Page 125 - gas transport in porous media

γ
s γ
t 118 scalar that maps K eq ∂ c Aγ /∂t onto ˜c Aγ , s/m Whitaker
time, s
T temperature, K
t A(n) species A stress vector, N/m 2
T A species A stress tensor, N/m 2
T total stress tensor, N/m 2
u p pulse velocity, m/s
u A v A − v γ , mass diffusion velocity for species A, m/s
u Aγ v Aγ − v γ , species A mass diffusion velocity in the γ -phase, m/s
v A velocity of species A, m/s
v Aγ velocity of species A in the γ -phase, m/s
A=N
6
v ω A v A , mass average velocity, m/s
A=1
A=N
6
v γ ω Aγ v Aγ , mass average velocity in the γ -phase, m/s
A=1
γ
v γ intrinsic mass average velocity in the γ -phase, m/s
v γ superficial mass average velocity in the γ -phase, m/s
γ
˜ v γ v γ − v γ , spatial deviation velocity in the γ -phase, m/s
V averaging volume, m 3
V A (t) volume of a species A body, m 3
V a (t) volume of an arbitrary, moving volume, m 3
V γ volume of the γ -phase contained within the averaging volume, m 3
V κ volume of the κ-phase contained within the averaging volume, m 3
w arbitrary velocity, m/s
x A c A /c, mole fraction of species A
x Aγ c Aγ /c γ , mole fraction of species A in the γ -phase
x position vector locating the center of the averaging volume, m
y position vector locating points on the γ –κ interface relative to the center
of the averaging volume, m

Greek Letters

β coefficient of expansion, K −1
ε γ volume fraction of the γ -phase (porosity)
ρ A mass density of species A,kg/m 3
mass density of species A in the γ -phase, kg/m 3
ρ Aγ
ρ total mass density, kg/m 3
ρ γ total mass density for the γ -phase, kg/m 3
ω A ρ A /ρ γ , mass fraction of species A
ω Aγ ρ Aγ /ρ γ , mass fraction of species A in the γ -phase
ν A stoichiometric coefficient for species A for a single independent reaction
λ thermal conductivity, kcal/s m K
2
τ viscous stress tensor, N/m , tortuosity tensor