A Three-Dimensional Model of Two-Phase Flows in a Porous Medium Accounting for Motion of the Liquid–Liquid Interface

摘要: A new three-dimensional hydrodynamic model for unsteady two-phase flows in a porous medium, accounting the motion of interface between flowing liquids, is developed. In minimum number interpretable geometrical assumptions, complete system macroscale flow equations derived by averaging microscale viscous flow. The velocities phases may be non-parallel, while them is, on average, inclined to directions phase velocities, as well direction saturation gradient. last gradient plays specific role determination geometry. resulting far generalization classical Buckley–Leverett model, explicitly describing and velocity liquid close it. Apart from propagation two volumes, their expansion or contraction also described, rotation has been proven negligible. detailed comparison with previous studies micro- carried out. numerical algorithm developed allowing solution multiple dimensions. Sample computations demonstrate that results sharpening displacement front more piston-like character displacement. It demonstrated indeed non-collinear, especially at zone intersection sharp permeability variation.