A general, finite element procedure for reservoir simulation is presented. This effort is directed toward improving the numerical behavior of standard upstream, or upwind, finite difference techniques, without significantly increasing the computational costs. Two methods from previous authors' work are modified and developed: 1) upwind finite elements and 2) the Petrov-Galerkin method. These techniques are applied in a one- and two-dimensional, surfactant/ polymer simulator. The paper sets forth the mathematical formulation and several details concerning the implementation. The results indicate that the Petrov-Galerkin method does significantly reduce numerical-diffusion errors, while it retains the stability of the first-order, upwind methods. It is also relatively simple to implement. Both the upwind, and Petrov-Galerkin, finite element methods demonstrate little sensitivity to grid orientation.

Keywords:
equation, application, upstream oil & gas, reservoir simulation, chemical flooding methods, enhanced recovery, finite element method, dispersion, artificial intelligence, petrov-galerkin method
Subjects:
Fluid Characterization, Reservoir Fluid Dynamics, Improved and Enhanced Recovery, Reservoir Simulation, Formation Evaluation & Management, Information Management and Systems, Phase behavior and PVT measurements, Flow in porous media, Chemical flooding methods
Copyright 1985, Society of Petroleum Engineers
You can access this article if you purchase or spend a download.