Ind. Eng. Chem. Process Des. Dev. 1904, 23, 833-845 Nace, D. M.; V o k , S. E.; Weekman, V. W., Jr. Ind. Eng. Chem. Process Des. Dev. 1971. 70. 530. Paraskos, J. A.; S&h, Y.T.; McKinney, J. D.; Carr, N. L. Ind. Eng. Chem. Process Des. Dev. 1976, 75. 165. Qader, S. A.; Hill, G. R. Ind. Eng. Chem. Process Des. Dev. 1969, 8, 98. Qader, S. A.; Singh, S.; Wiser, W. H.; Hill, G. R. J. Inst. Pet. 1970, 56(550), 187. Reif, H. E.; Kress, R. F.; Smith, J. S. Pet. Refiner 1961. 40(5), 237. Salterfield. C. H. AIChE J. 1975, 27(2). Schnaider, G. J.; Mukhim, I. I.; Chueva, M. A.; Kogan, Y. S. Khim Tekhno/. Topi. hfasei. 1969, NO. 7 , OI. Shah. Y. T. “Gas-Liquid-Soli Reactor Design”; McGraw-Hill: New York, 1979. Shah, Y. T. Ind. Eng. Chem. ProcessDes. Dev. 1980, 79, 328. Shah, Y. T.; Huling, 0. P.; Paraskos, J. A.; McKinney, J. D. Ind. Eng. Chem. Process Des. Dev. 1977, 16, 89. Stangeland, 6. E. Ind. Eng. Chem. ProcessDes. Dev. 1974, 73, 74. Sullivan. R. F.; Stangeland, 6. E.; Rudy, C. E.; Green, D. C.; Frumkin, H. A.
.
833
“Refining and Upgrading of Synfuels from Coal and Oil Shales by Advanced Cataiytic Processes,” First Interim Report, U.S. Dept. of Energy, April 1978, UC-gOd, FE-2315-25. Venuto, P. 6.; Habiie, E. T., Jr. “Fluid Catalytic Cracking with Zeolite Catalysts”; Marcel Dekker: New York, 1979. Voltz, S. E.; Nace, D. M.; Jacob, S. M.; Weekman, V. W.. Jr. Ind. Eng. Chem . Process Des. Dev. 1972. 7 1 , 26 1. Weekman, V. W., Jr. Ind. Eng. Chem. Process Des. Dev. 1968, 7, 90. Weekman, V. W., Jr.; Nace, D. M. AIChE J. 1970, 76(3), 397. Weekman, V. W., Jr. Ind. Eng. Chem. Process Des. Dev. 1969, 8, 305. Weekman, V. W., Jr. AIChEMonog. Ser. 1979, 75(11). Zhorov, Yu. M.; Panchenkov, G. M.;Tatarintseva, G. M.; Kuzimin, S. T.; Zenkovski, S. M. Int. Chem. Eng. 1971, 77(2), 258.
Received for review June 13, 1983 Accepted January 16, 1984
Thermophysical Properties of Complex Systems: Applications of Multiproperty Analysis Michael R. Brul6” Kerr-McGee Corporation, Oklahoma City, Oklahoma 73 125
Kenneth E. Starllng University of Oklahoma, Norman, Oklahoma 730 79
The “therm-trans” method is presented for predicting characterization parameters (e.g., critical properties) required in multiparameter corresponding-states correlations. Multiproperty analysis of thermodynamic and transport data is used to extract the characterization parameters through simultaneous calculation of the property data by an equation of state and a viscosity correlation. The property data needed are similar to the inspection data obtained for pseudocomponent fractions resolved from standard TBPdistillation analyses. This new approach for determining correlation parameters altogether circumvents the need for critical properties per se. Application to complex petroleum and coal-liquid fractions is demonstrated.
Prediction of Thermophysical Properties A modified Benedict-Webb-Rubin (BWR) equation of state has been applied to predict the thermodynamic properties of the simpler hydrocarbons found in petroleum and coal-derived fluids (Brul6 et al., 1979, 1982). This three-parameter corresponding-states correlation has been used in conjunction with a conformal-solution model to describe the vapor/liquid-equilibrium (VLE) bahavior of model multicomponent mixtures representative of the actual systems found in fossil-fuels processing (Watanasiri et al., 1982; Brul6 et al., 1983; Brul6 and Corbett, 1984). Equation-of-state characterization parameters and idealgas thermodynamic properties have been estimated, by using empirical correlations, as functions of the average measurable properties of fractions such as normal boiling point and specific gravity (Brul6 et al., 1982). Many problems remain in predicting complex-system thermophysical properties. Correlations must be capable of predicting properties of high-molecular-weight, multifunctional organic compounds at mild-to-severe operating temperatures and pressures. Multipolar and associating effects exhibited by some coal fluids are attributable to 0196-430518411123-0833$0 1.5010
the presence of heteroatomic and attached functional groups such as -N-, -NH,and -OH. Such intermolecular behavior cannot be described accurately by conventional three-parameter corresponding-states correlations. Characterization of Complex Fluids The problem of characterization further compounds the problem of correlation. A standard characterization procedure must be available for resolving a complex fossil fluid, with hundreds of diverse distillable and nondistillable organic compounds, into a pseudocomponent mixture with 20 or so fractions representing the overall properties of the parent full-range fluid (Brul6 et al., 1981). Once a full-range fossil fluid is resolved into effective pseudocomponent fractions, characterization parameters that enable properties correlations to predict accurate thermophysical properties must be determined for each of the fractions. As complex fluids increase in molecular weight, the determination of characterization parameters at the normal boiling point becomes less feasible. This presents an impasse, especially for many of the pure model compounds used for correlation development, since only low-temper0 1984 American
Chemical Society
834
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
ature, subatmospheric vapor pressures are typically available. If the usual approach of developing correlations for critical properties as functions of inspection data were extended to fluids that boil a t very high temperatures, many correlations would have to be developed, each covering a specific range identified by some reference boiling temperature. Using the API-42 data set (API, 1966) as an example, there would have to be correlations for estimating characterization parameters as functions of Tbat 100,40, 10, and 0.1 mmHg pressure. However, even this unwieldy approach is doomed; direct correlation of critical properties vs. subatmospheric data is not possible since experimental data on the critical properties of hydrocarbons with high molecular weights (say, >200) are virtually nonexistent. The measurement of new critical data is unlikely since many polycyclic aromatic compounds in coal fluids begin to decompose far below their critical points (Johns et al., 1962). The traditional method applied to heavy systems is to simply extrapolate subatmospheric boiling-point information to atmospheric conditions and use the resulting normal boiling point in yet another extrapolation to estimate the characterization parameters used in corresponding-states correlations (Maxwell and Bonnell, 1958). Such "double" extrapolation for a well-behaved homologous series like the paraffins is tenable as evidenced by the widespread use of these procedures in the petroleum industry (API, 1976). However, petroleum-resid, coal, and shale-oil fluids, which are comprised of a diverse spectrum of multifunctional organic compounds, may not be amenable to this treatment, especially if the correlations extrapolated are based on data for light petroleum systems. The purpose of the present work is to circumvent many of these and other problems related to estimating the characterization parameters used in corresponding-states correlations. Multiproperty analysis is the primary tool for doing so, and its use will be shown to provide more reliable prediction of thermophysical properties overall.
