prediction of vle for asymmetric systems at low and hp with the psrk model

8/18/2019 Prediction of VLE for Asymmetric Systems at Low and HP With the PSRK Model

1/12

Ž .Fluid Phase Equilibria 143 1998 71–82

Prediction of vapor–liquid equilibria for asymmetric systems at lowand high pressures with the PSRK model

Jiding Li b, Kai Fischer c, Jurgen Gmehling a,)¨a

UniÕersitat Oldenburg, Technische Chemie, Postfach 2503, D-26111 Oldenburg, Germany¨b

Department of Chemical Engineering, Tsinghua UniÕersity, Beijing, Chinac

Ecole des Mines de Paris, Centre Reacteurs et Processus, 35 Rue Saint-Honore, F-77305 Fontainebleau, France

Received 11 January 1996; revised 20 May 1997; accepted 5 August 1997

Abstract

The idea of effective R) , Q) for the subgroups CH , CH , CH and C of UNIFAC in PSRK is proposed.k k 3 2Based on this idea, an empirical expression has been developed, allowing the reliable prediction of vapor–liquid

equilibria for asymmetric systems at low and high pressures with the help of the PSRK model. Published by

Elsevier Science B.V.

Keywords: Asymmetric systems; Equation of state; Group contribution; Vapor–liquid equilibria

1. Introduction

w xSince Huron and Vidal 1 proposed an approach that allowed to incorporate excess Gibbs energymodels into the mixing rules for cubic equations of state, many group contribution equations of state

w xhave been developed. One of them is the PSRK model proposed by Holderbaum and Gmehling 2 , inw xwhich the PSRK mixing rule combines the UNIFAC model 3 with the SRK equation of state. A

w x w xcomparison with other group contribution equations of state, such as the MHV2 4,5 , LCVM 6 ,w x w x w x w xW-S 7,8 , UNIWAALS 9 , GCEOS 10 , showed 2,11 that the PSRK model has some very

Ž . Žimportant advantages, as 1 the PSRK mixing rule has a well defined reference state the liquid.mixture at atmospheric pressure , whereby the constant A s y0.64663 used in the PSRK mixingo

Ž .rule is basically calculated using quasi liquid volumes of many substances at one atmosphere; 2 the

PSRK model gives reliable results for vapor–liquid equilibria and gas solubility in a large temperatureŽ .and pressure range; and 3 the parameter matrix of the PSRK model is much larger than for the other

methods, meaning PSRK has a larger range of applicability.

)

Corresponding author.

0378-3812r98r$19.00 Published by Elsevier Science B.V.Ž .PII S 0 3 7 8 - 3 8 1 2 9 8 0 0 2 0 6 - 9


2/12

( ) J. Li et al.r Fluid Phase Equilibria 143 1998 71–8272

The PSRK model has been successfully used for different applications. However, poor results areobtained when the model is applied to highly asymmetric systems; for example, asymmetric alkane

w xsystems as also observed by Kalospiros et al. 12 . The same situation occurs in other groupcontribution equations of state, such as the MHV2 model. In this work, the idea of effective R ) andk Q ) for the different subgroups k s CH , CH , CH and C in UNIFAC is presented, overcoming thisk 3 2weakness, and allows reliable predictions of the PSRK model not only for systems with similar

compounds, but also for those with different sizes.The suggestion of modifying the R and Q values of the different alkane subgroups, dependingk k on the size of the molecule, is strongly motivated by the request to extend the range of applicability of the PSRK method to asymmetric systems. The empirical function given below, used as empiricallyadjusted, has the advantage not to influence the results on those systems, where excellent results are

Ž .already obtained not too asymmetric, limitation: ratio of molecular size lower than about 8 . Newapplications, e.g., the prediction of the phase equilibrium behavior exploited for supercritical fluidextraction, are opened, which means that PSRK with the idea of effective van der Waals propertiesextends again the range of applicability.

There had been several attempts to understand and overcome the error that leads to the poor resultsE Ž w x.of group contribution G mixing rules LCVM 6,13 . The proposed modifications of the model

equations do not differ much in the weakness of their theoretical justification. But the problem isclearly located in the insufficient way of characterizing the molecule dimensions in the sense of

w xBondi’s method 14 , that means the simple addition of the group dimensions. It can be shown that theŽ . Eterm Ý x ln brb used in G mixing rules corresponds almost exactly to the combinatorial part of

i i 0

the UNIFAC method. But the covolumes b are molecular properties and the van der Waals propertiesare summed up by group dimensions, leading to a discrepancy in asymmetric systems. Thisunderstanding leads to two possible ways of improvement.

