Ind. Eng. Chem. Process Des. Dev. 1904, 23, 577-586
577
Heat Capacity of Coal Liquids Stephen C. M a w Exxon Research and Engineering Company, Cllnton, New JerS8y 0880 1
John L. Heldman, Shuen-Cheng Hwang, and Constantlno Tsonopoulos" Exxon Research and Engineering Company, Flomem Park, New Jersey 07932
Experlmental procedure and technlques are described for using differentlal scanning calorimetry to obtain accurate liquid heat capacities of organic materials, particularly coal liquids, at high temperatures. The heat capacity of coal liquids, produced with the Exxon Donor Solvent process from Illinois and Wyoming coals, has been experimentally determined at temperatures up to 404 O F . Measurements were also made up to 530 O F on the heat capacity of defined compounds found in coal liquids. These data, along with literature data for defined compounds and coal liquids from other processes, were used to investigate the applicability of the Watson-Nelson and API Technical Data Book correlations and to develop modifications of these correlations for predicting the liquid heat capacity of coal liquids. With the modified correlation, the average deviation in predicting the liquid heat capacity of coal liquids was reduced from 8.0 to 3.7%.
Introduction Coal liquefaction has drawn a lot of attention in the past few years. Several processes are currently being investigated, and in every case the process development has been hampered by the unavailability of phase-equilibrium, physical, and thermal property data at the conditions of interest. The need for phase-equilibrium data has been addressed by Wilson et al. (1981) and Hwang et al. (1983), while the need for physical properties has been addressed by Hwang et al. (1982). Here we will discuss the liquid heat capacity of coal liquids produced with the EDS (Exxon Donor Solvent) coal liquefaction process. We will also examine the liquid heat capacity of several defined compounds found in coal liquids, as well as literature data for defined compounds and coal liquids produced by other processes. The EDS Process is being developed by Exxon Research and Engineering Company as a unique cooperative undertaking involving government and industry, who provide funding and guidance. An overview of the development is given in a recent publication (Vick and Epperly, 1982). The coal-derived liquids are significantly more aromatic than the conventional petroleum fractions. Most of what is known about petroleum fractions only covers normal boiling points up to 800 O F and specific gravities at 60/60OF up to 1.08, while the coal liquids of interest have a boiling point range up to 1100 O F and a specific gravity up to about 1.2. The aromaticity of liquids processed in refineries is commonly measured by the Watson characterization factor, K ,
K, = [Tb(oR)]1/3/S
(1)
where Tbis the mean average boiling point in OR and S is the specific gravity at 60/60O F . Crude oil fractions have a K, of around 12, while heavy paraffins have Kw's in excess of 13. Aromatic fractions such as coal liquids have Kw's less than 11. Heat capacities and heat of vaporization are used in heat balance calculations for process units, as well as in the design of heat exchangers, etc. In view of the differences between petroleum fractions and coal liquids, there is a need to investigate the applicability of the existing heat capacity and heat of vaporization correlations to coal li0196-4305/84/1 123-0577$Q1.5OIO
Table I. BoilingPoint Distribution, Specific Gravity, and Molecular Weight of Coal Liquids Illinois Wyoming coal liquids liquid I-VGO WA-5' WA-6a WV-1 boiling-point distribution, "F (by GC distillation) wt % distilled 1 55 5 350 350 350 10 761 390 390 414 30 815 430 432 473 50 865 478 488 528 70 909 545 563 601 90 968 695 658 713 99 1067 805 735 805 specific gravity 1.12c 0.970 0.987 0.998 (60/60 O F ) molecular weight 267 167 169 192 Watson characterization 9.82 10.14 10.02 9.96 factord The boiling-point distribution, specific gravity, and molecular weight for WA-5 and WA-6 have been reported by Hwang et al. (1983) and are included here for completeness. b Determined by freezing-point depression of benzene; estimated accuracy is +3%. Estimated value. Calculated with eq 1; Tb is the mean average boiling point.
