DISQUAC behaviour close to critical points application to methanol + alkane mixtures

J.A. Gonzalez et al.: DISOUAC Behaviour Close to Critical Points - Application to Methanol+Alkane Mixtures 219

DISQUAC Behaviour Close to Critical Points Application to Methanol +Alkane Mixtures

Juan Antonio Gonzalez'), Isaias Garcia de La Fuente and Jose Carlos Cobos Departamento de Termodinhica y de Fisica Aplicada, Univenidad de Valladolid, 47071 Valladolid, Spain

Key Words: Critical Phenomena / Groups Contributions / Solutions / Thermodynamics

Interactions present in binary mixtures of methanol +alkanes have been previously characterized in terms of the DISQUAC group contribution model. It was shown that DISQUAC is a reliable tool to represent thermodynamic properties such as molar excess functions: Gibbs energies, GE, enthalpies, H E , or heat capacities at constant pressure, C;. In this work, we examine the ability of the model to represent liquid-liquid equilibria, LLE, for the whole series of methanol + n-alkanes mixtures, as well as for methanol+cyclohexane, +cycloheptane, or +cyclooctane Up to now, we had only considered LLE of those solutions involving n-hexane, n-heptane, or cyclohexane

Using the interaction parameters previously reported for methanol + n-alkanes mixtures, which are independent of the non-polar compound, DISQUAC predicts UCSTs (upper critical solutions temperatures) of the methanol+n-alkanes mixtures which are lower than the experimental values for those systems containing the longer n-alkanes. This is in contradiction with the critical exponents theory. The possibility of improving results by rnodifymg only the third interchange coefficients is discussed. So, two groups of these parameters are given de- pending on n, hereafter the number of carbon atoms in the n-alkane (n 5 7; n 2 8). The coordinates of the critical points are then fairly well represented. Nevertheless, the shape of the LLE curves (the experimental ones being much flatter than those calculated) is rather poorly described, mainly for mixtures containing the longer n- alkanes. The new interaction parameters are tested predicting vapor-liquid equilibria, VLE, at very high temperatures (up to 473.15 K) and at moderate pressures (up to 40 atm) of methanol+ n-alkanes mixtures. It is noteworthy that DISQUAC correctly predicts the formation of azeotropes for systems with the lower n-alkanes, and the absence of azeotropes for mixtures with the longer n-alkanes (from n-nonane).

Properties of mixtures containing cycloalkanes are more difficult to represent because these compounds do not form an homologous series in terms of the c-CH, groups. Nevertheless, it has been shown that the interaction parameters of 1-alkanols (# methanol)+cyclohexane systems can be applied to calculate H E of mixtures with other cycloalkanes. In the case of LLE of rnethanol+cycloalkanes mixtures, different first dispersive parameters are needed for each cycloalkane The quasichemical parameters are, as usually, independent of the n-alkane. The LLE coexistence curves are better represented than in the case of solutions including n-alkanes.

The possibility of modyfing the scaling temperature (equal to 298.15 K in DISQUAC) in order to improve LLE results is also briefly examined.

As usually, the experimental H E curves are much flatter than the calculated ones at temperatures close to the critical. Results for methanol + n-propane, or + n-heptane are shown in order to complete information previously

given.

1. Introduction Solvent extraction, azeotropic distillation, or pumping

are some examples of industrial processes where limited miscibility plays a very important role. Hence, one must be able to determine, by experiment or by calculation, whether one, two or more liquid phases are present.

However, the description of the LLE behaviour is more difficult than the calculation of VLE, or solid-liquid equilibria, SLE, since for the latter the activity coefficient is only a correction term to account for the deviation from ideal behaviour (Raoult's law, ideal solubility). In the case of LLE, unfortunately one can not start from ideal inmiscibili- ty. This means that the activity coefficient is responsible for composition and temperature dependence and even small differences in the activity coefficients can lead to poor results, e.g., for the binodal curve.

Particularly, it must be underlined that, according to the critical exponents theory, mean field theories provide LLE coexistence curves which are too high at the UCST and too low at the LCST (lower critical solution temperature) [l]. In

*) e-mail: [email protected]

fact, these curves are calculated by extrapolation from values of GE in the homogeneous region on the implicit assumption that the critical exponent, y , which represents instability, is equal to 1 111. So, any deviation from this behaviour underlines the presence of effects which should be investigated because lead to an inadequacy of the model parameters used when calculating LLE curves. In this way, it is possible to reach to a deeper understanding of the proposed model, which is useful to carry out further improvements.

This theoretical basis is often removed. So, attention has been focused on the capability to correlate LLE, without simultaneous consideration of other properties, of semi- empirical equations such as Wilson or UNIQUAC, being tested different functions to represent the temperature dependence of the parameters [2 - 61. Developers of group contribution models, e.g. UNIFAC in the different avail- able versions, only report an overall, and certainly useful comparison, between experimental data and calculations [7, 81, but details related on the observed deviations are not considered [7, 81.