Ž . Ž .a Skipping the combinatorial part of UNIFAC as well as the term Ý x ln brb in the PSRKi i

mixing rule. This leads to surprisingly good results, e.g., for symmetric and asymmetric alkane–al-kane systems, where no group interaction parameters are required. But the use of UNIFAC fornon-alkane systems leads generally to poor results. This can be overcome by refitting all the

parameters, which would be extremely time-consuming.Ž .b An empirical recorrection of the error introduced by the additive way of calculating the group

dimensions: that is the subject of this work. The correction of R and Q values given below wask k found to be generally, applicable and thus represents a simple way to extend the range of applicabilityof PSRK.

2. Corrected R ) and Q ) for the subgroups CH , CH , CH and Ck k 3 2

The concept of group contributions is, that the distribution of free groups is homogeneous in thesolution. For small molecules, there is no large difference between the partition of groups, ormolecules in the solution. If the differences between small and large molecules are not considered,and the R and Q values for small molecules are generally used, poor results are obtained when thek k group contribution equation of state is applied for asymmetric systems containing components verydifferent in size. The results listed in Table 1 show that the above explained inference is apparent. Inthe examples shown in Table 1, all systems consist only of alkane groups CH . It should be noticed2


3/12

( ) J. Li et al.r Fluid Phase Equilibria 143 1998 71–82 73

Table 1Ž .Results of the PSRK model original R and Q used for ethaneq n-alkanesk k

a bŽ . Ž . Ž .System T K P bar NDP D PrP %

C H –C H 127–369 0.1–51.8 503 2.12 6 3 8C H – nC H 260–394 0.6–55.7 119 3.62 6 4 10C H – nC H 277–450 0.3–68.3 94 2.72 6 5 12C H – nC H 290–450 0.9–79.1 76 5.82 6 6 14

C H – nC H 338–450 27.6–88.2 78 3.42 6 7 16C H – nC H 273–373 4.1–66.0 68 2.22 6 8 18C H – nC H 277–510 0.1–118.3 244 6.82 6 10 22C H – nC H 318 12.0–52.5 10 7.62 6 11 24C H – nC H 273–373 3.6–62.8 155 11.02 6 12 26C H – nC H 323–573 3.7–167.6 102 41.82 6 20 42C H – nC H 360–360 2.7–92.8 7 46.02 6 22 46C H – nC H 348–573 5.6–51.8 36 80.82 6 28 58C H – nC H 373–573 3.7–47.6 25 117.12 6 36 74C H – nC H 423 5.3–29.8 6 168.02 6 44 90

aNDPsnumber of data points.

b Ž .


4/12


Ž .Fig. 1. The relationship between the correction factor f n and the number of carbon atoms n in the molecule.c c

quasi to define new subgroups for each different molecule. The new values R ), Q ) are used in allk k Ž .calculations required to obtain the activity coefficients combinatorial and residual part . It should be

noticed, that, e.g., the R ), Q ) values of the subgroup CH in hexane has another value than ink k 3hexadecane. But it still belongs to the same main group.

Ž .It is well known that in most cases the alkyl –C H chain forms the main portion of largen 2 nq1

molecules, while the other functional groups, such as –OH, –CHO, NH , NO represent a smaller2 2portion, except for aromatic components. A correction of R , Q for aromatic groups is not required,k k

because the geometry of the aromatic CH groups is independent on the molecular size. Thus, it can beconcluded that the problem occurring for the group contribution models applied to asymmetricsystems might be solved only by means of corrected R ), Q ) of the subgroups CH , CH , CH and Ck k 3 2in a quite empirical, but general way. A similar approach of simply correcting the relative van derWaals group dimensions might be promising also to improve the problems of group contributionmethods with isomeric effects, which cannot be considered up to now.

