The Characteristic Finite Difference Methods for Enhanced Oil Recovery Simulation and L 2 Estimates

A 2-dimensional, multicomponent, multiphase, and incompressible compositional reservoir simulator has been developed and applied to chemical flooding (surfactants, alcohol and polymers) and convergence analysis. The characteristic finite difference methods for 2-dimensional enhanced oil recovery can be described as a coupled system of nonlinear partial differential equations. For a generic case of the cross interference and bounded region, we put forward a kind of characteristic finite difference schemes and make use of thick and thin grids to form a complete set, and of calculus of variations, the theory of prior estimates and techniques. Optimal order estimates in L 2 norm are derived for the error in the approximate solutions. Thus we have thoroughly solved the well-known theoretical problem proposed by a famous scientist, J. Douglas, Jr.