Mathematical Description of the Implementation of the Adaptive Newton-Raphson Method in Compositional Porous Media Flow

Abstract—Models for multiphase-multicomponent flow in
porous media are described in systems of PDEs. Solving them
using finite difference discretization method can be of three ways; explicit, semi-implicit, and fully implicit. In this study, we present the implementation of an adaptive Newton-Raphson method in the context of IMPECS (Implicit Pressures Explicit Concentrations and Saturations) method of solution.