Page 124 - gas transport in porous media

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Chapter 6: Conservation Equations
H reaction
3
enthalpy per unit mass, kcal/kg m
h molar heat of reaction for a single independent reaction, kcal/kmol m 3
I unit tensor
2
c B u B , mixed-mode diffusive flux for species B, mole/m s
J B
c Aγ u Aγ mixed-mode diffusive flux for species A in the γ -phase,
J Aγ
2
mole/m s
K Darcy’s law permeability tensor, m 2
K eq linear adsorption equilibrium coefficient for species A,m
adsorption rate coefficient for species A, m/s
k Al
k −Al desorption rate coefficient for species A, s −1
i i = 1, 2, 3, lattice vectors for a spatially periodic model of a porous
medium, m
γ small length scale associated with the γ -phase, m
L large length scale associated with the porous medium, m
M second order tensor that maps v γ onto ˜v γ
γ
γ
m vector that maps µ γ v γ on to ˜p γ ,m −1
M A molecular mass of species A, kg/kg mole
N JA elements of the composition matrix
n unit normal vector
unit normal vector directed from the γ -phase to the κ-phase
n γκ
p total pressure, N/m 2
p γ total pressure in the γ -phase, N/m 2
γ
˜ p γ p γ − p γ , spatial deviation pressure, N/m 2
partial pressure for species A,N/m 2
p A
P AB diffusive force per unit volume exerted by species B on species A,
N/m 3
2
energy flux (conduction and radiation) vector for species A, kcal/m s
q A
2
q energy flux (conduction and radiation) vector, kcal/m s
2
q R radiation energy flux vector, kcal/m s
3
Q AB energy exchange between species A and species B, kcal/m s
r o radius of averaging volume, m
r position vector, m
R reference position vector, m
r A position vector for species A,m
R A reference position vector for species A,m
3
r A mass rate of homogeneous chemical reaction, kg/m s
3
R A molar rate of homogeneous chemical reaction, moles/m s
molar rate of homogeneous chemical reaction in the γ -phase,
R Aγ
3
moles/m s
R As molar rate of heterogeneous chemical reaction associated with the
2
γ –κ interface, moles/m s
R As γκ area average molar rate of heterogeneous chemical reaction for
2
species A, moles/m s
s total entropy per unit mass, kcal/kg K m 3