Chapter7
Equilibrium-Based
Methods for
Multicomponent
Absorption,
Stripping,
Distillation, and
Extraction
Purpose and Requirements:


Know Equilibrium-Based Methods for Multicomponent
Learn to use ASPEN PLUS, ChemCAD, HYSIM, PRO/II
Key and Difficult Points:
Key Points


Theoretical Model for an Equilibrium Stage
General Strategy of Mathematical Solution
Difficult Points



Equation-Tearing Procedures
Simultaneous Correction Procedures
Inside-Out Method
Outline
7.1 THEORETICAL MODEL FOR AN
EQUILIBRIUM STAGE
7.2 GENERAL STRATEGY OF MATHEMATICAL
SOLUTION
7.3 EQUATION-TEARING PROCEDURES
7.4 SIMULTANEOUS CORRECTION
PROCEDURES
7.5 INSIDE-OUT METHOD
Absorption
(Gas Absorption/Gas Scrubbing/Gas
Washing吸收)





Gas Mixture (Solutes or Absorbate)
Liquid (Solvent or Absorbent)
Separate Gas Mixtures
Remove Impurities, Contaminants, Pollutants, or
Catalyst Poisons from a Gas(H2S/Natural Gas)
Recover Valuable Chemicals


Physical Absorption
Chemical Absorption
(Reactive Absorption)
Figure 6.1 Typical Absorption Process
Absorption Factor
(A吸收因子)

A = L/KV
Component A = L/KV K-value
Water
1.7
0.031
Acetone
1.38
2.0
Oxygen
0.00006
45,000
Nitrogen
0.00003
90,000
Argon
0.00008
35,000
•Larger the value of A，Fewer the number of stages required
•1.25 to 2.0 ，1.4 being a frequently recommended value
Stripping
(Desorption解吸)

Stripping
Distillation

Stripping Factor

(S解吸因子)

S = 1/ A= KV/L
High temperature
Low pressure is desirable
Optimum stripping factor ：1.4.
7.1 EQUIPMENT
trayed tower
packed column
bubble column
spray tower
centrifugal contactor
Figure 6.2 Industrial Equipment for Absorption and Stripping
Trayed Tower
(Plate Clolumns板式塔)
Figure7.3 Details of a contacting tray in a trayed tower
(a) perforation
(b) valve cap (c) bubble cap
(d) Tray with valve caps
Figure 7.4 Three types of tray openings for
passage of vapor up into liquid
(a) Spray(b) Froth(c) Emulsion(d) Bubble(e)Cellular Foam
Liquid carries no vapor bubbles
to the tray below
Vapor carries no liquid droplets
to the tray above
No weeping of liquid through the
openings of the tray
Equilibrium between the exiting
vapor and liquid phases
is approached on each tray.
Figure 7.5 Possible vapor-liquid flow regimes for a contacting tray
Packed
Columns
Figure 7.6 Details of internals
used in a packed column
Packing
Materails
•More surface area for mass transfer
•Higher flow capacity
•Lower pressure drop
(a) Random Packing
Materials
(b) Structured Packing
Materials
•Expensive
•Far less pressure drop
•Higher efficiency and capacity
Figure 7.7 Typical materials used in a packed column
7.2 ABSORBER/STRIPPER
DESIGN








7.2.1 General Design Considerations
7.2.2 Trayed Towers
7.2.2.1 Graphical Equilibrium-Stage
7.2.2.2 Algebraic Method for Determining
the Number of Equilibrium
7.2.2.3 Stage Efficiency
7.2.3 Packed Columns
6.2.3.1 Rate-based Method
6.2.3.2 Packed Column Efficiency, Capacity,
and Pressure Drop
7.2.1 General Design Considerations
Design or analysis of an absorber (or stripper) requires
consideration of a number of factors, including:
1. Entering gas (liquid) flow rate, composition, temperature,
and pressure
2. Desired degree of recovery of one or more solutes
3. Choice of absorbent (stripping agent)
4. Operating pressure and temperature, and allowable gas
pressure drop
5. Minimum absorbent (stripping agent) flow rate and actual
absorbent (stripping agent) flow rate as a multiple of the
minimum rate needed to make the separation
6. Number of equilibrium stages
7. Heat effects and need for cooling (heating)
8. Type of absorber (stripper) equipment
9. Height of absorber (stripper)
10. Diameter of absorber (stripper)
SUMMARY





1. Rigorous methods are readily available for computersolution of equilibrium-based models for multicomponent,
multistage absorption, stripping, distillation, and liquidliquid extraction.
2. The equilibrium-based model for a countercurrent-flow
cascade provides for multiple feeds, vapor side streams,
liquid side streams, and intermediate heat exchangers.
Thus, the model can handle almost any type of column
configuration.
3. The model equations include component material
balances, total material balances, phase equilibria relations,
and energy balances.
4. Some or all of the model equations can usually he
grouped so as to obtain tridiagonal matrix equations, for
which an efficient solution algorithm is available.
5. Widely used methods for iteratively solving all of the
model equations are the bubble-point (BP) method, the
sum-rales (SR) method, the simultaneous correction (SO
method, and the inside-out method.




