LLE Predictions for Hydrogen Fluoride Mixtures Using an

Ind. Eng. Chem. Res. 2002, 41, 4863-4872

4863

VLE/VLLE/LLE Predictions for Hydrogen Fluoride Mixtures Using an Improved Thermodynamic Equation of State Barath Baburao and Donald P. Visco, Jr.* Department of Chemical Engineering, Tennessee Technological University, Box 5013, Cookeville, Tennessee 38505

Recently a model has been introduced describing the heat effects of hydrogen fluoride (HF) more accurately than other models available. In this work, we extend this model to predict the coexistence properties of some binary HF mixtures. Twelve HF mixtures are explored initially (R12, R22, R32, R113a, R123, R124, R134a, R142b, R152a, n-propane, HCl, and Cl2) because these are the systems where experimental data are available. Good agreement with experiment, especially in the correlation of miscibility gaps, is realized through the use of two mixing rules, namely, van der Waals (VDW) and Wong-Sandler. We also correlate the binary interaction parameter from the VDW mixing rule using the dipole moment to predict the properties of the HF-R141b system. We also use this model to correlate and predict the properties of an aqueous HF system, including a prediction for a double azeotrope of this system at very dilute concentrations of HF. Introduction In the production of hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs), hydrogen fluoride (HF) provides the fluorine ion source. Accordingly, the design of heat exchange and separation equipment for the multicomponent mixtures that exit the reactor, especially during the process analysis phase, requires robust models to predict the thermodynamic properties of these mixtures. Development and evaluation of models for HF mixtures are hampered by two specific problems. First, HF is a caustic and toxic substance. A spill of concentrated HF to the skin of 2% of the total body area is fatal. Thus, it is not surprising that experimental data for HF, both as a pure component and in mixtures, are quite limited. This lack of data inhibits parametrization and testing of models. The second problem is that HF associates substantially in all phases, including the vapor phase (even at very low pressures).1 Thus, any model that attempts to describe HF (and HF mixtures) must specifically include a term that accounts for this important attractive force. For equations of state (EOS) developed for HF, normally pressures and/or phase densities have been used during the parametrization process. Unfortunately, if one uses an EOS parametrized in this fashion, derivative properties (heat of vaporization, heat capacity, etc.) need not be adequately represented by these parameters. The plan for this paper is as follows. First we will briefly review EOS that have been used to describe HF and HF mixtures. Next we will describe, in brief, one particular model and discuss a recent improvement to this model. After this, we will show correlations and predictions of coexistence properties from this improved model for HF mixtures that are available in the open literature. Such information is very valuable because a priori knowledge of azeotropes and potential miscibility * To whom correspondence should be addressed. Phone: 931-372-3606. Fax: 931-372-6352. E-mail: [email protected].

gaps aid in efficient process design. Finally, we will draw conclusions about the suitability of this improved model for HF mixtures and discuss future work in this area. Review of Models In this section we will briefly review recent attempts to model HF and HF mixtures. For a more detailed account, we refer the reader to the following references.2-4 All useful EOS approaches to model HF requires a term to account for the association interactions of HF. Where the models differ is both in what HF oligomers will form as a result of the association and how the association term is described. The nonassociation interactions are also modeled in a variety of ways. Kao et al.5 have developed a model for HF that assumes the formation of monomers and hexamers and describes fugacity coefficients for the formed species through the Peng-Robinson EOS (PREOS).6 Their approach is computationally demanding because combined phase and chemical equilibria equations must be solved. Additionally, the parametrization is quite extensive, though a recent work has attempted to put this model into a more convenient form.7 No work was reported on HF mixtures from this model. Galindo et al.2 used the statistical associating fluid theory (SAFT) to describe HF and HF mixtures with varying success. Specifically, the heat effects for pure HF were not modeled correctly.3 Recent modifications to this SAFT approach have improved the correlation of the heat effects somewhat, but it still lags behind less complex approaches.8 The rest of the approaches treat the association in the manner of Heidemann and Prausnitz,9 where it is possible to separate the chemical and physical contributions to the compressibility factor and, thus, a closed-form EOS results. Economou and Peters10 add an association term onto the perturbed anisotropic chain theory (APACT) while assuming an association scheme of 1-2-3-6-9 for HF. They correlate HF properties and report results for some HF mixtures. Though their approach is “closed-form”, it still requires iteration to determine the amount of

10.1021/ie020341g CCC: $22.00 © 2002 American Chemical Society Published on Web 09/11/2002

