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Ind. Eng. Chem. Res. 2007, 46, 1254-1258
SEPARATIONS Extractants Design Based on an Improved Genetic Algorithm Li-Li Wu, Wei-Xian Chang, and Guo-Feng Guan* College of Chemistry and Chemical Technology, Nanjing UniVersity of Technology, Nanjing, 210009, Jiangsu, People’s Republic of China
A method based on an improved genetic algorithm for the computer-aided molecular design for extractive distillation is presented. Many enhancements, including new encoding schemes and improved genetic algorithm operators, such as cross-generatent elitist selection, dislocation crossover, and mutation operators have been included. The accuracy and reliability of the method have been verified by designing the extractants for the extractive distillation processes of acetone-methanol and water-acetic acid systems. For the acetone-methanol system, the prediction precision of the relative volatility is higher in this work. For the water-acetic acid system, the average relative deviations between the predicted value and the experimental value of the infinite dilution activity coefficients of water and acetic acid in N-methylpyrrolidone (NMP) and N-methylacetamide (NMA) are 7.85% and 12.66%, respectively. Introduction Extractive distillation is an important separation process in the chemical industry. The effectiveness of an extractive distillation is reliant on the choice of extractive agents. Moreover, computer-aided molecular design (CAMD) is one of the main approaches for selecting the extractants. CAMD may be broadly classified as follows: enumeration method, graph theory, knowledge-based method, mathematical programming method, and genetic algorithm (GA). In comparison to the other searching methods, GA is simpler and easier to implement; it particularly does not require continuous solution space and special field knowledge. Contributions to the GA for design solvents have been reported by Gani and co-workers.1,2 Dyk and Nieuwouldt3 have improved the GA method of solvent design, relative to extraction distillation. However, procedures in regard to how to avoid the disadvantages of GAs (low performing efficiency, converging early and easily losing globally optimal results) have not been given. In this paper, an improved GA for designing extractants is presented. To simplify the molecule forms and provide an easy link to the database for calculation of the physicochemical properties of the molecules, a new encoding scheme that greatly enhances the performing efficiency is established. To avoid the disadvantage of converging early, the cross-generatent elitist selection, dislocation crossover, and mutation operators are improved. The results presented in this work show that the proposed design strategy is successful for extractive distillation. Problem Formulations By combining improved GAs with the universal quasichemical functional group activity coefficients (UNIFAC) group contribution to design extractants, the entire process may be * To whom correspondence should be addressed. Tel.: 86-2583587198. E-mail address:
[email protected].
summarized as follows:2 (i) give the characteristics and goals of an extractive distillation process; (ii) select the groups that should be considered; (iii) determine and evaluate the extractant structure by solving the combinatorial problems and using the feasibility criteria; and (iv) use the fuzzy comprehensive judgment model to make a final selection of one or more molecules to satisfy the particular needs of the given process. (1) Selecting Groups and Encoding Scheme. The structures of the molecules are designed using the functional groups shown in Table 1. The groups are based on the definition of the UNIFAC functional groups.4 To design a molecule easily, the groups in Table 1 are divided into classes and categories. The class of a group indicates the number of free attachments available to the group. The category of a class of groups indicates the restriction degree of the groups that are connected to other groups. To enhance the performing efficiency of the algorithm, a new encoding scheme is developed. Groups are represented by their own group number, and the molecular structure is described by a combination of the figures. The computer program is simplified, because each number represents a specific functional group. (2) Initialization Population. The first generation, which contains 500 simple molecules, is designed by the groups in Table 1 according to the rules introduced by Gani et al.5 It ensures that the design molecules have no free attachments. (3) Evaluation Scheme. In this work, two types of fitness functions are used, depending on the nature of property constraints. The relative volatility, melting point, molecular weight, and boiling point are related to designing an extractant for extractive distillation. The former three properties are prompted by the sigmoidal fitness function, and the boiling point is prompted by the Gaussian function. A fitness value is calculated for each property, and the weighted mean of these values is taken as the overall fitness for the molecule. In this work, the weighting factors are as
10.1021/ie060022f CCC: $37.00 © 2007 American Chemical Society Published on Web 01/19/2007
Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007 1255 Table 1. Preselected Groups for Molecular Synthesis Category 1
Category 2
Category 3
Category 4