On the other hand, association theories usually forget LLE [9, 101, perhaps due to the essential role of the needed

Ber. Bonsenges. Phys. Chem. 101. 219-227 (1997) No. 2 0 VCH Verlagsgesellschaft mbH, 0-69451 Weinheim, 1997 0005-9021/97/0202-0219 $15.00+.25/0

220 J.A. Gonzalez et al.: DISQUAC Behaviour Close to Critical Points - Application to Methanol+Alkane Mixtures

physical term to predict this property because the type of association normally observed is not sufficient by itself to produce phase separation [ 1 11. Several solutions have been proposed to interpretate the phase separation in this framework. So, it has been introduced the concept of competition between statistical mixing (the universal tendency of matter to approach random mixing) and of chemical mixing (the tendency of intermolecular interactions to cause local enrichment or deprivation) [12, 131. But systematic comparison between experimental data and results is not usually given. This has been done by Nagata and Miyamoto in terms of the so-called UNIQUAC association model, which yields a good representation of the LLE curves of methanol + n-alkanes mixtures [14]. The fitted parameters are used to calculate activity coefficients in the miscible region and LLE of ternary systems, but unfortunately other thermodynamic properties such as H E or C: are not simultaneously considered [ 141.

Application of DISQUAC [15, 161 to the determination of LLE is rather scarce, although some examples can be found in the literature: dimethyl carbonate + n-Clo, + n- Clz, + n-C14, or + n-C16 [17, 181; methanol + n-C6, + n-C, [19] (Fig. 1) or +C6HI2 [20] (Fig. 2); ammonia +n-CS +n- c6 or + n-Cs [21], acetic acid anhydride + C6H12 [22]. unfortunately, the study of complete homologous series is even more scarce, namely n-alkanenitriles [23] or phenol + n-alkanes [24]. Along these investigations, attention has been essentially paid to the more or less accurate prediction of the critical points, while no answers have been given to the observed discrepancies. So, in agreement with the critical exponents theory, usually the calculated LLE curves are higher than the experimental ones, but only in the critical region because the latter are much flatter than the former.

340

320

300 Y \ +

280

260

240 6

Fig. 1

m n m

3 0.'2 014 016 0.'8 1

X 1

a

LLE phase diagrams for methanol(1) + n-alkanes(2) mixtures; (-), DISQUAC predictions; points experimental results [54];

340 -

Y \ 320 - !-

300 -

280 -

260 I I I I 0.0 0.2 014 0.6 0.8 1.0

X 1 Fig. 2 LLE phase diagrams for methanol( 1) + cycloalkanes(2) mixtures; (-), DISQUAC predictions; points experimental results: 0 , cyclohexane (541; m, cycloheptane; A, cyclooctane [57]

However, in the n-alkanenitriles + n-alkanes series it is observed that the calculated UCSTs are lower than experimental values for the longer n-alkanes, as in the case of solutions of acetonitrile, or systematically lower as in mixtures containing propanenitrile or butanenitrile [23]. A similar behaviour is also observed in the methanol + n-alkanes series. This type of mixtures have been previously treated by us, reporting interaction parameters determined on the basis of GE and HE data in the homogeneous region for methanol + n-hexane, or + heptane mixtures [19, 251 (Table 1). A detailed comparison between experimental data and DISQUAC results for GE, H E , CF and lny? (natural logarithms of activity coefficients at infinite dilu-

Table 1 Interchange coefficients, dispersive and quasichemical, Cg,: and Cxypc (1 = 1, Gibbs energy; I = 2, enthalpy; 1 = 3, heat capacity), for the contacts (s, h), s = a, c (Type a, CH, or CH, groups in methanol or n-alkanes; Type c, c-CH2 group in cycloalkanes; Type h, OH group in methanol); n means the number of carbon atoms in the n-alkane). For the QUAC part, the coordination number used was z = 4

Solvent

s = a

(V n , option a)

(n 5 7,option b)

(n z 8, option b)

cyclohexane3 1.67 2.10 -9.10 12.20 8.10 71.10 cycloheptaneb) 1.90 2.10 -9.10 12.20 8.10 71.10 cyclooctaneb) 2.15 2.10 -9.10 12.20 8.10 71.10

cxyfc C8yPc C x Y cDIS cDIS cDIS sh.1 sh.2 sh.2

n-alkanes ") 1.35 1.60 -9.10 12.20 8.10 71.10

n-alkanes 1.35 1.60 -9.10 12.20 8.10 71.10

n-alkanes b, 1.35 1.60 -15.00 12.20 8.10 65.00

s = c

0 , n-hexane; i, n-heptane ") (19, 251; b, this work; ') [20].

