New Analytic Techniques for Petroleum Fluid Characterization Using Molar Refraction

Transcription

1 SPE New Analytic Techniques for Petroleum Fluid Characterization Using Molar Refraction Hassan Touba, SPE, G.Ali Mansoori, SPE, U. of Illinois at Chicago, and Amir M. Sam Sarem, SPE, Improved Petroleum Recovery Consultants where n is the index of refraction and v is the molar volume. The molar refraction of a substance can also be expressed in terms of the polarizability by using Clausius-Masotti. 1 equation R=(4/3)N 0 a... (2) Abstract Molar refraction of pure hydrocarbons, petroleum fractions, and other compounds present in petroleum are shown to represent well the asymmetry of such fluids. Molar refraction is used to correlate density, parachor, and other properties of hydrocarbons with an accuracy that was not achieved before. Various calculations are made to demonstrate the accuracy of the proposed new analytic techniques for various reservoir fluids characterizing properties. Molar refraction characterizes the pure as well as the complex hydrocarbon mixtures and can be measured directly and accurately. It is shown that molar refraction is a more appropriate property to correlate the asymmetry of hydrocarbon fractions than the other existing methods. Plenty of the molar refraction data have been reported in the API Data Book for all the hydrocarbons and non-hydrocarbon compounds making it possible to extend the applicability of the proposed technique to high molecular weight ranges. Introduction The molar refraction which can be measured in the laboratory is a direct measure of the London dispersion forces which affect the PVT behavior of pure fluids and mixtures. The molar refraction, 2 2 R=[(n -1)/(n +2)]v R. is... defined by the following equation: (1) where N 0 is the Avogadro number and a is the polarizability. If a substance has a permanent dipole moment. then the polarizability a is the sum of two tenns: o. = O.o+O. µ -... ( 3) where a 0 is the distortion polarizability related to the displacement of the electronic cloud of a molecule with no permanent dipole moment in an electrical field and o. µ is the orientation polarizability which arises from the tendency of the permanent dipole moment µ to be oriented in the direction of the applied field. The orientation polarizability, ' w is related to the dipole moment and is inversely proportional to the absolute temperature l. 2 a µ =µ /(3kT)... (4) In this equation, k is Boltzmann constant and T is the absolute temperature. Substituting Eqns. (3) and (4) into Eq. (2), we get the following equation for the molar refraction. 2 R = (4/3) N 0 [o. 0 + µ /(3kT)]... (5) We may assume methane as a reference substance for which the dipole moment is zero (µ CHI = 0), and obtain the molar refraction of other substances with respect to methane. 507

2 H. Touba, G.A. Mansoori, A.M. Sam Sarem 2 R* = R/Rc84 = [a0 + µ 2 /(3k1)] /«o,ch4... ( 6) Fig. 1 represents the variations of R "' with respect to o./=a.0/o.0,ch4 for the nonpolar pure liquids listed in Table 1. According to Fig. 1, it can be seen that R "' is linearly proportional to a./. It can be shown that the interaction between molecules are intimately related to light dispersion. As light travels through a substance, the valance electrons of the molecules are disturbed so that the light is refracted. The degree of absorption and transmission of light depends on the instantaneous charge distribution of these electrons. The same charge distribution is responsible for the induced dipole moment expressed in London dispersion potential energy, <I> d which is approximated by the following equation 1. clld = -(2/3) hv 0 2 tr6... (7) where