Ind. Eng. Chem. Res. 1997, 36, 3999-4007
3999
CORRELATIONS Correlation of Viscosity of Coal Liquids Raj Sharma* and Sunil Goel Department of Chemical Engineering, Malaviya Regional Engineering College, Jaipur 302017, India
Applicability of viscosity correlations for predicting viscosities of coal liquids was tested against experimental viscosity data of seven coal liquids. The data considered in this work were at ambient pressure and moderate temperatures (294-360 K). The predicted viscosities were much lower than the experimental viscosities with an average absolute deviation of about 30% at best and 70% maximum. It appears that the association effects owing to hydrogen bonding in coal liquids are responsible for this deviation since the petroleum correlations for viscosity predictions were developed for nonpolar, nonassociating fluids. A simple correction is suggested which helps in predicting coal liquid viscosities more accurately to within an average absolute deviation of 12%. Introduction Coal-derived liquids have always been considered as an alternative to petroleum crude, and after proper treatment and refining can be substituted wherever petroleum finds its uses. Transport properties of coal liquids, among other property data, are required for efficient design of equipment for processing these coal liquids. Viscosity is one such property which requires immediate attention. Information on viscosity is generally required for designing process equipment such as heat exchangers, pumps, and distillation columns. Viscosity data for coal liquids is scarce, and a method for predicting their viscosities is of great practical interest. However, before attempting to develop a new predictive approach, it is important to determine the applicability of existing correlations for predicting viscosities of coal liquids. This article presents the results of testing the applicability and accuracy of selected existing petroleum-fraction viscosity correlations against the limited experimental data of coal liquids and their model compounds and our attempts at development of a new correlation for coal-derived liquids. Data Bank For our correlational effort, viscosity data for coal liquids of Sharma (1980) were used. An average error of (5% in the experimental values was reported by Sharma (1980). Table 1 presents a compilation of the coal liquids viscosity data used in this work. In addition to coal liquids, several model compounds were chosen on the basis of the work of Holliman (1979), representative of the chemical species believed to be present in coal liquids. Viscosity data for these model compounds and three model mixtures reported by Oshmyansky, et al. (1987) were used in this work and are summarized in Table 2. The entire data considered in this work is at ambient pressure and moderate temperatures (294-360 K). * Author to whom all correspondence should be addressed. Tel: 91-141-521 591. Fax: 91-141-520 954. E-mail: rajsh@ recjai.ernet.in. S0888-5885(96)00733-6 CCC: $14.00
Application of Petroleum Correlations To Predict Viscosities of Coal Liquids and Pure Compounds Comparison of Viscosity Predictions with Experimental Data. As an initial stage in the effort to correlate the viscosity data for coal liquids, the experimental viscosities were compared with the predicted viscosities using correlations developed for petroleum fractions. However, it is important to note that the conditions under which the coal liquids are formed and the hydrocarbon-type distribution often differ radically from those of petroleum fractions (Sharma et al., 1982). For example, coal liquids contain a significant amount of heteroatoms (2-20 mol %) and are more aromatic than the conventional petroleum fractions (Sharma, 1980; Holliman, 1979; Sharma et al., 1982; Probstein and Hicks, 1982). Several correlations exist for estimating viscosities of “mixtures” and petroleum fractions (Hanley et al., 1975; Hanley, 1976; Ely and Hanley, 1981; Baltatu, 1982; Twu, 1985,1986) and have been discussed in detail by Goel (1987). More recently, Moharam and Fahim (1995) extended the work of Peterson et al. (1991) to predict viscosities of heavy petroleum fractions and crude oils. Most of these correlations are based on the corresponding states approach with variations in the choice of reference fluid(s). In this work, Ely and Hanley’s method (1981) (mainly because it set the tone for later developments in correlations for predicting viscosities of undefined mixtures using the corresponding states approach) and Twu’s correlations (1985 and 1986) (because the industry-accepted bulk properties of undefined mixtures and petroleum fractions as reference fluids are used to predict petroleum liquid viscosities) are applied for predicting coal liquid viscosities. Table 3 presents a summary of correlations considered in this work. Also included are methods applied for estimating the various characterization parameters of coal liquids for use with the Ely and Hanley correlation. As shown in Table 3, since Ely and Hanley’s correlation is based on the corresponding states approach, estimation of critical properties and the acentric factor (psuedocritical constants for defined and undefined mixtures) acquires utmost importance. There is no © 1997 American Chemical Society
4000 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 1. Coal-Derived Liquids Used in This Work (Sharma, 1980) coal-liquid
conversion process
no. of viscosity measmnts
temp range, K (°F)c 294.3-343.2 (70-158) 300.9-330.9 (82-136) 298.7-348.7 (78-168) 289.8-331.5 (62-137) 289.8-332.0 (62-138) 297.6-359.8 (76-188) 300.9-359.8 (82-188)
Utah distillate
Utah
COEDa
6
Western Kentucky whole oil
Western Kentucky
COED
4
Western Kentucky distillate
Western Kentucky
COED
6
SRC-I naphtha
SRC-Ib
5
1046 naphtha
SRC-II
5
middle distillate
SRC-II
6
synthoil
6
synthoil distillate a
coal
Kentucky bituminous
Char oil energy development. b Solvent refined coal. c All data reported are at atmospheric pressure.