J.A. Gonzalez et al.: DISQUAC Behaviour Close to Critic

tion) was shown [19]. However, the study of LLE was limited to mixtures of methanol with n-hexane or n-heptane (Fig. 1). When the whole series is considered we observe that the UCSTs calculated are lower systematically than the experimental values from n-octane (Table 2). As mentioned above, this is in contradiction with the critical exponents theory and means that the interchange coefficients used are not valid for such type of n-alkanes. In this work, we also include DISQUAC results on LLE for methanol + cycloheptane, or + cyclooctane systems. Those for methanol + cyclohexane have already been given [20] (Fig. 2). We remark here that the representation of thermodynamic properties of such systems is more difficult because cycloalkanes do not form an homologous series [26].

Along the present article, we'll try to analyze the DIS- QUAC results for methanol + alkane mixtures, if they can be improved, and if this improvement is meaningful when other thermodynamic properties are considered, essentially VLE at high temperatures and moderate pressures (up to 40 atm). At this point, we remark the interest of the study of this phase behaviour because, for multicomponent mixtures, plays a very important role in many engineering processes such supercritical extraction, enhanced oil recovery, or storage and transportation of fluids. High pressure studies are also useful in elucidating the role of repulsive interactions between molecules resulting in improved models of the fluid state in general. In this way, we extent our previous studies on methanol +alkane mixtures in terms of DISQUAC, and continue with our extensive project on the characterization of alcoholic solutions in the framework of this model. Up to now, the following binary systems have been successfully treated: 1-alkanols + n-alkanes [19,

Table 2 Comparison of experimental (exp.) coordinates of critical points: mole fraction xc and temperature, rC/K for methanol(1) + alkanes(2) mixtures with values calculated (calc.) from DISQUAC using the coefficients given in Table 1

~

n-butane n-pentane n-hexane n-heptane n-octane

n-nonane

n-decane

n-dodecane n-tetradecane n-hexadecane cyclo hexane cycloheptane cyclooctane

265.8") 287.4")

324.06b) 338.9")

351.2") 352.6d) 364.1 ") 363.9d) 3 84.6 ")

41 3.3 ") 318.93b) 340.303 358.453

306.75b)

339.37

400.8")

~~ ~~

274.9 - 295.7 - 312.4 - 326.2 - 337.7 346.5

347.3 361.1

355.4 373.6

368.2 392.6 377.8 405.7 385.2 415.2

321.8 345.1 363.7

0.403 0.484 0.546 0.610 0.653 0.639 0.694 0.662 0.729 0.703 0.789 0.837 0.876 0.506 0.580 0.640

~ ~~

0.468 - 0.579 - 0.615 - 0.668 - 0.716 0.724

0.755 0.767

0.787 0.801

0.835 0.851 0.868 0.884 0.892 0.906

0.520 0.558 0.579

221 :al Points - Application to Methanol+ Alkane Mixtures

27 - 301, + cycloalkanes [20, 3 1, 321, +benzene or + toluene (33, 341, +CC14 [32, 351, or + 1-alkanols [25, 361; sec- or tert-alkanols+ n-alkanes or + cyclohexane [37, 381. The problem of the presence of an hydroxyl group in a ring: aliphatic [31] or aromatic [24] has been also considered.

2. Theory Methanol + alkane mixtures are regarded as possessing

three types of surfaces: (i) type a, (CH, or C H 2 in methanol or n-alkanes); (ii) type h, (OH in methanol); (iii) type c, (c-CH3 in cycloalkanes.

2.1 Assessment of Geometrical Parameters

The relative molecular volumes, ri , the surface, qi , and the surface fractions, asi, of all the non-cyclic molecular species have been calculated on the basis of the group volumes and surfaces recommended by Bondi [39], ar- bitrarily taking the volume and surface of the methane as unity. The geometrical parameters of the cyclic aliphatic groups have been estimated previously [26]. Table 3 lists the geometrical parameters of the groups referred to in this work.

Table 3 Relative group increments for molecular volumes, rG = VG / V,,,, and areas, qG = AG/AcH, calculated by Bondi's method [39] (VcH4= 17.1210-6m3mol-'; ACH4=2.9016m2mol-')

Group 'G 4c

CH,") 0.79848 0.73103 CH,") 0.59755 0.46552 c-CHZb) 0.58645 0.66377-0.0385 m 4 s r n s 8 OH- 3 0.46963 0.50345

2.2 Equations The temperature dependence of the interaction parame-

ters, gst, hSt and cpstr has been expressed in terms of the dispersive (DIS) and quasichemical (QUAC) interchange coefficients Czrk and C$yAC, where s, t = a, c or h; and

(To ) / R To) ; bIS/QUAC = DISIQUAC 1 = 1 (Gibbs energy; Cst g (To)/R To); 1 = 3 1 = 2 (enthalpy; Cst DIS/QUAk - hDIS/Q&C

(heat capacity; CbIS/QUAC-- st,3 - Cpst SbIS/QUAC (To)/R). To= 298.15 K is the scaling temperature. This dependence with temperature is as follows:

g St St, 1 st.2 [ ( T o m - 11 DIS/QUAC/R T = cDIS/QUAC + cDISIQUAC

Pn(To/T)-(To/T)+ 11 (1) + cSq.fS/QUAC

where T is the system temperature. Accordingly:

(TOIT) DIS/QUAC/R T = cDWQUAC h st st,2

[ ( T o m - 11 + cDIS/QUAC st,3


and

C D I S / Q U A C / ~ = cDIS/QUAC Pst st.3 (3)

In the DISQUAC model the activity coefficient is given by:

In yi = In yCoMB +~n $Is +~n yi QUAC (4)

Here In yfoMB is the combinatorial term represented by the Flory-Huggins equation, whereas In yprs and In y?UAC are the dispersive and quasichemical contributions, respectively. Expressions for each of the three terms are given elsewhere [40]. For the QUAC part, the standard coordination number was used (z = 4).

