I n d . Eng. Chem. Res. 1987,26, 2419-2423
Dividing eq B2 by N yields an expression for the mean irrigation rate,
The probability distribution of mk is the probability of choosing mk nonempty channels followed by an open channel, n-k+l k - 1 mk dmk)
=
(
mk
2419
n
( j }= G I C l / k
)(T)
k=l
c(:"of
= 0,1,2,...,+m
> G1
The expected value of mk is thus (m,) = 0 (mk) =
n - k + l k-1
= Gl ln subbituminous > lignite. For example, V removal was 73% for bituminous coal and 27% for lignite. We did not attempt to optimize demetalation of solubilization processing conditions for each of the coals used. Our objective was to apply the optimum processing conditions for visbreaking of the petroleum components used. Demetalation and Petroleum Source. For the three petroleum substrates used in this study, vacuum residue A, vacuum residue B, and Bmcan crude slurried with 30% Illinois No. 6 coal, the extent of V removal at 870 O F and 12-h-l LHSV is 73%, 57%, and 51% (Table VIII), respectively. The susceptibility of the three materials for Ni removal in terms of percent demetalation does not vary significantly. However, the actual amount of metal removed increased as the initial metal content of the substrate increased. For example, 620 ppm of V was removed from Boscan crude, i.e., 51% demetalation, and 106 ppm of V was removed from residue B, i.e.,, 57% demetalation. Thus, this approach of coprocessing with coal to demetalation is most useful for high metals containing petroleum residues, heavy crudes, or tar sand bitumens. These observations indicate that demetalation of residues is not limited by the initial amount of metals present in the residue and could be related to the types of structures with which the metals are associated. It appears, however, that in the demetalation reactions involved in this process, about 50% of the metals is reactive toward coal and are easily removed by coprocessing. The remaining 50% is less reactive and may require processing of a different nature. Postulated Mechanism for Demetalation. Adsorption of large organic molecules on charcoal, alumina, nodules, and other solids is a well-known phenomenon. It was thus considered essential to determine if this observed demetalation of the residue is adsorptive in nature. Two approaches were used. In the first, vacuum residue was coprocessed in admixture with chemically nonreactive Davidson's Grade 12 silica gel, 700 m2 surface area/g at 870 O F , 400 psig, and 12-h-l LHSV. Notwithstanding the
Table VIII. Effect of Petroleum Source on CoDrocessing' (Illinois No. 6 Coal) crude vacuum residue Ab vacuum residue B coal added, wt 90 petroleum, wt % yield, wt % gas liquid solid coal conversion, w t % coal solubilized, wt % demetalation, 90 Ni V liquid product Ni, ppm PPm solid product Ni, ppm v , PPm
y,
0 100
20 80
30 70
1
3.9 86.6 9.5 53 37
4.3 79.5 16.2 46 34
45 52
53 73
29 120
25 67
99
53 250
110 360
0 100
20 80
Boscan 30 70
0 100
2 80
30 70
43 46
45 51
60
656
58 600
155 1880
210 1690
25
58 186
36 44
55 57
37 105
26 80
160 225
110 250
OConditions: 870 O F , 400 psig, 12-h-' LHSV. *Yield conversion and solubilization data for 850 O F .
106 1220
I n d . Eng. Chem. Res. 1987,26, 2423-2430 Table IX. Coprocessing of Vacuum Residue A with Silica Gel and Bituminous Coal silica gel bituminous coal tme Grade 12 Illinois No. 6 temp, OF 870 75 0 pressure, psig 400 LHSV, v/v/h 12 0.5 time, h 72 solvent none toluene 20 30 solid, wt % 80 70 residue, wt % demetalation, % 9 2 Ni 13 1 v liquid properties Ni, ppm 48 52 v , PPm 218 248 OSurface area 700 m2/g.