r is the intermolecular distance, his Plank's constant and v 0 is the characteristic frequency of the molecule which is the same as the one used for dispersion of light by a molecule. Therefore, molar refraction is a direct measure of London dispersion forces which influence the volumetric behavior of fluids. Riazi and Al-Sahhaf 2, 3 proposed the following correlation for the estimation of molar refraction in terms of molecular weight for n-alkanes, n-alkylcyclopentanes, n-alkylcyclohexanes, n alkylbenzenes and single carbon number hydrocarbons existing in crude oils and hydrocarbon-plus fractions. Rip =d 1 -exp(di -d 3 M d4 )... (8) In this equation, Rand p are the molar refraction and density, respectively, M is the molecular weight, and constants d 1, dz, d 3 and d 4 are given for various hydrocarbons in Table 2. The above correlation can also be applied to petroleum mixtures using a pseudocompound approach. The authors assumed that the pseudocompounds in a petroleum mixture are n-alkanes (paraffins), n-alkylcyclopentanes (naphthenes), and n alkylbenzenes (aromatics), each having a molecular weight the same as that of the fraction in the petroleum mixture. Variations of the dimensionless molar refractions R* for the compounds listed in Table 3 have been plotted versus their dimensionless critical properties <T/ =T/I c,ch4 p c * =P/P c, CH 4 v / =v/v c, rn4) in Figs According to these figures, there is not a direct relationship between the molar refraction and critical temperature and pressure. However, Fig. 4 depicts an approximate linear relationship between the dimensionless molar refraction and critical volume, which arises from the fact that the molar refraction is linearly related to molar volume as shown by Eq. (1). Therefore, the molar refraction which can be measured easier and more accurately than the critical volume may be utilized as the third parameter in equations of state. There has been an extensive study on the development of mixing rules for the molar refraction of liquid mixtures. These mixing rules have been tested for binary systems at specified conditions 4 7. Some of these mixing rules such as Lorentz Lorentz and Galdstone-Dale relations are based on the electromagnetic theory of light assuming molecules to be dipoles or assemblies of dipoles induced by an external field. In the literature, there have been different approaches to deal with molar refraction to predict various macroscopic properties. A summery of some of the applications of molar refraction in PVT and surface tension calculations is given in the following sections. Prediction of the Density of Two-Phase Hydrocarbon Mixtures Using Molar Refraction One of the earliest approaches to predict the density of hydrocarbon mixtures using molar refraction was proposed by Sarem and Campbell 8. They introduced the molar refraction as the third parameter in the corresponding states treatment of petroleum fluids to predict the PVT behavior of hydrocarbons. Then using an appropriate mixing rule, they were also able to predict the liquid density of hydrocarbon mixtures fairly well particularly in the two phase region near the critical point Sarem and Campbell 8 showed that the molar refraction has a linear relationship with the critical compressibility factor, Z c, for a number of pure normal hydrocarbons which are found in heptane-plus portion of gas condensate and volatile oil. They used an average molar refraction with the following pseudocritical mixing rules to predict the molar volume of liquid and vapor of several binary and ternary systems in the two phase and single phase region near the critical point. and P pc = T pc 2, x iz cj I, I, X; Xi n ij ( 1 0) where T and P pc I I J pc are pseudocritical temperature and pressure, respectively, X;, x i are the mole fraction of components i and j, and z c. is its critical compressibility factor of component i. I The authors proposed two mixing rules for - and n ii in Eqs. IJ (9) and ( 10). In the first case, they used the geometric mean: 508