As it is known, the condition of stability with respect to diffusion is given by

(8' G M / a x i ) p , T > 0 ( 5 )

where GM = G E + Gidd [ll]. This inequality has a simple geometrical interpretation. If, for given values of T and P , GM is plotted vs. x2, then Eq. ( 5 ) expresses the fact that for the system to be stable the curve must be convex down- wards. If between certain values of x2 the curve is convex upwards, then in this range the mixture ceases to be in stable equilibrium and separates in two phases. The mole fractions x i and 2; in the two phases formed may be calculated by solving the following set of equations:

That is, the values of x2 ( x i , x ; ) relating to the two phases in equilibrium are such that the functions GM and G M have a common tangent. This procedure was applied in this work to calculate the LLE coexistence curve.

2.3 Estimation of Interaction Parameters

Methanol + n-Alkanes Mixtures

This type of mixtures is characterized by a single contact (a, h). As mentioned above, application of interchange coefficients independent of the n-alkane (option a, Table 1) [19, 251 leads to UCSTs lower than the experimental values for the longer n-alkanes (Table 2). At least a part of the observed differences may be attributed to the Patterson effect [15] (see below). In mixtures of cyclohexane, benzene or tetrachloromethane and n-alkanes, the Patterson effect is responsible of interaction parameters dependent on n [41, 421. Such dependence if particularly stronger for the third interchange coefficients [42]. In order to keep a low number of interaction parameters, in option b we have considered FA,; and Csypc (1 = 1, 2) coefficients constant with n and equal to those given in option a, and only two different groups for 1 = 3 ( n s 7 and n z 8 , respectively). For n r 8 ,

the Cz:3 and CSyf" coefficients were obtained in such way that the UCSTs were higher than the experimental values. In the case of phenol + n-alkanes mixtures, we pro- ceeded in similar way [24]. For n 5 7 , they remain unchang- ed in relation to option a (Table 1).

Methanol + Cycloalkanes

These systems are characterized by three types of contacts: (a, c); (a, h) and (c, h).

The non-polar (a, c) interaction is represented by dispersive parameters only. Cycloheptane and cyclooctane can be described by the parameters of cyclohexane. Cyclopentane behaves differently [26]. Constant values were used:

ac,l = 0.03 and Ct:,: = 0.126 [42]. Being the interchange coefficients for the (a, h) contacts

known (equal to those for methanol + n-alkanes mixtures; n 5 7; option a), only it is necessary to determine the interaction parameters for the (c,h) contacts. As usually, the QUAC coefficients are considered as independent of the alkane, i.e., Cs,pc = Csypc. This rule has been applied to many types of mixtures containing cyclohexane, such as cyclohexane + organic carbonates [17, 181; +ethers [43], ketones [44], or 1-alkanols, cycloalkanols or phenol [20, 24, 311.

So, only the dispersive parameters should be fitted. In a previous work, we showed that CZ',: coefficients of l-alkanols ( # methanol) + cyclohexane mixtures can be used to give a fairly good representation of HE of those mixtures containing cyclopentane, cycloheptane or cyclooctane (3 11. This is a remarkable result because, as it is known, cycloalkanes do not form an homologous series in terms of c- CH, groups [26]. For the methanol + cyclopentane system, a specific Cz,s2 coefficients was needed. This was attributed to H E was measured close to the critical point [31]. Here, we have fitted the Cz:l coefficients for each system in order to give a good representation of the critical points. The remainder dispersive parameters were assumed to be equal to those for the methanol + cyclohexane system. Final parameters are listed in Table 1.

cDIS

3. Results and Discussion

Liquid-Liquid Equilibria Predictions

Critical points of methanol + alkanes mixtures calculated on the basis of interaction parameters given in Table 1 are listed in Table 2 together with the corresponding experimental data. Of course, interchange coefficients included in option b improve the predictions on UCSTs for systems with the longer n-alkanes (Table 2).

However, it is obvious that the shape of the LLE curves is poorly represented (Figs. 1 - 3): the experimental curves are much flatter than the calculated ones for the lower n-alkanes, and become extremely shifted to the region rich in methanol for the longer n-alkanes, existing a large miscibility gap at temperatures far from the UCST hardly described by the model.

