NUMERICAL RESERVOIR SIMULATION USING AN ORDINARY-DIFFERENTIAL-EQUATIONS INTEGRATOR.

The method of lines used in conjuction with a sophisticated ordinary-differential-equations integrator is an effective approach for solving nonlinear, partial differential equations and is applicable to the equations describing fluid flow through porous media. Given the initial values, the integrator is self-starting. Subsequently, it automatically and reliably selects the time step and order, solves the nonlinear equations (checking for convergence, etc. ), and maintains a user-specified time-integration accuracy, while attempting to complete the problem in a minimal amount of computer time. The advantages of this approach, such as stability, accuracy, reliability, and flexibility are discussed. The method is applied to reservoir simulation, including high-rate and gas-percolation problems, and appears to be readily applicable to compositional models. Equations and tables demonstrate method.