3 H. Touba, G.A. Mansoori, A.M. Sam Sar 3 j)+l 1/2 +l 1/2 lj I I l J J J.. =(Z c.t c. /P c.) (Z c.t c. /P c )... (11) 1/2 1/2 n. i J = ( Z c.t c./p c.) (Z c.tjp c.)...( 12) I I l J J J and in the second case they used the harmonic mean: which predicts densities of hydrocarbon systems very accurately. In their equation, the repulsion term of Redlich-Kwong equation has been modified using molar refraction data. P = RT/ (v-b) - a/ [T 0 5 v(v+ b) J... (1 7) In this equation, the parameter "a" is a= r 2 T}. 5 / P c (1 8) The exponent p in the above equations has the following values: = 2.2 for F 0.4 = F for 0.4 < F < (15) = 1.0 for F 2.0 where the parameter "F' is defined by F =(PI, xl c ) / (TI, xl c.)... ( 16) i I i 1 To calculate densities, the following steps were proposect8: First the parameter "F' has to be calculated in order to determine p. Using Eqs. (9) and (10), pseudocritical pressure and temperature (P pc and T p c ), and reduced pressure and temperature (P p r and T p r) are obtained. The next steps are the computation of the average molar refraction and the selection of a reference pure nonnal hydrocarbon which has the same molar refraction as the mixture. Based on the critical properties of the reference hydrocarbon and pseudocritical properties of the mixture, equivalent pressure and temperature can be obtained (P 0 = P 0 P p r' T' = T c T p r > The compressibility factor of the reference substance at P' and T' will be equivalent to the compressibility factor of the mixture at P and T. Sarem and Campbell applied their method to predict the densities of three binary and ternary hydrocarbon mixtures and seven gas condensates having properties of the heptane-plus fractions. They reported an overall absolute average deviation in density of 3.70% for the mixing rules where the geometric mean was used, and an overall average deviation of 2.86% where the harmonic mean was used. Appllcatlon of Molar Refraction In Prediction of Hydrocarbon Densities Riazi and Mansoori 9 presented a simple cubic equation of state 509 The authors have considered the fact that for liquid systems in which the free space between molecules decreases, the role of parameter "b" becomes more important than that of parameter "a". Since the parameter "b" and molar refraction have the same physical meaning, "b" can be expressed in terms of molar refraction. b=[ rt C /P c ]o(r*,t, )... (19) where R* is the ratio RIR ch4 as defined by Eq. (6), and o has the following form. o 1 = 1 + (R * -1) { 0.02 ( exp(-1000 I T,11 )] (T,-1) }... (2 0) In this derivation, the authors have considered that R* is almost insensitive to temperature. According to Table 3, the proposed equation was reported to have an overall absolute average deviation of 2.80% for the liquid density prediction of 94 compounds. In Table 3, molar refraction data were taken from TRC Thermodynamic Table 10 or calculated using Eq. (1), R CH4 = for the reference fluid (methane). Riazi and Mansoori 9 have reported an average error of 1.3% for the density prediction of pure C 1 -C 40 hydrocarbons and 1.7% for hydrocarbon mixtures (C 1 -C 40 ) at pressures as high as 700 bars and temperatures of 1000 K. For mixtures, the authors have recommended the van der Waals one-fluid mixing rules for critical temperature and pressure 11. R * * m = I, I, x i x i R.....(23) i j lj Although Riazi-Mansoori equation has a very good accuracy for the mixture density calculations, it can not predict the excess