Ž .The function f n plotted in Fig. 1 shows that the correction factor increases very slowly with thecchain length, and remains almost equal to 1.0 when n is less than 5, increases quite slowly betweenc

Ž .5-n -12, and increases faster when n )12. The reliability of Eq. 3 has been tested from n s 2c c c

to n s44 using all experimental vapor–liquid equilibrium data found in the Dortmund Data Bank cw x Ž .15,16 . It is suggested that if Eq. 3 is used for components with more than 45 carbon atoms, theresults should be checked by experimental data. However, efforts to extend the idea explained abovenot only for large molecules but also for polymers seems to be promising.

3. Results and discussion

The results for systems with CO q large alkanes, CH q large alkanes, small alkanesq large2 4alkanes predicted by PSRK model are summarized in Tables 2 and 3. There are about 400 VLE data

Ž .sets 2469 data points for the gases CO , CH with large alkanes, and small alkanes with large2 4alkanes in the Dortmund Data Bank. The large amount of papers reporting the experimental

information referred to in Tables 1–3 would extend this article too much for this journal. Thecomplete bibliographic information can be requested from the authors. The mean deviation betweenexperimental and predicted results with the PSRK model is less than 5.6% for the pressure, and less

Ž .than 0.0085 for the vapor-phase mole fraction Tables 2 and 3 . These results show that the PSRK


5/12


Table 2

Results for CO qlarge alkanes, CH qlarge alkanes2 4

Ž . Ž . Ž . Ž .System T K P bar NDP D PrP % 100=D y NDP D PrP % 100=D y

) ) ) )PSRK PSRK PSRK PSRK PSRK LCVM PSRK LCVM

CO – nC H 288–594 0.1–188.4 197 3.5 2.7 0.82 0.94 157 2.6 4.4 0.36 0.802 10 22CO – nC H 288–305 9.0–71.2 12 6.8 3.82 12 26CO – nC H 240–305 8.3–64.9 23 4.9 4.5

2 14 30CO – nC H 313 17.0–64.2 8 1.2 16.52 15 32CO – nC H 297–663 4.3–257.0 47 6.3 25.7 0.33 1.69 21 4.3 5.5 0.29 1.002 16 34CO – nC H 396–605 10.1–61.9 24 7.5 33.7 0.50 1.052 18 38CO – nC H 313 9.4–79.6 35 5.2 29.3 35 5.2 6.32 19 40CO – nC H 310–573 5.1–76.0 110 3.9 33.2 0.05 0.26 70 4.4 5.02 20 42CO2– nC H 323–373 9.6–71.8 44 6.6 45.2 44 6.6 4.022 46CO – nC H 373–573 10.1–50.7 15 4.3 46.8 0.06 0.02 15 4.3 3.4 0.06 0.202 24 50CO – nC H 348–573 8.1–96.0 38 7.4 67.5 0.04 0.05 30 5.8 3.7 0.04 0.002 28 58CO – nC H 348–573 9.5–72.3 52 9.8 85.4 0.02 0.01 41 8.1 5.5 0.02 0.002 32 66CO – nC H 373–573 5.2–86.3 33 8.7 102.1 18 5.4 5.82 36 74CH – nC H 244–583 0.1–362.0 596 4.8 6.6 0.85 0.76 126 3.6 3.5 0.53 0.204 10 22CH – nC H 323–373 13.3–103.8 13 6.7 18.04 12 26

CH – nC H 373–423 9.8–456.0 25 9.0 25.5 0.20 0.274 13 28CH – nC H 373–623 20.3–563.9 123 5.3 31.3 0.82 1.184 16 34CH – nC H 323–573 10.1–106.9 27 10.5 48.4 0.08 0.21 5 10.5 2.14 20 42CH – nC H 373–573 10.1–50.7 25 6.7 58.0 0.05 0.024 24 50CH – nC H 348–573 9.3–70.9 23 9.5 60.6 0.05 0.06 5 9.5 9.54 28 58CH – nC H 473–623 10.1–50.7 20 6.1 85.9 0.04 0.014 32 66CH – nC H 473–573 10.2–50.6 29 6.5 118.6 5 6.5 10.64 36 74Total indices 1519 5.4 572 4.4 4.6

