Znd. Eng. Chem. Res. 1990,29, 2101-2106
2101
GENERAL RESEARCH Asymptotic Effects Using Semicontinuous vis -&is Discrete Descriptions in Phase Equilibrium Computations Kraemer D. Luks,* Edward A. Turek, and Tor K. Kragas Amoco Production Company, Box 3385, Tulsa, Oklahoma 74102 The use of continuous vis4-vis discrete descriptions for the C7+ portion of a live oil is examined for a calculation especially sensitive to the nature of the C7+description, specifically, liquid dropout near an upper dew point of a live oil gas mixture. Conservation-of-mass failure in the semicontinuous flash problem, a recognized formal shortcoming of continuous thermodynamics, is shown to lead to a previously unexplained bias that occurs in saturation calculation results.
+
Introduction
F(Z) = C exp(-aZ)
There has been interest among users of equations of state in employing continuous descriptions for the characterization of the C7+ portion of crude oils when performing phase equilibrium computations. When coupled with a discrete description of the lighter components, this “semicontinuous” approach appears to be formally attractive and offers the potential to reduce computational time as well. The literature on techniques to exploit continuous thermodynamics in saturation and flash calculations (e.g., involving crude oils) has opted, for the most part, to mimic the continuous thermodynamic description with a set of pseudocomponents obtained from Gaussian quadrature procedures, primarily out of convenience, since algorithms for the (completely) discrete problem are usually available. It is recognized that the continuous or semicontinuous flush problem has internal inconsistency with respect to continuous species conservation, but this shortcoming is generally considered to be no more than an annoyance. There is a history of attempts to calculate the phase equilibria of continuous systems. Some of these efforts have been explicitly restricted to specific physicochemical models such as Raoult’s law or specific applications such as polymers. More recently, there have been attempts to formalize a continuous thermodynamic system independent (at least, relatively speaking) of the model and apply it to process design. Cotterman and Prausnitz (1985), Cotterman et al. (1985a,b; 1986), Behrens and Sandler (1988), and Shibata et al. (1987) have used this approach. Their papers are closely related to the work presented here and provide a complete set of references to earlier studies on continuous systems. Herein, for illustrative purposes, a live crude oil will be considered as a semicontinuous mixture of discrete components plus a continuous C7+fraction. The C7+fraction will be assigned an exponential distribution F(Z)extending from carbon 7 to, say, 100:
* To whom correspondence should be directed at College of
Engineering, University of Tulsa, 600 S. College, Tulsa, OK 74014-3189. 0888-5885/90/2629-2101$02.50/0
(1)
where Z is the carbon number. The mathematical framework of the continuous thermodynamic formalism incorporating this single parameter (a)distribution is detailed in Appendix I. The simplicity of this distribution combined with the wide carbon number range assigned will impose a severe test on the continuous thermodynamic formalism; one manifestation of this simplicity will be nonnegligible failure of conservation of species in flash calculations as a function of I , the continuous species designation variable. This conservation of species (mass) problem will hereafter be referred to as the “CM problem”. Given this semicontinuous mathematical framework, an example calculation will be performed and analyzed that places special attention on the heavy end portion of the C7+fraction, namely, the liquid dropout from a live crude oil + C02mixture at pressures just below that of its upper dew point at a given temperature. In this example, the heavier C7+species differentially drop out as the pressure is lowered from that of the upper dew point. Special attention will be paid to the effect of the CM problem on the computation of the upper dew point itself. For a saturation calculation, the differentially present phase has its a parameter determined by aF of the feed (see Appendix I), and the fugacity equality (eq 1-16) is satisfied for all values of I. The same fugacity compliance is met for the vapor and liquid phases in a flash calculation; however, conservation of mass at every value of Z is not ensured: ?