4 4 H. Touba, G.A. Mansoori, A.M. Sam Sar volume with the same ac.curacy. Therefore, we will present a method to derive an interaction parameter for this equation in the following section using corresponding states theories. Development of a Correlation for Molecular Interaction Parameter of Rlazl-Mansoorl EOS Interaction parameter i has been used in equations of state for mixtures in order to take into account the interaction between unlike molecules of a mixture. The interaction term is proposed according to the following combining rules. RM 1/2 T c.. =(1- J. )(T c,t c.)...(2 4) lj l J 1/3 1/3 3 P c.. =8T c.,/ [(TJP c.) +(TJP c.) ]... (2 5) lj lj I I J J * * 1/3 * 1/3 3 R.. = (R. IJ I J +R. ) / 8... (26) In this work we will derive a correlation to predict the interaction parameter k i i RM. According to the theories of corresponding states, macroscopic critical properties (v c, T c P, c ) are related to the molecular properties (energy parameter) and o (distance parameter) by: 2 2 a= r T c / P c... (33) The van der Waals mixing rule may be used for mixtures: aa =I. L x;xi (aa)...(34) i j with the following interaction term IJ PR 1/2 (aa). = (1- i )[(aa). (aa)j......(35) IJ I J The Peng-Robinson parameter "a", is related to T/!P c and the corresponding molecular parameters. aext/fp c ext CJ 3.. (36) Using the equivalent of "a" from the above proportionality in Eq. (35), we can derive the following equation: Comparing Eqs. (31) and (37), we will find a relationship between k i i PR, k i i RM and molecular properties. T c ex. (27) v c ex CJ (2 8) p c ex /CJ (29) Applying molecular parameters to Eq. (24 ), the following relationship will be obtained. RM 1/2 E ij = (1- j )(E;E) ( 3 0) Multiplying both sides of the above equation by CJ ii 3 At this stage, we will apply the same theory to Peng Robinson equation of state to derive a relation between interaction parameter and molecular properties. Peng-Robinson equation of state is widely used for thermodynamic property calculations: P =RT / (v-b) - aa / [v(v+b)+b(v-b)j... (32 ) Rearranging the above equation and considering that O;=(o;+cri)/2, we obtain RM PR 3 3 1/]. 3 (1-k;i )=(1- i )( CJ ; CJ i) / [ ( CJ;+cr}/2]... (39) This relationship will be further simplified to contain only measurable quantities by considering that CJ 3 0< TPc RM PR 1/2 (1-k;i ) = 8 (1- i ) [(TJP 0.) (T 0/P 0 )] / I I J J 1/3 1/3 3 [(T 0. /P 0.) +(TJP c.) ]... (40) I I J J Gao 12 developed a simple correlation to evaluate binary interaction parameters of the Peng-Robinson equation of state for light hydrocarbon mixtures (C 1 -C 10 ). In that correlation binary interaction, k;i PR, is a function of critical temperatures and compressibility factors of the components. PR 1/2 { 1-k i j )=[2{T c T c.) /{T c +T c )]... (41) l J l J where Z c.. = (Z c _+ZJ / 2. lj l J z ij 510

5 H. Touba, G.A. Mansoori, A.M. Sam Sar 5 Replacing Eq. (41) into Eq. (40), we get Tr = T I Tc. and P O is a temperature-independent, compounddependent constant which is related to molar refraction. P 0 = (T/ 3112 ;P/ 16 ) [ * 2 x 10 (R /T b, )]... (45) Applying the above equation for the interaction parameter, the densities of the binary system benzene-heptane are calculated at 20 c for various compositions. The results are compared with the experimental data 13 in Table 4. The absolute average deviation in density for this binary system has decreased from 0.27% for the original equation to 0.20% by utilizing the proposed interaction parameter equation. Similar comparisons with experimental data 13 are made for other binary