Page 181 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 4.4 Pressure Drop in Reactors 153
4.4 Pressure Drop in Reactors
Pressure drop IS
ignored for liquid- In liquid-phase reactions, the concentration of reactants is insignificantly
phase kinetics affected by even relatively large changes in the total pressure. Consequently,
calculations
we can totally ignore the effect of pressure drop on the rate of reaction when
sizing liquid-phase chemical reactors. However, in gas-phase reactions, the
concentration of the reacting species is proportional to the total pressure and
consequently, proper accounting for the effects of pressure drop on the reaction
system can, in many instances, be a key factor in the success or failure of the
reactor operation.

4.4.1 Pressure Drop and the Rate Law

We now focus our attention on accounting for the pressure drop in the
rate law. For an ideal gas, the concentration of reacting species i is
For gas-phase
reactions pressure F,,(O, + v,X)
drop may be very C,=L UO(1 f &X)(P,/P)(TITo) (3 -46)
important
For isothermal operation

(4- 18)

We now must determine the ratio PlP, as a function of volume V or the cata-
lyst weight, W, to account for pressure drop. We then can combine the coricen-
tration, rate law, and design equation. However, whenever accounting for the
effects of pressure drop, the differential form of the mole balance (design
equation) must be used.
If, for example, the second-order isomcrization reaction
A-B

When P+P, one is being carried out in a packed-bed reactor, the differential form of the mole
use *e balance equation in terms of catalyst weight is
differential forms
of the PFRIPBR
design equations FA, - - -rA gram moles (2-17)
dX -
I
dW gram catalyst min
The ralte law is

-rb, = kC2 (4-19)
From stoichiometry for gas-phase reactions,