A United Chemical Thermodynamic Model: COSMO-UNIFAC

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Research Note/Communication

A United Chemical Thermodynamic Model: COSMO-UNIFAC Yichun Dong, Ruisong Zhu, Yanyan Guo, and Zhigang Lei Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b04870 • Publication Date (Web): 02 Nov 2018 Downloaded from http://pubs.acs.org on November 3, 2018

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Industrial & Engineering Chemistry Research

A United Chemical Thermodynamic Model: COSMO-UNIFAC Yichun Dong, Ruisong Zhu, Yanyan Guo, and Zhigang Lei* State Key Laboratory of Chemical Resource Engineering, Beijing University of Chemical Technology, Box 266, Beijing 100029, China

ABSTRACT: A united chemical thermodynamic model, i.e., COSMO-UNIFAC model, was first proposed to predict the phase equilibrium of multicomponent systems where the UNIFAC model parameters are missing. This model combines the advantages of the UNIFAC model (accurate prediction) and the COSMO-based models (a priori prediction). The predicted vapor-liquid equilibrium (VLE) results by COSMO-UNIFAC model were compared with experimental data from literatures and this work, confirming that it can provide a moderate quantitative prediction even if the UNIFAC model parameters are missing. 1. INTRODUCTION It is well-known that the UNIFAC model is one of the most successful group contribution methods (GCMs). Since the UNIFAC model was first developed by Fredenslund et al. in 1975,1 the model has been successfully extended by Gmehling et al.2 and Lei et al.,3 and now contains 103 main groups and over 200 subgroups. Although the UNIFAC model gets great success, there still exist some disadvantages. All the UNIFAC group binary parameters need to be fitted through experimental data. To get plenty of reliable experimental data, high financial cost and human resources are required. Moreover, the model can’t be used for the components containing new functional groups. More importantly, not all the UNIFAC group binary parameters are available, and some parameters are only available for 1

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the members of the UNIFAC-Consortium;2 thus, more than 50% of group parameters are vacant for general chemical engineers. These vacant parameters restrict the wider application of the UNIFAC model. In some commercial process simulation softwares (such as PROII and Aspen Plus), if the UNIFAC group binary parameters are missing, the default values will be set as zero. Herein, the UNIFAC model with the missing group binary parameters taking on as zero is named as UNIFAC(0). Two common COSMO-based (Conductor-like Screening Model) models are the COSMO-RS (Real Solvation) and COSMO-SAC (Segment Activity Coefficient) models which were developed by Klamt et al.4 and Lin et al.,5 respectively. Unlike GCMs, the COSMO-based models don’t need plenty of experimental data. They only need a few experimental data to fit the basic parameters, but the COSMO calculations need to be implemented through quantum chemistry software (such as Turbomole, Gaussian, or DMol3). The prediction accuracy of UNIFAC model is generally superior to the COSMO-based models because the UNIFAC model is based on lots of experimental data. Many researchers further combined the UNIFAC model (or COSMO-based models) with equations of state.6,7 These methods may serve as supplementary thermodynamic models for predicting the vapor-liquid equilibria in special conditions, such as high temperature, high pressure, and supercritical gases, but are not proposed to replace the useful methods like the UNIFAC model. However, in this work, a united chemical thermodynamic model, i.e., COSMO-UNIFAC model, is proposed to extend the UNIFAC group parameter matrix. The COSMO-UNIFAC model is established actually based on the original UNIFAC model and extends the UNIFAC model through fitting the infinite dilution activity coefficient (γ∞)

