Liquid Saturation Density from Predictive Correlations Based on the

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Liquid Saturation Density from Predictive Correlations Based on the Corresponding States Principle. 2. Results for 49 Families of Fluids Angel Mulero,*,† Isidro Cachadin˜ a,† and M. Isabel Parra‡ Departamento de Fı´sica and Departamento de Matema´ ticas, UniVersidad de Extremadura, AVda. de ElVas s/n, 06071 Badajoz, Spain

Nine empirical correlations for the calculation of the liquid saturation density of pure fluids are studied for their accuracy and applicability. All of them are based on the corresponding states principle, and we include very recent proposals. They require as inputs the critical parameters, the acentric factor, and/or the LennardJones molecular parameters. In the first part of this paper we applied these models to 552 fluids grouped into 30 families. In this second part, we use the data accepted by the DIPPR project for 873 substances more, grouped into 49 families. Recommendations are given for the use of each model and for the choice of the adequate model for each family of fluids, including for particular fluids. Introduction The saturated liquid density for pure substances is an important property used, for example, as a first step in the calculation of the compressed liquid density1-5 or as an input for an equation of state.6 As is well-known, there are many accurate empirical correlations giving this property,7-13 which are usually applied for design purposes. In the first part of this paper,14 we focused our attention on the predictive correlations on the basis of the corresponding states principle. In particular, we used nine empirical correlations, including well-known classical models as well as recent proposals, giving then a detailed description. These correlations are the so-called Rackett,15 YG,16 RRPS,1,17 Bhirud,18 COSTALD,19-20 QSMC1,21 QSMC2,21 SNM0,22 and FMC23 models. The first model requires only the knowledge of critical parameters, the following seven need the critical parameters and acentric factor as inputs, and the last requires the Lennard-Jones molecular parameters and the acentric factor as input data. The Rackett, YG, RRPS, Bhirud, and COSTALD models are considered to be classical models, whereas the others are recent proposals. Thus, the QSMC1 and QSMC2 models were constructed using a firstorder and a second-order corresponding states principle and using the specific DIPPR correlations for two or three n-alkanes as referents. The SMN0 model was proposed by Mchaweh et al.22 and uses the Soave-Redlich-Kwong equation of state temperature-dependent term and, hence, no adjustable coefficients. Finally, the FMC model is a new kind of correlation for the vapor-liquid properties of nonpolar fluids,23,24 on the basis of the application of the molecular version of the corresponding states principle and then on the use of the Lennard-Jones molecular parameters and the acentric factor as input data. In particular, for the saturated liquid density the correlation model is a cubic function of the molecular reduced temperature and a quadratic function of the acentric factor. In the first part of this paper14 we presented the results obtained for 552 fluids, grouped into 30 families, by taking as referents the liquid saturation values accepted by the DIPPR project.25 Our results showed that the recent SNM0, QSMC1, and QSMC2 models are very adequate for predicting the liquid * To whom correspondence should be addressed. E-mail: mulero@ unex.es. † Departamento de Fı´sica. ‡ Departamento de Matema´ticas.

saturation densities of most of the 552 fluids selected, with only a few exceptions. In particular, the results obtained with these recent models clearly improve those obtained with the classical models for n-alkanes (especially for the higher n-alkanes), alkylcyclohexanes, 1-alkenes, n-alkylbenzenes, n-alcohols, cycloaliphatic alcohols, aromatic alcohols, other aliphatic alcohols, and polyols. There was perhaps a less clear improvement for dimethylalkanes, other alkanes, and alkynes. On the other hand, for other alkylbenzenes, other monoaromatics, naphthalenes, other condensed rings, and other hydrocarbon rings the classical YG, COSTALD, and RRPS models gave the best results. There were also some other families of fluids (such as cycloalkanes, 2,3,4-alkenes, dialkenes, diphenyl/polyaromatics, aldehydes, ketones, and some others) for which the choice of one of the aforementioned classical or recent models had no influence on the general results. The QSMC1 and QSMC2 models were constructed using data only for n-alkanes, but we have shown that they can be applied to more families of fluids. QSMC2, being less straightforward than QSMC1, provides generally poorer accuracy than QSMC1, and its use is only justified for some higher n-alkanes. From a practical point of view, the SNM0 model is straightforward (it contains only 7 coefficients and 3 input parameters), so that we recommend the use of this model for most of the 30 families of fluids considered in the first part14 of this work. Perhaps new coefficients could be obtained to improve the results for some families of fluids such as naphthalenes, other condensed rings, and polyols. We have also shown that the Rackett model does not behave homogeneously: it can give poor results for some fluids and excellent ones for some others. Moreover, our results showed that neither the Bhirud nor the FMC model is very adequate in a general sense, especially for low temperatures (i.e., near the triple point) and/or high temperatures (i.e., near the critical point). The use of these models can only be recommended if one requires small deviations for terpenes. Despite the above conclusion, these two models are the only ones giving predictions for the available data for some particular fluids far from the critical point. Obviously, all the above conclusions are general rules with some particular exceptions for particular fluids of those families. Thus, for example, the results found for polyols indicate that the models must be carefully chosen for some fluids of this family, because some of the results were heterogeneous.

