Jointly updating the mean size and spatial distribution of facies in reservoir history matching

Abstract

There exist several methods for history matching of reservoir facies distribution. When using these methods, the facies mean size is usually supposed to be prior information known without uncertainty. However, in reality, it is often difficult to acquire an accurate estimation of the facies mean size due to limited measurement data. Thus, it is more reasonable to treat the facies mean size as an uncertain model parameter for updating. In this work, we propose a methodology to jointly update the mean size and spatial distribution of facies in reservoir history matching. In the parameterization step, we utilize a Gaussian random field and a level set algorithm to parameterize each facies. The range of the Gaussian field controls the facies mean size of the generated facies distribution realizations. To accomplish jointly updating the mean size and spatial distribution of facies, the Gaussian random field is further parameterized by the Karhunen–Loeve (KL) expansion. We choose the range of the Gaussian field and the independent Gaussian random variables in the KL expansion as model parameters. After model parameterization, we use the Levenberg–Marquardt ensemble randomized maximum likelihood filter (LM_EnRML) to perform history matching. Three synthetic cases are set up to test the performance of the proposed method. Numerical results show that for estimating the facies field, the mean size and spatial distribution of facies can be jointly updated to match the reference distribution using the proposed method.