Microscopic Flow and Generalized Darcy’s Equations

In view of a better understanding of the macroscopic be haviour of multiphase flows in porous media, we first discuss equations which govern these flows at the pore level. Difficulties arising from boundary conditions on moving fluid-fluid interfaces and fluid-fluidsolid contact lines are stressed. Molecular dynamics and lattice gas models offer new approaches to the discussion of the validity of these boundary conditions; some recent works along these lines are briefly reviewed. Another approach uses capillary tubes with a square cross section as simple geometric models of porous media. Approximate solutions of the flow equations obtained for these models suggest, for real porous media, some modifications of the widely used generalized Darcy’s equations. Results drawn from the analysis of more complicated models (networks of interconnected capillary tubes), about the effects of the capillary number and the viscosity ratio of the displacing and displaced fluids, are reviewed. Finally, methods for the derivation of macroscopic equations governing multiphase flow in porous media, starting from equations valid at the pore level, are discussed.