Using exact Jacobians in an implicit Newton method for solving multiphase flow in porous media

We present a new numerical approach to solve the fully coupled equations for two-phase flow in porous media with exact Jacobians. The method is based on a space and time discretisation and a linearisation of the arising non-linear algebraic system with Newton’s method, where the required Jacobians are obtained with automatic differentiation (AD), providing the exact derivatives. We compare the forward AD differentiation mode to the standard finite difference method and the complex variable method in terms of precision and performance. It turns out that AD performs favourably compared to both methods. We also illustrate the advantages of exact Jacobians in a test example for two-phase flow in porous media investigating the evolution of pressure and saturation in a CO2 sequestration scenario.