systems at 20 C in Table 5. It can be seen from this table that the overall absolute average deviation in density is reduced from 0.95% to 0.93%. The improvement in the excess volume calculations is by far more appreciable. Table 6 presents the experimental molar excess volumes of the system n-heptane and 2,2- dimethylbutane 14 at 25'C, the calculated excess volumes using the original Riazi-Mansoori equation and the equation with the interaction parameter. Similar calculations have been performed for other binary systems 14 at 25 'C in Table 7. The results show that by using Eq. (42) for the interaction parameter, the absolute average deviation decreases considerably for most of the binary systems. Prediction of Surface Tensions Using Molar Refraction One of the important properties of liquids is the surface tension which is the force exerted in the plane of the surface per unit length. Hirschfedler et al. 1 reviewed several methods to estimate the surface tension of pure liquids and liquid mixtures. Macleod15 proposed a simple empirical formula which was modified later by Sugden 16 as follows. 4 <1=[P(p 1 -pv)]... (43) In this equation p 1 and p v are the molar densities of liquid and vapor, respectively, and Pis the parachor constant. Boudh-Hir and Mansoori 17 derived a statistical mechanical expression for surface tension which has the same density dependency as in Eq. (43). However the parameter P depends on the molecular structure and has a temperature functionality. Recently, Escobedo and Mansoori 18 proposed the following expression for the parameter P which is molar refraction dependent P = P 0 (1-T,) T, Exp ( /Tr T, )... (44) where R* is the ratio of molar refractions, R/R c84 defined by Eq. (6) and T hr is the reduced normal boiling point. Since the parachor and the molar refraction both depends on the molecular structure, the above relationship can exist between these two properties. In order to obtain the liquid and vapor molar densities in Eq. (43), the molar refraction-dependent equation of state by Riazi and Mansoori 9 has been used. Using Eqs. (43)-(45), Escobedo and Mansooril 8 were able to predict the values of surface tension for 94 compounds. The results are reported in Table 3 from which it can be seen that the predictions obtained from these equations are quite in agreement with experimental data 10, I Experimental parachors were taken from the values reported by Quayle 22 and the physical properties from Reid et al. 23. According to Table 3, the overall absolute average deviation for surface tension calculations is 2.57% for all temperatures considered. Eqs. (43) and (44) have been extended to mixtures by Escobedo 24. The following expression is proposed for the calculation of the surface tension of mixtures <J m = [(l-t) T, exp ( /Tr Tr ). I v 4 (P o.m P 1.m -P o,,. P v.m)]... (46) where o m is the surface tension of the mixture; T =T / T 0 ; T r m c m is defined by Eq. (21); p 1 and p are the equilibrium,jll v,m densities of the liquid and vapor phase, respectively, which can be calculated using Riazi-Mansoori equation along with the interaction parameter equation developed in the preceding section. To determine the temperature-independent parameters P o. m and P\, m for the liquid and vapor phase, the following mixing rule is proposed. The cross-parameter P 0.. is based on the following combining JJ rule. 511