10.1021/ie0600442 CCC: $33.50 © 2006 American Chemical Society Published on Web 09/07/2006

Ind. Eng. Chem. Res., Vol. 45, No. 20, 2006 6865 Table 1. Mean Absolute Percentage Deviations (MAPD) of the Calculated Liquid Saturation Densities for Several Families of Fluids with Respect to the DIPPR25 Data When Using Correlationsa-c family of fluids

N

ND

R

YG

RRPS

B

COSTALD

FMC

QSMC1

QSMC2

SNM0

N-aliphatic acids other aliphatic acids dicarboxylic acids aromatic carboxylic acids Anhydrides formates acetates propionates and butyrates other saturated aliphatic esters unsaturated aliphatic esters aromatic esters aliphatic ethers other ethers/diethers

20 19 7 5 8 15 22 13 21 23 25 32 22

404 202 21 15 46 242 439 279 186 134 157 300 321

13.5 9.9 7.7 9.9 10.7 3.6 4.3 2.5 13.2 6.0 11.1 3.9 9.5

13.1 10.7 14.0 19.9 7.0 2.7 4.1 2.0 13.0 8.2 10.8 4.1 9.2

11.1 9.1 9.7 16.0 6.7 2.5 4.2 2.1 10.7 7.2 9.0 4.2 9.0

14.4 14.9 11.2 44.5 14.3 5.0 4.1 2.3 14.0 9.1 8.7 4.6 8.5

11.9 9.7 11.6 17.6 6.6 2.6 3.9 2.0 11.8 7.5 10.2 3.9 8.6

9.3 9.8 4.4 27.3 11.3 4.4 3.4 2.9 7.4 6.0 4.1 4.2 6.6

5.0 3.8 4.4 6.3 4.7 2.0 2.1 2.3 5.9 3.4 5.9 2.2 4.4

3.9 3.7 6.8 2.7 5.3 2.6 2.2 2.6 5.0 3.1 5.5 2.3 3.8

4.2 3.5 5.0 5.5 4.4 1.7 2.0 2.0 4.8 3.2 5.4 2.2 4.5

a The shaded cells represent the lowest MAPDs, and the numbers in bold are MAPDs that are similar (difference less than 1%) to the lowest one. b R ) Rackett;15 YG ) Yamada and Gunn;16 RRPS ) Reid et al.;1 B ) Bhirud;18 COSTALD;19,20 FMC ) Fauńdez et al.;23 QSMC1 ) Queimada et al.;21 QSMC2 ) Queimada et al.;21 SNM0 ) Mchaweh et al.22 c N ) number of fluids, ND ) number of data.

In this second part of our work, we made a similar study of 873 fluids grouped into 49 families (see Tables 1-4). Results In this work, we used the Rackett, YG, RRPS, Bhirud, COSTALD, QSMC1, QSMC2, SNM0, and FMC models to calculate the liquid saturation density. No adjustable parameters were used, and values for the critical properties and acentric factor were those given by the DIPPR database.25 For the molecular model, the values of the parameter of the LennardJones potential were obtained using the method given by Cuadros et al.26 All the models require three input parameters, except the Bhirud model, which requires four. We calculated the percentage deviation (PD), in absolute value, of the values obtained with each correlation from those accepted by the DIPPR project for each fluid at every temperature. We also calculated the absolute average percentage deviation (AAD) for each fluid (within the range where data are available) and the mean value of the absolute PD (MAPD) for a family of fluids (i.e., by taking into account the number of available data for a family and not the number of fluids for each family). Tables 1-4 list the MAPDs for every family of fluids and every model. Results for particular fluids are shown in Figures 1-9. For some fluids we found very large deviations between the DIPPR data and those predicted by all the models used here, so that we have not considered these fluids in our analysis. These fluids will be clearly identified in the following subsections. Also, we revised all the accepted DIPPR data and found erroneous values for some fluids. These erroneous values (which clearly do not agree with all the other accepted values for the same fluid) are clearly mistakes, and they were eliminated from our analysis. These values are available upon request. 1. Results for Organic Acids, Anhydrides, Formates, Acetates, Propionates, and Butyrates, Esters, and Ethers. Results for 232 fluids grouped into 13 families are given in Table 1. As can be seen, the recent models clearly improve the results obtained with the classical ones for n-aliphatic and other aliphatic acids. There are, nevertheless, some particular exceptions. Thus, for example, for acetic acid the classical models are better over all the studied temperature range. We note also that none of the models used here lead to AADs below 8.8% for formic acid. For dicarboxylic acids and aromatic carboxylic acids the models for predicting the saturation density behave heterogeneously, perhaps due to the reduced number of accepted data.

Figure 1. Absolute average percentage deviations (AAD, %) for the liquid saturation density of propionates and butyrates, obtained using different correlations. The number of available data for each fluid is given in parentheses.

The recent models give smaller deviations than the classical ones, except when the FMC model is used for aromatic carboxylic acids. In any case, more data are needed before definitive conclusions can be drawn. The Rackett, Bhirud, and FMC models are not adequate, in a general sense, for the 8 anhydrides included in the DIPPR project (for which data near the critical point are not available). One exception is for glutaric anhydride, for which only the FMC model gives a low AAD. In general, the recent models slightly improve the results given by the classical ones, with only one exception (phthalic anhydride). As can be seen in Table 1, all the models give MAPDs less than 5% for formates. In particular the SNM0 and QSMC1 models give the lowest MAPDs. Classical models must be used with caution for some particular fluids of this family, although they behave adequately for some others. We also note that the Rackett model behaves heterogeneously (it gives especially poor results for some fluids but very good results for others). Classical models must be used with caution for acetates. Although they can give slightly better results for some fluids, they are clearly inadequate for most of them. For propionates and butyrates all the models give MAPDs from 2% to 3%. As is shown in Figure 1, the recent models have a very homogeneous and excellent behavior, although there are seven fluids for which the classical models give the smallest AADs. For some other fluids the classical models give clearly greater deviations than the recent ones. As can be seen in Table 1, the classical models are inadequate for general use when they are applied to other saturated

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Table 2. Mean Absolute Percentage Deviations (MAPD) of the Calculated Liquid Saturation Densities for Several Families of Fluids with Respect to the DIPPR25 Data When Using Correlationsa family of fluids

