Transport in Porous Media, Vol.57, No.1, 17-34, 2004
Higher-order terms in the capillary limit approximation of viscous-capillary flow
We propose a new approximation to the solution of the steady state equations describing two-phase immiscible flow in a porous medium. It is demonstrated that the general procedure contains the capillary equilibrium approximation as a special case. The solution is approximated by a perturbation series in a parameter related to the capillary number. The expansion of the solution results in a sequence of decoupled linear elliptic boundary value problems. This sequence is solved numerically by a Finite Element method, and the accuracy of the approximations is evaluated.
Keywords:capillary equilibrium;capillary limit;perturbation series;asymptotic expansion;finite element method