The Buckley-Leverett solution to the one-dimensional, two- phase, incompressible, immiscible fluid displacement problem in permeable media forms the basis of fractional flow theory. In cases with S-shaped fractional flow curves, the problem of triple saturations is resolved by shock assumption. The Welge integration is then applied for recovery and frontal-advance calculations.

We present an alternative approach in fractional flow theory in which the two-phase displacement problem is analyzed without invoking the shock assumption. The shock- free approach eliminates the triple-saturation problem and identifies that saturation velocities are time dependent.

The shock-free solution is realistic and remarkably dynamic. It results in a simple procedure for recovery and frontal-advance calculations. It provides new insights into the fluid displacement problem by helping to better understand mechanisms that trigger fingering and cause dissipation.

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