quids. In this paper, we have focused our attention on the liquid heat capacity. To provide a data base for testing and modifying existing correlations, and, eventually, developing new correlations, an experimental program was undertaken to measure the heat capacity of coal liquids and defined compounds found in coal liquids. One Illinois bituminous and three Wyoming subbituminous coal liquids produced by the EDS process were studied. Their boiling-point distribution, specific gravities at 60/60OF, molecular weights, and Watson characterization factors are summarized in Table I. The next section, "Experimental Program,"describes the apparatus, procedure, data reduction, and experimental results for liquid heat capacity. The section "Analysis of Experimental Data" provides a brief review of the existing correlations and then proceeds with the comparison of correlation predictions with experimental data. 0 1984 American Chemical Society
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Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984
Experimental Program The purpose of the experimental work was to assess the feasibility of using DSC (differential scanning calorimetry) to obtain accurate heat capacities for small samples of organic materials, particularly coal liquids, at high temperatures. Although Smith et al. (1980) report heat-capacity data obtained by DSC for several coal liquids, in some cases to 650 and 750 O F , they indicate that difficulties were encountered in making these measurements reliably. Furthermore, Gray et al. (1981) concluded that DSC is not suitable for measurements on coal liquids at high temperatures. In our laboratories, we have used DSC (although with techniques different from those of Smith et al., 1980, and Gray et al., 1981) to obtain accurate heatcapacity data over a wide temperature range (-280 to 980 OF) for inorganic materials (Mraw and Naas, (1979) and over a limited range (-280 to 125 O F ) for organic materials (Mraw and Naas-O’Rourke, 1980). The research described in this paper had two objectives: to extend our techniques to organic compounds a t higher temperatures and to obtain accurate data on samples of coal liquids. We met the first objective by successfully measuring the heat capacities of two pure compounds, acenaphthene and n-heptadecane, to an accuracy of i l % from 80 to 385 OF (Mraw and O’Rourke, 1981). We have since reported further results on the heat capacity of four additional pure compounds: phenylbenzene, phenylcyclohexane, cyclohexylcyclohexane, and dibenzothiophene (O’Rourke and Mraw, 1983). A comprehensive review on the use of DSC for heat-capacity measurement will appear shortly (Mraw, 1985). The present paper concentrates on our second objective, the use of these same accurate techniques for heat capacities of coal-liquid samples. In the following subsections, the experimental apparatus and procedures will be described (along with special precautions regarding samples of organic materials and, especially, coal liquids), the experimental results for acenaphthene will be summarized as an example, and the results on liquids from Illinois and Wyoming coals will be presented. Experimental Apparatus and Procedures General. The differential scanning calorimeter used for this work was the Perkin-Elmer DSC-2, augmented by the digital interface andd Tektronix calculator system available from Perkin-Elmer. (We have since replaced the Tektronix calculator system with a Hewlett-Packard 9845 computer system; O’Rourke and Mraw, 1983.) For the measurement of heat capacity, except for some runs on the Illinois coal liquid, we used the “enthalpy method,” complete details of which have been given by Mraw and Naas (1979), Mraw and Naas-O’Rourke (1980), and Mraw and O’Rourke (1981). Briefly, the total enthalpy of a sample over an 18 O F interval is measured by means of a scan at 4.5 OF/min. This is done for a series of runs on an empty sample pan, a pan containing sapphire, A1203,and then a series of pans containing the samples whose heat capacities are to be measured, with all series being run on the same day over the same temperature range. The deviation of the observed heat capacity of sapphire from the literature value (Ginnings and Furukawa, 1953) at each temperature is used as a calibration factor to correct the observed heat capacity of each sample at that temperature. These corrected values are taken as the experimental heat capacities of the samples. In addition, a final series of heat-capacity runs on a sample of pyrite, FeS2, was often included at the end of the day as a further check of the instrument. All heat-capacity measurements were made using dry ice-acetone coolant and nitrogen purge gas in