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Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002

association present at a particular state. Twu et al.11 combine a 1-6 model for association of HF with the Redlich-Kwong EOS. Such an approach also requires iteration, and they did not use this model for any mixture calculations involving HF. The model reported by Lencka and Anderko,12 referred to here as AEOS (for “association + EOS”), however, removes the need for iteration and makes it quite appealing for further study. It also does not assume a specific association scheme a priori. Specifically, Anderko determined that the chemical contribution to the compressibility factor can be given as a function of a reduced density.13 Accordingly, he fit a ratio of polynomials to this reduced density. Thus, after initial parametrization of this function, no iteration is required to use this EOS. Anderko did report results for some HF mixtures. AEOS Model The AEOS model applied to HF has been discussed in detail elsewhere.3,12,14 Here, we will review the basics. Specifically, the model separates the association contributions to the compressibility factor, Z, from that of the other system interactions (called “physical”). Accordingly, one writes

Z ) Zch + Zph - 1

(1)

where the superscript “ch” should be read as “chemical” while the superscript “ph” should be read as physical. To form oligomers (here only chains) in this model, selfassociation chemical reactions are assumed. The higherorder association equilibrium constants are given as a function of the dimerization equilibrium constant, K, and a Poisson-like distribution function. The dimerization equilibrium constant is made temperature-dependent, and the distribution function has a parameter that describes, roughly, its peak value. Such an approach provides a simple method to utilize a nonconstrained association scheme. Within the framework of the nonconstrained association scheme, the chemical contribution to the compressibility factor, Zch, is written exactly as a ratio of infinite sums, both implicit in Zch. Anderko showed, however, that Zch could be written as a function in terms of a reduced density q ) RTK/v, where R is the gas constant, T is the absolute temperature, and v is the molar volume.13 Though the exact, closed-form function is not available, Anderko was able to solve exactly for Zch at a wide range of q. Accordingly, he then fit a ratio of polynomials in terms of q to the exact Zch values. Namely, 8

F(q) ) (1 +

Diqi)/(1 + q)8 ∑ i)1

Zch ) F(q)

(2) (3)

where Di are fitted parameters, given elsewhere.12 Using such an approach removes the need for iteration when applying the EOS. Finally, Anderko chose the PREOS to describe the nonassociative interactions in the system. For HF, the energy parameter, a, in the PREOS was made temperature-dependent while the excluded volume parameter, b, was a constant value. Upon parametrization against one- and two-phase densities as well as vapor pressure, the AEOS reproduces vapor

Figure 1. Superheated vapor heat capacity of hydrogen fluoride at 721 mmHg. The empty symbols are the experimental data,22 the solid line is the prediction from AEOS-VK, the dashed lined is from AEOS-LK, and the dotted line is from AEOS.

pressures for HF to within 0.7% and liquid volumes to within 2%.12 Because of its correlative ability, the use of an unconstrained association scheme, and its relative simplicity, Visco et al.7,14 looked at the heat effects prediction for HF from the AEOS. The results of that study indicated that the AEOS applied to HF resulted in very large peaks in the superheated vapor heat capacity as well as some nonphysical shouldering, as seen in Figure 1. It was subsequently determined that the cause of these problems was the fact that the functional fit used for Zch (eq 2) did not adequately represent the exact derivative of this quantity, with respect to q. Such a term appears in the heat capacity, so it is not surprising that this quantity is poorly predicted. To fix this deficiency, Visco et al.3,4 proposed a fit to the exact value of dZch/dq and then integrated this functional form to get Zch. The improved results for the heat capacity prediction are seen in Figure 1. The functional form for Zch is provided elsewhere.4 We will refer to this model as AEOS-VK. Two years after the AEOS-VK model was published, a modification to the original AEOS was proposed by Lee and Kim (here called AEOS-LK).15 Specifically, these authors did not use the unconstrained scheme of Anderko but used the association scheme for HF as proposed by Schotte,16 namely, a 1-2-3-6-8 model. However, Lee and Kim fit the new Zch exact results (as per this new association scheme) to the same functional form as eq 2. Accordingly, this model still cannot predict the heat capacity accurately, as seen in Figure 1. AEOS-VK Model with Mixtures The AEOS model assumed that the non-HF species in a mixture do not associate.12 As such, modifications to the definitions of q and Zch are required. Namely, q ) xHFRTK/v and Zch ) xHFF(q) + (1 - xHF), where xHF is the mole fraction of HF in that phase of the binary mixture. For the temperature dependence of the energy

Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002 4865 Table 1. m and n Parameters for the Temperature Dependence of the Energy Parameter in the PREOSa system

m

n

system

m

n

R32 R22 R12 R123 R124 R134a R141b

0.7796 0.6993 0.6391 0.7842 0.7933 0.8455 0.7046

0.2537 0.2813 0.2915 0.2633 0.2515 0.2279 0.2820

R142b R152a R113 R290 Cl2 HCl water

0.7141 0.7756 0.7477 0.5909 0.5014 0.6018 0.8893

0.2697 0.2695 0.2786 0.3997 0.3624 -0.0507 0.0151

and kij ) 0 for i ) j. Hence, for a binary, this mixing rule has one adjustable parameter, k12. For the WS mixing rule, we utilized the modifiedNRTL model, and the mixture parameters are given as18

amix

x2AE∞

)

bmix

ln(x2 - 1)

a ) 0.45724R2Tc2R/PcA

(4)

R ) m[1 - Tr] + n[1 - xTr]2

(5)

where Tc is the critical temperature, Pc is the critical pressure, and Tr is the reduced temperature (T/Tc). Thus, there are two parameters, m and n, that describe the temperature dependence of the energy parameter in the PREOS. We report the following values for these parameters, which were fit to the experimental vapor pressure, in Table 1. Note that the values in italics were taken from the original Melhem et al. work. To determine mixture values of the parameters in the PREOS, we utilized two mixing rules: van der Waals (VDW) and Wong-Sandler (WS). For VDW, we used the classic expressions

1-

(b - RTa

)

a

AE∞

[( ) )

N

-

(RT/x2) ln(x2 - 1) bi -

ij

(8)

i

∑ ∑xixj b - RT ij i)1 i)1

bmix )

parameter, a, in the PREOS, we used a relationship suggested by Melhem et al.17 Specifically,

xi ∑ i)1 b

(

N N

a The parameters in italics (the last four in the list) are taken from the work of Melhem et al.17

ai

N

+

( )

xi ∑ RTb i)1

i

)]

) (

(9)

ai

ai aj + bj (1 - kij) RT RT 2

(10)

N

AE∞

N

)

RT

xi ∑ i)1

xjGjiτji ∑ j)1

(11)

N

∑ xkGki

k)1

Here, Gji ) bj exp(-0.3τji). For a binary mixture, this mixing rule has three adjustable parameters.

N N

amix )

∑ ∑xixjx(aiaj)[1 - kij] i)1 i)1

(6)

Mixtures

(7)

We have broken our mixture study into two parts. The first part examines HF mixtures with compounds that contain only carbon, hydrogen, chlorine, and/or fluorine atoms. We examine these systems, where experimental data are available, at constant temperature. Additionally, we predict phase coexistence properties for these

N

bmix )

xibi ∑ i)1

where N is the number of components in the mixture

Ndata Table 2. Mixing Parameters and Percent Average Absolute Deviation [% AAD ) (100/Ndata)∑i)1 (|Pexp - Pmodel |/ i i a )] for the Various Mixtures Studied in This Work Pexp i

WS system

source

state

VDW kij

VDW AAD (%)

τ12

τ21

k12

WS AAD (%)

HF-R124

23

-0.0413

0.045 12

0.726 68

23

-0.264 81

0.001 06

0.380 58

HF-R134a

23

-0.084 07

0.019 62

0.611 45

HF-R12 HF-R123 HF-R152a

24 25 26

-0.022 04 -0.205 89 -0.243 00

0.049 86 0.030 94 0.007 29

0.942 98 0.908 50 0.425 32

HF-R22 HF-HCl

27 28 29

-0.044 76 -0.000 031 -0.110 45

0.027 06 0.003 05 0.063 93

0.660 08 0.673 50 0.567 64

HF-Cl2 HF-R290

25 30

HF-R142b

27

0.050 50 0.030 95 0.007 1 -0.047 26

0.090 51 0.070 30 0.086 80 0.025 85

0.907 52 0.970 6 0.956 0 0.748 64

HF-R113a HF-R141b

31 27

-0.009 6

0.074 16

0.957 96

0.90 0.71 0.39 0.65 0.93 0.43 5.73 2.87 0.50 0.26 0.85 0.96 1.77 3.41 5.46 9.59 8.35 1.96 1.74 7.01

HF-H2O

32

1 atm

1.44 0.81 6.72 7.20 2.13 2.36 2.97 3.43 6.97 6.44 1.08 1.46 2.99 6.16 6.06 1.65 1.91 1.84 2.13 4.55 7.45 14.51 0.68

-0.000 27

HF-R32

298.20 K 283.45 K 283.32 K 298.15 K 283.27 K 298.15 K 303.15 K 393.15 K 288.23 K 298.35 K 298.15 K 258.15 K 244.15 K 193.55 K 323.15 K 293.15 K 303.15 K 283.15 K 303.15 K 383.15 K 283.15 K

a

-0.1075 -0.0765 0.0548 -0.0172 -0.1784 0.0083 -0.0044 0.0634 0.2255 0.1314 -0.0260 -0.0035 0.0203 -0.0908 -1.2950

Note that the column “source” indicates where in the literature this experimental data can be found.

