Conditions Under Which The Capillary Term May Be Neglected (original) (raw)

The effect the capillary term in the fractional flow equa-tion has on saturation profiles is important, because these profiles determine the ultimate economic oil recovery. Buckley-Leverett's original solution to the non-capil-lary, two-phase flow problem became multiple-valued in saturation. As it is physically unrealistic for the saturation to have more than one value at a given position, Buckley and Leverett resolved this difficulty by introducing a .vaturation discontinuity or shock. This paper demonstrates that the Buckley-Leverett solu-tion iv, in reality, the steady-state solution to a second-order. non-linear, parabolic, partial differential equation. It also demonstrates that the steady-state (non-capillary, Buckley-Leverett) solution is an accepta ble approximation to the transient solution, provided the capillary number is sufficiently small. Finally, it is shown that the discrepancy between the transient and steady-state solutions increases with decreasing mobility ratio for any given value of the capillary number. Introduction In 1942, Buckley and Leverett"' presented the first ap-proach to predicting the linear displacement of one fluid by another. Their original solution to the non-capillary, two-phase flow problem became multiple-valued in satura-tion. As it is physically unrealistic for the saturation to have more than one value at a given position, Buckley and. Leverett resolved this difficulty by introducing a saturation discontinuity or shock. They evaluated the strength and position of the shock from materialbalance considerations.