Evolutionary Algorithms Applied to History Matching of Complex Reservoirs
- R.W. Schulze-Riegert (Scandpower) | J.K. Axmann (Scandpower) | O. Haase (Scandpower) | D.T. Rian (Scandpower) | Y.-L. You (Scandpower)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- April 2002
- Document Type
- Journal Paper
- 163 - 173
- 2002. Society of Petroleum Engineers
- 5.5.8 History Matching, 5.5 Reservoir Simulation, 5.5.3 Scaling Methods, 5.1.5 Geologic Modeling, 4.6 Natural Gas, 4.1.5 Processing Equipment, 5.6.9 Production Forecasting, 5.6.4 Drillstem/Well Testing, 5.3.2 Multiphase Flow, 5.1 Reservoir Characterisation, 4.1.2 Separation and Treating, 5.4.2 Gas Injection Methods
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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.
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.
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.
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