2


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values as calculated by COSMO-based models to get the vacant UNIFAC binary group parameters. Through this method, the COSMO-UNIFAC model combines the respective advantages of accurate prediction (UNIFAC model) and a priori prediction (COSMO-based models). In the Short Communication, the COSMO-UNIFAC model refers to two sub-models — the COSMO-RS-UNIFAC and COSMO-SAC-UNIFAC models. The former represents the combination of the UNIFAC and COSMO-RS models, while the latter represents the combination of the UNIFAC and COSMO-SAC models. The comparison of prediction accuracy among the UNIFAC model (the missing group binary parameters being correlated to experimental data), UNIFAC(0) model (the missing group binary parameters being zero by default), COSMO-RS-UNIFAC model, and COSMO-SAC-UNIFAC model was made. 2. EXPERIMENTAL AND COMPUTATIONAL DETAILS 2.1. Apparatus and Procedure. The vapor-liquid equilibrium (VLE) data were measured in a circulation VLE still (a modified Othmer still) at atmospheric pressure. The details are shown in Supporting Information Tables S1 and S2 and Figures S1 and S2. The ternary VLE data measured in this work were used to test the applicability of COSMO-UNIFAC model. 2.2. COSMO-based Models. The COSMO-based models are widely used to predict thermodynamic properties. In this work, both the COSMOtherm software (version C30_1301) incorporating the COSMO-RS model and the Aspen Plus software with the COSMO-SAC model were used to calculated the infinite dilution activity coefficients (γ∞) of binary systems over a wide temperature range from 273.15 K to 393.15 K (or less than the critical

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temperature). For the COSMO-RS model, all molecules were first optimized at the B3LYP/def2TVZP level of Gaussian 09 package to generate the COSMO files, and then the files were introduced into the COSMOtherm package. For the COSMO-SAC model, all the parameters in Aspen Plus database come from the literature.8 The interested readers can see the website at https://www.design.che.vt.edu/VT-Databases.html for more details. 2.3. UNIFAC Model. The original UNIFAC model was used in this work, and the details are given in Supporting Information. The vacant UNIFAC group binary parameters were obtained by fitting the experimental data coming from literatures using Aspen Plus software (version 8.4). The detailed fitting procedure is described in Supporting Information, and the fitting results were evaluated by the average relative deviations (ARDs) between experimental data and calculated results, which are defined as ARD 

ARD P 

N

γi,cal -γi,exp

1

γi,exp

1 N



1 N



N

Pi,cal -Pi,exp

1

Pi,exp

(1)

(2)

The ARD and ARD P were used to evaluate the deviations of VLE and vapor pressure data, respectively. All the fitting results are listed in Supporting Information Tables S3-S13. 2.4. COSMO-UNIFAC Model. The COSMO-UNIFAC model, based on the UNIFAC model, is suitable for predicting the phase equilibria when the UNIFAC group binary parameters are vacant. The vacant UNIFAC group binary parameters were obtained by fitting the γ∞ values as calculated by the COSMO-based models. For example, the γ∞ values of hexafluoroethane and acetone were used to fit the group binary parameters between CF3 and CH3CO groups. All the representative molecules used for data correlation are given in

4


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Supporting Information Table S14. The fitting procedure was carried out through Aspen Plus software, and the fitting results were evaluated by the ARD  between the calculated γ∞ (  i,cal ) by the COSMO-UNIFAC model and the calculated γ∞ (  i,COSMO-based ) by the COSMO-based models. The ARD  was calculated by ARD  

1 N

N

 1

γi,cal -γi,COSMO-based γi,COSMO-based

(3)

All the COSMO-UNIFAC group binary parameters as well as the fitting results are listed in Supporting Information Tables S15-S26. 3. RESULTS AND DISCUSSION 3.1. Slightly Non-ideal Systems. For slightly non-ideal systems, the component activity coefficients are often near 1. If the missing UNIFAC group binary parameter is zero, the predicted VLE results by the UNIFAC, UNIFAC(0), and COSMO-UNIFAC models may be all close to the experimental data. To compare the prediction accuracy of all the three models, the predicted VLE results for four slightly non-ideal systems (i.e., methanol + N,N-Dimethylacetamide (DMAC), benzene + DMAC, allyl alcohol + ethylene glycol (EG), and acetic acid + N-methyl-2-pyrrolidone (NMP)) were compared with experimental data (see Supporting Information Tables S6-S9 for more details). As shown in Figures 1(a) and 1(b), the calculated VLE results for the methanol (1) – DMAC (2) and benzene (1) - DMAC (2) systems by the three models exhibit the right trend because of the nearly ideal behavior of these systems. The UNIFAC and COSMO-UNIFAC models are only slightly better than the UNIFAC(0) model. However, when the non-ideal behavior becomes stronger, as shown in the Figures 1(c) and 1(d), for the allyl alcohol (1) + EG (2) and acetic acid (1) + NMP (2) systems, the UNIFAC(0) model performs the worst 5