N

ND

R

YG

RRPS

B

COSTALD

FMC

QSMC1

QSMC2

SNM0

epoxides peroxides C1/C2 aliphatic chlorides C3 and higher aliphatic chlorides aromatic chlorides N-aliphatic primary amines other aliphatic amines aromatic amines other amines, imines nitriles isocyanates/diisocyanates mercaptans sulfides/thiophenes

14 12 18 26 14 13 21 28 26 20 7 23 24

135 19 431 361 259 107 288 528 121 192 49 236 325

6.8 2.4 7.0 3.7 4.5 13.9 7.8 9.3 11.7 14.8 7.7 8.4 6.5

4.2 15.9 4.3 2.1 1.4 9.6 6.6 5.2 8.2 7.4 9.6 5.1 4.2

4.4 13.3 4.1 1.9 1.5 9.0 6.0 5.2 7.5 7.3 9.5 5.5 4.6

3.4 34.7 4.1 6.2 4.7 6.5 9.8 5.4 9.9 19.5 14.5 2.4 3.8

4.2 14.5 4.3 2.1 1.4 9.4 6.2 5.2 8.1 7.7 9.5 4.9 4.1

3.4 25.4 4.5 6.6 5.9 4.4 7.4 5.1 8.1 20.9 7.4 2.4 3.5

4.3 4.5 4.0 2.2 1.1 8.7 3.9 6.0 7.8 10.1 6.6 3.2 3.6

4.2 3.2 5.1 3.3 1.9 9.1 4.1 6.2 8.4 10.5 6.1 2.6 3.0

4.2 4.0 4.3 2.4 1.3 8.6 3.5 6.1 7.8 10.1 7.3 3.0 3.4

a See caption to Table 1 for the meaning of each column. The shaded cells represent the lowest MAPDs, and the numbers in bold are MAPDs that are similar (difference less than 1%) to the lowest one.

aliphatic esters. There are only two exceptions: diethyl succinate, and -caprolactone. Within the recent models, QSMC2 is the only one predicting adequately the trend of the data for dibutyl sebacate. Even the most recent models are not capable of predicting adequately the data for 5 fluids: n-butyl stearate, bis(2-ethylhexyl) adipate, γ-butyrolactone, γ-valerolactone, and isopropyl myristate. For most of the other fluids the SNM0 model is the most straightforward and accurate. For unsaturated aliphatic esters we found that the most recent models give clearly improved results when compared with the classical models. In any case we found that for 4 fluids (allyl methacrylate, ethyl methacrylate, methyl acrylate, and ethyl acrylate) the classical models behave slightly better than the recent ones. We also found that for 3 fluids (dibutyl maleate, methyl oleate, and cetyl methacrylate) for which the data predictions of the models differ widely, the SNM0 model should definitely not be used. None of the models used agree with the available data for diethyl maleate (PDs > 10%). QSMC1 can be considered, therefore, as the most straightforward model for general use for this kind of fluid, although some of the exceptions mentioned above must be taken into account. For aromatic esters we found 6 fluids for which only one datum is available and for which the models behave heteregeneously; i.e., no best model for all of them can be chosen. Although the FMC model gives the smallest MAPD, this model can only be applied far from the critical point, and moreover, the curve obtained does not always adequately represent the trend of the data. For that reason, the most recent models are the adequate choices for most of the aromatic esters. The MAPDs obtained for other ethers and diethers are given in the last row in Table 1. The recent models clearly improve the results obtained with the classical ones, except for 1,2-epoxy3-phenoxypropane. For paraldehyde and methylal, no model agrees with the DIPPR data, with the PDs being greater than 7.5% and 9% respectively. Finally, for tetraethylene glycol dimethyl ether only the QSMC2 works properly, whereas for 1,2-dimethoxyethane only the Bhirud or FMC models must be used. In sum, for the families of fluids included in Table 1, the recent SNM0, QSMC1, and QSMC2 models clearly improve the general results obtained with the classical ones. Classical models can only be an alternative to the recent ones for formates and for propionates and butyrates, for which even the simple YG model gives adequate results. Despite this, some exceptions (which were detailed in the preceding paragraphs) are found. Thus, the FMC model seems to be a very adequate choice for dicarboxylic acids and some aromatic ethers for temperatures far from the critical point. For aromatic carboxylic acids, and

also for some n-aliphatic acids and other aliphatic acids, the QSMC2 model clearly improves the results obtained with the other recent models. For the other families, the simpler SNM0 and QSMC1 models give similar or better results than QSMC2. We found that for some fluids (clearly identified in the preceding paragraphs) none of the models used here agree with the DIPPR data. Therefore, revision of the source of the data or of the values used for their critical properties and acentric factor or a search for different models is called for. 2. Results for Epoxides, Peroxides, Organic Chlorides, Amines, Imines, Nitriles, Isocyanates and Diisocyanates, Mercaptans, and Sulfides and Thiophenes. Results for 246 fluids grouped into 13 families are given in Table 2. As can be seen, for epoxides we found that both the Bhirud and FMC models give slightly better overall results than the other models. The Rackett model gives the poorest results. Nevertheless, the results change significantly from one fluid to another. As can be seen in Figure 2, the Bhirud and FMC models give excellent results for 9 fluids, but AADs greater than or equal to 5% are found for the other 5 epoxides. The Rackett model gives good results for 6 fluids although it gives clearly poorer results for all the others. As can be seen in Table 2, few data are available for peroxides. Actually, only one datum is available for 8 of the fluids selected and for the other 4 the temperature range is very small. The Rackett model gives the smallest MAPD, probably because a modification of this model was used by DIPPR to obtain some of the available data. In any case, the Rackett model does not agree with the 2 available data for n-butyl hydroperoxide. All the other classical models and also the FMC one clearly disagree with the DIPPR data. For C1/C2 aliphatic chlorides, most of the models give deviations near 4%. We found that for ethyl chloride and methyl chloride no model gives low AADs. For another two fluids (cis1,2-dichloroethylene, shown in Figure 3a, and dichloromethane) only the Rackett model predicts the selected data adequately. Finally, for another 4 fluids (1,2-dichloroethane, chloroform, tetrachloroethylene, shown in Figure 3b, and trans-1,2-dichloroethylene), the Bhirud or the FMC models should be used, except very close to the critical point. With respect to the C3 and higher aliphatic chlorides and aromatic chlorides families, none of the models considered is in good agreement with the available data for hexachloro-1,3butadiene, and 1,3,5-trichlorobenzene. On the other hand, the Rackett model is the only one that is in good agreement with the DIPPR data for 1,4-dichloro-cis-2-butene, 1,4-dichloro-trans2-butene, 2,3-dichloropropene, and 3-chloropropene. For n-aliphatic primary amines the FMC model is the only

