Diffusive Riemann Solutions for 3-phase flow in Porous Media

Resumo

We study the diffusive effect caused by capillary pressure in three-phase flow in porous media, which is modeled by a system of two nonlinear conservation laws. We solve a class of Riemann problems where one of the viscosities is higher than the other two; we first develop a methodology using artificial diffusion and identify the transitional surfaces and associated shocks, resulting from loss of strict hyperbolicity at an isolated point in the space of saturations. We identify the surfaces that characterize solutions which require transitional shocks. We use the wave curve method to determine the solutions for arbitrary Riemann data, except for a small set of right states that utilize transitional rarefactions. We present the transitional surface for the general case where diffusion arises from capillary effects.