because it underestimates the non-ideal behavior, while the COSMO-UNIFAC model performs close results to the experimental data. That is, when there aren’t enough UNIFAC group binary parameters available, the COSMO-UNIFAC model can provide a closer prediction to experimental data than the UNIFAC(0) model. Moreover, the predicted results by the COSMO-RS-UNIFAC and COSMO-SAC-UNIFAC models are almost similar. 3.2. Strongly Non-ideal Systems. For strongly non-ideal systems, the component activity coefficients are often far away from 1; thus, the UNIFAC(0) model can’t exactly reflect the real phase equilibrium of systems. The experimental data and predicted VLE results for four strongly non-ideal systems (i.e., HF + H2O, dimethyl sulfide + ethanol, chlorodifluoromethane (CHClF2) + dimethyl ether (DME), and methyl nonafluorobutyl ether (HFE-7100) + acetone) are shown in Figure 2 (see Supporting Information Tables S10-S13 for more details). It is clear that the more the vacant UNIFAC parameters, the worse the predicted results by the UNIFAC(0) model. For the HF + H2O and dimethyl sulfide + ethanol systems, more than 50% of group parameters are vacant, and thus the UNIFAC(0) model can’t describe the azeotropic behavior correctly. For such systems, the prediction accuracy of the COSMO-UNIFAC model mainly depends on that of the COSMO-based models. In addition, as shown in Figures 2(c) and 2(d), although the UNIFAC (0) model can predict the azeotropic behavior to some degree, the predicted trend by this model is just contrary to that by the UNIFAC and COSMO-UNIFAC models (see Figure 2(d)). As a whole, the COSMO-UNIFAC model can still provide closer results to experimental data than the UNIFAC(0) model in this case. Moreover, it seems that the predicted results by the COSMO-RS-UNIFAC and COSMO-SAC-UNIFAC models are comparable to each other in

6


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most cases. 3.3. Ternary systems. Extractive distillation has been widely used in chemical separation processes, and the accurate prediction for phase equilibrium data is important to ensure an economic and efficient process design. The x′ - y′ (on an entrainer-free basis) relations for four ternary systems (i.e., benzene + thiophene + NMP, cyclohexane + benzene + DMAC, toluene + acetic acid + NMP, and allyl alcohol + H2O + EG) were predicted (see Supporting Information Tables S27-S30 for more details). As shown in Figures 3(a) and 3(b), due to the non-ideal behavior between the key component and entrainer being not so strong, all the models can give good prediction, while the COSMO-UNIFAC model is only slightly better than the UNIFAC(0) model. With the increase of non-ideal behavior, the UNIFAC(0) model can’t reflect the real microscopic thermodynamic state. In Figure 3(c), the UNIFAC(0) model underestimates the separation ability of the entrainer NMP, whereas in Figure 3(d) the UNIFAC(0) model even predicts the opposite VLE trend. Furthermore, the separation of toluene and acetic acid by extractive distillation with NMP as entrainer was simulated by Aspen Plus software with the aforementioned models. The operating conditions and simulated results are given in Supporting Information Tables S31 and S32. It can be seen from Table S32 that under the same operation conditions, the simulation results using different models show that the mole purity of toluene at the top of extractive distillation column follows the order: UNIFAC ≈ COSMO-SAC-UNIFAC > COSMO-RS-UNIFAC > UNIFAC(0), which is consistent with the tendency of relative volatility as shown in Figure 3(c). Therefore, the COSMO-UNIFAC model could be a useful tool to screen the entrainers for extractive distillation.

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4. CONCLUSIONS The COSMO-UNIFAC mode was first proposed in this Short Communication to combine the UNIFAC model with the COSMO-based model. The united chemical thermodynamic model can provide a moderate quantitative prediction for the systems (especially containing the toxic and harmful compounds) where some UNIFAC group binary parameters are vacant. In most cases, the prediction accuracies by the COSMO-RS-UNIFAC and COSMO-SAC-UNIFAC models are comparable, but the COSMO-SAC model is an open access to general chemical engineers. In the future work, we will complete all the vacant group binary parameters in this way. ■ ASSOCIATED CONTENT Supporting Information The Supporting Information is available free of charge on the website. The experimental and calculated VLE data of binary and ternary systems, and the experimental and calculated γ∞ can be found in the online version (XLS). ■ AUTHOR INFORMATION Corresponding Author *Tel.: +86-1064433695. E-mail: [email protected]. ORCID Zhigang Lei: 0000-0001-7838-7207 Notes The authors declare no competing financial interest.

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■ ACKNOWLEDGMENTS This work is financially supported by the National Natural Science Foundation of China under Grant (No. 21476009).

■ REFERENCES (1)

Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Group-Contribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21, 1086–1099.

(2)

Wittig, R.; Lohmann, J.; Gmehling, J. Vapor−liquid Equilibria by UNIFAC Group Contribution. 6. Revision and Extension. Ind. Eng. Chem. Res. 2003, 42, 183–188.

(3)

Lei, Z.; Dai, C.; Wang, W.; Chen, B. UNIFAC Model for Ionic Liquid-CO2 Systems. AIChE J. 2014, 60, 716–729.

(4)

Klamt, A. Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena. J. Phys. Chem. 1995, 99, 2224–2235.

(5)

Lin, S.-T.; Sandler, S. I. A Priori Phase Equilibrium Prediction from a Segment Contribution Solvation Model. Ind. Eng. Chem. Res. 2002, 41, 899–913.

(6)

Holderbaum, T.; Gmehling, J. PSRK: A Group Contribution Equation of State Based on UNIFAC. Fluid Phase Equilib. 1991, 70, 251–265.

(7)

Constantinescu, D.; Klamt, A.; Geană, D. Vapor–liquid Equilibrium Prediction at High Pressures Using Activity Coefficients at Infinite Dilution from COSMO-Type Methods. Fluid Phase Equilib. 2005, 231, 231–238.

(8)

Mullins, E.; Oldland, R.; Liu, Y. A.; Wang, S.; Sandler, S. I.; Chen, C.-C.; Zwolak, M.; Seavey, K. C. Sigma-Profile Database for Using COSMO-Based Thermodynamic Methods. Ind. Eng. Chem. Res. 2006, 45, 4389–4415.

(9)

Horstmann, S.; Constantinescu, D.; Gmehling, J. Vapor–Liquid Equilibrium and Excess Enthalpy Data for Systems Containing N,N-Dimethylacetamide. J. Chem. Eng. Data 2017, 62, 2776–2786.

(10)

Řehák, K.; Klajmon, M.; Strejc, M.; Morávek, P. Isothermal Vapor–liquid Equilibria for Binary Mixtures of Methyl Nonafluorobutyl Ether + Acetone, Cyclopentyl Methyl Ether, Ethyl Acetate, n -Aeptane, Methanol, and Toluene. J. Chem. Eng. Data 2017, 62, 3878–3888.