class
compound
code
compound
code
compound
code
0 1
CH3OH CCl4 CH3
15 52 1
CH3CN CH3NO2 CH2CN CH2NO2 CH2NH2
40 54 41 55 29
2
CH2
2
CHNO2
56
H2O HCOOH CH3CO CONHCH3 CONHCH2 CON(CH3)2 CONCH2CH3 CH2CO CH2COO CH2O CON(CH2)2
16 43 18 92 93 94 95 19 22 25 96
3
CH
3
4 5
C ACH
4 9
ACCH2 ACCH AC
12 13 10
compound
Category 5 code
compound
code
DMSO
67
COOH OH CHO CH3COO CH3O CHNH2 CHCl CH2NH
42 14 20 21 24 30 45 32
NMP DMF CCl3 CHCl2 CH3NH
63 72 51 48 31
CCl2 CH3N COO
49 34 77
CHNH CCl CH2N
33 46 35
ACCH3
11
ACCl ACNH2 ACOH
53 36 17
Table 2. System Estimates for Molecular Evaluation system solvent selectivity, S for S > 15 for 5 e S e 15 for 2 e S < 5 for 0 e S < 2 solvent power, SP for SP g 0.2 for 0.14 e SP e 0.2 for 0.02 e SP e 0.14 for 0 e SP e 0.02 viscosity, η for 0 e η e 3 for η > 3 heat capacity, CP for 0 < CP e 1 for 1 < CP e 2.5 for CP > 2.5 boiling point, Tb for tb < (Tb + 50) or tb > 600 for (Tb + 50) e tb e 600 molecular weight, MW for MW e 150 (chain) for MW e 240 (circular) for MW > 150 or MW > 150 toxicity, T for T ) 0 for T ) 0.25 for T ) 0.5 for T ) 0.75 for T ) 1 a
estimatea
calculation method S∞ ) γ∞A/γ∞B S∞ ) γ∞A/γ∞B S∞ ) γ∞A/γ∞B
S* ) 1 S* ) [(S - 5)/50] + 0.8 S* ) 4(S - 2)/15 S* ) 0
S∞P ) (1/γ∞A,S)(MWA/MWS) S∞P ) (1/γ∞A,S)(MWA/MWS) S∞P ) (1/γ∞A,S)(MWA/MWS) S∞P ) (1/γ∞A,S)(MWA/MWS)
S∞P ) 1 S∞P ) 0.7[(SP - 0.14)/0.07] + 0.3 S∞P ) 0.3(SP - 0.02)/0.12 S∞P ) 0
from Cheng7 from Cheng7
η* ) -(η/3) + 1 η* ) 0
from Wang8 from Wang8 from Wang8
C/P ) 1 C/P ) -0.67(CP - 1) + 1 C/P ) 0
from Wang8 from Wang8
t/b ) 0 t/b ) (600 - u7i)/(600 - Tb - 50)
group contribution method group contribution method group contribution method
MW* ) 1 - (MW/150) MW* ) 1 - (MW/240) MW* ) 0
from Cheng7 from Cheng7 from Cheng7 from Cheng7 from Cheng7
high middle low tiny no
As determined from ref 6.
follows: relative volatility (40%), boiling point (30%), melting point (20%), and molecular weight (10%). (4) Improvement of GA Operators. (a) Cross-Generatent Elitist Selection. To prevent the random error of selecting a molecule using roulette wheel rules in generation reproduction, a cross-generatent elitist selection method is presented. In the general reproduction, new generation is created from the current set of molecules and the new generation then replaces the old generation entirely. In this work, the different superior offspring produced by crossover and mutation is added to the old generation, and then parent molecules are selected, with a probability calculated from their fitness value. (b) Dislocation Crossover. The GA is mainly reliant on crossover. In this paper, dislocation crossover is proposed. The particular process is as follows: crossover position occurs in the half of the molecules that are chosen by cross-generatent
elitist selection and then the four offspring are created by connecting the four segments of the two parents. The entire dislocation crossover process is shown in Figure 1. (c) Mutation Operators. The mutation operator is used when the algorithm almost achieves constringency stage. During the early age of evolution, the diversity of the population is quite good, and the effect of the mutation operator is not obvious. As the evolution proceeds, because of the affinity of the selection and dislocation crossover operators, the superior molecule will be selected with a high probability, which causes it to converge early. At this time, mutation is used to disturb the population and make improvements. (5) Molecular Evaluation. A large number of designed extractants from which to select are required to evaluate the specific solvent properties. Based on the complexity and indeterminant nature of extractive distillation, extractant selec-
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Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007
comprehensive judgment formulas of the seven factors are established by fuzzy transformation. Single-factor calculating and judging methods are shown in Table 2, and some of the property values are based on the prediction of infinite dilution activity coefficients. Two groups of weighting factors, shown in Table 3, are presented to assess the factors. They are changed by the user to suit the specific problem. The candidate extractants then will be able to be evaluated and the superior extractants will be selected. Application Examples (1) System 1: Acetone-Methanol. The extractants generated for this system are shown in Table 4. Water and glycol, as industrial extractants, are obtained in this work. Reported literature results using N,N′-dimethyl-1,3-propanediamine, dimethyl sulfoxide (DMSO), and undecane are also used in this work.3 To evaluate the candidate extractants further, a fuzzy comprehensive judgment model is used. Properties of the extractant components for the acetone-methanol system are shown in Table 5. The evaluation of the extractants for this system is shown in Table 6. DMSO, water, and glycol are shown to be the superior extractants. This result agrees well with the literature reports.3 To check the accuracy of the design results, the predicted value of the relative volatility of DMSO in this work is compared with the value reported in the literature.3 The results are shown in Table 7. The relative deviation of the relative volatility for DMSO in this work is higher. (2) System 2: Water-Acetic Acid. The extractants generated for the water-acetic acid system are listed in Table 8.
