Properties of coexisting fluid phases of a binary system methanolethane by computer simulation

FLUIDPHAS[ EQUILIgRIA ELSEVIER

FluidPhaseEquilibria 129 (1997) l-13

Properties of coexisting fluid phases of a binary system methanol-ethane by computer simulation I.Yu. Gotlib a, E.M. Piotrovskaya a,., S.W. de Leeuw b a Department of Chemistry, St.Petersburg State University, St.Petersburg, Russia b Computational Physics Group, Faculty of Applied Physics, Delft University of Technology, Delft, The Netherlands

Received 21 May 1991; accepted 2 September 1996

Abstract

Methane-ethane and methanol-ethane binary mixtures were simulated by the Gibbs ensemble Monte Carlo method. Thermodynamic properties and structural characteristics of coexisting fluid phases were calculated. Reasonable agreement with experiment was obtained, in particular, for the liquid-liquid-vapour coexisting pressure in the methanol-ethane system at 298.15 K. A lyophobic effect, which affects the phase behaviour and the hydrogen-bonding characteristics of the liquid phase, was observed. In order to improve agreement with experiment, the values of the Lennard-Jones interactions parameters for CH3OH and C2H 6 molecules were adjusted. © 1997 Elsevier Science B.V. Keywords: Molecularsimulation; Vapour-liquid equilibria; Mixture; Alkanols; Alkane

1. I n t r o d u c t i o n

In recent years, calculations of the phase behaviour and properties of the coexisting phases for binary and multicomponent systems using computer simulations has become the subject of numerous studies. Systems containing non-polar and polar components attract special attention because of their complex phase behaviour, which strongly depends on the particular characteristics of molecular interactions in a given system. This is particularly true for mixtures containing amphiphylic components consisting of a polar " h e a d " able to form hydrogen bonds and a non-polar (usually hydrocarbon) " t a i l " . The methanol-ethane system is one of the simplest examples of such systems. A three-phase liquid-liquid-vapour (LLV) equilibrium is observed in this system at sufficiently low temperatures. Its phase behaviour was experimentally investigated in detail [1,11,10]. Fig. 1 shows the

* Corresponding author, e-mail: [email protected]. 0378-3812/97/$17.00 © 1997ElsevierScienceB.V. All rights reserved. PII S0378-3812(96)03182-2

2

l.Yu. Gotlib et al. / Fluid Phase Equilibria 129 (1997) 1-13

20

(MPa)

12

C

|

i

i

T (K) Fig. ]. Experimenta] temperature-pressure critica] diagram for the system CH3OH-CzH6: M is the critical point of pure methanol, E is the critical point of pure ethane, and C is the point of critical identity between the vapour and the ethane-rich

liquid phase.

experimental Tp diagram for this system [1]. Point C, at which one of the liquid phases is critically identical to the vapour, corresponds to a temperature T = 309.6 K and a pressure p = 5.176 MPa. The Gibbs ensemble Monte Carlo (GEMC) method [14-16], which allows direct simulation of coexisting phases at the same time, is very useful in simulations of systems with phase separation, including binary and multicomponent systems [3,16,17,7]. In this paper, we report the results of our simulations where the GEMC method was applied to methane-ethane ( C H 4 - C 2 H 6 ) and methanolethane ( C H 3 O H - C 2 H 6) binary systems. In particular, we tried to estimate the value of the LLV equilibrium pressure in the methanol-ethane mixture. There are numerous publications on the computer simulation of real binary systems using molecular dynamics, the traditional Monte Carlo and the GEMC method. Among the publications on computer simulations of real hydrocarbon-containing binary systems, concerning their phase behaviour, the molecular dynamics (MD) calculations of the C O 2 - C 2 H 6 mixture by Fincham et al. [4,5] should be mentioned. These authors managed to reproduce qualitatively the experimentally observed azeotropy with the pressure maximum. The system C H 4 - C 2 H 6 was simulated by Coon et al. [2] and by MSller et al. [13] using MD, and more recently by de Pablo and Prausnitz [3] using the GEMC method. In the GEMC method for systems containing more than one component, it is possible to choose between NVT and NpT varieties of the Gibbs ensemble method [16,17]. It was shown that for some simple systems with liquid-liquid immiscibility the NpT version gives greater fluctuations in the densities and compositions of the coexisting phases [ 17]. However, for our purposes the NpT version is somewhat more convenient, as it allows a direct calculation of the LLV equilibrium pressure in the methanol-ethane mixture. As a test case, we performed GEMC simulations of the methane-ethane system. This system is of considerable practical importance, and its components have been thoroughly investigated in the recent years, as mentioned above. The calculations were performed for pure components and the equimolar

