Energy Fuels 2010, 24, 5624–5633 Published on Web 09/09/2010
: DOI:10.1021/ef100375k
Empirical Approach for Predicting Viscosities of Liquid Hydrocarbon Systems: Defined Compounds and Coal Liquids and Fractions Vijayaragavan Krishnamoorthy,* Sharon Falcone Miller, and Bruce G. Miller EMS Energy Institute, The Pennsylvania State University, University Park, Pennsylvania 16802 Received March 30, 2010. Revised Manuscript Received July 24, 2010
A single-parameter empirical method, based on the effective carbon number concept, was developed to predict the viscosities of defined (alkanes, alkenes, aromatics, alicyclics, and hydrocarbon mixtures) and undefined (coal liquids and coal liquid fractions) hydrocarbon liquids at various temperatures and for pressures up to 700 bar. The only parameter required for estimating the viscosities of a hydrocarbon system is the effective carbon number, which can be obtained from a single liquid viscosity datum of the compound using one of two proposed correlations, that is, n-alkane correlation or aromatic correlation. Also, experimental data on the viscosities of laboratory-generated coal liquid oils were generated and used in the evaluation of the model. The new method, when tested on viscosity data of defined and undefined hydrocarbon liquid compounds at various pressures and temperatures, yielded an overall average absolute deviation (AAD) of 4.11% and 9.99%, respectively. The model was also found to compare favorably with other methods available in the literature.
for predicting the viscosities of undefined hydrocarbon liquids require too many parameters that are not readily available and cannot be accurately estimated11 or cannot be applied to predict viscosities at various pressures.4-6,11,12 Moreover, Riazi and Al-Otaibi claim that a model that uses too many estimated input parameters predicts the viscosities of hydrocarbon systems with significant error.11 Teja et al1 applied the Generalized Corresponding States Principle (GCSP)13 to predict the viscosities of four Exxon Donor Solvent (EDS) coal liquids (undefined hydrocarbons). The overall average absolute deviation (AAD), which is defined as the average of the percent absolute differences between predicted and experimental viscosity data P points with respect to experimental viscosity data points (( (|μCalc| - |μExp|) 100/|μExp|)/N), for four EDS coal liquids was 13.61% and 17.79%, when the critical parameters and acentric factor were obtained from the Starling correlations and the Wilson correlations, respectively. However, this method requires estimating the viscosities of two reference fluids and the critical parameters, acentric factor, and molecular weight of the CLO as input parameters. The group contribution approach proposed by Kabadi and Palakkal9 was applied to fifteen fractions of Solvent Refined Coal-II (SRC-II) liquid fractions compiled by Gray et al.14 The overall AAD for all the fractions was 25.01%. Moreover, the method of Kabadi and Palakkal9 requires significant chemical analysis data of coal liquids as input, which are not usually available.
1. Introduction Viscosity is one of the most important transport properties required for developing equipment designs1 and optimizing operating conditions for liquefaction processes. Also, coal liquefaction plants operate at very high pressures and temperatures when converting coal to liquids.2 Therefore, a simple and reliable model that predicts the viscosities of coal liquids over a wide range of pressures and temperatures is highly desirable. Although coal liquid oils (CLOs) are considered as an alternative to crude oil, traditional viscosity prediction methods for undefined liquids, such as the Ely and Hanley method3 and Twu’s methods,4,5 have been shown to predict viscosities of coal liquids with considerable errors.6 These errors in predicting the viscosities of coal liquids by traditional methods have been attributed to the differences in crude oil and coal liquid composition.6 Most of the currently available methods for predicting viscosities of liquids, specifically synthetic fuels, are based on semitheoretical or empirical methods.1,3-9 This is because there are no widely accepted theoretical methods for predicting liquid viscosities.10 Moreover, most of the available methods *To whom correspondence should be addressed. Telephone: 8148653093. E-mail:
[email protected] or
