EFFECT OF HYDRODYNAMIC-FORCES ON THE PRESSURE-DIFFERENCE EQUATION

Because of the influence of hydrodynamic forces, the difference in macroscopic pressure which exists, at static equilibrium, between two immiscible phases located in a porous medium may be different from that which pertains during flow. In this paper, the concept of relative pressure difference, together with a new pressure-difference equation, is used to investigate the impact that the hydrodynamic forces have on the difference in macroscopic pressure which pertains when two immiscible fluids flow simultaneously through a homogeneous, water-wet porous medium. This investigation reveals that, in general, the equation defining the difference in pressure between two flowing phases must include a term which takes proper account of the hydrodynamic effects. Moreover, it is pointed out that, while neglect of the hydrodynamic effects introduces only a small amount of error when the two fluids are flowing cocurrently, such neglect is not permissible during steady-state, countercurrent how. This is because failure to include the impact of the hydrodynamic effects in the latter case makes it impossible to explain the pressure behaviour observed in steady-state, countercurrent flow. Finally, the results of this investigation are used as a basis for arguing that, during steady-state, countercurrent flow, saturation is uniform, as is the case of steady-state, cocurrent flow.