The model consists of two partial differential equations in three dimensions. The velocity equation has a component due to Darcy's law and a random (Wiener) component representing the impact the effect that the porous medium has on the water. This is analogous to Brownian motion
The model equation which describes the velocity of fluid in the porous media is (Kulasiri ,1997):
(1) 
where
V(x,t) 
is velocity 
x(t) 
is position in 3 dimensional space 
K(x) 
is hydraulic conductivity 
(x) 
is porosity 
(x,t) 
is piezometric head 
W(x,t) 
is the stochastic (Wiener) component of velocity due to pore structure 
represents the integration step length
N(0,1) represents a standard normal variate
e is the eigenvalue of the matrix which models the space correlation which occurs due to the Wiener process W
s represents the size of the random component
The solute flux equation has a component due to water velocity, a component due to Fick's law of diffusion and a stochastic component representing the additional dispersive effect the porous medium has on the diffusion (Kulasiri ,1997):

(2) 
where:
J 
is solute flux 
C 
is solute concentration 
D 
is Fick diffusion 
W_{d} 
is the stochastic (Wiener) component of flux due to pore structure 