Development of Viscosity Correlation In order to use the new characterization method presented here, a viscosity correlation cast in the corresponding-states framework is required. The Chung-Lee-Starling (CLS) viscosity correlation (Chung et al., 1980, 1983) is a five-parameter corresponding-states expression applicable to Newtonian fluids. Extensive density dependence is incorporated in the CLS correlation for predicting viscosities over the whole fluid range from dilute gases to dense fluids to liquids. The CLS correlation uses five characterization parameters: critical temperature T,, critical density po acentric factor w, reduced dipole moment p*, and association factor a. The use of these five characterization parameters facilitates the prediction of dense-fluid viscosities for many low-molecular-weight organic compounds, including those that are polar and hydrogen-bonding. As with the modified-BWR equation of state, a conformal-solution model is used with the CLS correlation to represent the composition dependence of viscosity (Chung et al., 1983). In this work the CLS correlation was modified to make its characterization parameters compatible with those of the modified-BWR equation of state. In addition, the data base for developing the viscosity correlation was expanded to include polycyclic aromatic hydrocarbons typical of synfuels and heavy crudes. So that viscosities could be calculated in terms of the more frequently specified process conditions of temperature and pressure, the modifiedBWR equation of state is used to calculate density, which is in turn needed for viscosity prediction. This provides
Table I. Universal Constants a; and b; for Obtaining Parameters E; for the Modified-CLS Viscosity Correlation: E, = a; rb;
+
i
a,
0
1. 17.4499 -0.961125E-3 51.0431 -0.605917 21.3818 4.66798 3.76241 1.00377 -0,7774233-1 0.317523
1
2 3 4 5 6 7 8 9 10
b, -0.2756 34.0631 0.723459E-2 169.460 71.1743 -2.11014 -39.9408 56.6234 3.13962 -3.58446 1.15995
Table 11. Coefficients for Calculating the Transport Collision Integrals for the Lennard-Jones 12-6 Potential (Neufeld et al., 1972): Q(2,2)* = A / T * B C / g P E/@" RTWB sin (ST*W- P ) coefficients values A 1.16145 B 0.14874 C 0.52487 D 0.77320 E 2.16178 F 2.43787 R -6.4353-4
+
S W P
+
+
18.0323 -0.76830 7.27371
a correlation of viscosity that ultimately is a function of temperature and (implicitly) pressure (T,P),rather than temperature and density (T,p). The resulting unified framework is practical since density is not an easily and routinely measured process quantity. The coupling of the modified-BWR and the modified-CLS correlations in this manner is a necessary step in establishing the consistency needed to simultaneously predict thermodynamic and transport properties. The new modified-CLS viscosity correlation is q =
[
viscosity = 26.693 d m / n 2 ] q * p P,
where q* = reduced viscosity = qK* qK*
+ qm*
= kinetic contribution to reduced viscosity =
~ o * [ E+~1Y/ G n b ) I q+* = potential contribution to reduced viscosity = E7y2[crib)],$a+Eg/p+E~ol pz qo*
= dilute-gas contribution to reduced viscosity = E~?CE*
qcE* = Chapman-Enskog relation for dilute gases = y'?;;/Q(2.2,'
Gnb) = [E,(1 - e - E a ) / y + EzGeEu + E,G]/[E1E4 + E z + E3]
Viscosity-correlation parameters E, are calculated as a function of orientation parameter y using the relation and universal constants a, and bi given in Table I. The colis evaluated as a function of temlision integral, W*2)*, perature using an empirical expression, based on the Lennard-Jones intermolecular potential model, which is given in Table 11. The modified-CLS correlation is able to predict the viscosities of high-molecular-weight paraffins typical of petroleum and polycyclic aromatic hydrocarbons preponderant in fossil fluids derived from petroleum resid, shale
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 835
oil, and coal. The viscosity of light gases, and petroleum and coal liquids can also be well predicted over wide ranges of temperature and pressure as shown in Table 111. Most of the viscosity predictions for the model hydrocarbons listed in Table I11 are within 10% of the experimental values. Many predictions are under 570, well within the range of experimental error incurred in measuring the viscosity of these complicated compounds. To illustrate that the multiproperty basis used in correlation development facilitates the reliable prediction of other properties as well, deviations for thermodynamic properties are also given in Table 111. All the properties listed for each model compound are calculated using the same characterization parameters and are expressed as functions of the same independent variables (T,P). Viscosities of some polycyclic aromatic compounds are not always well predicted by the modified-CLS, even after regression analysis of the new petroleum and coal-liquid data base (see Table 111). The accuracy of viscosity measurements for some of these complicated compounds is questionable. However, inaccurate predictions may result because the ability of multiparameter corresponding-states correlations to predict liquid viscosity deteriorates rapidly at low reduced temperatures (Chung et al., 1983). Indeed the corresponding-states assumption hardly holds for transport properties at these conditions. The present modified-CLS correlation was found to be incapable of predicting hydrocarbon viscosities above 10 cP, which, for the model compounds shown in Table 111, corresponds to reduced temperatures (TIT,) below about 0.35. Fortunately, many of the unit operations in fossilfuels processing are carried out at reduced temperatures above 0.5. Although the modified-CLS is not as accurate in predicting viscosity as the modified-BWR is in predicting thermodynamic properties, these correlation vehicles have nonetheless been put in a useful working order for testing the proposed characterization technique for complex fluids.
Multiproperty Analysis of Thermodynamic and Transport Properties The method described in this work depends on the ability to calculate many different properties using the same characterization parameters in each property correlation. This idea indirectly stems from earlier concepts of multiproperty analysis and its application. The method also has theoretical roots in findings concerning the determinancy of intermolecular-force “constants” using different types of property data for dilute gases (Tee et al., 1966, Reichenberg, 1973; Chu et al., 1975; Reid et al., 1977). The first ideas leading to multiproperty analysis for dense fluids came about in work dealing with complex mixtures (Starling, 1966). The systems under study involved reservoir condensates composed of high-molecular-weight hydrocarbons for which equation-of-state characterization parameters could not be measured and were otherwise unavailable. The equation of state and expressions for estimating characterization parameters were developed by regression analysis of pressure-volume-temperature (PVT) data for low-molecular-weight components and VLE data for high-molecular-weight fractions, which were treated as pseudocomponents in properties calculations. This approach is unique in that k-value data were used in lieu of density data for the high-molecular-weight pseudocomponents. The method was successful and sparked more ideas on the simultaneous use of many different property data in regression analysis to determine coefficients for equations of state (Cox et al., 1971; Lin et al., 1973; Starling, 1973; Wang et al., 1976).
Characterization Parameters
Figure 1. Companion-correlation network
interrelationships among thermophysical-property correlations based on the multiparameter corresponding-states principle.
Although transport properties are not interrelated to the degree implied by statistical mechanics (i.e., one property cannot be easily derived in terms of the other as in classical thermodynamics),the different property correlations can still be closely related in their development. In practice the thermodynamic correlations can serve as “companions” to the transport correlations, and vice versa, to enhance overall prediction consistency, and hence, capability. All the correlations can be coanchored, within the multiparameter corresponding-states framework, by using the same correlation characterization parameters. Such a network of companion correlations is shown in Figure 1. Clearly, density is the central linking property in the network. Accurate predictions of density by an equation of state are necessary for accurate prediction of other thermodynamic properties derived from that equation of state-such as enthalpy, entropy, and fugacity. The modified-CLS viscosity and thermal-conductivity correlations use temperature and density (T,p) as the independent variables, so density must also be as accurate as possible to make reliable predictions of transport properties. Although cubic equations of state are relatively simple and computationally efficient, they do a poor job of predicting liquid densities (typically 10 to 15% in error) and probably cannot be used effectively in the framework proposed here. The modified-BWR and other more complicated equations of state, although less computationally efficient, do afford the advantage of being able to predict exceptionally accurate liquid densities, as shown in Table 111. Other links between the various property correlations are also evident in the network shown in Figure 1. Since the thermodynamic-property correlation (i.e., the equation of state) and the transport-property correlations all use the same characterization parameters, the values of the respective parameters must be such that all the companion correlations in the network will be able to accurately predict their respective properties. This hypothesis was first found to be true when determining one of the characterization parameters used in the modified-BWR equation of state (Brul6 et al., 1979). The orientation parameter y can be reliably obtained for prediction of thermodynamic properties by regression analysis of only vapor-pressure data. In fact, one vapor-pressure datum, which may conveniently be the normal boiling point Tb, can be used to determine y by sensitivity analysis, as shown in Figure 2. For comparison, prediction results obtained using y regressed from different data sets are given in Table IV. Table IV further indicates that accurate predictions can also result for transport properties
836 Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 Table 111. Simultaneous Prediction of Thermodynamic and Transport Properties of Model Fossil-Fuel Compounds Using the Generalized Modified-BWR Equation of State and Modified-CLS Viscosity Correlation model compounds emp fluid form. name H2 hydrogen
characterization parameters" crit crit vol, orient. mol wt, temp, cm3/mol, param, M K, T, V, Y prop.b 49.24 0. Pk) 2.0159 32.95 dg)
N2
28.013
CHI
nitrogen
methane
C2HB ethane
16.043
30.070
126.2
190.7
305.4
9o.io
99.50
148.0
0.0263
180 26
pres, kPa 100-25 000 100-20 000
P.
