Page 64 - Applied Process Design For Chemical And Petrochemical Plants Volume II

Distillation 53

Example 8-15: Batch Distillation, Vapor Boil-up Rate for
Fixed Trays (used by permission of Treybal[129];
clarification added by this author)

Distill a small quantity each day to obtain relatively pure
*xylene from a mixture of ortho and para xylene, having
boiling points of 142.7"C and 138.4"C, respectively. The
feed is 15 lbmols (about 225 gallons) per batch, at 0.20
mol fraction para. The desired residue product is 0.020 in
the kettle, while the distillate is to be 0.400 mol fraction N,i, +1=-- 1'514 -24.6
para. A distillation column equivalent to 50 theoretical 0.06145
plate is to be used.
The time requirement is to complete the distillation/ Nmin (in column) + 1 (kettle) = 24.6
recovery in six hours, allowing an extra two hours for
charging, emptying, and cleaning. What is the constant The results indicate that 25 theoretical plates are mini-
rate that the distillation must be carried out? mum; then by assuming an efficiency of 50%, total actual
trays of 50 should be adequate. Choose values of k (see
F = 15 lb-mols/hr nomenclature) and solve for b and xs by:

Xf = 0.20 b = (ak/c) - k

XD = 0.400 c = 1 + (a - 1)k

x, = 0.02 AX: + Bx, + C = 0
The material balance: The tabulated results are:

k b xs
D = 15 (0.2 - 0.02)/(0.400 - 0.020) = 7.105 mols 0.0200 0.00297 0.01899
0.0500 0.00716 0.04842
Then, F = D - W 0.0750 0.01043 0.07301
0.1000 0.01347 0.09728
W = 15 - 7.105 = '7.893 mols 0.1250 0.0 163 1 0.12109
0.1500 0.01895 0.14470
el = D/G 0.1750 0.02137 0.17145
0.2000 0.02360 0.18133
and, 0 = 7.105/G
Graphical integration shows the area under the curve,
(1 - xsi la a-1 (1 - Xf 1" Figure 8-38A, to be 15.764. Applying this to:
Xsi
02 = (W/G)r (dx, / b)
(1 - 0.18330)1.'52 (1 - 0.2)1.'52 xw
0.18530 0.2
Then, 02 = 7.895 (15.764)/G = 124.46/G
4.26 = 4.26
81 + 02 = 6 hr = 7.105/G + 124.46/G
At 138.4"C, the vapor pressures of ortho and para are
660 and '760 mm Hg, respectively. Because Raoult's law G = 21.93 Ib-mols vapor/hr
applies:
This is the boilup rate, which is approximately 3.3 ft3
CI = 760/660 = 1.132 vapor/sec. An approximately 1 ft 0 in. diameter column
can handle this rate; however, because it is in the usual size
Solving the equation by trial and error shows that xsi = for a packed tower (or cartridge trays), the diameter must
0.18330. Solving for the minimum number of plates be checked using the packed tower calculations in Chap-
required: ter 9 of this volume.