PSRK: original R and Q are used.k k PSRK ): effective R ) and Q ) are used.k k

Table 3

Results for small alkanes with large alkanes with zero interaction parameters

Ž . Ž . Ž . Ž .System T K P bar NDP D PrP % 100=D y NDP D Pr P % 100=D y

) ) ) )PSRK PSRK PSRK PSRK PSRK LCVM PSRK LCVM

C H – nC H 277–510 10.1–118.3 244 4.0 6.8 0.80 0.78 113 3.8 7.3 0.33 0.302 6 10 22C H – nC H 318–318 12.0–52.5 10 4.1 7.6 10 4.1 4.82 6 11 24C H – nC H 273–373 3.6–62.8 155 4.2 11.0 50 4.9 9.12 6 12 26C H – nC H 323–573 2.3–167.6 194 10.1 41.8 0.20 0.42 137 8.9 8.22 6 20 42C H – nC H 300–360 2.1–92.8 47 13.9 46.0 47 13.9 13.72 6 22 46C H – nC H 348–573 5.6–51.8 36 9.9 80.8 28 9.6 5.62 6 28 58C H – nC H 373–573 3.7–47.6 25 7.3 117.1 17 8.3 5.82 6 36 74C H – nC H 423–423 5.3–29.8 6 6.1 168.0 6 6.1 5.52 6 44 90

C H – nC H 277–510 0.1–70.9 65 3.7 5.0 0.47 0.433 8 10 22C H – nC H 293–313 0.6–12.7 30 1.6 10.83 8 16 34nC H – nC H 310–510 0.1–49.2 138 2.1 2.4 0.59 0.534 10 10 22Total indices 950 5.7 408 7.4 8.3



6/12


) ) )Ž . ŽFig. 2. Prediction of bubble point pressures for gas– n-alkane systems. PSRK -model effective R , Q valuesk k . Ž . Ž . Ž . Ž . w x Ž . Ž .used , v, B, l experimental values; a v CO 1 q nC H 2 , 473.15 K 1 7 , B CO 1 q nC H 2 , 473.45 K2 20 42 2 28 58

w x Ž . Ž . w x Ž . Ž . Ž . w x Ž . Ž .18 , l CO 1 q nC H 2 , 473.35 K 19 ; b v CH 1 q nC H 2 , 573.15 K 18 , B CH 1 q nC H 2 ,2 36 74 4 20 42 4 28 58w x Ž . Ž . w x Ž . Ž . Ž . w x573.25 K 18 , l CH 1 q nC H 2 , 573.15 K 19 ; c v C H 1 q nC H 2 , 410.93 K 20 , B C H4 36 74 2 6 10 22 2 6

Ž . Ž . w x Ž . Ž . w x1 q nC H 2 , 423.2 K 21 , l C H 1 q nC H 2 , 423.2 K 21 .36 74 2 6 44 90

model with the modified R ), Q ) values proposed in this work can be used to predict reliably VLEk k Ž .for the gases CO , CH with large alkanes and small alkanes C H , C H , nC H with large2 4 2 6 3 8 4 10

alkanes.

Ž . Ž . Ž . Ž .Fig. 3. Prediction of vapor–liquid equilibria for CO 1 q nC H 2 and CH 1 q nC H 2 in a large temperature2 16 34 4 16 34) ) )Ž . Ž . Ž . Žand pressure range. PSRK -model effective R , Q values used , - - - PSRK model original R , Q valuesk k k k

. Ž . Ž . Ž . Ž . w x Ž . Ž . Ž . Ž . w x Ž . Ž . Ž .used , v, ` experimental data. a CO 1 q nC H 2 22 ; b and c CO 1 q nC H 2 23 ; d , e and f ,2 16 34 2 16 34Ž . Ž . w xCH 1 q nC H 2 24 .4 16 34


7/12



8/12



9/12


Table 4

Results for different binary and ternary asymmetric systems

Ž . Ž . Ž .System T K P bar NDP D PrP % References

)PSRK PSRK

w xCO – nC H – nC H 313 17–64 8 4.32 14.02 272 15 32 16 34w xH –C H – nC H 573 200 6 6.68 26.86 282 6 6 16 34w xH –C H – nC H 473 101 5 17.46 32.83 23