l.Yu. Gotlib et al./Fluid Phase Equilibria 129 (1997) 1-13

3

Table 1 Thermodynainic properties of pure ethane, pure methane and their equimolar mixture at 104 K calculated by the MC method (this work) and molecular dynamics, and experimental data [13] Pure ethane Pure methane Equimolar mixture

Configurational energy of the liquid (kJ mol-1)

MC

MD

MC

MD

MC

MD

- 16.51 +0.04

- 17.21 +0.01

-7.62 +0.01

-7.61 +0.01

- 12.00 +0.04

- 12.32 +0.01

65 + 12

90 + 10

41.25 +0.07

41.51 +0.03

- 0.63 +0.09

- 0.58 +0.025

Excess enthalpy (J mol 1) Molar volume of the liquid (cm3 mol- 1)

46.61 +0.08

47.071 +0.003

37.15 +0.05

Excess volume (cm 3 mol- 1)

37.105 +0.003

Experiment

74

- 0.45

mixture. The results are collected in Table 1, together with the experimental data and the results o f MSller et al. [13] concerning M D simulation o f this system with the same model potential parameters.

2. Methanol-ethane system Our main task was the G E M C simulation o f the C H 3 O H - C 2 H 6 system. A L e n n a r d - J o n e s ( 1 2 - 6 ) site-site model was used here in combination with the Coulomb point charge model for representing electrostatic interactions between methanol molecules (for ethane, these interactions were not included in the model because their influence on macroscopic properties is very small). The model and the values o f the potential parameters for C2H 6 were the same as in the works o f Fischer et al. [6] and MSller et al. [13]. In this model, a site-site L e n n a r d - J o n e s potential was used: qbdtd ( r ) = 4 G ~ [ ( crt3/r~t3 ) 1 2 _ (~r~t3/r~t3

)6]

where a , /3 are L e n n a r d - J o n e s sites ( " a t o m s " ) , r,,~ is the distance between them, and G ~ , %t3 are, correspondingly, the energetic and geometric interaction parameters. C 2 H 6 molecules were represented as L e n n a r d - J o n e s dumbbells (two-site particles). The parameters of the intermolecular potential for C 2 H 6 are given in Table 2. For C H 3 O H , the model o f Jorgensen [9] was used, and two sets o f potential parameters were considered: the J2 parameter set [9,8,12,7] and the modified parameter set (L1 model) introduced by van L e e u w e n and Smit [18]. Until recently, the J2 model was treated as predicting the thermodynamic properties o f methanol over a wide temperature range with the highest accuracy (see the comparison of four sets o f the model potential parameters by H a u g h n e y et al. [8]). Therefore, this model was used in our simulations o f pure methanol [7]. H o w e v e r , according to the recent calculations o f van L e e u w e n and Smit [18], the L1 potential gives a phase diagram o f pure CHBOH in the temperature

4

1.Yu. Gotlib et al./Fluid Phase Equilibria 129 (1997) 1-13

Table 2 Model potential parameters Ethane E / k (K) o" (nm) L (rim)

