Efficient region decomposition for parallel simulation accounting for uncertainty in the reservoir model

Reservoir region delineation is essential for parallel flow simulation of large reservoir models. We argue that the delineation of least correlated, most sensitive regions mitigates the requirements for load-balancing and flux-matching that are the bane of current parallel simulation procedures. The optimal choice of sub-regions satisfies two conditions. First, the values of permeability in the sub-regions should have the greatest influence on the performance of injection and/or production wells. Second, the sub-regions should exhibit the least possible correlation with one another. Principal component analysis (PCA) of sensitivity matrices readily identifies regions meeting both the conditions. There are two methods for obtaining sensitivity matrices: i) the Hessian matrix calculated internally by a flow simulator, and ii) a covariance matrix calculated using a suite of realizations. The latter method is more robust and effective in terms of fluid flow connectivity, computational cost, availability to implement and capability of capturing uncertainty of reservoir models. In this paper, we focus on domain delineation using the covariance matrix and apply the method to a series of examples. We discuss key advantages of this method over the alternative of using the Hessian matrix.