Table 2. Model Compounds and Model Mixtures Used in This Work (Oshmyansky et al., 1987)a,b compound/mixture
no. of viscosity measurements
temp range, K
m-cresol decalin 2,6-lutidine 1-methylnaphthalene quinoline tetralin tetrahydrofuran thiophene m-xylene base syn coal liquid 3.5 wt % oxygen syn coal liquid 10.0 wt % oxygen syn coal liquid
4 4 4 4 4 4 2 3 4 4 2 2
298-358 298-358 298-358 298-358 298-358 298-358 298-318 298-338 298-358 298-358 298-358 298-358
a All data reported are at atmospheric pressure. b Average errors of (2% in the experimental measurements have been reported by Oshmyansky et al. (1987).
“best” correlation to estimate the characterization parameters of coal liquids; therefore, several of these correlations were used in conjunction with Ely and Hanley’s correlation to predict coal liquid viscosities. Twu’s internally consistent correlation (1985) is based on the fact that the properties of a real system can be expanded about the values for a reference system. In this correlation, the kinematic viscosity of the petroleum fraction (the “real” system) is estimated. The correlation uses n-alkanes as the reference fluid and employs the mean average boiling point (MeABP) and specific gravity (SG) as the characterization parameters. The correlation is capable of predicting liquid viscosity of petroleum fractions with a MeABP of up to 1000 K and an API gravity as low as -30° (SG ) 1.394). Twu’s generalized correlation (1986) considers the choice of reference viscosities carefully. Since the accuracy of any corresponding-states approach also depends on the choice of the reference system, in addition to the accuracy of the critical constants and the acentric factor, the closer the system of interest to the reference system, the more accurate the predictions. Therefore, Twu (1986) selected petroleum fractions, with the same MeABP as that of the petroleum fraction under investigation, as the reference fluids. As in Twu’s earlier correlation (1985), MeABP and specific gravity are used here also as the characterization parameters. The above correlations were used to predict the viscosities of coal liquids listed in Table 1. Comparisons of these methods were then made with the experimental data for the above mentioned coal liquids. Some of the typical results are presented in Figures 1 and 2. Table
4 summarizes the results of all the comparisons. The “signs” are presented for those systems where there was a distinct bias in the results, the negative sign indicating that the calculated viscosities were lower than the experimental ones. Also presented in this table are the API gravity, the Watson characterization factor, K, which is an indicator of the aromatic content of an oil, and Sharma’s (1980) association factor, β, which indicates the extent of association in coal liquids. For all the coal liquids, and for all the correlations considered, the predicted values were biased low, relative to the experimental values. However, in some cases, evident from the tables, the comparisons were good, while in others the deviations were too large for the petroleum correlations to be used for prediction of viscosities of coal liquids. Moreover, there appears to be a considerable variation in these differences, depending largely upon the coal liquid. Of the three correlations, Twu’s generalized correlation (1986) gave the least errors for all the coal liquids, except for the Western Kentucky whole oil. The largest errors were associated with the Ely and Hanley method (1981). As discussed earlier, four different sets of correlations were applied for estimating the various characterization parameters required for use with the Ely and Hanley correlation (1981). From Table 4, it is also apparent that the estimates of the characterization parameters obtained by the Lee-Kesler correlation (1976)sset 2 of Table 3sgave the least errors in the viscosity predictions when used with Ely and Hanley’s method (1981). Origins of the “Deviations” in Viscosity Predictions. The origin of the errors in viscosity predictions can be traced to the use of reference fluids in the correlations that are not of the same nature as that of the coal liquids. For example, Ely and Hanley’s correlation (1981) uses n-alkanes as the reference fluids which are an entirely different class of hydrocarbons than those found in coal liquids. Similarly, Twu’s correlation (1986) uses petroleum fractions as the reference fluids, the hydrocarbon-type distribution of which often differs radically from that of the coal liquids. Also, it was originally believed that the high level of aromatics in coal-derived liquids would result in major property differences between coal liquids and petroleum fractions. Sharma (1980) and Sharma et al. (1982) have, however, shown that the presence of aromatics causes only a minor difference between the predicted values and the experimental data in the case of enthalpies of coal liquids. This line of reasoning seems to hold true for viscosity as well. As mentioned earlier, the Watson characterization factor (K) is, in a manner, a
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 4001 Table 3. Summary of Correlations Used in This Work set no. 1.
