STEADY-STATE SOLUTIONS TO BENTSENS EQUATION

Based on experimentally observed phenomena and the physical requirement of a unique value of saturation at any location within a porous medium, a restrictive condition for a valid solution to Bentsen's equation is derived: partial derivative(2)f/partial derivative S-2 less than or equal to 0. The steady-state solution to Bentsen's equation is shown to be identical to the Buckley-Leverett solution to the displacement equation, and the steady-state solution for the fractional flow is shown to be independent of the capillary number. It is proved that under steady-state conditions, the capillary term of the fractional how equation in the frontal region does not depend on the capillary number. Therefore, the unrealistic triple-valued saturation profile of the original Buckley-Leverett solution resulted because the capillary term was in-appropriately neglected. The break-through recovery efficiency, tau(bt), is shown to be a function of the capillary number. As the capillary number decreases, the break-through recovery efficiency increases and the maximum value of tau(bt) can be obtained as N-c --> 0. The Buckley-Leverett solution is the limiting solution as N-c --> 0.