508
Ind. Eng. Chem. Process Des. Dev. 1981, 20, 508-511
viscosity index of the products is decreased, in the manner similar to that occurring in conventional solvent dewaxing. Removal of waxes is needed to decrease the pour point of the oil to meet the specification as lubricating oil. The dewaxing selectivity defined as the decrease in viscosity index per degree of pour point lowering for the catalytic treatment was found to be about the same as the solvent dewaxing. Conclusions It is well known that hydrocracked lubricating oils are unstable and form sediment upon exposure to light and air. Such unstable oils can be stabilized by catalytically treating them with paraffins over shape selective proprietary zeolite catalysts. In practice, the waxy hydrocracked oils which contain slack wax can be treated directly over the catalyst to simultaneously stabilize them and decrease their pour point to specification. This catalytic treating process can be integrated with the hydrocracker by adding a second stage reactor or replacing the catalyst in the last zone. The reaction sequence includes shape selective cracking of the normal paraffins (or slack wax) to form olefinic intermediates, which in turn alkylate the sludge forming precursors and aromatic compounds in the oil. Both catalytic cracking and alkylation reactions are catalyzed by the proprietary zeolite catalyst. The mechanism of hydrocracked oil stabilization involved in this catalytic stabilization process has not yet been ascertained, but it
is postulated that the sludge precursors are deactivated and the base oil itself is improved in its ability to dissolve the oxidized product by alkylation with olefins obtained in the course of normal paraffin cracking.
Literature Cited Argauer, R. J.; Landoh, G. R. (To Mobil Oil corp.) U S . Patent 3 702 888, Nov 1972. Assef, P. A. API Proc., Dlv. Ref. 1970, 50. 775. Bryer, R. P.; Dklot, F. E. SAE Pap. 730-781 (Sept 1973). Espenscheid, W. F.; Yan, T. Y. (To Mob11 Oil Corp.) U.S. Patent 3 853 749, Dec 1974. Franz, W. G.; Smilskl, M.T. (To Mobil Oil Corp.) U.S. Patent 3 562 145, Feb 9, 1971. Frlllette, V. J.; b a g , W. 0.; Lago, R. M. J. Catal. 1981, 67, 218. Gilbert, J. 0.; Walker, J. 8th WorMPet. Congr. 1971, 4, 147. l$&ocarbon Process. 1978, 57(5), 185. Kokotallo, G. T.; Lawton, S. L.; Olson, D. H.; M e r , W. M. Nature (London), 1978 272, 437. Langlols, G. E.; Cerrho, E.; Whlte, R. J. (To Chevron Research Co.) U S . Patent 3 463 724, Aug 1969. Orkin, B. A.; Braid, M. (To Mobil Oil Corp.) U.S. Patent 3 438 334, Aprl 1989. Stelnmetz, I.; Reif, H. E. API Roc., Mv. Ref. 1973, 53, 702. Vlugter, J. C.; Van't Spijker, P. 8th WorM Pet. Congr. 1971, 4, 159. Yan, T. Y. (To Mobil Oil Corp.) US. Patent 3989617, Nov 1978. Yan, T. Y. Ind. Eng. Chem. Prod. Res. Dev. 1978, 17, 368. Yan, T. Y.; Brldger. R. F. (To Mobil Oil Corp.) U.S. Patents 3 928 171, Dec 1975; 4 181 597, Jan 1980.
Received for review September 5, 1980 Accepted March 16, 1981 Presented at the Division of Petroleum Chemistry, Second Chemical Congress of the North American Continent, Las Vegas, Aug 1980.
Correlation of the SolubMty of Carbon Dioxide in Hydrocarbon Solvents Herbert M. Sebastlan, Ho-mu Lln, and Kwang-Chu Chao' School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
A correlation is developed for the solubility of carbon dioxide in hydrocarbon solvents at temperatures from 340 to 700 K and pressures up to 170 atm. The fugacity of dissolved carbon dioxide at zero pressure is correlated as a function of solubility parameter and temperature. The high-pressure fugacity is obtained upon applying a Poynting correction for which the required partial molal volume of carbon dioxide is correlated as a function of temperature. The Henry constant of carbon dioxide is Included in the correlation. When compared with 339 experimental data points of 15 mixture systems, the correlation shows an overall average absolute deviation of 6%.
