Page 187 - Separation process principles 2

152 Chapter 4 Single Equilibrium Stages and Flash Calculations

diagrams, unless only one of the three components (called the can be represented algebraically or graphically by adsorption
solute) is soluble in the two liquid phases and the system is dilute isotherms.
in the solute. In that case, the conditions can be readily determined 8. Solubility of gases that are only sparingly soluble in a liquid ,
algebraically using phase-distribution ratios for the solute. are well represented by a Henry's law constant that depends on .
6. Liquid-liquid equilibrium conditions for multicomponent temperature.
mixtures of four or more components are best determined with 9. Solid vapor pressure can be used to determine equilibrium
process-simulation computer programs, particularly when the sys- sublimation and desublimation conditions for gas-solid systems.
tem is not dilute with respect to the solute(s). Adsorption isotherms and y-x diagrams are useful in determining
7. Solid-liquid equilibrium commonly occurs in leaching, adsorption-equilibrium conditions for gas mixtures in the presence
crystallization, and adsorption. Leaching calculations commonly of a solid adsorbent.
assume that the solute is completely dissolved in the solvent and 10. Calculations of equilibrium when more than two phases are
that the remaining solid leaving in the underflow is accompanied present are best made with computer simulation programs. How-
by a known fraction of liquid. Crystallization calculations are ever, approximate manual procedures are readily applied to vapor-
best made with a solid-liquid phase equilibrium diagram. For liquid-solid systems when no component is found in all three
crystallization of inorganic salts from an aqueous solution, for- phases and for vapor-liquid-liquid systems when only one compo-
mation of hydrates must be considered. Equilibrium adsorption nent distributes in all three phases.

REFERENCES

1. PERRY, R.H., D.W. GREEN, and J.O. MALONEY, Eds., Perry 's Chemical 10. JANECKE, E., Z. Anorg. Allg. Chem., 51,132-157 (1906).
Engineers'Handbook, 7th ed., McGraw-Hill, New York, Section 13 (1997).
11. FRANCIS, A.W., Liqurd-Lrquid Eqiiilibriurns, Interscience, New York
2. GMEHLING, J., and U. ONKEN, Vapor-Liquid Equilibrium Data (1963).
Collection, DECHEMA Chemistry Data Series, 1-8 (1977-1984).
12. FINDLAY, A,, Phase Rille, Dover, New York (1951).
3. KEYES, D.B., Ind. Eng. Chem., 21,998-1001 (1929).
13. FRITZ, W., and E.-U. SCHULUENDER,
Chem. Eng. Scr., 29, 1279-1282
4. HUGHES, R.R., H.D. EVANS, and C.V. STERNLING, (1974).
Chem. Eng. Prog~,
49,78-87 (1953).
14. FELDER, R.M., and R.W. Rouss~~u, Elementary Principles of
5. RACHFORD, H.H., JR., and J.D. RICE, J. Pet. Tech., 4 (lo), Section 1, Chemical Processes, 3rd ed., John Wiley and Sons, New York, pp. 613416
p. 19, and Section 2, p. 3 (Oct. 1952). (1986).
6. PRESS, W.H., S.A. TEUKOLSKY,
W.T. VETTERLING, and B.P. FLANNERY, 15. LEWIS, W.K., E.R. GILLILAND, B. CHERTON, and W.H. HOFFMAN,
Numerical Recipes in FORTRAN, 2nd ed., Cambridge University Press, J. Am. Chem. Soc., 72,1153-1157 (1950).
Cambridge, chap. 9 (1992).
16. HILDEBRAND, J.H., Principles oj Chemistry, 4th ed., Macmllan, New
7. GOFF, G.H., P.S. FARRINGTON, and B.H. SAGE, Ind. Eng. Chem., 42, York (1940).
735-743 (1950).
17. HENLEY, E.J., and E.M. ROSEN, A4aterial and Energy Balance
A.,
8. CONSTANTINIDES, and N. MosToun, Numerical Methods for Computations, John Wiley and Sons, New York, pp. 351-353 (1969).
Chemical Engineers with MATLAB Applications, Prentice Hall PTR, Upper
18. CONWAY, J.B., and J.J. NORTON, Ind. Eng. Chem., 43, 1433-1435
Saddle River, NJ (1999).
(1951).
9. ROBBINS, L.A., in R.H. PERRY, D.H. GREEN, and J.O. MALONEY, Eds.,
Perry's Chemical Engineers' Handbook, 7th ed., McGraw-Hill, New York,
pp. 15-10 to 15-15 (1997).
EXERCISES

Section 4.1 (b) The same as part (a), except that the stage is not adiabatic.
4.1 Consider the equilibrium stage shown in Figure 4.35. Conduct (c) A multicomponent vapor of known temperature, pressure, and
a degrees-of-freedom analysis by performing the following steps: composition is to be partially condensed in a condenser. The outlet
(a) List and count the variables. pressure of the condenser and the inlet cooling water temperature
are fixed. Calculate the cooling water required.
(b) Write and count the equations relating the variables.
4.3 Consider an adiabatic equilibrium flash. The variables are all
(c) Calculate the degrees of freedom.
as indicated in Figure 4.36.
(d) List a reasonable set of design variables.
(a) Determine the number of variables.
4.2 Can the following problems be solved uniquely?
(b) Write all the independent equations that relate the variables.
(a) The feed streams to an adiabatic equilibrium stage consist
(c) Determine the number of equations.
of liquid and vapor streams of known composition, flow rate, tem- j
perature, and pressure. Given the stage (outlet) temperature and (d) Determine the number of degrees of freedom.
pressure, calculate the composition and amounts of equilibrium (e) What variables would you prefer to specify in order to solve a /
vapor and liquid leaving the stage. typical adiabatic flash problem? \
t