[email protected]. (1) Teja, A. S.; Thurner, P. A.; Pasumarti, B. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 344–349. (2) Probstein, R. F.; Hicks, R. E., Synthetic Fuels, Dover Publications, Inc.: New York, 2006. (3) Ely, J. F.; Hanley, H. J. M. Ind. Eng. Chem. Fundam. 1981, 20, 323– 332. (4) Twu, C. H. Ind. Eng. Chem. Process Des. Dev. 1985, 24, 1287–1293. (5) Twu, C. H. AIChE J. 1986, 32, 2091–2094. (6) Sharma, R.; Goel, S. Ind. Eng. Chem. Res. 1997, 36, 3999–4007. (7) Johnson, S. E.; Svrcek, W. Y.; Mehrotra, A. K. Ind. Eng. Chem. Res. 1987, 26, 2290–2298. (8) Mehrotra, A. K.; Svrcek, W. Y. J. Can. Pet. Technol. 1987, 26, 60–66. (9) Kabadi, V. N.; Palakkal, M. Energy Fuels 1996, 10, 341–347. (10) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. the Properties of Gases and Liquids, 4th ed.; McGraw-Hill: New York, 1987. r 2010 American Chemical Society
(11) Riazi, M. R.; Al-Otaibi, G. N. Fuel 2001, 80, 27–32. (12) Allan, J. M.; Teja, A. S. Can. J. Chem. Eng. 1991, 69, 986– 991. (13) Teja, A. S.; Rice, P. Ind. Eng. Chem. Fundam. 1981, 20, 77–81. (14) Gray, J. A.; Brady, C. J.; Cunningham, J. R.; Freeman, J. R.; Wilson, G. M. Ind. Eng. Chem. Process Des. Dev. 1983, 22, 410–424. (15) Sharma, R. Enthalpy measurements for a coal-derived naphtha and middle distillate and characterization of coal liquids for their extent of association. Ph.D. Dissertation, Colorado School of Mines, Golden, CO,1980
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: DOI:10.1021/ef100375k
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Sharma and Goel extended the method of Twu to predict the viscosity of seven coal liquids compiled by Sharma.16 The method of Sharma and Goel6 predicted the viscosities of seven coal liquids better than the methods of Twu4,5 and the method of Ely and Hanley.3 However, the correlation has limitations in predicting viscosities at various pressures. Allan and Teja12 proposed a single parameter correlation for predicting viscosities of defined liquids (alkanes, alkenes, aromatics, alicyclics, and hydrocarbon liquid mixtures) and undefined mixtures (petroleum fractions) based on the effective carbon number concept. The concept is to correlate the constants in any viscosity-temperature relationship to the carbon numbers of defined compounds used in the development of the model. Allan and Teja used n-alkanes for their model deveoplement, and the effective carbon number of a hydrocarbon indicates the n-alkane’s carbon number that has the same viscosity at a given temperature as that of the compound of interest. The method of Allan and Teja12 was shown to predict viscosities of defined compounds and petroleum fractions more accurately. However, the correlation has limitations in predicting viscosities at various pressures and fails to calculate the effective carbon number for high carbon number liquid fractions. The objective of this work was to develop a simple and reliable method that involves estimating a few input parameters to predict the viscosities of coal liquids at various pressures and temperatures. Therefore, the effective carbon number concept proposed by Allan and Teja12 was modified and extended for model development because of its simplicity and reliability.
Table 1. Summary of Results of Reference Compounds Used in Developing the n-Alkane Correlationa compound
temperature range, K
AAD, %
N
ref
n-hexane n-heptane n-octane n-nonane n-decane n-undecane n-dodecane n-tridecane n-tetradecane n-pentadecane n-hexadecane n-heptadecane n-octadecane n-nonadecane n-eicosane
253.15-423.15 253.15-453.15 253.15-483.15 253.15-503.15 253.15-523.15 263.15-533.15 273.15-553.15 273.15-573.15 283.15-583.15 293.15-593.15 293.15-603.15 303.15-613.15 303.15-633.15 313.15-633.15 353.15-603.15
4.28 3.58 3.07 2.63 2.12 1.81 2.05 2.50 3.35 3.50 4.64 5.02 7.71 7.87 7.98
18 21 24 26 28 28 29 31 31 31 32 32 34 33 26
16
4.23
424
total
17
a
N = no. of P data points predicted; AAD, % = average absolute deviation = ( (|μCalc| - |μExp|) 100/|μExp|)/N.
Table 2. Summary of Results of Reference Compounds Used in Developing the Aromatic Correlationa compound
temperature range, K
AAD, %
N
ref
naphthalene 1-methylnaphthalene phenylether biphenyl o-terphenyl
353.15-603.15 303.20-503.20 303.20-483.20 343.15-663.15 333.15-673.15
2.49 3.17 2.39 2.81 11.82
26 27 22 33 35
20 21 21 20 20
4.96
143
total a
N = no. of data P points predicted; AAD, % = average absolute deviation, % = ( (|μCalc| - |μExp|) 100/|μExp|)/N.