Introduction The solubility of carbon dioxide in hydrocarbon solvents is of interest to a number of industrial processes. Carbon dioxide is found in petroleum reservoir fluids, natural gases, coal gases, and liquids. Carbon dioxide flooding is a method of tertiary oil recovery. As a consequence of this interest, a substantial amount of vapor-liquid equilibrium data of C02-containingmixtures has become available in the literature. In this work we develop a correlation of the fugacity of dissolved carbon dioxide in liquid hydrocarbon solutions. The fugacity is expressed as a function of temperature, pressure, and concentration with solubility parameter 0196-4305/81/1120-0508$01.25/0
Table I. Constants in Eq 3 A, A, A3
A4
A5 A6
3.4156 7.1715 X -4.1542 X 1.4655 X -8.7574 x 10-8 -1.2158X l o 3
lo-)
employed to characterize the solutions. Correlation of Fugacity Sebastian, Lin, and Chao (1981) recently developed a correlation of solubility of hydrogen in hydrocarbon solvents. The method employed in this work for the corre0 1981 American Chemical Society
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981 509
lation of the solubility of carbon dioxide is similar. The logarithm of the ratio of the fugacity of carbon dioxide to its mole fraction v / x ) is expressed as the sum of a zero pressure term and a Poynting correction In ( f / x ) = In (f/x),=,, pV/RT (1) The zero pressure term is a function of temperature T and solubility parameter of the solution 6. In (f/~),=~ = F(6,T) (2)
a-
+
F) n
a
Y
-
7
X \ L ... L L
0
ISOBUTRNE
0
N-BUTRNE
A
N-PENTRNE
0
N-OECRNE
-___ --- ---.
377.OOK iPloERRbR BOUND
.
I
In the temperature range 340-700 K, the F function is represented by F(6,T) = Ai + A2T/6 + ABT A4T8 A,S2/P (3)
+
+
+
in which the coefficients Ai are given in Table I, and Tis in Kelvins and 6 in (cal/mL)'12. The mixture solubility parameter, 6, is the core volume average of the solubility parameters of its components
4 ' 3
I
I
I
I
1
I
5
6
7
a
1
4
9
10
SOLUBILITY
PARRMETER MIXTURE
Figure 1. Comparison of F function with data at 377 K.
(4)
462.00K QUINOLINE
o
where V,i is the molecular core volume obtained upon summing Bondi's (1968) van der Waals volumes of the groups. For carbon dioxide Vwi= 19.7 mL/g-mol. The solubility parameter is by definition
1
a
-E-, x \
~
6i = (AUj/Vi)'12 (5) where the energy of vaporization into vacuum AU and the volume V of the liquid are both for the saturated liquid of component i at the temperature of interest. Sebastian et al. (1981) described the method used in this work to calculate the solubility parameter of solvents. For carbon dioxide which is supercritical at the temperatures of this work, eq 5 does not apply and a constant value of 3.0 (cal/mL)'12 was chosen as its solubility parameter. At conditions near the critical temperature of carbon dioxide (304 K), the use of this constant value becomes unacceptable. The present correlation is limited to temperatures above 340 K. The partial molal volume of carbon dioxide that is required in eq 1 is expressed as a function of T VCD= 9.167 0.00869T + 1.345 X 10-4P (6)
+