#(I) = T’F’(Z)L
+ q”F”(Z)V
(2)
where L = 1 - V is the mole fraction of the feed that is the phase (e.g., liquid). The K-value function KI (eq 1-18) assures that a* is a function of a between the ‘ and ” phases, but the feed has an a priori parameter aF in F ( I ) , the value of which should dictate a, and therefore a*. Given this one independent parameter aF,eq 2 cannot be satisfied for all Z. (If F ( I ) ,and corresponding F’(Z)and F”(Z), has an infinitely large number of parameters governing the form of the distribution, satisfaction of eq 2 could be ensured by the method of moments, as in eq 1-17, for all possible Z n where n is a positive integer.) 0 1990 American Chemical Society
2102 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 Table I. Coefficients for Equation 111-1” coeff
for allz 534.66 0.81446 X lo-’ 179.85 -0.25175 X
go
R1 hn
hl
for b 0.99961 -0.72840 X 0.121 59 0.12008 X
“ f is a1I2 (psia1Iz ft3 OR1I4/lb-mol)and b (ft3/lb-mol).
It is customary in the case of a one-parameter distribution function such as eq 1 to let a (and therefore a*) be determined by the first moment of eq 2:
vMl = v’LMl’
+ I~”VM~’’
(3)
where
This step ensures that the average molecular weight of the feed and its flash products would be consistent. There will still be inconsistency in general with respect to conservation of species a t a particular value of I. Given the integral nature of continuous fractions, quadrature techniques provide excellent methods for optimally replacing the continuous fraction with a small number of pseudocomponents without serious degradation of the description. The immediate benefit of quadrature is that one can retain existing discrete mixture algorithms to perform subsequent phase equilibrium calculations. Additionally, the discrete pseudocomponents themselves do not experience conservation-of-mass failure. Appendix I1 presents the discrete formalism apropos to the adoption of the exponential distribution function for what would otherwise be the continuous portion of the semicontinuous mixture.
Example Calculation: Liquid Dropout from a Live Oil + C 0 2 Mixture near Its Upper Dew Point Pressure. Continuous thermodynamics offers the opportunity to characterize the C7+portion of an oil in detail up to arbitrarily large values of the carbon number (size) parameter. In turn, it is these heaviest C7+species that directly affect the upper dew point (UDP) pressure and the compositional makeup of the liquid that drops out at pressures less than the upper dew point pressure. For this example, a mixture of 20 mol % oil A (described in Tables I and I1 and Appendix 111) + 80 mol ?% C02 at 130 O F will be flashed near its UDP state. Of special interest here are (1)the UDP pressure, (2) the liquid-phase mole fraction, and (3) the liquid-phase molecular weight, the latter two expressible as functions of the pressure reduction PUDP - P from the UDP pressure. The upper carbon number limit of the continuous fraction is important, as is the particular choice of discrete pseudocomponents used to mimic the continuous fraction. The computations to follow will employ (1)an exponential continuous description of the C7+portion, extending from carbon 7 to carbon 100 (CT-100), consistent with the C7+ molecular weight of oil A (178); and (2) discrete descriptions of the C7+ portion in (l),using finite LaguerreGaussian quadrature for two to six”pseudocomponentswith an upper carbon number limit of 100 (Q2-100, $3-100, 64-100, Q5-100, and Q6-100). The pseudocomponents of the C7+ portion for the descriptions in (2) are given in Table 111. In Table IV, the results are given by using these continuous and discrete descriptions. The upper dew point for CT-100 is 3596 psia, the largest for all the descriptions. It is sensitive to its upper carbon number limit (for an upper limit of 50, the UDP pressure is 3340 psia). The liquid-phase molecular weights are higher a t pressures nearer the UDP pressure.
Table 11. Mole Fraction Composition of Oil A Used in the Example Calculationa binary interaction parameters component C1 COZ
CZ CS
NC, IC5 NCb C6 c7+
MW of C7+
oil A 0.3214 0.0000 0.1079 0.1443 0.0787 0.0090 0.0205 0.0117 0.3065 178
c,,
U ~ / ~ / R Tl/psia1I2 ~/‘, 103(b/RT),l/psia 0.013 226 0.017 591 0.022 025 0.030044 0.038 059 0.045 932 0.046 952 0.055 073
0.077 67 0.068 25 0.106 51 0.145 03 0.189 18 0.236 02 0.235 47 0.278 89
i = C1 0.17547 0.005 00 0.01000 0.01000 0.01000 0.01000 0.01000
D
C i = 60, 0.17547
-0.031 81
0.165 44 0.159 44 0.154 10 0.151 53 0.147 96 0.142 67
-0.02808 -0.025 84 -0.023 85 -0.022 90 -0.021 57 -0.019 60
i = 60,
Also given are the EOS pure component and binary interaction parameters for the discrete components at 130 O F .
