Page 330 - Elements of Chemical Reaction Engineering Ebook

Sec. 6.3 Algorithm for Solution to Complex Reactions 30 1

where
rt
FT=c 6 (6-20)
J=1
and

((5-21)

For isothermal systems with no pressure drop

Gas phase (6-22)

and we can express the rates of disappearance of each species as a function of
the molar flow rates (Fl, ... ?q):

(6-23)

(6-24)

where .fn represents the functional dependence on concentration of the net rate
of formation such as that given in Equation (E6-4.12) for NS.

6.3.6 Combining Step

VVe now insert rate laws written in terms of molar flow rates [e.g., Equa-
tion (3-45)] into the mole balances (Table 6-1). After performing this operation
for each species we arrive at a coupled set of first-order ordinary differential
equations to be solved for the molar flow rates as a function of reactor volume
(i.e., distance along the length of the reactor). In liquid-phase reactions, iricor-
porating and solving for total molar flow rate is not necessary at each step
along the solution pathway because there is no volume change with reaction.
Combining mole balance, rate laws, and stoichiometry for species 1
through speciesj in the gas phase and for isothermal operation with no pres-
sure drop gives us

Coupled ODES

(6-26)