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We study three different time integration methods for a dynamic pore networkmodel for immiscible two-phase flow in porous media. Considered are twoexplicit methods, the forward Euler and midpoint methods, and a newsemi-implicit method developed herein. The explicit methods are known to sufferfrom numerical instabilities at low capillary numbers. A new time-stepcriterion is suggested in order to stabilize them. Numerical experiments,including a Haines jump case, are performed and these demonstrate thatstabilization is achieved. Further, the results from the Haines jump case areconsistent with experimental observations. A performance analysis reveals thatthe semi-implicit method is able to perform stable simulations with much lesscomputational effort than the explicit methods at low capillary numbers. Therelative benefit of using the semi-implicit method increases with decreasingcapillary number $\mathrm{Ca}$, and at $\mathrm{Ca} \sim 10^{-8}$ thecomputational time needed is reduced by three orders of magnitude. Thisincreased efficiency enables simulations in the low-capillary number regimethat are unfeasible with explicit methods and the range of capillary numbersfor which the pore network model is a tractable modeling alternative is thusgreatly extended by the semi-implicit method.

Stable and efficient time integration of a dynamic pore network model for two-phase flow in porous media