Ind. Eng. Chem. Res. 1994,33, 1631-1635
1631
RESEARCH NOTES Thermodynamic Analysis of Continuous Distillation Processes Using ASOG Group Contribution Methods for Excess Enthalpy and Excess Entropy Hiroyuki Hayashi and Kazuo Kojima' Department of Industrial Chemistry, College of Science and Technology, Nihon University, 8 Kanda Surugadai, 1 -Chome, Chiyoda-Ku, Tokyo, Japan
A thermodynamic analysis based on the second law of thermodynamics has been applied to the separation of binary and ternary systems by continuous distillation. Previously developed analytical solution of groups (ASOG) group contribution methods were used for estimating phase equilibria and liquid-phase excess enthalpy and excess entropy. Thermodynamic efficiency of the distillation processes was studied as a function of reflux ratio. An incorporation of a heat recovery system was also tested. In the studied cases, a heat recovery system showed almost no effect on the thermodynamic efficiency of the processes. A maximum of the thermodynamic efficiency was observed at the minimum reflux ratio.
Introduction Thermodynamic analysis of separation processes is necessary for economicalutilization of energy and material resources in the chemical industry. It is also considered as a potential tool for solving environmental problems. A basis of the analysis is provided by the second law of thermodynamics (Perry et al., 1984;Daubert, 1985). Until recently, however, direct applications of its principles have not been frequently found in practice (Kenney, 1989).One reason for that can be seen in difficulties associated with estimating mixture entropy, the key property for the thermodynamic analysis. In our recent work (Hayashi and Kojima, 1993),we have proposed a method to calculate the thermodynamic efficiency, and we have described a predictive method for the excess entropy based on a combination of analytical solution of groups (ASOG) group contribution methods for calculating excess properties. The model uses a newly developed ASOG method for predicting excess enthalpy (Hayashi et al., 1992). In this work, the two ASOG methods for calculating excess entropy and excess enthalpy are applied to a thermodynamic analysis of continuous distillation processes. The separations of the binary system methanol water and the ternary system acetone + benzene + toluene are considered in this example development.
The lost work in the separation process is given by the sum of lost works in its individual subprocesses, Le.,
where A S b d is the entropy change of the subprocess. The actual work in the process is therefore given by = Wlost + Wided = c T s A s + b Widad t a l (3) The thermodynamic efficiency of the process is defined as a ratio of the ideal work and the actual work necessary for the separation of components, Le., Wactud
If the changes in entropy and enthalpy during the process are estimated, the thermodynamic efficiency can subsequently be calculated by eqs 1-4. The entropy and enthalpy of a nonideal liquid mixture can be calculated by eqs 5 and 6
+
Fundamental Relations for the Second Law Analysis In a continuous separation process with steady flows, the influence of potential and kinetic energy can usually be neglected (Perry et al., 1984). The minimum work necessary for the separation of components in such a process system is then given by the following equation Wide*
= AH - T,AS
(1)
where T, is the temperature of surroundings, and AH and A S are, respectively, the changes of enthalpy and entropy in the course of the process. We consider that the receipt work from its surroundings is positive. 0888-5885/94/2633-1631$04.50/0
where S0,iLand H0,iLare the entropy and enthalpy of pure liquid component i at a reference state (temperature, TO; pressure, PO). The entropy and enthalpy of a saturated liquid mixture can be calculated by replacing T with its bubble temperature T b in eqs 5 and 6, respectively. A previously developed ASOG method for calculating excess Gibbs energy (Tochigi et al., 1990) is used for estimating bubble and dew temperatures of saturated mixtures. 0 1994 American Chemical Society
1632 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 Table 1. Specifications for the Calculation of a Continuous Distillation Column Specifications of Design binary system feed flow rate (kg-mol/h) 100 feed composition 40 mol % methanol feed temperature (K) specification column 1 column 2 pressure of 1st stage (kPa) pressure drop (kPa/stage) column heat loss product temperature (K)
ternary system 100 20 mol % acetone 30 mol % benzene 293.15 distillate, bottom 98 f 0.03 mol % acetone, -, 98 f 0.03 mol % toluene 101.3 0.05 5% of reboiler duty 303.15
293.15 distillate 98 f 0.03 mol % methanol 101.3 0.05 5 % of reboiler duty 303.15 Specifications of Utility
binary system
ternary system
segment
utility
inlet temp (K)
outlet temp (K)
segment
utility
condenser reboiler preheater cooler 1,2
cooling water 2Ka-steam 2K-steam cooling water
293.15 392.76 (vapor) 392.76 (vapor) 283.15
313.15 392.76 (liquid) 392.76 (liquid) 293.15
condenser 1,2 reboiler 1 reboiler 2 preheater cooler 1, 2, 3
cooling water 2K-steam 3K-steam 2K-steam cooling water
inlet temp (K) 293.15 392.76 (vapor) 406.03 (vapor) 392.76 (vapor) 283.15
outlet temp (K) 313.15 392.76 (liquid) 406.03 (liquid) 392.76 (liquid) 293.15
A t = kg/cm2 G.