2. Technical Development A review of some of the models suggests that the effective carbon number (ECN) concept proposed by Allan and Teja12 is the most simple and reliable method. Therefore, the effective carbon number concept was used in developing the new model. The technical development of the model is given as follows: 2.1. Viscosity-Temperature Relationship. In the model development, liquid viscosity data of n-alkanes (n-hexane until n-eicosane) over a wide range of temperatures, adapted from the work of Isdale16 and Rossini et al,17 was made to fit Andrade’s equation10 ln μsl ¼ ðA=T Þ þ B ð1Þ
the development of the correlation. This was done to ensure that the correlation does not significantly overpredict the viscosity of liquids beyond their boiling point. A and B, obtained by correlating the natural log of viscosity and inverse temperature, were further correlated with the carbon number of n-alkanes. The n-alkane correlation thus obtained can be written as follows: A ¼ ð - 2:90 n2 Þ þ ð142:55 nÞ þ 196:99
ð2Þ
B ¼ ð0:0027 n2 Þ - ð0:10 nÞ - 3:87
ð3Þ
where n is the effective carbon number. The above correlation predicted the viscosities of n-hexane to n-eicosane used in developing the n-alkane correlation with an overall AAD of 4.23%, with no compound’s AAD exceeding 8.00%. A summary of their results is provided in Table 1. Large deviations (>10.00%) for high carbon number liquids were mostly observed outside the temperature range of 320-500 K. These errors were mainly due to slight deviations from the perfect linear correlation of natural log of viscosity and inverse temperature (i.e., R2 was 10.00%) for decane were mostly found at temperatures beyond its boiling point, as well as at higher pressures (>100 bar). This was primarily because of the nonuniformity of the data set used in developing the correlation. However, the limitation can be addressed after a more uniform data set becomes available. Also, the developed pressure correlation involving all the high-pressure viscosity data of n-alkanes ranging from n-pentane to n-octadecane was found to predict viscosities of n-alkanes with considerable error. This led to the development of another equation for all liquids having an effective carbon number (n) g 12. The pressure factor for compounds having a carbon number (n) g 12 was obtained by correlating the increase in viscosity (μp/μsl) to the increase in pressure from 168 high pressure data points representing seven major compounds, which includes synthetic heavy distillates of crude oils. The data for these compounds were adapted from various literature sources.27-31
Figure 1. Schematic procedure for calculating viscosity using the model.
The equation for liquids having carbon number g 12 and for those liquids using the aromatic correlation is μp ¼ μsl ð1 þ ððP - Po Þ 0:0016ÞÞ
ð8Þ
A summary of results for 166 data points (the other two data points were used in evaluating the effective carbon number of two synthetic crude oils) that were used in generating the aromatic correlation is provided in Table 4. It was found that the AAD for 166 predicted viscosity data points to be 3.52%, with no compound’s AAD greater than 4.69%. The proposed method was extended to predict the viscosities of a defined mixture assuming it as a single-fluid component with an effective carbon number. The underlying assumption is that the effective carbon number, n, of the mixture is calculated using a simple mole-averaging mixing rule, that is,12 X nmix ¼ xi n i ð9Þ
(22) Audonnet, F.; Padua, A. A. H. Fluid Phase Equilib. 2001, 181, 147–161. (23) Kiran, E.; Sen, Y. L. Int. J. Thermophys. 1992, 13, 411–442. (24) Assael, M. J.; Papadaki, M. Int. J. Thermophys. 1991, 12, 801– 810. (25) Caudwell, D. R.; Trusler, J. P. M.; Vesovic, V.; Wakeham, W. A. J. Chem. Eng. Data 2009, 54, 359–366. (26) Naake, L. D.; Wiegand, G.; Franck, E. U. Z. Phys. Chem. 2002, 216, 1295–1310. (27) Boned, C.; Z-Mikkelsen, C. K.; Baylaucq, A.; Dauge, P. Fluid Phase Equilib. 2003, 212, 143–164. (28) Caudwell, D. R.; Trusler, J. P. M.; Vesovic, V.; Wakeham, W. A. Int. J. Thermophys. 2004, 25, 1339–1352. (29) H-Galvan, M. A.; G-Sanchez, F.; M-Salinas, R. Fluid Phase Equilib. 2007, 262, 51–60. (30) Hogenboom, D. L.; Webb, W.; Dixon, J. A. J. Chem. Phys. 1967, 46, 2586–2598. (31) Dymond, J. H.; Young, K. J.; Isdale, J. D. Int. J. Thermophys. 1980, 1, 345–373.
