Buckley–Leverett equation

In fluid dynamics, the Buckley–Leverett equation is a conservation equation used to model two-phase flow in porous media. The Buckley–Leverett equation or the Buckley–Leverett displacement describes an immiscible displacement process, such as the displacement of oil by water, in a one-dimensional or quasi one-dimensional reservoir.

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

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

where

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

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

Assumptions

The Buckley–Leverett equation is derived based on the following assumptions:

• Flow is linear and horizontal
• Both wetting and non-wetting phases are incompressible
• Immiscible phases
• Negligible capillary pressure effects (this implies that the pressures of the two phases are equal)
• Negligible gravitational forces

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

External links

• Buckley-Leverett Equation and Uses in Porous Media