Znd. Eng. Chem. Res. 1991,30,1931-1936 Kun, K. A.; Kunin, R. Macroreticular Resins. Formation of Macroreticular Styrene-Divinylbenzene Copolymers. J. Polym. Sci. A-1 1968, 6, 2689. Kunin, R. Polymeric Adsorbents for Treatment of Waste Effluents. Polym. Eng. Sci. 1977, 17, 58. Marton, G.;Szokonza, L.; Havas-Dencs, J.; Illes, 2s. Removal of Organics from Waste Water by Macromolecular Resins 11. Separation of two Components by Liquid Adsorption. Hung. J. Znd. Chem. (Vesprem) 1981,9, 263. Podlesnyuk, V. V.; Levchenko, T. M. Adsorption Properties of Styrene-Divinylbenzene Copolymers. Chim. Tekh. Vody 1981,3,327 (in Russian). Podlesnyuk, V. V.; Klimenko, N. A. Experimental Methods of Adsorbents Recovery. Chim. Tekh. Vody 1988,10,303 (in Russian). Rees, G. H. V.; An, L. Use of Amberlite XAD-2 Macroreticular Resin for the Recovery of Ambient Base Levels of Pesticides and Industrial Organic Pollutants from Water. Bull. Enuiron. Contam. Toxicol. 1979, 22, 761. Urano, X.;Kano, H.; Tabceta, T. The Reversibilities of the Adsorption and Desorption of Organic Compounds in Water. Bull. Chem. SOC.Jpn. 1984,57, 2307.
1931
Voloshchuk, A. M.; Dubinin, M. M.; Erashko, I. T. Structure of Microporous Adsorbents and Kinetia of Physical Adsorption 2. Evaluation of Diffusion Coefficientsof Benzene and +Pentane in Micropores of Carbon Adsorbents. Zzu. Akad. Nauk. USSR Ser. Khim. 1974a, 1943. Voloshchuk, A. M.; Zolotarev, M. M.; Illin, V. I. Using the Method of Statistical Moments for Determination of Internal Diffusion Coefficients in Adsorbents with Bidisperse Porous Structure and Linear Adsorptions Isotherms. Zzu. Akad. Nauk. USSR Ser. Khim. 1974b, 1250. Weber, W. J.; Wet, B. M. Synthetic Adsorbents and Activated Carbons for Water Treatment. J.Am. Water Works Assoc. 1981, 73, 420. Zolotarev, P. P.; Pilipenko, A. I. Conection between Process of Adsorption and Desorption in Particles with Bidisperse Porous Structure. Izv. Akad. Nauk USSR Ser. Khim. 1979, 1188 (in Russian).
Received for reuieu October 1, 1990 Revised manuscript received May 1 , 1991 Accepted May 8,1991
Rheology of Oil in Water Emulsions with Added Kaolinite Clay Yuhua Yan, Rajinder Pal,' and Jacob Masliyah* Department of Chemical Engineering, University of Alberta, Edmonton, Canada T6G 2G6
The present paper deals with the rheological measurements of oil in water emulsions with added kaolinite clay. The percent oil concentration, solids-free basis, was varied up to 70% by volume. The volume fraction of clay was varied up to 0.2 based on the total volume. The clay/emuIsion mixtures displayed shear thinning behavior. Yield stress was observed, and its value increased with clay volume fraction and with oil concentration. The shear stress versus shear rate data could be fitted by the Casson model for low oil concentrations (below 40%) and by the Herschel-Bulkley model for higher oil concentrations. On the basis of the experimental data,a correlation was developed to evaluate the relative viscosity of the clay/emulsion mixtures, where the relative viscosity was defined as the ratio of the viscosity of clay/emulsion mixtures to that of emulsions alone. A viscosity equation was also developed for calculating the viscosity of clay/emulsion mixtures.