Ind. Eng. Chem. Res., Vol. 45, No. 20, 2006 6867

Figure 2. Absolute average percentage deviations (AAD, %) for the liquid saturation density of epoxides, obtained using different correlations. The number of available data for each fluid is given in parentheses.

Figure 3. Reduced density versus reduced temperature for two C1/C2 aliphatic chlorides: (a) cis-1,2-dichloroethylene; (b) tetrachloroethylene. Points are DIPPR25 data, and lines are values given using different correlations.

one giving a low MAPD, although it must not be used near the critical point. For other aliphatic amines the most recent models are the adequate choice for general use. Nevertheless, for 2-methyl-2-aminobutane and isobutylamine, in particular, none of the models considered agree with the DIPPR data. For trin-octylamine, only the QSMC2 model predicts adequately the trend of the available data. The classical models are the adequate choice for di-n-octylamine. Finally, for isopropylamine and diethylamine, the FMC and Bhirud models are the most adequate choice, being moreover the only models that predict the available data for sec-butylamine and trimethylamine. As can be seen in Table 2, all the models give MAPDs from 5.1% to 6.2% for aromatic amines with the only exception of the Rackett model. The FMC and Bhirud models are the only ones that agree with the DIPPR data for 8 fluids. Nevertheless,

they are clearly inadequate for another 5 fluids (including 2,6diethylaniline for which the AAD is near 36%). For quinaldine none of the models considered predicts accurately the available data. Finally, for some fluids of this family (for example, 2,6diethylaniline and m-toluidine), the choice of a classical or a recent model clearly leads to different results. Within the other amines and imines family we found 6 fluids for which all the models clearly disagree with the DIPPR data. These fluids are pyrazine, pyrazole, pyrimidine, indole, 1,2propanediamine, and ethyleneimine, and they were eliminated from the calculation of the MAPDs given in Table 2. Moreover, for pyridazine and n-methylpyrrole, all the models give PDs greater than 5%. As can be seen, none of the models give low MAPDs. In our analysis we found a high level of disagreement between the data reported by the DIPPR project for 5 nitriles and those predicted by all the models selected. These nitriles are malononitrile, acetonitrile, propionitrile, succiononitrile, and cyanogen chloride and have not been considered. As can be seen in Table 2, none of the models considered predicts the data with a low MAPD. For cyanogen only the Bhirud or the FMC models agree with the DIPPR data. Within the isocyanates and diisocyanates, we did not consider the DIPPR data for 2 fluids (2,6-toluene diisocyanate and methyl isocyanate) because they are in clear disagreement with those predicted by the models. In the results presented in Table 2, one needs to bear in mind that 38 of the selected 49 data belong to only 2 of the fluids included in this family. Analyzing the results for mercaptans, we found that the Bhirud, FMC, QSMC1, QSMC2, and SNM0 models give the smallest MAPDs. In particular, for 1,2-ethanedithiol no model gives a low AAD. For isopropyl mercaptan, benzyl mercaptan, and tert-butyl mercaptan neither the Bhirud nor the FMC model should be used. For sulfides and thiophenes, the Bhirud and FMC models give heterogeneous results, with excellent results for some fluids but clear disagreement for others. The recent models are the adequate choice. In any case for three fluids (di-n-octyl sulfide, di-n-propyl disulfide, and ethyl 2-octyl sulfide), the agreement of these recent models with the DIPPR data is only moderate. In summary, we did not considered the data for 13 fluids within the families included in Table 2, because we found a great disagreement with respect to the values predicted by all the models. Moreover, for another 9 fluids included in the

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N

ND

R

YG

RRPS

B

COSTALD

FMC

QSMC1

QSMC2

SNM0

C-H-Br compds C-H-I compds C-H-F compds C-H-multihalogen compds C-H-NO2 compds polyfunctional acids polyfunctional esters other polyfunctional C-H- O polyfunctional nitriles polyfunctional amides/amines polyfunctional C-H-O-N polyfunctional C-H-O-S polyfunctional C-H-O-halide polyfunctionalC-H-N-halide-(O)