where V c D is in mL/g-mol. In developing the correlation we determined the ratio v / x ) C D from experimental vapor-liquid equilibrium data (f/x)CD = 6 C D P K C D (7) where the fugacity coefficient in the vapor 4 a is calculated from the Redlich-Kwong equation of state modified by Prausnitz and Chueh (1968). The constants 9, and Qb needed for this equation of state have been correlated with the acentric factor by Yao et al. (1978). The interaction constant kij was obtained by fitting the equation to experimental values of the solvent fugacity coefficients as described by Sebastian et al. (1981). The kij so obtained for carbon dioxide interactions with hydrocarbons was correlated in terms of the critical volume of the solvents kij = 0.018 + O.O0042V, (8) where V , is in mL/g-mol. The correlated values of kij, a,, and a b were used to calculate 4. The F function of eq 2 was established by the Henry constant of carbon dioxide in various solvents. When the vapor pressure of the solvent is low the Henry constant H = lim ( f / x ) (9) X-0
o
1-METHYLNRPHTHRLENE
A
N-DECANE
o
TETRRLIN
v
M-XYLENE
0
DIPHENYLNETHRNE
v
z 6 -
-
5-
LiI 3
I
I
I
I
1
i
4
5
6
7
B
9
I
10
S O L U B I L I T Y PARRMETER MIXTURE
Figure 2. Comparison of F function with data at 462 K. 9
I
1
3 1
2 'r
I
i
0
QUINOLINE
0
TOLUENE
V
TETRRLIN
0
M-XYLENE
I
I
1
Si3 .OOK
--- _ _=- - -I
-I
5
3
i
I
I
I
I
I
4
5
6
7
8
9
S O L U B I L I T Y PARAMETER
I
io
MIXTURE
Figure 3. Comparison of F function with data at 543 K.
is equal to the F function with 8 a t the value of the pure solvent. Once the F function was established, the partial molal volume needed for the Poynting correction was determined from high-pressure equilibrium data according to eq 1. Results and Discussion Figures 1-5 show the comparison of the F function of eq 3 with reduced experimental data at five temperatures from 377 to 703 K. The dashed lines in the f i i e s are the 10% error bounds. The majority of the data points fall within the bounds.
Ind. Eng. Chem. Process Des. Dev., Vol. 20, No. 3, 1981
510
Table 11. Comparison of Correlation with Data for Carbon Dioxide Binary Mixtures
T,K
P,atm
no. of points
AADa in ( f i x )
source
3441411 3441394 3441377 3521477 3441511 4621583 4631663 4731533 3931477 3521477 3931502 4621582 4621664 4621664 4621702 4621703 4621703
13168 2/61 4/95 41130 131170 20150 20150 201100 61147 31150 9/50 20150 20150 20150 20150 20150 20150
24 17 24 23 33 16 16 31 16 25 21 16 14 16 15 16 16
8.19 7.80 8.65 9.11 6.64 2.20 12.85 7.52 2.79 1.58 2.94 4.11 7.57 3.80 1.31 4.39 1.24
Oids et al. (1949) Besserer and Robinson (1973a) Besserer and Robinson (1973b) Kalra e t al. (1978) Reamer and Sage (1963) Sebastian et al. (1980d) Sebastian et al. (1980d) Krichevskii and Sorina (1960) Np. and Robinson (1979) Ng and Robinson (1978) Sebastian et al. (1980e) Sebastian et al. (1980e) Sebastian et al. (1980a) Sebastian et al. ( 1 9 8 0 ~ ) Sebastian et al. (1980b) Sebastian et al. (1980a) Sebastian et al. (1980b)
solvent
n-bu t ane isobutane n-pentane n-heptane n-decane n-hexadecane cyclohexane methylcyclohexane toluene m-xylene m-cresol tetralin 1-methylnaphthalene quinoline diphenylmethane
9 ,
1
I
I
I
QUINOLINE 1-METHYLNAPHTHALENE
0
0
I
,
I
__-1 0 0 ~ o E R R B RB O W 3
*
TETRRLIN
0
DIPHENYLMETHRNE
I
622.COK
.___---
4I I
//
2
3
I
I
I
I
I
1
Li
5
6
7
8
9
10
PARRMETER MIXTURE
SOLUBILITY
Figure 4. Comparison of F function with data at 622 K.