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Figure 2. Pxy diagram for the HF-R12 system. The symbols are the experimental data (see Table 2 for source), and the lines are the correlations/predictions from the AEOS-VK model. The solid line is for the VDW mixing rule, while the dashed line is for the Wong-Sandler mixing rule. Temperatures are as indicated.

systems at states where experimental data are not available. We do this to provide a means to evaluate the effect of temperature on the azeotropic composition as well as the width and/or presence of miscibility gaps in these systems (where applicable). The second part of the study looks at predictions of aqueous HF systems. We have isolated 13 nonaqueous HF mixtures in the open literature. In what follows, we look at 12 of those systems as we will attempt to correlate the binary interaction parameter of the remaining system to predict the phase behavior of that mixture. We examine each system using both mixing rules. For the mixture parameters, we fit to the experimental bubble-point pressures and, where applicable, the miscibility gaps. All mixture parameters are given in Table 2. Note that we use only one set of parameters per mixture (per mixing rule), except for the HF-R22 system (both VDWMR and WSMR) and the HF-R290 system (only WSMR). HF-R12 (CCl2F2). In Figure 2 we show the Pxy curves for the HF-R12 system at three temperatures. At 303 K, both VDWMR and WSMR can correlate the miscibility gap, though there is a discrepancy as to the width of the gap as well as to the composition of the azeotrope. At 283 K, both mixing rules predict a phase split in the liquid, while at 323 K, VDWMR predicts a totally miscible liquid whereas WSMR predicts a very wide miscibility gap. HF-R22 (CHClF2). In Figure 3 we show the Pxy curves for the HF-R22 system at two temperatures. At the lower temperature, WSMR predicts a miscibility gap while VDWMR does not. The presence of phase instability in the liquid at this temperature is experimentally observed. At the higher temperature both mixing rules properly correlate the bubble point and the complete miscibility of this system including the dilute HF azeotrope. Note, once again, the use of separate mixing parameters at each temperature because poor correlation using only one set of parameters would have resulted.

Figure 3. Pxy diagram for the HF-R22 system. Lines and symbols are as in Figure 2.


HF-R32 (CH2F2). In Figure 4 we show the Pxy curves for the HF-R32 system at three temperatures. Clearly, the results with WSMR correlate the experimental data best. Note that both mixing rules predict a dilute HF azeotrope for all of the temperatures examined which is not seen experimentally. HF-R113a (CCl3CF3). In Figure 5 we show the Pxy curves for the HF-R113a system at two temperatures. Both mixing rules predict the experimentally observed miscibility gap at 383 K, but the width of such a gap differs. At 333 K, both mixing rules predict the width of the miscibility gap to increase. HF-R123 (CHCl2CF3). In Figure 6 we show the Pxy curves for the HF-R123 system at two temperatures. At 393 K, where experimental data are available, only WSMR predicts a miscibility gap whose presence has not been seen by experiment. At 323 K, both mixing rules predict a miscibility gap, but the azeotropic concentration remains fairly constant between the two temperatures explored.

Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002 4867

Figure 5. Pxy diagram for the HF-R113a system. Lines and symbols are as in Figure 2.




HF-R124 (CHClFCF3). In Figure 7 we show the Pxy curves for the HF-R124 system at two temperatures. Both mixing rules correlate the experimental data well at both temperatures, and each predicts the presence of a miscibility gap at 283 K that has not been reported experimentally. Both mixing rules predict a totally miscible liquid phase at 298 K. HF-R134a (CH2FCF3). In Figure 8 we show the Pxy curves for the HF-R134a system at three temperatures. Both mixing rules correlate the experimental data well at both temperatures. At 233 K, however, WSMR predicts a small miscibility gap in the liquid, while VDMR does not. HF-R142b (CClF2CH3). In Figure 9 we show the Pxy curves for the HF-R142b system at three temperatures. At 283 and 303 K, both mixing rules can correlate the experimental data. However, WSMR predicts a miscibility gap in the liquid phase at both 283

and 303 K, while VDWMR predicts two liquid phases only at 283 K. A miscibility gap is reported experimentally for this system at 293 K. HF-R152a (CHF2CH3). In Figure 10 we show the Pxy curves for the HF-R152a system at three temperatures. WSMR does a better job than VDWMR at correlating the bubble- and dew-point pressures at the temperatures where experimental data exist. Additionally, both mixing rules predict a dilute HF azeotrope at the three temperatures examined as well as a completely miscible liquid phase. Note that the azeotropes predicted here are not seen experimentally. HF-HCl. In Figure 11 we show the Pxy curves for the HF-HCl system at three temperatures. Both mixing rules predict similar behavior including the experimentally reported miscibility gap in this system at 193 K. HF-Cl2. In Figure 12 we show the Pxy curves for the HF-Cl2 system at two temperatures. Though both

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Figure 9. Pxy diagram for the HF-R142b system. Lines and symbols are as in Figure 2.

