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Buckley–Leverett equation

In fluid dynamics, the Buckley–Leverett equation is a transport equation used to model two-phase flow in porous media. The Buckley–Leverett equation or the Buckley–Leverett displacement can be interpreted as a way of incorporating the microscopic effects to due capillary pressure in two-phase flow into Darcy's law.

In a 1D sample (control volume), let S(x,t) be the water saturation, then the Buckley–Leverett equation is

\frac{\partial S}{\partial t} = U(S)\frac{\partial S}{\partial x}


U(S) = \frac{Q}{\phi A} \frac{\mathrm{d} f}{\mathrm{d} S}.

f is the fractional flow rate, Q is the total flow, φ is porosity and A is area of the cross-section in the sample volume.

Assumptions for validity

The Buckley–Leverett equation is derived for a 1D sample given

General solution

The solution of the Buckley–Leverett equation has the form S(x,t) = S(xU(S)t) which means that U(S) is the front velocity of the fluids at saturation S.

See also

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Buckley–Leverett_equation". A list of authors is available in Wikipedia.
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