Ind. Eng. Chem. Res. 1999, 38, 1057-1064
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GENERAL RESEARCH Development of a Corresponding-State “Association Enthalpy” Function for Use in the Prediction of Coal Liquid Enthalpies Raj Sharma,* Abhishek Baid, and Iyer S. Jayaram Department of Chemical Engineering, Malaviya Regional Engineering College, Jaipur 302 017, India
A simple corresponding-state “association enthalpy” function in terms of reduced temperature, reduced pressure, and an “association factor” which accounts for the effect of “association” has been developed for use in estimating coal liquid enthalpies. This “association enthalpy” function when added to the Kesler-Lee enthalpy correlations helps in predicting coal liquid enthalpies more accurately, with the maximum average deviation being 23.9 kJ/kg for a synthoil distillate, one of the most associating coal liquids considered in this work. Without the correction for the association enthalpy, the maximum average deviation in the predicted enthalpy values was 83.0 kJ/kg. Enthalpies of m-cresol, a highly associating compound, were also predicted using the association enthalpy function, and the average deviation was reduced from 166.3 to 20 kJ/kg. The Association Enthalpy function does not require any detailed structural characterization of coal liquids and should prove to be of significant practical interest. Introduction Coal liquids are a vital class of industrial compounds and have always been considered as a viable alternative to petroleum. Thermodynamic properties of coal liquids are required for the efficient design of processing equipment. Enthalpy is one such property which offers a substantial amount of information to the design engineer as it can be used directly in the determination of process heat loads. Enthalpy data for coal liquids are scarce, and a simple “predictive” method is of great practical interest. Data Bank Table 1 (Sharma et al.1) presents a compilation of the enthalpy data of coal liquids used in this work along with the temperature and pressure ranges. An average error of (0.5% in the experimental values was reported by Sharma et al.1 Various characterization parameters of coal liquids used in this work are presented in Table 2. Existing Predictive Methods Use of Petroleum Fraction Correlations for Coal Liquid Enthalpy Predictions. As an initial stage in the effort to correlate enthalpy data for coal liquids, Sharma et al.1 compared the experimental enthalpies with the predicted values using correlations developed for petroleum fractions: the Johnson-Grayson2 and the Kesler-Lee correlations.3,4 Table 3 (Sharma et al.1) presents the results of comparisons between experimental enthalpy data for coal liquids and the predicted * Author to whom all correspondence should be addressed. Tel: 91 141 624808. Present address: 14 Uniara Garden, Jaipur 302004, India.
values using the Kesler-Lee correlations3,4 developed for predicting petroleum fraction enthalpies. For almost all of the coal liquids and for both the correlations considered, the predicted enthalpies were biased low relative to the experimental values. However, it is important to note that the hydrocarbon-type distribution and the conditions under which the coal liquids are formed often differ radically from those of petroleum fractions.1,5 For example, coal liquids are more aromatic than the conventional petroleum fractions and contain a significant amount of heteroatoms (2-20 mol %).1,6-8 Although it was originally believed that the high level of aromatics in coal liquids would result in major property differences between coal liquids and petroleum fractions, Sharma6 and Sharma et al.1 have shown that the presence of aromatics causes only a minor difference between the predicted values and the experimental enthalpies. The other major difference between coal liquids and petroleum liquids is the high level of organic oxygen and nitrogen compounds in coal liquids. Sharma et al.1,9 have shown that the fact that experimental enthalpies are higher than the predicted values is consistent with an association effect and an energy of association. Sharma et al.1 have further argued that the association effects such as “hydrogen bonding are quite likely in such fluids” and that the hydrogen bonding effects depend mainly on whether the oxygen present in the coal liquids is tied up in an ether linkage or a phenolic linkage. Sharma et al.9 have also shown that the slope of the cryoscopic molecular weight determination as a function of concentration in a nonpolar solvent, in particular benzene, appears to be a “reliable means of characterizing association in coal-derived liquids”. They defined this slope of the molecular weight versus concentration curve as the “association factor”, β, and showed that there was a relationship between β
10.1021/ie970820t CCC: $18.00 © 1999 American Chemical Society Published on Web 02/06/1999
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Ind. Eng. Chem. Res., Vol. 38, No. 3, 1999
Table 1. Coal Liquids Used in This Work (Sharma et al.1) no.
