Ind. Eng. Chem. Process Des. Dev.
lustrated by Figures l a and b. All the dye was quickly mixed throughout the tank in the Lane and Rice (1981) design. In conclusion, a valid quantitative comparison of the three designs for liquid jet mixing illustrates that the design proposed by Lane and Rice (1981) has the best mixing performance in terms of the shortest mixing time. This can be attributed to the elimination of poorly mixed regions which secrete liquid, prolonging the mixing process. Nomenclature
d = jet diameter, m D = tank diameter, m F = mixing time factor, dimensionless g = gravitational acceleration, m Rej = jet Reynolds no. = ( V d ) / v ,dimensionless T = mixing time, s V = jet velocity, m s-l y = height of liquid in the tank, m
1982,21, 653-658
653
Greek Letters p u
= liquid density, kg m-y = liquid kinematic viscosity, m2 s-l
Literature Cited Coldrey, P. Paper to Institution of Chemical Engineers, University of Bradford, England July, 1978. Fossett, H; hosser, L. E. Roc. Inst. Mech. Eng. London 1949, 160, 224. Fossett, H. Trans. Inst. Chem. Eng. 1951, 29, 322. Fossett, H. Paper presented to ASME Meeting, Atlanta, GA, June 1973. Hiby, J. W.; Modlgell, M. Paper to 6th CHISA Congress, Prague, 1978. King, R. BHRA FluM Engineering, CranfieM, England, 1980;Report TN 1609. Lane, A. G. C.; Rice, P. Inst. Chem. Eng. England Symp. Ser. 1881; No. 6 4 , KI. Okita, N.; Oyama, Y. Kagaku Kogaku 1963,27, 252. Racz, I.; Groot Wassink, J. Chem. Ing. Tech. 1974,6 , 261. Van de Vusse, J. G. Chem. Ing. Tech. 1859,31, 583.
Receiued f o r review July 10, 1981 Revised manuscript received April 15, 1982 Accepted May 11, 1982
Grateful thanks are due to the Science Research Council for the financial support of one of the authors, A. G. C. Lane.
High-pressure Vapor-Liquid Equilibria in Asymmetric Mixtures Using New Mixing Rules Macle1 Radosr,' Ho-Mu Lin, and Kwang-Chu Chao' School of Chemical Englneering, Purdue Unlverslv, West Lafayetfe, Indiana 47907
Improved representation of vapor-liquid equilibria is obtained for asymmetric mixtures up to high pressures by = for the equation of state of Soave. The using new mixing rules, b = and improvement over previous results is particularly significant for highly asymmetric mixtures of hydrogen and a heavy hydrocarbon. Excellent agreement is obtained for methane mixtures and carbon dioxide mixtures. A correlation is developed for the energy interaction constant of hydrogen with heavy hydrocarbons.
xxx@,
Introduction
High-pressure vapor-liquid equilibria in asymmetric mixtures of a light gas (such as hydrogen, methane, carbon dioxide) and heavy hydrocarbons are important in engineering process design. Two aspects of the phase equilibrium phenomenon are of major interest: solubility of light gases in the liquid and volatility of the heavy solvents. Solubility of light gas in the liquid can be viewed as a liquid solution phenomenon, and correlations have been developed for hydrogen (Sebastian et al., 1981a), methane (Sebastian et al., 1981b), and carbon dioxide (Sebastian et al., 19814 based on the use of solubility parameter. An alternate approach is by way of an equation of state to describe both gas solubility and heavy solvent volatility. Equations of state have been used for a wide variety of mixtures. However, for highly asymmetric mixtures, equation of state calculations have not been particularly successful. In this work, we investigate improved equation-of-state calculations with new mixing rules for asymmetric mixtures. The Soave E q u a t i o n of S t a t e In this work we introduce new mixing rules to the cubic equation of state of Soave (1972) 'Exxon Research and Engineering Co., P.O. Box 101, Florham Park, NJ 07932. 0196-4305/82/1121-0653$01.25/0
