Page 97 - Separation process principles 2

62 Chapter 2 Thermodynamics of Separation Operations

Product Product Product Section 2.2
Feed 1 2 3
2.5 Which of the following K-value expressions, if any, is (are)
Phase condition Liquid Liquid Liquid Liquid rigorous? For those expressions that are not rigorous, cite the
Temperature, "F 305 299 304 3 14 assumptions involved.
Enthalpy, 29,290 29,750 29,550 28,320
(a) K; = &L/$v
B tu~lbmol
Entropy, 15.32 12.47 13.60 14.68 (b) Ki = +L/+L
Btu/lbmol-"R (c) Ki = +L
2.3 Distillation column C3 in Figure 1.9 separates stream 5 into (dl K; = ~~L+L/&v
streams 6 and 7, according to the material balance in Table 1.5. A (e) K; = Pis/ P
suitable column for the separation, if carried out at 700 kPa, con- (0 K; = Y;L~L/Y;V+V
tains 70 plates with a condenser duty of 27,300,000 Wh. Using the (g) K; = 7iLPisIP
following data and an infinite surroundings temperature, To, of 2.6 Experimental measurements of Vaughan and Collins [Ind. Eng.
298.15 K, compute: Chem., 34,885 (1942)l for the propane-isopentane system at 167°F
(a) The duty of the reboiler in kJ/h and 147 psia show for propane a liquid-phase mole fraction of 0.2900
(b) The irreversible production of entropy in kJh-K, assuming the in equilibrium with a vapor-phase mole fraction of 0.6650. Calculate:
use of cooling water at a nominal temperature of 25°C for the con- (a) The K-values for C3 and iC5 from the experimental data.
denser and saturated steam at 100°C for the reboiler (b) Estimates of the K-values of C3 and iC5 from Raoult's law
(c) The lost work in kJh assuming vapor pressures at 167°F of 409.6 and 58.6 psia,
respectively.
(d) The minimum work of separation in kJh
(e) The second-law efficiency Compare the results of (a) and (b). Assuming the experimental values
are correct, how could better estimates of the K-values be achieved?
Assume the shaft work of the reflux pump is negligible.
To respond to this question, compare the rigorous expression
Feed Distillate Bottoms Ki = y;L+L/&.v to the Raoult's law expression Ki = Pis/P.
(Stream 5) (Stream 6) (Stream 7)
2.7 Mutual solubility data for the isooctane (1)lfurfural (2) sys-
Phase condition Liquid Liquid Liquid tem at 25°C are [Chem. Eng. Sci., 6, 116 (1957)l
Temperature, K 348 323 343
Liquid Phase I Liquid Phase I1
Pressure, kPa 1,950 700 730
Enthalpy, 17,000 13,420 15,840
Wflunol
Compute:
Entropy, 25.05 5.87 21.22
kJ/kmol-K (a) The distribution coefficients for isooctane and furfural
(b) The relative selectivity for isooctane relative to furfural
2.4 A spiral-wound, nonporous cellulose acetate membrane sepa- (c) The activity coefficient of isooctane in liquid phase 1 and the
rator is to be used to separate a gas containing Hz, CH4, and C2H6. activity coefficient of furfural in liquid phase 2 assuming
The permeate will be 95 mol% pure Hz and will contain no ethane. -yz(" = 1.0 and = 1.0.
The relative split ratio (separation power), SP, for H2 relative to
2.8 In petroleum refineries, streams rich in alkylbenzenes and
methane will be 47. Using the following data and an infinite sur-
alkylnaphthalenes result from catalytic cracking operations. Such
roundings temperature of 80nF, compute:
streams can be hydrodealkylated to more valuable products such as
(a) The irreversible production of entropy in Btuh-R benzene and naphthalene. At 25"C, solid naphthalene (normal
(b) The lost work in Btuh melting point = 80.3"C) has the following solubilities in various
(c) The minimum work of separation in Btuh. Why is it negative? liquid solvents [Naphthalene, API Publication 707, Washington,
What other method(s) might be used to make the separation? DC (Oct. 1978)], including benzene:
Feed flow rates,
Mole Fraction
lbmoh
Solvent Naphthalene
Benzene 0.2946
Cyclohexane 0.1487
Carbon tetrachloride 0.2591
Stream properties: n-Hexane 0.1168
Water 0.18 x 10-5
Feed Permeate Retentate
Phase condition Vapor Vapor Vapor For each solvent, compute the activity coefficient of naphthalene in
Temperature, OF 80 80 80 the liquid solvent phase using the following equations for the vapor
Pressure, psia 365 50 365 pressure in tom of solid and liquid naphthalene:
Enthalpy, 8,550 8,380 8,890
In Psolld = 26.708 - 8,7121 T
BtuAbmol
Entropy, 1.520 4.222 2.742 In PL ,.+,, = 16.1426 - 3992.1)1/(T - 71.29)
Btu/lbmol-R where T is in K.