LATTICE-BOLTZMANN STUDIES OF IMMISCIBLE 2-PHASE FLOW THROUGH POROUS-MEDIA

Using a recently introduced numerical technique known as a lattice-Bol tzmann method, we numerically investigate immiscible two-phase flow in a three-dimensional microscopic model of a porous medium and attempt to establish the form of the macroscopic flow law. We observe that the conventional linear description of the flow is applicable for high le vels of forcing when the relative effects of capillary forces are smal l. However, at low levels of forcing capillary effects become importan t and the flow law becomes nonlinear. By constructing a two-dimensiona l phase diagram in the parameter space of nonwetting saturation and di mensionless forcing, we delineate the various regions of linearity and nonlinearity and attempt to explain the underlying physical mechanism s that create these regions. In particular, we show that the appearanc e of percolated, throughgoing flow paths depends not only on the relat ive concentrations of the two fluids but also on a dimensionless numbe r that represents the ratio of the applied force to the force necessar y for nonwetting fluid to fully penetrate through the porous medium. F inally, we fit a linear model to our simulation data in the high-forci ng regions of the system and observe that an Onsager reciprocity holds for the viscous coupling of the two fluids.