J.A. Gonzalez et al.: DISQUAC Behaviour Close to Critical Points - Application to Methanol+Alkane Mixtures 223

450

400

Y \ 350 I-

300

250 c

Fig. 3

I 3 0.2 0.4 0.6 0.8 1.0

X 1

LLE phase diagrams for methanol(1) + n-alkanes(2) mixtures; ( - - -), DISQUAC predictions using interchange coefficients given in option b; (-), DISQUAC predictions using Cg,s3 = 15.00 and C$ytc = 65.00 and different scaling temperatures To; points experimental results: [3]; A, [ 5 5 ] , n-octane (To= 312K); ., n-hexadecane [60] (To = 350 K)

As already mentioned, in the case of mixtures containing the longer n-alkanes, a part of the differences noted between experimental and calculated UCSTs using interchange coefficients given in option a is due to the so-called Patterson effect. This effect is found, e.g., in mixtures of 1-propanol or 1-butanol with long-chain n-alkanes, and leads to a lower experimental H E not represented by the model [28 ] . In effect, the endothermic contribution to H E due to the breaking of the orientational order of the n- alkane is compensated by the decreasing of the number of broken H-bonds in relation to the case of the shorter n- alkanes. So, attractive forces between methanol molecules are really stronger than those assumed by the model. In consequence, the fitting of the alkane into cavities or holes in the hydrogen bonded structure of the methanol becomes more difficult and the experimental UCST is higher than the calculated one. This also justifies the major asymmetry of the LLE curves of the systems including long-chain n-alkanes. In summary, DISQUAC predicts deviations from Raoult's law which are less positive than the real ones and so the applied interchange coefficients (option a ) need to be modified (option b).

Predictions on VLE for Methanol + n-Alkane Mixtures at High Temperatures and Moderate Pressures

deviations for pressures, P , defined by: Table 4 (see also Figs. 4 - 6 ) lists the relative standard

1.1

1.0

0.9

00.8 a r \ a0.7

0.6

0.5

0 . 4 6

Fig. 4

I 4 I I i 1 0.2 0.4 0.6 0.8 1.0

X I 9 Y 1

VLE phase diagram for the methanol(1) + n-hexane(2) mixture at 398.15 K; (-), DISQUAC predictions; points, experimental results [58]

Table 4 DISQUAC predictions on VLE for methanol + n-alkanes mixtures using the interchange coefficients given in Table 1 (Nis the number of data points for each system). The relative standard deviations in pressure are defined by Eq. (8)

n-alkane T/K N or (PI

n-hexane 3 13.15 3 19 0.038 398.15 d, 4 0.062 473.15 3 8 0.48

n-heptane 448.159 9 0.15 n-octane 423.157 7 0.080 0.034

473.153 7 0.17 0.080

473.153 7 0.13 0.054 n-decane 423.153 6 0.033 0.013

473.153 6 0.081 0.019 n-dodecane 423.153 4 0.017 0.004

473.15 3 4 0.036 0.005

473.159 3 0.016 0.009

n-nonane 423.159 7 0.053 0.020

n-tetradecane 423.15 3 3 0.012 0.01 1

") Calculated using interchange coefficients given in option a. b, Calculated using interchange coefficients given in option b. '1 191; d, PSI ; 9 WI.

calculated accordingly to the sets of interchange coefficients considered in this work (N stands for the number of data points of each system). Along VLE calculations, vapor phase imperfections were accounted for in terms of the sec- ond virial coefficients estimated by the method of Hayden and O'Connell [45]. As in the case of LLE, for methanol + n-alkanes mixtures (n 2 8), results are improved using the interaction parameters given in option b. We


0 , ' s 0. '2 0:4 0.'6 0:s 1.0

remark that, in agreement with experience, DISQUAC predicts positive azeotropes for systems including an n- alkane up to octane; while no azeotrope is found for those mixtures containing n-nonane, n-decane, n-dodecane of n- tetradecane. It is noteworthy, that the entire VLE diagram at 398.15 K of the methanol+n-hexane mixture is qualita- tively well described by the model (Fig. 4).

Results are very promising as many calculations were car- ried out not far from the gas-liquid critical temperature (= 50 K below). In our opinion, this means that it would be very useful the development of an equation of state using the GE mixing rule at zero pressure with DISQUAC. Group contribution equations of state have been already developed on the basis of ASOG or UNIFAC [46, 471.

m e t h a n o l ( 1 ) + n - o c t a n e ( 2 ) - 1

I I I I

0.0 0.2 0.4 0 .6 0.8 1 .0 X 1

Fig. 5 VLE phase diagrams for the methanol(1) + n-octane(2) mixtures at different temperatures; (-), DISQUAC predictions using interchange coefficients given in option b; points, experimental results (591

5

methanol( 1 ) + n - d e c o n e ( 2 )

- I

0 . 0 0 : 2 e:4 016 s.'e 1 .I0 X 1

Fig. 6 VLE phase diagrams for the methanol(1) + n-decane(2) mixture at different temperatures; (-), DISQUAC predictions using interchange coefficients given in option b; points, experimental results [59]

HE Predictions

As in the case of LLE, experimental HE curves are much flatter than the calculated ones close to the UCST. This behaviour has been observed in mixtures of n-alkanes with linear organic carbonates [ 17, 181, tetraethers [43]; 2-propanone [48], alkanoic acid anhydrides [22] or methanol [ 19, 201. Figs. 7 - 8 shows the same trend for the methanol + n-butane, or + n-propane systems. It can be seen that results become better when temperature increases.