17
-184-147
200-3130
0.74
P(g) P(1)
30 11
-196-116 -196-153
101-+8960 1040-55 300
0.23 0.69
H - H"(g)
49
-184-10
1379-13800
0.81
H - H"(1) dg)
38 68
-184-73 17-727
3450-17 240 167-+17600
0.99 1.3
d1)
176
17-727
100-3000
4.1
29
-1614-83
101-4610
0.78
Pk)
19
-98-350
1300-16000
0.66
P(1)
16
-128--48
3530-14 500
0.80
H - H"(g) H - H"(1) dg)
16 15 52
-73-10 -129-46 7-247
310+13800 3100-13800 100-20000
1.6 1.6 2.2
?(1)
143
74247
100-20 000
1.8
21
-129-29
6-4620
1.1
8 21 15
38-154 -112-138 -104-154
2760-17200 101-27600 3450-20700
0.96 1.8 0.48
d1)
46 10 515
-105-154 427-477 27-477
1380-20700 100-20000 100-20000
0.50 1.1 1.7
P,
33
-57-29
517-7120
0.76
Pk) P(1)
16 25
-30-30 -30-140
1517-7380 1520-31 900
0.65 0.65
H - H"(g) H - H"(1) dg)
15 24 150
-30-30 -30-140 37-627
1520-7380 3040-50700 1W7000
3.2 2.8 3.0
d1) P,
173 59
374627 -73-97
100-20000 20-4250
0.40
P(P) P(1)
15 33
7-227 -183-227
2-19 700 282-25 700
0.49 1.5
H - H"(g) H - H"(1) dg) dl)
2 33 65 319
93-121 -129-121 17-477 17-477
3450 3450-13800 100-3000 100-25000
0.89 0.84 3.8 4.2
P,
19
-71-152
2-3800
0.41
Pk)
P(1)
9 18
71-221 38-154
13-47 460-673
0.36 0.51
H - H"(g) H - H"(1) dg) d1)
1
30 83 287
204 38-221 7-577 7-577
6900 1380-27600 100-3000 100-20 000
1.1 0.43 2.8 6.5
0.01289 P,
0.09623 P, Pk)
H - H"(1) dg)
carbon dioxide
C3HB propane
C4H,, n-butane
44.010
44.097
58.124
304.2
369.9
425.2
94.00
200.0
255.0
0.2093
0.1538
0.1991
range temp, "C 127-527 100-727
P(1) H - Ho(g)
COP
no. of data pts
%
AARDc 0.56 3.5
data ref Vargaftik (1975) Stephan and Lucas (1979) Friedman and White (1950) Vargaftik (1975) Street and Staveley (1968) Canjar and Manning (1967) Mage et al. (1963) Stephan and Lucas (1979) Matthews and Hurd (1946) Douslin et al. (1964); Vennix et al. (1970) Vargaftik (1975); Van Itterbeek et al. (1963) Jones et al. (1963) Yesavage (1968) Stephan and Lucas (1979) Canjar and Manning (1967) API-44 (1979) Vargaftik (1975) Sage and Lacey (1950) Starling (1962) Stephan and Lucas (1979) Canjar and Manning (1967) Vargaftik (1975) Sage and Lacey (1955) Din (1961) Stephan and Lucas (1979)
7.0 Canjar and Manning (1967) Vargaftik (1975) Sage and Lacey (1950) Yesavage (1968) Goodwin (1977) Starling (1962) Stephan and Lucas (1979) Canjar and Manning (1967) Vargaftik (1975) Sage and Lacey (1950) Starling (1962) Stephan and Lucas (1979)
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
837
Table 111 (Continued) model compounds emp fluid form. name C5H12 n-pentane
characterization parameterso crit crit vol, orient. m o l d , temp, cm3/mol, param, M K, Tc Vc Y prop.* 72.151 469.5 311.1 0.2530 P,
benzene
78.115
562.2
259.0
206-4140 101-19000 1380
0.94 2.1 1.8
H - HO(l) 14
38-238
5520-34500
0.72
dg)
60
47-527
100-.3000
2.1
d1)
dg)
306 68 19 19 13
474527 7-289 10-260 10-260 47-277
100-20000 8-4920 6-3400 6-3400 32-4220
3.1 1.2 1.1 0.60 5.9
dl) 0.3054 P, P(l)
144 22 22
674277 7-235 -46-171
66-20000 4-3030 101-20100
7.5 1.3 0.54
dg)
62
107-577
100-25000
2.1
70)
261 33
107-577 0-310
100-.15000 1-3770
3.1 1.9
37
H - Ho(g) 7 H -Ho(l) 76
0-300 315-343 10-371
1-101 1380-17200 346-17200
2.8 4.2 1.9
28 3
0-270 200-600
1-2350 100
1.5 2.5
242 15
0-277 140-300
100-25000 14.3-770
3.9 0.89
PO)
23
40-400
0.06-3110
6.5
AHH,
d1) 0.3499 Pa
18 3 31
100-420 160+190 -68-258
3830 101 0.004-2410
6.2 3.7 0.75
P(1)
23
-68-238
10-21200
0.65
H - Ho(g) 9
267-375
543-5430
2.1
H - HO(1)
8 45
267-321 107-371
47-16300 100-2000
1.4 1.3
273 82 59 1 12 23 15 23 157
274347 0-358 20-275 250 30-140 0-220 0-140 0-220 27-287
100-25 OOO 0.2-3800 100-40 000 882 1490 0.254623 0.25-112 0.254623 100-25 000
2.5 0.76 1.5 2.4 8.2 1.2 1.9 1.2 2.6
20
180-434
43-4900
4.7
7 17 10 63 6 20
80-200 100-400 90-180 -57-293 204-266 -18-254
1-200 2-3200 101 0.002-2410 101-1660 1379-9650
14. 5.2 7.7 0.69 1.7 0.83
H - Ho(g) 4
304-316
1380-2760
1.8
H - HO(1)
0.2180 P, P(1) A H V
C6H14
C7Hs
n-hexane
toluene
86.178
92.142
507.3
591.7
368.09
316.0
0.2640 Pa P(1)
A H V
?k) C7Hs0 m-cresol
C7H16
n-heptane
108.14
100.21
705.8
540.29
312.1
426.13
d1) 0.4625 P,
dg) C8Hlo
o-xylene
106.17
630.3
369.0
CSHlo
ethylbenzene
106.17
617.1
374.0
122.17
707.1
334.5
CsHloO 2,5-xylenol
0.4969 P, PO)
AH" C8H18
n-octane
114.23
568.6
486.2
% AARDc 0.28
71-221 -1294238 154
Pk) P(l) H - Ho(g)
C6H,
range no. of data temp, pres, pts "C kPa 20 -29-197 5-3380
P(1) 0.3987 Pa Pk)
P(l)
12 11 1
&)!
28 51
271-316 127-397
4140-9650 100-2000
0.95 1.5
d1)
223
47-397
100-10000
3.6
data ref Canjar and Manning (1967) Vargaftik (1975) API-44 (1979) Sage and Lacey (1950) Lenoir et al. (1970) Stephan and Lucas (1979) API-44 (1979) Chao (1978) Vargaftik (1975) Stephan and Lucas (1979) Vargaftik (1975) Stewart et al. (1954) Stephan and Lucas (1979) Vargaftik (1975); Kobayashi et al. (1979) API-44 (1979) Vargaftik (1975) Eakin et al. (1972) Stephan and Lucas (1979) Nasir et al. (1980) Kudchadker et al. (1978a) Kay (1938); API-44 (1979) Stuart et al. (1950) Gilliland and Parekh (1942) Stephan and Lucas (1979) Vargaftik (1975) API-44 (1979) Vargaftik (1975) Vargaftik (1975) API-44 (1979) Vargaftik (1975) Stephan and Lucas (1979) Kudchadker et al. (1978b)
API-44 (1979) Vargaftik (1975) Felsing and Wataon (1942) Lenoir et al. (1968) Stephan and Lucas (1979)
838
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
Table I11 (Continued) model compounds emP fluid form. name
C;H7,N
C9HB
quinoline
indene
CgHlo indan
characterization parameters" crit crit vol, orient. no. of mol wt, temp, cm3/mol, param, data M K, Tc Vc y prop.* pts 129.16
116.16
118.18
782.2
702.5
685.6
364.5
368.3
381.6
0.3258
0.2765
0.3013
CIoH,
naphthalene
CIoHl2 tetralin
ClOHZz n-decane
CllHlo l-methylnaphthalene
Cl,Hz4 n-undecane
128.18
132.21
142.29
142.20
156.31
594.5
748.4
716.5
617.6
772.0
638.8
542.9
410.0
438.0
602.0
454.2
660.0
0.4463
0.2963
0.3403
0.4880
0.3509
0.5291
0.01-3530
2.6
p(l) AHv
q(l)
16 19 12
30-240 70-+360 10-200
0.01-107 0.2-876 101
3.4 2.6 15.