2.
3.
viscosity correlation Ely and Hanley (1980)
Twu’s internally consistent correlation (1985)
characterization parameters reqd correlation used
main viscosity eq µx(F,T) ) µ0(F0,T0)Fµ
Tc, Pc, Vc, MW ω Tc, Pc, Vc, MW, ω Tc, Pc, Vc, ω, MW
Riazi and Daubert (1980) Edmister (1961) Lee and Kesler (1976) Roman et al. (1986) Riazi and Daubert (1980) Tc, Pc, Vc, ω, MW Roman et al. (1986) Lee and Kesler (1976) MeABP, SG not required
ln(ν + 450/MeABP) ) 1 + 2f ln(ν + 450/MeABP) 1 - 2f 0
Twu’s generalized correlation
ν ) ν10
() ν20
(
(k-10)/2
)
I.D. No. (this work) remarks set 1
a
set 2 set 3
a a
set 4
a b
2
MeABP, SG
not required
c
0
ν1
a This method is based on one-fluid corresponding states principle and is a predictive procedure to estimate the viscosity of nonpolar pure fluids and mixtures over the entire range of fluid states, from the dilute gas to the dense liquid. Reference fluid is methane. b Used for the calculation of liquid viscosities of petroleum fractions, with MeABP up to 1000 K and API as low as -30°. Uses n-alkanes as reference fluids. c Used for calculating liquid viscosities of petroleum fractions and is based on two reference fluid corresponding states method. Uses petroleum fractions with K of 10 and 12 as reference fluids.
Figure 1. Viscosity vs temperature curves for Utah distillate using different correlations.
measure of aromaticity of oils; a comparison of the errors in the viscosity prediction between the Utah distillate, the Western Kentucky whole oil, and the Western Kentucky distillate, that have the same K, shall illustrate the point further that the effect of aromatics is minor in the viscosity predictions. From Table 4 it is evident that even at the same K, for the above coal liquids, the error is the lowest for the Western Kentucky whole oil and the highest for the Utah distillate despite the fact that the Utah distillate (MeABP ) 469.9 K, 29.4° API) is “lighter” than the Western Kentucky whole oil (MeABP ) 550 K, 21.8° API). The other major difference between coal liquids and petroleum liquids is the higher level of organic oxygen and nitrogen compounds in coal liquids (Holliman, 1979; Sharma et al., 1982). Since the experimental viscosity data for the coal liquids are higher than the calculated values, this would be consistent with an association
Figure 2. Viscosity vs temperature curves for synthoil distillate using different correlations.
effect and an energy of association. Sharma et al. (1982, 1983) have shown that this is so in the case of enthalpies of coal liquids. Sharma et al. (1983) have further argued that the association effects such as “hydrogen bonding are quite likely in such fluids” and that the hydrogen bonding effects depend on whether the oxygen present in the coal liquids is tied up in an ether linkage or a phenolic linkage. To further illustrate the effect of association, comparisons were made between the predicted viscosities, by the three correlations discussed above, and the experimental data for several model compounds and model mixtures presented in Table 2. The critical constants, molecular weights, acentric factors, and the normal boiling points of the model compounds that were used in the viscosity correlations are presented in Table 5. For the model mixtures of Table 6, pseudocritical properties and the characterization parameters were calculated by the different sets of correlations (as
4002 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 4. Average Differences between Experimental and Predicted Viscosity Data of Coal Liquids average error % Ely and Hanley (1981) coal liquid
no. of points
set 1
set 2
set 3
set 4
Twu (1985)
Twu (1986)
APIa
Ka
βb-d
Utah distillate Western Kentucky whole oil Western Kentucky distillate SRC-I naphtha 1046 naphtha middle distillate synthoil distillate
6 4 6 5 5 6 6
-52 -36 -46 -25 -27 -61 -70
-41 -4 -40 -19 -18 -52 -62
-55 -64 -50 -30 -33 -56 -67
-53 -61 -48 -28 -31 -54 -65
-44 -19 -38 -17 -21 -49 -54
-36 -20 -30 -11 -12 -39 -50
29.4 21.8 28.5 49.7 41.0 13.5 13.2
10.8 10.8 10.8 11.3 11.0 9.9 10.0
11.9 1.2 3.1 4.8 11.6 19.3 24.1
a Data taken from Sharma (1980). b Data taken from Sharma (1980). c β for m-cresol ) 34.9 (Sharma, 1980). (Sharma, 1980).
