Ind. Eng. Chem. Res. 1993,32, 241-244
241
CORRELATIONS New Acentric Factor Correlation Based on the Antoine Equation Daniel
H.Chen*
Department of Chemical Engineering, Lamar University, Beaumont, Texas 77710
Murty V. Dinivahi Chemtex Environmental Lab, Port Arthur, Texas 77642
Chang-Y uan Jeng Enertech Engineering Go., Taipei, Taiwan, R.O.C.
The Edmister method for the estimation of acentric factor, a widely used parameter in thermodynamic and transport property correlations, is modified. The new method requires only two vapor pressure data points for each compound (the normal boiling point and the critical point) as in the methods of Edmister and Lee-Kesler while employing the three-parameter Antoine vapor preasure correlation. The average absolute error is 3.69% based on the most recent literature data (498 compounds). This compares favorably with the Edmister method (5.10%) and the LeeKesler method (7.09%). A correlation is also developed to relate the third parameter C/T, in the Antoine equation with 8 (i.e., Tb/ Tc)*
Daubert, 1983); (h) equations of state (Soave, 1972; Peng and Robinson, 1976). A fair amount of acentric factor data have been accuThe acentric factor (Pitzer, 1955; Pitzer et al., 1955) is mulated over the years, especially for hydrocarbons (Paasut an important physical constant used in calculating the and Danner, 1973; Henry and Danner, 1978; Ambrose, physical properties of pure compounds as well as mixtures, 1980). However, there are many instances where experiespecially in the corresponding-states type correlations. mentally determined acentric factor values are not availThe acentric factor, w , is defined as able. For example, the vapor pressure has not been (1) 0 = -log(Pvp)rlTr=O., - 1.00 measured near/at T,= 0.7 or the critical constants are simply not available. Under these circumstances, the where (P,), = P,/P,; P, = vapor pressure, atm; T,= acentric factor can not be obtained from eq 1. As a result, T/T,, reduced temperature; T = absolute temperature, K the estimation methods must be used to facilitate the T,= critical temperature, K; and P, = critical pressure, above-mentioned calculations (a)-(h). atm. As can be seen, critical constants and the vapor Most literature methods for estimating the acentric pressure data at T,= 0.7 are needed to determine the factor require the normal boiling point (Tb),critical conacentric factor. stanta (T,, PJ, molecular weight (MW),and specific gravity The acentric factor is supposed to represent the acen(SG).The method of Hoshino et al. (1982) based on group tricity or nonsphericity of a molecule. For example, the contributions is an exception. Table I provides more inw values of argon, methane, and ethane are very small formation (input data needed, percent deviation (% dev), (0.001,0.012, and 0,099, respectively). The value of w number of compounds used, and comments) about these increases with carbon chain length (0.907 for n-eicosane) predictive methods. All the % dev values in Table I were and generally rises with increasing polarity (0.644 for given by the references listed under the comment column. ethanol). Actually some large w values (e.g., for alcohols) Note that the methods based on SG, Tb,and MW (Lin and are more closely related to polarity than acentricity. Chao, 1984; Watanasiri et al., 1985; Roman et al., 1986) The acentric factor values are widely used in estimating can be used to predict w for coal-liquid or petroleum thermodynamic and transport properties for gases and fractions. Because the input values can be estimated by liquids. Examples of these applications are given as folgroup contributions, the methods based on Tb,T,,and P, lows: (a) compressibility factor (Pitzer, 1955; Pitzer et d., are still applicable even when some or all of the input data 1955; Edmister, 1958; Lee and Kesler, 1975); (b) heat ca(experimental) are missing. pacity of real gases (Lee and Kesler, 1975); (c) enthalpy In this work an empirical correlation based on the Anof vaporization (Nath, 1979); (d) aaturated density or molar toine equation is developed (eq 15; see later derivation). volume of liquids (Rackett, 1970; Thompson et al., 1982); The new correlation can predict the acentric factor more (e) vapor pressure of pure liquids (Lee and Kesler, 1975); accurately than the Edmister and the LeeKesler methods (f) liquid heat capacity (Rowlinson, 1969); (g) saturated while utilizing essentially the same input information. liquid viscosity (Letsou and Stiel, 1973; Danner and 0SSS-5SS5/93/2632-0241~~4.O0/0 0 1993 American Chemical Society
Introduction
242 Ind. Eng. Chem. Res., Vol. 32, No. 1, 1993
Development of Correlation
Edmister (1958) proposed an equation to correlate the acentric factor with the normal boiling point and critical constants: w=--
e
log P,- 1
7 1-8 where 8 = Tb/Tc. Tb = normal boiling point, K; T,, P, = as defined in eq 1. Equation 2 is based on the Clapeyron equation: In Pv = A - B / T (3) in which two data points are needed to specify the constants A and B. A similar relationship was reported by Lee and Kesler (1975): w = (-ln P, - 5.92714 + 6.096486' + 1.28862 In 8 0.16934786)/(15.2518 - 15.68758-1 - 13.4721 In 8 + 0.4357786) (4) where P,, T,, 8 = as defined in eqs 1 and 2. Equation 4 is obtained from the following vapor pressure relation (eqs 5-7): the Pitzer expansion:
ln(P,),
= po)(Tr)+ wfc*)(T,)(5)
The Lee and Kesler functions are Po'(Tr) = 5.92714 - (6.O9648/Tr) - 1.28862 In T, +0.169347T,6 (6)