Table 111. Soecification of the Discrete DescriDtion for the C , Portion of Oil A. whose C,, Molecular Weight Is 1 7 8 O pseudocomponents description
i
Q2-100
CN, 2,
$3-100
CN,
Q4-100
2N,
65-100
2N, 2,
66-100
CN, 2,
1 10.06 0.8535 9.02 0.7103 8.44 0.5984 8.05 0.5084 7.76 0.4345
2 27.23 0.1465 20.40 0.2792 16.97 0.3602 14.77 0.4033 13.22 0.4198
3
4
5
6
44.58 0.0105 33.64 0.0408 27.45 0.0835 23.30 0.1298
62.25 0.OOO 64 47.34 0.004 8 38.53 0.0152
76.90 0.OOO 054 59.65 0.OOO 63
86.38 0.000 0087
“For the carbon number upper limit of 100, (Y = 0.16471 and C = 15.31760. CN, = carbon number; z, = mole fraction normalized with respect to C7+. Qn-100 (where n = 2 , 3 , 4 , 5 , and 6) stands for quadrature with n pseudocomponents for a discrete C7+description with an upper carbon number limit of 100.
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 2103 Table IV. Vapor-Phase Fraction, Vapor-Phase Molecular Weight, and Liquid-Phase Molecular Weight for the Semicontinuous and Discrete Descriptions of Oil A as a Function of the Pressure Reduction from the Upper Dew Point at 130 OFa carbon no. description
100
200
0.9946 177.0 238.2
300 CT-100 (3596, 238.7)* 0.9889 0.9835 176.0 174.9 236.9 237.6
400
500
1000
0.9797 173.6 240.9
0.9722 172.5 236.8
0.9430 165.0 233.6
0.9897 176.3 231.6
0.9801 174.5 231.5
$2-100 (3038, 231.6) 0.9710 172.6 231.3
0.9623 170.6 230.9
0.9540 168.6 230.3
0.9119 157.0 222.6
0.9966 177.2 246.9
0.9929 176.4 244.8
Q3-100 (3225, 248.8) 0.9888 175.5 242.5
0.9840 174.5 239.9
0.9784 173.4 237.1
0.9299 164.6 221.4
0.9975 177.4 247.9
0.9943 176.7 244.5
Q4-100 (3244, 251.5) 0.9899 175.8 241.3
0.9846 174.6 238.5
0.9783 173.5 236.0
0.9338 164.8 223.3
0.9976 177.4 247.6
0.9942 176.7 244.4
Q5-100 (3244, 251.5) 0.9899 175.8 241.6
0.9847 174.8 239.0
0.9786 173.6 236.3
0.9333 164.8 223.1
0.9977 177.4 247.7
0.9942 176.7 244.5
QS-100 (3246, 251.7) 0.9899 175.8 241.6
0.9847 174.8 238.9
0.9786 173.6 236.3
0.9334 164.8 223.1
'Units of pressure are psia. $,-lo0 (where n = 2, 3, 4, 5, and 6) stands for quadrature with n pseudocomponents for a discrete C7+ description with an upper carbon number limit of 100. *Upper dew point pressure, MWL.
