Page 123 - gas transport in porous media

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NOMENCLATURE
A a (t) surface area of an arbitrary, moving volume, m 2 Whitaker
A γ e area of entrances and exits of the γ -phase contained in the
macroscopic region, m 2
area of the γ –κ interface contained within the averaging volume, m 2
A γκ
a v A γκ /V area per unit volume, m −1
b A species A body force per unit mass, N/kg
b total body force per unit mass, N/kg
γ
vector that maps ∇ c Aγ onto ˜c Aγ for a dilute solution, m
b γ
γ
closure variable that maps ∇ c Aγ onto ˜c Aγ for a non-dilute
b EA
solution, m
c A bulk concentration of species A, moles/m 3
c Aγ bulk concentration of species A in the γ -phase, moles/m 3
c Aγ superficial average bulk concentration of species A in the γ -phase,
moles/m 3
γ
c Aγ intrinsic average bulk concentration of species A in the γ -phase,
moles/m 3
c Aγ γκ intrinsic area average bulk concentration of species A at the γ –κ
interface, moles/m 3
γ
˜ c Aγ c Aγ − c Aγ , spatial deviation concentration of species A, moles/m 3
A=N
6 3
c γ c Aγ , total molar concentration, moles/m
A=1
c As surface concentration of species A associated with the γ –κ interface,
moles/m 2
c As γκ area averaged surface concentration of species A associated with the
γ − κ interface, moles/m 2
2
D AB binary diffusion coefficient for species A and B,m /s
B=N
D −1 6 2
D Am = x B /D AB , mixture diffusivity, m /s
Am
B=1
B =A
2
effective diffusivity tensor for the γ -phase, m /s
D eff
2
D γ hydrodynamic dispersion tensor for the γ -phase, m /s
D ∗ γ D eff + D γ , total dispersion tensor for the γ -phase, m /s
2
2
[D] diffusivity matrix, m /s
2
D AE element of the diffusivity matrix, m /s
γ 2
D AE intrinsic average element of the diffusivity matrix, m /s
˜ γ
D AE D AE − D AE , spatial deviation of an element of the diffusivity
2
matrix, m /s
e A species A internal energy, kcal/kg m 3
F Forchheimer correction tensor
2
g gravitational acceleration vector, m /s
species A enthalpy or partial mass enthalpy, kcal/kmol m 3
h A
H A species A partial molar enthalpy, kcal/kmol m 3