Patent Document ID: 8972232
Application ID: 13029534
Patent Flag: 1

Claim One:
1. A computer-implemented method for updating simulation models of a subterranean reservoir, the method comprising: (a) providing an ensemble of reservoir models representing a subterranean reservoir having non-Gaussian characteristics; (b) providing reservoir data from the subterranean reservoir; (c) solving, via a computer, for each of the reservoir models in the ensemble of reservoir models, using a ensemble Kalman filter represented by a kernel function, a constrained optimization with equality constraints and inequality constraints including constraints on the physical bounds of saturation and pressure to obtain a constrained optimal solution, wherein using the ensemble Kalman filter represented by the kernel function includes using an equation, wherein the equation is: y n + 1 = θ 1 + θ ⁢ y n + 1 1 + θ ⁢ ∑ i = 1 M ⁢ ⁢ b ij ⁢ ∑ k = 1 q ⁢ ⁢ k ⁡ ( y i f · y n ) k - 1 ⁢ y i f ∑ k = 1 q ⁢ ⁢ k ⁡ ( y n · y n ) k - 1 ⁢ ∀ j = 1 , … ⁢ , M wherein θ is a relaxation factor; wherein M refers to number of ensemble members of the ensemble of reservoir models; wherein y is a state vector; wherein n is an iteration number; wherein y f is a forecasted state vector; wherein q refers to an order of the kernel; and wherein b is a coefficient of the ensemble Kalman filter represented by the kernel function; and (d) assembling, via the computer, the constrained optimal solutions to update the ensemble of reservoir models, the updated ensemble of reservoir models being consistent with the reservoir data provided from the subterranean reservoir and preserving the non-Gaussian characteristics of the subterranean reservoir.