System and method for predicting fluid flow in subterranean reservoirs

Abstract

A reservoir prediction system is disclosed that uses a kernel-based ensemble Kalman filter (EnKF) capable of representing non-Gaussian random fields characterized by multi-point geostatistics. The EnKF uses only the covariance and cross-covariance between the random fields (to be updated) and observations, thereby only preserving two-point statistics. The kernel-based EnKF allows the creation of nonlinear generalizations of linear algorithms that can be exclusively written in terms of dot products. By deriving the EnKF in a high-dimensional feature space implicitly defined using kernels, both the Kalman gain and update equations are nonlinearized, thus providing a completely general nonlinear set of EnKF equations, the nonlinearity being controlled by the kernel. By choosing high order polynomial kernels, multi-point statistics and therefore geological realism of the updated random fields can be preserved.