139.81 0.3512 0.2353

Methanol eCH3- CH3/ k (K) O'CH3_CH3 (rim) e o _ o / k (K) O-o_o (nm) qcH~([e[)

qo([ el) Lcn3_ o (nm) Lo H (nm) /_COH

J2 set

L1 set

104. 17 0.3775 85.55 0.3071 0.265 - 0.700 0.14246 0.09451 108.53°

105.2 0.374 86.5 0.303

Lorentz-Berthelot interaction parameters are obtained as: e.t3 = ~

E~tJ and o'~t~ =

½(o-oo

+ o-~). Charge neutrality gives:

qn = -(qcrt 3+ qo)-

range from 300 to 450 K that is much closer to the experimental data than any other model previously used, including J2. The values of the parameters for both models are given in Table 2. L o r e n t z - B e r t h e l o t combining rules were used for the description o f unlike interactions. A spherical cut-off procedure for all interactions in all the systems was used with the cut-off radius r c = ( 5 / 2 ) o - , where o- refers to interactions between the methyl groups in C H 3 O H molecules. So, if the distance between the CH 3 groups o f two methanol molecules was less than r c, the interaction energy was calculated using a site-site L e n n a r d - J o n e s plus Coulomb model; otherwise, the energy was regarded as zero. The possibility of using this cut-off procedure (not only for L e n n a r d - J o n e s but also for Coulombic interactions) was discussed by Mezei [12]. He came to the conclusion that including the long-range electrostatic interactions (by means o f the Ewald summation procedure) in the model does not essentially improve the results when the thermodynamic properties o f polar molecular liquids (such as methanol and chloroform) are calculated. In order to test this conclusion, we also performed several additional MC runs for the m e t h a n o l - e t h a n e system (with different total numbers o f particles), in which long-range interactions were taken into account using the Ewald algorithm. W e carried out the simulations for the C H 3 O H - C 2 H 6 system at a temperature o f 298.15 K, in the pressure range from 1.0 to 4.5 MPa (the experimental L L V equilibrium pressure at 298.15 K is 4.128 MPa). In order to estimate system-size effects, we simulated systems with total n u m b e r o f particles N = 216 and N = 864. Periodic boundary conditions were imposed for both G E M C cells. Densities, compositions, configurational energies and a t o m - a t o m correlation functions were calculated for both coexisting phases. Hydrogen-bonding characteristics for the methanol-rich liquid phase (hereafter called " p h a s e I " ) and the virial pressure for the ethane-rich phase (gaseous at pressures below the L L V equilibrium point and liquid above it; henceforth referred to as phase II) were also calculated. The Jorgensen [9] energetic criterion was used for the definition o f the hydrogen bonding,

l.Yu. Gotlib et al./ Fluid Phase Equilibria 129 (1997) 1-13

5

i.e. two CH3OH molecules were regarded as H-bonded if their interaction energy was lower than ( - 12.56) kJ mol-1 Markov chains of 10-12 mln. configurations were generated; averaging was done over 3 - 5 mln. configurations. The standard GEMC technique was used with only one modification: not only were particle transfers from one phase (MC box) to another allowed, but also exchanges between particles of different components in different phases. The results of the simulations for the J2 model with N = 216 together with the experimental data are given in Table 3 (thermodynamic properties) and in Table 4 (hydrogen-bonding characteristics for phase I at pressure p = 3.7 MPa; the ethane content in the solution is Xc2H6= 0.24). The calculated thermodynamic properties for the L1 model with N = 216 are presented in Table 5, and for the " l a r g e " system with N = 864 (using both the J2 and L1 models) in Table 6. The results calculated both with and without long-range interactions are given in Table 7. The calculated and experimental phase diagrams are presented in Fig. 2; the atom-atom correlation functions are shown in Figs. 3-6.

