Equilibrium-Based Methods for Multicomponent Absorption, Stripping, Distillation, and Extraction

Chapter10

Key and Difficult Points:Key PointsTheoretical Model for an Equilibrium StageGeneral Strategy of Mathematical SolutionDifficult PointsEquation-Tearing ProceduresSimultaneous Correction ProceduresInside-Out MethodPurpose and Requirements:Know Equilibrium-Based Methods for Multicomponent Learn to use ASPEN PLUS, ChemCAD, HYSIM, PRO/II

Outline10.1 THEORETICAL MODEL FOR AN EQUILIBRIUM STAGE10.2 GENERAL STRATEGY OF MATHEMATICAL SOLUTION10.3 EQUATION-TEARING PROCEDURES10.4 SIMULTANEOUS CORRECTION PROCEDURES10.5 INSIDE-OUT METHOD

Absorption (Gas Absorption/Gas Scrubbing/Gas Washing)

Gas Mixture (Solutes or Absorbate)Liquid (Solvent or Absorbent)

Separate Gas MixturesRemove Impurities, Contaminants, Pollutants, or Catalyst Poisons from a Gas(H2S/Natural Gas)Recover Valuable Chemicals

Chemical Absorption (Reactive Absorption)

Figure 6.1 Typical Absorption Process Physical Absorption

Absorption Factor(A)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 AFewer the number of stages required1.25 to 2.0 1.4 being a frequently recommended value

Stripping (Desorption) StrippingDistillation

Stripping Factor (S)S = 1/ A= KV/LHigh temperature Low pressure is desirable

Optimum stripping factor 1.4.

6.1 EQUIPMENTFigure 6.2 Industrial Equipment for Absorption and Stripping trayed towerpacked columnspray towerbubble columncentrifugal contactor

Trayed Tower(Plate Clolumns)Figure 6.3 Details of a contacting tray in a trayed tower

Figure 6.4 Three types of tray openings for passage of vapor up into liquid(d) Tray with valve caps(b) valve cap(c) bubble cap (a) perforation

Figure 6.5 Possible vapor-liquid flow regimes for a contacting tray (a) Spray(b) Froth(c) Emulsion(d) Bubble(e)Cellular Foam FrothLiquid carries no vapor bubbles to the tray belowVapor carries no liquid droplets to the tray aboveNo weeping of liquid through the openings of the tray

Equilibrium between the exiting vapor and liquid phases is approached on each tray.

Packed Columns

Figure 6.6 Details of internals used in a packed column

Packing MaterailsFigure 6.7 Typical materials used in a packed column(a) Random Packing Materials(b) Structured Packing MaterialsMore surface area for mass transferHigher flow capacityLower pressure drop Expensive

Far less pressure drop Higher efficiency and capacity

6.2 ABSORBER/STRIPPER DESIGN6.2.1 General Design Considerations6.2.2 Trayed Towers 6.2.2.1 Graphical Equilibrium-Stage 6.2.2.2 Algebraic Method for Determining the Number of Equilibrium 6.2.2.3 Stage Efficiency 6.2.3 Packed Columns 6.2.3.1 Rate-based Method 6.2.3.2 Packed Column Efficiency, Capacity, and Pressure Drop

6.2.1 General Design Considerations1. Entering gas (liquid) flow rate, composition, temperature, and pressure2. Desired degree of recovery of one or more solutes3. Choice of absorbent (stripping agent)4. Operating pressure and temperature, and allowable gas pressure drop5. 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

Design or analysis of an absorber (or stripper) requires consideration of a number of factors, including:6. Number of equilibrium stages7. Heat effects and need for cooling (heating)8. Type of absorber (stripper) equipment9. Height of absorber (stripper)10. Diameter of absorber (stripper)

SUMMARY1. Rigorous methods are readily available for computer-solution of equilibrium-based models for multicomponent, multistage absorption, stripping, distillation, and liquid-liquid 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.

REFERENCES1. 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. Prentice-Hall. 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 CompulationsComputer 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. Vapor-Liquid 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, 241-2% 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.

9. Boston. J.F.. and S.L. Sullivan. Jr.. Can. J. Chem. Eng. 50, 663-669 (1972).10. Johanson, P.J., and J.D. Seader, Stagewi.se Computations-Computer Programs for Chemical Engineering Education (ed. by J.Christensen). A/tee Publishing, Austin. TX pp. 349-389, A-16(1972).11. Lapidus, L.. Digital Computation for Chemical Engineers, McGraw-Hill. New York pp. 308-309 (1962).12. Orbach. ().. and C.M. Crowe, Can. J. Chem. Eng. 49, 509-513(1971).13. Scheibel. E.G.. Ind. Eng. Chem 38,397-399 (1946).14. Sujata. A.D.. Hydrocarbon Processing 40(12). 137-140 (1961).15. Burningham, D.W., and F.D. Otto, Hydrocarbon Processing 46(10). 163-170 (1967)

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. McGraw-Hill. New York (1950).36. Broyden, C.G.. Math Comp. 19, 577-593 (1965).37. Kister, H. Z.. "Distillation Design". McGraw-Hill, Inc., NY (1992)