The symbols are explained in the Nomenclature section. Two parameters appear in eq 1: the cohesive energy parameter a and the covolume b. According to Soave a = a,a
(2)
The constant a, is determined by the critical state,while a varies with temperature. a, = 0.42147R2T,2/p,
(3)
and a = [l
+ m(l - T,1/')I2
(4)
with
+
m = 0.48 1 . 5 7 4 ~- 0 . 1 7 6 ~ ~ (5) The covolume b is also determined by the critical state b = 0.08664RTc/p, (6) The (Y function of eq 4 is fitted to the vapor pressure of normal fluids. In this way the boundary condition of vapor-liquid equilibria in the limit of a pure fluid is taken into account in the Soave equation. However, the data base of eq 5 was limited: paraffins were limited to n-decane and lighter, and non-paraffins were limited to @ 1982 American Chemical Society
654
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982
Table I. Vapor Pressure Data Source pressure range, atm
substance benzene toluene
0.07 -46 0.01-40'
m-xylene m-cresol
0.07-30 0.07-41
l-methylnaphthalene
0.06-35
diphenylmethane
0.04-29'
quinoline
0.3-30'
te tr a1i n
0.02-33
naphthalene
0.02-34
thianaphthene
0.15-11
source S t u l l ( l 9 4 7 ) ; Timmermans (1950) Boublik e t al. (1973); Krase and Goodman (1930); Simnick e t al. (1978a,b); Stull (1947); Timmermans (1950); Wilhoit e t al. (1971) Boublik e t al. (1973); Glaser and Ruland (1957); Simnick e t al. (1979a); S t u l l ( l 9 4 7 ) Biddiscombe and Martin (1958); Boublik e t al. (1973); Glaser and Ruland (1957); Nasir e t al. (1980); Simnick e t al. (1979a); S t u l l ( l 9 4 7 ) ; Zwolinski (1977) Camin and Rossini (1955); Glaser and Ruland (1957); Wieczorek and Kobayashi (1981); Wilson e t al. (1981); Yao e t al. (1977) Boublik e t al. (1973); Glaser and Ruland (1957); Simnick e t al. (1978a,b); Stull (1947); Wieczorek and Kobayashi (1980); Wilson e t al. (1981) Boublik e t al. (1973); Glaser and Ruland (1957); Kobayashi (1978); Sebastian e t al. (1978a); S t u l l ( l 9 4 7 ) ; Wilson e t al. (1981) Boublik e t al. (1973); Nasir e t al. (1980); Simnick e t al. (1977); S t u l l ( l 9 4 7 ) ; Wilson e t al. (1981) Boublik e t al. (1973); Kobayashi (1978); Stull (1947); Wilson e t al. (1981); Wilhoit e t al. (197 1) Wieczorek and Kobayashi (1980); Sebastian e t al. (1978b)
'
The data reported by Krase and Goodman over 40 atm were discarded. critical states were all excluded in the calculations.
Where i = j , we have aii = ai. Where i # j , we express aij in terms of Cij by aij = (1 - Cij)(aiaj)1/2. Equations 7 and 8 will be referred to as the van der Waals one fluid mixing rules. They are useful for mixtures of molecules of comparable size, but the result deteriorates for asymmetric mixtures. More general mixing rules were introduced by Smith (1971,1972) in extending the isotropic mixture conformal solution method. In terms of the parameters a and b the conformal solution mixing rules are
1.3, 0
12-
I1
-
B e s t Values f r o m Vapor P r e s s u r e Data
S o a v e . eq 5
-
/
I
,/'
Quino
' The data reported by Glaser and Ruland at
ne
09
a"b@= CCxixjaijab$ i l
07 015
02C
025
030
035
040
045
050
W
Figure 1. Extrapolation of Soave equation for heavy hydrocarbons.