d
β for m-xylene ) 2.2
Table 5. Characterization Parameters of Model Organic Compounds compound
MWa
T c ,b K
Pc,b Vc,b atm cc/gmol
m-cresol cis-decalin trans-decalin 2,6-lutidine 1-methylnaphthalene quinoline tetrahydrofuran tetralin thiophene m-xylene
108.14 138.25 138.25 107.16 142.20 129.16 72.11 132.21 84.14 106.17
705.8 702.3 687.1 623.8 772.0 782.0 540.1 719.2 579.4 617.0
45.0 31.6 28.8 38.5 32.1 44.8 51.2 34.7 56.2 35.0
309.0 576.1 543.5 343.1 462.0 456.7 224.0 427.9 219.0 376.0
ωb
T b ,b K
0.454 0.287 0.270 0.367 0.310 0.262 0.217 0.303 0.196 0.331
475.42 468.96 460.46 417.20 517.80 510.78 338.00 480.70 357.15 412.30
a Data taken from Reid et al. (1977). b Data taken from Oshmyansky et al. (1987).
Table 6. Composition, Normal Boiling Point, and Specific Gravity of Model Mixtures (Oshmyansky et al., 1987) model mixture
wt %
mol %a
base syn coal liquid decalin 1-methylnaphthalene tetralin m-xylene
26.4 27.9 25.4 20.3
24.8 25.5 24.9 24.8
3.5 wt % oxygen syn coal liquid decalin 1-methylnaphthalene tetralin m-xylene m-cresol
20.2 21.3 19.4 15.4 23.7
18.1 18.5 18.2 18.0 27.2
10.0 wt % oxygen syn coal liquid decalin 1-methylnaphthalene tetralin m-xylene m-cresol
8.5 9.0 8.2 6.6 67.7
7.0 7.2 7.1 7.1 71.6
Tb, K
SG
469.2
0.938
471.0
0.958
473.6
1.009
a Weight percent was converted to mol % using the molecular weights given in Table 5.
discussed earlier for coal liquids) for use with the Ely and Hanley method (1981). Some of the typical results for model compounds and model mixtures are presented in Figures 3, 4, and 5. Tables 7 and 8 present a summary of the results of the comparison of predicted viscosities by various correlations with the experimental data of model compounds and model mixtures, respectively. As is evident from Table 7, except for m-xylene and 2,6-lutidine, the predicted viscosities of all model compounds were lower than the experimental ones when predicted by the Ely and Hanley correlation (1981). The predicted viscosities from Twu’s internally consistent correlation (1985) also follow the same trend. However, this was not the case with Twu’s generalized correlation (1986) where predicted viscosities were more than the
Figure 3. Viscosity vs temperature curves for m-cresol using different correlations.
experimental ones in the case of 2,6-lutidine, 1-methylnaphthalene, thiophene, and m-xylene. The calculated viscosities by this correlation in the case of quinoline, tetrahydrofuran, and tetralin were close to the experimental data. The large errors obtained in the viscosity prediction by Ely and Hanley’s method (1981) in the case of cisdecalin, trans-decalin, and quinoline can be explained by the limitation of the method. The Ely and Hanley’s method (1981) uses methane as the reference fluid and is applicable in a reduced density range of less than 3.4. Since the data for cis-decalin, trans-decalin, and quinoline were taken at reduced densities of above 3.4 (Osmyansky et al., 1987), accurate estimation of viscosities for these model compounds was not possible. Since Twu’s generalized correlation (1986) is also based on the corresponding states principle, the same reason holds for the large errors associated with it in the viscosity predictions. Largest deviations in the viscosity predictions (∼70%) were obtained in the case of m-cresol. It is known that m-cresol is a highly self-associating compound and the
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 4003 Table 7. Average Errors between Experimental and Predicted Viscosities of Model Compounds average error % compound
no. of points
Ely and Hanley (1981)
Twu (1985)
Twu (1986)
m-cresol cis-decalin trans-decalin 2,6-lutidine 1-methylnaphthalene quinoline tetrahydrofuran tetralin thiophene m-xylene
4 4 4 4 4 4 2 4 3 4
-68 -53 -62 +4 -40 -42 -16 -34 -13 +18
-71 -41 -45 +5 0 -13 -12 -13 -2 +25
-66 -34 -39 +22 +15 +2 +1 -1 +15 +42
Table 8. Average Errors between Experimental and Predicted Viscosities of Model Mixtures average error % Ely and Hanley (1981) model mixture
no. of set points 1b
base syn coal liquid 3.5 wt % oxygen syn coal liquida 10.0 w % oxygen syn coal liquida a
Figure 4. Viscosity vs temperature curves for base syn coal liquid using different correlations.
