Buckley-leverett Equation

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Buckley-leverett Equation

In a 1D sample ( Control Volume ), let

S(x,t)

be the Water Saturation , then the Buckley–Leverett equation is
:

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

where
:

U(S) = rac{Q}{\phi A} rac{\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 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

$\mathrm{d}p_c/\mathrm{d}S = 0$ 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