Introduction Crude oil is often produced in the form of an oil/ water emulsion. Both oil in water (O/W) and water in oil types of emulsions are produced depending upon the reservoir conditions. Quite often the produced emulsions also carry some solids, mainly sand and clays. Solids content in the emulsions is normally low, although higher concentrations are encountered occasionally. The knowledge of the rheological properties of emulsions with added solids is important for the design and operation of production gathering facilities and emulsion pipelines. In the available literature, the rheological properties of solids suspensions and of oil/water emulsions have been studied extensively (see van Olphen (1977)for clay suspensions and Sherman (1970)and Pal (1987)for emulsions). However, little work has been reported on the flow behavior of emulsions with added solids. Following the study on the rheology of oil in water emulsions with added silica sand, glass beads, and polystyrene particles (Pal and Masliyah, 1990;Yan et al., 1991a,b),the present study investigates the effects of kaolinite clay addition to oil in water emulsions.
* Author to whom
correspondence should be addressed. Present address: Department of Chemical Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
Experimental Section Materials. The oil used was a refined mineral oil (Bayol-35),having a density of 780 kg/m3 and a viscosity of 2.4 mPa-s at 25 "C. The prepared emulsions were oil in water type; Le., the oil droplets formed the dispersed phase and the aqueous emulsifier solution formed the continuous phase. The emulsifier used to stabilize the emulsions was Triton X-100,a nonionic-type emulsifier. The concentration of the emulsifier was kept at 1% by volume, based on the aqueous phase. The clay used was kaolinite Hydrite-Flat D supplied by Georgia Kaolin Company. The median diameter of the dry clay particles was 5 pm. Experimental Procedure. The clay particles were first dispersed in the 1% Triton X-100water solution in an 1-L beaker. To ensure a good dispersion of the clay particles, shear was applied by a Gifford-Wood homogenizer (model 1-LV),which is a rotor and stator type mixer. Then, a known volume of oil was slowly added to the clay suspension while shear was applied. The mixture of clay and oil was continuously sheared for another 10-15 min after the completion of the oil addition. The mixing speed of the homogenizer was carefully chosen to avoid air entrainment and at the same time maintain a fairly high shear. Rheological measurements were carried out by use of a coaxial cylinder viscometer (Contraves Rheomat 115)
0888-5885/91/2630-1931$02.50/00 1991 American Chemical Society
1932 Ind. Eng. Chem. Res., Vol. 30, No. 8, 1991 100.0- r
100 r
1
.
_ 7
--___
-
-----
Oil7Concentration
Synthetic 0 'W Emulsions
-
10
0.1
*/
' 1 1 L
10
100
1000
10
1E4
100
1000
1E 4
7 ,( l , / S ) Figure 2. Rheograms of synthetic oil in water emulsions. 1000
n v,
d
a
E
V
6
F
100
1
1\
1
-
1000
Clay Suspensions
20% O/W Emulsion
h
'?
A 0078 A 0 109 V 0 143
6
a
V 0.118
100
0
0.150
V 0.185
E
I
'PC
A 0.064 A 0.090
'PC
v
I
B-
$ c
101
10
I
1 ' 10
1
I
100
1000
1E4
b) ?* ( l / s ) Figure 1. (a) Rheograms of clay suspensions. (b) Variation of viscosity of clay suspensions with shear rate.
with a double-gap system (gap width 500 pm). The bottom clearance of the cylinder was 330 pm. During the measurements, the sample was kept at a temperature of 25 "C.