where nmix and ni are the effective carbon numbers of a mixture and pure components, respectively. However, the model requires no compositional information of the mixture and the calculations are completely predictive. 5627
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Table 7. Comparison of Different Reference Points in Calculating ECNa compound
temperature range, K/pressure range, bar
p-xylene
293.15-533.15/1.01
cyclohexane (0.4) þ n-octane (0.6)
298.15-348.15/1-608
reference temperature, K
reference pressure, bar
ECN
AAD, %
ref
313.15 333.15 373.15 393.15 298.15 298.15 298.15 323.15 323.15 323.15 348.15 348.15 348.15
1.01 1.01 1.01 1.01 1.00 296.00 606.00 1.00 106.00 603.00 1.00 204.00 608.00
8.46 8.72 9.01 9.14 8.32 9.54 10.69 8.40 8.96 10.99 8.41 9.54 11.36
7.32 5.92 4.90 5.26 4.05 7.70 23.76 2.44 2.56 19.28 2.30 5.92 16.98
20
a
N = no. of data points predicted; AAD, % = average absolute deviation, % = (
P (|μCalc| - |μExp|) 100/|μExp|)/N.
35
Figure 2. Evaluation of defined compounds by the developed method. Table 8. Summary of Results for Defined Hydrocarbon Liquids at Saturation/Atmospheric Pressurea
3. Experimental Data To evaluate the method proposed in this work, experimental viscosity data of coal liquids, in addition to the viscosity data of pure hydrocarbons and mixtures, are required. Unlike petroleum fractions, viscosity data of coal liquids from the literature is limited. To test coal liquids over a wide range of compositions, SRC-I naphtha,15 SRC-II coal liquid fractions,14 EDS liquids,32 CharOil-Energy-Development (COED) process coal liquids and fractions,15 and Hydrocarbon Technology Inc. (HTI) process coal liquid fractions33 (Shenhua coal liquids) were obtained from the literature. To add one more variation in composition to the above-mentioned coal liquids, two laboratory-generated coal liquid oils derived from a Montana Powder River Basin subbituminous coal (i.e., Dietz seam) using microreactors were also used in testing the new method. The boiling cuts of the coal liquid oils were measured as per ASTM D2887 procedure using a Hewlett-Packard 5890 Simulated Distillation Gas Chromotography fitted with a Restek column. The mean average boiling point was then calculated from the boiling cuts using equations given in the API technical data book.34 The physical properties of the two coal liquid oils are given in Table 5. To obtain the viscosity data of these liquids, a Bohlin Gemini HR nano rheometer fitted with 40 mm flat plate geometry was used at a fixed shear stress of 1 Pa. Dynamic viscosity of all samples was measured at temperatures between 311 and 334 K. Each measurement was repeated twice to
compound cyclopentane methylcyclopentane ethylcyclopentane n-propylcyclopentane n-butylcyclopentane n-pentylcyclopentane n-hexylcyclopentane n-heptylcyclopentane n-octylcyclopentane n-nonylcyclopentane n-decylcyclopentane cyclohexane methylcyclohexane ethylcyclohexane benzene toluene o-xylene m-xylene p-xylene 2-propyltoluene 2-phenylpropane 2-phenylbutane 1-hexene 1-heptene 1-octene 1-nonene 1-decene
(32) Thurner, P. A. A corresponding states approach for the calculation of viscosity over a wide range of temperature and pressure, M.S. Dissertation, Georgia Institute of Technology, Atlanta, GA, 1984 (33) Zhang, H.; Ling, K.; Shen, J.; Sheng, Q.; Wang, Y. Coal Conversion 2006, 29, 40–44. (34) ASTM standard D2887-procedure 2B1.3, Characterizing boiling points from simulated distillation data, API technical data book, 2008.
overall a
temperature range, K ECN AAD, % N ref 248.15-318.15 248.15-343.15 253.15-373.15 253.15-383.15 253.15-383.15 253.15-383.15 253.15-383.15 253.15-383.15 253.15-383.15 253.15-383.15 253.15-383.15 283.15-353.15 248.15-373.15 248.15-383.15 283.15-473.15 253.15-513.15 253.15-543.15 253.15-543.15 293.15-533.15 253.15-593.15 253.15-563.15 253.15-563.15 273.15-423.15 273.15-453.15 273.15-473.15 273.15-503.15 273.15-523.15
6.85 7.36 8.19 8.92 9.90 10.92 12.03 13.15 14.28 15.43 16.64 9.75 9.02 9.77 8.42 8.33 9.53 8.62 8.72 10.57 9.38 9.97 5.647 6.60 7.55 8.55 9.57
5.09 5.82 5.98 7.02 5.07 3.67 2.66 2.01 1.61 1.45 1.62 4.99 1.12 6.02 2.93 5.15 4.76 7.64 5.92 5.31 4.10 3.04 3.47 3.27 3.31 3.63 3.65 4.10
14 17 19 24 26 26 26 26 26 26 26 26 14 25 27 19 20 26 29 29 24 34 31 31 15 36 18 20 23 25 655
N = no. of data P points predicted; AAD, % = average absolute deviation, % = ( (|μCalc| - |μExp|) 100/|μExp|)/N.
