Page 298 - Distillation theory

P1: JPJ/FFX P2: FCH/FFX QC: FCH/FFX T1: FCH
0521820928c08 CB644-Petlyuk-v1 June 11, 2004 20:20

272 Synthesis of Separation Flowsheets

F 1,J = 0
F 2,J = S 2,J,1
F 3,J = min (S 3,J,K + F K−J+1,J + F 3−K,K+1 ) (8.6)
K 3,J
.............................................................
F n,1 = min (S n,1,K + F K1 + F n−K, K+1 )
K n,1
The method of dynamic programming synthesizes the optimal sequence start-
ing from its end. Therefore, expenditures S I,J,K should be determined without
calculation of the previous part of the flowsheet. For this purpose, it is necessary
to determine the composition of feeding of column I,J,K. It can be done easily,
if it is accepted that each product of separation sequence i contains as impurity
components only adjacent components (i − 1) and (i + 1) (i.e., the set permissible
concentrations of impurity components):
L i−1
η = η (8.7a)
i i
H i+1
η = η (8.7b)
i i
H
L
Where η and η are set permissible concentrations of light and heavy impurity
i i
components in product i correspondingly, η i−1 and η i+1 concentrations of compo-
i i
nents (i − 1) and (i + 1) in product i correspondingly.
At this assumption, the amount P i of the product i can be determined from
the system of linear equations of componentwise material balance that has three-
diagonal form:
H
f 1 = P 1 (1 − η ) + P 2 η L
1 2
L
H
H
f 2 = P 1 η + P 2 (1 − η − η ) + P 3 η L (8.8)
3
2
2
1
....................................................
L
f n = P n−1 η H + P n (1 − η )
n−1 n
After that, the feeding of column I, J can be determined:
I,J
f = 0 (for i < J − 1)
i
f I,J = P J η L (for i = J − 1)
i J
f I,J = f J − P J−1 η H (for i = J)
i J−1
f i I,J = f i (for J + 1 ≤ i ≤ J + I−2) (8.9)
I,J L
f = f J+I−1 − P J+I η (for i = J + I−1)
i J+I
I,J H
f = P J+I−1 η (for i = J + I)
i J+I−1
f I,J = 0 (for i ≥ J + I + 1)
i
The above-described algorithm was used for the synthesis of separation flow-
sheet of mixture of hydrocarbon gases C 3 H 8 , i-C 4 H 10 , n-C 4 H 10 , i-C 5 H 12 , n-C 5 H 12 ,
i-C 6 H 14 , and n-C 6 H 14 (n = 7). At (n = 7), the number of alternative sequences is
132. Composition and flow rate of feed, permissible impurities in the products, and
flow rates of the products are given in Table 8.1. The comparison of alternative
sequences was made in accordance with the value of annual expenditures. The
calculation of the columns were executed in accordance with simplified method
Fenske–Underwood–Gilliland. Figure 8.2a shows the graph of dependence of total