1E4
50% O/W Emulsion
A 0.041
h
d
Results and Discussion Rheology of the Clay Suspensions. Figure 1 shows the rheological data for the clay suspensions without any oil addition. Figure l a shows the rheograms of the clay suspensions at different clay volume fractions. A t low values of shear rate and high clay concentration, the shear stress tends to level off. This is indicative of the presence of a yield stress. The variation of the apparent viscosity, defined as the ratio of the shear stress to the shear rate, with the shear rate is shown in Figure lb. As would be expected, at a given shear rate, the viscosity of the clay suspensions increases with the clay volume fraction. Also, Figure l b shows that the viscosity of the clay suspensions decreases with increasing shear rate, Le., the clay suspensions display shear thinning behavior. Rheology of O/WEmulsions with Added Clay. The rheology of the oil in water emulsions was reported by Pal and Masliyah (1990) and by Yan et al. (1991a). These emulsions exhibited Newtonian behavior at low oil concentrations (below 40%) and exhibited shear thinning behavior at oil concentration higher than 40%. The rheograms for the oil in water emulsions are shown in Figure 2. Figure 3 shows the variation of the viscosity of the oil in water emulsion with the presence of clay. Results for two oil concentrations are shown, namely, 20% and 50%. Here the percent oil concentration is given on solids-free basis. This is a convenient mode of quantifying the oil concentration. For a given clay/emulsion mixture, irrespective of the clay volume fraction, the volume ratio of the oil to water remains constant. The clay volume fraction
1
a
1000
v
100
10
I-
5' 0.1
I
1.0
10.0
100.0
1000.0
1.OE4
b) 7, ( l / s ) Figure 3. Variation of viscosity of clay/emulsion mixtures with shear rate: (a) 20% oil concentration; (b) 50% oil Concentration. pc is based on the total volume of the clay/emulsion mixture. The addition of the clay to both the 20% and 50% oil emulsions has a profound effect on the clay/emulsion mixtures. The mixture viscosity increases considerably by the clay addition. In all cases the clay/emulsion mixtures display shear thinning behavior. All the rheological data shown were obtained with the use of a double-gap measuring device as was indicated earlier. Measurements with a single gap (a gap width of 1855 km) gave rheograms similar to those obtained with the double measuring device. Yield Stress. Examination of rheograms for the clay suspension (Figure la) and those for the clay/emulsion mixture corresponding to Figure 3 reveals that the shear stress tends to approach a plateau as the shear rate decreases, particularly at high clay content. This is a characteristic for systems having a yield stress ( T J . There are several methods for direct measurement of yield stress, e.g.,
Ind. Eng. Chem. Res., Vol. 30,No. 8, 1991 1933 8
I
100.0 , 'pc A 0.064 v 0.090
I
v
c >
20% O/W Emulsion
I
50% O/W Emulsion
0.118
h
m
0 0.150 0.185
a
+
10.0
v
t-"
4
I
t-
0 ' 0
1
10
20
30
40
50
1.0
0.1 0.1
1.0
10.0
100.0
1000.0
1.OE4
60
Y ! (l/s)
dY Figure 4. Evaluation of yield stress wing the Casson model for clay/emuleion mixtures for 20% oil concentration.
Figure 6. Evaluation of yield stress using the Herschel-Bulkley model for clay/emulsion mixtures for 50% oil concentration. 10
10
70%
50% O/W Emulsion
i
I
i
I
Oil C o n c e n t r a t i o n
c >
1
0
10
20
30
40
50
0.25
60
dY
Volume F r a c t i o n of Clay, 'p,
for clay/emulsion mixtures for
Figure 7. Variation of yield stress with clay volume fraction and oil concentration.