1
A
A
-
I
::, 0
-
N-OECANE M-XYLEN:
,
OIPHENYLnETnANE
{
,
\
,
I
I
TREHPER L P R A U S Y I T Z
0 S E B A S T I A N e:
I-METHYLNRPHTHALENE{:
dl
~~~~~~~A~
TO L U E NE o
QUINOLINE
0
1-METHYLNRPHTHRLENE
A
OIPHENYLMETHANE
Lt
5
300
-___
7
350
YO0
'450
500
550
600
650
700
750
T ,K
-------.
6
I O8
703 .OOK 100iOERROR
8
BOUND
9
Figure 6. Comparison of the correlation with experimental values of Henry's constant.
10
SOLUBILITY PRRAMETER MIXTURE Figure 5. Comparison of F function with data at 703 K.
Table I1 shows the result of comparison of the correlation with experimental data for 15 binary mixture systems. The average absolute deviation (AAD) for all systems is 6%. The AAD is found to exceed 10% only in the case of carbon dioxide dissolved in n-hexadecane which is an exceptionally long chain molecule. The Henry constant of carbon dioxide in hydrocarbon solvents is included in this correlation. To calculate a Henry constant, set 8 in eq 3 to be equal to 6 of the solvent
and set p in eq 1 to be equal to the vapor pressure of the solvent. Figure 6 shows the calculated Henry constant of carbon dioxide in five systems. Agreement with experimental data is about the same as indicated in Table 11. Acknowledgment Funds for this research were provided by the Electric Power Research Institute through Grant RP-367. Nomenclature AAD = absolute average deviation f = fugacity, atm F = zero pressure f / x function, atm H = Henry's constant, atm K = vaporization equilibrium ratio k = interaction parameter for Prausnitz-Chueh equation of state p = pressure, atm T = temperature, K AU = intemal energy change upon vaporization into vacuum, cal/g-mol V = molar volume, mL/g-mol
Ind. Eng. Chem. Process Des. Dev, 1081, 20, 511-519
x = liquid mole fraction 6 = solubility parameter, (cal/mL)’I2 fl,,fl, = constants in Prausnitz-Chueh equation of state
511
Besserer, G. J.; Robkraon, D. B. J . Chem. Eng. Dat 1973a, 18, 298. Beserer, G. J.; Robinson, D. B. J. Chem. Eng. Data 1973b, 18, 418. Bondi, A. “Physical Properties of Mdecuiar Crystals, Liquids. and ( y a w s ” ;
Ng, H. J.; Robinson, D. B. J . Chem. Eng. Data 1978, 23, 325. Ng, H. J.; Robinson, D. B. Fluid phase Equilib. 1979, 2, 283. O b , R. H.; Reamer, H. H.; Sage, 8. H.; Lacey, W. N. Ind. Eng. Chem. 1949, 41, 475. Prausnitz, J. M.; Chueh, P. L. “Computer Calculations for High-Presswe Vaporliquid Equilibria”; Prentice-Hail: Englewood Cliffs, MI, 1988. Reamer, H. H.; Sage, B. H. J . Chem. €ng. &7t8 1983, 8 , 508. Sebastian, H. M.; Lin, H. M.; Chao, K. C. AICM J. 1961, 27, 138. Sebastlan, H. M.; Un. H. M.; Chao, K. C. J. Chem. Eng. Data 1980a, 25, 381. Sebastlan, H. M.; Nageshwar, 0. D.; Lin, H. M.; Chao, K. C. J. Chem. Eng. Data 1980b, 25, 145. Sebastian. H. M.; Nageshwar, G. D.; Lin, H. M.; Chao, K. C. Nukl M s e Equilllb. 1980~.4, 257. Sebastlan, H. M.; Simnick, J. J.; Lin, H. M.; Chao, K. C. J. Chem. Eng. Data 1980d, 25, 138. Sebastlan, H. M.: Simnick, J. J.; Lin. H. M.; Chao, K. C. J . Chem. ,Em. Data ISBOr, 25, 248. Tremper, K.; Prausnitz, J. M. J. Chem. Eng. Data 1978, 21, 295. Yao, J.; Sebastlan, H. M.; Lin, H. M.; Chao, K. C. Flukl Phase Equlllb. 1978, 1 , 293.