ethylene, propylene, cyclopentane, and toluene. In order to apply the Soave equation to heavy hydrocarbons, we examine eq 5 with respect to its fitting of vapor pressure data of heavy hydrocarbons. Much of the data has become available only recently. Table I gives the substances, data sources, and the pressure ranges of the data used in this work. A value of m was determined for each substance for the best fit of its vapor pressure. Using the best value of m, the calculated vapor pressure shows an average absolute deviation of about 6% for all the substances studied. Figure 1 shows these best values of m as a function of w for a number of heavy substances. Equation 5 is the curve in this figure. Extrapolating into the range of the figure it gives a remarkably good fit of the data. Graboski and Daubert (1978) gave a refined fitting of m as a function of w. When plotted in Figure 1 their equation practically coincides with eq 5. The difference between their equation and eq 5 is insignificant. We conclude that the Soave equation can be extended to apply to the heavy hydrocarbons of this work. Mixing Rules Soave extended his equation of state to mixtures by using the mixing rules a =
ECxixjaij i l
b = Exibi 1
(7) (8)
(9)
The four exponents a,j3, y, and 6 can be determined empirically. This is an excessively large number of parameters. To simplify and to retain contact with the van der Waals one fluid model, we set a = 0 and y = 1 bb =
CCxlx1b,B 1 1
ab6 = CCx,xlallblj6 1 1
(11) (12)
A similar set of mixing rules was used by Leland and co-workers (1959,1968) for the characteristic energy and size parameters e and Q for molecules of appreciably different sizes. Recently, Lee et al. (1979) applied similar mixing rules in their equation of state. Values of 6 and 6 were searched for the best fitting of vapopliquid equilibrium data on a large number of binary mixtures of a light gas (hydrogen, methane, and carbon dioxide) and a hydrocarbon with the result P = 1 and 6 * -0.25. The optimum values are not precise. A band of values within about &20% of an average value fits almost equally well. The band of best values of 6 also slightly shifts from hydrogen mixtures, through methane mixtures, to carbon dioxide mixtures. But the three bands share a common value of -0.25. We therefore adopt the mixing rules
CCxlxlb,j 1 1
(13)
abdz5 = CCxlxlallbll-025
(14)
b=
1
1
PlFker et al. (1978) applied a similar set of rules to T, and V , in extending the Lee and Kessler equation (1975)
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982 655
Table 11. Comparison of Calculated K Values in Hydrogen-Containing Binary Mixtures
temp range, K
no. pressure of range, data atm points
best hi;
AAD in K H , % (I)" (11) (111)
AAD in K s , % (I) (11) (111)
carbon dioxide
220-290
10-370
40
0.010
6.1
6.1
6.5
2.0
2.1
1.2
methane
116-172
33-272
13
-0.053
8.3
9.8
8.7
3.4
5.9
2.7
propane n bu t ane n-hexane n-heptane
278-361 328-394 378-478 424-499
34-544 27-166 34-680 24-774
34 60 40 27
0.016 0.024 0.191 0.190
3.5 3.3 3.8 2.8
4.0 3.2 3.9 4.5
6.9 5.3 9.4 7.9
1.8 2.6 3.1 3.6
1.8 2.7 3.2 4.3
3.8 3.4 4.9 8.0
n-octane
463-543
10-148
50
0.381
4.7
4.7
7.1
3.8
3.9
3.3
n-decane n-hexadecane benzene toluene m -xylene m-cresol te tralin quinoline 1-methylnaphthalene bicyclohexyl thianaphthene diphenylmethane
462-584 462-664 433-533 462-575 462-582 462-662 463-662 462-702 462-730 462-702 461-702 463-702
19-252 19-250 21-152 20-250 20-251 20-250 20-250 20-250 20-250 20-250 20-250 20-250
26 29 49 24 27 41 24 27 36 28 24 27
0.521 1.076 0.148 0.230 0.303 0.195 0.500 0.463 0.492 0.558 0.442 0.456
5.7 7.1 3.6 4.2 3.5 4.7 4.1 3.3 4.1 6.4 4.3 2.9
7.0 7.1 4.2 4.3 3.5 4.8 4.0 3.6 5.0 6.6 4.5 3.3
5.7 8.0 6.3 7.3 8.2 8.8 11.4 8.1 9.6 9.7 9.9 9.1
7.9 8.0 3.1 4.2 2.8 5.8 6.3 4.7 7.1 5.0 4.0 5.6
8.6 8.0 3.7 4.2 2.8 5.8 6.4 4.8 7.6 4.9 3.9 5.8
6.4 9.4 3.2 6.4 6.1 3.3 8.1 4.7 4.6 5.2 7.0 8.3
4.5
4.9
8.1
4.5
4.8
5.3
solvent
-
grand average
data source Spanoet al. (1968); Yorizane et al. (1970) Benham and Katz (1957) Burisset al. (1953) Klink e t al. (1975) Nicholset al. (1957) Peter and Reinhartz (1960) Connoly and Kandalic (1963) Sebastian et al. (1980d) Lin e t ai. (19801 Connoly ('1962 j Simnick et al. (1978b) Simnick e t al. (1979a) Simnick e t al. (1979a) Simnick et al. (1977) Sebastian e t al. (1978a) Yao e t al. (1977) Sebastian et al. ( 1 9 7 8 ~ ) Sebastian e t al. (1978b) Simnick et al. (1978a)
" See text for definition of calculations I, 11, and 111. to mixtures, but their exponent had a different value. The unlike pair parameters (i # j ) in eq 13 and 14 were determined as follows
where kij is a constant characteristic of i and j and independent of the state variables. An optimum value of kij was determined for each binary system at the same time as j3 and 6 were calculated. For the optimum seeking, we define the objective function 02t
"0
02
04
OG
08
10
12
k,, (eq 22)
Figure 2. Comparison of correlated k, with best values.