Figure 1. Description of the dislocation crossover operator process.
tion is considered using a model for the comprehensive judgment of extractants which uses seven factors, including solvent selectivity, solvent power, viscosity, specific heat capacity, boiling point, molecular weight, and toxicity properties. The Table 3. Weighting Factors for the Two Groups of Parameters group
solvent selectivity, S
solvent power, SP
viscosity, η
heat capacity, CP
boiling point, Tb
molecular weight, MW
toxicity, T
1 2
0.4 0.2
0.2 0.4
0.1 0.1
0.1 0.1
0.08 0.06
0.06 0.1
0.06 0.04
Table 4. Output of Molecular Design for Extraction Distillation Extractants for the Acetone-Methanol System structure
extractant
relative volatility
melting point (K)
boiling point (K)
molecular weight, MW
H2O 2CH2‚2OH dimethyl sulfoxide, DMSO 3CH2‚2OH‚CH2O 2CH3‚2CH‚2OH CH3‚CH2‚CH‚2OH dimethyl formamide, DMF 2CH3NH‚3CH2 2CH3‚9CH2 2CH3‚10CH2
water glycol dimethyl sulfoxide, DMSO diethylene glycol 2,3-butanediol 1,2-propanediol dimethyl formamide, DMF N,N′-dimethyl-1,3-propanediamine undecane dodecane
2.94 3.61 3.36 2.91 2.74 3.08 1.77 4.64 2.26 2.28
273.15 245.50 291.60 266.70 267.19 220.38 212.15 261.34 220.02 232.50
373.15 480.70 462.20 517.95 525.21 472.31 425.95 385.65 465.62 485.07
18 62 78 106 90 76 73 102 156 170
Table 5. Properties of the Extractants for the Acetone-Methanol System extractant
solvent selectivity, S
solvent power, SP
molecular weight, MW
boiling point, Tb (K)
viscosity, η (mPa s)
heat capacity, Cp (J/(g K))
water glycol DMSO DMF dodecane undecane 1,2-propanediol diethylene glycol
3.6686 3.6046 3.2827 1.5567 4.3451 4.4017 2.9462 3.2268
0.3586 0.2461 0.4188 0.7026 0.1168 0.1221 0.2801 0.2555
18 62 78 73 170 156 76 106
373.15 480.70 462.20 425.95 485.07 465.62 472.31 517.95
1.01 2.90 0.21 0.48 1.51 1.16 56.00 3.00
4.18 2.40 1.95 2.14 2.22 2.23 2.34 2.31
toxicity, T no tiny tiny tiny tiny low tiny tiny
Table 6. Evaluation of the Extractants for the Acetone-Methanol System
estimate ranking
water
glycol
DMSO
DMF
dodecane
undecane
propanediol
diethylene glycol
0.1428 2
0.1297 3
0.1518 1
0.1152 6
0.1172 5
0.1199 4
0.1114 8
0.1120 7
Ind. Eng. Chem. Res., Vol. 46, No. 4, 2007 1257 Table 7. Comparison Results of the Relative Deviation for the DMSO Extractant Relative Volatility of the Acetone-Methanol System, R12
Relative Deviation (%)
this work (UNIFAC)
from ref 3 (experiment)
from ref 3 (UNIFAC)
this work
from ref 3
3.36
3.21
2.98
4.67
7.17
Table 8. Output of Molecular Design for Extraction Distillation Extractants for the Water-Acetic Acid System structure
extractant
relative volatility, R12
boiling point, Tb (K)
melting point (K)
molecular weight, MW
N-methylacetamide, NMA N-methylpyrrolidone, NMP CH3‚6CH2‚COOH 2CH3‚3CH2‚CH2CO 5(ACH)‚AC‚CH3CO CH3‚CH2CN CH2CN‚CH2‚CH3 3CH3‚2CH2‚CH 2CH3‚8CH2
N-methylacetamide, NMA N-methylpyrrolidone, NMP caprylic acid 4-heptanone acetophenone propionitrile butyronitrile 2-methylpentane decane
4.35 5.42 8.61 8.38 10.68 2.12 2.68 8.75 8.90
479.15 477.15 513.85 418.64 459.22 361.12 391.09 333.86 444.93
303.7 248.75 294.58 235.69 206.31 181.77 161.25 132.68 207.44
73 99 144 114 120 55 69 86 142
Table 9. Properties of Extractants for the Water-Acetic Acid System extractant
