| 摘要 |
A reservoir prediction system and method are provided that use generalized EnKF using kernels, capable of representing non-Gaussian random fields characterized by multi-point geostatistics. The main drawback of the standard EnKF is that the Kalman update essentially results in a linear combination of the forecasted ensemble, and the EnKF only uses the covariance and cross-covariance between the random fields (to be updated) and observations, thereby only preserving two-point statistics. Kernel methods allow 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. The method is applied to two non-limiting examples where permeability is updated using production data as obserations, and is shown to better reproduce complex geology compared to the standard EnKF, while providing reasonable match to the production data. |