2 6 6 16 34 w xH –C H – nC H 473 201 5 22.35 49.58 232 6 6 16 34w xH –C H – nC H 473 301 5 25.04 60.81 232 6 6 16 34w xH –C H – nC H 573 101 3 11.40 34.86 232 6 6 16 34w xH –C H – nC H 573 301 3 4.44 42.02 232 6 6 16 34w xH – nC H – p-CH C H OH 353 20–135 14 5.54 11.71 292 10 22 3 6 4w xH – nC H – p-CH C H OH 393 20–135 15 5.26 11.18 292 10 22 3 6 4w xH – nC H – p-CH C H OH 433 25–101 12 1.74 6.19 292 10 22 3 6 4w xH S– nC H – nC H 323 10–30 15 8.18 23.60 302 16 34 20 42w xC H – nC H – nC H 273 1–4 14 1.12 4.16 313 8 6 14 16 34w xC H – nC H – nC H 283 1–5 20 1.77 7.88 313 8 6 14 16 34w xC H – nC H – nC H 293 1–6 17 1.66 7.26 313 8 6 14 16 34w xC H – nC H – nC H 303 2–8 17 1.50 6.89 313 8 6 14 16 34

w xC H – nC H – nC H 313 2–10 17 3.47 8.68 313 8 6 14 16 34 w xCH – n – nC H 311 69–345 44 8.32 16.17 324 2 10 22w xC H – N – nC10H 344 69–345 41 6.17 13.72 324 2 22w xCO – nC H CH5CH 314 10–51 5 2.25 9.68 332 14 29 2w xCO – nC H CH5CH 288 10–51 5 2.26 14.28 332 14 29 2w xCO – nC H CH5CH 531 10–51 5 3.57 12.81 332 14 29 2w xN – nC H 303 21–341 26 5.20 12.58 342 10 22w xN – nC H 297 48–103 2 8.03 20.91 352 12 26w xN – nC H 423 25–490 20 6.70 32.76 242 16 34w xCO– nC H 311 28–100 6 8.54 15.98 3610 22w xCO– nC H 473 10–51 5 16.02 55.24 2520 42w xCO– nC H 573 10–51 5 16.1 96.99 2528 58w xCO– nC H 473 10–51 5 9.55 137.58 2536 74

w xH – nC H 453 19–118 6 5.97 12.94 372 10 22w xH – nC H 573 100–300 3 15.84 54.64 282 16 34w xH – nC H 373 10–51 5 20.64 64.10 252 20 42w xH – nC H 573 10–51 5 25.34 117.29 252 28 58w xH – nC H 573 10–51 5 21.18 179.29 252 36 74w xH S– nC H 473 3–10 5 7.59 18.01 262 13 28w xH S– nC H 423 11–112 8 4.87 15.82 382 15 32w xH S– nC H 423 6–74 8 7.14 25.00 392 16 34w xH S– nC H 361 5–52 6 5.20 29.08 402 20 42w xH S– nC H 523 3–10 5 24.45 102.91 262 30 62


Ž . Ž . Ž . Ž . Ž . Ž .Fig. 4. Prediction of bubble-point pressures for CO 1 q nC H 2 , CO 1 q nC H 2 , H 1 q nC H 2 , H28 58 36 74 2 28 58 2) ) )Ž . Ž . Ž . Ž . Ž . Ž1 q nC H 2 , and H S 1 q nC H 2 at different temperatures. PSRK model effective R , Q36 74 2 30 62 k k

. Ž . Ž . Ž . Ž . Ž . Ž . w x Ž .values used , - - - PSRK model original R , Q values used , v experimental data. a CO 1 q nC H 2 25 ; bk k 28 58Ž . Ž . w x Ž . Ž . Ž . w x Ž . Ž . Ž . w x Ž . Ž . Ž .CO 1 q nC H 2 25 ; c H 1 q nC H 2 25 ; d H 1 q nC H 2 25 ; e and f H S 1 q nC H36 74 2 28 58 2 36 74 2 30 62

Ž . w x2 26 .


