The Buckley–Leverett equation is a fundamental equation in petroleum engineering and reservoir engineering that describes the movement of two-phase fluids (typically oil and water) in porous media. It models the flow behavior of immiscible fluids in a reservoir when one fluid displaces another, commonly used to analyze waterflooding operations during oil recovery. The equation is derived from the conservation of mass principle and reflects the dynamics of the interfaces between the two fluids.
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The one-dimensional mass conservation equation for saturation when total Darcy flux is constant and capillary pressure and gravity are neglected. It is a scalar conservation law with dimensional characteristic speed . Shock speeds obey a Rankine-Hugoniot condition; physically admissible solutions satisfy an entropy selection. Capillary diffusion regularizes the saturation transition.