Buckley-Leverett equation
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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
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.
[edit] Assumptions for validity
The Buckley–Leverett equation is derived for a 1D sample given
- mass conservation
- capillary pressure pc(S) is a function of water saturation S only
- dpc / dS = 0 causing the pressure gradients of the two phases to be equal.
[edit] 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.
[edit] See also
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