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Table 9. Summary of Results for Defined Hydrocarbon Liquids at Various Temperatures and Pressuresa compound
temperature range (K)/pressure range (bar)
benzene toluene cyclohexane cyclohexane (1) þ n-octane (2) cyclohexane (1) þ n-octane (2) cyclohexane (1)þ n-octane (2) cyclohexane (1) þ n-octane (2) cyclohexane (1) þ n-dodecane (2) cyclohexane (1) þ n-dodecane (2) cyclohexane (1)þ n-dodecane (2) cyclohexane (1) þ n-dodecane (2) cyclohexane (1) þ n-hexadecane (2) cyclohexane (1) þ n-hexadecane (2)
298.15-348.15/1.00-617.00 217.60-353.52/1.01-255.30 318.15-413.15/69.00-620.50 298.15-348.15/1.00-615.00 298.15-348.15/1.00-608.00 298.15-348.15/1.00-604.00 298.15-348.15/1.00-604.00 298.15-348.15/1.00-602.00 298.15-348.15/1.00-613.00 298.15-348.15/1.00-613.00 298.15-348.15/1.00-612.00 318.15-413.15/69.00-620.50 318.15-413.15/69.00-620.50
overall a
N = no. of data points predicted; AAD, % = average absolute deviation, % = (
mole fraction
ECN
AAD, %
N
ref
x1 = 0.2 x1 = 0.4 x1 = 0.6 x1 = 0.8 x1 =0.2 x1 = 0.4 x1 = 0.6 x1 = 0.8 x1 = 0.7 x1 = 0.3
8.51 8.07 9.98 8.18 8.40 8.71 9.14 11.59 11.26 10.85 10.38 12.74 14.78
5.13 2.92 4.13 2.98 2.56 2.22 6.15 6.91 6.03 7.50 7.64 4.55 3.91
14 82 53 17 16 15 12 11 11 09 11 53 53
37 38 39 35
4.12
357
P (|μCalc| - |μExp|) 100/|μExp|)/N.
39
than 5.00%. Summaries of the results for various defined compounds are provided in Tables 8 and 9. The proposed correlations, when tested with the viscosity data of various coal liquids, yielded an overall AAD of 9.99%. A summary of the results for the coal liquid oils is provided in Table 10. Figure 3, a series of probability plots, show the predictability of the model for coal liquid oils based on their boiling points and temperatures at which their viscosities were measured. It is evident from Figure 3 that the model predicts both middle distillates and light distillates very well (673 K) with large errors (>20% AAD). Poor predictability of viscosities of heavy distillates, especially at low temperatures, can be attributed to their wide range of viscosities. Figure 4 shows the viscosity-temperature relationship of a SRC-II (fraction 16) heavy distillate. It is evident from the figure that a small increase in temperature significantly reduces the viscosity of this SRC-II fraction. Such a wide range of viscosities of heavy distillates can be attributed to the presence of a significant amount of solid asphaltenes and solid maltenes at low temperatures.40 Therefore, it is not surprising that a model that was designed specifically for liquid hydrocarbon systems will predict viscosities of heavy distillates, especially at low temperatures, poorly. However, this limitation can be addressed after more viscosity data of heavy distillates or compounds having a wide range of viscosities become available. The other limitation of the model is that the viscosity predictions of light and middle distillates at high temperatures (>673 K) were found to be relatively poor. This can be attributed to the low viscosity values of coal liquid oils at high temperatures (>673 K) and that a slight difference between experimental and predicted viscosities significantly magnifies the error. However, additional high temperature viscosity data of light and middle distillates of coal liquid oils are needed to evaluate the reliability of the model at high temperatures. Despite these limitations, the developed model compares favorably, in terms of its accuracy, with the method of Kabadi and Palakkal9 for SRC-II coal liquid fractions14 and the method of Sharma and Goel6 for seven other coal liquid oils.15 Figures 5 and 6
check the repeatability of the viscosity data reported in the work. To check the accuracy of the data, the viscosity of N4-Canon standard liquids was measured and compared to its reported values. Deviations between measured and reported values were within (8.00%. The viscosity data are provided in the Table 6.