Figure 11. Pxy diagram for the HF-HCl system. Lines and symbols are as in Figure 2.


Figure 12. Pxy diagram for the HF-Cl2 system. Lines and symbols are as in Figure 2.

mixing rules predict a wide miscibility gap for this mixture at 323 K as seen experimentally, the composition of the azeotrope is different. Additionally, at 353 K, VDWMR predicts a much smaller miscibility gap than does WSMR. HF-R290 (CH3CH2CH3). In Figure 13 we show the Pxy curves for the HF-R290 system at three temperatures. Both mixing rules can correlate the experimental data at the two lower temperatures well and predict the experimentally observed liquid-liquid-phase splitting. However, the location of the azeotrope and the width of the miscibility gap are different for both mixing rules. At 323 K we see the predicted miscibility gap shrink substantially for VDWMR. Note that we do not report results at this temperature for WSMR because we parametrized using this mixing rule at both experimental temperatures (293 and 303 K).

Miscibility Gaps and Dipole Moments Economou and Peters have discussed liquid-liquid equilibrium (LLE) in HF mixtures in terms of polarity arguments.10 Basically, the HF molecules prefer a polar environment (µHF ) 1.83 D)19 and, thus, will phase separate if in a mixture where the other substance has a small dipole moment. To explore this issue in a little more detail, we have listed the systems reported in this study as well as other refrigerants and have provided their dipole moment in Table 3. We also list whether this substance in a mixture with HF will show (either experimentally confirmed, predicted, or estimated) a miscibility gap in the liquid phase at 300 K. Qualitatively speaking, the argument of Economou and Peters seems valid based on Table 3 and could serve as a rough guide to predict LLE in HF mixtures. Additionally, we have provided the specific compositions of the miscibility gaps and the azeotropes as predicted by both mixing rules in Table 4.


Figure 13. Pxy diagram for the HF-R290 system. Lines and symbols are as in Figure 2. Table 3. Dipole Moments for the Various Substances Studied in This Work and a Listing as to Whether This Mixture Has a Miscibility Gap at 300 Ka nonassociating component

dipole moment (D)

propane Cl2 R113a R12 R114 R134 HCl R123a R123 R22 R124 R125 R143 R134a HF H2O R32 R141b R124a R142b R152a R143a

0 0 0.48 0.51 0.67 0.99 1.08 1.30 1.36 1.46 1.47 1.56 1.68 1.80 1.83 1.85 1.98 2.01 2.06 2.14 2.30 2.34

source

miscibility gap at 300 K?

10 10 33 34 10 33 33 33 34 34 34 35 19 36 33 33 34 36 35 34

Figure 14. VDW kij value as a function of the dipole moment. The empty circles are the best-fit values of these parameters obtained through minimization of the AAD. The line is the regression equation. The bow-tie symbol indicates the VDW kij value for R141b as obtained through minimization of the AAD, while the filled inverted triangle is the VDW kij as predicted from the regression equation.

yes yes yes yes no yes no no no no no maybe maybe no

a Note that “maybe” implies a conflict between experiment and this modeling effort.

Correlation of the Binary Interaction Parameter At this point we have correlated and predicted (based on correlation to experimental data) the vapor-liquid equilibrium (VLE)/vapor-liquid-liquid equilibrium (VLLE) for 12 HF mixtures (excluding the aqueous system). Each of these 12 non-HF compounds has contained only four types of atoms: carbon, hydrogen, chlorine, and fluorine. We have one set of experimental data left that includes only these four atoms, namely, R141b (CCl2FCH3). We would like to use the model to predict the properties of this system without first fitting to the experimental data of the mixture. For simplicity, we will explore the predictive nature of the model only with VDWMR. Because the binary interaction parameter for VDWMR is seen to vary with the system (see

Figure 15. Pxy diagram for the HF-R141b system. The solid line is the AEOS-VK correlation using the VDW mixing rule with the kij value obtained through minimization of the AAD (kij ) 0.0203). The dashed line is the AEOS-VK prediction using the VDW mixing rule with the kij value obtained from the linear regression equation in Figure 14 (kij ) -0.0908).

