Page 82 - gas transport in porous media

Chapter 6: Conservation Equations
and the chemical composition matrix for this reaction is represented by
Molecular species → C 2 H 6 O 2 H 2 OCO 2 75
⎡ ⎤
carbon 2 0 0 1
hydrogen ⎣ 6 0 2 0 ⎦
oxygen 0 2 1 2
Equation (6.21) can be used to determine stoichiometric coefficients and the number
of independent reactions that are needed to describe any given system (Cerro et al.,
2004). In addition, it represents the fundamental axiom concerning conservation of
mass for reacting systems since it can be used to derive Eq. (6.6).

6.1.3 Mechanics
To describe multicomponent systems we use four axiomatic statements concerning
(1) the linear momentum of species A, (2) the angular momentum of species A, (3) the
total diffusive force in a mixture, and (4) the rate of production of linear momentum
owing to chemical reactions. These axioms take the form:

AXIOM I:
d
ρ A v A dV = ρ A b A dV + t A(n) dA (6.23)
dt
V A (t) V A (t) A A (t)
B=N

+ P AB dV + r A v A dV
B=1
V A (t) V A (t)
AXIOM II:

d
r × ρ A v A dV = r × ρ A b A dV + r × t A(n) dA (6.24)
dt
V A (t) V A (t) A A (t)
B=N

+ r × P AB dV + r × r A v A dV
B=1
V A (t) V A (t)
AXIOM III:
A=N B=N

P AB = 0 (6.25)
A=1 B=1
AXIOM IV:
A=N

r A v A = 0 (6.26)
A=1