P,
12
1-422
8-3800
0.70
p(1) AHv q(1)
13 14 6
100-422 8-3800 100-320 8-1440 70-120 101
2.3 0.70 5.1
Pa
19
1-412
9-3950
0.30
p(1)
22 19 10
0-412 10-240 30-120
9-3950 0.07-379 101
1.0 1.2 3.2
q(1)
16 191
384178 27-197
1-200 100-25000
1.3 3.1
API-44 (1979) Stephan and Lucas (1979)
Pa
50
91-475
3-4050
1.3
p(1)
25
100-440 3-2730
3.9
Wilson et al. (1981); Kobayashi et al. (1979) Kudchadker et al. ( 1978d)
AHv q(1)
20 16
100-460 90-280
1.1 4.7
Pa
32
100-340 3-1060
1.2
p(1)
17
100-400
3-2170
3.0
AHv q(1)
26 9
20-400 40-140
0.03-2170 101
2.2 6.8
Pa p(1)
18 24
-29-204 38-238
0.001-207 1379-20700
0.59 1.1
q(1)
224
7-247
100-25000
3.6
P,
57
1514482 8-3030
0.90
Wilson et al. (1981)
p(1)
21
0-150
101-962
1.6
AHH,
27
151-482
8-3030
1.1
q(1)
q(1)
3 25 3 2 154
38-99 20-367 20-30 25-196 -10-247
101 0.08-1940 101 0.05-101 100-25000
8.4 0.66 0.10 0.23 2.4
Camin and Rossini (1955) Wieczorek and Kobayashi (1981a,b) API-42 (1966) Vargaftik (1975) API-44 (1979)
P,
15
182-288
9-126
0.74
P(l)
1
99
101
0.64
q(1)
6
99-140
101
1.9
12 13 8 10 54 23 2 130
123-328 100-380 240-380 75-210 10-386 0-210 25-216 27-247
2-400 1-380 71-880 101 0.05-+1810 101 0.02-101 100-20 000
1.3 0.45 2.0 6.9
Nasir et al. (1980) Vargaftik (1975)
1.1
Vargaftik (1975) API-44 (1979)
Pa
P, AHv
154.21
824.1
460.1
C,zH,o biphenyl
154.21
789.0
480.7
ClZHz, n-dodecane
170.34
658.3
713.0
0.3564
data ref
30-480
p(1)
CI2Hl0 acenaphthene
%
AARD'
28
q(1) 128.26
pres, kPa
Pa
AHv CgHzo n-nonane
range temp, "C
3-3340 101-345
1.3 0.72 2.5
Wilson et al. (1981): . .. Kobayashi e t al. (1979) Viswanath (1979) Coal Tar Data Book (1965) Kudchadker and Kudchadker (1980)
Kudchadker and Kudchadker (1980)
Wilson et al. (1981); Nasir et al. (1980) Kudchadker et al. (19784
API-44 (1979) Sage and Lacey (1950) Stephan and Lucas (1979)
Stephan and Lucas (1979) Kudchadker e t al. (1981) Anderson and Wu (1963) Coal Tar Data Book (1965)
Stephan and Lucas (1979)
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 839 Table 111 (Continued) model compounds emp fluid form. name
C13H10 fluorene C13HB n-tridecane
C14Hlo anthracene
CllHlo phenan-
characterization parameters" crit crit vol, orient. no. of mol wt, temp, cm3/mol, param, data M K, T, V, y prop.* pts 166.22 826.2 574.5 0.4131 P, 36 AH" 26 27 d1) 675.8 780.0 0.6087 P, 19 184.37 25 P(1) AH, 2 16 ?(1). 178.24 889.2 553.2 0.4390 P. 13 7 PiU 13 M V 10 dl) 178.24 890.0 540.23 0.4123 P, 12
range temp,
%
"C
pres, kPa 115-340 0.3-230 115 0.3-230 115-260 101 70-403 0.2-1720 0-230 101 25-235 0.004-101 0-200 101 216-400 5-261 216-320 5-67 216-400 5-261 2204310 101 180-454 200-320
AARD' 2.4 4.0 2.7 0.84 0.50 1.5 1.8 5.9 4.3 4.8 4.6 2.7
data ref Kudchadker et al. (1981) Coal Tar Data Book (1965) Vargaftik (1975) API-44 (1979) Kudchadker et al. (1979a)
Wilson et al. (1980)
threne Kudchadker et al. (1979a)
186.30
849.3
609.4
0.5201
p(l)
7 11 10 2
198.40
694.0
846.5
0.6364
?(I) P,
2 16
60-99 120-421
101 1-1621
5.9 0.28
Anderson and Wu (1963) Vargaftik (1975)
P(1)
26 1
101 101 101 2-1520
0.67 0.45 1.8 0.84
API-44 (1979)
P(1) AH"
s(l)
200-320 200-360 100-316 60-99
3-69 3-143 101
101
3.3 3.2 19. 0.28
API-42 (1966)
octahydrophenanthrene
C1,HM n-tetradecane
P,
16
10-250 254 10-100 140-434
P(1)
27 1 9 9 7 41
10-260 101 271 101 20-100 101 260-400 5-110 158-213 101 110-400 0.024135
32 18 11
110-400 120-179 190-444
0.02-135 101 7-1420
28 1 16 16
20-280 287 20-240 160-460
101 101 101
28 1 18 15
tl(U
P(1)
A H V
dl)
Cl6HS2 n-pentade-
212.42
707.
911.2
0.6869
10
cane
AH" C16H10
pyrene
C16Hlo fluoran-
202.26
982.1
602.1
0.3855
202.26
943.8
782.2
0.3700
d1) P, d1) P,
0.70 0.16 1.1 3.2 2.9 2.6
Vargaftik (1975) Kudchadker et al. (1979b) Kudchadker et al. (1981)
thene
AH" d1)'
C16HM n-hexade-
226.45
717.0
973.9
0.7550
P,
1.8 28. 0.95
Coal Tar Data Book (1965) Vargaftik (1975)
cane P(1) A H V
Cl7HX n-heptade-
240.48
733.0
1039.5
0.7683
d1) P,
API-44 (1979)
141317
0.82 0.30 1.1 0.83
30-300 302 30-300 260-500
101 101 101 2-500
1.0 0.37 1.27 2.2
API-44 (1979)
6 15
200-250 190-472
101 3-1210
4.9 0.81
API-42 (1966) Vargaftik (1975)
28 1 8 16 27 1 12
30-300 316 30-100 200-502 40-300 343 40-220
101 101 101
0.87 0.74 0.97 1.1 0.91 0.26 2.0
API-44 (1979)
Vargaftik (1975)
cane PO)
AH" ClsHlz tri-
228.30
1063.6
254.50
750.0
814.8'
0.3090
d1) P,
0.7786
P,
Kudchadker et al. (1979b)
phenylene
C18HM n-octade-
1092.6
cane A H V
CzoHlz n-eicosane
282.56
767.0
1227.6
0.8853
d1) P, P(1)
AH" d1)
24502 101 101 101
Vargaftik (1975) API-44 (1979)
"Experimental critical parameters were taken from Reid et al. (1977), Ambrose (1980). and Lin et al. (1980a,b,c) and from the listed data sources. If experimental data were unavailable, characterization parameters were determined from multiproperty analysis of the thermodynamic and transport data listed for the model compound. The orientation parameter was determined from multiproperty analysis in all cases. * P. = vapor pressure; p = density; H - H" = enthalpy departure; AHv = heat of vaporization; q = viscosity; g = gas; 1 = liquid. % AARD = average absolute relative deviation = (1/N)ElNl[(exptl- calcd)/exptl]l X 100.
by using only Tbto determine y. The salient advantages of the technique are that the boiling point does not have to be at 1 atm, and the specific gravity is not needed as in conventional characterization correlations.
The need arises to be able to determine all the characterization parameters when making a property calculation for complex fluids for which critical data are not available. A logical extension of the technique for determining the
840
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
Table IV. Comparison of Results of Thermophysical Property Predictions Using Orientation Parameters -Y from Vapor-Pressure P, Data Sets of Varying Sizes orientation parameters determined from regression analysis of
P, at T b model compd
p,
toluene
all properties to crit.
Y
% AARD
7
%AARD
7
% AARD
0.2694
2.1 2.7 2.8 4.5 3.1 3.3 8.3
0.2660
1.7 2.8 2.1 4.1 2.0 3.1 8.1
0.2665
1.7 2.8 2.1 4.2 1.4 3.0 7.3
0.2640
1.9 2.8 1.9 3.9 1.2 3.0 6.8
H - H” 71
P,
P, t o crit.
%AARDa
P
Tetralin
P, t o 2 atm
Y
prop.
0.3222
P
R
0.3336
0.3380
0.3403
Predictions checked for entire set of data for properties shown.