Table 2), we have attempted to correlate this value as a function of the type of refrigerant in the mixture, though we note that this approach used here is not novel.20 In Figure 14 we show the kij value as a function of the dipole moment of the nonassociating component and a corresponding linear regression equation. Noting that the dipole moment of R141b is 2.01 D, we predict a value for kij of -0.0908. HF-R141b (CCl2FCH3). As can be seen in Figure 15, the results using the predicted value of kij underestimate the peak system pressure for this temperature by a few tenths of a bar. However, the existence of a

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Table 4. Specific Listings of the Miscibility Gaps and Azeotropic Compositions of the Mixtures Tested in This Studya VDWMR

WSMR yAZ HF

xRHF

xβHF

xRHF

xβHF

0.4468 0.4301 0.0020 0.0038 2.6 × 10-3 0.0953 0.0968 0.2230 0.3454 0.3329 0.3243 0.7777 0.7244 0.0201 0.0094 0.0068 0.1379 0.0775 N/A N/A 1.9 × 10-3 0.2953 0.2916 0.2590 0.2558

0.7558 N/A N/A N/A N/A N/A N/A N/A 0.9403 0.8830 N/A 0.9168 N/A N/A N/A N/A N/A N/A 0.7758 N/A N/A 0.9444 0.8453 0.9748 0.9708 0.9611 0.8005 N/A N/A 0.7938 0.9742 0.9720 0.7439 N/A N/A N/A N/A N/A N/A

0.2922 N/A N/A N/A N/A N/A N/A N/A 0.1043 0.2518 N/A 0.1520 N/A N/A N/A N/A N/A N/A 0.1179 N/A N/A 0.0260 0.1005 0.0716 0.1145 0.4772 0.2271 N/A N/A 0.2559 0.1723 0.0288 0.2394 N/A N/A N/A N/A N/A N/A

0.8124 N/A N/A N/A N/A N/A N/A 0.6938 0.9615 0.9544 0.9475 0.9684 0.9426 N/A N/A N/A 0.7553 N/A 0.6732 N/A N/A 0.9279 0.9114 0.9578 0.9539

0.2619 N/A N/A N/A N/A N/A N/A 0.4037 0.0642 0.0896 0.1196 0.2033 0.3346 N/A N/A N/A 0.2660 N/A 0.3514 N/A N/A 0.0123 0.0379 0.0472 0.0598

0.8732 0.8272 N/A 0.9794 0.9977

0.2228 0.3371 N/A 0.1603 0.0600

system

state

yAZ HF

HF-R124

HF-R141b

283.45 K 298.20 K 283.32 K 298.15 K 253.15 K 283.27 K 298.15 K 233.15 K 283.15 K 303.15 K 323.15 K 323.15 K 393.15 K 298.35 K 288.23 K 258.15 K 258.15 K 298.15 K 193.55 K 244.15 K 273.15 K 323.15 K 353.15 K 293.15 K 303.15 K 323.15 K 283.15 K 303.15 K 333.15 K 383.15 K 333.15 K 283.15 K

HF-H2O

1 atm

0.4474 0.4320 0.0143 0.0181 1.0 × 10-4 0.1421 0.1380 0.1296 0.3857 0.4027 0.3620 0.7528 0.6866 0.0696 0.0626 0.0400 0.0909 0.0900 N/A N/A 4.2 × 10-3 0.3717 0.3983 0.3420 0.3575 0.4005 0.4719 0.4520 0.4070 0.8029 0.8610 0.8419 0.7563 0.3930 0.0109 0.4068 0.0049 0.4172 0.0020

HF-R32 HF-R134a HF-R12 HF-R123 HF-R152a HF-R22 HF-HCl HF-Cl2 HF-R290 HF-R142b HF-R113a

0.5 atm 2 atm

0.4830 0.4630 0.4166 0.8314 0.8643

VDWMR

WSMR

a Here, “y” indicates the vapor-phase composition of HF in the azeotrope (with superscript “AZ”), though some liquid phases at this azeotropic composition are unstable. Here, “x” indicates the composition of the two liquid phases that form (R and β) for some mixtures at some states. Note that the italics for R141b indicate the results using the predicted VDW kij value of -0.0908. Empty cells indicate that this state (for a particular mixing rule) was not studied. N/A implies that the mixture did not possess an azeotrope and/or a miscibility gap at a particular state (for a particular mixing rule).