10/12


A limited comparison with the results of the LCVM model is also shown in Tables 2 and 3. Thedata sets used for the comparison and their results calculated with the LCVM model are equal to those

Ž w x.presented by Boukouvalas et al. Tables 5–7 in Ref. 6 . It can be seen that the results of PSRK areslightly better than those of the LCVM model. In addition, the theoretical basis of the PSRK mixingrule is better than that of the LCVM model in which no explicit reference state is defined.Furthermore, the idea of effective R ), Q ) values proposed in this paper is applicable for any groupk k

contribution method.Some results for CO with large alkanes, CH with large alkanes, small alkanes with large alkanes2 4are presented in Figs. 2 and 3. Fig. 2 shows the results of the bubble point pressure calculations for

Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .CO 1 q nC H 2 , CO 1 q nC H 2 , CO 1 q nC H 2 , CH 1 qnC H 2 ,2 20 42 2 28 58 2 36 74 4 20 42Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .CH 1 q nC H 2 , CH 1 q nC H 2 , C H 1 q nC H 2 , C H 1 q nC H 2 ,4 28 58 4 36 74 2 6 10 22 2 6 36 74

Ž . Ž . Ž .C H 1 q nC H 2 . Fig. 3 presents the vapor–liquid equilibrium behavior for CO 1 q nC H2 6 44 90 2 16 34Ž . Ž . Ž .2 , and CH 1 q nC H 2 in a large temperature and pressure range. From Figs. 2 and 3 it can4 16 34be concluded that the PSRK model with the corrected R ), Q ) values works reliably for thesek k systems.

Besides the systems composed of CO with large alkanes, CH with large alkanes and small2 4alkanes with large alkanes, the PSRK model has been used to predict the vapor–liquid equilibria for

CO q large alkanes, H q large alkanes, H S q large alkane. Fig. 4 gives the results for CO2 2Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž .1 q nC H 2 , CO 1 q nC H 2 , H 1 q nC H 2 , H 1 q nC H 2 , and H S28 58 36 74 2 28 58 2 36 74 2Ž . Ž .1 q nC H 2 . It is shown again, that a great improvement is made for the PSRK model with the30 62corrected R ), Q ) values.k k

w xIt should be noticed that the interaction parameters published by Holderbaum and Gmehling 2 ,w xand Fischer and Gmehling 11 for the PSRK model were used without changes or adjustment in this

) ) Ž Ž . Ž ..work. Probably the results would be even better, if the corrected R , Q Eqs. 1 – 3 werek k included in the PSRK model before fitting the model interaction parameters, in spite of the convincingresults obtained by PSRK in this work.

In Table 4 the results for selected data, which are fully referenced in this article, are shown. Theyindicate the typical improvement of the PSRK method for binary and ternary systems.

4. Conclusion

The idea of effective R ), Q ) values for the subgroups CH , CH , CH and C of UNIFAC used ink k 3 2the PSRK model has been proposed. Based on this idea, an empirical expression correcting the vander Waals properties of the alkane subgroups, depending on the chain length of the molecules, hasbeen developed. The expression combined with the PSRK model has been used to predict vapor–liquidequilibria for many asymmetric systems. For CO q large alkanes, H q large alkanes, H S q large2 2alkane, the predictive results are in good agreement with the experimental data. For CO q large2

Ž .alkanes, CH q large alkanes, small alkanes q large alkanes more than 2400 data points , the total4

mean deviation between experimental and predicted is smaller than 5.6% for pressure, and themaximum deviation less than 0.0085 for vapor phase mole fraction. These results show that the PSRKmodel using modified R ), Q ) values as proposed in this work can provide a reliable prediction of k k vapor–liquid equilibria at low and high pressures for highly asymmetric systems, apart from those

w x w xmentioned by Holderbaum and Gmehling 2 , and Fischer and Gmehling 11 .


11/12


It should be pointed out that the idea of the effective R ), Q ) values proposed in this paper can bek k used for all group contribution methods or group contribution equations of state.

Acknowledgements

Ž .The authors thank BMWi, ‘Arbeitsgemeinschaft Industrieller Forschungsvereinigungen AIF ’,Project No. 10931Nr1, and K.-C. Wong Foundation for financial support.

References

w x1 M. Huron, J. Vidal, New mixing rule in simple equations of state for representing vapour–liquid equilibria of stronglyŽ .nonideal mixtures, Fluid Phase Equilib. 3 1979 255–272.

w x2 T. Holderbaum, J. Gmehling, PSRK: A group contribution equation of state based on UNIFAC, Fluid Phase Equilib. 70Ž .1991 251–265.

w x3 H.K. Hansen, P. Rasmussen, Aa. Fredenslund, M. Schiller, J. Gmehling, Vapor– liquid equilibria by UNIFAC groupŽ .contribution: 5. Revision and extension, Ind. Eng. Chem. Res. 30 1991 2352–2355.

