Page 273 - Elements of Chemical Reaction Engineering 3rd Edition

Sec. 5.4 Differential Reactors 245

catalyst, W, is known, the rate of reaction per unit mass of catalyst, 1.6, can be
calculated. Sinice the differential reactor is assumed to be gradientless, the
design equation will be similar to the CSTR design equation. A steady-state
mole balance on reactant A gives

+ r rate of 1 - r rate of 1
-
1 generatioh]
jaccumulatioo]

The subscript e refers to the exit of the reactor. Solving for --& we have

(5-20)

The mole balance equation can also be written in terms of the concentration

Differential reactor
design equation (5-21)

or in terms of the conversion or product flow rate F,:

I i
(5-22)

I I
The term FAOX gives the rate of formation of the product, Fp, when the
stoichiometric coefficients of A and of P are identical.
For constant volumetric flow, Equation (5-21) reduces to

(5-23)

Consequently, we see that the reaction rate, -(,, can be determined by mea-
suring the product concentration, Cp .
By using very little catalyst and large volumetric flow rates, the concen-
tration difference, (C, - C,,), can be made quite small. The rate of reaction
determined from Equation (5-23) can be obtained as a function of the reactant
concentration in the catalyst bed, CAb:

-ri -I' A( C Ab) (5-24)
by varying the inlet concentration. One approximation of the concentration of
A within the bed, CAB, would be the arithmetic mean of the inlet and outlet
concentrations: