A Modified UNIFAC (Dortmund) Model. 4. Revision and Extension

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A Modified UNIFAC (Dortmund) Model. 4. Revision and Extension Ju 1 rgen Gmehling,* Roland Wittig, Ju 1 rgen Lohmann,† and Ralph Joh‡ Lehrstuhl fu¨ r Technische Chemie (FB9), Carl von Ossietzky Universita¨ t Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany

The group contribution method modified UNIFAC (Dortmund) has become very popular because of its large range of applicability and the reliable results predicted for vapor-liquid equilibria, solid-liquid equilibria, activity coefficients at infinite dilution, azeotropic data, and excess enthalpies over a wide temperature range. However, in a few cases, especially at high and low temperatures, poor results are obtained. To overcome this problem, the modified UNIFAC (Dortmund) parameters have been refitted to an extended database. Additionally, new groups for different amides, used as selective solvents, have been introduced. Altogether, 43 new or revised pairs of group interaction parameters for modified UNIFAC (Dortmund) are given. Introduction For the synthesis, design, and optimization of separation processes, the knowledge of the phase equilibrium behavior is necessary. Because experimental data are often not available, at least for process synthesis, group contribution methods can be used to predict the required phase equilibria and the excess properties. In the past few decades, the group contribution method modified UNIFAC (Dortmund)1-6 has become very popular. Therefore, modified UNIFAC (Dortmund) has been integrated into most commercial process simulators. Because of ongoing research work, the large range of applicability of this approach is being continuously extended, and at the same time, the reliability of modified UNIFAC (Dortmund) is being improved. Figure 1 provides an overview of the different applications of group contribution methods and group contribution equations of state (GC-EOS) such as predictive Soave-Redlich-Kwong (PSRK).7,8 In addition to the prediction of phase equilibria and excess properties, the models can be used for many other applications of industrial interest, e.g., synthesis and design of thermal separation processes, selection of cosolvents for biphasic reactions, calculation of chemical equilibria (Kγ, Kφ), prediction of flash points, and estimation of the fate of a chemical in the environment. Because of the temperature-dependent group interaction parameters used in modified UNIFAC (Dortmund):

[

]

(anm + bnmT + cnmT2) Ψnm ) exp T

(1)

this method allows for the reliable prediction of different properties of thermodynamic mixture such as vaporliquid equilibria (VLE), activity coefficients at infinite dilution (γ∞), excess enthalpies (hE), liquid-liquid equi* Correspondence concerning this article should be addressed to Prof. Dr. J. Gmehling. Tel.: +49 441 798 3831. Fax: +49 441 798 3330. E-mail: [email protected]. Internet: http://www.uni-oldenburg.de/tchemie. † Present address: BASF Coatings AG, Werk Mu ¨ nster, Postfach 6123, D-48163 Mu¨nster, Germany. ‡ Present address: Siemens Axiva GmbH & Co. KG, Industriepark Ho¨chst, D-65926 Frankfurt/Main, Germany.

libria (LLE), solid-liquid equilibria of eutectic systems (SLE), and azeotropic data over a wide temperature range. The group interaction parameters of modified UNIFAC (Dortmund) are fitted simultaneously to all available, reliable mixture data. Figure 2 shows the typical temperature ranges covered by the different thermodynamic properties. The required experimental data are mainly taken from the Dortmund Data Bank (DDB). Additionally, a large number of systematic measurements have been carried out in our laboratory to extend the necessary database. This paper provides revised parameters and new group interaction parameters for the main groups dialkylated formamides, monoalkylated amides, and dialkylated amides. Problems Because the temperature dependence of the activity coefficient γi is described by the Gibbs-Helmholtz equation

( ) ∂ ln γi ∂(1/T)

P,x

)

h h iE R

(2)

the excess enthalpy data are most important, particularly as supporting data at high temperatures9 (up to 450 K) for fitting temperature-dependent group interaction parameters. Unfortunately, however, most of the published hE data were determined around room temperature (see Figure 3). To overcome the lack of experimental hE data, systematic measurements at higher temperatures for more than 300 systems have been carried out in our laboratory using isothermal flow calorimetry.10-13 On the other hand, solid-liquid equilibria of eutectic systems cover the temperature range below 273 K. The use of SLE as supporting data allows for the reliable prediction of activity coefficients (γi) at low temperatures. To enlarge the database for SLE, systematic measurements have been performed in our laboratory using the synthetic, visual technique.14-20 The results obtained when hE data and solid-liquid equilibria are not included in the database for fitting reliable temperature-dependent group interaction pa-

10.1021/ie0108043 CCC: $22.00 © 2002 American Chemical Society Published on Web 02/23/2002

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Figure 1. Different applications of industrial interest for which reliable phase equilibrium information is required.

Figure 2. Typical temperature ranges covered by the different thermodynamic mixture data.

Figure 4. Experimental and predicted hE data for the system cyclohexane (1) + N-butylmercaptan (2)30 (A, before revision; B, after revision) at (b) 283.15, (0) 298.15, and (2) 333.15 K. (s) Modified UNIFAC (Dortmund). Figure 3. Number of hE data sets stored in the DDB as a function of temperature.

rameters are shown in Figures 4A and 5. Only poor agreement between the experimental and predicted excess enthalpies for the system cyclohexane + Nbutylmercaptan (Figure 4A) is obtained. This means that the temperature dependence is described incorrectly. Regarding the solid-liquid equilibrium of the system nitrobenzene + chlorobenzene (Figure 5), in particular, the temperature of the eutectic point is

predicted poorly. The results are not surprising as the group interaction parameters used for the predictions for cyclic alkanes and thiols were fitted only to VLE data, and in the case of nitro- and chlorobenzene, they were fitted only to VLE and γ∞ data. Because of the poor results, the group interaction parameters have been revised using new supporting data at high and low temperatures. Figures 4B and 5 show the results obtained after the revision. It is obvious that neglecting hE data or solid-liquid equilibria can lead to poor temperature extrapolation. The range of applicability

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Figure 5. Experimental and predicted SLE data for the system nitrobenzene (1) + chlorobenzene (2): (b)31 modified UNIFAC (Dortmund), (- - -) before revision and (s) after revison.

mainly depends on the size and completeness of the parameter matrix.

If the description of the thermodynamic behavior of mixtures with compounds of industrial interest is not possible, the required parameters have to be fitted, or new main groups have to be introduced into modified UNIFAC (Dortmund). In this paper, new main groups are introduced for the amides, which are, for example, important selective solvents for extractive distillation and extraction. The original UNIFAC21-23 method provides three main groups for the description of amides: dimethylformamides (no. 39), N-methyl pyrrolidone (no. 44), and acetamides (no. 46). The group assignment is given in Table 1. Because of the different polarities of the amides, which depend on the degree of alkylation of the nitrogen and carbon atoms, a satisfying prediction of the thermodynamic behavior of mixtures is not achieved with this group assignment. For this reason, the amides have been divided into six main groups in modified UNIFAC (Dortmund) (Figure 6). The main group dialkylated formamides (no. 39)2 already exists in modified UNIFAC

Figure 6. Structural groups of the different amides [modified UNIFAC (Dortmund)].


Figure 7. Database used to fit modified UNIFAC (Dortmund) Parameters. Table 1. UNIFAC Rk and Qk Parameters and Group Assignments for the Main Groups Dialkylated Formamides (No. 39), Cyclic Monoalkylated Amides (No. 44), and Amides (No. 46)21-23 main group

subgroup

no.

Rk

Qk

example

group assignment

39 DMF

DMF HCON(CH2)2 NMP CONH2 CONHCH3 CONHCH2 CON(CH3)2 CONCH2(CH3) CON(CH2)2

72 73 85 94 95 96 97 98 99

3.0856 2.6322 3.9810 1.4515 2.1905 1.9637 2.8589 2.6322 2.4054

2.736 2.120 3.200 1.248 1.796 1.488 2.428 2.120 1.812

N,N-dimethylformamide N,N-diethylformamide N-methyl pyrrolidone acetamide N-methylacetamide N-ethylacetamide N,N-dimethylacetamide N,N-methylethylacetamide N,N-diethylacetamide

1 DMF 2 CH3,1 HCON(CH2)2 1 NMP 1 CH3,1 CONH2 1 CH3,1 CONHCH3 2 CH3,1 CONHCH2 1 CH3, 1 CON(CH3)2 2 CH3, 1 CONCH2(CH3) 3 CH3,1 CON(CH2)2

44 NMP 46 CON

(Dortmund). Furthermore, two flexible main groups for the description of cyclic alkylated amides (no. 46)3,24 and dialkylated amides (no. 48)13,25 have already been introduced. The new main group monoalkylated amides (no. 47)25 is presented for the first time in this paper. The introduction of main groups for monoalkylated formamides (no. 49)26 and cyclic amides (no. 62) is in progress. Parameters and results for these main groups will be published later. Fitting Procedure Within the past 20 years, a sophisticated software package has been developed for the fitting of reliable temperature-dependent group interaction parameters. Before the fitting procedure is begun, the main groups for which the interaction parameters are to be fitted have to be defined. After the components for each main group have been selected from the stored connection tables, the thermodynamic mixture data are searched. To fit the modified UNIFAC (Dortmund) group interaction parameters, up to seven different types of thermodynamic mixture data (VLE, γ∞, hE, cEp , LLE, SLE, and azeotropic data) are used. First, however, the mixture data have to be evaluated using consistency (RedlichKister area and Van Ness point) and plausibility tests. To fit the remaining reliable data, the following objective function F is used !

F ) (anm, amn, bnm, bmn, cnm, cmn, Rk, Qk) ) min (3) The van der Waals values Rk and Qk are fitted only when the basic parameters for a new main group are fitted.

In the objective function F, the deviations between experimental and calculated data for the different phase equilibria and excess properties (see Figure 7) are summed. By varying the weighting factors wi for the different thermodynamic properties in the objective function, the results can be influenced in the desired direction. Each type of mixture data provides specific information about the real mixture behavior (see Figure 7): (1) VLE data and azeotropic data are the most important data. They provide the information about the composition dependence of the activity coefficients. (2) hE data provide the most important information about the temperature dependence of the activity coefficient. Additionally, hE data at high temperatures up to 413.15 K (measured mainly in our research group) are most important as supporting data at high temperature. (3) cEp data provide information about the temperature dependence of the excess enthalpies. (4) γ∞ data not only provide information about the temperature dependence of the activity coefficients but also deliver the only reliable information for the dilute region and for asymmetric systems. (5) SLE data of eutectic systems are used as supporting data at low temperatures ( 1), a binary azeotrope with a pressure maximum (temperature minimum) occurs when the following condition is fulfilled

ln γ∞2 > ln

Figure 8. (A) Experimental and predicted P-x behavior for the system toluene (1) + N,N-dimethylformamide (2) (b)32 at 378.2 K. (B) Experimental and predicted hE data for the systems toluene (b), p-xylene (2), and 1,3,5-trimethylbenzene (9) (1) + N,Ndiethylacetamide (2) 33 at 303.15 K. (s) Modified UNIFAC (Dortmund).

(e.g., crystallization)? (2) Must separation problems (e.g., azeotropic points, where the separation factor R12 becomes unity) be considered? (3) Are there suitable solvent for extractive or azeotropic distillation to solve these separation problems? (4) How many theoretical stages (Nth) are required for the different columns? (5) What is the most economical separation sequence? As mentioned before, amides are suitable solvents for extractive distillation. In the following discussion, this aspect is explained in detail.

PS1 PS2

> - ln γ∞1

(5)

This means that, with the help of the activity coefficients at infinite dilution (γ∞i ) and the pure-component vapor pressures (PSi ) as a function of temperature, it is possible to predict the occurrence and disappearance of azeotropes. In the case of azeotropic systems, separation by ordinary distillation becomes impossible even with an infinite number of stages. However, separation processes such as azeotropic or extractive distillation can be used to separate azeotropic systems. In extractive distillation, a solvent (entrainer) is used that alters the separation factors, so that R12 or 1/R12 takes values far from unity (zeotropic behavior). A criterion for the selection of selective solvents is the selectivity at infinite ∞ dilution S12 ∞ ) R12,S

γ∞1,S PS1

PS1 ∞ ) S 12,S S γ∞2,S PS2 P2

(6)

Thus, the entrainer should alter the activity coefficients of the components of the azeotropic system for the system to exhibit zeotropic behavior (binary mixture and entrainer). In addition, it should have a boiling point usually higher (e.g., ∆T ) 40 K) than those of the components of the system to be separated and a high

Table 4. Suitable Solvents for the Separation of Benzene from Cyclohexane by Extractive Distillation components to be separated

(1) benzene (2) cyclohexane system pressure 101.325 kPa azeotropic data for system (1)-(2) type of azeotrope ) homPmax model modified UNIFAC (Dortmund) minimum boiling point difference (entrainer - binary mixture) minimum required value for R∞1,2 (or inverse)

C6H6 C6H12

Tb ) 353.25 K Tb ) 353.86 K

71-43-2 110-82-7

Tb ) 350.68 K 40.00 K 1.500

list of solvents for the extractive distillation types of azeotropes introduced selective solvent (3)

Tb(3) (K)

R∞1,2 a

N-methyl-2-pyrrolidone (NMP) N,N-dimethylacetamide (DMA) N,N-dimethylformamide (DMF) N,N-dimethylbutyramide N-methyl-6-caprolactam N-methylacetamide N-octyl-2-pyrrolidone

475.13 438.96 426.50 462.83 510.21 480.70 603.84

0.205 0.229 0.275 0.302 0.340 0.366 0.547

a

All at 353.35 K.

(1)-(3)

(2)-(3)

(1)-(2)-(3)

none none none none none none none



Tm(3) (K) 248.75 251.42 212.15 233.15 279.70 303.72 253.15

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Figure 9. (A, B) Experimental and predicted data for the system octane (1) + N-methylacetamide (2): (A) P-x data (b)34 at 398.05 K; (B) hE data (b) 34 at 398.15 K. (C) Activity coefficients at infinite dilution for N-methylacetamide in pentane, hexane, and heptane (b).35 (D-F) Experimental and predicted data for the system N-methylacetamide (1) + naphthalene (2): (D) P-x data (b)36 at 413.51 K, (E) hE data (b)37 at 413.15 K, (F) SLE data (b).38 (s) Modified UNIFAC (Dortmund).

flash point. The entrainer used for extractive distillation should also be thermally and chemically stable, nontoxic, noncorrosive, easily available, and inexpensive. By using the proposed procedure, one can obtain a list of selective solvents that can be applied for the separation of the binary system benzene + cyclohexane (this system is representative of the separation of aromatics from aliphatics) by extractive distillation (see Table 4).28 The table gives only a sample of the results that were obtained using the modified UNIFAC (Dort∞ ) mund) method and the criteria ∆T ) 40 K and R12 ∞ 1.5 or 1/R12 ) 1.5. In addition to the listed amides, solvents such as aniline, 1,2-ethanediol, sulfolane, and

N-formylmorpholine are also suitable. From the table, it can be seen that the separation factors are always lower than unity. This means that the volatility of the lower-boiling compound (benzene) becomes smaller than that of cyclohexane in the presence of the entrainer, so that the slightly higher-boiling compound cyclohexane is obtained at the top of the extractive distillation column. Figures 11 and 12 show a comparison of experimental and predicted results for the selectivities and capacities of various amides for the separation of benzene from cyclohexane. In addition to the selectivity, the capacity is also important. It provides information about the amount of entrainer needed, which


Figure 10. (A) Experimental and predicted T-x behavior for the system 2-methylbutane (1) + N,N-dimethylacetamide (2) (b)39 at 101.32 kPa. (B) Experimental and predicted hE data for the system hexane (1) + N,N-diethylacetamide (2) (b)40 at 298.15 K. (C, D) Experimental and predicted data for the system water (1) + N,N-dimethylacetamide (2): (C) T-x data (b)41 at 26.66 kPa; (D) hE data42 at (b) 298.15, (2) 308.15, and (9) 318.15 K. (s) Modified UNIFAC (Dortmund).

Figure 11. Temperature dependence of S∞12 for different amides for the separation of benzene from cyclohexane.

can be calculated according to

capacity )

1 ∞ γcomponent i in entrainer

Figure 12. Selectivities and capacities of different amides for the separation of benzene from cyclohexane.

(7)

From the figures, it can be seen that N-methyl pyrrolidone (NMP) and N,N-dimethylformamide (DMF) show the highest selectivities, whereas N,N-dibutylformamide has the highest capacity. It can be seen that there is quite good agreement between the experimental data and the results predicted using modified UNIFAC (Dortmund). A software package has already been developed for the selection of selective solvents that can be applied

for extraction and extractive and azeotropic distillation.28 The selection of a suitable solvent is carried out by accessing the Dortmund Data Bank (DDB), which contains γ∞ and azeotropic data, or by using a thermodynamic method such as modified UNIFAC (Dortmund). Conclusion The examples presented in this paper show that the new or revised modified UNIFAC (Dortmund) parameters allow for a reliable prediction of phase equilibria

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Figure 13. Current parameter matrix, including the refrigerant submatrix, for modified UNIFAC (Dortmund) (August 2001).

and excess enthalpies. Therefore and because of the large range of applicability, modified UNIFAC (Dortmund) is a suitable model for a variety of applications of industrial interest that can help chemical engineers during their daily work. Because of ongoing research, the range of applicability of modified UNIFAC (Dortmund) will be further enlarged and the reliability continually improved.

Many gaps in the modified UNIFAC (Dortmund) parameter matrix have already been filled with the help of the huge amount of data on thermodynamic phase equilibria and excess properties continuously stored in the DDB or measured in our laboratory. The main groups for amides are just one example of a newly introduced substance class in modified UNIFAC (Dortmund). Many other main groups of industrial


interest have already been introducd into the parameter matrix of modified UNIFAC (Dortmund) within the UNIFAC consortium project, including groups for monoalkylated formamides, aromatic nitriles, isocyanates, anhydrides, sulfones, aromatic aldehydes, aromatic acids, aromatic esters, sulfides, cyclic amides, cyclic esters, peroxides, refrigerants, acetals, and dialkylated anilines. The present status of the group interaction parameter matrix is given in Figure 13. The most up-to-date status of the research work is always available via the Internet at http://www.unioldenburg.de/tchemie/consortium. Outlook Research work on the revision and extension of modified UNIFAC (Dortmund) will be continued with the support of the members of the UNIFAC consortium. Within this consortium is planned the introduction of additional main groups for components of industrial interest, such as monoalkylated anilines (e.g., N-methylaniline), aromatic ethers (e.g., anisole), cyclic amines (e.g., piperidine), cyclic sulfides (e.g., tetrahydrothiophene), and cyclic carbonates (e.g., propylene carbonate). However, because of the lack of data for these compounds, a large number of additional measurements of VLE, γ∞, hE, SLE, and azeotropic data have to be performed before. Furthermore, the well-known weaknesses of group contribution methods (isomer and proximity effects) will be examined and hopefully soon be minimized. In the future, the combination of modified UNIFAC (Dortmund) with a generalized volume-translated cubic equation of state is planned. This combination allows for the extension of the group contribution concept to systems with supercritical compounds. This approach will also provide densities and enthalpies for both the liquid and vapor phases as functions of temperature, pressure, and composition, which is required as additional information in the γ-φ approach. Additionally, the effects of strong electrolytes on phase equilibrium behavior (LIFAC)43 will be combined with modified UNIFAC (Dortmund). Acknowledgment The authors thank the members of the UNIFAC consortium for financial support of the ongoing research work. Furthermore, we thank the DDBST GmbH (Oldenburg, Germany) for providing the latest version of the Dortmund Data Bank. Nomenclature anm, bnm, cnm ) modified UNIFAC (Dortmund) group interaction parameters between main groups n and m cEp ) molar excess heat capacity (J mol-1K-1) DMA ) N,N-dimethylacetamide DMF ) N,N-dimethylformamide F ) objective function GLC ) gas-liquid chromatograhpy GLE ) gas-liquid equilibrium h ) molar enthalpy (J mol-1) hE ) molar excess enthalpy (J mol-1) ∆hm,i ) molar enthalpy of fusion (J mol-1) homPmax ) homogeneous pressure maximum azeotrope i, j ) components n, m ) main groups

KOW ) octanol-water partition coefficient K ) chemical equilibrium constant LLE ) liquid-liquid equilibrium NMP ) N-methyl pyrrolidone P ) pressure (kPa) PSi ) saturation vapor pressure of component i (kPa) Qk ) relative van der Waals surface area of subgroup k R ) general gas constant (J mol-1 K-1) Rk ) relative van der Waals volume of subgroup k s ) molar entropy (J mol-1 K-1) S∞12 ) selectivity at infinite dilution of solvent S for the binary system of components i and j SLE ) solid-liquid equilibrium T ) absolute temperature (K) Tb ) boiling temperature (K) Tm ) melting temperature (K) vE ) molar excess volume (cm3 mol-1) VLE ) vapor-liquid equilibrium V ) volume (cm3) wi ) weighting factor xi ) mole fraction of component i in the liquid phase yi ) mole fraction of component i in the vapor phase Rij ) separation factor for components i and j γ∞ ) activity coefficient at infinite dilution γi ) activity coefficient of component i φi ) fugacity coefficient of component i Ψnm ) modified UNIFAC (Dortmund) temperature term (eq 1)

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Received for review September 28, 2001 Revised manuscript received December 17, 2001 Accepted January 7, 2002 IE0108043

A Modified UNIFAC (Dortmund) Model. 4. Revision and Extension

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