On the other hand, the difference between the temperature of the measurements and the critical temperature of the alkane has a large effect on HE, with the effect of pressure increasing as the temperature difference decreases [49 - 5 11. The effect of pressure in the system methanol + n-butane at temperatures well below the critical temperature of the alkane (425.10K [51]), even at 348.15 K is small [49, 511. Of course, the pressure effect is much important when temperature increases for the methanol + -n-propane mixture [50] (critical temperature of the alkane: 369.88 K [51]). DIS- QUAC predictions, which are obviously independent of the pressure, are in reasonable agreement with experimental data at the higher pressures.

1 5 0 0 j I: 1000

-

I . n


0 l I I I I Y 0.0 0.2 0.4 0.6 0.8 1.0

X 1 Fig. 8 HE for the methanol(1) + n-butane(2) mixture at different temperatures and 5.0MPa; (-), DISQUAC predictions; ( - - -), UNIFAC (Lyngby version) predictions; points, experimental results 1491: 0 , r = 2 9 8 . i s ~ ; w , T = ~ ~ ~ . I s K ; A, T = M ~ . I S K

4. Comparison with UNIFAC (Lyngby Version)

Comparison with other group contribution methods if difficult because they do no consider structure dependent interaction parameters. So, the conditions of application of the models are different. In the case of e.g., UNIFAC (Lyngby version), methanol is treated as a main group, with interchange coefficients which are different to those for the

16

8

6 - Y - - 4

E h \

W P u 2

0 0

/II_____ , I 1

/

3 0 . b5 L ‘ l b 0.‘15 0 X I

3

Fig. 9 CF for the methanol(1) + n-heptane(2) mixture; (-), DISQUAC predictions; ( - - -), UNIFAC (Lyngby version) predictions; points, experimental results (611

remainder alcohols [7]. A comparison should be then possible. Nevertheless, geometrical parameters of methanol are not calculated on the basis of the method recommended by Bondi, but fitted in order to provide a good representation of the H E . We remark the excellent results of the model when describing H E of methanol + n-alkanes mixtures at 298.15 K (see, e.g., Figs. 7 -8). However the dependence with the temperature is poorer. This is important when predicting CF (Fig. 9) or LLE. For methanol( 1) + n-propane(2), both models, DISQUAC and UNIFAC, give very asymmetrical CF curves in agreement with those calculated taking into account the variation of H E with temperature [50]. At x1 = 0.3, 348.15 K and 15 MPa, DISQUAC gives CF = 18.3 J/mol K, while UNIFAC gives only 11 J/mol K, being the experimental value close to 18 in the same units at the same conditions [50]. Moreover, UNIFAC predicts UCSTs for mixtures of methanol and n-hexane, or hexadecane which are much higher than the experimental values (see Table 2): 376.2 and 51 1.3 K, respectively.

As a matter of interest, it should be remarked that UNIFAC (Dortmund version) [8] improves meaningfully the H E results given by the Lyngby version (Rarey, 1996, personal communication).

5. Further Improvements

As it is known, DISQUAC is not a corresponding states theory, and this is an important weakness of the model. So, in DISQUAC TO is always 298.15 K and the behaviour of systems is compared at different reduced temperatures. Further investigations should take into account different To for each system in order to make possible comparisons at the same reduced temperature, as well as to investigate how the structure dependence of the interaction parameters is modified.

To could be related to properties of pure compounds in the mixture, or be treated as a fitting parameter. In this work, we have considered To as adjustable parameter, and we show two examples for the methanol + n-octane (To = 312 K), or +n-hexadecane (To = 350K) systems (Fig. 3) using C,s1’,s3 = 15; C s y f c = 65 and C,91’,s1, C s y f c (1 = 1,2) coefficients equal to those listed in Table 1.

Although the improvement is rather meaningful, a complete description of the entire LLE curves is not given. So, it is impossible to represent simultaneously excess functions and LLE with enough accuracy for the latter property. Here, we remark that the LLE calculations were developed on the basic and wrong assumption that GE is an analytical function close to the critical point [l]. Similarly it occurs in the case of the gas-liquid critical point of a monocomponent system. The physical consequence of the assumption that F (free energy) is a continuous differentiable function of V (volume) and T is that the coexistence curve is quadratic in the volume.

On the other hand, calculations show that the sets of interaction parameters reported in this work (Table 1) are the best when the purpose is to represent simultaneously excess functions and LLE. Essential variations in FA,:, C!$yfc

226 J. A. Gonzalez et al.: DISQUAC Behaviour Close to Critical Points - Application to Methanol + Alkane Mixtures

(1 = 1,2) do not lead to important improvements in the shape of the LLE curves.