In this work, excess enthalpies ( A W L ) ) and excess entropies (ASEcL)) of liquid mixtures are calculated by ASOG group contribution methods (Hayashi and Kojima, 1993; Hayashi et al., 1992). The entropy and enthalpy of a nonideal vapor mixture can be calculated by eqs 7 and 8
where TBJis the pure component boiling temperature at pressure PO. The entropy and enthalpy of a saturated vapor mixture can be calculated by replacing T with its dew temperature T d in eqs 7 and 8, respectively. Vapor-phase excess entropy ASE(V)and excess enthalpy AHE(V) are calculated by the virial equation of state of Berlin type (Malanowski and Anderko, 1992), truncated after the second virial coefficient B,
A?fE(')
=(B -Tg)P -
$
y i( Bii - T>)P
(10)
where
follows
Specification of Process Parameters and Physical Properties The second-law analysis was applied to the separations of the binary system methanol + water and the ternary system acetone + benzene + toluene by a conventional continuous distillation. The specification for the separation was to produce components with a purity of 98 f 0.003 mol %. The distillation calculation was performed by a matrix method (Wang and Henke, 1966). Number of theoretical plates, composition, and temperature profiles of the distillation columns were determined in order to evaluate q dependencies. Heat recovery systems, in which feeds are preheated by waste heat of top condensers, were also tested. Design parameters of the units and the specifications for utilities are given in Table 1. Vapor-liquid equilibria were determined by the ASOG group contribution method (Tochigi et al., 1990). Pure component vapor pressures were calculated by the Wagner equation using parameters by Reid et al. (Reid et al., 1987). Liquid-phase excess enthalpy and excess entropy were determined by specifically developed ASOG methods (Hayashi et al., 1992; Hayashi and Kojima, 1993). Pure component molar heat capacities of liquids were taken from Zabransky et al. (Zabransky et al., 1992). For calculating vapor-phase excess properties, the second virial coefficient correlation by Tsonopoulos (Tsonopoulos, 1974) was used. The ideal gas heat capacity was evaluated by Reid et al. (Reid et al., 1987). Pure component enthalpies of vaporization were taken from Majer and Svoboda (Majer and Svoboda, 1985). The reference condition for calculating enthalpy and entropy was a pure liquid at 101.3 kPa and 273.15 K.
Calculated Results and Discussion The vapor-phase isobaric heat capacity of a pure component Cp,iv is given by the virial equation of state as
Continuous Distillation of the Binary System Methanol + Water. The thermodynamic efficiency of the continuous distillation of the system methanol + water
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1633 Table 2. Converged Results of a Second-Law Analysis for the Distillation Process of a Methanol + Water System 1
2
3
4
5
6
7
0.821 28 1 no 0.195 122
0.850 20 1 no 0.192 122
0.915 16 1 no 0.188 122
0.998 14 1 no 0.183 122
1.230 12 1 no 0.167 122
1.590 10 1 no 0.147 122
2.050 9 1 no 0.128 122
92 254 43 69 2 44 not used not used 626
95 258 44 69 2 44 not used not used 634
99 267 46 69 2 44 not used not used 648
128 108 278 311 47 54 69 69 2 2 44 44 not used not used not used not used 670 730
168 361 62 69 2 43 not used not used 829
318 425 75 69 2 43 not used not used 955
case reflux ratio no. of stages P
heat recovery
thermodynamic efficiency [1O3kJ/h1 [1O3kJ/h1( W d Waetud column top condenser reboiler preheater cooler 1 cooler 2 top condensep cooler 2 O Wa,td[lO3kJ/h1 Wid4
8 3.290 8
9
10
3.290 8
1 no 0.095 122
1 yes 0.103 122
11.00 7 1 no 0.037 122
344 598 105 69 2 43 not used not used 1284
344 563 105 notused 2 18 28 9 1193
1132 1672 309 69 2 43 not used not used 3350
W1-t
Equipment for heat recovery.
