Page 93 - Separation process engineering

ε = 0.005 is used here.
R
D. Do It. The first guess is made by arbitrarily assuming that T drum = 15°C and V/F = 0.25. Since
convergence of the program is rapid, more effort on an accurate first guess is probably not
justified. Using Eq. (2-46) as illustrated in Example 2-2, the following V/F values are obtained [K
values from Eq. (2-30)]:

Note that convergence is monotonic. With V/F known, x and y are found from Eqs. (2-38) and (2-
i
i
39).
Compositions are: x = 0.0124, x = 0.5459, x = 0.4470, and y = 0.8072, y = 0.1398, y =
p
H
H
m
p
m
0.0362.
Flow rates L and V are found from the mass balance and V/F value. After determining enthalpies,
Eq. (2-56a) is used to determine T = 27.9°C. Obviously, this is still far from convergence.
drum,2
The convergence procedure is continued, as summarized in Table 2-6. Note that the drum
temperature oscillates, and because of this the converged V/F oscillates. Also, the number of trials
to converge on V/F decreases as the calculation proceeds. The final compositions and flow rates
are:

x = 0.0108, x = 0.5381, x = 0.4513
m
p
H
y = 0.7531, y = 0.1925, y = 0.0539
H
P
m
V = 382.3 kmol/h and L = 1117.7 kmol/h
Table 2-6. Iterations for Example 2-3

E. Check. The results are checked throughout the trial-and-error procedure. Naturally, they depend

upon the validity of data used for the enthalpies and Ks. At least the results appear to be self-
consistent (that is, Σ x = 1.0, Σ y = 1.0) and are of the right order of magnitude. This problem was
i i
also solved using Aspen Plus with the Peng-Robinson equation for VLE (see Chapter 2 Appendix
A). The results are x = 0.0079, x = 0.5374, x = 0.4547, L = 1107.8, and y = 0.7424, y =
m p H m p
0.2032, y = 0.0543, V = 392.2, and T drum = 27.99°C. With the exception of the drum temperature
H
these results, which use different data, are close.

F. Generalization. The use of the computer greatly reduces calculation time on this double trial-and-
error problem. Use of a process simulator that includes VLE and enthalpy correlations will be
fastest. However, any software package must be validated (Shacham et al., 2008).