w x4 S. Dahl, M.L. Michelsen, High pressure vapour–liquid equilibrium with a UNIFAC based equation of state, AIChE J.Ž .36 1990 1829–1836.w x5 C. Lermite, J. Vidal, A group-contribution equation of state for polar and nonpolar components, Fluid Phase Equilib. 72

Ž .1992 111–130.w x6 C. Boukouvalas, N. Spiliotis, P. Coutsikos, N. Tzouvaras, D. Tassios, Prediction of vapor–liquid equilibrium with the

LCVM model: A linear combination of the Vidal and Michelsen mixing rules coupled with the original UNIFAC andŽ .the t-mPR equation of state, Fluid Phase Equilib. 92 1994 75–106.

w x Ž .7 D.S.H. Wong, S.I. Sandler, A theoretically correct mixing rule for cubic equations of state, AIChE J. 38 1992671–680.

w x8 K. Tochigi, K. Kurihara, K. Kojima, Prediction of high-pressure vapor–liquid equilibria using the Soave–Redlich–Ž .Kwong group-contribution method, Ind. Eng. Chem. Res. 29 1990 2142–2149.

w x9 P. Gupte, P. Rasmussen, Aa. Fredenslund, A new group-contribution equation of state for vapor– liquid equilibria, Ind.Ž .Eng. Chem. Fundam. 25 1986 636–645.

w x10 S. Skjold-Jørgensen, Gas solubility calculations: II. Application of a new group-contribution equation of state, FluidŽ .Phase Equilib. 16 1984 317–351.

w x11 K. Fischer, J. Gmehling, Further development, status and results of the PSRK method for the prediction of vapor– liquidŽ .equilibria and gas solubilities, Fluid Phase Equilib. 121 1996 185–206.

w x E12 N.S. Kalospiros, N. Tzouvaras, P. Coutsikos, D.P. Tassios, Analysis of zero reference pressure EOSrG models,Ž .AIChE J. 41 1995 928–937.

w x13 C. Zhong, H. Masuoka, Mixing rules for accurate prediction of vapor–liquid equilibria of gasrlarge alkane systemsŽ .using SRK equation of state combined with UNIFAC, J. Chem. Eng. Jpn. 29 1996 315–322.

w x14 A. Bondi, 1968. Physical Properties of Molecular Crystals, Liquids and Glasses. Wiley, London.w x15 J. Gmehling, 1985. Dortmund data bank—basis for the development of prediction methods, CODATA Bulletin 58,

Pergamon, Oxford, pp. 56–64.w x16 J. Gmehling, Development of thermodynamic models with a view to the synthesis and design of separation processes,

Ž .in: J. Gmehling Ed. , Software Development in Chemistry, 5th edn., Springer Verlag, Berlin, 1991, pp. 1– 14.w x17 S.H. Huang, H.-M. Lin, K.-C. Chao, Solubility of carbon dioxide, methane, and ethane in n-eicosane, J. Chem. Eng.

Ž .Data 33 1988 145–147.w x18 S.H. Huang, H.-M. Lin, K.-C. Chao, Solubility of carbon dioxide, methane, and ethane in n-octacosane, J. Chem. Eng.

Ž .Data 33 1988 143–145.w x19 F.-N. Tsai, S.H. Huang, H.-M. Lin, K.-C. Chao, Solubility of methane, ethane, and carbon dioxide in n-hexatriacon-

Ž .tane, J. Chem. Eng. Data 32 1987 467–469.


12/12


w x20 H.H. Reamer, B.H. Sage, Phase equilibria in hydrocarbon systems. Volumetric and phase behavior of the ethane-n-de-Ž .cane system, J. Chem. Eng. Data 7 1962 161–168.

w x21 K.A.M. Gasem, B.A. Bufkin, A.M. Raff, R.L. Robinson, Solubilities of ethane in heavy normal paraffins at pressuresŽ .to 7.8 MPa and temperatures from 348 to 423 K, J. Chem. Eng. Data 34 1989 187–191.

w x22 R. D’Souza, J.R. Patrick, A.S. Teja, High pressure phase equilibria in the carbon dioxide-n-hexadecane and carbonŽ .dioxide–water systems, Can. J. Chem. Eng. 66 1988 319–323.

