MULTILEVEL MONOTONE CONSTRAINED PRESSURE RESIDUAL MULTISCALE TECHNIQUES

摘要

Computing systems, methods, and computer-readable media for modeling behavior of at least one fluid in a reservoir are disclosed. More particularly, the techniques provide consistent and robust numerical formulations for solutions to linear system of equations arising from the linearization of coupled nonlinear hyperbolic/parabolic (elliptic) partial differential equations (PDEs) of fluid flow in heterogeneous anisotropic porous media.

主权项

1. A computer-implemented method for modeling behavior of at least one fluid in a reservoir, the method comprising:
obtaining a plurality of measurements of a plurality of physical parameters at a plurality of locations within the reservoir, the plurality of physical parameters comprising at least pressure; discretizing a system of partial differential equations that model, based on the plurality of measurements, the plurality of physical parameters; iterating, for each of a plurality of time steps, and until convergence upon a solution to the system of partial differential equations:
approximating a rough solution to the system of partial differential equations;applying a constrained pressure residual technique to extract a system of pressure linear equations from the rough solution to the system of partial differential equations;applying a pre-smoothing technique at a fine scale to determine an approximate solution to the system of pressure linear equations;applying multi-scale multi-level processing to improve the approximate solution to the system of pressure linear equations;applying a post-smoothing technique at a fine scale to further improve the approximate solution to the system of pressure linear equations; andsolving the system of partial differential equations for remaining physical parameters based on the further improved approximate solution to the system of pressure linear equations; and outputting the solution to the system of partial differential equations.