6. The BP method is generally restricted to distillation
problems involving narrow-boiling feed mixtures.
7. The SR method is generally restricted to absorption and
stripping problems involving wide-boiling feed mixtures or
in the ISR form to extraction problems.
8. The SC and inside-out methods are designed to solve any
type of column configuration for any type of feed mixture.
Because of its computational efficiency, the inside-oi
method is often the method of choice; however, it may fail
to converge when highly! nonideal liquid mixtures are
involved, in which case the slower SC method should j be
tried. Both methods permit considerable flexibility in
specifications.
9. When both the SC and inside-out methods fail, resort can
be made to the much slower relaxation and continuation
methods.
REFERENCES








1. Wang. J.C.. and G.E. Hcnkc, Hydrocarbon Processing
45(8). 155-163 (1966).
2. Myers. A.L.. and W.D. Seider. Introduction to Chemical
Engineering and Computer Calculations, Prentice-Hall,
Englewood Cliffs. NJ. 4X4-507 (1976).
3. Lewis. W.K.. and G.L. Matheson, Ind. Eng. Chem. 24,
496-498 (1932).
4. Thiele, E.W.. and R.L. Geddes. Ind. Eng. Chem. 25, 290
(1933).
5. Holland. C.D.. Mullicomponent Distillation. PrenticeHall. Englewood Cliffs. NJ (1963).
6. Amundson. N.R.. and A.J. Pontinen. Ind. Eng. Chem. 50,
730-736 (1958).
7. Friday. J.R.. and B.D. Smith. AlChE J. 10, 698-707 (1964).
8. Boston. J.K. and S.L. Sullivan. Jr., Can. J. Chem. Eng.
52,52-63 (1974).







16. Shinohara, T.. P.J. Johansen. and J.D. Seader, Stagewise
Compulations—Computer Programs for Chemical
Engineering Education, J. Christensen, Ed.. Aztec
Publishing, Austin, TX pp. 390-428, A-17 (1972).
17. Tsuboka. T.. and T. Katayama. J. Chem. Eng. Japan 9,
40-45 (1976).
18. Hala, E.. I. Wiehterle. J. Polak. and T. Bouhlik. VaporLiquid Equilibrium Data at Normal Pressures. Pergamon.
Oxford p. .108 ! (1968).
19. Steih. V.H.../. Praki. Chem. 4, Reihe. Bd. 28. 252-280
(1965).
20. Cohen, G.. and H. Renon. Can.J. Chem. Eng. 48, 2412% j (1970).
21. Goldstein, R.P.. and R.B. Stanlield, Ind. Eng. Chem.,
from' De.s. Develop. 9, 78-84 (1970).
22. Naphtali, L.M.. "The distillation column as a large
system." paper presented at the AIChE56th National
Meeting. San Francisco. May 16-19. 1965.








23. Naphtali. L.M.. and P.P. Sandholm. AlChE J. 17, 14S-I53
(1971).
24. Fredenslund. A.. J. GmehJing, and P. Rasmussen.
Vapor-Liquid; Equilibria Using UNIFAC, A Group
Contribution Method. Elscvicr, ; Amsterdam (1977).
25. Beveridge, G.S.G., and R.S. Schechter. Optimization:
Theory and Practice, McGraw-Hill, New York pp. 180-189
(1970). ;
26. Block, U.. and B. Hegner, AIChE .I. 22, 582-589 (1976).
27. Hofeling, B.. and J.D. Seader. AlChE J. 24, 1 131-1134
(1978). ,
28. Boston, J.F., and S.L. Sullivan. Jr., Can. .J. Chem. Engr.
52,52-63(1974).
29. Boston. J.F., and H.I. Britt. Comput. Chem. Engng. 2,
109-122 (1978).
30. Boston, J.F.. ACS Symp. Ser, No. 124. 135-151 (1980).







31. Russell, R.A., Chem. Eng. 90(20), 53-59 (1983).
32. Trevino-Lo/ano. R.A.. T.P. Kisala, and J.F. Boston.
Comput. Chem. Engng. 8, 105-115 (1984).
33. Jelinek. J., Comput. Chem. Engng. 12, 195-198 (1988).
34. Venkataraman. S.. W.K. Than, and J.F. Boston. Chem. %
Prog. 86(8), 45-54 (1990).
35. Robinson. C.S., and E.R. Gilliland, Elements of
Fractional Distillation, 4th edition, pp. 232-236. McGrawHill. New York (1950).
36. Broyden, C.G.. Math Comp. 19, 577-593 (1965).
37. Kister, H. Z.. "Distillation Design". McGraw-Hill, Inc.,
NY (1992)