Efficient Inference of Reservoir Parameter Distribution Utilizing Higher Order SVD Reparameterization

Abstract

Reservoir parameter inference is a challenging problem to many of the reservoir simulation workflows, especially when it comes to real reservoirs with high degree of complexity and non-linearity, and high dimensionality. In a history matching problem that adapts the reservoir properties grid blocks, the inverse problem leads to an ill-posed and very costly optimization schemes. In this case, it is very important to perform geologically consistent reservoir parameter adjustments as data is being assimilated in the history matching process. Therefore, ways to reduce the number of reservoir parameters need to be sought after. In this paper, we introduce the advantages of a new parameterization method utilizing higher order singular value decomposition (HOSVD) which is not only computationally more efficient than other known dimensionality reduction methods such as, SVD and DCT, but also provides a consistent model in terms of reservoir geology. HOSVD power is due to its ability to supply a reliable low-dimensional reconstructed model while keeping higher order statistical information and geological characteristics of reservoir model. In HOSVD, we take the snapshots in a 2D or 3D approach, i.e., do not vectorize original replicates, and stack them up into a tensor form, i.e. a multi-way array in multilinear algebra which leads to implementing tensor decomposition. Technically, we performed HOSVD to find the best lower rank approximation of this tensor that is an optimization problem utilizing alternating least square method. This results in a more consistent reduced basis. We applied this novel parameterization method to the SPE10 benchmark reservoir model to show its promising parameterization performance. We illustrate its advantages by comparing its performance to the regular SVD (PCA) in a history matching framework using EnKF, as well as characterization performance of the ensemble-based history matching approaches along with HOSVD. Overall, HOSVD outperforms SVD in terms of reconstruction and estimation performance.