02 0’4
r-7 \
\
\
Y
=
0 3222
\
Orientation Parameter 7
Figure 2. Sensitivity analysis of the normal boiling point T,, to the orientation parameter y for toluene and Tetralin.
orientation parameter would be to incorporate several diversified types of data in multiproperty analysis to determine the other characterization parameters as well. T h e “Therm-Trans” Characterization Technique The new use of multiproperty analysis proposed here is of a sort different than that practiced before in equation-of-state development. To develop a generalized thermodynamic correlation, multiproperty analysis has been used to ensure that the universal constants delivered via regression will enable the correlation to predict all derived thermodynamic properties accurately. In the application at hand, multiproperty analysis would be used to deliver characterization parameters that would enable the companion thermodynamic and transport correlations to simultaneously predict accurate thermophysical properties. For ease of reference, this concept, when applied to characterize complex fluids, is referred to as “therm-trans.” This unorthodox but simple technique determines correlation characterization parameters, for high-molecularweight complex fractions, via multiproperty regression analysis of vapor pressure (e.g., average normal boiling point), density (specific gravity), and viscosity (kinematic), which constitute typical inspection data for fractions. Testing of Therm-Trans The easiest way to test therm-trans is by using properties data for pure model compounds with known critical properties. The first trend that becomes evident in testing is that the more types of data that are incorporated in a therm-trans regression analysis, the more likely that effective characterization parameters can be determined. It follows that a therm-trans analysis is best carried out by using a “diversified portfolio of properties”. When only one type of property, such as vapor pressure, is available, the values of the three characterization pa-
rameters T,, po and y can wander during regression analysis to completely unrealistic values in obvious disaccord with physical principles. If viscosity data are included in the therm-trans analysis, the analysis will deliver realistic densities since density is required to calculate viscmity (as illustrated in the correlation network of Figure 1). Although relatively small, there can be a compensatory effect in the viscosity correlation that allows some error in density predicted by the equation of state. Thus, when possible, density data should also be provided in the therm-trans analysis to eliminate that respective degree of freedom in regression. Since the viscosity of a fluid is very much affected by the shape of its molecules, the inclusion of viscosity data provides implicit information on compound structure. Compounds with the same empirical formula and molecular weight, but with dissimilar structures, can exhibit quite disparate viscosity behavior. Several investigators have recognized that viscosity offers additional information that can aid in the characterization of complex fluids (Nelson, 1958). Suggestions to include viscosity as an additional parameter in conventional correlations for estimating characterization parameters have followed (e.g., Kesler and Lee, 1977). The value of using viscosity data in a therm-trans analysis to determine characterization parameters for a complex fraction is also significant. Simultaneous regression of both vapor-pressure and viscosity data usually delivers parameters that facilitate the reliable prediction of the other properties, as shown in Table V. If two types of properties are used in a therm-trans analysis, the prediction accuracy of the other property types deteriorates slightly. For example, vapor pressure is not as well predicted using parameters determined from just density and viscosity. If Tbis also included, results generally improve for vapor pressure and in some cases for all the properties (see Table V). Note, however, that prediction accuracies are still reasonable when Tbis not available. If traditional correlations that estimate characterization parameters as functions of Tband specific gravity are used, a prediction cannot even be made. In summary, vapor pressure (if the fluid is distillable), density, and viscosity should be used in a therm-trans analysis to yield the best possible set of parameters. These data appear to be the most reliable for determining parameters that enable the companion three-parameter corresponding-states correlations presented here to predict consistent properties over extended ranges of temperature and pressure.
Application of Therm-Trans to Process Fluids The densities, viscosities, and volatilities (bubble-point pressures) of several coal liquids from the Exxon Donor Solvent process have been reported (Wilson et al., 1981; Hwang et al., 1982). The experimentaldata were measured
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984 841 Table V. Comparison of Results of Thermophysical Property Predictions Using Characterization Parameters Determined from Different Sets of Inspection Data'
50
% AARDb obtained by using
characterization parameters regressed fromC model compd indene
acenaphthene anthracene
n-hexadecane
d
P(lh d l ) ,
pa,?(I) Pa 0.36 p(1) 4.5 0.53 AHv ~ ( 1 ) 3.6 Pa 0.85 p(1) 2.2 ~(1) 2.3 P, 7.2 p(1) 5.6 AHv 5.7 v(l) 4.7 P, 0.67 p(1) 0.69 AHv 0.56 q(1) 1.3
prop.
P(l), 0.66 2.3 0.76 5.0 0.86 1.9 2.6 8.0 0.59 6.6 5.7 0.63 0.68 0.50 1.4
P(l), d1) 6.9 2.1 2.3 3.3 0.80 0.10 1.4 8.6 0.15 4.7 4.6 3.4 0.75 0.42 1.1
Tb
0.54 2.7 0.37 4.3 0.86 0.34 1.4 6.8 1.1 6.2 5.3 1.1 0.68 0.15 1.2
OTwo data points for each property were used in regression analysis to determine characterization parameters. Predictions checked for entire set of data for properties shown. CRegressionof only one property usually cannot deliver realistic values for all three characterization parameters.
at conditions ranging from 21 to 454 "C and 6.8 to 218 atm (70 to 850 OF and 100 to 3200 psia). Normal boiling temperature and average molecular weight, but not specific gravity, are given for each liquid, and from this information initial guesses for the characterization parameters were first roughly estimated by the correlations of Brul6 et al. (1982). One vapor pressure (normal boiling temperature), three densities, and three viscosities were selected for each of the Exxon coal fluids. The data were selected according to what could be easily measured for a fraction in routine laboratory analyses, i.e., only moderate temperature and pressure as close to atmospheric as possible. A therm-trans regression analysis was then carried out to determine the three characterization parameters from the seven inspection-data points for each coal liquid. Using parameters determined in this way, the accuracies of density and viscosity predictions for all the data for each coal fluid are acceptable, as shown in Table VI.
% Deviation of Critical Temperature from Experimental Value Figure 3. Sensitivity of predictions, of toluene thermophysical properties, to small deviations in critical temperature used by the modified-BWR equation of state and modified-CLS viscosity correlation: % AARD = average absolute relative deviation = (l/N)zyl[(exptl- calcd)/exptl]l X 100; P, = vapor pressure; q = viscosity; AHv = heat of vaporization; H - H" = enthalpy departure; p = density; (9) denotes gas, (1) liquid.
As was observed for the pure fluids, the modified-CLS viscosity correlation breaks down at reduced temperatures below 0.35 (some errors for viscosity prediction are as high as 40%). As reduced temperature increases beyond 0.5 (above 100 OC in most cases), prediction accuracy approaches better than 5%. In any case, one can circumvent the problem of having to deal with highly viscous fluids by simply elevating the temperature of the fluid to lower viscosities into the range in which therm-trans can be used. Calculations for Gulf SRC-I1 liquids (Gray et al., 1981) are similarly presented in Table VII. Again, parameters
Table VI. Comparison of Exson Coal-Fluid Density, Viscosity, and Volatility Data with Prediction via the Modified-BWR Equation of State and the Modified-CLS Viscosity Correlation. Data of Wilson et al. (1981) and Hwang et ai. (1982) Exxon coal liq"
IHS
av MW 179
av TbboC( O F ) 271 (520)
prop. P(1)
IA-3
167
246 (520)
d1) P(1) dl)
IA-6
172
260 (500)
P(1)
IA-10
164
244 (471)
?(1) P(1)
wv-1
192
276 (528)
PO)
N- 1 N-2
164 205 134 179 158 225
237 (458) 346 (458) 208 (406) 287 (549) 245 (473) 346 (655)
p,' p,' p,' p,' p,' p,'
d1) dl)
s-1 s-2 u-1 u-2
no. of points 33 25 30 8 36 20 32 30 26 5 16 14 15 17 11 17
range temp OC 24-454 38-454 444424 177-427 22-428 93-427 43-429 93-427 21-371 93-371 1824454 200-454 175-427 114-482 214-454 219-454
pres. kPa 6890-13 800 6890-13 800 2300-20 500 1380-13 800 2300-20 500 1380-13 800 2300-20 500 1380-13 800 1380-20 700 1380-13 800 21-2100 3-567 47-3010 5-1670 4942420 54579
% AARD
1.1 8.3 0.32 6.0 0.59 6.4 1.1 4.6 1.8 11. 3.7 4.9 1.2 1.2 1.3 5.4
'I = Illinois No. 6 coal; W = Wyoming Wyodak coal. bFor most of the cases, Tb was matched within 5% in regression analysis. ' P a denotes volatility (bubble pressure) of fraction, which are the only data given. Parameters thus determined by using correlations of Brul6 et al. (1982); orientation parameter determined by regressing Tb and the next two closest bubble pressures. The bubble pressures are usually better predicted than Tb, probably because bubble-pressure measurements are generally more accurate than a Tb determination by laboratory distillation.