4. Calculation Procedure A schematic procedure for calculating viscosities by this method is shown in the Figure 1. The first important step in using this method is the selection of appropriate viscosity datum for calculating the effective carbon number. Table 7 shows the effect of viscosity datum of p-xylene and a cyclohexane þ n-octane mixture on AAD. For p-xylene, the data show that the reference viscosity chosen for calculating ECN does not have a significant effect since the AAD is ∼5-7%. However, for the cyclohexane þ n-octane mixture, the AAD increases considerably for the ECN calculated using the viscosity datum measured at high pressure. Therefore, to obtain better predictive results from the correlations over a wide range of temperatures and pressures up to 700 bar, the reference viscosity datum measured at a low pressure and relatively high temperature is recommended. A sample calculation for predicting viscosity using this method is shown in the Appendix. The calculations require no iterations; consequently, that the viscosities can be calculated using a handheld calculator. 5. Evaluation of the Model To evaluate the proposed correlations, viscosity data of pure hydrocarbon liquids,17,20,36-39 defined hydrocarbon mixtures,35,39 coal liquids14,15,32,33 from various literature sources, and liquid viscosity data of two laboratory-generated coal oils derived from the Dietz seam subbituminous coal have been tested. Figure 2 shows the predictive ability of the model for defined compounds. It is evident from the figure that the model predicts defined compounds extremely well. The AADs for all the liquids, except for aromatics, were found to be less (35) Tanaka, Y.; Hosokawa, H.; Kubota, H.; Makita, T. Int. J. Thermophys. 1991, 12, 245–264. (36) Isdale, J. D. Viscosity of Liquid Aliphatic Hydrocarbons: Alkenes, Item 80015; ESDU International Plc: London, 1980. (37) Vieira dos Santos, F. J.; Nieto de Castro, C. A. Int. J. Thermophys. 1997, 18, 367–378. (38) Assael, M. J.; Dalaouti, N. K.; Polimatidou, S. Int. J. Thermophys. 1999, 20, 1367–1377. (39) Rajagopal, K.; Andrade, L. L. P. R.; Paredes, M. L. L. J. Chem. Eng. Data 2009, 54, 2967–2970.
(40) Hasan, A. M. D.; Fulem, M.; Bazyleva, A.; Shaw, J. M. Energy Fuels 2009, 23, 5012.
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Table 10. Summary of Results for Coal Liquids compounds
temperature range, K/pressure range, (bar)
ECN
AAD, %
N
ref
Deitz-1-CLO Deitz-2-CLO SRC-II;Cut-1 SRC-II;Cut-2 SRC-II;Cut-3 SRC-II;Cut-4 SRC-II;Cut-5 SRC-II;Cut-6 SRC-II;Cut-7 SRC-II;Cut-8 SRC-II;Cut-9 SRC-II;Cut-10 SRC-II;Cut-11a SRC-II;Cut-12a SRC-II;Cut-13a SRC-II;Cut-15a SRC-II;Cut-16a Utah distillate W. Kentucky whole oila W. Kentucky Distillate SRC-1 naphtha 1046 naphtha 878 middle distillate synthoil distillatea IHS-EDS-CLO IA-3-EDS-CLO IA-6-EDS-CLO IA-10-EDS-CLO Shenhua-1-CLO Shenhua-2-CLO Shenhua-3-CLO Shenhua-4-CLOa
314.35-333.35/1.01 311.75-333.25/1.01 300.3-424.5/7.91-14.80 295.5-421.3/7.91-14.80 297.8-424.3/4.46-14.80 295.0-421.4/7.91-14.80 294.8-501.8/7.91-14.80 295.8-502.0/7.91 296.8-505.0/7.91 295.8-503.7/7.91-42.38 296.8-504.8/7.91-14.8 341.4-500.2/7.91 296.9-504.0/7.91-44.61 342.6-506.9/28.59-42.38 342.9-496.3/7.91 340.4-501.5/7.91 341.9-500.0/56.17 294.26-343.15/1.01 300.93-330.93/1.01 298.71-348.71/1.01 289.82-331.48/1.01 289.82-332.04/1.01 297.59-359.82/1.01 300.93-359.82/1.01 311.0-728.0/6.70-138.00 450.0-700.0/13.79-137.90 366.5-700.0/13.79-137.90 366.5-700.0/13.79-137.90 293.15-353.15/1.01 293.15-353.15/1.01 293.15-353.15/1.01 293.15-353.15/1.01
17.67 16.92 6.89 8.62 8.50 9.46 12.42 15.73 16.43 20.44 19.85 24.90 17.30 18.40 18.92 18.06 19.29 14.92 13.60 15.01 8.81 9.85 18.53 14.43 17.43 17.95 16.60 15.04 11.30 16.77 20.52 15.72
3.05 5.49 4.14 5.44 5.22 7.41 3.35 10.30 10.36 9.56 10.97 8.90 30.16 24.14 22.87 14.50 25.19 4.77 7.12 1.92 1.94 1.25 9.72 16.15 12.67 8.10 8.14 12.61 14.02 6.71 9.68 20.85
17 20 3 3 3 3 5 5 5 5 5 4 4 4 4 4 4 5 3 5 4 4 5 5 27 26 77 72 6 6 6 6
current work
9.99
355
overall
14
15
32
33
P ECN calculated using the aromatic correlation; N = no. of data points predicted; AAD, % = average absolute deviation, % = ( (|μCalc| - |μExp|) 100/|μExp|)/N. a
Figure 3. Probability plots of absolute error in predicting the viscosities of coal liquid oils and fractions.
