Page 297 - Modeling of Chemical Kinetics and Reactor Design

Introduction to Reactor Design Fundamentals for Ideal Systems 267

Substituting Equation 5-10 into Equation 5-7 gives

dX A
− ( r A )V R = N AO (5-11)
dt

Rearranging and integrating Equation 5-11 between the limits at
t = 0, X = 0 and at t = t, X = X results in
A
AF
A
t X AF dX
∫ dt = N AO ∫ − ( rV ) A
0 0 A R

X AF dX
=
tN AO ∫ − ( rV ) A (5-12)
0 A R

where the concentration C = N  moles  (5-13)
A
A  
V R volume
The fractional conversion X at constant volume is
A

X = C AO − C A
A (5-14)
C AO

Substituting Equation 5-13 into Equation 5-11, rearranging
and integrating between the limits at t = 0, X = 0 and at t = t,
A
X = X yields
A
AF
t X AF dX
∫ dt = C AO ∫ r − ( A ) (5-15)
A
0 0

X AF
t = C AO ∫ dX r − ( A ) (5-16)
A
0

Equation 5-16 is the time required to achieve a conversion X for
A
either isothermal or non-isothermal operation. Equation 5-16 can also
be expressed in terms of concentration at constant fluid density as