the vane method and the stress relaxation method (Dzuy and Boger, 1985). The yield stress can vary to a great extent depending on the method and the equipment used (Barnes and Waters, 1985). For indirect measurements, i.e., extrapolation of the shear stress to zero shear rate, the yield stress is often evaluated by fitting the experimental data with a model. In the present study, the Casson model (Casson, 1959) and the Herschel-Bulkley (Herschel and Bulkley, 1926) model are used. The Casson model is given by T1I2 = TY1l2 + qm1/2?1/2 (1)
where k is a consistency coefficient and n is the power-law index. Plots of log ( T - T ~ versus ) log are shown in Figure 6 for the 50% O/W emulsion with added clay. It can be seen that by adjusting the values of the yield stress ( T ~ ) the , Herschel-Bulkley model can fit the data well. The yield stress at oil concentrationsabove and at 40% is determined by using the Herschel-Bulkley model. Figure 7 shows the variation of the yield stress with clay and oil concentration. The yield stress increases with the clay volume fraction and also with the oil concentration. At the same clay volume fraction, the mixtures of clay/ emulsion with higher oil concentrations have a higher yield stress than the mixtures with lower oil concentrations. Viscosity Correlation. Figure 8 shows a photomicrograph of the clay/emulsion mixtures. It can be seen that the clay particles form flocsthat are much larger than the oil droplets. The oil droplets have a mean diameter of about 10 pm, and the clay flocs have a mean diameter of about 50 pm, Previous studies by Pal and Masliyah (1990) and Yan et al. (1991a) indicated that, for oil in water emulsions with added solids, the emulsions behaved as a continuous phase toward the solids when the size ratio of the solids to the oil droplets is above 3. Consequently, in order to obtain a meaningful correlation for the viscosity of clay/emulsion mixtures, the O/W emulsions have to be treated as a continuous phase and the added clay (flocs) as the dispersed phase. The use of an O/W emulsion at a fixed value of oil concentration, solids-free basis, would mean a continuous phase having a constant viscosity a t a fixed shear rate. The variation of the apparent viscosity with clay volume fraction for various O / W emulsions is shown in Figure 9
Figure 6. Plota of 7lI2 versw 50% oil concentration.
where qm is the limiting viscosity at higher shear rate. According to (1) and + I f 2 follow a linear relationship and the intercept on d 2axis is the square root of the yield stress rY. Figure 4 shows the plots suggested by (1)for the mixtures of clay/emulsion where the oil concentration, solids-free basis, is 20%. It is evident that the data at a given volume fraction of clay essentially follow a straight line; i.e., the Casson model fits the experimental data quite well. As can be seen from Figure 4, the intercept of the straight lines, Le., the square root of the yield stress, increases with clay volume fraction. The yield stresses for mixtures of clay with a 30% O/W emulsion are also determined by use of the Casson model. Figure 5 shows a similar plot of T ~ versus / ~ +lI2 for the mixtures of clay and a 50% O/W emulsion. It can be seen that the experimental data can no longer be represented by straight lines, and the Casson model cannot be used to evaluate the yield stress. Thus, an alternative model, namely, the Herschel-Bulkley model, is used: T - T~ = k+" (2)
+
1934 Ind. Eng. Chem.
Res., Vol. 30, No. 8,1991 Oil Concentration
7=
0 ox
e
23.8 (l/s)
20%
A 30% A 40% V 50% 60% 0 70%
V
0.00
0.10
0.15
0.20
0.25
Volume Fraction of Clay, Qc Figare 10. Variation of relative viacoeity q-/q,,,,, with clay voli ne fraction at fixed shear rates.
't
1000 I
Clay Flocs
Oil Droplets
0.05
Figure 8. Photomicrograph of clay/emulsion mixtures. E
'2
100
Q)
a
1
Oil Concentration
0)
n
?
,oox
cd
a E
F
e
10
20%
A 30%
\
W
5
F 1
0
10
1
1
100
1000
7cow/70w, calculated 1 0.00
a)
0.05
0.10
0.15
Volume Fraction of Clay,
0.20 (pc
n
v! cd
a
E
10
5
0
1
1 0.00
b)
e 1
100 I
U
0.25
0.25
0.05
0.10
0.15
0.20
Volume Fraction of Clay, (pc
Figure 9. Variation of viscosity of clay/emulsion "Swith clay volume fraction at different oil concentrations: (a) y = 23.8 l/s; (b) y = 1231 l/s.
at shear rates of 23.8 and 1231 s-*. It can be seen that the viscosity increases with clay volume fraction and with the oil concentration. The experimental data, a t a given oil concentration (solids-freebasis), follow a straight line that can be described as (3) log tlam = log tlm + bvc where qam is the viscosity of clay/emulsion mixture, qm is the viscosity of the O/W emulsion, b is the slope of a straight line, and 4pc is the volume fraction of clay. Equation 3 can be rewritten as log (tlam/tlm)= bvc
(4)
Figure 11. Comparison of relative viacoeity q-/q,,,,, between experimental and calculated data.