present the comparison of the developed method with the method of Sharma and Goel6 and Kabadi and Palakkal,9 respectively. The temperature and pressure ranges of coal
liquids used for comparing the developed method with the above-mentioned methods are shown in Table 10. The poor predictability of the method of Kabadi and Palakkal9 was 5630
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Figure 4. Prediction of the viscosities of SRC-II (cut 16) coal liquids using the new method (% AAD = 25.19).
Figure 5. Comparison of the developed method with the method of Sharma and Goel.
Figure 6. Comparison of the developed method with the method of Kabadi and Palakkal for SRC- II coal liquid fractions.
GCSP þ Wilson and the GCSP þ Starling method reported in the work of Teja et al1 was used for the comparison. The Wilson and Starling methods are the correlations that were used in estimating acentric factors and critical parameters (ω, Tc, and Pc) of CLOs for the GCSP method. Molecular weights of coal liquids required for the GCSP model, if unavailable, were obtained from the correlation proposed by Brule et al.41 Specific gravities at 293.15 K, which are required
attributed to the inaccuracies in estimating one of the input parameters, that is, molecular weight, while the slight inaccuracies in estimating viscosity correction factors required for the correlation may have resulted in poor prediction of some of the coal liquids by the method of Sharma and Goel.6 The GCSP model was selected from all the published models for comparison with the developed model, over the entire data set, because of its applicability over a wide range of temperatures and pressures for coal liquids. Also, it requires only average boiling point and specific gravity data from which most of the input parameters can be estimated. The
(41) Brule, M. R.; Lin, C. T.; Lee, L. L.; Starling, K. E. AIChE J. 1982, 28, 616–625.
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Table 11. Comparison of the Developed Method with the GCSP Method for Coal Liquidsa coal liquids and fractions
N
AAD of the developed method, %
AAD of the GCSP þ Wilson method, %
AAD of the GCSP þ Starling method, %
IHS IA-3 IA-6 IA-10 SRC-II Shenhua CLO Deitz CLO (1 and 2) Utah distillate Western Kentucky whole oil Western Kentucky distillate SRC-1 naphtha 1046 naphtha 878 middle distillate Synthoil distillate
27 26 77 72 61 24 37 5 3 5 4 4 5 5
12.67 8.10 8.14 12.61 12.99 12.82 4.37 4.77 7.12 1.92 1.94 1.25 9.72 16.15
13.19 10.13 19.59 17.90 24.02 16.07 48.59 35.80 39.19 29.65 17.45 11.38 30.14 51.89
14.48 11.46 14.40 11.74 27.39 25.10 50.83 28.79 41.56 23.22 11.02 9.85 35.81 55.86
22.62
21.73
overall
355
9.99 P AAD, % = average absolute deviation, % = ( (|μCalc| - |μExp|) 100/|μExp|)/N.
a
Figure 7. Comparison of the developed method with the GCSP methods for predicting viscosities of CLOs.
Figure 8. Comparison of the developed method with the GCSP þ Starling method for coal liquid oils.