The quadrature results for an upper carbon number limit of 100 are essentially identical for four to six pseudocomponents (Q4-100, Q5-100, and QS-100). The UDP pressure is about 10% lower than that for CT-100, while the liquid-phase molecular weight is somewhat higher; the fraction liquefied (1- fv) is also higher. One might intuitively expect sensitivity of the UDP pressure prediction to the carbon number of the heaviest C7+species admitted by a description and thus anticipate that there would be a shortcoming in the quadrature C7+ descriptions/results since each of their heaviest species, which varies with the number of C7+pseudocomponents, has a carbon number less than 100. However, this shortcoming does not occur, as can be seen from the uniformity of the quadrature results Q4-100 to Q6-100 for the UDP pressure. Each of these descriptions has a different carbon number for its heaviest component; the effect of the carbon number increase of the heaviest component from descriptions Q4-100 to Q6-100 is apparently offset by its decreasing mole fraction (see Table 111). It is important to note that, given more than six pseudocomponents, the quadrature result for the UDP pressure will remain the same. Furthermore, this limiting quadrature result is not the same as that obtained from the semicontinuous thermodynamics description CT-100. We will now analyze why there is this discrepancy. The CM problem for continuous flash calculations is well-known. It is often used as a justification for employing quadrature, as the pseudocomponents do not in themselves experience a CM failure. In turn, it is sometimes claimed that continuous thermodynamics will not experience this CM failure for two-phase saturation calculations, since the feed and the dominant phase (e.g., the vapor for a dew point calculation) are by definition identical. Strictly speaking, however, a dew point calculation is the limit of a series of flash calculations with decreasing liquid-phase fractions, as shown in Table IV, each flash calculation
Table V. ( V + L - F ) / L at the Six Carbon Numbers of the Discrete Description QS-100 as a Function of the Difference between the Pressure and the UDP Pressure for the System 80% COz 20% Oil A at 130 OF for the Semicontinuous DescriDtion CT-100 (V + L - F ) / L for carbon no. P U D p .- P, fraction Dsia of vaDor 7.76 13.22 23.23 38.53 59.65 86.38
+
~~
500 400 300 200 100 50 18
0.9722 0.9777 0.9834 0.9892 0.9948 0.9976 0.9993
0.34 0.33 0.32 0.31 0.32 0.32 0.32
-0.19 -0.18 -0.17 -0.17 -0.17 -0.16 -0.16
-0.23 -0.22 -0.22 -0.22 -0.22 -0.23 -0.23
0.27 0.26 0.25 0.24 0.23 0.23 0.23
0.74 0.73 0.72 0.72 0.71 0.71 0.71
0.94 0.94 0.94 0.93 0.93 0.93 0.93
experiencing a CM failure and therefore being affected by that failure. Examination of the flash calculations for description CT-100 at pressures less than the UDP pressure reveals that the sum of the liquid + vapor ( L V) for a given carbon I does not equal feed F. Specifically, in the example calculation, L + V > F for low and high carbon numbers in the C7+fraction and L V < F for the intermediate carbon numbers. If one compares the size of these deviations to the size of L, one obtains a function ( V + L - F ) / L that is virtually unchanged between 3100 psia and the UDP pressure 3596 psia. See Table V and Figure 1. The function (V + L - F ) / L is by nature indeterminate at the UDP pressure; from Table V, it can be seen that the function has an asymptotic limit that is nonzero. We therefore conclude that, in this example, the CT calculation has an asymptotic bias toward the ends of the C,+ distribution (and away from the middle of the distribution) that enhances the UDP pressure prediction from semicontinuous thermodynamics (CT-100)compared to that of the limiting quadrature results (i.e., for n I 4). The failure of the UDP pressure from CT-100 to match that of, say, QS-lo0 is due to the CM failure and suggests that in general the CM problem in flush calculations will
+
+
2104 Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 furctior
0 25
c -0
i
+
I = $"IA
I
1
'
c!
P = R T / ( u - b) - a / ( v ( u + b)T1I2)
(1-6)
The values of the parameters used for this EOS are presented in Appendix 111. The a and b parameters that would be required in this two-parameter equation of state are for a semicontinuous system of n discrete components and a single continuous fraction:
/
-0 50+
-
-
1
\/,
2s$-
-0 7 5 4
1
I
!
