System and method for modeling a subterranean reservoir

摘要

A computer-implemented reservoir prediction system, method, and software are provided for updating simulation models of a subterranean reservoir. An ensemble of reservoir models representing a subterranean reservoir having non-Gaussian characteristics is provided, along with reservoir data from the subterranean reservoir used to condition the ensemble of reservoir models. For each of the reservoir models in the ensemble of reservoir models, a constrained optimization with equality constraints and inequality constraints are solved using a constrained Kernel Ensemble Kalman Filter to obtain a constrained optimal solution. The constrained optimal solutions are assembled to update the ensemble of reservoir models. The updated ensemble of reservoir models are consistent with the reservoir data provided from the subterranean reservoir and the non-Gaussian characteristics of the subterranean reservoir are preserved.

主权项

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:yn+1=θ1+θ⁢yn+11+θ⁢∑i=1M⁢⁢bij⁢∑k=1q⁢⁢k⁡(yif·yn)k-1⁢yif∑k=1q⁢⁢k⁡(yn·yn)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 yf is a forecasted state vector;wherein q refers to an order of the kernel; andwherein 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.