6 6 H. Touba, G.A. Mansoori, A.M. Sam Sar P.. =(l-m.. )(P 0.P 0. }1 12 (48) 0>J IJ J where m; j is a binary interaction parameter. The crossparameters for temperature and pressure are calculated using Eqs. (24) and (25). respectively. Escobedo 2 4 predicted the surface tensions for 32 sets of data of binary mixtures and compared the results against the experimental surface tension data In general, a good agreement between the predicted and the experimental values has been reported for surface tensions as shown in Table 8. a = distance parameter in potential energy function, A O'= surface tension, dyne/cm Subscripts c = critical property i & j = component i & j I= liquid m = mixture property pc = pseudocritical property r = redoced property v = vapor Conclusion The results shown herein indicate that the use of molar refraction as the measure of asymmetry of reservoir fluid fractions is inherently simple and yields more precise results than other available methods. It can be applied for various reservoir engineering calculations in which reservoir fluid characterization are needed. The applications of molar refraction have been studied in predicting various properties including PVT behavior of hydrocarbons and surface tension. Nomenclature a= equation of state parameter b = equation of state parameter -27 h = Plank's constant, x 10 erg-sec k= Boltzmann constant, x erg/k k; J = interaction parameter M = molecular weight, g/mol n = index of refraction 23 = Avogadro number, x 10 molecules/mo! P = pressure, bar P = parachor constant P 0 = parameter defmed by Eq. (46) r = intennolecular distance, A R = molar refraction. cm 3 /mo! T = absolute temperature. K v = molar volume, cm 3 /mol :x = mole fraction Z = compressibility factor Greek letters a= polarizability, cm 3 o = molar refraction-dependent parameter in Eq. ( 19) e = energy parameter in potential energy function, erg <t> d = dispersion potential energy. erg µ = pennanent dipole moment, Debye v O = characteristic frequency p = molar density, movcm 3 Acknowledgments The authors are indebted to Dr. Joel Escobedo for helpful discussions. This research is supported in part by The National Science Foundation grant No. CTS References l. Hirschfelder, J. 0., Curtiss, C. F. and Bird, R. B.: Molecular Theory of Gases and Liquids, John Wiley & sons, New York, NY (1964). 2. Riazi, M. R. and Al-Sahhaf, T. A.: "Physical Properties of n Alkanes and n-alkylhydrocarbons: Application to Petroleum Mixtures," Ind. Eng. Chem. Res. (1995) 34, Riazi, M. R. and Al-Sahhaf, T. A.: "Physical Properties of Heavy Pelroleum Fractions and Crude Oils," Fluid Phase Equilibria (1996) 117, Heller, W. J.: "Remarks on Refractive Index Mixture Rules," J. Phys. Chem (1965). 69, Shindo, Y. and Kusano, K. J.: "Densities and Refractive Indices of Aqueous Mixtures of Alkoxy Alcohols," Chem. Eng. Data (1979) 24, Aminabhavi, T. M. J.: "Use of Mixing Rules in the Analysis of Data for Binary Liquid Mixtures," J. Chem. Eng. Data (1984) 29, Taslc, A. Z., Djordjevic, B. D., Grozdanic, D. K. and Radojkovic, N.: "Use of Mixing Rules in Predicting Refractive Indices and Specific Refractivities for Some Binary Liquid Mixtures," J. Chem. Eng. Data (1992) 37, Sarem, A. M. and Campbell, J. M.: "Prediction of the Density of Two-phase Hydrocarbon Systems Particularly Near the Critical Region," SPE J. (1965) 234, Riazi, M. R. and Mansoori, G. A.: "Simple Equation of State Accurately Predicts Hydrocarbon Densities," Oil and Gas J. (1993) 91, Hall, K. R., (ed.): TRC Thermodynamic Table-Hydrocarbons, Thermodynamic Research Center, Texas A&M Univ. System, College Station (1986). 11. Mansoori, G. A.: "Mixing Rules for Cubic Equation of State," American Chemical Society Symposium Series 300, Part 15, Washington, D. C.(1993),