Nevertheless, as the temperature range considered is enough wide, it would be interesting the introduction of a fourth interchange coefficient which represents the linear temperature dependence of the heat capacity.

Finally, it should be underlined that the temperature dependence used in the model and represented by Eqs. (1)-(3) has shown to be enough flexible. So, DISQUAC yields good predictions on C;, what is a difficult taks for any theoretical model. The temperature dependence of CF is also fairly well described as in the case of 1-butanol + n- decane, or +toluene [28, 331.

In spite of this, other temperature dependences with a stronger physical basis should be tested [52].

Conclusions

The main conclusion of this work is that it results impossible to describe through a mean field theory excess functions and LLE with enough accuracy for the latter property. However, if one keeps in mind that LLE calculations are developed assuming that GE is an analytical function (what is wrong), then results become consistent. The model usually yields good predictions on excess functions, while the critical points are represented in the right range of composition and temperature.

[291

[301

p i ]

[321

WI

The authors are in debt to Dr. Rarey for helpful comments during [34] the review process of the paper. This work was supported in part by the Spanish DGICYT, PB93-0017 Project. [351

[361

[17] H. V. Kehiaian, J.A. G o d e z , 1. Garcia, J. C. Cobos, C. Casanova, and M. J. Cocero, Fluid Phase Equilibria 64, 1 (1991).

[18] J. A. G o m e z , I. Garcia de la Fuente, J. C. Cobos, C. Casanova, and H.V. Kehiaian, Thermochim. Acta 217, 57 (1993).

[19] J. A. Gonzlez, I. Garcia, J.C. Cobos, and C. Casanova, Ther- mochim. Acta 189, 115 (1991).

[20] J.A. Gonzlez, I . Garcia de la Fuente, J.C. Cobos, and C. Casanova, J. Solution Chem. 23, 399 (1994).

[21] I. Velasco, J. Fernhdez, S. Otin, and H.V. Kehiaian, Fluid Phase Equilibria 69, 15 (1991).

(221 H.V. Kehiaian, J.A. Gonzlez, I. Garcia, R. Escarda, J.C. Cobos and C. Casanova, Fluid Phase Equilibria 69, 91 (1991).

[23] B. Marongiu, B. Pittau, and S. Porcedda, Thermochim. Acta 221, 143 (1993).

[24] J.A. Gordlez, I . Garcia de la Fuente, and J.C. Cobos, Ber. Bunsenges. Phys. Chem., in press.

[25] J.A. Gonzdez. I . Garcia de la Fuente, J.C. Cobos, and C. Casanova, Fluid Phase Equilibria 78, 61 (1992).

[26] M.R. Tine and H.V. Kehiaian, Fluid Phase Equilibria 32, 211 (1987).

[27] J.A. G o d l e z , J.C. Cobos, I, Garcia, and C. Casanova, Ther- mochim. Acta 171, 153 (1990).

[28] J.A. Gonzlez, I. Garcia de la Fuente, J.C. Cobos, and C.

References

J. S. Rowlinson and F. L. Swinton, Liquids and Liquids Mixtures, Butterworths, Nonvich, 1982. J.M. Sorensen, Th. Magnussen, P. Rasmussen, and A.A. Fredenslund, Fluid Phase Equilibria 3, 47 (1979). H. Higashiuchi, Y. Sakuragi, Y. Iwai, Y. Arai, and M. Nagatani, Fluid Phase Equilibria 36, 35 (1987). H. Higashiuchi, Y. Sakuragi, Y. Arai, and M. Nagatani, Fluid Phase Equilibria 58, 147 (1990). I. Nagata, Thermochim. Acta 210, 281 (1992). Y. Arai, H. Higashiuchi, and Y. Sakuragi, Fluid Phase Equilibria 89, 187 (1993). B. Larsen, P. Rasmussen, and A.A. Fredenslund, Ind. Eng. Chem. Res. 26, 2274 (1987). J. Gmehling, J. Li, and M. Schiller, Ind. Eng. Chem. Res. 32, 178 (1993). A. Liu, K. Pusicha, A.M. Demiriz, and F. Kohler, J. Solution Chem. 20, 39 (1991). T . Hofman and C. Casanova, J . Chem. SOC. Faraday Trans. 92, 1175 (1996). I. Prigogine and R. Defay, Chemical Thermodynamics, Longmans, Green and Co. Ltd., 1954. F. Becker, M. Kiefer, and A. SpOrner, Ber. Bunsenges. Phys.