2.1. Thermodynamic properties. The calculated phase diagram for the system methanol-ethane is shown in Fig. 2; the results are also given in Tables 3, 5 - 7 . As seen from both the figure and the tables, reasonable agreement with experiment is achieved. The calculations lead to a value of the LLV equilibrium pressure for the system with N --- 216 of at least 3.7 MPa at 298.15 K. This is somewhat lower than the experimental value 4.128. The calculated critical mole fraction of ethane is also underestimated in comparison with the experimental value. For a larger system ( N - - 8 6 4 ) at a higher pressure p = 3.9 MPa, we still observe a liquid and a vapour phase, but there are large fluctuations in composition, which confirms that the system is near the critical point. In general, in computer simulations it is sometimes rather difficult to define the point of phase separation. These discrepancies in LLV equilibrium pressure and compositions of the phases can be interpreted taking into consideration the relatively small average number of particles, combined with the strong clustering of the few CH3OH molecules, in the vapour phase (phase II), which leads to uncertainties in the calculated methanol concentration in that phase. The effect of artificial clustering ( " c o h e s i o n " ) of methanol particles has already been observed in our simulation of pure CH3OH. The phase diagram for this system was also calculated using the quasichemical hole model [19], and the data are presented in Fig. 2. The discrepancies between the experimental and calculated results are similar to those obtained by computer simulations. As mentioned above, several additional GEMC runs for the methanol-ethane mixture were performed using the Ewald summation for evaluating long-range electrostatic interactions. The calculations were held for systems with both N = 216 and N = 864 (Table 7). As seen from the table, there is no real improvement of the thermodynamic results in comparison to the spherical cut-off for the systems of both sizes. This is not surprising for the systems with methanol, in which the dispersive interactions dominate such that the tail of the long-range interactions has less effect. There is a small, systematic effect, however, even for large-size systems. Spherical cut-off leads to a somewhat lower ethane content in phase I and a smaller volume of that phase. Comparison of the results obtained using the J2 and L1 sets of model potential parameters (Tables 3 and 5) reveals that differences between the experimental and calculated data (densities of phase I and ethane contents therein) have opposite signs. While the J2 model somewhat overestimates the

2.01 4- 0.10

44.5 ± 0.9 1000 ± 200

-33.8:t:0.6 -1.2±0.2

0.109 + 0.010 0.99 +_ 0.01

2.51 5:0.19

44.9 ± 0.9 700 + 150

-32.3:t:0.5 -1.3+0.2

0.115 ± 0.011 0.99 + 0.01

3.05 5:0.25

45.3 ± 0.9 600 + 100

-31.0±0.5 -1.7_+0.25

0.134 ± 0.015 0.99 + 0.01

3.0 M P a

3.60 ± 0.35

45.8 ± 0.9 450 5 : 1 0 0

-28.9±0.6 -1.9:1:0.25

0.147 + 0.013 0.99 5:0.01

3.5 M P a

4 5:1.3

48.5 ± 0.9 100 __. 20

-28.95:0.6 -7.45:0.5

0.239 + 0.015 .900 5 : 0 . 0 1 3

3.7 M P a

42.0t

0.0370

43.59

0.0871

2.0 M P a

45.98

0.1565

3.0 M P a

50.78

0.3210

4.0 MPa

a Experimental data on the L L V equilibrium point at 298.15 K: pressure p = 4.128 MPa, molar content o f ethane in phase I XZc:H6 -- 0.3528, molar volume o f phase I V l = 51.61 cm 3 m o l - ~ [11]; p ffi 4.107 MPa, x~2rL = 0.3705, V l = 51.9 cm 3 tool- ~, molar content of ethane in phase II x C2H Ix 6 = 0.9128, molar volume o f phase II V H = 79.8 cm 3 m o l - L [10].

1.03 5:0.08

43.8 5:0.9 2000 ± 250

Molar volume (cm 3 m o l - l ) : of phase I of phase II

" V i r i a l " pressure in phase I1 (MPa)

-34.0±0.6 -0.9±0.15

l):

0.068 + 0.013 0.99 + 0.01

2.5 M P a

1.0 M P a

2.0 M P a

1.0 M P a

Configurational energy (kJ mol for phase I for phase I1

Ethane molar content: in phase I in phase 11

Experiment

Gibbs ensemble Monte Carlo

Table 3 Thermodynamic properties of the methanol-ethane binary mixture along the phase coexistence curve at 298.15 K (pressure range from 1.0 to 3.7 MPa) calculated by the G E M C method using the J2 model, with the n u m b e r of particles in the M C cell N ffi 216 (this work), and experimental data [11] a

~,u

,~

E"

~.

