Page 73 - Elements of Chemical Reaction Engineering Ebook

44 Conversion and Reactor Sizing Chap. 2

dm.s
V = 0.867 [ 800 mol (OX)] = 554.9 dm3
S
The CSTR volume necessary to achieve 80% conversion at the specified temper&-
ture and pressure is 555 dm3.

Example 2-3 Sizing a PFR

The reaction described by the data in Tables 2-1 and 2-2 is to be carried out in a
PFR. The entering molar flow rate of A is 0.867 mol/s. Calculate the reactor volume
necessary to achieve 80% conversion in a PFR (a) First, use one of the integration
formulas given in Appendix A.4 to determine the PFR reactor volume. (b) Next,
shade the area in Figure 2-1 which when multiplied by FA0 would give the PFR vol-
ume. (c) Make a qualitative sketch of the conversion, X, and the rate of reaction,
-rA, down the length (volume) of the reactor.

Solution
(a) For the PFR, the differential form of the mole balance is

(2-15)

Rearranging and integrating gives

(2-16)

For 80% conversion, we will use the five-point quadratic formula with AX = 0.2.

1 +-+- 4 2 4
-rA(0.6)
-rA(X = 0) -rA(0.2) -rA(0.4) f-+- -rA(0.8)
Using values of 1 / - r, in Table 2-2 yields

s.dm3
V = (0.867 mol/s)(0.2/3)[189 + 4(200) + Z(250) + 4(400) + (800)J mol
= (0.867 mol/s)(259.3 s dm3/m01)
= 225 dm3
(b) The integral in Equation (2-16) can be evaluated for the area under the curve of
a plot of (l/-rA) versus X.

-!!- % = area under the curve between X = 0 and X = 0.8
=
F*O (see appropriate shaded area in Figure E2-3.1)