7 H. Touba, G.A. Mansoori, A.M. Sam Sar Gao, G.: "A Simple Correlation to Evaluate Binary Interaction Parameters of the Peng-Robinson Equation of State," Fluid Phase Equilibria (1992) 74, Qin, A., Hoffman, D. E. and Munk, P.: "Excess Volume of Mixtures of Alkanes with Aromatic Hydrocarbons," J. Chem. Eng. Data (1992) 37, Kimura, F. and Benson, G. C.: "Excess Volumes of Binary Mixtures of n-heptane with Hexane Isomers," J. Chem. Eng. Data (1983) 28, Macleod, D. B: "Relation Between Surface Tension and Density," Trans. Faraday Soc. (1923) 19, Sugden, S.: "The Variation of Surface Tension with Temperature and some Related Functions," J. Chem. Soc. (1924) 12S, Boudh-Hir, M. E., and Mansoori, G. A.: "Statistical Mechanics Basis of Macleod's Formula," J. Phys. Chem. (1990) 94, Escobedo, J. and Mansoori, G. A.: "Surface Tension Prediction for Pure Fluids," AJChE J. (1996) 42, Jasper, J. J.: "The Surface Tension of Pure Liquid Compounds," J. Phys. Chem. Ref. Data (1972) 1, Beaton, C. F., and Hewitt, G. F.: Physical Property Data for the Design Engineer, Hemisphere, New York (1989). 21. Grigoryev, B. A., Nemzer, B. V., Kurumov, D. S. and Sengers, J. V.: "Surface Tension of Normal Pentane, Hexane, Heptane, and Octane," Int. J. Thermophys. (1992) 13, Quayle, 0. R.: "Surface Tension and Parachor of Hydrocarbons," Chem. Rev. (1953) S3, Reid, C.R., Prausnitz, J. M. and Poling, B. F.: The Properties of Gases and Liquids, McGraw-Hill, 4th Edition, New York (1988). 24. Escobedo, J.: Flow Behavior and Deposition of Heavy Organic Particles Contained in Crude Oil, Ph.D. Thesis, University of Illinois at Chicago, IL ( 1995). 25. Schmidt, R. L., Randall, J. C., and Clever, H. L.: "The Surface Tension and Density of Binary Hydrocarbon Mixtures: Benzene-n-Hexane and Benzene-n-Dodecane," J. Phys. Chem. (1966) 70, Shipp, W. E.: "Surface Tension of Binary Mixtures of Several Organic Liquids al 25 C," J. Chem. Eng. Data (1970) 1S, Evans, H. B., Jr. and Clever, H. L.: "Surface Tensions of Binary Mixtures of Isooctane with Benzene, Cyclohexane, and n-dodecane at 30," J. Phys. Chem. (1964) 68, Deam, J. R and Maddox, R. N.: "Interfacial Tensions in Hydrocarbon Systems," J. Chem. Eng. Data (1970) IS, Teixeira, P. I. C., Almeida, B. S., Telo da Gama, M. M., Rueda, 1. A., and Rubio, R. G.: "lnterfacial Properties of Mixtures of Molecular Fluids. Comparison between Theory and Experiment: CH 3 I + CCl 4 and CH 3 CN + CCl 4," J. Phys. Chem. (1992) 96, Lam, V. T. and Benson, G. C.: "Surface Tensions of Binary Liquid Systems: I. Mixtures of Nonelecrolytes," Can. J. Chem. (1970) 48, TABLE 1-VALUES OF R AND a; FOR NONPOLAR COMPOUNDS Components Methane Ethane Propane n-butane Ethylene I so-butane n-pentane n-hexane n-heptane Cyclohexane Benzene Carbon Tetrachloride TABLE 2-VALUES OF CONSTANTS IN EQ. (8) FOR VARIOUS HVDROCARBONS2, 3 Hydrocarbon Cno. range d, d, d, -alkanes C 5 -C ' n-alkylcyclopentanes C 5 -C n-alkylcyclohexanes C 6 -C :;n n-alkylbenzenes t C a -C, single carbon number Cs -C 5l (SCN) hydrocarbons « d d tfor n-alkylbenzenes, Eq. (8) takes the form RI p=-d 1 + exp (d 2 -d 3 M ') 513

8 8 H. Touba, G.A. Mansoori, A.M. Sam Sar TABLE 3-PROPERTIES OF ORGANIC COMPOUNDS AND COMPARISONS AGAINST EXPERIMENTAL DATA FOR DENSITY AND SURFACE TENSION 18 Compound T. pc Ft Tb p Po Temp. density u [K] [bar] [K] [K] AAD% AAfY'!o Methane Ethane Propane n-butane Ethylene Isa-butane n-pentane lsa-pentane n-hexane Methylpentane Methylpentane ,2-Dimethylbutane ,3-Dimethylbutane n-heptane Methylhexane Methylhexane n-octane ( Methylheptane Methylheptane methylheptane n-nanane Cyclopentane Methylcyclopentane Cyclohexane , 1-Dimethylcyclopentane Methylcyclohexane Ethylcyclopentane , 1-Dimethylcyclohexane ,2-Dimethylcyclohexane Cis ,2-Dimethylcyclohexane Trans ,3-Dimethylcyclohexane Cis ,3-Dimethylcyclohexane Trans ,4-Dimethylcyclohexane Cis ,4-Dimethylcyclohexane Trans Ethylcyclohexane Benzene n Toluene a-xylene m-xylene p-xylene Ethylbenzene ,2,3-Trimethylbenzene ,2,4-Trimethylbenzene ,3,5-T rimethylbenzene n-decane n-undecane n-tridecane ,2-Dimethylhexane ,4-Dimethyl Hexane ,5-Dimethylhexane ,3-Dimethylhexane ,4-Dimethylhexane Methyl-3-Ethylpentane Methyl-3-Ethylpentane n 2,2,4-Trimethyl pentane ,2-Dimethylheptane ,2,4-Trimethylhexane ,2,5-Trimethylhexane ,3-Diethylpentane ,2,3,4-Tetramethylpentane n-propylcyclopentane so-propylcyclopentane ln -Propylcyclohexane