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for the Starling correlations, were obtained by extrapolating specific gravities of petroleum standards at 288.71 K. Comparison of the GCSP model with the developed model is shown in Table 11 and Figure 7. From Table 11 and Figure 7, it is clear that the developed method is a significant improvement in predicting viscosities of coal liquid oils compared to the GCSP þ Wilson and the GCSP þ Starling methods. Figure 8 shows the comparison of the developed method with the GCSP þ Starling method for all coal liquid distillates. Also from Table 11, it can be observed that the difference in the predictions between the newly developed method and the GCSP method are greater for some of the heavy and middle distillates. The predictive ability of the GCSP method strongly depends upon the similarity of the reference liquids to the liquids under investigation,42 and therefore, the poor predictions of some of the heavy and middle distillates by the GCSP method might have been the result of the use of inappropriate reference components. The other limitation of the GCSP method is that most of the input parameters have to be estimated: acentric factors of coal liquid oils, molecular weights of coal liquid oils, and critical temperatures and critical pressures of coal liquid oils; specific gravities of coal liquid oils at 293.15 K for use in the GCSP þ Starling; and viscosities of benzene and decane over a wide range of temperatures and pressures. Application of the GCSP method to CLOs may lead to significant errors, as the above-mentioned parameters may likely be estimated with slight deviations compared to precise experimental values. Most importantly, the predictability of the GCSP method strongly depends on the accuracy of average boiling point and specific gravity data of CLOs from which most of the input parameters have to be estimated. In the case of the developed method, however, only one parameter, ECN, is estimated. Therefore, it is not surprising that the newly developed single parameter method was able to predict viscosities of CLOs better than the multiparameter GCSP method.
Appendix To further clarify the method, we present a sample calculation for predicting viscosities of a coal liquid oil. The calculation requires single viscosity datum of this coal liquid oil. One viscosity data point of SRC-II (fraction-1) coal liquid oil, μExp = 0.2557 mPa s measured at T = 339.6 K and Po = 7.9 bar, from Gray et al14 is chosen for calculation. μExp ¼ 0:2557 mPa s,
T ¼ 339:6 K,
Po ¼ 7:9 bar
The ECN of the coal liquid oil can be calculated using eq 1 ln μsl ¼ ðA=T Þ þ B Substitution of A and B of the n-alkane correlation, μ and T in the eq 1 results in lnð0:2557Þ ¼ ððð - 2:90 n2 Þ þ ð142:55 nÞ þ 196:99Þ=339:6Þ þ ðð0:0027 n2 Þ - ð0:10 nÞ - 3:87Þ Solving the above quadratic equation yields n (ECN) = 6.89. A and B for the SRC-II (fraction-1) coal liquid oil can be obtained by substituting n in eqs 2 and 3 A ¼ 1041:49,
B ¼ - 4:43
Since n < 12, viscosities should be calculated using eq 7 μp ¼ expððA=T Þ þ BÞ ð1 þ ððP - Po Þ 0:00112ÞÞ or μp ¼ expðð1041:49=T Þ þ ð - 4:43ÞÞ ð1 þ ððP - 7:9Þ 0:00112ÞÞ Viscosities over a wide range of pressures and temperatures can be calculated by varying P and T in the above equation viscosity ðμCalc Þ at T ¼ 300:3 K and
6. Conclusions
P ¼ 7:91 bar is 0:3819 mPa s
A simple and reliable technique for predicting viscosities of defined and undefined compounds (coal liquid oils and fractions) over a wide range of temperatures and pressures (up to 700 bar) was developed. Measured viscosities of laboratory-generated coal liquid oils at different temperatures were also reported in this work. The developed method was found to predict viscosities of defined compounds and light and middle distillates of coal liquid oils extremely well. Furthermore, the method was also found to predict viscosities of heavy distillates at temperatures higher than their pour points with reasonable accuracy. Accuracy of the developed method was better than the GCSP method in estimating the viscosities of 32 coal liquid fractions. The method was better than other models that were specifically designed for coal liquids using a limited coal liquid data set that is publically available.
ðμExp ¼ 0:3545 mPa sÞ viscosity ðμCalc Þ at T ¼ 424:5 K and P ¼ 14:80 bar is 0:1395 mPa s ðμExp ¼ 0:1342 mPa sÞ Nomenclature A and B = fitting constants in Andrade’s equation P AAD, % = average absolute deviation, % = ( (|μCalc| |μExp|) 100/|μExp|)/N n = effective carbon number (ECN) N = number of data points predicted Po= pressure at which the single viscosity datum was measured (in bar) P = pressure at which viscosity has to predicted (in bar) Tb = boiling point (in K) ref = reference μCalc = calculated viscosity in mPa s μExp= experimental viscosity in mPa s μsl = viscosity of saturated liquid measured in mPa s μp = viscosity of liquid at pressure P in mPa s. xi = mole fraction of the component i
Acknowledgment. The following EMS Energy Institute personnel are acknowledged for their assistance: Dr. Harold Schobert for providing input on coal liquefaction; Mr. Gareth Mitchell for supplying the coal for testing; and Dr. Qiujing Yang for assisting with the tubing bomb testing and viscosity measurement training. (42) Monnery, W. D.; Svrcek, W. Y.; Mehrotra, A. K. Can. J. Chem. Eng. 1995, 73, 3–40.
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