high surface area of the silica gel, the Ni and V removals were only 9% and 13%, respectively (Table IX). In the second approach, the residue in toluene solution was allowed to contact pulverized bituminous coal for 72 h at room temperature. The bituminous coal at room temperature is obviously not reactive. Ni and V demetalation were merely 2 % and 1% , respectively. These observations suggest that physical adsorption makes a very small contribution to the total demetalation observed with bituminous coal. The results from coprocessing with silica gel suggest that the physical adsorption component of demetalation should be less than 9% and 13% of Ni and V, respectively. Furthermore, the fact that demetalation increased as the process temperature and severity are increased suggests that the demetalation reaction is a chemically activated process and not a simple physical adsorption of large metal-containing organic species on the
2423
unconverted coal. On the basis of our results, we believe that the demetalation of residues involves the following steps: (1) thermal breakdown of metal-containing and asphaltenic compounds in the residues; (2) thermal conversion and liquefaction of coal leading to reactive radical species; (3) conversion of metal and carbonaceous fragments to solids by reaction with the radicals from the coal. The radicals from the dissolved coal serve as the metal scavengers, while the unconverted coal serves as the carrier to deposit insoluble metal reaction products which can be readily separated from the liquid product, thus reducing its metals concentration. Literature Cited Adachi, Y.; Nakada, M.; Kawazu, K.; Shibata, M.; Sakaki, T.; Arita, S.; Kakiyama, H.; Honda, H. Nenryo Kyokaishi 1983,62(669),16. Curtis, C. W.; Tsai, K. J.; Guin J. A. Ind. Eng. Chem. Process Des. Deu. 1985,24, 1259. Espenscheid, W. F.; Yan, T. Y. US.Patent 4035 281,March 2,1977. Fukui, Y.; Shiroto, Y. Chem. Econ. Eng. Reu. 1983, 15(3), 15. Moschopedis, S. E.; Hawkins, R. W.; Fryer, J. F.; Speight, J. G. Fuel 1980, 59, 647. Osafune, J.; Arita, S.; Yamada, Y.; Kakiyama, H.; Honda, H.; Tagawa, N. Nenryo Kyokaishi 1978,57(2), 132. Osafune, K.; Arita, S.; Kakiyama, H.; Honda, H. Nenryo Kyokaishi 1980,59(638), 396. Sakaki, T.; Adachi, Y.; Shibata, M.; Arita, S.; Kakiyama, H.; Honda, H. Nenryo Kyokaishi 1981, 60(656), 994. Yan, T. Y. U.S. Patent 4334976, March 2, 1982. Yan, T. Y.; Espenscheid, W. F. US.Patent 4 151066, April 24,1979. Yan, T. Y.; Espenscheid, W. F. Fuel Processing Technol. 1983, 7, 121.
Received for review March 10, 1986 Revised manuscript received July 21, 1987 Accepted August 17, 1987
Correlation and Prediction of Enthalpies of Mixing for Systems Containing Alcohols with the UNIQUAC Associated-Solution Theory Vincenzo B r a n d a n i * and F r a n c o Evangelista Dipartimento di Chimica, Ingegneria Chimica e Materiali, Universitd de’ L’Aquila, 67100 L’Aquila, Italy
The UNIQUAC associated-solution theory is presented and applied t o systems containing alcohols for the purpose of correlating enthalpies of mixing. The enthalpy of mixing of an associated solution can be separated into two additive contributions, one physical and the other chemical. The physical part, expressed by the residual part of the UNIQUAC model, presents two adjustable parameters which are temperature dependent. The chemical part, obtained from Flory’s theory, presents two parameters, the equilibrium association constant and the enthalpy of hydrogen-bond formation, which depend on the properties of the pure associating component. By use of both contributions, good correlation is obtained with a n average absolute error of 5.1%. By use of only the chemical contribution, good prediction is obtained with an average absolute error of 14.7%. By use of the parameters obtained by the fitting of enthalpies of mixing, VLE data are predicted quite well with average absolute errors in vapor pressure and vapor composition of 5.7% and 3.9%, respectively. Evaluation of thermodynamic consistency of isobaric
VLE data requires knowledge of the enthalpies of mixing, especially when the two pure components differ markedly in volatility. Moreover, prediction of enthalpies of mixing in systems containing alcohols is important in several chemical engineering applications. 08S8-5885/87/2626-2423$01.50/0
Recently, Stathis and Tassios (1985) have developed a correlation, based on a UNIFAC association model, for predicting the enthalpies of mixing of systems containing alcohols. This model gives good results with typical average absolute errors between 5% and 15%. However, the model developed by Stathis and Tassios (1985) does 0 1987 American Chemical Society
