Diffuse-interface Modeling of Two-phase Flow for a One-component Fluid in a Porous Medium

The diffuse-interface (DI) model for the two-phase flow of a one-component fluid in a porous medium has been presented by Papatzacos 2002, Transport Porous Media 49, 139–174] and by Papatzacos and Skjæveland 2004, SPE J. (March 2004), 47–56]. Its main characteristics are: (i) a unified treatment of two phases as manifestations of one fluid with a van der Waals type equation of state, (ii) the inclusion of wetting, and (iii) the absence of relative permeabilities. The present paper completes the presentation by including the implementation of wetting in the general case of a mixed-wet rock. As a result of this implementation, some statements are made about capillary pressure, confirming similar statements by Hassanizadeh and Gray 1993, Water Resour. Res. 29, 3389–3405]. As an application of the model, we show that relative permeabilities depend on the spatial derivatives of the saturation.