[CLzrTG-] Pressure Drop : O.OSkPa/stage
2
Methanol
@@
I
cooler 1
i 'Iz
%
0Ent ha1 py(kJ/mol)
column
:
~
Figure 1. Result of second-law analysis for the distillation process of the methanol
was studied at nine different levels of reflux ratio. The calculated results are given in Table 2. Figure 1illustrates details of the second-law analysis in the process flow sheet for case 8, when the reflux ratio is set to 3.29 and q equals 1. Figure 2 shows the influence of reflux ratio on thermodynamic efficiency and theoretical stage. It can be seen that as the reflux ratio approaches its minimum value of 0.8, its overall thermodynamic efficiency increases. The maximum thermodynamic efficiency at the minimum reflux ratio has a small value (20.0%). Enthalpy balance showed that 10% of the waste heat from the top condenser can be used to preheat the feed for the distillation column. As seen in Figure 3 and Table 2 (case 91, the incorporation of the heat recovery system does not significantly affect the thermodynamic efficiency of the process. Continuous Distillation of the Ternary System Acetone + Benzene + Toluene. The flow sheet for the
+ water system (case 8).
continuous distillation of the ternary system is shown in Figure 4. The process was studied at reflux ratio values of 4.5 (first tower) and 3.8 (second tower) and a q value of 1. The calculated results by the second-law analysis are given in Table 3 and Figure 5. Similar to the binary case, it is found that the inclusion of a heat recovery system can increase the thermodynamic efficiency of the process by only 1% .
Conclusion
A thermodynamic analysis based on the second law of thermodynamics has been applied to the separation of binary and ternary systems by continuous distillation. Previously developed ASOG group contribution methods were used for estimating phase equilibria and liquid-phase excess enthalpy and excess entropy. The thermodynamic efficiency of the separation processes was studied as a function of the reflux ratio. An
1634 Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 Table 3. Converged Results of a Second-Law Analysis for the Distillation Process of an Acetone + Benzene + Toluene reflux ratio no. of stages q
p
:.I
O,l~-.~--N,~..ie.i., 0
1
heat recovery thermodynamic efficiency wideal [1O3kJ/h1 W1-t [1O3kJ/h1 (W1-J Wactud column 1 top condenser 1 reboiler 1 preheater 1 condenser 1" reboiler 1" column 2 top condenser 2 reboiler 2 condenser 2" cooler 1 cooler 2 cooler 3 cooler 3" Wad, [1O3kJ/h1
.,...
2 3 4 1 0 1 1 1 2 Reflux Ratio
Figure 2. Effect of reflux ratio on thermodynamic efficiency and theoretical stage for the methanol + water system ( X F = 0.40, XD = 0.98, xw = 0.02, q = 1).
p 0.4C
0---
.-3
s
---_Wl,,,(condenser) ------o
- 600
2
0.118
190
190
182 228 89 130 not used not used 249 606 16 not used 6
182 194 78 not used 40 4 249 559 16 24 6 21 48 2 1423
21
95 not used 1622
Equipment for heat recovery.
3
5
2
-400
$0.2
y
Wl,,,(condenser
$ 0.2-
O-------_.
