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Pressure at reflux divider outlet
Pressure at total condenser outlet
Heat transfer rate for each stage, except reboiler
Heat transfer rate for divider
Feed mole fractions (only count C  1)
Reflux rate
Mole fraction of component in distillate
Mole fraction of component in bottoms
Total
Need 5 more specifications, which might be:
Feed rate
Feed temperature
Feed pressure
Optimal feed location
Saturated liquid leaving condenser N
1
1
N1
1
1
1
1
1
______
2N + 6 Exercise 5.28
Subject:
Verification of numbers of degrees of freedom for 3 operations, and effect
of adding another feed.
Given: Degrees of freedom for operations (b), (c), and (g) in Table 5.4. Find: Verify values of ND and determine effect of adding another feed.
Analysis: Operation (b), distillation with total condenser and partial reboiler:
From Eq. (570),
ND unit = ND
all elements e − NR C + 2 + N A (1) e −9 C+2 (2) NR = 9 and NA = 0
Therefore, Eq. (1) becomes,
N D unit = ND
all elements Let N1 = number of rectifying stages and N2 = number of stripping stages.
Using the values of ND for the elements in Table 5.3:
C+4
Total condenser
Reflux divider
C+5
Rectifying section
2N 1 + 2C + 5
Feed stage with heat transfer
3C + 8
Stripping section
2N 2 + 2C + 5
C+4
Partial reboiler
N D e = 2(N1 + N2) + 10C + 31 (3) all elements Substituting Eq. (3) into (2),
N D unit = 2 N 1 + N 2 + 10C + 31 − 9 C + 2 = 2 N1 + N 2 + C + 13 (4) However, in Operation (b) of Table 5.4, the feed stage and the partial reboiler are counted
in N.
Therefore, N1 + N2 = N  1  1 = N  2. Substituting this into Eq. (4), gives ( N D )unit = 2( N − 2) + C + 13 = 2 N + C − 9
which verifies the result given in Table 5.4. (5) Exercise 5.28 (continued)
If a second feed is added, we add C + 2 degrees of freedom for the feed variables and
for feed location.
Then,
( N D )2 feeds = ( N D )1 feed + C + 3 = 2 N + 2C + 12
Operation (c), distillation with a partial condenser and partial reboiler:
With a partial condenser instead of a total condenser, there are only 8 redundant streams
and no reflux divider. Therefore, Eq. (4) becomes: ( N D )unit = 2 N + C + 9 + (C + 2) − (C + 5) = 2 N + C + 6 (6) which verifies the result given in Table 5.4. With two feeds, ( N D )2 feeds = ( N D )1 feed + C + 3 = 2 N + 2C + 9
Operation (g), distillation with a partial reboiler and a mixed condenser that
produces both vapor distillate and liquid distillate:
With a mixed condenser, we can modify Operation (c), by adding a reflux divider and
one redundant stream. Therefore, Eq. (6) becomes: ( N D )unit = 2 N + C + 6 + (C + 5) − (C + 2) = 2 N + C + 9
which verifies the result given in Table 5.4.
With two feeds, ( N D ) 2 feeds = ( N D )1 feed + C + 3 = 2 N + 2C + 12 Exercise 5.29
Subject:
Verification of numbers of degrees of freedom for 2 operations, and effect
of adding a vapor sidestream..
Given: Degrees of freedom for operations (e) and (f) in Table 5.4. Find: Verify values of ND and determine effect of adding a vapor stream
Analysis: Operation (e), reboiled absorber:
From Eq. (570),
ND unit = unit = ND
all elements e − NR C + 2 + N A (1) e − 6(C + 2...
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 Spring '11
 Levicky
 The Land

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