the sample-holder assembly of the DSC-2. It is important to maximize the DSC signal by encapsulating as large a sample of the material whose heat capacity is to be measured as possible. The masses of the sapphire and pyrite samples can then be adjusted so that the total heat capacity of each sample matches that of the unknowns as closely as possible over the temperature range of interest. These precautions help to cancel any systematic errors in the DSC measurements. Specific Considerations for Organic Materials. In addition to the normal care required in obtaining accurate heat capacities by DSC, there are several precautions specific to organic materials which should be observed. These are mainly associated with the volatility or chemical instability of organic compounds at high temperatures. The samples should be hermetically sealed under inert atmosphere to avoid oxidation. It is often desirable to use a reduced pressure of gas, so that the total pressure inside the pan will not greatly exceed one atmosphere when high temperatures are reached. Such an overpressure, even if it does not open the pan, can often cause the pan bottom to bulge (depending on its particular design), and this effect can increase the temperature lag between sample holder and sample pan, often causing a systematic error. A simple device can usually be built to allow the sample pan to be evacuated and sealed under reduced pressure. The filled sample pans should be rinsed with solvent after sealing to remove any sample that might accidentally have gotten onto the outside of the pans. The filled pan should then be weighed on a microbalance capable of a precision of 2-3 wg; the sample should be reweighed after every run to ensure that the pan has not opened. As the temperature is progressively raised, the sample may begin to volatilize into the space within the sealed sample pan. Even though a relatively small amount of sample enters the vapor phase, the enthalpy of vaporization required can be large enough to cause an error in the heat-capacity measurement. Calculations on selected compounds have shown that, in general, the error in the heat capacity due to vaporization will be less than 1% if the vapor pressure over the liquid is below about 0.25 atm, assuming a sample size of about 10 mg in a pan with an internal volume of about 0.03 cm3. While the above precautions are necessary for any defined organic materials, further care must be taken when dealing with coal liquids. The volatility and reactivity of pure compounds is generally known or can be predicted, since the chemical nature of the sample is well-specified. In a coal-liquid sample, however, there is a wide variation in volatility and thermal reactivity that cannot be predicted accurately. Regarding the volatility problem, the temperature where the vapor pressure reaches the limit of 0.25 atm often cannot be predicted accurately for a coal-liquid sample that has not been adequately characterized. Therefore, it is preferable to remain well below the estimated temeprature of any significant volatilization of a particular sample. Gray et at. (1981) indicate that it was primarily the volatility of the coal-liquid samples that prevented their measurement of accurate heat capacities by DSC, but the implication in their comment is that their sample pans were not hermetically sealed. The difficulties of Smith et al. (1980) were also attributed to poor sealing of sample pans. Regarding reactivity, it is important to cool samples which have been heated to high temperatures back to a temperature range where the heat capacity has previously been measured and to run a repeat series on the heat-
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984
treated sample. Significant chemical breakdown caused by the thermal treatment may produce a different value for the heat capacity of the sample, although the absence of such a difference does not guarantee that some breakdown may not have occurred. In any case, heat-capacity results at high temperatures which show any sign of unusual curvature should be viewed with caution, since volatilization or endothermic reaction would produce upward-curving results, while exothermic reaction would produce results which curve downward. Since such curvature will initially be slight, it is generally not wise to extrapolate heat capacities, because the extrapolation may enhance the slight errors in the last few data points. Finally, the greatest confidence in the data will result from those cases where several different samples of the same material have been run and overlapped in various temperature ranges.
