Buckley–Leverett equation

From Wikipedia, the free encyclopedia

In fluid dynamics, the Buckley–Leverett equation is a transport equation used to model two-phase flow in porous media[1] . 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}

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, φ is porosity and A is area of the cross-section in the sample volume.

Contents

[edit] Assumptions for validity

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

[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

[edit] References

  1. ^ S.E. Buckley and M.C. Leverett (1942). "Mechanism of fluid displacements in sands". Transactions of the AIME (146): 107–116. 
This fluid dynamics-related article is a stub. You can help Wikipedia by expanding it.