842
Ind. Eng. Chem. Process Des. Dev., Vol. 23,No. 4, 1984
Table VII. Comparison of Gulf Coal-Fluid Density, Viscosity, and Volatility Data with Predictions via the Modified-BWR Equation of State and the Modified-CLS Viscosity Correlation. Data of Gray et al. (1981) Gulf coal liq cut n0.O I
av
MW
av Tb,d "C
85
66.7 (152)
sp gr 0.7234
2
95
99.4 (211)
0.7538
3
108
121 (249)
0.7658
4
114
137 (279)
0.8106
5
118
167 (332)
0.8968
5HCb
116
163 (325)
0.8827
6
126
196 (384)
0.9538
7
137
220 (428)
0.9623
8
154
252 (485)
0.9761
8HC
158
250 (482)
0.9718
9
156
274 (526)
0.9802
10
166
300 (572)
0.9972
11
214
342 (648)
1.0407
llHC
212
343 (650)
1.0359
12
246
377 (711)
1.0793
13
243
398 (749)
1.0906
15
214
369 (696)
1.0773
16
238
403 (757)
1.0973
16HC
237
387 (728)
1.0885
17HC
258
426 (799)
1.1132
(OF)
prop.
no. of points 6 4 6 4 6 4 6 4 6 4 14 5 6 5 6 5 6 5 16 5 6 5 6 6 6 4 12 5 5 3 5 3 5 3 13 3 8 4 6 3
temp, "C 27-231 27-151 26-148 22-148 27-229 24-151 24-226 22-226 24-225 21-229 77-373 93-315 26-227 68-229 19-230 68-232 26-226 70-231 148-475 204-427 24-217 67-232 22-223 68-227 66-226 69-281 234-510 260-482 68-220 153-233 30-225 147-227 30-224 150-228 27-225 147-227 288-482 315-482 343-482 371-482
rangee pres. kPa 446-1480 791-1480 446-1480 790-1480 446-1830 446-1480 446-1830 790-1480 446-791 791-1480 7-3510 13-1790 791-4240 791 446-791 791 791-4240 1480-4240 5.9-3240 37-1870 791 791 791 791 446 791 8-1410 17-897 446-791 4240 446 5617 446 791 446 5620 11-422 23-472 22-284 41-284
70AARD 0.56 2.6 0.28 6.2 0.28 3.6 0.38 5.1 0.29 5.3 3.6 7.8 0.90 9.8 0.71 9.4 0.36 5.0 2.6 5.6 1.1 13. 1.3 13.0 0.39 7.0 4.4 3.9 0.29 9.2 0.48 8.0 0.61 8.9 0.48 7.8 1.4 6.0 2.6 5.4
= heat of vaporization; these Powhatan No. 5 mine coal. HC = heart cut. P, denotes volatility (bubble pressure) of fraction and AH,, were the only data available for the fraction. Parameters thus predicted by using methods of Brul6 et al. (1982); orientation parameter determined by regressing Tband the next two closest bubble pressures. Tb matched within 10% in most cases. e Viscosity correlation reliable only above lowest temperature indicated in range.
are determined by regressing only seven inspection data for each fraction. In Table VI11 the same technique is illustrated for domestic and foreign crude oils, except that molecular weights were not available and had to be estimated with a conventional characterization correlation by Riazi and Daubert (1980). Some important heuristics discovered in using thermtrans should be noted. Fractions do not have a single boiling point per se; rather, the midpoint of a boiling range is usually reported. If this boiling point is not representative of the true boiling point of the fraction, the therm-trans regression may have trouble converging. This problem was overcome by allowing relatively large error tolerances (ca. 5 to lo%),in the prediction of the average normal boiling temperature, while the regression is being performed. Determination of Tb by laboratory distillation may not be as reliable as volatility measurements because a small change in Tb may actually represent a relatively larger change in fraction bubble pressure (Nasir and Kobayashi, 1981). Volatility predictions are much improved if additional bubble-pressure data, other than just Tb,are included in a therm-trans analysis (see results for P, predictions given in Tables V and VI). The difficulty in assigning a single boiling temperature to a pseudocomponent fraction also alludes to a troublesome aspect in using conventional correlations that predict
characterization parameters as functions of fraction inspection data. If Tb is changed by just 3%, predictions of T,, p,, and y (or w ) can change by 5 to 10%. Further, a 1% to 3% error in T,, which is typical for most conventional correlations for estimating characterization parameters, can ultimately propagate into much larger errors in predicted thermodynamic and transport properties, as shown in Figure 3. For example, the Penn State T , correlation (Riazi and Daubert, 1980) predicts the T, of toluene to be 601.77 K, which is high by only about 1.7% (cf. 591.79 K given in API, 1976). With this slightly high value of T,, the average error in vapor pressures predicted by the modified-BWR equation of state escalates to a whopping 13%, as shown in Figure 3. For comparison, the average error in vapor pressures predicted by the PengRobinson equation of state, using the same slightly high T,, is 15%; by the Redlich-Kwong-Soave, 16%, which emphasizes that other equations of state are similarly sensitive. Another particularly glaring problem shown in Figure 3, which can be turned into an advantage, is that deviations in predictions of liquid viscosity are also extremely sensitive and skyrocket with only minor deviations in critical temperature. This sensitivity, which far exceeds that for the other properties, probably is the reason that P, and ~ ( 1 have ) been observed to be the most valuable fraction
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
843
Table VIII. Comparison of Petroleum-Fraction Kinematic-Viscosity Data with Prediction by the Modified-BWR Equation of State and the Modified-CLS Viscosity Correlation. Data of Amin and Maddox (1980) petroleum crude Pennsylvania California Wyoming Oklahoma Minas (Sumatra) Safaniya (Saudi Arabia) Stabilized Arabian Crude Boscan Iranian export
Waxy Light Valley Midway Special
av M W" 123 153 185 117 129 144 120 149 180 121 148 178 130 167 127 160 113
av 137.5 (279.5) 187.5 (369.5) 237.5 (459.5) 137.5 (279.5) 162.5 (324.5) 187.5 (369.5) 137.5 (249.5) 187.5 (369.5) 237.5 (459.5) 137.5 (279.5) 187.5 (369.5) 237.5 (459.5) 149 (301) 211 (412) 144 (127) 201 (394) 159 (319)
SP gr 0.7459 0.7728 0.7972 0.7818 0.8049 0.8179 0.7640 0.7968 0.8222 0.7579 0.7958 0.8279 0.7531 0.7857 0.7455 0.7848 0.7674
no. of points 3 3 3 3 3 3 3 3 3 3 3 3 2 3 2 3 3
134 156 141 177 206 97
159 (319) 196 (385) 182 (360) 247 (476) 290 (554) 90 (194)
0.7674 0.7887 0.8141 0.8659 0.8883 0.7190
3 3 2 3 3 2
38-99 38-99 38-99 38-99 38-99 38-99
0.31 0.39 0.14 0.40 8.2 2.0
119 144 173 112 133 164 130 158 181 99 136 175
135 (225) 178 (353) 223 (434) 124 (256) 165 (329) 217 (423) 159 (319) 213 (415) 253 (487) 100 (212) 179 (354) 245 (473)
0.7569 0.7805 0.8012 0.7624 0.7945 0.8246 0.7905 0.8373 0.8697 0.7495 0.8285 0.8702
3 3 3 2 2 2 2 2 3 2 3 3
38-99 38-99 38-99 38-54 38-54 38-54 38-54 38-99 38-99 38-54 38-99 38-99
1.7 0.12 0.09 0.24 1.8 2.8 4.3 0.01 2.7 7.2 1.4 8.3
Tb: OC
(OF)
temp range, "C 40-100 40-100 40-100 40- 100 40-100 40-100 40-100 40-100 40-100 40-100 40-100 40-100 38-54 38-99 38-54 38-99 38-99
% AARD
3.5 2.6 2.3 5.5 3.0 2.4 4.6 1.8 1.1 3.1 2.1 4.8 0.71 1.2 1.7 0.75 0.60
"Estimated using method of Riazi and Daubert (1980). * Tbmatched within 2% in most cases.