~" E"

.~

l.Yu. Gotlib et a l . / F l u i d Phase Equilibria 129 (1997) 1-13

7

Table 4 Hydrogen-bonding characteristics for methanol molecules in phase I calculated by the GEMC method at T = 298.15 K, p = 3.7 MPa (this work), in pure methanol [7] and in the system methanol-carbon tetrachloride [20] Phase I (Xc2H6 ~- 0.24) Pure methanol CH3OH-CCI 4 (Xccl4 = 0.3) Average number of H-bonds per CH3OH molecule 1.805_+0.035

1.81 _+0.03

Percentage of molecules forming n H-bonds (%): n= 0 n= 1 n= 2 n= 3

2.1 _+0.6 22.1 _+ 1.6 68.7 _+2.1 6.9_+ 1.0

2.3_+0.6 18.4_+ 1.5 75.5 _+ 1.7 3.7_+ 1.1

3.1 _+0.3 21.4___0.6 70.0 _+ 1.0 5.8_+0.2

C 2 H 6 p e r c e n t a g e in the liquid and its m o l a r v o l u m e , L1 u n d e r e s t i m a t e s these values. This can be easily e x p l a i n e d b y the fact that the L1 p a r a m e t e r s a s s u m e a d e e p e r m i n i m u m o f L e n n a r d - J o n e s interaction e n e r g y b e t w e e n the C and O a t o m s o f C H 3 O H m o l e c u l e s and thus increase the interaction f a v o u r i n g a closer p a c k i n g o f these m o l e c u l e s . So, u s a g e o f the L1 m o d e l leads to a h i g h e r absolute value o f the c o n f i g u r a t i o n a l e n e r g y f o r p h a s e I, a h i g h e r density and d e g r e e o f h y d r o g e n b o n d i n g , and a m o r e n o t a b l e " l y o p h o b i c " effect o f " p u s h i n g o u t " the h y d r o c a r b o n m o l e c u l e s f r o m the m e t h a n o l rich liquid p h a s e (see also below). T h e p a r a m e t e r s o f the L1 set w e r e adjusted a c c o r d i n g to the e x p e r i m e n t a l t h e r m o d y n a m i c properties o f pure C H 3OH o v e r a w i d e t e m p e r a t u r e range. T h e r e f o r e , it is not surprising that in o u r calculations the densities o f p h a s e I o b t a i n e d using this set are v e r y close to the e x p e r i m e n t a l o n e s at low pressures w h e n the C 2 H 6 c o n t e n t in p h a s e I is also low, with the d i s c r e p a n c y g r o w i n g as the pressure increases. A t the s a m e time, for the J2 m o d e l the difference b e t w e e n the calculated and e x p e r i m e n t a l liquid densities is already noticeable for pure m e t h a n o l and m i x t u r e s c o n t a i n i n g small a m o u n t s o f ethane.

Table 5 Thermodynamic properties of the methanol-ethane binary mixture along the phase coexistence curve at 298.15 K calculated by the GEMC method using the L1 model, with the number of particles in the MC cell N = 216 (this work) Pressure 1.0

2.5

Ethane molar content: in phase I in phase II

0.034_+ 0.009 0.99 _+0.01

0.097 _+0.012 0.99 __0.01

Configurational energy (kJ mol - 1): for phase I for phase II

- 36.8 -+0.5 - 0.37 _+0.04

- 35.2 -+0.6 - 1.4_+0.15

Molar volume (cm 3 mol- t): of phase I of phase II

41.5 _+0.4 2200-+ 250

42.7 -t- 0.6 670_+ 90

"Virial' ' pressure in phase II (MPa)

