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.

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

where

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

• mass conservation
• capillary pressure p_c(S) is a function of water saturation S only
• dp_c / dS = 0 causing the pressure gradients of the two phases to be equal.

General solution

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

See also

• Capillary pressure
• Permeability (fluid)
• Relative permeability
• Darcy's law