inspection data in determining characterization parameters via a therm-trans regression analysis (as illustrated in Table V). The finding that ~ ( 1 )appears to be just as sensitive as P, supports the idea of using ~ ( 1data ) in lieu of P, data for nonvolatile residuum fractions (for which measurements cannot be made with presently available inspection methods). Interestingly, most vapor-phase bulk properties, such as vapor viscosity, are not tremendously affected by T, deviations. However, if vapor pressure (which is related to liquid fugacity) is poorly predicted, phase equilibria and liquid enthalpies, among the most important fluid properties needed in process design and reservoir engineering, are not likely to be accurately predicted either. Other observations provide additional hints on how therm-trans should be used. The lack of symmetry in the curves of Figure 3 can be partly explained by the trend identified in Table V. If inspection data related to a certain thermophysical property are used in a therm-trans analysis, the related properties are better predicted. For example, inclusion of the average normal boiling point in the analysis generally improves prediction of P, and AH, (recall that AHv is directly related to P,by the ClausiusClapeyron relation). In Figure 3, the regression analysis (to determine the coefficients of the properties correlations, not the characterization parameters) has sought, with all of the characterization parameters fixed, a point where the errors for all the predictions of the property data are minimized simultaneously. Figure 3 shows that the minima of the property curves appear in slightly different locations along the T,-deviation axis. Leaving out a particular property type from the inspection data inputted
into a therm-trans analysis frees the regression to seek an average minimum point for the remaining properties. In Table V the minimum points derived from the various pairs of properties result in lower prediction deviations for those properties included in a therm-trans analysis, and slightly higher deviations for those properties not included. Obviously, one would expect that if a correlation's characterization parameters were obtained by regression analysis of inspection data, the correlation would, by definition, be able to predict the inspection data. However, Tables V through VI11 support the general applicability of therm-trans in that the use of just two or three property types in the analysis results in overall satisfactory prediction accuracy, for all properties and over wide ranges of temperature and pressure. Figure 3 further illustrates that the accuracies of most conventional characterization correlations are not sufficient to guarantee reliable properties predictions when parameters estimated by these correlations are used in equations of state and corresponding-states correlations for transport properties. Therm-trans circumvents this problem entirely by delivering characterization parameters that force the corresponding-states correlations to directly predict accurate thermophysical properties, which totally eliminates the indirect route along which traditional characterization correlations accumulate errors. Conclusions Simultaneous prediction of fossil-fluid thermophysical properties has been demonstrated by using multiparameter corresponding-states correlations coanchored with the same characterization parameters. A corresponding-states
844
Ind. Eng. Chem. Process Des. Dev., Vol. 23, No. 4, 1984
viscosity correlation has been successfully modified to predict the vapor- and liquid-phase viscosities of dense fossil fluids, while preserving the ability of the correlation to predict viscosities of low-molecular-weight gases. A new approach for characterizing fossil fluids has been demonstrated. This characterization method is based on multiproperty analysis of vapor pressure, density, and viscosity inspection data for complex fractions. Properly used, the therm-trans characterization procedure is able to deliver effective characterization parameters that can be used to predict many thermophysical properties reliably. Another significant finding is that the values of characterization parameters are very sensitive to liquid viscosity. Further, characterization parameters can be determined when vapor-pressure (boiling-point) data are not available, i.e., when the fluid is not distillable by conventional methods. This is not possible when using correlations that are dependent on inspection data obtained from the usual TBP-distillation analyses. This suggests that therm-trans may be the key to determining characterization parameters for residuum fractions separated by way of supercritical distillation (Brul6 et al., 1981; Warzinski and Ruether, 1983). The new modified-CLS viscosity correlation and the modified-BWR equation of state have been applied with the therm-trans characterization procedure to coal liquids from the Exxon Donor Solvent and Gulf SRC-I1 processes, and also to domestic and foreign crude oils. As more experimental data become available, the therm-trans characterization method should undergo further testing. Also, new theory should be developed to enable corresponding-states viscosity correlations to cover lower reduced temperatures. Nomenclature M = molecular weight T* = reduced temperature = k T / t T = temperature, K t / k = potential parameter TJ1.2593, K T , = critical temperature, K G = ( 1 - 0.5~)/(1 -Y ) ~ y = reduced number density = ( a / 6 ) 5 c 3= (n/6)p* = molecule number density = pNA/c g = collision diameter = [ 0 . 3 1 8 9 c / ( p f l ~ ) ]A '/~, p* = reduced density = 5u3 N 0.3189p/pc p = molar density, mol/cm3, calculated, e.g., using the modified-BWR equation of state pc = critical density, mol/cm3 c = conversion factor = 102*A3/cm3 N A = Avogadro's constant = 6.02252 X loz3mol-' h = Boltzmann constant = 1.38054 X J/K Literature Cited Ambrose, D. "Vapor-Liquid Critical Properties"; National Physicai Lab., Teddington, Middlesex TWII OLW, U.K., Feb 1980. American Petroleum Institute (API) "Properties of Hydrocarbons of High Molecular Weight"; API Research Project 42: New York, 1966. API. Division of Refining, "Technical Data Book-Petroleum Refining", 3rd ed.; Washington, DC, 1976. API-44ITRC Data ProJect. "Selected Values of Properties of Hydrocarbons and Related Compounds"; Texas A & M University, College Station, TX, loose-leaf data sheets extant, 1980. Amin, M. B.; Maddox, R. N. Hydrocarbon Process. Dec 1980, 131. Anderson, H. C.; Wu, W. R. K. Bureau of Mines Bulletin 606, Washington, DC, 1963. Brulb. M. R.; Lee, L. L.; Starling, K. E. Chem. Eng. (NY) 1979, 86(25), 155. Brulb. M. R.; Rhodes, D. E.; Starling, K. E. Fuel 1981, 60, 538. Brulb, M. R.; Lin, C. T.; Lee, L. L.; Starling, K. E. A I C M J . 1982, 28(4), 616. Brulb, M. R.: Corbett. R. W.; Watanasiri. S. Energy Prog. 1983, 3(1), 54. Brulb, M. R.; Corbett, R. W. Hydrocarbon Process. June 1084. 73. Camin, D. L.; Rossini, F. D. J. Phys. Chem. 1955, 59, 1173. Canjar, L. N.; Manning, F. S. "Thermodynamic Properties and Reduced Correlations for Gases", Gulf Publishing Company: Houston, 1967. Chao, J. "Key Coal Chemicals Data Books"; Texas AbM University, College Station, TX, 1978.
Chao, K. C.; Lin, H. M.; Nageshwar, G. D.; Kim, H. Y.; Ollphant, J. M.; Sebastian, H. M.; Slmnlck, J. J., et al. Electric Power Research Institute (EPRI) Final Report AP-1593, Oct 1980. Chu, T. C.; Chappelear, P. S.; Kobayashi, R. AIChE J. 1975, 27(1), 173. Chung, T. H.; Ajlan, M.; Lee, L. L.; Starling, K. E. Paper presented at AIChE 83rd National Meetlng, Houston, March 27-31, 1983 ( and to appear in Ind. Eng. Chem. Process Des. Dev.). Chung, T. H.; Lee, L. L.; Starling, K. E. I n t . J. Thermophys. 1980, 1(4), 399. Coal Tar Research Association "Coal Tar Data Book", 2nd ed.: Oxford Road, Gomersal, Leeds, England, 1965. Cox, K. W.; Bono, J. L.; Kwok, Y. C.; Starling, K. E. Ind. Eng. Chem. Fundam. 1971, 10, 254. Din, F. "Thermodynamic Functions of Gases"; Butterworth: London, 1961. Douslin, D. R.; Harrison, R. H.; Moore, R. T.; McCullough, J. P. J. Chem. Eng. Data 1964, 9(3). 