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Abstract

Summary

History matching is a challenging optimization problem that involves numerous evaluations of a very expensive objective function through the simulation of complex fluids flows inside an oil reservoir. Typically, the gradient of such a function is not always available. Therefore derivative free optimization methods such as Powell’s NEWUOA are often chosen to try to solve such a problem. One way to reduce the number of evaluations of the objective function is to exploit its specific structure, for example its partial separability. A function F:x->F(x1,…,xp) is said to be partially separable if there exists some subfunctions fi such that F=f1+…+fn and that for all i, fi depends only on pi<p parameters.

In this paper, we study history matching of geostatistics realizations. With an appropriate parameterization by introducing local parameters, one can generally consider the history matching objective function to be partially separable. In fact, if the parameters are localized in space, for example the local gradual deformation parameters or parameters linked to a specific well, we can easily consider that some parameters do not influence certain subfunctions fi which are associated to the wells. We propose in this paper an efficient optimization technique for partially separable functions and show an application of this derivative free optimization method to three cases of oil reservoir. The first one is a simple case constructed to easily identify the partial separability of the objective function while the other two are modified versions of the PUNQ and Brugge cases. Compared to the classic derivative free methods, we were able to significantly reduce the number of objective function evaluations while having a better matching of the production data. Our results confirm the validity of the partial separability assumption on the tested cases and show that our method is well suited to history matching problems.

© EAGE Publications BV
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/content/papers/10.3997/2214-4609.20141828
2014-09-08
2024-04-26

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A Derivative Free Optimization Method Adapted to Partially Separable Functions for History Matching Problems
Conference Proceedings 2014, 1 (2014); https://doi.org/10.3997/2214-4609.20141828
/content/papers/10.3997/2214-4609.20141828
/content/papers/10.3997/2214-4609.20141828
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