(1-5)
The equation of state (EOS) used in the example calculation is the Redlich-Kwong EOS:
I
/
j
F ( I ) d~ = function of a
I
I
also be present in saturation calculations. From another viewpoint, it may be pointed out that the CM failure illustrated here is caused by the imposition of the same form of analytical distribution (herein, one-parameter exponential) on all the phases, including the infinitesimal one, constraining the equilibrium result unfavorably. This failure is especially pronounced for the exponential distribution because of its mathematical simplicity. At the same time, it would appear that any a priori designation of analytical distributions for the phases is a similar mathematical constraint and likewise invites CM failure. Summary The well-known conservation-of-massfailure that occurs in continuous thermodynamic flash calculations asymptotically affects saturation calculations (where one phase is infinitesimal) as well. The seriousness of the conservation-of-mass failure is directly related to the parametric simplicity of the distribution function describing the continuous portion, or correspondingly to the range of the variable describing the continuous portion. Appendix I The Continuous Formalism. For a two-phase equilibrium computation at a given temperature and pressure, the mass flow equilibria between phases G and L are governed by f i G (T,P,lyil) = f i L ( TP,lxil )
(1-7) where 7 is the continuous mole fraction and b ( I ) is a function expressing how b depends on I in the continuous fraction. This form of b above is from Turek et al. (1984) and will reduce to the more familiar arithmetic average expression if all the binary interaction parameters Dij are zero. In the same way,
Binary interaction parameters are also used with the a parameter. For ai, = a,,. and for ajr, the binary interaction parameter c j k appears in the form ajk
E
a j 1 ~ 2 a k 1 ~-z C( jlk ) , k = i or I
(1-9)
for discrete + discrete discrete and discrete + continuous fraction pairs; no interaction parameters were used for azl+ the continuous + continuous pairs:
all+ at/2az+1/2
(1-10)
The fugacity coefficients for a semicontinuous system using eq 1-6 are expressible as minor modifications of those for a discrete system. In the case of the coefficient $i for a discrete component i in a semicontinuous mixture, the continuous fraction enters in the same manner as a discrete component:
(1-1)
for discrete components and by (1-2) for carbon I of the continuous portion or fraction. The distribution function describing the continuous fraction is chosen to be exponential (see eq 1):
F ( I ) = ae-al/(e-aA - e-aB) =0, ICA, I>B
where S i a 1 1 J 2 F ( IdI ) can be calculated in advance. For the continuous fraction, a species of carbon I has a fugacity coefficient:
(1-3)
where I is the carbon number and A and B are the bounds of the distribution. As written here, the function F ( Z ) is normalized:
Given A and B , the parameter a may be determined by information such as the average carbon number (equivalently, the average molecular weight):
Linear forms are chosen for convenience for the functions b(Z) and aI1l2(I): b(Z) = bo + blI (1-13) a t J 2 ( Z )= a.
+ alZ
(1-14)
Ind. Eng. Chem. Res., Vol. 29, No. 10, 1990 2105 where the coefficients bo, bl, ao, and al are functions of temperature. These enable one to express 4 ( I ) in the form (1-15) N)= exp(C1 + C21) where C1 and C2 are functions of the state (u,T). The fugacity equality for carbon I for phases ’ and ’’ is expressible as 7’Ff(Z)&(I ) = 7°F ”(I)&’(I ) (1-16) To ensure this equality for all values of I (between A and B ) , the method of moments is applied: q ’ L B I n F’(I) $’(I) dI = q ” l B I n F”(I) 4 ” ( I ) dI (1-17) A
for all n. If a is the parameter for F’(I) and a* for F”(I), then a K value can be constructed for the continuous fractions of two phases based on eq 1-17:
0 are found, and the coefficients (wi)are evaluated. The ( x i ) identify the pseudocomponent carbon numbers between A and B, and the {wi)can be normalized into mole fractions of the pseudocomponents that represent the continuous fraction. An alternative but equivalent method of determining { x i )and {wi)is suggested by Shibata et al. (1987). As an example, let the continuous fraction have an average molecular weight of 200 and extend from carbon 7 to carbon 100. The a parameter in F ( I ) is determined by (11-7) where molecular weight and carbon number may be approximately related by 200 = 14.01 2.0 (11-8)
+
and
F ( I ) = ae-al/(e-aA- e-aB)
in which one customarily defines the bounds of the function F ( I ) to be
where a* = a - c,
+ c2*
(1-19)
in which the “starred” functions refer to the ” phase (e.g., the vapor phase).
