Higher-Order Terms in the Capillary Limit Approximation of Viscous-Capillary Flow

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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.

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