Page 212 - Elements of Chemical Reaction Engineering 3rd Edition

184 Isothermal Reactor Design Chap. 4

and of butane to butene:

- + H2
C4H8
The dehydrogenation of propane is another reaction that has proven successful with
a membrane reactor [J. Membrane Sci., 77, 221 (1993)l.
C3H8 __j C,H,+H*

All the dehydrogenation reactions above can be represented symbolically as
A ~ B + C

and will take place on the catalyst side of an IMRCF. The equilibrium constant for
this reaction is quite small at 227°C (i.e., Kc = 0.05 mol/dm3). "he membrane is
permeable to B (e.g. H2) but not to A and C. Pure gaseous A enters the reactor at
8.2 atm and 227°C at a rate of 10 mol/min.
As a first approximation assume that the rate of diffusion of B out of the reac-
tor per unit volume of reactor, R,, is taken to be proportional to the concentration of
B (i.e., RB = k&).
(a) Perform differential 'mole balances on A, B, and C to arrive at a set of coupled
differential equations to solve.
(b) Plot the molar flow rates of each species as a function of space time.
Additional information: Even though this reaction is a gas-solid catalytic reaction,
we will make use of the bulk catalyst density in order to write our balances in terms
of reactor volume rather than catalyst weight (recall -rA = -rap,). For the bulk
catalyst density of ph = 1.5 g/cm3 and a 2-cm inside diameter of the tube contain-
ing the catalyst pellets, the specific reaction rate, k, and the transport coefficient, kc,
are k = 0.7 min-l and k, = 0.2 min-' , respectively.

Solution

We shail choose reactor volume rather than catalyst weight as our independent vari-
able for this example. The catalyst weight, W, and reactor voIume, V, are easily
related through the bulk catalyst density, Pb, i.e. w= pbv. First we shall perform
mole balances on the volume element A V shown in Figure E4- 10.1.

FA
FB

'ane

*8
I Figure E4-10.1