(11)

Rolemberg, M. P.; Krähenbühl, M. A. Vapor−liquid Equilibria of Binary and Ternary Mixtures of

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Benzene, Cyclohexane, and Chlorobenzene at 40.0 KPa and 101.3 KPa. J. Chem. Eng. Data 2001, 46, 256–260. 150

450

(a)

(b)

100

T /K

P /kPa

400

50

350

T = 343.15 K

0

0.0

0.2

0.4

0.6

0.8

P = 101.325 kPa

300

1.0

0.0

0.2

0.4

x1, y1

0.6

0.8

1.0

x1, y1 500

500

(d)

(c)

450

T /K

450

T /K

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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400

400

P = 101.33 kPa

P = 101.3 kPa 350

0.0

0.2

0.4

0.6

0.8

350

0.0

1.0

0.2

x1, y1

0.4

0.6

0.8

1.0

x1, y1

Figure 1. Vapor-liquid equilibrium of the (a) methanol (1) + DMAC (2), (b) benzene (1) + DMAC (2), (c) allyl alcohol (1) + EG (2), and (d) acetic acid (1) + NMP (2) systems. Black solid line, calculated results by UNIFAC model; blue dashed line, calculated results by UNIFAC(0) model; red solid line, calculated results by COSMO-RS-UNIFAC model; red dashed line, calculated results by COSMO-SAC-UNIFAC model. ■, experimental data.9

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400

400

(b)

(a) 350 300

T /K

P /kPa

350

300

250 200 150

P = 101.325 kPa 250

0.0

0.2

0.4

0.6

100

0.8

T = 350.40 K

50

0.0

1.0

0.2

0.4

2000 1800

0.6

0.8

1.0

0.8

1.0

x1, y1

x1, y1 90

(c)

(d)

1600

80

1400

P /kPa

1200

P /kPa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1000

T = 323.15 K

800 600

200 0.0

T = 318.15 K

60

400

0

70

T = 283.15 K 0.2

0.4

0.6

0.8

50

1.0

0.0

x1, y1

0.2

0.4

0.6

x1, y1

Figure 2. Vapor-liquid equilibrium of the (a) HF (1) + H2O (2), (b) dimethyl sulfide (1) + ethanol (2), (c) CHClF2 (1) + DME (2), and (d) HFE-7100 (1) + acetone (2) systems. Black solid line, calculated results by UNIFAC model; blue dashed line, calculated results by UNIFAC(0) model; red solid line, calculated results by COSMO-RS-UNIFAC model; red dashed line, calculated results by COSMO-SAC-UNIFAC model. ■, experimental data.10

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1.0

1.0

(a)

(b) 0.8

0.6

0.6

y1´

y1´

0.8

0.4

0.4

x3 = 0.4

0.2

0.0 0.0

0.2

0.4

0.6

0.8

x3 = 0.5

0.2

0.0 0.0

1.0

0.2

0.4

x1´

0.6

0.8

1.0

x1´

1.0

1.0

(c)

(d)

0.8

0.8

0.6

0.6

y1´

y1´

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.4

0.4

x3 = 0.5

0.2

0.0 0.0

0.2

0.2

0.4

x1

´

0.6

0.8

0.0 0.0

1.0

x3 = 0.6

0.2

0.4

0.6

0.8

1.0

x1´

Figure 3. Vapor-liquid equilibrium of the (a) benzene (1) + thiophene (2) + NMP (3), (b) cyclohexane (1) + benzene (2) + DMAC (3), (c) toluene (1) + acetic acid (2) + NMP (3), and (d) allyl alcohol (1) + H2O (2) + EG (3) systems at P = 101.3 kPa. Black dashed line, calculated results by UNIFAC model on an entrainer-free basis; black solid line, calculated results by UNIFAC model; blue solid line, calculated results by UNIFAC(0) model; red solid line, calculated results by COSMO-RS-UNIFAC model; red dashed line, calculated results by COSMO-SAC-UNIFAC model. ▼, experimental data with entrainer; ■, experimental data without entrainer.11 12


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Table of Content (TOC) Graphic

400 12

350

10

300

P (kPa)

P (σ)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8 6

250 200

4

150

2

100

-0.02

-0.01

0

0.01

0.02

COSMO-UNIFAC Model

50 0.0

2

T = 350.4 K 0.2

0.4

0.6

x1, y1

σ (e/Å )

13


0.8

1.0

A United Chemical Thermodynamic Model: COSMO-UNIFAC

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