17 8 27 34 20 11 21 41 5 23 21 13 34 12

189 106 1256 1391 233 40 100 385 41 224 154 104 316 87

10.8 5.6 1.8 1.9 7.7 5.7 21.1 5.3 5.3 8.8 9.9 14.7 8.4 10.8

4.0 3.1 2.1 1.2 5.9 9.7 9.8 8.4 4.1 12.2 4.4 5.8 4.1 6.2

3.6 2.6 2.1 1.3 5.6 6.9 7.0 7.3 3.4 10.1 3.5 4.9 4.1 6.1

10.2 9.5 5.7 3.3 9.1 18.7 23.7 20.8 12.1 21.8 12.5 16.3 12.1 3.2

4.0 3.1 2.1 1.2 6.1 8.5 8.5 7.5 4.1 11.6 4.3 5.4 3.7 6.6

10.3 9.3 6.7 4.2 10.0 15.5 19.7 15.7 14.8 17.9 13.0 15.4 10.7 4.6

3.8 2.8 2.7 1.1 9.8 6.5 3.0 2.7 7.7 10.1 5.2 2.2 2.6 10.5

5.0 4.1 3.5 2.2 10.4 8.0 2.9 2.7 8.3 11.3 5.3 2.4 3.0 10.9

4.1 3.1 2.5 1.2 10.1 6.8 2.7 2.5 8.5 11.0 5.4 2.1 2.8 10.8


calculation of the MAPDs, we found that none of the models predicts accurately the DIPPR data. For other amines and imines, nitriles, and isocyanates and diisocyanates, none of the models predict the available data with MAPDs below 6%. Few data are available for peroxides and for isocyanates and diisocyanates, so new measurements need to be made and included in the DIPPR database. Unfortunately, none of the models selected gives the smallest MAPDs for all the families of fluids included in Table 2. In fact, even within each family the choice of one or another model must be made carefully. In particular, we found that the Bhirud and FMC models predict adequately the data for 40 fluids of different families, with a clearly greater accuracy than the other models. Nevertheless, these models are clearly inadequate for a good number of other fluids and also for the temperature range near the critical point and sometimes near the triple point. Similarly, the Rackett model also gives hetereogeneous results: it is the only model giving small AADs for most peroxides and another 18 fluids, but it gives the largest AADs for other fluids and also the largest MAPDs for 8 of the 13 families studied. The YG, RRPS, and COSTALD classical models give large MAPDs for peroxides, n-aliphatic primary amines, and isocyanates and diisocyanates. They are, however, very adequate, in a general sense, for epoxides, C1, C2, C3, and higher aliphatic chlorides, aromatic chlorides, aromatic amines, nitriles, and sulfides and thiophenes. For some particular fluids the classical models are the only ones in agreement with the DIPPR data. Finally, we have shown that for the families included in Table 2 the less straightforward COSTALD model does not improve the results obtained with the simple YG and RRPS models. The recent QSMC1, QSMC2, and SNM0 models give similar values for the MAPDs. In most of cases, the simpler QSMC1 model gives smaller MAPDs than the less straightforward QSMC2 one, although, as indicated above, this model is sometimes the only one in good agreement with the available data. Only for a small number of fluids can the choice of one or another recent model lead to different results. In a general sense, these recent models improve the results over to the other models for most peroxides, most other aliphatic amines, most isocyanates and diisocyanates, and some n-aliphatic primary amines, some aromatic amines, and some mercaptans. In any case, some of the recent models can be the best choice for some other particular fluids. 3. Results for Other Compounds Containing Carbon and Hydrogen and Other Polyfunctional Substances. The MAPDs for 14 families of fluids including 287 compounds containing

carbon and hydrogen and other polyfunctional substances are given in Table 3. As can be seen, the Rackett, Bhirud, and FMC models do not agree with the most of data for both C-H-Br and C-H-I compounds. All the other models give good overall results, with only a few exceptions. Finally, we note that for these two families of fluids the QSMC2 model does not give better general results than other simpler models. As can be seen in Table 3, there are a lot of available data for C-H-F compounds. Indeed, there are 5 fluids of this family for which 110 or more data are available. Nevertheless, for 1,2difluoroethane only one datum is given in the DIPPR database. The Rackett model gives the smallest MAPD, although some other models can be used with accuracy. As in the preceding case, the distribution of the data for C-H-multihalogen compounds is not homogeneous. Thus, for 11 fluids more than 50 data are available, whereas for another 8 only 1 or 2 data can be used. As can be seen in Table 3, several models give MAPDs from 1.1% to 1.3%. The results obtained with these models are homogeneous; i.e., they generally do not change from one fluid to another. For C-H-NO2 compounds the obtained MAPDs are always greater than 5.5%. In particular, for nitromethane the smallest AAD is 5% (using the RRPS model), so that all the models should be used with caution. Although the most recent models are adequate for some particular fluids, they should not routinely be used for this family of fluids. Analyzing the available data for polyfunctional acids, we found a very great disagreement between the densities predicted by the models and the only datum accepted for ascorbic acid. Only the Rackett model agrees, probably because a modified Rackett equation was used by DIPPR to predict that datum. Therefore, this fluid was not included in the results given in Table 3. Moreover, the MAPDs obtained are influenced by the small number of data available. Indeed, only for 4 fluids of this family are more than 3 data available. For most fluids of this family, we found a clear disagreement between the liquid saturation densities predicted by each of the models. The Rackett model gives the smallest MAPD, although it gives AADs > 5% for 4 fluids. In any case, more data are needed for a clear conclusion to be drawn about the use of the models for polyfunctional acids. For polyfunctional esters the most recent models clearly improve the results obtained with all the other models. Some exceptions are found. Thus, for 2-ethoxyethyl acetate only the classical models agree with the DIPPR data, and for dioxin all the models give PDs greater than 6%. Despite the high MAPD found when the Rackett model is used, this model predicts


Figure 4. Absolute average percentage deviations (AAD, %) for the liquid saturation density of polyfunctional amides/amines, obtained using the Rackett, RRPS, and QSMC1 correlations. The number of available data for each fluid is given in parentheses.