where the summation is carried out for all the data points and for both components of a binary mixture. The K value is calculated by
and the fugacity coefficient is given by RTln4i = RTln
-+ -+
RT p(V-b)
RTb[ V-b
ab/ b ( v b) (19)
Correlation of kijand Results The best values of kij for the hydrogen-containing binaries are presented in Table 11. They are all in the range 0-0.6 with kij of hydrogen + methane (-0.05) and of hydrogen + n-hexadecane (1.076) being the only exceptions. The best values are correlated with the acentric factor w and the Soave equation constant a, of the non-hydrogen components as follows kij
= -0.9504
+ 0.63414 - 0.0901A2 + 0.00446A3+ (0.8783 - 2.6369w)/A
+
(for A L 1) (22)
and with
kij = 0
(for A
< 1)
(23)
A is a scaled value of a, A = lo-' a, atm (cm3/g-moU2
and b[
2CXkbik - b k
(21)
(24)
We have found A 2 1 and kij > 0 for all C4+ hydrocarbons. Figure 2 shows the reasonable agreement between the correlated kij of eq 22 with the best values.
656
Ind. Eng. Chem. Process Des. Dev., Vol. 21, No. 4, 1982
Table 111. Comparison of Calculated K Values ofMethane Mixtures with Data ~
no. of data points
temp range, K
pressure range, atm
ethane
56 33 33 36
138-183 230-270 173-219 158-283
7-49 15-84 24-62 2-68
best k ii 0.033 0.110 0.086 -0,012
propane n-bu tane isobu tane n-pentane isopen tane neopentane n-hexane n-decane n-hexadecane cyclohexane benzene toluene m-xylene m -cresol tetralin quinoline 1-methylnaphthalene diphenylmethane
40 43 41 33 21 18 16 28 24 54 18 25 22 25 24 28 18 25
217-361 294-394 311-378 311-444 344-41 1 344-411 311-412 4 2 3-58 3 462-704 294-444 421-501 422-543 461-582 462-663 462-665 463-703 464-704 462-703
7-99 4-122 5-1 14 1-153 34-149 21-119 3-17 30-184 20-249 13-278 19-239 20-249 20-199 20-250 20-250 20-250 20-248 20-250
0.010 0.002 0.002 -0.021 -0.032 -0.004 0.011 -0.032 0.052 -0.038 -0.025 -0.007 -0.025 0.011 0.054 0.055 0.053 -0.015
solvent nitrogen carbon dioxide
grand average
AAD, % KM
KS
0.7 1.9 5.1 2.7
2.6 2.4 1.4 6.1
3.1 4.2 2.6 3.6 2.5 3.3 1.6 4.0 8.0 3.7 4.1 6.2 4.5 3.7 4.8 5.2 4.2 5.5
1.1 3.0 2.4 5.8 4.5 3.1 2.7 4.5 6.4 5.8 7.2 6.5 5.5 3.5 6.0 7.4 9.3 7.4
3.8
4.8
data source Stryjek e t al. (1974) Davalos e t al. (1976) Mraw e t al. (1978) Price and Kobayashi (1959); Wichterle and Kobayashi (1972) Reamer e t al. (1950) Sage e t al. (1940) Olds e t al. (1942) Sage e t al. (1942) Prodany and Williams (197 1) Prodany and Williams (1971) Gunn et al. (1974) Lin e t al. (1979) Lin et al. (1980) Reamer e t al. (1958) Lin e t al. (1979) Lin e t al. (1979) Simnick et al. (1979b) Simnick e t al. (1979b) Sebastian e t al. (1979) Simnick e t al. ( 1 9 7 9 ~ ) Sebastian e t al. (1979) Sebastian et al. (1979)
Table IV. Comparison of Calculated K Values of Carbon Dioxide Mixtures with Data
solvent
no. of data points
temp range,
K
pressure range, atm
best Kii
233-273 273-343 250 222-289 244-266 311-411 311-394 278-378 311-477 463-584 463-664 473-533 311-477 393-543 462-583 462-665 462-665 462-703 463-704 463-704
43-130 20-80 14-24 7-56 6-26 7-7 5 7-7 1 2-9 1 2-131 19-50 20-50 20-100 3-147 10-51 20-52 19-51 20-51 20-50 21-51 19-50
0.124 0.142 0.131 0.142 0.144 0.146 0.155 0.130 0.132 0.221 0.025 0.122 0.093 0.100 0.071 0.154 0.092 0.140 0.105