; B
- 200
thermodynamic efficiency
-------Wl,,,(prehealer)
thermodynamic efficiency W,,,,(prchcater)
--
Nb
cooler 1
I
column 1 acetone
column 2
YES
Heat Recovery
0
top condenser 1
reboiler 1 1
---- - - _
NO ,. YES
Heat Recovery Figure 3. Effect of heat recovery on thermodynamic efficiency for the methanol + water system ( X F = 0.40, X D = 0.98, nw = 0.02, R = 3.290, q = 1).
preheater
1)
--------_____
0
L L
0'
0.105
ZL c,
W 0.3-
.-3
0.1 -
a
4.5 (first tower) + 3.8 (second tower) 16 (first tower) + 16 (second tower) 1 (first tower) + 1 (second tower) no Yes
cooler 2 ,,cooler 3 toluene
reboiler 2
Figure 4. Flow sheet of continuous distillation for the acetone benzene + toluene system.
+
incorporation of a heat recovery system was also tested. In the studied cases, the heat recovery system showed almost no effect on the thermodynamic efficiency of the processes. A maximum of the thermodynamic efficiency was observed at the minimum reflux ratio. The results of this work will be useful not only for the design of operation units but also for the effective utilization of energy.
Figure 5. Effect of heat recovery on thermodynamic efficiency for the acetone + benzene + toluene system ( R = 4.5 [first tower] and 3.8 [second tower], q = 1).
Nomenclature B= second virial coefficient Cp,+ molar heat capacity of liquid pure for component i Cp,iv= molar heat capacity of vapor pure for component i HL= liquid-phase enthalpy W =vapor-phase enthalpy H0,iL= enthalpy of pure liquid component i at reference state AP(L)= excess enthalpy of liquid mixture A P ( V ) = excess enthalpy of vapor mixture Hiew= enthalpy of vaporization for pure component i P= pressure PO= reference pressure q= measure of thermal condition of feed R= gas constant SL=liquid-phase entropy Sv=vapor-phase entropy S0,iL= entropy of pure liquid component i at reference state ASE(L)= excess entropy of liquid mixture ASE(V)= excess entropy of vapor mixture ASbw= entropy change of subprocess T= absolute temperature Tb= bubble temperature TB,~= boiling temperature of pure component i Td= dew temperature
Ind. Eng. Chem. Res., Vol. 33, No. 6, 1994 1635
T,= temperature of surroundings To= reference temperature Wactud=actual work Wided= ideal work Wlost= lost work xi= liquid mole fraction of component i yi= vapor mole fraction of component i Greek Symbol Q=
thermodynamic efficiency
Literature Cited Daubert, D. E. Chemical Engineering Thermodynamics; McGrawHill, Inc.: New York, 1985;p 111. Hayashi, H.; Kojima, K. Prediction of Excess Entropy for Binary Systems by ASOG Group Contribution Method. Znd. Eng. Chem. Res. 1993, 32, 2187. Hayashi, H.; Tochigi, K.; Kojima, K. Prediction of Excess Enthalpy by Using Thirty-One ASOG Groups. Ind. Eng. Chem. Res. 1992, 31, 2795. Kenney, W. F. Current Practical Applications of the Second Law of Thermodynamics. Chem. Eng. Prog. 1989,85, 57. Majer, V.; Svoboda, V. Enthalpies of Vaporization of Organic Compounds; Blackwell: Oxford, 1985.
Malanowski, S.; Anderko, A. Modeling Phase Equilibria, Thermodynamic Background and Practical Tools; John Wiley & Sons, Inc.: New York, 1992;p 81. Perry, R. H.; Green, D.; Maloney, J. 0.Perry’s Chemical Engineer’s Handbook, 6th ed.; McGraw-Hill: New York, 1984;p 4-89. Reid, R. C.; Prausniz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw-Hill Book Company: New York, 1987;p 657. Tochigi, K.; Tiegs, D.; Gmehling, J.; Kojima, K. Determination of new ASOG parameters. J . Chem. Eng. Jpn. 1990,23,453. Tsonopoulos, C. An empirical correlation of second virial coefficients. AIChE J. 1974,20, 163. Wang, J. C.; Henke, G. E. Tridiagonal matrix for distillation. Hydrocarbon Process. 1966,45, 155. Zabransky, M.; Ruzicka, V., Jr.; Majer, V.; Domalski, E. S. Critical Compilation of Heat Capacities ofliquids;Manuscript: Praghe,
1992.
Received for review November 16, 1993 Revised manuscript received March 22, 1994 Accepted March 29, 1994@ @
Abstract published in Advance ACS Abstracts, May 1,1994.