358. Eakin, B. E.; Wilson, G. M.; Devaney, W. E. NGPA Research Report RR-6, Natural Gas Processors Association, Tulsa, OK, 1972. Felsing, W. A.; Watson, G. M. J. Am. Chem. SOC. 1942, 64, 1822. Friedman, A. S.; White, D. J. J. Am. Chem. SOC. 1950, 72, 3931. Giliiland, E. R.; Parekh M. D. Ind. Eng. Chem. 1942, 34, 360. Goodwin, R. D. National Bureau of Standards Interim Report (NBSIR) 77-860, 1977. Gray, J. A.; Brady, C. J.; Cunningham, J. R.; Freeman, J. R.; Wilson, G. M. Ind. Eng. Chem. Process Des. Dev. 1980, 22(3), 410. Hwang. S. C.; Tsonopoulos, C.; Cunningham, J. R.; Wilson; G. M. Ind. Eng. Chem. ProcessDes. Dev. 1982, 21(1), 127. Johns, I.8.; McElhill, E. A.; Smith, J. 0. J. Chem. Eng. Data 1962, 7(2), 277. Jones, M. L.; Mage, D. T.; Faulkner, R. C., Jr.; Katz, D. L. Chem. Eng. f r o g . Sym. Ser. 1963, 59, 52. Kay, W. B. Ind. Eng. Chem. 1938, 30, 459. Kesler, M. G.; Lee, B. I.ACS Symp. Ser. 1977, 60, 236. Kobayashi, R.; EPRI Report AF-1209, Nov 1979. Kudchadker, A. P.; Kudchadker, S. A.; Wilhoit, R. C. "Key Coal Chemicals Data Books", Texas A&M University, College Station, TX, Jan 1978a. Kudchadker, A. P.; Kudchadker, S. A. "Key Coal Chemicals Data Book", Texas A&M University, College Station, TX, March 1976b. Kudchadker, A. P.; Kudchadker, S. A,; Wilhoit, R . C. API Monograph 705, Washington, DC, Oct 1978c. Kudchadker, A. P.; Kudchadker, S. A,; Wiihoit. R. C. API Monograph 707, Washington, DC, Oct 1978d. Kudchadker, A. P.; Kudchadker, S. A.; Wilhoit. A. C. "Phenanthrene," API Monograph 708, Washington, DC, Oct 1979a. Kudchadker, A. P.; Kudchadker, S. A.; Wilhoit, R. C. "Aromatic Compounds," API Monograph 709, Washington, DC, March 1979b. Kudchadker, A. P.; Kudchadker, S. A. "Indan and Indene," API Monograph 709, Washington, DC, April 1980. Kudchadker, A. P.; Kudchadker, S. A,; Wilhoit, R. C.; Gupta. S. K. API Moncgraph 715, Washington, DC, Jan 1981. Lenoir, J. M.; Robinson, D. R.; Hipkin, H. G. Preprint No. 20-68, 33rd Midyear Meeting. API Division of Refining, Philadelphia, May 15, 1968. Lenoir, J. M.;Robinson, D. R.; Hipkin, H. G. J. Chem. Eng. Data 1970, 15, 23. Lin, C. J.; Kwok, Y. C.; Starling, K. E. Can. J. Chem. Eng. 1972, 50, 644. Lin, C. T.; BrulO, M. R.; Young, F. K.; Lee, L. L.; Starling, K. E.; Chao, J. Hydrocarbon Process 1980a, 59(5), 229. Lin, C. T.; Young, F. K.; BrulB. M. R.; Lee, L. L.; Starling, K. E.; Chao, J. Hydrocarbon Process. 1980b, 59(8), 117. Lin, C. T.; Young, F. K.; BrulO, M. R.; Lee, L. L.; Starling, K. E.; Chao, J. Hydrocarbon Process. I98Oc, 59(1 l), 225. Mage. D. T.; Jones, M. L.; Katz, D. L.; Roebuck, J. R. Chem. Eng. frog. Symp. Ser. 1963, 59, 61. Matthews, C. S.; Hurd, C. 0. Trans. AIChE 1947, 42, 55. Maxwell, J. B.; Bonnell, L. S. Ind. Eng. Chem. 1957, 49, 1187. Nasir, P.; Kobayashi, R. AIChE J. 1981, 27(3), 516. Nasir, P.: Hwang, S. C.; Kobayashi, R. J. Chem. Eng. Data 1980, 25(4), 208. Neufeld, P. D.; Janzen, A. R.; Aziz, R . A. J. Chem. Phys. 1972, 57, 1100. Nelson, W. L. "Petroleum Refinery Engineering", McGraw-Hill: New York, 1958. Reichenberg, D. AIChE J. 1973, 79(4), 854. Reid, R . C.; Prausnitz, J. M.; Sherwood, T. K. "The Properties of Gases and Liquids", McGraw-Hill: New York, 1977. Riazi, M. R.; Daubert, T. E. Hydrocarbon Process. March 1980, 115. Sage, B. H.; Lacey. W. N. "Some Properties of the Lighter Hydrocarbons, Hydrogen Sulfide and Carbon Dioxide"; API: New York, 1955. Sage. B. H.; Lacey, W. N. "Thermodynamic Properties of the Lighter Paraffin Hydrocarbons and Nitrogen", API, New York, 1950. Starling, K. E. SOC. Pet. Eng. J. 1986 6(4). 363. Starling, K. E. "Fluid Thermodynamic Properties for Light Petroleum Systems", Gulf Pub. Co: Houston, 1973. Starling. K. E. Ph.D. Dissertation, Illinois Inst. Tech., Chicago, 1962. Stephan, K.; Lucas. K. "Viscosity of Dense Fluids", Plenum: New York and London, 1979. Stewart, D. E.; Sage, B. H.; Lacey, W. N. Ind. Eng. Chem. 1954, 46, 2529. Streett, W. B.; Staveley, L. A. K. Adv. Cryog. 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Ind. Eng. Chem. Process Des. Dev. 1984, 23, 845-847
a45
Yesavage, V. F. Ph.D. Dissertation, University of Michigan, 1968.
Wang, J. S.; Van Daei, W.; Starling, K. E. Can. J. Chem. Eng. 1076, 54, 241. Warzinski, R. F.;Ruether, J. A. Paper presented at Direct Coal Liquefaction Contractors’ Meeting, U.S. Dept. of Energy, Pittsburgh, Nov 16, 1983 (and to appear in Fuel). Watanasiri, S.; Brul6, M. R.; Starling. K. E. AIChE J. 1982, 28(4), 626. Wleczorek, S. A.; Kobayashi, A. J. Chem. Eng. Data 1061, 26(1), 11. Wieczorek, S. A.; Kobayashl, R. J. Chem. Eng. Data 1081, 26(4), 8. Wilson. G. M.; Johnston. R. H.; Hwang, S. C.; Tsonopouios, C. Ind. Eng. Chem. Process Des. Dev. 1981, 20, 94.
Received for review October 11, 1982 Accepted October 24, 1983 Support for this work was provided by the U.S. Department of Energy Pittsburgh Energy Technology Center (DOE PETC), and the Oklahoma Mining and Mineral Resources Research Institute. This paper was presented in part at the AIChE 82nd Annual Meeting in Los Angeles, Nov 8-12, 1982.
COMMUNICATIONS New Procedure Generating Suboptimal Configurations to the Optimal Design of Multipurpose Batch Plants The optimal design of a multipurpose batch plant is considered. The problem has been formulated as a mixed integer nonlinear program (MINLP) by previous authors and they have proposed a strategy consisting of a method of generating the optimal or near-opthnel confgurations, from which proper horizon constraints are extracted. These constraints are then applied to MINLP. I n this paper, a new algorithmic solution procedure for generating the optimal or nearsptimal configurations is presented. The method is based on the rigorous solution procedure of a set partitioning problem of operations research. A simple example illustrates how the method proposed works. A more detailed analysis, especially in the applicationto large size problems, must be made before any generalization.
each Pi within the horizon H (total time available for production in a year). Suhami and Mah (1982) have formulated this problem as a mixed integer nonlinear program (MINLP) as follows. Determine Bi, TL,,V,, nj to minimize
Introduction Suhami and Mah (1982) have formulated a problem of optimal design of the multipurpose batch plants as a mixed integer nonlinear program (MINLP). In order to design the multipurpose batch plant, the production scheduling must be made before determining the batch size, volume of the unit, and the number of batch equipments. The reason for this is that in the multipurpose batch plant, two or more products may be manufactured at any one time. To find the optimal or near-optimal production scheduling, Suhami and Mah have proposed a strategy consisting of a method of generating feasible sequences and nonredundant horizon constraints and a set of rules for selecting the opitmal or near-optimal configurations based on heuristic considerations. In this paper we propose a new method for determining the optimal or near-optimal configurations of the multipurpose batch plant design. The method is based on the solution procedure of the set partitioning problem of operations research. Problem Formulation The problem to be considered has been defined by Suhami and Mah (1982). Briefly, consider a plant consisting of M type of batch equipment (R,), which are used to produce N kinds of products. k, IM types of batch equipment are available for processing each product PI, each corresponding to a stage j = 1,2, ..., k,. In each stage j , the types of batch equipment are prespecified, nj units can be operated independently in parallel, and all units within the given stage j have the same size VI. I t is also assumed that ki types of batch equipment are all distinct, the intermediate tank is not considered, and the sequence in which the k , types of batch equipment are going to be used is specified beforehand for each product PI. With the above assumptions, the design problem is to determine VI, the size of each equipment R,, the number of equipment nl required per stage and the batch size B, for each product P, so as to minimize the capital investment, and satisfy Q,, yearly production requirement for 0196-4305/84/1123-0845$01.50/0
M
minCn,cr;V,B, ;=l
subject to
V, =max(S&) (j = I , 2, ..., M) i€UJ
(3)
vi” Ivj Ivju 0‘ = 1, 2, ..., M)
(4)
..., M )
(5)
nIL Inj 5 nju Qi
= 1, 2,
(i = 1, 2, ..., N)
Ti = -TLi Bi N
E T i IH
i=l
C Ti I H
0’ = 1, 2, ..., M )
(7) (8)
i€ UJ
where Tij = time required to process one batch of product
Pi in a stage involving equipment type Rj;Si;= characteristic size of equipment needed at stage j to produce unit mass of product Pi;Ci= {RjlRjrequired for product of Pi); U, = (PiIRECiJ;CY,, pi, Si,, Qi, H are given positive constants, and nj in integer. Constraints ( 7 ) and (8) are referred to as horizon constraints. As pointed out by Suhami and Mah (1982), the design problem of the multipurpose batch plants (referred to as (Pl))lies between two problems. Namely, one is constituted by relations (1)-(7), which corresponds to the formulation of the multiproduct plant design treated by 0
1984 American Chemical Society