Experimental Results on Acenaphthene and Other Pure Compounds Materials and Sampling Handling. Acenaphthene was obtained commercially (Baker Ultrex quality, J. T. Baker Chemical Company, Phillipsburg, NJ) with a stated purity of 99.99 mol %. The sample was used without further purification. The sapphire calibration standard consisted of chips broken from commercially available sapphire optical slides (General Ruby and Sapphire, New York, NY). Sapphire samples are also available from Perkin-Elmer. The pyrite sample was kindly provided by Professor Frederik Gr~nvold(Mraw and Naas, 1979). The acenaphthene, sapphire, and pyrite samples were hermetically sealed in the aluminum "volatile sample" pans available from Perkin-Elmer. A small press was used to pelletize the acenaphthene sample in ~II effort to maximize sample mass. The acenaphthene samples were exposed briefly to the ambient atmosphere during handling prior to sealing, but that did not seriously affect the purity of the samples. Different samples were sealed either in a glove bag under atmospheric pressure of nitrogen or in vacuum, depending on the anticipated temperature range to be studied. For the measurement series on acenaphthene, the sapphire and pyrite standards were encapsulated under ambient pressure. The sample masses were in the ranges: acenaphthene, 8-9 mg; sapphire, approximately 20 mg; and pyrite, 30-40 mg. Comparison of DSC Results to Literature Values. The measurements on acenaphthene were undertaken to prove the accuracy of the DSC technique by comparing our DSC results to heat-capacity values already in the literature. Heat capacities for acenaphthene were reported by Finke et al. (1977) at temperatures up to 330 O F , with an accuracy of fO.l to 0.270, considerably better than that obtainable by DSC. Thus, it is not necessary to tabulate our individual data points, but only to show the comparison of our results with the literature values. This is done in Figure 1 (from Mraw and O'Rourke, 1981). All of the experimental points for each phase of acenaphthene were smoothed graphically and the curves were used to determine the finalvalues at selected temperatures. This was purposely done without reference to the literature values to avoid any artificial enhancement of accuracy. D1 in Figure 1 is the percentage deviation of each experimental point from the smooth curve and is thus the internal precision of our DSC results. D2in the inset of Figure 1is the percentage deviation of our accepted smooth curve from the literature values and is thus our absolute accuracy. The results for acenaphthene, as seen in the inset of Figure 1, indicate that an absolute accuracy of approxi-
570
LIQUID
SOLID t2
t
Pfl
Figure 1. Precision and accuracy of the DSC results for acenaphthene. D1is the % deviation of each experimental point from our chosen smooth curves. D, is the % deviation of our chosen smooth curves from those of Finke et al. (1977). Table 11. Coefficients of the Straight-Line Fits to the Heat Capacity Data for Pure Compounds coefficients temp compound range. "F a b x lo3 RMSDb D c phenylbenzene phenylcyclohexane cyclohexylcyclohexane dibenzothiophene
156-404 45-386
0.358 0.369 0.353 0.507
0.003 0.7 0.004 0.9
39-386
0.360 0.606
0.004 0.1
208-530
0.300 0.304
0.003 0.7
RMSD is the roota CpL (Btu/lb, O F ) = a + & ( O F ) . mean-square deviation (in Btu/lb, O F ) of the experimental D is the approximate results from the straight-line fit. percent deviation of the experimental results from the straight-line fit. mately fl% is indeed obtainable on organic solids and liquids up to high temperatures, when careful procedures are followed. This implies that a similar accuracy can be expected for measurements on actual industrial stocks at high temperatures, as will be discussed in subsequent subsections. Although the acenaphthene results terminate at 370 OF, the results on dibenzothiophene to 530 OF (O'Rourke and Maw, 1983), and results on graphite to 800 OF (Mraw and O'Rourke, 1980) indicate that careful measuremenb by DSC on organic compounds can be accurate to approximately 12% at temperatures well above 400 OF. The temperature limitation, therefore, is usually due to the volatility or reactivity of the sample itself and not to the DSC instrument or method. Table 11presents the straighbline fit of the experimental liquid heat capacity for the four defined compounds investigated by O'hurke and Mraw (1983): phehylbenzene, phenylcyclohexane, cyclohexylcyclohexane, and dibenzothiophene. Experimental Results on Illinois and Wyoming Coal Liquids Heat Capacities were measured on one Illinois coal liquid, I-VGO, and three Wyoming coal liquids, WA-5, WA-6, and WV-1. Because the problems encountered with I-VGO were different from those with the other samples, the discussions are presented separately. Tables I11 and IV present the experimental data for the Illinois VGO and the Wyoming coal liquids, respectively, and Table V contains the coefficients of the straight-line fits for each sample. Figure 2 shows the experimental and smoothed data for the Illinois VGO, while Figure 3 shows the straight-line fits for all four coal liquid samples.
