Mathematical Methodology for Evaluating Simulations of Flow in Porous Media. Final Report, February 1, 1980-August 31, 1983

摘要

This report concerns development of a methodology for evaluation of reservoir simulators. Although validity and usefulness of reservoir simulations might be questioned on various grounds, this study involves tests of resolution of numerical computational difficulties and of compatibility of correlations used in representation of fluid properties and phase flow interference. A similarity concept is used which allows testing of simulators to be based on solution of a system of ordinary differential equations, referred to as a Similarity Porous Media System (SPMS), rather than on the usual system of partial differential equations, referred to as a Porous Media System (PMS). The SPMS can be solved with the same computational effort as would be required for a single time step in the usual application of the PMS itself. The SPMS consists of study of possible level curves, also called similarity curves, on which all the unknowns in the PMS are constant. The curves can be chosen to be either a family of coaxial, common vertex parabolas or of parallel lines for evaluation of a simulator restricted to a linear reservoir. Moreover, the SPMS can be used, on a family of parabolas, for a simulator restricted to porous media problems with circular symmetry. Simulation of an actual reservoir problem imposes field conditions on a simulator's solution of the PMS, but use of the similarity concept in evaluation of a simulator involves imposition of selected samples from a solution of the SPMS as conditions on a solution of the PMS by the simulator. Then, this solution of the PMS can be checked against a solution predicted by the solution of the SPMS. Examples have been tested and data are available on request. 7 references, 2 figures, 5 tables. (ERA citation 09:007193)