solvent selectivity, S
solvent power, SP
molecular weight, MW
boiling point, Tb (K)
viscosity, η (mPa s)
heat capacity, Cp (J/(g K))
toxicity, T
NMA NMP caprylic acid 4-heptanone acetophenone propionitrile butyronitrile 2-methylpentane decane
3.3498 3.7518 6.6231 6.4463 8.2162 1.6303 2.0612 6.7272 6.8423
0.3201 0.2221 0.0403 0.0177 0.00994 0.02846 0.01904 0. 00451 0.00311
73 99 144 114 120 55 69 86 142
479.15 477.15 513.85 418.64 459.22 361.12 391.09 333.86 444.93
3.23 1.02 4.69 0.69 1.64 0.39 0.52 0.30 0.86
2.51 2.11 0.31 2.31 3.77 2.17 2.47 2.24 1.65
tiny low low low tiny high middle low low
Table 10. Evaluation of the Extractants for the Water-Acetic Acid System
estimate ranking
NMA
NMP
caprylic acid
4-heptanone
acetophenone
propionitrile
butyronitrile
2-methylpentane
decane
0.1782 2
0.2114 1
0.0961 7
0.0976 6
0.1045 4
0.538 8
0.0453 9
0.1003 5
0.1128 3
Table 11. Relative Deviation of the Infinite Dilution Activity Coefficients between the Experimental Value and Predicted Value in NMP and NMA Extractants Infinite Dilution Activity Coefficient of Water in the Extractant, γ∞1
Infinite Dilution Activity Coefficient of Acetic Acid, γ∞2
extractant
experiment
UNIFAC
relative deviation (%)
experiment
UNIFAC
relative deviation (%)
NMP NMA
0.8681 0.9582
0.9249 0.8705
-6.54 9.15
1.6137 1.7970
1.8543 1.6099
-14.91 10.41
Reported literature values for N-methylacetamide (NMA), N-methylpyrrolidone (NMP), caprolactam, and butyronitrile also are given in this work.9,10 In addition, several extractants, such as acetophenone, 4-heptanone, and decane, which are predicted to result in higher relative volatilities, are also generated. The properties of the extractant components for the water-acetic acid system are shown in Table 9. An evaluation of the extractants for this system is shown in Table 10. NMP and NMA are shown to be the relatively superior extractants. The infinite dilution activity coefficients11-13 of water in NMP and NMA are obtained using a gas-liquid chromatography method, and the results are shown in Table 11. The average relative deviations of the infinite dilution activity coefficients of water and acetic acid in NMP and NMA, between the predicted value and the experimental value, in this work are 7.85% and 12.66%, respectively. Conclusions (1) In this work, an improved genetic algorithm (GA) for designing extractants is proposed. A novel encoding scheme is developed, which greatly enhances the performing efficiency of the algorithm. Cross-generatent elitist selection, dislocation
crossover, and mutation operators are developed to avoid the disadvantages of GAs, in regard to the algorithm converging early and easily losing globally optimal results. (2) The extractants of the acetone-methanol and wateracetic acid system are designed to test the accuracy and reliability of the method. For the acetone-methanol system, in this work, the result agrees well with the reported literature results and the prediction precision of the relative volatility is greater. For the water-acetic acid system, the average relative deviation of the infinite dilution activity coefficient between the predicted value and the experimental value is