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Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984
Table 111. Experimental Heat-Capacity Points for Illinois Coal Liquid I-VGO t, "F
c
c =,
=I
"F
Btu/&,
t, "F Btu/l%, "F Series 3b3c 80.3 0.342 98.3 0.410 116.3 0.440 134.3 0.438 152.3 0.443 170.3 0.453 188.3 0.462
Series l',c 161.3 0.425 179.3 0.438 197.3 0.446 215.3 0.451 233.3 0.460 251.3 0.461 269.3 0.467 287.3 0.474 Series 2'9cpe 152.3 0.420 170.3 0.427 188.3 0.434 206.3 0.440 224.3 0.447 242.3 0.453 260.3 0.462 278.3 0.466 296.3 0.472
series
Series 4u9dse 98.3 0.386 116.3 0.451 134.3 0.424 152.3 0.426 170.3 0.434 188.3 0.442 206.3 0.451 224.3 0.461 242.3 0.469 260.3 0.480 278.3 0.489
Series 5b,d 0.319 206.3 0.460 224.3 0.448 242.3 0.447 260.3 0.452 278.3 0.460
98.3 116.3 134.3 152.3 170.3 188.3
Table IV. Experimental Heat-Capacity Points for Wyoming Coal Liquids CDL,Btu/lb, "F
0.470 0.477 0.484 0.491 0.498
Sample 15-2 (7.620 mg). As received I-VGO sample sealed under 1 atm of nitrogen. Sample 42-1 (9.944 mg). As received I-VGO sample evacuated for 20-30 min, then sealed under 1 atm of argon. Enthalpy method. Single-scan method. e Sample 15-2 heated in sealed pan t o 455 "F after series 1,before series 2 and 4. 0 50
I
I
I
1
I
V
I
A ' 0.48
-
0.46
-
0.44
-
0.42
-
I
I I
A
-
WA-6b
WV-1'
0.412 0.421 0.428 0.438 0.444 0.453 0.442 0.448 0.455 0.465 0.472 0.481 0.481 0.489 0.497 0.504 0.511 0.519 0.503 0.510 0.520 0.527 0.529 0.545 0.439 0.448 0.456 0.462 0.471 0.480 0.495 0.503 0.512 0.527 0.530 0.539
0.397 0.407 0.415 0.426 0.432 0.441 0.421 0.426 0.436 0.445 0.454 0.463 0.464 0.474 0.482 0.492 0.499 0.508
0.407 0.415 0.422 0.432 0.438 0.448 0.428 0.434 0.450 0.456 0.462 0.469 0.476 0.483 0.493 0.501 0.507 0.516 0.507 0.513 0.520 0.528 0.537 0.545 0.418 0.435 0.443 0.450 0.4 59 0.468 0.497 0.500 0.508 0.518 0.524 0.534
0.422 0.434 0.446 0.456 0.467 0.478 0.504 0.510 0.514 0.538 0.538 0.551
Table V. Coefficients of the Straight-Line F i b to the Heat Capscity Data for Illinois and Wyoming Coal Liquidsd
I 0.38
WA-5'
80.3 98.3 116.3 134.3 152.3 170.3 143.3 161.3 179.3 197.3 215.3 233.3 233.3 251.3 269.3 287.3 305.3 323.3 314.3 332.3 350.3 368.3 386.3 404.3 134.3 152.3 170.3 188.3 206.3 224.3 278.3 296.3 314.3 332.3 350.3 368.3
Sample masses were 9.961 mg for series 1, 3 , 4 , 5, and 6, and 11.864 mg for series 2. Sample masses were 10.505 mg for series 1 , 12.468 mg for series 2 and 3, and 5.945 mg for series 5 and 6. Sample masses were 11.571 mgfor series 1, 3 , 4 , 5, and 6, and 14.363 mg for series 2.
I 0
0.40 -
t, "F
I
I
Experimental Data
I
0 Series1
I
Series 2
I
0 A V
1
I
sample
temp range,"F
I-VGO WA-5 WA-6 WV-1
150-296 80-404 80-368 80-404
coefficientsu a
0.379 0.385 0.352 0.369
bx
lo3 RMSb D c
0.357 0.401 0.514 0.442
0.012 0.004
0.008 0.003
2.5 0.9 1.6 0.7
Quadratic fit reduced the RMSD for See Table 11. WA-5 and WA-6 by only 0.1%, which is statistically insignificant.