coal liquid
no. of enthalpy measurements
temp range (K)
pressure range (kPa)
1 2 3 4 5 6 7
Western Kentucky syncrude Western Kentucky distillate SRC-I naphtha SRC-II naphtha Utah distillate SRC-II middle distillate synthoil distillate
66 81 145 38 86 52 57
291.5-644 291.5-673 291.5-655 291.5-511 291.5-655 291.5-630 291.5-666
690-10340 415-10340 205-10340 690-2070 415-10340 895-6895 1035-10340
Table 2. Coal Liquids Data Table no.
coal liquid
TCa (K)
PCa (MPa)
ωa
βb (MW/conc)
MWa
Kc
°APId
1 2 3 4. 5 6 7
Western Kentucky syncrude Western Kentucky distillate SRC-I naphtha SRC-II naphtha Utah distillate SRC-II middle distillate synthoil distillate
763.3 697.2 575.0 608.9 694.4 727.8 761.1
2.227 2.668 3.247 3.282 2.654 3.206 2.868
0.56 0.47 0.36 0.20 0.46 0.45 0.46
1.2 3.1 4.8 11.6 11.9 19.3 24.1
218.3 168.3 103.0 95.0 167.8 174.6 170.0
10.8 10.8 11.3 10.0 10.8 10.0 10.0
21.8 28.6 49.7 41.0 29.4 13.4 13.2
a Kesler-Lee correlation.3 et al.1
b
Sharma.6
c
Watson characterization factor {(Tb)1/3/SG60/60)}; Tb, mean average boiling point in °R.
d
Sharma
Table 3. Average Difference between Experimental and Predicted Enthalpies of Coal Liquids Using Kesler-Lee Correlations3,4 (Sharma et al.1) no.
coal liquid
no. of points
average error (kJ/kg)
1 2 3 4 5 6 7
Western Kentucky syncrude Western Kentucky distillate SRC-I naphtha SRC-II naphtha Utah distillate SRC-II middle distillate synthoil distillate
13 42 51 29 33 36 19
-3.7 -8.4 9.5 -25.8 -28.1 -62.1 -83.0
Table 4. Comparison of Predicted and Experimental Enthalpies of Western Kentucky Syncrude previous work temp, K
∆HEXPTa (kJ/kg)
∆HK-Lb (kJ/kg)
472.6 532.7 593.8
382.4 537.8 728.7
382.9 531.5 701.3
537.6 557.8 579.1 612.1 647.4
549.4 606.8 667.5 772.4 889.3
548.2 599.9 659.7 756.1 868.5
average deviation no. of data points 8 a
∆HErrorc (kJ/kg)
this work ∆HASSOCe (kJ/kg)
∆HTf (kJ/kg)
∆HErrorg (kJ/kg)
%Error2h
Pressure ) 0.689 MPa 0.5 0.1 -6.4 -1.2 -27.4 -3.8
0.0 0.0 0.0
382.9 531.5 701.3
0.5 -6.4 -27.4
0.1 -1.2 -3.8
Pressure ) 3.457 MPa -1.2 -0.2 -6.8 -1.1 -7.8 -1.2 -16.3 -2.1 -20.8 -2.3
0.0 0.0 0.0 0.0 0.0
548.2 599.9 659.7 756.1 868.5
-1.2 -6.8 -7.8 -16.3 -20.8
-0.2 -1.1 -1.2 -2.1 -2.3
-10.7
-1.5
-10.7
%Error1d
-1.5
Omid.16 b Omid.16 c ∆HError ) ∆HK-L - ∆HEXPT. d %Error1 ) ((∆HK-L - ∆HEXPT)/∆HEXPT) × 100. e Association enthalpy (from eq 3). ) ∆HK-L + ∆HASSOC. g ∆HError ) ∆HT - ∆HEXPT. h %Error2 ) ((∆HT - ∆HEXPT)/∆HEXPT) × 100.
f∆H T
and the “error” in the enthalpy predictions. Values of the association factor for the coal liquids used in this work are also listed in Table 2. Group Contribution Methods. Subsequent work on thermodynamic property prediction of coal liquids has been based on structural characterization and group contribution methods. Hartounian and Allen10 used a group contribution method for predicting vapor pressures of coal liquids obtained from the SRC-II and ITSL processes. They argued that the molecular interactions in coal liquids made use of only bulk properties, such as density and normal boiling point as in the case of petroleum fractions, inadequate in the estimation of thermodynamic properties, and, as such, more “structural information” needs to be incorporated. They reported reasonable predictions of vapor pressure as compared to the experimental values for low-boiling distillates (
