Unformatted text preview: turated liquid reflux,
alcohol concentration in bottoms, and optimal feedstage location. Exercise 5.34
Subject: Degrees of freedom and specs for distillation column with a boilup divider.
Given: Column flow diagram in Fig. 5.26 and specifications listed below.
Find: (a) Number of degrees of freedom.
(b) The reason why a feed rate cannot be specified.
Analysis: (a) From Eq. (570),
N D unit =
NR =10 and NA = 0
Therefore, Eq. (1) becomes,
N D unit = ND
all elements ND
all elements e − NR C + 2 + N A (1) e − 10 C + 2 (2) Let N1 = number of rectifying stages and N2 = number of stripping stages.
Using the values of ND for the elements in Table 5.3:
Total condenser
C+4
C+5
Reflux divider
Rectifying section
2N 1 + 2C + 5
Feed stage with heat transfer
3C + 8
Stripping section
2N 2 + 2C + 5
Boilup divider
C+5
C+4
Total reboiler
N D e = 2(N1 + N2) + 11C + 36
(3)
all elements Substituting Eq. (3) into (2),
N D unit = 2 N 1 + N 2 + 11C + 36 − 10 C + 2 = 2 N1 + N 2 + C + 16
(4)
However, the feed stage is counted in N.
Therefore, N1 + N2 = N  1. Substituting this into Eq. (4), gives
(5)
( N D )unit = 2( N − 1) + C + 16 = 2 N + C + 14
(b) The specified variables are:
Number of stages and feed stage
2
Pressures of all stages, condenser, reboiler, and 2 dividers N + 4
Adiabatic for all stages and 2 dividers
N+2
Feed composition , temperature, and pressure
C+1
2
Reflux rate set by L/V = 1.2 and vapor rate by velocity
Condensate temperature set by water temperature
Concentrations of A in distillate and C in bottoms
Total 1
2
2N + C + 14 Thus, all of degrees of freedom are utilized and the column feed rate can not be specified. Exercise 5.35
Subject:
Degrees of freedom and specifications for a mixedfeed, tripleeffect
evaporation system to concentrate an aqueous solution of an organic acid.
Given: Flow diagram of system in Fig. 5.27, and design specifications listed below
Assumptions: Organic acid is nonvolatile. No heat losses from evaporator effects.
Find: Number of degrees of freedom. Any additional specifications needed.
Analysis: The system in Fig. 5.27 consists of 3 evaporator effects, a total condenser,
and a pump. Number of interconnecting streams = NR = 6, and NA = 0. First determine
the number of degrees of freedom for one evaporator effect.
Let: V = vapor mass rate leaving an effect.
L = aqueous solution mass rate leaving an effect.
F = aqueous solution mass feed rate to an effect.
S (= D) = heating steam mass rate to and from an effect.
wF = weight fraction of organic acid in feed.
wL = weight fraction of organic acid in aqueous solution leaving effect.
TF and PF be temperature and pressure of feed.
T and P be temperature and pressure of leaving vapor and liquid.
TS and PS be temperature and pressure of steam to effect.
TC and PC be temperature and pressure of condensate from effect. Therefore, NV = 14.
The relationships among the variables are:
Total material balance: F = V + L
Acid material balance: FwF = LwL
Equilibrium temperature: T = f{P, wL}, i.e. a modified Raoult's law
Energy balance: LHL + VHV  FHF = S(HS  HC)
Therefore, NE = 4...
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 Spring '11
 Levicky
 The Land

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