9 H. Touba, G.A. Mansoori, A.M. Sam Sar 9 TABLE 3-CONTINUED... Compound T, P.,t Tb p Po Temp. density er [K] [bar] [K] [K] AAD% AAD% lso-butylcyclohexane Sec-butylcyclohexane Tert-butylcyclohexane Hexene , clen Decene O.&:I 1-Dodecene n-propylbenzene , lso -propytbenzene (Cumene} EthylToluene Elhyltoluene Elhyltoluene n-butylbenzene lso-butylbenzene n Sec-Butyl benzene Tert -Butylbenzene ,4-Diethylbenzene Methylnaphlhalene : I Tetradecene Carbon Tetrachloride Chloroform , 1,2 T ricloroethane l Chlorobutane Fluorobenzene 560, Chlorobenzene Bromobenzene lodobenzene Acetone Benzonitrile Dibutylether Cyclooctane OVERALL AAD'% TABLE 4-OENSITIES OF BENZENE+ HEPTANE MIXTURE USING RIAZI-MANSOORI EQUATION TABLE 5-ABSOLUTE AVERAGE DEVIATION IN DENSITY CALCULATION FOR BINARY MIXTURES x, p-exp p-cal %error p-cal %error Components MfY% k RM AAO'/o ltm {glcm3) (k. =O) (wi1h k _ ""') (kt = 0) (witl kt) Benzene (1) + Heptane (2) Benzene (1) + Octane (2) Benzene (1) + Cyclohexane (2) Toluene (1) + Cyclohexane (2) o.n Ethylbenzene (1) + Heptane (2) Ethylbenzene (1) + Octane (2) Ethylbenzene (1)-+- Cyclohexane (2) a-xylene (1) + Hexane a-xylene (1) + Heptane (2) a-xylene (1) + Cyclohexane (2) m-xylene (1)-+- Hexane (2) AAD% m- Xylene (1) + Heptane (2) m-xylene ( 1) + Cyclohexane (2) p-xylene (1) + Hexane (2) p-xylene (1) + Heptane (2) p-xylene (1) + Cyclohexane (2) Overall AAD%

10 10 H. Touba, G.A. Mansoori, A.M. Sam Sar TABLE 6-MOLAR EXCESS VOLUMES OF N-HEPTANE (1) + 2,2 DIMETHYLBUTANE (2) x, EV-exp EV-cal %error EV-cal %error RM [an 3 /moll =O) (with k.rm) AAD% TABLE 7-ABSOLUTE AVERAGE DEVIATION IN MOLAR EXCESS VOLUME FOR BINARY MIXTURES TABLE 8-ABSOLUTE AVERAGE DEVIATION IN SURFACE TENSION FOR BINARY MIXTURES USING ESCOBEDO EQUATION Binary system m ij T[KJ AAJY¾ Ref. Benzene - Acetone a3 Benzene - Carbon tetrachloride a3 Benzene - Ethyl acetate a3 Benzene - n-dodecane Benzene - n-dodecane Benzene - n-dodecane Benzene - n-dodecane Benzene - n-hexane Benzene - n-hexane Benzene - n-hexane Benzene - n-hexane Benzene - o-xylene ) n-butane - n-decane a3 Carbon tetrachloride - Ethyl acetate a3 Cyclopentane - Carbon tetrachloride ) Cyclopentane - Benzene ) Cyclopentane - Toluene ) Cyclopentane - Tetrachloroethylene ) Cyclohexane Benzene ) Cyclohexane. Benzene ) Cyclohexane Toluene ) lodomethane - Carbon tertrachloride lodomethane Carbon tertrachloride lodomethane - Carbon tertrachloride lodomethane - Carbon tertrachloride Isa-Octane - Benzene 'Zl Isa-Octane - Cyclohexane 'Zl Isa-Octane - n-dodecane 'Zl Methane n-nonane Methane n-nonane Methane n-nonane Methane n-nonane a3 Overall AAD% 0.88 Components RM AAD%(k, =O) n Heptane + n Hexane n Heptane + 2 Methylpantane n Heptane + 3 Methylpantane n Heptane+ 2,2 Dimethylbutane n Heptane+ 2,3 Dimethylbutane Overall AAD%

11 H. Touba, G.A. Mansoori, A.M. Sam Sar ' * * i:t: 5-. i:ic: I I I I * * CX P O c 0 I I I I Fig. 1-Variations of R with respect to ao for non-polar Fig. 3-Variations of R* with respect to dimensionless compounds. critical pressure ;... - * *.... : 5-5- i:t: ',,, 0 I I I I * T c I I I Fig. 2-Varlatlons of R* with respect to dimensionless Fig. 4-Variations of R 0 with respect to dimensionless crlllcal temperature. critical volume. 517