Reservoir Model Uncertainty Quantification Through Computer-Assisted History Matching

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Abstract Quantification of uncertainty in production forecasting is an important aspect of reservoir simulation studies. The uncertainty in the forecasting stems from the uncertainties of various model-input parameters, such as permeability, porosity, relative permeability endpoints, etc. Traditionally, the outcome of history matching is a set of parameter values that result in a good match of the historical production data. Clearly, the history matching process will be even more valuable if the uncertainties of these model-input parameters can be quantified in the process. In this paper, we present a systematic history matching approach to condition a reservoir model to production data and quantify the uncertainties of history matching parameters in terms of probability density functions. The new approach utilizes experimental design and multi-objective global optimization techniques. More specifically, for a given list of uncertain parameters, the history matching process is treated as a combinatorial optimization problem to find the best combination of these parameters to achieve the minimum history match error. The combinatorial optimization problem is solved by applying a hybrid metaheuristic method that combines evolutionary algorithms, Tabu search, and experimental design techniques. In the optimization process, reservoir models containing different combinations of parameter values are automatically generated to cover a wide range of possibilities based on the principles of experimental design and Tabu search. The search space of the optimization problem is gradually reduced by adopting the natural selection mechanism to discard parameter values that do not fit field data. Finally, the posterior probability density functions of the uncertain parameters are estimated by applying Bayesian theory. The proposed methodology is demonstrated in a real field case study of a complex oil field, which has 12 production wells and 10 years of production history. Some of the wells in the reservoir are found to be difficult to match using the traditional manual history matching approach. After applying the new approach, all the well histories are successfully matched. More importantly, the posterior probability density functions of uncertain parameters are estimated in the history matching process. The results can be further used to quantify the uncertainty in the production forecasting of follow-up recovery processes.