Serter 3 Series 4 Series 5
01 I
- -- --
Smoothed Approximate Chreeter Of Phare Transition
0 30 50
1W
200
150
250
300
t i'F)
Figure 2. Heat capacity of Illinois VGO coal liquid.
A High-Boiling "Liquid"from Illinois Coal. The as-received I-VGO "liquid" was actually a brown solid, although it appeared to be on the verge of transforming
to a fluid, an impression which was confirmed by the heat-capeeity data. Aa shown in Figure 2, tb.b a t capocitiea between 80 and 150 O F indica* tbnt ai" type of phase transition occura in the sample over this temperature range. As will be discussed below, there was considerable difficulty obtaining reproducible heat-capacity results on I-VGO. Because of these problems, only a limited series of measurements were made, covering the range 80 to 296 OF,but the resulta are reportad here both to .idin correktbn &velwrd k provide 0 ) of the
e
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984 581 0.56
0.54
I
1
......._. --
I
I
I
I
I
I
I
I-VGO WA.5 WA6
1
properties were determined.) Since the initial boiling point of each liquid was estimated to be about 330 O F and the mean average boiling point from 500 to 540 OF, the heat-capacity series were terminated at 404 O F to avoid any errors due to vaporization within the sealed sample pans. Indeed, no signs of curvature in the heat-capacity data at high temperatures were observed for any of the samples. The individual data points for the WA-5, WA-6 and WV-1 samples are given in Table IV in the order in which they were taken. Each series of six heat-capacity results on the three materials is the work of a separate day. More than one sample of each material was used for these measurements. For each material, the results were fitted to polynomials using a least-squares regression method. In all cases, as shown in Table V and Figure 3, a straight line represented the data within experimental error, and only for the WA-5 and WA-6 did a quadratic fit lead to a marginal improvement. Given the scatter of the poinh with respect to the chosen smooth curves, particularly for the WA-6 sample, the smoothed results should be considered accurate within maximum error limits of approximately f2%.
oo 0
50
100
200
150
t
250
3W
350
400
I’FI
Figure 3. Smoothed results for the heat capacities of EDS coal liquids.
difficulties in obtaining accurate data on this type of material. The experimental data points on I-VGO are shown in Figure 2 and given in Table 111. Series 1, 2, and 3 were done by the “enthalpy” method described earlier. Because of the difficultieswhich these measurements revealed, that is, a 5% discrepancy between the data for two separate samples, two further series were run by a different experimental method. For series 4 and 5, a single scan was made over a wide temperature range, 98 to 278 O F , and the heat capacities were calculated from the power output at selected temperatures. This is the DSC method first proposed by O”eill(l966) and commonly described in the literature (Smith et al., 1980; Gray et al., 1981). We have found that our own results by this method are generally accurate within 2 to 3%. Since the heat-capacity points below 150 OF show the phase transition mentioned earlier, only points above the transition will be discussed further. Although heating the sample labeled 15-2 to 455 O F between series 1 and 2 had no effect on the values obtained, there is a considerable offset between all the runs (series 1,2, and 4) on sample 15-2and those on sample 42-1 (series 3 and 5). This offset is presumably due to the difficulty of obtaining a homogeneous sample of the solid or semi-solid I-VGO, even though both samples came from the same bottle. This problem could presumably be overcome if materials like the I-VGOare always warmed to a temperature where the material is fully melted before samples are taken. The limited data on I-VGO above 150 O F were fitted by a least-squares method, yielding a straight line with the coefficients given in Table V. Medium-Boiling Liquids from Wyoming Coal. Neat capacities for the Wyoming coal liquids were measured from 80 to 404 O F . The samples were again hermetically sealed under nitrogen in aluminum pans, with the sample sizes given below. (The experience of other workers in our laboratory has shown that some properties of coal-derived materials change with time, depending on the degree of hydrotreatment, the method of storage, and the degree to which the samples have been exposed to air and light. Our samples of WA-5, WA-6, and WV-1 had been stored in tightly-capped metal containers since their inspection
