This applet simulates the flow of a DNAPL (Dense Nonaqueous Phase Liquid) into an initially water saturated porous medium. Initally, the DNAPL is confined to the upper left quarter of the vertical cross section. At time t = 0, the DNAPL is released and is free to infiltrate the water saturated region. The mathematical model is based on Darcy's law and conservation of mass. Darcy's law asserts that the mass flux of each fluid is given by

$$q_{i} = -K_{i} \nabla (p_{i} - \rho_{i} g z), i = w,n$$

where i = w denotes the wetting fluid (water) and i = n denotes the nonwetting DNAPL. In Darcy's law, g is the gravitational constant, z is the vertical distance from the top of the flow region and the proportionality factor K_i is the hydraulic conductivity of the phase-i fluid. Let S_i denote the relative saturation of phase-i fluid and $\phi$ the porosity of the porous medium. Then conservation of mass implies

$$\frac {\partial(\phi S_{i})}{\partial t} = \nabla \cdot(K_{i}\nabla (p_{i} - \rho_{i} g z), i = w,n)$$

To complete the mathematical model, we introduce the capillary pressure

p_c = p_n - p_w

and assume constitutive relationships of the form:

S_w = F(p_c)

S_n = 1 - S_w

K_i = G_i(S_i)

For physical reasons, F'(p_c) < 0 where 0 < S_w < 1 and $G_{i}'(S_{i}) \geq 0$for i = w,n. This leads to model equations of the form

$$\left\vert\phi F'(p_{c}) \right\vert (\frac {\partial (p_{w}... ...}{\partial t} = \nabla \cdot(K_{w}\nabla (p_{w} + \rho_{w} g z)$$

$$\left\vert\phi F'(p_{c}) \right\vert (\frac {\partial (p_{n}... ...}{\partial t} = \nabla \cdot(K_{n}\nabla (p_{n} + \rho_{n} g z)$$

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