1.03 _+0.11

2.8 _+0.4

8

l.Yu. Gotlib et al./Fluid Phase Equilibria 129 (1997) 1-13

Table 6 Thermodynamic properties of coexisting phases of the methanol-ethane binary system at 298.15 K and 1.0 MPa calculated by the GEMC method using the J2 model, the LI model, and the LI model with deviations from Lorentz-Berthelot rules (~: = 1.02, ~"= 1.025), with the number of particles in the MC cell N = 864 (this work) L1 set

J2 set

L1 set (~: = 1.02, r = 1.025)

Ethane molar content: in phase I in phase II

0.025 _+0.002 0.984_+ 0.009

0.039 _+0.002 0.98 ± 0.01

0.039 + 0.002 0.98 _+0.01

Configurational energy (kJ mo171): for phase I for phase lI

- 36.0 + 0.2 - 0.40 +_0.04

- 34.0 + 0.2 - 0.55 _+0.06

- 36.4+ 0.2 - 0.42 _+0.05

Molar volume (cm 3 mol-1): of phase I of phase II

41.3 + 0.3 2270_+ 120

42.8 _+0.3 2240 _+ 190

42.1 + 0.2 2250 _+ 180

"Virial" pressure in phase II (MPa)

1.01 _+0.07

1.00_+ 0.06

1.01 _+0.05

R e g a r d i n g the r e s u l t s for the s y s t e m with N = 8 6 4 o b t a i n e d u s i n g b o t h the J2 a n d L1 m o d e l p o t e n t i a l s , it s h o u l d b e c o n c l u d e d that the s y s t e m - s i z e effect exists ( c o m p a r e T a b l e 6 with T a b l e s 3 a n d 5), first o f all, c o n c e r n i n g the c o m p o s i t i o n o f a l i q u i d phase. F o r both m o d e l s , the c a l c u l a t e d e t h a n e c o n c e n t r a t i o n in the l i q u i d p h a s e b e c o m e s l o w e r in the " l a r g e " s y s t e m . H e n c e , the L1 m o d e l n o w g i v e s v a l u e s o f this c o n c e n t r a t i o n w h i c h are too low, w h i l e the s i m u l a t e d c o m p o s i t i o n o f the l i q u i d for the J2 p o t e n t i a l is r a t h e r c l o s e to the e x p e r i m e n t a l one. H o w e v e r , the d e n s i t y o f the l i q u i d s o l u t i o n o f e t h a n e in m e t h a n o l is u n d e r e s t i m a t e d b y the J2 m o d e l , as it is for p u r e m e t h a n o l [7,18]. It c a n be s u p p o s e d that the J2 p o t e n t i a l to s o m e e x t e n t u n d e r e s t i m a t e s the t e n d e n c i e s for a s s o c i a t i o n b e t w e e n m e t h a n o l m o l e c u l e s w h i l e the L I m o d e l , d e s c r i b i n g these t e n d e n c i e s m o r e a d e q u a t e l y ,

Table 7 Thermodynamic properties of coexisting phases of the methanol-ethane binary system at 298.15 K and 1.0 MPa calculated by the GEMC method using the J2 model and the Ewald summation for electrostatic interactions, with the number of particles in the MC cell N = 216 and N = 864 (this work) N = 216 Ethane molar content: in phase I in phase II Configurational energy (kJ molfor phase I for phase II Molar volume (cm 3 mol- l): of phase I of phase II

N = 864

0.07 ___0.01 0.98 + 0.02

0.050 + 0.012 0.98 + 0.02

- 33.5 + 0.9 - 0.8 + 0.05

- 33.8 + 0.5 - 0.7 _ 0.06

43.0 + 0.3 2100 _ 170

42.0 +__0.4 2200 + 190

1):

l.Yu. Gotlib et a l . / Fluid Phase Equilibria 129 (1997) 1-13 •

1

+

2

3

•

9

4

6 p(MPa) +

4

+

: , j .. .. .. .41

+

•

A

&'IV' /

4

/ 2

l

/~

0/ 0.00

'6

i 0.40

I 0.20

i 0.60

i 0.80

1.00

XC=Hs

Fig. 2. Pressure-coexisting phase composition diagram for the system CH3OH-C2H 6 at 298.15 K: 1, GEMC simulation (this work); 2, results of the group contribution hole quasichemical model [19]; 3, experimental data; 4, experimental LLV equilibrium point.

