, for a three-phase problem, this will be pressure; oil-, gas-, and water-production rates; and fluid contacts. The procedure of history matching is time-consuming and difficult. The formulation of the problem is of a general nature and is not reduced to history matching in reservoir engineering. In many engineering applications, simulations are based on a multidimensional solution space that generally contains a number of local optima. For reservoir characterizations, a number of previous works have concentrated on local gradient-based optimization strategies. 1–5 Gómez et al.6 have coupled a gradient method to a tunneling method with global optimization features. To accelerate the computation of large numbers of independent simulations, Leitão and Schiozer7,8 have used direct optimization methods in connection with parallel computing. Most recently, genetic algorithms9–11 have been applied to reservoir characterization by Romero et al.11 In this work, we concentrate on evolution strategies, which are generally robust and less sensitive to the nonlinearities and discontinuities of the solution space. One of the most challenging problems is the improvement of the convergence. In this context, the introduction of heuristics derived from geostatistical information is discussed. The scope of this work is to analyze the potential of direct methods, particularly evolution strategies, for optimizing large and complex reservoirs. We assume that the reservoir under investigation has a multidimensional search space and many wells (more than 20), and it is characterized by a three-phase black-oil model. In addition, we assume that no information on the reservoir is available beyond geostatistical information and geological, seismic, and history data. For this purpose, an interface program was developed for linking a standard industry black-oil simulator to the Multipurpose Environment for Parallel Optimization (MEPO). This optimization environment has been applied previously to various scientific and industrial engineering problems.12–15 In this work, the application of evolution strategies to the problem of history matching in reservoir engineering is presented. The methodology is introduced, and the implementation of evolutionary algorithms on parallel processors is addressed. Results are discussed on the basis of a synthetic reservoir model that is derived from a real North Sea reservoir. Methodology The choice of numerical methods supporting the process of history matching in reservoir engineering depends heavily on the formulation of the problem. The setup of an initial model requires different strategies and information compared to the fine-tuning process once an acceptable history match is obtained. There is no tool that covers the whole range of tasks in history matching today. During the initial phase of setting up a reservoir model to be used for reservoir prediction, various combinations of model parameters have to be tested. At this stage, several initial configurations are usable. The location of model parameters in a search space of possible realizations that are near optima is not known. Any numerical method that searches for local optima is therefore not appropriate to be used at this stage. Often, initial reservoir models for simulation are derived from an upscaled geostatistical model. However, the upscaling process generates new uncertainties, and the dynamics of the reservoir during production are usually not included. Therefore, the search of model parameters near acceptable solutions needs to be repeated in the initial simulation phase. Once a location of acceptable parameters in the search space is found, local methods can be used to fine-tune the model (i.e., to find the nearest optimum near any point in the search space that produces results close to an acceptable solution). In general, gradient methods have proven to be quite successful in this domain. 1–3 In addition, sensitivity analyses based on gradient methods can be used to determine model parameters that are most sensitive to the results in the vicinity of any point in the search space for which the gradients are calculated.4 This allows us to reduce the number of model parameters to improve convergence and run times. Evolutionary algorithms are capable of searching beyond local optima and have the potential to identify configurations in the search space of model parameters that generate acceptable solutions.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractConventional direct optimization methods and Evolutionary Algorithms are applied to the problem of history matching in reservoir engineering. For the optimization of complex reservoir models the potential of parallel computing is investigated. Methods to improve the convergence of Evolutionary Algorithms by introducing expert knowledge is discussed. An interface program has been developed which links an industry standard reservoir simulator to an optimization software package designed as a multipurpose environment for parallel optimization. Permeabilities, fault transmissibilities as well as relative permeabilites and barrier locations have been included in the optimization. Results are presented for synthetic and real reservoirs with up to 30 wells and 40 design parameters. The potential and the area of applicability of the optimization method to the problem of reservoir modeling in various modeling phases are discussed. The improvement of performance based on parallelism in a network environment is evaluated. In conclusion, results suggest that Evolution Strategies can be successfully applied for generating possible solutions in the early modeling phase. The introduction of expert knowledge to the optimization methods is essential for reducing the multidimensional search space and improving convergence.