Figure 5. Absolute average percentage deviations (AAD, %) for the liquid saturation density of 6 polyfunctional C-H-O-halides, obtained using a classic (COSTALD) and a recent (QSMC1) correlation. The number of available data for each fluid is given in parentheses.

adequately the data for some polyfunctional esters. Nevertheless, it cannot be used for most of others, especially for triolein (PDs > 150%). The recent models give the best agreement with the DIPPR data for other polyfunctional C-H-O fluids, whereas the classical YG, RRPS, and COSTALD models give the smallest MAPDs for polyfunctional nitriles. For a large number of these fluids, the Rackett model can be used with accuracy. Results for polyfunctional amides or amines are given in Table 3. Data for urea were not included, because they disagreed greatly with the predictions of all the models. Moreover there are two fluids (both included in the results) for which all the models give PDs greater than 7.5% (see Figure 4). Bhirud and FMC are the only models that agree with the liquid saturation density values given by the DIPPR project for monoethanolamine. In general, the models behave heterogeneously (they give adequate values for some fluids but clearly inadequate ones for others, as is clearly shown in Figure 4), and none of them can reproduce the data with MAPDs below 8.8%. The smallest MAPD is found using the Rackett model. In particular, this model is the only one that agrees with the available data for some fluids, as is shown in Figure 4. Nevertheless, it gives large

or even very large deviations for some others. In conclusion, it is very important to adequately choose the appropriate model for each fluid of this family. RRPS gives the smallest MAPD for polyfunctional C-HO-N substances and must be the model used with only few exceptions. For example, for nitroglycerine, all the models give PDs greater than 5%, with the QSMC2 model giving the best agreement with respect to the DIPPR data. For polyfunctional C-H-O-S and polyfunctional C-H-O-halide substances, the recent models give the smallest MAPD, with the classical YG, RRPS, and COSTALD being clear alternatives for general use, except for the substances included in Figure 5. Within the polyfunctional C-H-O-halide substances, we found that no model can predict the available data for trifluoroacetic acid or o-chlorobenzoic acid. Only the Bhirud and the FMC models agree with the available data for hexafluoroacetone. For polyfunctional C-H-N-halide-(O) substances, the highest reduced temperature is 0.67, and the Bhirud model gives the smallest MAPD, followed by the FMC one. Two exceptions are 3,4-dichlorophenyl isocyanate and 3-nitrobenzotrifluoride, for which only the Rackett model agrees with the DIPPR data. Some other classical models could be used for several fluids in

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N

ND

R

YG

RRPS

B

COSTALD

FMC

QSMC1

QSMC2

SNM0

silanes/siloxanes organic salts inorganic gases inorganic halides inorganic acids inorganic bases (ammonia) other inorganics organic/inorganic compds elements

35 13 23 10 7 1 3 5 11

524 244 438 148 100 99 87 43 243

6.8 22.7 10.1 26.2 29.3 3.0 6.2 6.2 3.5

3.6 7.5 5.7 3.4 4.9 3.9 3.8 5.3 1.2

3.3 7.8 5.9 3.3 4.8 3.4 3.3 4.9 0.9

9.3 43.9 3.9 23.0 22.0 12.7 12.2 9.0 4.3

3.4 7.3 5.7 3.4 5.0 3.9 3.8 5.4 1.1

8.5 41.9 4.4 23.2 23.4 12.8 11.8 10.3 4.2

4.0 6.2 5.0 4.0 5.8 4.3 5.4 7.2 3.0

4.7 6.2 5.8 4.3 6.4 5.6 6.1 7.5 1.1

4.2 5.6 5.4 3.7 5.5 4.2 5.2 7.4 1.5


Figure 6. Absolute average percentage deviations (AAD, %) for the liquid saturation density of silanes and siloxanes, obtained using a classic (RRPS) and a recent (QSMC1) correlation. The number of available data for each fluid is given in parentheses.

this family, whereas we do not recommend the use of the most recent models. In sum, the recent QSMC1, QSMC2, and SNM0 models improve the results obtained with the other models for polyfunctional esters, other polyfunctional C-H-O substances, polyfunctional C-H-O-S substances, and polyfunctional C-H-N-halide substances. The Bhirud and FMC models are not adequate for most of the substances included in Table 3, with the exception of polyfunctional C-H-N-halide-(O) substances, for which these models give the smallest MAPDs, and some other particular fluids of other families. For the families included in Table 3, the YG and RRPS models give practically the same results as the less simple COSTALD one. For polyfunctional nitriles and polyfunctional C-H-N-O, these models give smaller MAPDs than those obtained using the recent ones. For C-H-Br, C-H-I, C-HF, and C-H-multihalogen compounds, both the classical and the most recent models can be used with accuracy. The Rackett model behaves heterogeneously: it gives clearly the best agreement for polyfunctional acids, for polyfunctional amides/ amnes, and also for some particular substances. Nevertheless it gives clearly the worst results for some other families and fluids. For C-H-NO2 compounds, polyfunctional acids, and polyfunctional amides/amines, all the models give MAPDs greater than 5.5%. There are 9 substances for which none of the models agrees with the accepted DIPPR data, and moreover there are another 2 substances that were not considered because a high level of disagreement is found with the available data.