1 2

~

1

I .

o . . . . . 0.0 0.1 0.2

0.3

mum

2

•

3

~

0.4

O,at

0°6

0.7

0.8

0.9

r~nm} Fig. 3. C - C correlation function for methanol molecules: 1, results for the liquid phase I at 3.7 MPa; 2, results of GEMC simulation of pure CH3OH [7]; 3, results of N p T ensemble MC simulation of pure CH3OH [9].

i

1 iii

2

•

o o.o

o.1

0.2

0.3

0.4

0.8

0.6

0.7

0.8

3

0.9

r~mJ Fig. 4. O - O correlation functiori for methanol molecules (designations same as in Fig. 3).

10

I.Yu. Gotlib et al. / Fluid Phase Equilibria 129 (1997) l - 13

s .g"'"g~ ,4 1 S ~

2

2 •

3

1

0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

O.S

r~m)

Fig. 5. H - H correlation f u n c t i o n for m e t h a n o l m o l e c u l e s ( d e s i g n a t i o n s s a m e as in Fig. 3).

overrates the thermodynamic unfavourability of methanol-ethane mixing in the liquid phase. It is reasonable to try to improve the results for the binary system (using the L1 model potential for C H 3 O H - C H 3 0 H interactions) by introducing deviations from the Lorentz-Berthelot rules, taking into account the effect of polarization for ethane. With this in mind, we made some additional calculations with slightly modified values of • and o" for the interactions between L e n n a r d - J o n e s sites belonging to molecules of different components. The deviation parameters ~: and ~" were introduced:

2 o,~t3

So, for all combinations of L e n n a r d - J o n e s sites c~ and /3, where one of them belongs to a methanol molecule and the other to an ethane molecule, the " m i x e d " L e n n a r d - J o n e s interaction parameters were calculated using the coefficients sc and ~" characterizing the deviations from the Lorentz-Berthelot rules. Adjusting the values of these coefficients, for ~ = 1.02, ( = 1,025 we obtained at p = 1.0 MPa

5 1

4 3

------ 2

2

~

•

L

o 0.0

0.1

t

0.2

O.S

0.4

0.5

0.6

3

R

0.7

0.8

0.9

Fig. 6. O-H correlation function for methanol molecules (designations same as in Fig. 3).

l.Yu. Gotlib et a l . / Fluid Phase Equilibria 129 (1997) 1-13

11

results very close to the experimental data (see T a b l e 6; c o m p a r e with T a b l e 3). H o w e v e r , when the pressure is increased, the differences between the c o m p o s i t i o n and density o f the liquid calculated using this m o d e l and the experimental values increase, so this m o d e l appears to be no better than the J2 model with L o r e r i t z - B e r t h e l o t rules (see Table 8). Hence, the p r o b l e m o f finding the best model parameters for the m i x e d interactions in the m e t h a n o l - e t h a n e system still remains. W h e n the pressure in the system with two liquid phases decreases, it is rather difficult to return to the l i q u i d - v a p o u r equilibrium. H a v i n g decreased the pressure f r o m 3.7 to 3.2 MPa, we had to generate m o r e than 2 mln. configurations to obtain the required density o f phase II and about 5 mln. further configurations to restore the composition o f phase I corresponding to the l i q u i d - v a p o u r equilibrium. It can be concluded (also on the basis of the w o r k of van L e e u w e n et al. [18]) that NVT G E M C calculations can produce an additional, m o r e accurate vision o f the phase b e h a v i o u r o f the system under pressure near the L L V equilibrium point.

