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

1. Equilibrium-Based Methods for Multicomponent Absorption, Stripping, Distillation, and Extraction Chapter10 Exercises

2. Exercise10.1 • Revise the MESH equations (10-1) to (10-6) to allow for pumparounds of the type shown in Figure 10.2 and dis­cussed by Bannon and Marple [Chem. Eng. Prog. 74(7), 41-45 (1978)] and Huber [Hydrocarbon Processing 56(8), 121-125 (1977)]. Combine the equations to obtain modified M equations similar to (10.7). Can these equations still be partitioned in a series of C tridiagonal matrix equations?

3. Exercise10.2 • Derive an equation similar to (10-7), but with u,y = yi.jVj as the variables instead of the liquid-phase mole frac­tions. Can the resulting equations still be partitioned into a series of C tridiagonal matrix equations?

4. Exercise10.3 • One thousand kilogram-moles per hour of a saturated liquid mixture of 60 mol% methanol, 20 mol% ethanol, and 20 mol% n-propanol is fed to the middle stage of a distillation column having three equilibrium stages, a total condenser, a partial reboiler, and an operating pressure of 1 atm. The distillate rate is 600 kmol/h, and the external reflux rate is 2,000 kmol/h of saturated liquid. Assuming that ideal solu­tions are formed such that A'-values can be obtained from vapor pressures and

5. assuming constant molar overflow such that the vapor rate leaving the reboiler and each stage is 2,600 kmol/h, calculate one iteration of the BP method up to and including a new set of 7} values. To initiate the iteration, assume a linear temperature profile based on a distillate temperature equal to the normal boiling point of methanol and a bottoms temperature equal to the arithmetic average of the normal boiling points of the other two alcohols,

6. Exercise10.4 • Naphtali and Sandholm group the N(2C + 1) equa­tions by stage. Instead, group the equations by type (i.e., enthalpy balances, component balances, and equilibrium re­lations). Using a three-component, three-stage example, show whether the resulting matrix structure is still block tridi­agonal.

7. Exercise10.5 • A saturated liquid feed at 125 psia contains 200 Lbmol/ h of 5 mol% iC4, 20 mol% nC4, 35 mol% iC5, and 40 mol% nC5. This feed is to be distilled at 125 psia with a column equipped with a total condenser and partial reboiler. The distillate is to contain 95% of the nC4 in the feed, and the bottoms is to contain 95% of the iC5 in the feed. Use the SRK equation for thermodynamic properties to determine a suitable design. Twice the minimum number of equilibrium stages, as estimated by the Fenske equation in Chapter 9, should provide a reasonable number of equilibrium stages.

8. Exercise10.6 • A multiple recycle-loop problem formulated by Ca-vett[1] and shown in Figure 10.36 has been used extensively to test tearing, sequencing, and convergence procedures. The flowsheet is the equivalent of a four-lheoretical-stage. near-isothermal distillation (rather than the conventional near-isobaric type), for which a patent by Gunther[2] exists. The flowsheet does not include necessary mixers, compressors, pumps, valves, and heat exchangers to make it a practical system. For the specifications shown on the drawing, deter­mine the component flow rates for all streams in the process. • [1] R. H. Cavetl, Proc. Am. Petrol. Inst. 43, 57 (1963). • [2] A. Gunther, U.S. Patent 3.575,077 (April 13.1971).