14). This only underscores the complex behavior one is trying to account for by a simple correlation of the binary interaction parameter with dipole moment. At any rate, the dew-point line using either kij value is very similar for low to moderate HF amounts, and the azeotropic compositions predicted are similar. The width of the miscibility gap using the predicted kij value is much smaller than that from the optimized kij value. Predictions for an Aqueous HF System

Figure 16. Txy diagram for the HF-H2O system. The solid line is the AEOS-VK correlation/prediction using the VDW mixing rule.

miscibility gap for this system as well as an azeotrope at near 80 mol % HF is predicted. If we optimize the kij parameter to the experimental data, we find a value of 0.0203. Such a value is markedly different from the predicted value and not what one would expect based on the results of the previous 12 systems (see Figure

Water, like HF, associates in the liquid phase. One can attempt to account for this water association within the AEOS approach in a manner similar to the approach for HF. However, as a crude approximation, we have attempted to model the aqueous HF system by treating the water as an inert. HF-H2O. In Figure 16 we show the Txy curves for the aqueous HF system at three pressures. We correlate our model against the experimental data at 1 atm and predict the phase behavior for this system at 0.5 and 2.0 atm. At all three pressures, the model predicts a stable azeotrope with respect to composition. However, there is a second azeotrope predicted in the very dilute HF region. The existence of such an azeotrope in this region has not been reported experimentally, nor is it implied by the dilute aqueous HF experimental data of Munter et al.21 Note that we only explore the results using VDWMR for this system. In fact, a very large, negative, binary interaction parameter is required


(-1.2950). Such a value is indicative of an enhanced cross-interaction term that is, apparently, modeling “cross-association” between the various HF oligomers and the water species. Concluding Remarks In this work we have extended a recent modificationto the AEOS model of Anderko to correlate and predict phase equilibria of various HF mixtures. Using two mixing rules, it was seen that this model is quite robust because it was able to correlate VLE as well as liquid miscibility gaps for numerous systems where experimental data are available. Note that, for some systems, dilute HF azeotropy was predicted which is not seen experimentally. We also explored the purely predictive ability of this model on a mixture wherein the binary interaction parameter was determined solely from a correlation of other systems based on the dipole moment. Such a method did not prove fruitful and underscores the complex nature of this parameter, especially for the polar systems explored in this work. Additionally, this model showed utility in correlating the phase equilibria for an aqueous HF system and predicted the existence of a double azeotrope. Recall that the benefit of the improved model for pure HF was in its ability to predict the heat effects more accurately than previous models. The overall goal is to utilize this improved model to predict mixture heat effects. However, as a first test of the improved model with mixtures, we needed to determine if we could correlate experimental data that existed in the literature, specifically bubble-point pressures. Accordingly, the next step now is to look at the heat effects predicted by this improved model and compare those results to the very sparse experimental heat effects data that exist. Acknowledgment Partial financial support for this research has been provided by the Center for Manufacturing Research at Tennessee Technological University. Computational work on this project was performed at the Computer Aided Engineering Laboratory on the Tennessee Technological University campus. Helpful suggestions from the reviewers are acknowledged. Literature Cited (1) Suhm, M. A. HF vapor. Ber. Bunsen-Ges. Phys. Chem. 1995, 99, 1159. (2) Galindo, A.; Whitehead, P. J.; Jackson, G.; Burgess, A. N. Predicting the phase equilibria of mixtures of hydrogen fluoride with water, difluoromethane and (HFC-32), and 1,1,1,2-tetrafluoroethane (HFC-134a) using a simplified SAFT approach. J. Phys. Chem. B 1997, 101, 2082. (3) Visco, D. P. The Thermodynamic and Molecular Modeling of Hydrogen Fluoride; State University of New York at Buffalo: Buffalo, NY, 1999. (4) Visco, D. P.; Kofke, D. A. Improved Thermodynamic Equation of State for Hydrogen Fluoride. Ind. Eng. Chem. Res. 1999, 38, 4125. (5) Kao, C.-P. C.; Paulaitis, M. E.; Sweany, G. A.; Yokozeki, M. An equation of state/chemical association model for fluorinated hydrocarbons and HF. Fluid Phase Equilib. 1995, 108, 27. (6) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Fundam. 1976, 15, 59.