2.2. Structural characteristics The radial distribution functions characterizing correlations b e t w e e n methanol molecules for phase I at p = 3.7 M P a and Xc2rL = 0.24 (when the simulated system is at liquid-liquid equilibrium) are close to those calculated for pure methanol. H o w e v e r , the first peaks b e c o m e higher and sharper in the presence o f ethane (Figs. 3 - 6 ) . Thus, the addition o f a non-polar c o m p o n e n t (ethane) " c o m p r e s s e s " the a r r a n g e m e n t o f methanol molecules, especially that o f their h y d r o x y l groups (the peaks for the correlations o f O and H a t o m s sharpen significantly m o r e than for those for C - C correlations). This can be interpreted as the " l y o p h o b i c e f f e c t " when non-polar groups are " p u s h e d o u t " from the polar m e d i u m . T h e a v e r a g e n u m b e r o f hydrogen bonds per C H 3 O H molecule does not change m u c h on addition o f C 2 H 6, the chains o f H - b o n d e d molecules only b e c o m i n g less branched (this is expressed in the increase of the percentage o f molecules f o r m i n g two H - b o n d s and the decrease of the

Table 8 Thermodynamic properties of coexisting phases of the methanol-ethane binary system at 298.15 K (pressure range from 1.0 to 3.0 MPa) calculated by the GEMC method using the LI model with deviations from Lorentz-Berthelot rules (c = 1.02, ~"= 1.025), with the number of particles in the MC cell N = 864 (this work) Pressure (MPa) 1.0

2.0

3.0

Ethane molar content: in phase I in phase II

0.039 + 0.002 0.984 + 0.009

0.061 _ 0.002 0.99 + 0.01

0.096 + 0.003 0.99 + 0.01

Configurational energy (kJ tool 1): for phase I for phase II

- 36.4 _ 0.2 -0.42+0.05

- 36.2 _ 0.2 - 1.04+0.06

- 35.7 + 0.3 - 1.6+0.1

Molar volume (cm 3 mol 1): of phase I of phase II

42.1 + 0.2 2250 + 180

42.1 _ 0.3 1000+ 110

42.7 + 0.3 600+ 90

"Virial" pressure in phase II (MPa)

1.01 + 0.05

2.01 _-+-0.06

3.01 + 0.06

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amount of those forming three such bonds). In general, for all the systems under investigation the two-coordinated molecules are dominant (Table 4); this is also the case for pure methanol and the system methanol-carbon tetrachloride [20]. Notably, this fraction seems to be practically independent of the mole fraction for both solutions, CH3OH-C2H 6 and CH3OH-CC14. We also calculated O - O and O - H coordination numbers within the first coordination spheres in phase I at 3.7 MPa; the obtained values did not differ (within the limits of statistical uncertainty) from those for pure methanol at 298.15 K [7].

3. Conclusions In general, the results of this work allow the conclusion that reasonably satisfactory agreement with experiment can be achieved in the GEMC simulation of the CH3OH-C2H 6 binary system using relatively simple model potentials, although deviations in the calculated LLV equilibrium pressure and the compositions of the critical phases from the experimental values are noticable. The possibility of improving the model by adjusting the Lennard-Jones parameters of " m i x e d " interactions remains. At present, we plan to carry out calculations of binary mixtures containing ethanol and other longer alcohols and hydrocarbons; this will allow estimation of the influence of hydrocarbon chain lengths on the properties of alcohol-alkane binary systems.

4. List of symbols L~t~ bond length between sites oe and /3 p pressure q,~ charge on site oe r,~t~ distance between sites o~ and /3 T temperature V volume x mole fraction 4.1. Greek letters

E o-

Lennard-Jones well depth Lennard-Jones diameter

Acknowledgements Financial support by INTAS (contract N 1010-CT93-0022) and the Netherlands Organization for Scientific Research (NWO) is gratefully acknowledged.

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