longitudinal dispersion in nonuniform isotropic porous media

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f( £) = probability density for pore length by frequency (L- 1 )
G(a) = cumulative probability for pore radius by frequency (-)
g = gravitational acceleration (L/T2)
g(a) = probability density for pore radius by frequency (L- l )
h(d) = probability density for grain diameter by frequency (L- l )
J(d) = area-weighted cumulative probability for grain diameter (-)
jed) = area-weighted probability density for grain diameter (L- l )
K = hydraulic conductivity (L/T)
KL = longitudinal dispersion coefficient Ln a bidisperse
porous medium (L 2 /T)
k = permeability (L2)
k .. = permeability tensor (L2)
LJ
L = column length (L)
£ = pore length (L)
£ * = £/d = dimensionless pore length (-)
g
£d = £/£m = dimensionless pore length (-)
£ = maximum pore length (L)
m
£. = pore length in the unit cell (L)
J
£ = length scale of microporous regions (L)
mp
M = 3Pe o w/2D (-)
e
m = parameter in beta distribution for pore length (-)
N number of pores (-)
n = number of steps taken (-)
n = parameter in beta distribution for pore length (-)
P pressure gradient (M/L2T2)
Pe = V d /D = Peclet number (-)
s g