4. Results for Other Organic and Inorganic Substances. Results for 108 fluids grouped into 9 families are given in Table 4. Within the family of silanes and siloxanes, we did not consider the data for tetrafluorosilane and dimethyldimethoxysilane, because all the models give AADs greater than 9.6%. Moreover, for silane, trimethoxysilane, methyl vinyl dichlorosilane, and vinyltrichlorosilane we found PDs greater than 6.5% for all the models. For dichlorosilane all the models give AADs greater than 5.4% for the 3 available data. These 5 fluids have nevertheless been included in Table 4 and Figure 6. The Rackett, Bhirud, and FMC models give the largest MAPDs, although it must be used for some particular fluids. The other classical models and the most recent ones give similar general accuracy. Nevertheless, as is shown in Figure 6, the classical ones (represented by RRPS) should be used for 6 fluids whereas the recent ones (represented by QSMC1) give clearly smaller deviations for some 7 other fluids. Data for ethylaluminum sesquichloride and ethylene carbonate given in the DIPPR project were not included in the results shown in Table 4 for organic salts. The most recent models give the smallest MAPDs, whereas the Rackett, Bhirud, and FMC models are clearly inadequate for general use. For inorganic gases, we did not take into account the data accepted by the DIPPR project for nitrogen tetroxide, nitrogen trioxide, and boron trichloride, because they all deviate markedly from the predictions using the models. Moreover, we found that for three fluids included in Figure 7 none of the models (only some of them are included in the figure as examples) predict


Figure 7. Reduced density versus reduced temperature for three inorganic gases: (a) sulfur trioxide; (b) nitrogen dioxide; (c) nitric oxide. Points are DIPPR25 data, and lines are values given using different correlations.

adequately the trend of the data (although fairly small AADs are found using some models). The Bhirud and FMC models give the smallest MAPDs. In any case, they should not be used near the critical point. Moreover, neither these nor the Rackett model should be used for nitrosyl chloride and ozone. For sulfur hexafluoride and boron trifluoride the other models agree better with the available data than the Bhirud and FMC models do. We found three inorganic halides (phosphorus oxychloride, potassium bromide, and vanadium tetrachloride) and two inorganic acids (hydrogen fluoride and phosphoric acid) for which all the models clearly disagree with the data accepted by the DIPPR project. These fluids were not considered in the results shown in Table 4. As can be seen, the Rackett, Bhirud, and FMC models give very high MAPDs for both families of fluids, whereas all the other models give very similar general results. Nevertheless, these last models must be used with caution for antimony trichloride, vanadium oxytrichloride, nitric acid, and sulfuric acid, because no low AADs are found. We therefore recommend the use of the simple YG model with the aforementioned exceptions. Within the inorganic bases, we did not consider the available data for sodium hydroxide, so that only data for ammonia are included. As can be seen in Table 4 and Figure 8, the classical models (represented by RRPS model in the figure) agree with these data only slightly better than the most recent ones (represented by the SNM0 model). Neither the Bhirud nor the FMC models should be used. The DIPPR database includes data for magnesium oxide and silicon dioxide within the other inorganics family, but these data are in clear disagreement with the values obtained using the selected models, so we did not include these fluids in the results in Table 4. Despite the classical YG, RRPS, and COSTALD models giving the smallest AADs and good results for hydrogen peroxide, none of the models predicts the trend of data for water or deuterium oxide. Within the family denoted organic/inorganic compounds, we eliminated the data for triethylaluminum, because all the models clearly deviate from these data. The YG, RRPS, and COSTALD models should be used with two exceptions: trimethylgallium and methanesulfonyl chloride.

Figure 8. Reduced density versus reduced temperature for ammonia. Points are DIPPR25 data, and lines are values given using classical (RRPS) and recent (SNM0) correlations.

We considered the data for 11 simple elements but not for silicon, sulfur, iodine, or calcium. For bromine, the Rackett and QSMC2 models give the smallest AADs. The Rackett, Bhirud, and FMC are especially inadequate for silver, carbon, and zinc. The AADs obtained for several models for all the elements except bromine are shown in Figure 9. As can be seen, the QSMC1 model is very accurate for zinc, whereas it gives slightly worse results than the classical YG, COSTALD, and RRPS models (only the last is shown in the figure) and also than the other recent models for 6 simple elements. Despite the exception of bromine the simple RRPS model is accurate enough to give an MAPD below 1%. In sum, for the families included in Table 4, the most recent models do not in general improve the results obtained with the classical ones. Indeed, the very simple YG model is accurate for silanes and siloxanes, inorganic halides, inorganic acids, inorganic bases, other inorganics, organic/inorganic compounds, and simple elements. The general use of a recent model, SNM0 in particular, is only recommended to obtain a slightly smaller MAPD for organic salts. For inorganic gases, the Bhirud and FMC models give the smallest AADs. But these models are clearly inadequate, in a general sense, for all the other families and for temperatures

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Figure 9. Absolute average percentage deviations (AAD, %) for the liquid saturation density of 10 elements, obtained using different correlations. The number of available data for each fluid is given in parentheses.

near the critical point, although there are 5 fluids for which these two models are the only ones that agrees with the DIPPR data. The Rackett model behaves heterogeneously. It gives the best agreement with the available data for 7 fluids but high or very high AADs for a great number of fluids. Data for 20 fluids were not considered. For these fluids (all of which have been mentioned above), either the data, critical parameters, and acentric factor values should be revised, or specific models need to be used. Conclusions We have checked the validity of nine predictive empirical correlations, on the basis of the corresponding states principle, for the calculation of the liquid saturation density of 873 pure fluids grouped into 49 families. As reference, we take the data accepted by the DIPPR project. At least for 52 fluids, we found great or even very great disagreement between the reference data and the values obtained using all the models selected, so that some of those fluids were not further considered in our analysis. This lack of agreement may be due to the need to use more specific correlations or to unidentified mistakes in the accepted data for the saturation liquid density, the critical properties, and the acentric factor for those substances. Only a few data are available for several families: dicarboxylic acids; aromatic carboxylic acids; anhydrides; peroxides; isocyanates and diisocyanates; polyfunctional acids; polyfunctional nitriles; inorganic/organic compounds. New measurements need to be made and included in the DIPPR database. Unfortunately, none of the models selected gives the smallest MAPDs for all the families of fluids. Nevertheless, our results show that the recent SNM0, QSMC1, and QSMC2 models are very adequate for predicting the liquid saturation densities of most of the fluids selected, with only a few exceptions. In particular, the results obtained with these recent models clearly improve those obtained with the classical models for organic acids, anydrides, acetates, esters, ethers, polyfunctional esters, other polyfunctional C-H-O substances, polyfunctional C-HO-S substances, polyfunctional C-H-N-halide substances, and organic salts, as well as for most peroxides, most other aliphatic amines, most isocyanates and diisocyanates, and for some n-aliphatic primary amines, some aromatic amines, and some mercaptans. Only for a few families of fluids can the choice of one or another recent model lead to significantly different results. Thus, for aromatic carboxylic acids, and also for some n-aliphatic acids and other aliphatic acids, the QSMC2 model clearly improves the results obtained with the other recent models. For the other