Evolutionary Algorithms and local optimization methods are applied to the problem of history matching in reservoir engineering. Application of global optimization methods to history matching of complex reservoir models is generally limited by the convergence behavior. In this paper concepts for an integrated workflow of different optimization methods, parallel computing and statistical analyses are developed. Global optimization methods and a Bayesian approach to identify best results are combined to improve the convergence behavior. Result data generated in the course of an optimization cycle are used for analyzing sensitivities, correlations and trends of model parameters in a global search space. Statistics are used to reduce the search space by combining correlated model parameters, to exclude less important parameters and to identify regions by correlating well parameters. These techniques are applicable, irrespectively of the quality of a converging objective value. Results are presented for different complex real three phase reservoir models. The potential and area of applicability is discussed. In conclusion, results suggest that presented techniques are well prepared to extend the manual process of history matching. The introduction of a workflow based on parallel computing combined with global optimization methods effectively allows to investigate the solution space. Identification of different parameter sets which equally match history data represent an existing model diversity and prepares a basis for uncertainty estimations of production forecasts. Introduction In recent years local and global optimization methods with application to reservoir characterization received an increasing interest. Optimization methods were applied to history matching, well planning and more recently 4D seismic data was included as a match criteria. Usually limited information on the geological and geophysical background of the reservoir is available from well tests, seismic surveys, logs etc. Applications of reservoir simulations which intend to reproduce measured well production data on the basis of unknown model parameters define a procedure to solve the inverse problem of reservoir modeling. This procedure is often called history matching. History matching is defined by finding a set of model parameters which minimize the difference between calculated and observed measurement values like pressure, fluid production rates as well as fluid contacts etc. A number of previous works have concentrated on local gradient based optimization strategies2,3. Some have coupled a gradient method to a global optimization methods4,5. To accelerate the computation of large numbers of independent simulations, direct optimization methods were implemented on parallel networks6. Most recently, Evolutionary Algorithms7,8,9, Simulate Annealing8 as well as Monte Carlo methods10 have been applied to reservoir characterization. Global optimization methods have the potential to leave local optima and investigate the global search space. For realistic applications to history matching, there are no general criteria whether a global optimum was found. One strength of global search methods is to quantify the variability of models which equally generate acceptable solutions for the history matching problem. These models can be used as a basis for uncertainty quantification of production forecasts. This defines a different quality of uncertainty analyses compared to linear perturbation methods2 which are based on one single local minimum. In this work we concentrate on Evolution Strategies which are generally robust and less sensitive to non-linearities and discontinuities of the solution space. This method is used as part of a Multipurpose Environment for Parallel Optimization (MEPO). This optimization environment has previously been applied to various scientific and industrial engineering problems9,11–14. Methodology used in this work is described in the next chapter. Principals of an Evolution Strategy are covered. A Bayesian optimization approach is introduced as a mean to improve the convergence behavior and to investigate the solution space. Extensions of the objective formulation including correlation effects are described. Readers only interested in results, should refer to the application chapter. Methods are applied and discussed on the basis of two different test cases. Finally, conclusions are made.

Well placement and design under geological uncertainties defines a major risk for field development processes. Including alternative geological realizations in a manually optimized development plan has been cumbersome and time consuming. In practical cases, a single reference model was often used as a basis for the flow simulation model which included a major risk on underestimating geological uncertainties. Optimization approaches and related optimization methods applied in this field previously included an objective function definition which aggregates multiple objectives, e.g. cumulative well rates or economical indicators. These optimization methods do not allow distinguishing easily between correlated and uncorrelated objectives which defines a major limitation for efficiency. This paper presents a novel approach individually linking objectives and design parameters to multiple optimization processes which operate in parallel on a single simulation case. This approach increases the efficiency of stochastic optimization processes for complex application scenarios with multiple objectives. The extension to an uncertainty workflow including multiple geological models in the optimization processes is discussed.Well placement optimization of horizontal wells in independent target formations of the gas condensate field is used to verify the optimization methodology. Alternative geological models are included in the optimization workflow representing geological uncertainties. The specific objective of the case study is to find optimum well trajectories by maximizing cumulative gas production over the life cycle of the field. Performance indicators for all well candidates (design parameters) are related to individual objectives (regional production). Robustness criteria for well candidates are implicitly fulfilled on the basis of risk weighted geological realizations.

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