(7) Visco, D. P., Jr.; Juwono, E.; Kofke, D. A. Heat effects of hydrogen fluoride from two thermodynamic models. Int. J. Thermophys. 1998, 19, 1111. (8) Galindo, A.; Burton, S. J.; Jackson, G.; Visco, D. P.; Kofke, D. A. A study of the effect of ring formation on the fluid phase equilibria of hydrogen fluoride: The SAFT approach and the AEOS Model. Mol. Phys. 2002, in press. (9) Heidemann, R. A.; Prausnitz, J. M. A van der Waals-type equation of state for fluids with associating molecules. Proc. Natl. Acad. Sci. 1976, 73, 1773. (10) Economou, I. G.; Peters, C. J. Phase equilibria prediction of hydrogen fluoride systems from an associating model. Ind. Eng. Chem. Res. 1995, 34, 1868. (11) Twu, C. H.; Coon, J. H.; Cunningham, J. R. An equation of state for hydrogen fluoride. Fluid Phase Equilib. 1993, 86, 47. (12) Lencka, M.; Anderko, A. Modeling phase equilibria in mixtures containing hydrogen fluoride and halocarbons. AIChE J. 1993, 39, 533. (13) Anderko, A. Phase equilibria in aqueous systems from an equation of state based on the chemical approach. Fluid Phase Equilib. 1991, 65, 89. (14) Visco, D. P.; Kofke, D. A.; Singh, R. R. Thermal properties of hydrogen fluoride from an EOS + association model. AIChE J. 1997, 43, 2381. (15) Lee, J.; Kim, H. An equation of state for hydrogen fluoride. Fluid Phase Equilib. 2001, 190, 47. (16) Schotte, W. Collection of phase equilibrium data for separation technology. Ind. Eng. Chem. Process Des. Dev. 1980, 19, 432. (17) Melhem, G. A. S., R.; Goodwin, B. M. A Modified PengRobinson Equation of State. Fluid Phase Equilib. 1989, 47, 189. (18) Orbey, H.; Sandler, S. I. Reformulation of Wong-Sandler mixing rule for cubic equations of state. AIChE J. 1995, 41, 683. (19) Jedlovszky, P.; Vallauri, R. Computer simulations of liquid HF by a newly developed polarizable potential model. J. Chem. Phys. 1997, 107, 10166. (20) Morrison, G.; McLinden, M. Azeotropy in Refrigerant Mixtures. Int. J. Refrig. 1993, 16, 129. (21) Munter, P. A.; Aepli, O. T.; Kossatz, R. A. Hydrofluoric acid-water and hydrofluoric acid-hydrofluorosilicic acid-water. Ind. Eng. Chem. 1947, 39, 427. (22) Franck, E. U.; Meyer, F. Hydrogen fluoride III. Specific heat and gas-phase association at low pressure. Z. Electrochem. 1959, 63, 571. (23) Lee, J.; Kim, H.; Lim, J. S.; Kim, J.-D.; Lee, Y. Y. Vaporliquid equilibria for Hydrogen Fluoride + Difluoromethane + 1,1,1,2-Tetrafluoroethane, and + 1-Chloro-1, 2, 2, 2,-tetrafluoroethane at 283.3 and 298.2 K. J. Chem. Eng. Data 1996, 41, 43. (24) Kang, Y. W. Vapor-liquid equilibria for the systems difluoromethane + hydrogen fluoride, dichlorodifluoromethane + hydrogen fluoride, and chlorine + hydrogen fluoride. J. Chem. Eng. Data 1998, 43, 13. (25) Wilson, H. L.; Wilding, W. V. Vapor-liquid and liquidliquid equilibrium measurements on twenty-two binary mixtures; DIPPR Data Series; DIPPR: New York, 1994. (26) Lee, J.; Kim, H.; Lim, J. S.; Kim, J.-D.; Lee, Y. Y. Vaporliquid equilibria for Hydrogen Fluoride + 1,1-Difluoroethane at 288.23 and 298.35 K. J. Chem. Eng. Data 1997, 42, 658. (27) Kang, Y. W.; Lee, Y. Y. Isothermal vapor-liquid equilibria for the systems 1-chloro-1,1-difluoroethane + hydrogen fluoride, 1,1-dichloro-1-fluoroethane + hydrogen fluoride, and chlorodifluoromethane + hydrogen fluoride. J. Chem. Eng. Data 1997, 42, 324. (28) Wilson, L. C.; Wilding, W. V.; Wilson, G. M. Vapor-liquid equilibrium measurements on six binary mixtures. AIChE Symp. Ser. 1989, 85, 51. (29) Gillespie, P. C.; Cunningham, J. R.; Wilson, G. M. Vaporliquid equilibrium measurements for the hydrogen fluoride/ hydrogen chloride system. AIChE Symp. Ser. 1985, 81, 41. (30) Kang, Y. W. Phase equilibria for the binary mixtures containing hydrogen fluoride and nonpolar compound. Fluid Phase Equilib. 1999, 154, 139.

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Received for review May 3, 2002 Revised manuscript received July 24, 2002 Accepted July 26, 2002 IE020341G

LLE Predictions for Hydrogen Fluoride Mixtures Using an

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