Abstract
Calibrating subsurface reservoir models with historical well observations leads to a severely ill-posed inverse problem known as history matching. The recently proposed Ensemble Smoother with Multiple Data Assimilation (ES-MDA) method has proven to be a successful stochastic technique for solving this inverse problem, but its computational cost can be high in realistic scenarios and it remains challenging to incorporate certain non-Gaussian types of a-priori information into it. In this work we combine the ES-MDA method with Multiple-Point Statistics (MPS) and the K-SVD technique for building sparse dictionaries in order to obtain a novel sparsity-based history matching scheme that preserves non-Gaussian structural prior information and at the same time reduces computational cost. We present numerical experiments in 3D on a modified SPE10 benchmark reservoir model that demonstrate the performance of this new technique.
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Etienam, C., Velasquez, R.V., Dorn, O. (2019). Sparse Multiple Data Assimilation with K-SVD for the History Matching of Reservoirs. In: Faragó, I., Izsák, F., Simon, P. (eds) Progress in Industrial Mathematics at ECMI 2018. Mathematics in Industry(), vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-27550-1_72
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DOI: https://doi.org/10.1007/978-3-030-27550-1_72
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