It should be further noted from Figure 9 that the straight lines are nearly parallel to one another. In other words, the slope of the straight lines, b, is essentially a constant at a given shear rate, irrespective of the oil concentration. The relative viscoeity (flarw/flan) versus (pc is shown in Figure 10 at the two shear rates, i, = 23.8 and 1231 s-l. A t a fmed shear rate, it can be seen that the data for different oil concentrations (0-70%) follow the same straight line. Thus, Figure 10 (or eq 4) indicates that the relative viscosity of the clay/emulsion mixtures with respect to the viscosity of the pure emulsions is a function of clay volume fraction only, and independent of the oil concentration. However, it is clear from Figure 10 that the slope of the straight lines decreases with increasing shear rate. Leastsquaresanalysis gives the following equation for the slope b
b = 5.36
+ 6.75e-'.73x1e
(5)
Thus, the following correlation for the relative viscosity of qam/qm can be obtained: log (qam/vm)= (5.36
+ 6.75ec79x1e)(p,
(6)
Figure 11 shows the comparison between the experimental data and the calculated values from (6). It can be seen that (6) represents the experimental data quite well. There exist various classical equations to correlate viscosity data with volume fraction of dispersed phase, e.g., the Mooney-type equation (1951), the Krieger equation (1972), and the equation discussed by Kataoka et al. (1978) and Metzner (1985) which has the form tlr
= [1 - v*/A1-2
(7)
Ind. Eng. Chem. Res., Vol. 30,No. 8, 1991 1936 25
A
2o
i
1
y = 1764 (l/s)
I
/
\
E
F
i
increasing clay volume fraction and oil concentration. 2. Yield stress was observed for the mixtures of clay/ emulsion, which indicated the formation of structures due to the addition of clay. The yield stress increased with increasing clay volume fraction and oil concentration. 3. The relative viscosity of clay/emulsion mixtures with respect to the viscosity of the pure emulsions was a function of clay volume fraction only, and independent of the oil concentration, solids-free basis. A correlation was obtained for the relative viscosity, and it showed good agreement with the experimental data.
I 0.6
Acknowledgment
I
Bayol O/W Emulsions
t1
I
I
101
U
0 '
0.1
0.2
0.3
0.4
0.6
0.5
0.7
This work has been financially supported by the Alberta Oil Sands Technology and Research Authority, Contract No. 683. Drs. Vincente A. Munoz and Randy Mikula of CANMET are gratefully acknowledged for the assistance offered in taking the photomicrographs.
Volume Fraction of Oil, q0
a>
X
6
0.B
9
OS8 0.7
Y 0
1000
I
2000
3000
b) Shear Rate (l/s) Figure 12. (a) Evaluation of maximum packing fraction, qVariation of maximum packing fraction with shear rate.