Analysis of Experimental Data Two widely used correlations for predicting the liquid heat capacities of petroleum fractions are those of Watson and Nelson (1933) and of the API Technical Dat,. Book (1983). Both correlations require the specific gravity (S) and the Watson characterization factor (K,) in order to predict the liquid heat capacity at a given temperature. However, these correlations must be slightly modified to make them more suitable for coal liquids. Liquid Heat Capacity Correlations. There are basically four types of correlations for predicting liquid heat capacities: theoretical, group-contribution, corresponding-states, and empirical. A comprehensive review of liquid heat capacity correlations is given by Reid et al. (1977). In their review, they point out that reliable theoretical procedures for predicting liquid heat capacities have not yet been developed for engineering applications. In addition, although the group-contribution and corresponding-states methods have proved to be satisfactory for defined compounds, these methods cannot easily be applied to undefined mixtures, such as petroleum fractions and coal liquids, due to lack of information on molecular structure and critical properties. Finally, most corresponding-states methods also require the ideal-gas heat capcity (Bondi, 1966) in order to predict the liquid heat capacity of a compound or mixture. Although well-defined for most defined compounds, the ideal gas heat capacity is either uncertain or unknown for undefined mixtures and must be predicted from other generalized correlations. Consequently, additional error is introduced in the final predicted liquid heat capacity value. Recently, Starling et al. (1980) (see Brul6 et al., 1982) proposed a corresponding-states, equation-of-state correlation for predicting the enthalpy of coal liquids. As part of their correlation, Starling et al. also proposed a procedure for predicting the ideal gas heat capacity of coal fractions for use in their corresponding-states approach. However, Gray and Holder (1982) found that this correlation yielded large average absolute deviations for the ten SRC-I1 narrow-boiling coal liquids that they were investigating. These deviations ranged from 9.1 to 39.5%. A simpler method was proposed by Kesler and Lee (1976))who originally developed the method for calculating the liquid and vapor enthalpies of petroleum fractions. This method includes a corresponding-states, equation-
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Ind. Eng. Chem. Process Des. Dev., Vol. 23,No. 3, 1984
Table VI, Data Sources for Liquid Heat Capacity of Coal Liquid Model Compounds temp characterization,d range, no. of compound Kwls OF points benzene
9.71610.885
44-374
17
toluene ethylbenzene o-xylene m-xylene p-xylene n-propylbenzene isopropylbenzene 1,2,3-trimethylbenzene 1,2,4-trimethylbenzene
10.138/0.872 10.35810.872 10.27410.885 10.418/0.869 10.44810.866 10.609/0.867 10.56510.866 10.36310.899 10.534/0.880
-63-284 -63-80 -10-80 -46-116 62-440 -63-206 -10-80 -46-2 20
17 9 6 9 22 16 7 6 10
1,3,5-trimethylbenzene naphthalene 1-methylnaphthalene tetralin cis-decalin trans-decalin pheny lbenzene phenylcyclohexane cyclohexylcyclohexane phenanthrene 9 , l O-dihydrophenanthrene anthracene 1,2,3,4,5,6,7 &octahydroanthracene acenaphthene 2,6-dimethylpyridine quinoline thiophene dibenzothiophene phenol o-cresol m-cresolc
10.617/0.870 9.455/1.015 9.53611.024 9.77510.975 10.489/0.901 10.74710.874 9.54 611.030 10.221/0.950 10.904/0.892 9.14711.130 9.31 8/1.092 9.213/1.123 9.91111.016 9.63311.036 9.84810.923 8.84611.099 8.05 2/ 1.072 8.81011.168 8.64 711.082 8.961/1.051 9.13811.039
-46-80 177-206 - 10-1 7 0 -28-11 6 -28-170 -10-170 152-404 44-386 44-386 211-296 92-170 434-461 162-260 200-332 100-500 100-700 200-400 206-530 105-134 88-260 100-600
8 3 11 9 12 11 15b 20b 20b 6 6 4 7 9 21a 31 a 11= 19b 3 11 26"
80-200
source
San Jose et al. (1976); Swanson and Chueh (1972);Chao (1979) San Jose e t al. (1976); Scott et al. (1962) Scott and Brickwedde (1945) Chao (1979) Pitzer and Scott (1943) Chao (1979) Messerly et al. (1965) Schlinger and Sage (1952) Taylor e t al. (1955) Helfrey et al. (1955);Putnam and Kilpatrick (1957) Chao (1979) McCullough et al. (1957) McCullough et al. (1957) McCullough et al. (1957) McCullough et al. (1957) McCullough e t al. (1957) O'Rourke and Mraw (1983) O'Rourke and*Mraw(1983) O'Rourke and Mraw (1983) Finke et al. (1977) Lee-Bechtold et al. (1979) Goursot et al. (1970) Gammon et al. (1982) Finke et al. (1977) Kidnay and Yesavage (1981);Mohr et al. (1983) Kidnay and Yesavage (1982) Kidnay and Yesavage (1980b) O'Rourke and Mraw (1983) Andon et al. (1963) Andon e t al. (1967) Mohr et al. (1983)
a Smoothed data from experimental liquid enthalpies. Smoothed heat capacity data. Not included in correlation development. K , is Watson characterization factor (eq 1)and S is the specific gravity at 60/60 OF.