large negative errors obtained in this case can be due to its highly associative nature. As in the case of model compounds, the predicted viscosities of model mixtures were lower than the experimental values except in the case of the base “syn” coal liquid and the 3.5 wt % oxygen “syn” coal liquid where a positive bias was observed in the viscosity predictions by Twu’s generalized correlation (1986). It is also interesting to note that no two sets of correlations (listed in Table 3) gave the same set of
set 3b
set Twu Twu 4b (1985) (1986)
4 2
-20 -11 -12 -8 -27 -16 -21 -17
-8 -15
+18 +7
2
-64 -60 -60 -59
-60
-47
Model mixtures of Table 6. b Please refer to Table 3.
Table 9. Comparison of Characterization Parameter Estimates of Model Mixtures by the Different Correlations Listed in Table 3 model mixture
Figure 5. Viscosity vs temperature plot for 10 wt % oxygen syn coal liquid using different correlations.
set 2b
set 1
set 2
set 3
set 4
base syn coal liquid MW Tc, K Pc, atm Vc, cc/gmol ω
130.4 695.4 29.6 461.1 0.33
142.5 629.7 30.5 436.5 0.37
130.4 688.2 33.0 439.3 0.37
142.5 688.2 33.0 439.3 0.37
3.5 wt % oxygen coal liquid MW Tc, K Pc, atm Vc, cc/gmol ω
128.7 702.2 32.5 449.0 0.32
140.8 700.1 34.9 426.3 0.35
128.7 693.6 34.2 427.6 0.36
140.8 693.6 34.2 427.6 0.36
10.0 wt % oxygen coal liquid MW Tc, K Pc, atm Vc, cc/gmol ω
123.6 717.8 36.2 417.0 0.30
134.8 717.5 38.6 401.0 0.31
123.6 705.3 37.5 397.3 0.36
134.8 705.3 37.5 397.3 0.36
characterization parameters for any model mixture as seen from Table 9. The large errors in the predicted viscosities of model mixtures can also be because of the inaccuracy in estimating the different characterization parameters. However, of all the correlations considered for estimating the characterization parameters of model mixtures, the Lee and Kesler correlation (1976) (set 2 in Table 1) gave the least errors when used with the Ely and Hanley method (1981) for predicting the viscosities. Model mixtures of Oshmyansky et al. (1987) were selected to represent coal liquids with association effects ranging from negligible, in the case of the base “syn” coal liquid, to very high for 10 wt % oxygen “syn” coal liquid. It is to be noted here that for all the correlations considered, largest average “negative” errors (47%64%) in viscosity predictions were obtained for the 10.0 wt % oxygen “syn” coal liquid. Therefore, as in the case of m-cresol, a possible relationship between the extent of association and coal liquid viscosity is suggested.
4004 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997
Figure 6. Error vs temperature curves for coal liquids using Twu’s generalized correlation (1986).
In summary, it appears that association effects are responsible for experimental viscosities being higher than the values calculated from correlations developed for nonpolar, petroleum fluids. Since the predicted viscosity depends upon the various input parameters required in the correlations, the possibility certainly exists of a relationship between the extent of association and the characterization parameters. Temperature Effects on Viscosity Deviations. The results of comparisons between predicted and experimental viscosities show that, for all the coal liquids, model compounds and model mixtures, and for all the correlations considered, the error in viscosity prediction always decreased with an increase in temperature. This is illustrated in Figure 6. This is also consistent with our hypothesis of the effect of association resulting in higher experimental viscosities than the predicted values since one would also expect the error between the two to decrease as the association effects decrease, which is what happens when the temperature increases. It should also be pointed out that Twu’s generalized correlation (1986), among all correlations considered, gave the lowest errors in all cases and was selected for further modifications in order to extend its applicability to coal liquids. Sharma et al. (1982, 1983) have shown that cryoscopic molecular weight determination as a function of concentration in a nonpolar solvent, in particular benzene, appears to be a means of characterizing association. They defined the slope of the molecular weight versus the concentration curve as the “association factor”, β, and showed that there was a functional relationship between β and the enthalpy of coal liquids. Obviously, the higher the β, the greater the extent of association and vice versa. Values of Sharma’s association factor, β, for various coal liquids have been presented in Table 4. Also presented are values for m-cresol and m-xylene. As discussed earlier, Twu’s generalized correlation (1986) was selected for modifications to extend the range
Figure 7. Association factor vs Watson characterization factor for coal liquids, m-xylene and m-cresol.