Wiley: New York, 1988. Kaka, H.; Kubota, H.; Robinson, D. B.; Ng, H. J. J . Chem. Eng. Data 1980, 23, 317. Krlchevskil, I. R.; Sorina, 0.A. Russ. J. phys. Chem. 1980, 34, 879.
Received for review September 15, 1980 Accepted April 2, 1981
C#J
= fugacity coefficient
Superscripts - = average or partial molal quantity Subscripts cs = critical property of solvent CD = carbon dioxide i j = components p = 0 = at zero pressure
Literature Cited
Heat Transfer to a Fluidized Bed Using a Particulate Heat Transfer Medium Fathl D. Husseln, Partha P. Maitra, and Roy Jackson’ Depertment of Chemhxl €ng/neering, University of Houston, Houston, Texas 77004
Heat may be transferred to a fluidized bed by passing downward through the bed heated particles which are larger and denser than the bed particles. The rate of heat transfer attained depends on the feed rate of descending particles, their mean residence time, and the heat transfer Coefficient between these particles and the bed. Measurements have been made of the dependence of mean residence time on properties of the particulate materials employed and on the operating conditions of the bed. Conditions which limit the attainable downflow rate have also been identified, and some values for heat transfer coefficients have been determined.
Introduction The steam gasification of carbon according to the reaction C + H20 = CO + H2 is endothermic and, for kinetic reasons, it must be conducted at a temperature of the order of 800 “C. The most common method of generating the required energy is by burning part of the carbon by blowing air or oxygen into the bed together with the steam. If air is used, the product gas is much diluted by nitrogen, while the use of oxygen involves the high cost of an air separation plant. An alternative using a solid heat transfer medium has been proposed for two process concepta, the COz-acceptorprocess and the ash-agglomerating gasification process. In these systems a fluidized bed of coal char is gasified with steam, which also serves as the fluidizing medium. The heat of reaction for the endothermic gasification reaction is provided by a solid heat transfer medium in the form of heated particles, larger and denser than the char particles, which are rained down through the fluidized bed of char. The question then arises whether hot particle fluxes large enough to achieve the desired heat transfer rates can be attained in such systems, and what are the proper choices of size and density for the hot particles and operating conditions for the fluidized bed. Though this method is, in principle, of general utility for supplying heat 0196-4305/81/1120-0511$01.25/0
to endothermic gas-solid reactions (or, indeed, removing heat from exothermic reactions), very little is known about the mechanical or thermal behavior of system of this type. So far as we are aware, the only systematic studies reported in the open literature are those of Iya and Geldart (1978), who carried out cold testa with two types of sand and simulated char particles, to find the maximum attainable downward flux of the sand through a fluidized bed of simulated char. Chen and Keairns (1978) investigated a closely related system for the separation of agglomerated ash from a fluidized bed of simulated char, while Rowe et al. (1972) and Nienow et al. (1973) elucidated the mechanism by which two closely sieved powders, differing in size and density, segregate when they are fluidized. The purpose of the present work is to investigate the mechanical and thermal properties of systems in which larger, denser particles are passed downward through a fluidized bed of smaller and less dense particles. The first phase of the work determines the dependence of the mean residence time of the descending particles on their size and density, the properties of the bed particles, and the design and operating conditions of the fluidized bed. At the same time the maximum attainable flux of the descending particles is measured. In the second phase of the work, the particles fed to the bed are heated and temperature measurements are made which lead to estimates of the heat transfer coefficient between the descending particles 0 1981 American Chemical Society