w x23 G. Brunner, J. Teich, R. Dohrn, Phase equilibria in systems containing hydrogen, carbon dioxide, water andŽ .hydrocarbons, Fluid Phase Equilib. 100 1994 253–268.

w x24 R.G. Sultanov, V.G. Skripka, A.Y. Namiot, 1971. Phase equilibria in the systems methane-n-hexadecane andnitrogen-n-hexadecane at high temperatures and pressures, VINITI 2888-71 Dep., 15 pp.

w x25 S.H. Huang, H.-M. Lin, F.-N. Tsai, K.-C. Chao, Solubility of synthesis gases in heavy n-paraffins and Fischer–TropschŽ .wax, Ind. Eng. Chem. Res. 27 1988 162–169.

w x26 C. Yokoyama, A. Usui, S. Takahashi, Solubility of hydrogen sulfide in isooctane, n-decane, n-tridecane, n-hexadecaneŽ .and squalane at temperatures from 323 to 523 K and pressures up to 1.6 MPa, Fluid Phase Equilib. 85 1993 257–269.

w x27 H. Tanaka, Y. Yamaki, M. Kato, Solubility of carbon dioxide in pentadecane, hexadecane, and pentadecaneqŽ .hexadecane, J. Chem. Eng. Data 38 1993 386–388.

w x28 R. Dohrn, G. Brunner, Phase equilibria in ternary and quaternary systems of hydrogen, water and hydrocarbons atŽ .elevated temperatures and pressures, Fluid Phase Equilib. 29 1986 535–544.

w x29 S. Partzsch, 1992. Untersuchung von Fluessigkeit-Dampf-Gleichgewichten in Gemischen aus Kohlenwasserstoffen mitPhenolen und Wasserstoff. PhD thesis, Univ. Leipzig.

w x30 G.-X. Feng, A.E. Mather, J.J. Carroll, The solubility of hydrogen sulfide in mixtures of n-hexadecane and n-eicosane,Ž .Can. J. Chem. Eng. 73 1995 154–155.w x31 K. Ishida, K. Noda, K. Hirako, Vapor–liquid equilibria for the system containing liquified petroleum gas, Asahi Garasu

Ž .Kogyo Gijutsu Sh. Kenkyu Hokoku 29 1975 29–34.w x32 A. Azarnoosh, J.J. McKetta, Vapor–liquid equilibrium in the methane-n-decane-nitrogen system, J. Chem. Eng. Data 8

Ž .1963 513–519.w x33 H. Kim, H.-M. Lin, K.-C. Chao, Vapor–liquid equilibrium in binary mixtures of carbon dioxideqphenyloctane and

Ž .carbon dioxideq1-hexadecene, AIChE Symp. Ser. 81 244 1985 86–89.w x Ž .34 A. Azarnoosh, J.J. McKetta, Nitrogen-n-decane system in the two phase region, J. Chem. Eng. Data 8 1963 494–496.w x35 S.D. Rupprecht, G.M. Faeth, 1981. Investigation of air solubility in jet A fuel at high pressures. NASA Contractor

Report 3422, Grant NSG-3306, May 1981.w x36 S. Srivatsan, X. Yi, R.L. Robinson, K.A.M. Gasem, Solubilities of carbon monoxide in heavy normal paraffins at

Ž .temperatures from 311 to 423 K and pressures to 10.2 MPa, J. Chem. Eng. Data 40 1995 237–240.

w x37 J.F. Connolly, G.A. Kandalic, Gas solubilities, vapor–liquid equilibria, and partial molal volumes in some hydrogen–Ž .hydrocarbon systems, J. Chem. Eng. Data 31 1986 396–406.

w x38 S. Laugier, D. Richon, Vapor–liquid equilibria for hydrogen sulfideqhexane, qcyclohexane, qbenzene, qpentade-Ž . Ž .cane, and q hexaneqpentadecane , J. Chem. Eng. Data 40 1995 153–159.

w x Ž .39 G.-X. Feng, A.E. Mather, Solubility of H S in n-hexadecane at elevated pressure, Can. J. Chem. Eng. 71 19932327–328.

w x40 G.-X. Feng, A.E. Mather, Solubility of hydrogen sulfide in n-eicosane at elevated pressure, J. Chem. Eng. Data 37Ž .1992 412–413.

prediction of vle for asymmetric systems at low and hp with the psrk model

Documents