A Multiscale Method Coupling Network and Continuum Models in Porous Media II—Single- and Two-Phase Flows

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We present a numerical multiscale method for coupling mass conservation laws at the continuum scale with a discrete, pore scale network model for two-phase flow in porous media. Our previously developed single-phase flow algorithm is extended to two-phase flows, for the situations in which the saturation profile go through a sharp transition from fully saturated to almost unsaturated states. Our method evaluates the continuum equation by simulations using small representative networks centering at different physical locations, and thereby computes the effective dynamics of the two phase flow at the continuum scale. On the other hand, the initial and boundary data for the network simulations are determined by the variables used in the continuum model. We present numerical results for single-phase flows with nonlinear flux-pressure dependence, as well as two-phase flows.