Figure 8. Error vs temperature curves for coal liquid with Watson K of 10.0 and 11.0.
of its applicability to coal liquids. Since Twu’s correlation (1986) uses the API gravity and the MeABP to calculate the Watson characterization factor, K, and subsequently the viscosity, it was decided to investigate whether there exists a relationship between the association factor, β, and the Watson characterization factor, K. Figure 7 shows a plot of Sharma’s β as a function of the Watson K. It is evident that the points correspond-
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 4005
Figure 9. Error vs temperature for coal liquids with Watson K of 10.0 and 11.0.
ing to m-cresol, Utah distillate, SRC-I naphtha, 1046 naphtha, 878 middle distillate, and the synthoil distillate show a straight line trend with a negative slope. It is also interesting to note that in the case of m-xylene, Western Kentucky whole oil, and Western Kentucky distillate, Sharma’s association factor, β, seems to be independent of the Watson K. This would be expected in the case of nonassociating liquids. That these liquids are relatively nonassociating has been shown by Sharma (1980) by correlating their enthalpy data. Moreover, m-xylene is known to be a nonassociating compound. It should also be noted that the three nonassociating liquids have an association factor of less than or equal to 3.1. At present, however, due to lack of data on the association factor of Oshmyansky, et al.’s (1987) model compounds and model mixtures, it is very difficult to draw any definitive conclusions regarding the relationship between the association factor, β, and the Watson K to obtain a functional relationship.
Figure 10. Viscosity vs temperature curves for middle distillate using modified correlation, Twu’s generalized correlation, and experimental data.
Development of a “Correction” to Twu’s Correlation (1986) As seen from Figure 6, since the errors in the predicted viscosity of coal liquids always decrease with an increase in temperature and there is a “smooth” relationship between the two, it was decided, as a first attempt, to correlate the errors as a function of temperature. The average errors at the Watson characterization factors of 10 and 11 (almost the “limits” of the coal liquids under study; also, Twu uses petroleum fractions with Watson Ks of 10 and 12 as the reference fluids) were then found at different temperatures and exhibit a linear relationship of the following form (see Figures 7 and 8):
ln(-E) ) A + BT where
(1)
Figure 11. Viscosity vs temperature curves for synthoil distillate using modified correlation, Twu’s generalized correlation, and experimental data.
E)
νTwu - νact × 100 νact
(2)
Least squares estimates of A and B are given in Table 10. Since Twu (1986) used petroleum fractions with Watson K of 10 and 12, respectively, as the reference fluids for predicting the viscosities at 310.93 and 372.04
4006 Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 Table 10. Constants To Be Used in Equation 1 Watson K
A
10.0 11.0
6.0541 5.2559
B,
Table 12. Comparison of Experimental Viscosities of Coal Liquids with the Predicted Values Using Twu’s Generalized Correlation (1986) and the Modified Correlation of This Work
K-1
-0.0072 -0.0074
Twu (1986)
Table 11. Viscosity Correction Factors To Be Used in Equation 4 temperature, K
correction factor R
10.0
310.93 372.04 310.93 372.04
1.82 1.41 1.09 1.05
12.0
K (reference temperatures), it was decided to use coal liquids as reference fluids instead (keeping other conditions of Watson K and reference temperatures the same as those of the petroleum fractions) to reduce the error in viscosity predictions. For this, errors in viscosity predictions of coal liquids by Twu’s correlation were obtained using eq 1 at conditions of Watson K of 10 and 12 and 310.93 and 372.04 K, respectively. The errors thus obtained were the errors in predicting coal liquid viscosities by Twu’s correlation (1986) with petroleum fractions as the reference fluids at the given conditions of Watson K and temperature. These conditions of Watson K and temperature for coal liquids are the same as those of the reference fluids used by Twu (1986). Hence, in order to use coal liquids as the reference fluids in Twu’s correlation (1986), the corrected viscosities at the above conditions were then obtained using eq 2 as follows:
