Simulation of Three-Component Two-Phase Flow in Porous Media Using Method of Lines

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 two-phase, two-component flow problems, has generally been overlooked for problems concerning more than two components. This article presents the development of a numerical simulator for 1D, compressible, two-phase, three-component, radially symmetric flow using the method of lines (MOL) and a 3rd-order accurate spatial 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 CO2 injection into a reservoir containing a mixture of CH4 and H2O. Following an assumption of constant equilibrium ratios for CO2 and CH4, a ternary flash calculator is developed providing closed-form relationships for exact interpolation between equations of state for CO2–H2O and CH4–H2O binary mixtures. The numerical code is successfully tested and verified for a range of scenarios by comparison with an existing analytical solution.