Page 192 - Modeling of Chemical Kinetics and Reactor Design

162 Modeling of Chemical Kinetics and Reactor Design

C X C X
AO A = BO B (3-214)
a b

CASE 2: CHANGING DENSITY GASES

This case involves constant temperature T and total pressure π. In
this case, the density changes since the number of moles change during
the reaction, and the volume of a fluid element changes linearly with
conversion or V = V (1 + ε X ). The relationship between C and
A
A
O
A
X is as follows:
A
AO
X = C AO − C A and dX = − C (1 + ε A ) dC A

A
C + ε C A (1 + ε C ) 2
AO A A A A
1
y C 1 − X dC −+ ε
A = A = A and A = A dX (3-215)
+
y AO C AO 1 + ε A X A C AO (1 ε A X ) 2 A
A
for ε ≠ 0, where y = mole fraction of component A. The changes
A
A
between the reactants are:
ε X = ε X (3-216)
A A B B
aε A = bε B
C AO C BO (3-217)
and for the products and inerts:

y C ( ca X ) + C C
C = C = A CO AO
y AO C AO 1 + ε A X A (3-218)

y I = C I = 1
y IO C IO 1 + ε A X A (3-219)

CASE 3: GASES WITH VARYING DENSITY,
TEMPERATURE, AND TOTAL PRESSURE

Consider the following reaction: aA + bB → cC; a + b ≠ c. For an
ideal gas behavior with reactant A as the key component, the relation-
ship between concentration C , C AB , C , and X are as follows:
A
A
C