νactual )
100νTwu 100 + E
Fexpt,a
T, K
cp
g/cc
294.76 298.71 313.15 323.15 333.15 343.15
2.79 2.57 1.87 1.54 1.29 1.11
0.885 0.882 0.873 0.856 0.845 0.835
1.60 1.49 1.19 1.02 0.89 0.78
-43 -42 -37 -34 -31 -29
2.64 -5 2.37 -8 1.76 -6 1.45 -6 1.23 -5 1.05 -5
Western Kentucky 300.93 whole oil 313.15 323.15 330.93
5.66 3.92 3.08 2.57
0.920 0.908 0.896 0.887
4.29 3.13 2.49 2.12
-24 -20 -19 -17
6.67 4.59 3.52 2.92
18 17 14 14
Western Kentucky 298.71 distillate 313.15 322.04 333.15 343.15 348.71
2.57 1.88 1.59 1.34 1.15 1.07
0.890 0.875 0.865 0.854 0.840 0.834
1.63 1.28 1.12 0.96 0.84 0.78
-37 -32 -30 -29 -27 -27
2.61 1.90 1.60 1.32 1.13 1.04
2 1 1 -1 -2 -3
SRC-I naphtha
289.82 300.93 313.15 324.16 331.48
0.72 0.61 0.53 0.47 0.43
0.787 0.777 0.763 0.751 0.743
0.62 0.54 0.47 0.42 0.29
-13 -11 -11 -11 -10
0.86 0.73 0.61 0.53 0.48
19 20 15 13 12
1046 naphtha
289.92 303.15 314.26 322.05 332.04
0.98 0.77 0.67 0.61 0.54
0.826 0.808 0.799 0.790 0.779
0.82 0.68 0.60 0.54 0.49
-16 -11 -11 -11 -10
1.27 0.99 0.84 0.74 0.64
30 29 25 21 19
middle distillate
297.59 313.15 323.15 335.37 345.37 359.82
5.13 3.20 2.45 2.01 1.61 1.23
0.969 0.952 0.940 0.925 0.912 0.891
2.39 1.77 1.50 1.24 1.07 0.89
-53 -45 -39 -38 -33 -28
5.03 3.29 2.60 2.02 1.68 1.32
-2 3 6 1 4 7
synthoil distillate
300.93 313.15 323.15 330.93 344.26 359.82
9.87 5.89 4.28 3.37 2.35 1.81
0.974 0.960 0.950 0.940 0.922 0.901
3.35 2.53 2.08 1.80 1.44 1.14
-66 -57 -52 -47 -39 -37
6.47 4.49 3.46 2.88 2.18 1.64
-34 -24 -19 -15 -7 -9
coal liquid
Watson K
Utah distillate
(3)
or
(4)
νactual ) RνTwu R (correction factor) )
100 100 + E
(5)
The correction factor, R, then “converts” the viscosities of petroleum fractions obtained by Twu’s generalized correlation (1986) to those of coal liquids. The correction factors for viscosities of coal liquids at Watson K, of 10 and 12 and at 310.93 and 372.04 K, respectively, were obtained by substituting the errors in each case in eq 5 and are given in Table 11. The following stepwise procedure was then used for estimating coal liquid viscosities by Twu’s correlation (1986) with coal liquids substituted as reference fluids: 1. Viscosities of petroleum fractions as the reference fluids with Watson K of 10 and 12 and at 310.93 and 372.04 K, respectively, were found by Twu’s correlation (1986). 2. Viscosities of coal liquids as the reference fluids with Watson K of 10 and 12 and at 310.93 and 372.04 K, respectively, were then found by multiplying the corresponding viscosities of petroleum fractions in (1) above by the appropriate correction factor given in Table 11. 3. With the viscosities of coal liquids as reference fluids at Watson K of 10 and 12 and at 310.93 and 372.04 K known, the viscosities of coal liquids at other Watson Ks and temperatures of interest were then calculated by Twu’s generalized correlation (1986). Coal liquid viscosities thus estimated as a function of temperature were compared with the experimental
this work
µexpt,a
AAD % a
µ % µ % calc error calc error
29.7
11.6
Data taken from Sharma (1980).
values and the results are presented in Table 12. The viscosities predicted by the “modified correlation” of this work compare very well with the experimental values and the average absolute deviation in the error was around 12% whereas by Twu’s method (1986), it was around 30%. In most cases, the predictions by this work compared exceptionally well with errors in the range of 1-8% except for the synthoil distillate where the errors ranged between 9 and 34%. However, even in this case, these errors were much lower than those obtained by Twu’s generalized correlation (1986). Hence, without too much effort Twu’s correlation (1986) can be used for reasonable predictions of coal liquid viscosities with the modifications as suggested in this work until an approach that accounts explicitly for the extent of association in the viscosity predictions of coal liquids is developed. Future efforts will be directed toward expanding the model compound and model mixture association factor data base which can then be used to develop a generalized correlation specifically for predicting coal liquid viscosities.