(b)
where vr is the ratio of the viscosity of a dispersion to that of the suspending fluid and A is a constant. None of these equations was able to fit the present data for clay; however, (6) was capable of correlating the data of Figure 10 well. Finally, a viscosity equation can be given for q - In (6), the viscosity of the oil in water emulsion in the absence of clay, qW, can be well described by the Krieger equation, i.e. ~ o w / ~= w
(1 - p o / p o , m a J - [ 7 1 v o ~
(8)
where po is the volume fraction of oil and po,+= is the maximum packing fraction of oil. [VI is the intrinsic viscosity, which has a value of 2.5 for spherical particles, and qw is the viscosity of water. The evaluation of poposnar based on the experimental data is shown in Figure 12a. It was found that po," was a function of shear rate, which can be fitted by the equation 'Po,mlu
- 1 - (0.224/e1.26X10-'4)
-
(9)
-
Equation 9 is shown in Figure 12b. It is interesting to note that p,,max= 0.776 at i. = 0, and po,mcu 1.0 as 4 a. A similar study by Wildemuth and Williams (1985) also indicated that the maximum packing fraction was a function of the shear stress (or shear rate). Thus, one can combine (61, (8), and (9) to calculate the viscosity of clay/emulsion mixtures at any volume fractions of clay and oil, and at any shear rate. Conclusions 1. Mixtures of clay/emulsion displayed shear thinning behavior. The viscosity of the mixtures increased with
Nomenclature A = a constant involved in (7) b = slope as defined in ( 3 ) k = consistency coefficient involved in (2) n = power-law index in (2) O/W = oil in water emulsions Greek Symbols 4 = shear rate (l/s) q = viscosity (mPa.s) qr = ratio of the viscosity of a dispersion to that of the suspending fluid trow = viscosity of clay/emulsion mixtures (mPa.s) qcw = viscosity of pure clay suspensions (mPa.s) vow = viscosity of O/W emulsions (mPa.s) ow = viscosity of water (mPa.s) 7- = limiting viscosity at high shear rate 'p, = volume fraction of clay cpo = volume fraction of oil po," = maximum packing fraction of oil in emulsions 7 = shear stress (Pa) T,, = yield stress (Pa) Subscript 4 = measured at the same shear rate Registry No. Kaolinite, 1318-74-7.
Literature Cited Barnes, H. A.; Waters, K. The Yield Stress Myth. Rheol. Acta 1985, 24, 323-326. Casson, N. A Flow Equation for Pigment-oil Suspensions of the Printing Ink Type. Rheology of Disperse Systems; Mill, C. C., Ed.; Pergamon: London, 1959; pp 84-104. Dzuy, N. Q.; Boger, D. V. Direct Yield Stress Measurement with the Vane Method. J . Rheol. 1985,29 (3), 335-347. Herschel, W. H.; Bulkley, R. Kolloid Z. 1926, 39, 249. Kataoka, T.; Kitano, T.; Sasahara, M.; Nishijima, K. Viscosity of Particles Filled Polymer Melts. Rheol. Acta 1978, 17, 149-155. Krieger, I. M. Rheology of Monodisperse Latices. Adu. Colloid Znterface Sci. 1972, 3, 111-136. Metzner, A. B. Rheology of Suspensions in Polymeric Liquid. J. Rheol. 1985,29, 739-775. Mooney, M. The Viscosity of a Concentrated Suspension of Spherical Particles. J . Colloid Sci. 1951, 6, 162-170. Pal, R. EMULSIONS: Pipeline Flow Behavior, Viscosity Equation and Flow Measurement. Ph.D. Thesis, University of Waterloo, 1987. Pal, R.; Masliyah, J. H. Rheology of Oil in Water Emulsions with Added Solids. Can. J. Chem. Eng. 1990,68, 24-28. Sherman, P. Emulsion Science; Academic Press: New York, 1970. van Olphen, H. An Introduction to Clay Colloid Chemistry; Wiley: New York, 1977. Yan, Y.; Pal, R.; Masliyah, J. H. Rheology of Oil in Water Emulsions with Added Solids. Chem. Eng. Sci. 1991a, 46,985-994.
1936
Ind. Eng. Chem. Res. 1991,30, 1936-1945
Yan, Y.; Pal, R.; Masliyah, J. H. Viscosity Correlations for Emulsion-Solids Mixtures as Bimodal Systems. Chem. Eng. Sci. 1991b, 46,1823-1828.
Wildemuth, C.R.; Williams, M. C. A New Interpretation of Viscosity and Yield Stress in Dense Slurries: Coal and Other Irregular
Particles. Rheol. Acta 1985,24, 75-91.