Casanova, Ber. Bunsenges. Phys. Chem. 95, 1658 (1991). J. A. Gonzlez, I. Garcia de la Fuente, J. C. Cobos, C. Casanova, and U. Domanska, Fluid Phase Equilibria 94, 167 (1994). J. A. Gonz&lez, I. Garcia de la Fuente, J. C. Cobos, C. Casanova, and U., Domanska, Ber. Bunsenges. Phys. Chem. 98,955 (1994). J.A. Gonzalez, I . Garcia de la Fuente, and J.C. Cobos, Thermo- chim. Acta 278, 57 (1996). U. Domanska and J. A. GonzBlez, Fluid Phase Equilibria 123, 167 (1996). J.A. Gonzalez, I. Garcia de la Fuente, J.C. Cobos, and C. Casanova, Fluid Phase Equilibria 93, 1 (1994). U. Domanska and J.A. Gonzilez, Fluid Phase Equilibria 119, 1311 (1996). J.A. Gonzilez, I . Garcia de la Fuente, J.C. Cobos, and C. Casanova, Thermochim. Acta 237, 261 (1994). U. Domanska and J.A. Gonzilez, Fluid Phase Equilibria, in press. J.A. G o d e z , I. Garcia de la Fuente, and J.C. Cobos, Fluid Phase Equilibria 123, 39 (1996). J.A. G o d l e z , I. Garcia de la Fuente, J . C. Cobos, and U. Domanska, Fluid Phase Equilibria 119, 81 (1996). A. Bondi, Physical Properties of Molecular Crystals, Liquids and Glasses, J. Wiley, New York, 1968. V. Kehiaian, J.-P.E. Grolier, and G.C. Benson, J. Chim. Phys. 75, 1031 (1978). A. Ait-Kaci, Ph. D. Thesis, University of Lyon, France, 1982. J. A. Gonzilez, I. Garcia de la Fuente, J . C. Cobos, C. Casanova, and A. Ait-Kaci, Fluid Phase Equilibria 112, 63 (1995). H.V. Kehiaian, M.R. Tine, L. Lepori, E. Matteoli, and B. Marongiu, Fluid Phase Equilibria 46, 131 (1989). H.V. Kehiaian, S. Porcedda, B. Marongiu, L. Lepori, and E. Matteoli, Fluid Phase Equilibria 63, 231 (1991). J. G. Hayden and J. P. O’Connell, Ind. Eng. Chem. Process, Des. Dev., 14, 209 (1975). K. Tochigi, Fluid Phase Equilibria 104, 253 (1995). J. Gmehling, Fluid Phase Equilibria 107, 1 (1995). S . Shen, Y. Wang, J. Shi, G. C. Benson, and B.C.-Y. Lu, J. Chem. Thermodyn. 22, 387 (1990). J.T. Sipowska, J.B. Ott, A.T. Woolley, and R.M. Izatt, J. Chem. Thermodyn. 24, 1087 (1992). J.T. Sipowska, J.B. Ott, B. J. Neely, and R.M. Izatt, J. Chem. Thermodyn. 23, 551 (1991).

Chem. 81, 1084 (1977). F. Becker, M. Kiefer, P. Rhensius, and A. Sporner, Pol. J. Chem. 54, 1937 (1980). I . Nagata and K. Miyamoto, Thermochim. Acta 210, 293 (1992). H.V. Kehiaian, Fluid Phase Equilibria 13, 243 (1983). H.V. Kehiaian, Pure Appl. Chem. 57, 15 (1985).

(511 J.B. Ott, P.R. Brown, and J.T. Sipowska, J. Chem. Thermodyn.

[52] F. Kohler, and J. Gaube, Pol. J. Chem. 54, 1987 (1980). [53] A. Skrzecz, Thermochim. Acta 182, 123 (1991). [54] G. Hradetzky and H.-J. Bittrich, Int. DATA Ser. Sel Data Mix-

28, 379 (1996).

tures, Ser. A 3 , 216 (1986).

J.A. Gonzalez et al.: DISQUAC Behaviour Close to Critical Points - Application to Methanol+Alkane Mixtures 227

[55] J.B. Ott, I.F. Hdlscher, and G.M. Schneider, J . Chem. ThermO-

(561 I. F. Holscher, G. M. Schneider, and J.B. 0th Fluid Phase

[57] G. Hradetzky, D.A. Lempe and H.-J. Bittrich, Int. DATA Ser.

[58] A. Zawisza, J. Chem. Thermodyn. 17, 941 (1985). (591 Th. W. de Loos, W. Poot, and J . de Swaan Arons, Fluid Phase

[60] R. Stryjek, M. Luszczyk, and M. Fedorko-Antosik, Bull. Acad.

(611 R. Tanaka, S. Toyama, and S. Murakami, J. Chem. Thermodyn. dyn. 18, 815 (1986).

Equilibria 27, 153 (1986).

Sel. Data Mixtures Ser. A 4, 294 (1991).

Pol. Sci. Ser. Sci. Chim. XXIX, 203 (1982).

18, 63 (1986).

(Received: July 22, 1996 final version: October 18, 1996)

E 9335 Equilibria 42, 209 (1988).

DISQUAC behaviour close to critical points application to methanol + alkane mixtures

Documents

Transcript of DISQUAC behaviour close to critical points application to methanol + alkane mixtures