Unformatted text preview: streams and
N A = 0.
(a) and (b) The feed unit is like an absorber with an additional intermediate
feed. Therefore, from Table 5.3 for an N-stage cascade,
NV = (7 N + 2 NC + 2C + 7) + (C + 3) for extra feed +1 for extra feed location
= 7 N + 2 NC + 3C + 11
N E = (5 N + 2 NC + 2) + 1 for extra feed
= 5 N + 2 NC + 3
The second unit is a distillation column like that in Example 5.5, except with an
additional feed and two more sidestreams that are located at the two feed stages.
Therefore, from Example 5.5, using M for the number of stages, including the reboiler,
NV = (7 M + 2 MC + 5C + 20) +
3(C + 3) for extra feed and 2 extra sidestreams +1 for extra feed location
= 7 M + 2 MC + 8C + 30
N E = (5 M + 2 MC + 4C + 9) + 2(C + 2) for 2 extra sidestreams + 1 for extra feed
= 5 M + 2 MC + 6C + 14
From Eq. (5-68),
NV system =
NV u − N R C + 3 + N A
all units From Eq. (5-69), NE system = NE
all units u − NR (2) Therefore, since NR = 4 and NA = 0, Eqs. (1) and (2) become,
( NV )system = (7 N + 2 NC + 3C + 11)+ ( 7 M + 2 MC + 8C + 30 ) − 4 ( C + 3) ( N E )system = 7( N + M ) + 2C ( N + M ) + 7C + 29
= (5N +2NC +3)+(5M +2MC +6C +14) − 4
= 5(N + M )+2C ( N + M ) + 6C + 13 Analysis: (d) Exercise 5.37 (continued) (c) From Eq. (5-71),
( N D )system = ( NV )system − ( N E )system = [ 7( N + M ) + 2C ( N + M ) + 7C + 29] − [5( N + M ) + 2C ( N + M ) + 6C + 13]
= 2( N + M ) + C + 16
A reasonable set of specifications is as follows:
Pressure at each stage, reboiler, condenser, reflux divider
Heat transfer at each stage and, divider
Complete feed specification
Number of stages, N
Number of stages, M
Feed stage location
Locations of 3 sidestreams
Flow rates of 3 sidestreams
Saturated liquid reflux or reflux temperature if subcooled
2(N + M) + C + 16 Exercise 5.38
Subject: Degrees of freedom and specs for a column with a liquid sidestream. Given: Column in Fig. 5.30.
Find: (a) Number of degrees of freedom.
(b) Reasonable set of design variables.
Analysis: (a) The column in Fig. 5.30 has a partial condenser. A similar column with
total condenser is analyzed in Example 5.5, giving ND = 2N + C + 11. In Table 5.2, in
operations (b) and (c), it is seen that a column with a partial condenser has 3 less degrees
of freedom than a column with a total condenser. Therefore, here,
ND = (2N + C + 11) - 3 = 2N + C + 8.
(b) A reasonable set of specifications is:
Pressures of stages, reboiler, condenser
Heat transfer for stages
Feed completely specified
Feed stage and sidestream stage locations
Distillate (volatile impurities) rate
Number of stages
Total 2N + C + 8 Exercise 5.39
Subject: Degrees of freedom analysis for distillation with a sidecut reboiled stripper.
Given: Distillation system in Fig. 5.31.
(d) Number of variables.
Number of equations.
Number of degrees of freedom.
Reasonable set of design variables. Analysis: The system consists of (1) distillation column with 2 feeds and a sidestream,
(2) reboiled stripper, (3) cooler, and...
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