Received f o r review October 23, 1990 Revised manuscript received March 18, 1991 Accepted March 26, 1991
The MHV2 Model: A UNIFAC-Based Equation of State Model for Prediction of Gas Solubility and Vapor-Liquid Equilibria at Low and High Pressures Smen Dahl, Aage Fredenslund,* and Peter Rasmussen Znstitut for Kemiteknik, Technical University of Denmark, DK-2800Lyngby, Denmark
MHV2 is a group-contribution equation of state based on the modified Huron-Vidal mixing rule. It combines the SRK equation of state with a model for the excess Gibbs energy, the modified UNIFAC model. The MHV2 model can be used to predict vapor-liquid equilibria (VLE) and gas solubility a t low and high pressures. Useful predictions for process calculations can be made over a wide temperature and pressure range. This work considers VLE for mixtures with gases. It describes the main features of the MHV2 model and presents tables containing parameters between 9 modified UNIFAC solvent groups and 13 gases (H2,02,N2, CO, C 0 2 ,H2S, CH4, C2H2,C2H4,C2H6, C3H6,C,H,, and C4Hlo). The gas-gas interaction parameters are all assigned the value 0. It is shown that the MHV2 model compares very well with a density-dependent local composition model (DDLC) and the group-contribution equation of state (GC-EOS). Even for complex systems the multicomponent vapor-liquid equilibria are predicted well.
Introduction Many systems treated in the chemical industry involve mixed solvents and supercritical components. Calculation of high-pressure vapor-liquid equilibria for such complex systems requires a model that can represent a large number of chemically different systems at a wide range of conditions. This paper presents a model that is applicable to the prediction of binary and multicomponent vaporliquid equilibrium compositions over a wide range of temperatures and pressures. The model is called the modified Huron-Vidal second-order model (MHV2) and uses an approach developed by Michelsen (1990a, 1990b),in which a cubic equation of state is matched with an excess Gibbs energy model at zero pressure. This approach leads to an explicit Huron-Vidal (Huron and Vidal, 1979) type mixing rule for the a parameter in an equation of state like the Soave Redlich Kwong (SRK) equation (Soave, 1972). The capability of this model to reproduce low-pressure information stored in excess Gibbs energy models has been illustrated (Michelsen, 1990a, 1990b). Furthermore, the ability of MHV2 together with the modified UNIFAC parameter table (Larsen et al., 1987) for prediction of a high-pressure vapor-liquid equilibrium has been illustrated by Dahl and Michelsen (1990). In the present paper we demonstrate that MHV2 is also able to correlate and predict vapor-liquid equilibria of gas-solvent binary systems and to predict VLE for multicomponent mixtures using the new parameters for gas-solvent interactions together with the modified UNIFAC group-interaction parameter table of Larsen et al. We also discuss precautions to be observed when using the parameter table. Modified Huron-Vidal Mixing Rule Huron and Vidal(1979) determined the a parameter of a cubic equation of state from an excess Gibbs energy *To whom all correspondence should be sent. 0888-5885191/ 2630- 1936$02.50/0
model for the liquid state, applied to infiiite pressure. The match at infinite pressure renders it impossible to use excess Gibbs energy model parameters based on lowpressure VLE information. The modified Huron-Vidal mixing rule is based on a similar approach, but the equation of state is matched with the excess Gibbs energy model at zero pressure, where the existing parameters based on low- or normal-pressure VLE information may be applied. In this work we have used the SRK equation of state and the modified UNIFAC model. The SRK equation of state may be written as follows:
p = - -RT u-b
U
U(U
+ b)
where the mixture b parameter is derived from the conventional linear mixing rule
using for the corresponding pure component parameter bii = 0.08664RT~/Pc,
(3)
The pure component a parameter is given by ai, =
0.4286(R2T,2/Pci)[f(Trj)]2 ( 4 )
with (Mathias and Copeman, 1983)
f(T,i) = 1 + C l ( 1 - (Tri)'l2)+ CZ(1 - (Tri)1/2)2 + C,(1 - (Tri)'/2)3 Tri < 1 = 1 + Cl(1 - (Tri)1/2) Tri > 1
(5)
The pure-component vapor pressures used to estimate C,,C,, and C, were calculated by using the AICHE DIF'PR compilation constants (Daubert and Danner, 1986). Values of the C parameters used in this work are given in Table Q 1991 American Chemical Society
