Page 219 - Separation process principles 2

184 Chapter 5 Cascades and Hybrid Systems

Variable Specification Number of Variables In most separation operations, variables related to feed condi-
tions, stage heat-transfer rates, and stage pressure are known or set.
7. Feed temperature 1
Remaining specifications have proxies, provided that the variables
8. Feed pressure 1
are mathematically independent of each other and of those already
9. Condensate temperature 1
known. Thus, in the above list, the first nine entries are almost
(e.g., saturated liquid)
always known or specified. Variables 10 to 15, however, have sur-
10. Total number of stages, N
rogates. Some of these are
11. Feed stage location
12. Sidestream stage location 16. Condenser heat duty, Qc
13. Sidestream total flow rate, S 17. Reboiler heat duty, QR
14. Total distillate flow rate, D or DIF 18. Recovery or mole fraction of one component in bottoms
15. Reflux flow rate, LR, or reflux 19. Recovery or mole fraction of one component in distillate
ratio, LR/D

Heat duties Qc and QR are not good design variables because similar unit operation in Table 5.4. The closest unit is (b),
they are difficult to specify. Condenser duty Qc, for exam- which differs from the unit in Figure 5.22 by only a side-
ple, must be speciiied so that the condensate temperature lies stream. From Table 5.3, we see that an equilibrium stage
between that corresponding to a saturated liquid and the with heat transfer but without a sidestream [element (f)] has
freezing point of the condensate. Otherwise, a physically un- ND = (2C + 6), while an equilibrium stage with heat trans-
realizable (or no) solution to the problem is obtained. Simi- fer and with a sidestream [element (h)] has ND = (2C + 7)
larly, it is much easier to calculate QR knowing the total flow or one additional degree of freedom. In addition, when
rate and enthalpy of the bottom streams than vice versa. In this sidestream stage is placed in a cascade, an additional
general, QR and Qc are so closely related that it is not advis- degree of freedom is added for the location of the side-
able to specify both. stream stage. Thus, two degrees of freedom are added to
Other proxies are possible, such as a stage temperature, a ND = 2N + C + 9 for unit operation (b) in Table 5.4. The
I flow rate leaving a stage, or any independent variable that result is ND = 2N + C + 11, which is identical to that de-
characterizes the process. The problem of independence of termined in the above example.
I
variables requires careful consideration. Distillate product In a similar manner, the above example can be readily
11
I rate, Qc, and LRID, for example, are not independent. It modified to include a second feed stage. By comparing values
should also be noted that, for the design case, recoveries of of ND for elements (f) and (g) in Table 5.3, it is seen that a feed
no more than two species (items 18 and 19) are specified. adds C + 2 degrees of freedom. In addition, one more degree
These species are referred to as key components. Attempts to of freedom must be added for the location of this feed stage in
specify recoveries of three or four species will usually result a cascade. Thus, a total of C + 3 degrees of freedom are
in an unsuccessful solution of the equations. added, giving ND = 2N + 2C + 14.
The degrees of freedom for the complex distillation unit
of Figure 5.22 can be determined quickly by modifying a

SUMMARY

1. A cascade is a collection of contacting stages arranged to: 5. Single-section stage requirements for a countercurrent cascade
(a) accomplish a separation that cannot be achieved in a single for absorption and stripping can be estimated with the Kremser
stage, andor (b) reduce the amount of mass- or energy-separating equations, (5-48), (5-50), (5-54), and (5-55). A single-section,
agent. countercurrent cascade is limited in its ability to achieve a separa-
2. Cascades are single- or multiple-sectioned and may be config- tion between two components.
ured in cocurrent, crosscurrent, or countercurrent arrangements. 6. The Kremser equations can be combined for a two-section
Cascades are readily computed when governing equations are lin- cascade to give (5-66), which is suitable for making approximate
ear in component split ratios. calculations of component splits for distillation. A two-section,
3. Stage requirements for a countercurrent solid-liquid leaching countercurrent cascade can achieve a sharp split between two
andor washing cascade, involving constant underflow and mass key components. The rectifying section purifies the light compo-
transfer of one component, are given by (5-10). nents and increases recovery of heavy components. The stripping
section provides the opposite function.
4. Stage requirements for a single-section, liquid-liquid extrac-
tion cascade assuming a constant distribution coefficient and im- 7. Equilibrium cascade equations involve parameters referred to
miscible solvent and carrier are given by (5-19), (5-22), and (5-29) as washing W, extraction E, absorption A, and stripping S, factors
for cocurrent, crosscurrent, and countercurrent flow arrangements, that involve distribution coefficients, such as K, KD, and R, and
respectively. The countercurrent cascade is the most efficient. phase flow ratios, such as SIF and LIV.