families, the simpler SNM0 and QSMC1 models give similar or better results than QSMC2 one. However, this last model is sometimes the only one in good agreement with the available data. The Rackett model does not behave homogeneously. Despite the poor results obtained for some fluids, this very simple model predicts the data analyzed with MAPDs less than 4% for 9 of the 49 families selected. In particular, it is the only model giving small AADs for most peroxides, and it clearly gives the best agreement for polyfunctional acids and polyfunctional amides/ amines. The classical YG, RRPS, and COSTALD models give slightly better results than the recent ones for aromatic amines, nitriles, C-H-F and C-H-NO2 compounds, polyfunctional nitriles, polyfunctional C-H-O-N and C-H-N-halide-(O) substances, silanes and siloxanes, inorganic halides, inorganic acids, inorganic bases, other inorganics, organic/inorganic compounds, and simple elements. Moreover, they give similar results to the recent ones for formates, propionates and butyrates, epoxides, C1, C2, C3, and higher aliphatic chlorides, aromatic chlorides, n-aliphatic primary amines, other amines and imines, sulfides and thiophenes, C-H-Br, C-H-I, C-H-F, and C-Hmultihalogen compounds, and inorganic gases. For most of these families even the simple YG model gives adequate results. Indeed, our results show that for none of the studied families does the less straightforward COSTALD model significantly improve the results obtained with the simpler YG or RRPS models. We found that the Bhirud and FMC models predict the data adequately for several fluids of different families, with a clearly greater accuracy than the other models. Nevertheless, these models are clearly inadequate for a good number of other fluids and also for the temperature range near the critical point and sometimes near the triple point. The FMC model, in particular, is a very adequate choice, in a general sense, for dicarboxylic acids, some aromatic ethers, and n-aliphatic primary amines. Both the Bhirud and FMC models are adequate for epoxides, mercaptans, and polyfunctional C-H-N-halide-(O) substances, and inorganic gases. Finally, we note that for aromatic amines, other amines and imines, nitriles, isocyanates and diisocyanates, C-H-NO2 compounds, polyfunctional acids, polyfunctional amides/amines, and organic salts, none of the models predicts the available data with MAPDs below 5%. Acknowledgment This work was supported by the project BFM2002-00643 of the “Ministerio de Educacioń y Ciencia” of Spain and the


“Fondo Europeo de Desarrollo Regional” (FEDER) of the European Union. Literature Cited (1) Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids; McGraw-Hill: New York, 1977. (2) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids; McGraw-Hill: New York, 1987. (3) Aalto, M. M.; Keskinen, K. I.; Aittamaa, J.; Liukkonen, S. An improved correlation for compressed liquid densities of hydrocarbons. Part 1. Pure compounds. Fluid Phase Equilib. 1996, 114, 1. (4) Nasrifar, Kh.; Ayatollahi, Sh.; Moshfeghian, M. A compressed liquid density correlation. Fluid Phase Equilib. 2000, 168, 149. (5) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids; McGraw-Hill: New York, 2001. (6) Eslami, H. Equation of state for nonpolar fluids: prediction from boiling point constants. Int. J. Thermophys. 2000, 21, 1123. (7) Iglesias-Silva, G. A.; Hall, K. R. A saturated liquid density equation for refrigerants. Fluid Phase Equilib. 1997, 131, 97. (8) Nasrifar, Kh.; Moshfeghian, M. A saturated liquid density equation in conjunction with the PSRK EOS for pure refrigerants and LNG multicomponent systems. Fluid Phase Equilib. 1998, 153, 231. (9) Nasrifar, Kh.; Moshfeghian, M. Evaluation of saturated liquid density prediction methods for pure refrigerants. Fluid Phase Equilib. 1999, 158160, 437. (10) Nasrifar, Kh.; Ayatollahi, Sh.; Moshfeghian, M. A compressed liquid density correlation. Fluid Phase Equilib. 2000, 168, 71. (11) Eslami, H. Corresponding-states correlation for the saturated liquid density of metals and metal mixtures. Fluid Phase Equilib. 2002, 201, 57. (12) Eslami, H. Corresponding-states correlation for the compressed liquid density of metals. Fluid Phase Equilib. 2004, 215, 23. (13) Aalto, M. M. Correlation of liquid densities of some halogenated organic compounds. Fluid Phase Equilib. 1997, 141, 1. (14) Mulero, A.; Cachadinã, I.; Parra, M. I. Liquid saturation density from predictive correlations based on the corresponding states principle. 1. Results for 30 families of fluids. Ind. Eng. Chem. Res. 2006, 45, 1840.

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ReceiVed for reView January 11, 2006 ReVised manuscript receiVed April 18, 2006 Accepted June 30, 2006 IE0600442

Liquid Saturation Density from Predictive Correlations Based on the

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