Simulation of three component two phase flow in porous media using method of lines.

Abstract:

Numerical simulation of compositional flow problems commonly involves the use of 1st or 2nd order Euler time stepping. Method of lines (MOL), using highly accurate and efficient ODE solvers, is an alternative technique which, although frequently applied to the solution of Richard's equation, has generally been overlooked for partially miscible multi component problems. This article presents the development of a numerical simulator for 1D, compressible, two-phase, three-component, radially symmetric flow using method of lines (MOL) and a 3rd order accurate spacial discretization using a weighted essentially non oscillatory (WENO)scheme. The MOL implementation enables application of the MATLAB ODE-Solver, ODE15s, for time integration. Simulation examples are presented in the context of enhanced gas recovery due to CO$_2$ injection. Following an assumption of constant equilibrium ratios for CO$_2$ and CH$_4$, a ternary flash calculator is developed providing closed-form relationships for exact interpolation between equations of state for CO$_2$-H$_2$O and CH$_4$-H$_2$O binary mixtures. The numerical code is successfully tested and verified for a range of scenarios by comparison to an existing analytical solution.