Appendix I1 Discrete Formalism. The Gaussian quadrature approach presented here is for mixtures with a continuous fraction describable by an exponential distribution truncated at I = A and B as in eq 1-3; mathematically, the approach is referred to as the general, or finite, LaguerreGaussian quadrature scheme and is used to replace the continuous fraction with a small set of discrete pseudocomponents. The class of integrals to be represented herein can be expressed in the general form (11-1) where C = a(B - A ) . The appearance of exp(-x) is a result of having adopted an exponentialform of F ( I ) ;the variable x is the product al. The discrete representation of this integral in Gaussian quadrature is Jcf(x)
e-x dx = ? w i f ( x i )
(11-2)
i=l
where wi = x C L i ( x )e-x dx
(11-3)
are the weighting factors and (11-4) n
P(x) =
ncx -
j=l
(11-5)
Xj)
The ( x i ] are determined from roots of the polynomial P,(x) = P ( x ) , which satisfies JccX P,(x) P,(x) dx = 0, r = 1, ..., n;
(11-9)
s
< r (11-6)
Given a choice of order n for the discrete representation of the continuous fraction, the polynomial Pn(x)is determined from eq 11-6, the roots ( x i ! , i = 1, ..., n, of P,(x) =
A=7-’/,
(11-10)
B = 100 + y2
(11-11)
The value of A is determined to be 0.130 83, and C for this finite Laguerre-Gauss treatment is thus 12.29838. For the case of n = 3, e.g., the pseudocomponent carbon numbers for the continuous fraction for this value of C would be 9.64, 23.80, and 53.61, with mole fractions 0.7059, 0.2827, and 0.0114, respectively, when normalized to unity.
Appendix I11 EO$ Parameters. The particular choice of EOS parameters for eq 1-6 is not of primary importance to the arguments presented in this paper. Rather it is essential that, whatever description is used here for the parameters, it be used consistently for both semicontinuous and discrete versions of the computation. For example, an EOS parameter function expressed in terms of the carbon I can be used either as a parameter source for discrete components or integrated to apply to a continuous portion of a mixture. Such functions for all2 and b in the EOS will lead to a mathematically simple semicontinuous formalism (Cotterman et al., 1985a; Cotterman and Prausnitz, 1985) if they depend linearly on the variable I as in eqs 1-13 and 1-14, Therefore, linearity with respect to the carbon number is arbitrarily imposed here, and the coefficients ao, al, bo, and b, are in turn expressed as simple functions of the absolute temperature T: (111-1) f = go + g1T + (ho + hiT)I where f = a1/2or b and T is in OR. Table I lists the coefficients in eq 111-1for all2 and b used for the continuous/discrete C7+ components, while Table I1 lists the parameters used for the other discrete components of the live oil. The following binary interaction parameters were arbitrarily chosen for the continuous/discrete C7+species + methane and + carbon dioxide: cjI(C7+ - CHI) = 0.02 cjl(C7+ -
COJ = 0.14
(111-2)
Registry No. COz, 124-38-9.
Literature Cited Behrens, R. A.; Sandler,S. I. The Use of Semicontinuous Description to Model the C ,, Fraction in Equation of State Calculations. SPE
2106
Ind. Eng. Chem. Res. 1990,29, 2106-2111
Reservoir Eng. 1988,3, 1041-1047. Cotterman, R. L.; Prausnitz, J. M. Flash Calculations for Continuous or Semicontinuous Mixtures Using an Equation of State. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 434-443. Cotterman, R. L.; et al. Phase Equilibria for Mixtures Containing Very Many Components. Development and Application of Continuous Thermodynamics for Chemical Process Design. Ind. Eng. Chem. Process Des. Deu. 1985a, 24, 194-203. Cotterman, R. L.; et al. Design of Supercritical-Fluid-Extraction Processes Using Continuous Thermodynamics. In Supercritical Fluid Technology; Penninger, J. M. L., et al., Eds.; Elsevier Science: B. V., Amsterdam, 198513; pp 107-120.
Cotterman, R. L.; et al. Comments on ‘Flash Calculations for Continuous or Semicontinuous Mixtures Using an Equation State”. Ind. Eng. Chem. Process Des. Dev. 1986,25, 840-841. Shibata, S. K.; et al. Phase Equilibrium Calculations for Continuous and Semicontinuous Mixtures. Chem. Eng. Sci. 1987, 42, 1977-1988. Turek, E. A,; et al. Phase Equilibria in C0,-Multicomponent Hydrocarbon Systems: Experimental Data and an Improved PrePet. Eng. J . 1984, June, 308-324. diction Technique. SOC.
