Page 81 - gas transport in porous media

74
and use of the definition of the mass average velocity
A=N Whitaker

v = ω A v A , mass average velocity (6.16)
A=1
leads us to
∂ρ
+∇ · (ρv) = 0 (6.17)
∂t
This result has exactly the same form as the continuity equation for a single component
when there is no chemical reaction.

6.1.2 Molar Forms
Often the molar form of Eq. (6.11) is preferred because both reaction rates and phase
equilibria are expressed in molar quantities. We can divide Eq. (6.11) by the molecular
mass of species A and make use of the definitions
ρ A r A
c A = , R A = (6.18)
M A M A
in order to express Eqs. (6.11) and (6.6) as
∂c A
+∇ · (c A v A ) = R A , A = 1, 2, ... , N (6.19)
∂t

A=N

M A R A = 0 (6.20)
A=1
This latter constraint on the molar rates of production owing to chemical reactions is
not particularly useful, and one normally draws upon the concept that atomic species
are neither created nor destroyed by chemical reactions to provide the framework for
chemically reacting systems. This axiomatic statement can be expressed as
A=N

AXIOM II: N JA R A = 0, J = 1, 2, ... , T (6.21)
A=1
in which T represents the number of atomic species that take part in the reaction,
and N JA represents the number of J-type atoms contained in A-type molecules. The
matrix of coefficients, N JA , is often referred to as the chemical composition matrix.
The reaction in which ethane and oxygen undergo complete combustion to form
carbon dioxide and water can be expressed as

C 2 H 6 + O 2 → CO 2 + H 2 O (6.22)