of-state correlation for predicting all vapor enthalpies and liquid enthalpies in the critical region, but uses the wellknown correlation proposed by Watson and Nelson (1933) for predicting the liquid heat capacity (and enthalpy) at low temperatures. This correlation is given by C,L = (0.35 + 0 . 0 5 5 ~ ~[om11 ) - 0.308s
+
L
(0.815 where CPLis the liquid heat capacity in Btu 1bm-lO F 1 and t is the temperature in OF. The Kesler and Lee method uses the Watson and Nelson correlation to predict the liquid enthalpy up to a reduced temperature ( T / T , ) of 0.80, where T, is the critical temperature. A similar approach is presented in the API Technical Data Book (1983), which uses the Lee and Kesler (1975) corresponding-states, equation-of-state correlation for vapor and near-critical region liquid enthalpies. However, a correlation different from that of Watson and Nelson is given for predicting liquid heat capacities below a reduced temperature of 0.80 CPL= AI A2T A3!P (3)
+
A , = -1.17126
+
+ (0.023722 + Q.024907S)Kw+ (1.14982- 0.046535Kw)/ S (3a)
A2 = (1.0 + 0.82463Kw)(1.12172 - 0.27634/s)
X
(3b) A3 = -(1.0
+ 0.82463Kw)(2.90270 - 0.70958/S) XlO-' (34
where Tis the temperature in OR. The liquid heat capacity correlation proposed by API incorporates the many petroleum fraction enthalpy data which have been reported since the development of the original Watson-Nelson correlation and, therefore, should be more widely applicable. However, neither the Watson-Nelson nor the API correlations included liquid heat capacity data for highly aromatic materials in their original development. Consequently, one would not expect these correlations to yield satisfactory predictions of liquid heat capacities for coal liquids. In our earlier study (Exxon, 1980), we indicated that, although the Wataon-Nelson correlation may not be suitable in ita original form, improved predictions could be obtained by analyzing available liquid heat capacity data for coal liquids and model compounds in the development of a modified Wataon-Nelson correlation. Modified Watson-Nelson Correlation for Coal Liquids. Experimental liquid heat capacity data for 28 defined model compounds (a total of 342 data points) and 24 coal liquids (a total of 389 data points) were used as the data base for developing the new correlation. Data for defined model compounds are included in the analysis in order to extend the range of applicability of the final correlation. The data sources and characterization for the defined compounds and coal liquids are summarized in Tables VI and M,respectively. Our analysis of these data led to the following modified Watson-Nelson correlation CPL= (0.06759 + 0.05638Kw) X 0.6450
- 0.059593 + (1.2892 - 0.52643)-
1000
3
(4)
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 3, 1984
583
Table VII. Data Sources for Liquid Heat Capacity of Coal Liquids coal liquid EDS I-VGO EDS WA-5 EDS WA-6 EDS WV-1 COED Western Kentucky COED W. Kentucky distillate COED Utah distillate COED W. Kentucky syncrude