Ind. Eng. Chem. Res., Vol. 36, No. 9, 1997 4007
Acknowledgment Assistance of Doraj Vimal Jamuwa and Swati Jain of the Department of Chemical Engineering, M. R. E. C., Jaipur, with preparation of the manuscript is gratefully acknowledged. Nomenclature A: Constant in error-temperature function (eq 1) n |E/n| AAD %: Average absolute deviation; ∑i)1 API gravity: American Petroleum Institute gravity, (141.5/ SG) - 131.5 B: Constant in error-temperature function (eq 2) E: Error, (νcalc - νact)/νact × 100 Fµ: Viscosity equation parameter f: Function of boiling point and specific gravity used in calculation of viscosity (see Twu, 1986) K: Watson characterization factor, (MeABP, °R/SG)1/3 MeABP: Mean average boiling point, °R MW: Molecular weight Pc: Pseudocritical pressure, atm SG: Specific gravity (60 °F/60 °F) T: Temperature, K T0: Temperature of reference fluid (methane), K Tb: Normal boiling temperature, K Tc: Pseudocritical temperature, K Vc: Pseudocritical molar volume, cc/gmol Greek Symbols R: Correction factor to substitute petroleum fractions by coal liquids as reference fluids (eq 5) β: Association factor µ: Viscosity, µP µx: Viscosity of fluid of interest, µP ν: Kinematic viscosity, cSt νact: Actual kinematic viscosity, cSt νTwu: Predicted by Twu’s generalized correlation (1986), cSt ν10: Reference fluid kinematic viscosity at 310.93 K, cSt ν20: Reference fluid kinematic viscosity at 372.04 K, cSt F: Density, g/cc F0: Density of reference fluid (methane), g/cc ω: Acentric factor
Literature Cited Baltatu, M. E. Prediction of the Liquid Viscosity of Petroleum Fractions. Ind. Eng. Chem. Process Des. Dev. 1982, 21, 192195. Edmister, W. C. Applied Hydrocarbon Thermodynamics; Gulf: Houston, 1961. Ely, J. F.; Hanley, H. J. M. Prediction of Transport Properties. 1. Viscosity of Fluids and Mixtures. Ind. Eng. Chem. Fundam. 1981, 20, 323-332.
Goel, S. Correlation of Viscosity of Coal Derived Liquids. M. Tech. Dissertation, Indian Institute Of Technology, Kanpur, 1987. Hanley, H. J. M. Prediction of Viscosity and Thermal Conductivity Coefficients of Mixtures. Cryogenics 1976, 16, 643-651. Hanley, H. J. M.; McCarty, R. D.; Haynes, W. M. Equation for the Viscosity and Thermal Conductivity Coefficients of Methane. Cryogenics 1975, 15, 413-415. Holliman, S. L. Physical and Chemical Techniques and Results for Seven Coal-Derived Liquids. M.S. Dissertation, Colorado School of Mines, Golden, CO, 1979. Kesler, M. G.; Lee, B. I. Improve Prediction of Enthalpy of Fractions. Hydrocarbon Process. 1976, 55 (March), 153-158. Moharam, H. M.; Fahim, M. A. Prediction of Viscosity of Heavy Petroleum Fractions and Crude Oils Using a Corresponding States Method. Ind. Eng. Chem. Res. 1995, 34 (11), 4140-4144. Oshmyansky, Y.; Hanley, H. J. M.; Ely, J. F.; Kidnay, A. J. The Viscosities and Densities of Selected Organic Compounds and Mixtures of Interest in Coal-Liquefaction Studies, personal communication, 1987. Peterson, K. A.; Knudsen, K.; Fredenslund, Aa. Prediction of viscosities of hydrocarbon mixtures. Fluid Phase Equilib. 1991, 70, 293-308. Probstein, R. F.; Hicks, R. E. Synthetic Fuels; McGraw-Hill: New York, 1982. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. Riazi, M. R.; Daubert, T. E. Simplify Property Prediction. Hydrocarbon Process. 1980, 59 (March), 115-116. Roman, C. E.; Luther, J. E.; Wetzel, D. M. Energy Prog. 1986, 6 (4), 235. 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. Sharma, R.; Kidnay, A. J.; Yesavage, V. F. Measurement and Correlation of the Enthalpy of Coal-Derived Liquids. Energy Prog. 1982, 2, 1. Sharma, R.; Yesavage, V. F.; Kidnay, A. J. Effect of Association on Enthalpy of Coal Derived Liquids: Cryoscopic Molecular Weight as a Function of Concentration. A.I.Ch.E. J. 1983, 29 (3), 508-511. Twu, C. H. Internally Consistent Correlation for Predicting Liquid Viscosities of Petroleum Fractions. Ind. Eng. Chem. Process Des. Dev. 1985, 24 (4), 1287. Twu, C. H. Generalized Method for Predicting Viscosities of Petroleum Fractions. A.I.Ch.E. J. 1986, 32 (12), 2091-2094.
Received for review November 18, 1996 Revised manuscript received April 9, 1997 Accepted April 10, 1997X IE960733L
X Abstract published in Advance ACS Abstracts, June 1, 1997.