Received for review April 23, 1990 Accepted June 12, 1990
Evaluation of Excess Parameters from Densities and Viscosities of Binary Mixtures of Ethanol with Anisole, N,N-Dimethylformamide, Carbon Tetrachloride, and Acetophenone from 298.15 to 313.15 Kt Vidya A. Aminabhavi, Tejraj M. Aminabhavi,* and Ramachandra H. Balundgi Department of Chemistry, Karnatak University, Dharwad 580 003, India
Densities and viscosities of four binary mixtures containing ethanol have been measured a t 298.15, 303.15, 308.15, and 313.15 K over the entire mole fraction scale. These results are used to calculate excess molar volume and apparent values of excess viscosity and excess Gibbs energy of activation of flow. Efforts have also been made t o compute the excess isobaric thermal expansivity of liquid mixtures by using the refractive index mixing rules. Such results when compared with experiments agreed reasonably well.
Introduction The availability of a simple method such as densitometry for probing thermodynamic interactions in binary mixtures would have tremendous value. This technique has long been employed to study the role of intermolecular interactions in liquid mixtures (Rowlinson, 1959). This paper is part of our ongoing program to evaluate the excess properties of binary liquid mixtures of nonelectrolytes (Aminabhavi et al., 1986,1987,1988). In continuation of this study, we now present experimental densities, p, and viscosities, 1,of four binary mixtures of ethanol with anisole, N,N-dimethylformamide (DMF), carbon tetrachloride, or acetophenone from 298.15 to 313.15 K. The quantities such as excess molar volume, VE, apparent values of excess molar viscosity, 81,and excess molar Gibbs energy of activation of flow, AG *E, have been calculated from the results of densities and viscosities as a function of mole fraction at four different temperatures. Furthermore, attempts have been made to calculate the excess isobaric thermal expansivity, aE,of the mixtures by the use of the refractive index mixing rules (Bottcher, 1952). The validity of these results have been tested by comparison with the experimental aE values as obtained from mixture densities. The present mixtures have been selected due to the nonavailability of their densities and viscosities and the ready availability of their thermodynamic data on pure liquids. Alcohols have been the most common liquids used for the study of hydrophobic effects in view of their simple molecular structures, increasing hydrophobic character with chain length, and high solubility in water and other polar liquids (Roux and Desnoyers, 1987; Wilson et al., 1985; Karachewski et al., 1989). However, the strength of the interaction of ethanol may be varied systematically by +Taken from the Ph.D. thesis of Miss V. A. Aminabhavi, submitted to Karnatak University, 1990.
considering other liquids with steadily increasing polarity from carbon tetrachloride, anisole, and acetophenone to DMF. Thermodynamic interactions in such mixtures are being studied here.
Experimental Methods Spectroscopic-grade ethanol, Fluka, Switzerland, was obtained in its highest purity, exceeding 99 mol % as claimed by the supplier, and thus, it was used without further purification. The other solvents, namely, carbon tetrachloride, DMF, anisole, and acetophenone, were all BDH samples, which were purified by appropriate procedures (Vogel, 1989; Riddick et al., 1986). The purity of these solvents as tested by a chromatographic method was also found to be more than 99 mol %. Mixtures were prepared by mixing the accurately weighed quantities of pure solvents in ground-glass stoppered bottles. A Mettler balance, Switzerland, with a precision of f0.05 mg was used. The same stock solutions were used for measurements of p and 77. A Toshniwal precision thermostat was used to control the temperature of the bath up to fO.01 K. The temperatures were read by using a calibrated thermometer. The densities of pure solvents and their mixtures were measured with a double-armed pycnometer having a total volume of 10 cm3. Calibration of the pycnometer was done with water and benzene over the working temperature range. The estimated error in the density is f0.0003 g/ cm3,and a good agreement of the experimental densities with the literature values (Riddick et al., 1986; Timmermans, 1950) is found. Viscosities of the solvents and mixtures were measured by using Cannon Fenske viscometers, sizes 75 and 100, supplied by International Research Glassware, Roselle, NJ, ASTM D 445. An electronic stopwatch having a precision of fO.O1 s was used for measuring the flow times. Triplicate measurements of flow times were reproducible within 0.2% or less. The kinematic viscosities, u, in cSt were
0888-5885f 9012629-2106$02.50 f 0 0 1990 American Chemical Society