AAD, %
KCD
KS
data source
1.6 5.0 1.0 4.2 1.6 2.4 2.3 4.1 6.4 1.8 3.0 2.8 4.1 2.2 2.4 3.8 2.9 2.6 3.6 4.1
3.0 2.3 1.0 5.0 2.3 1.5 2.0 7.2 8.2 1.7 6.7 2.2 8.5 4.4 2.2 2.6 1.6 4.1 6.8 7.4
Kaminishi e t al. (1968) Bierlein and Kay (1953) Davalos et al. (1976) Hamam and Lu (1974) Hamam and Lu (1976) Olds e t al. (1949) Besserer and Robinson (1973a) Besserer and Robinson (1973b) Kalra e t al. (1978) Sebastian e t al. (1980e) Sebastian e t al. (1980e) Krichevskii (1960) Ng and Robinson (1978) Sebastian e t al. (1980f) Sebastian et al. (1980f) Sebastian e t al. (1980a) Sebastian e t al. ( 1 9 8 0 ~ ) Sebastian e t al. (1980a) Sebastian e t al. (1980b) Sebastian e t a]. (1980b)
3.1
4.0
~~
argon hydrogen sulfide ethane propane n-butane isobu tane n -pentane n -heptane n-decane n-hexadecane cyclohexane methylcyclohexane toluene m-xylene m-cresol tetralin quinoline 1-methylnaphthalene diphenylmethane
15 32 13 37 20 34 29 48 34 16 16 31 31 21 16 14 15 15 15 16
grand average
A considerable improvement in the calculated K values is obtained for the hydrogen-containingmixtures using the new mixing rules either with the individual optimum kij values or with kij of eq 22 and 23. Table I1 presents the comparison in terms of the absolute average deviations (AAD)in K values. Three calculations are compared: (I) the new mixing rules of eq 13 and 14 with the best kij for each system; (11) the new mixing rules of eq 13 and 14 with correlated kij of eq 22 and 23; (111) van der Waals one fluid mixing rules of eq 7 and 8 with the best Cij for each system. Case I1 represents the new correlation of this work, and in Table I1 it shows an AAD of 4.9% for KH and 4.8% for Ks. These results are about the same as case I using the best k , for each system. On the other hand, the van der Waals one fluid model of case I11 shows an AAD of 8.1% for KH and 5.3% for K,, which are distinctly less satisfactory. It is also noteworthy that the result of the new correlation is independent of the types of hydrocarbon,
0.088
while the van der Waals model tends to become worse for the heavier hydrocarbons. Detailed comparisons of the new correlation and van der Waals one fluid model are illustrated in Figures 3 and 4 for the K values of hydrogen and tetralin, respectively, in mixtures of hydrogen + tetralin. The new ccmelation represents the experimental data significantly better. The best kij values for methane binaries are presented in Table III. Also shown are comparisons of the calculated K values with experimental data. Generally good agreement is obtained. The best kij values for carbon dioxide binaries are presented in Table IV. The calculated K values generally agree very well with experimental data. Using the new combining rules, the calculated K values have been found to be insensitive to the kij values for the asymmetric mixtures. For example, altering the kij of methane + n-decane by 0.01 from its best value produces
Ind. Eng. Chem. Process Des. Dev., Vol.
21,
No. 4,
1982
657
Table V. Physical Properties of the Heavier Solvents
100-
80-
-
60
m-cresol tetralin
40-
quinoline
1-methylnaphthalene
bicyclohexyl
20-
thianaphthene diphenylmethane
I
705.9 716.5 782.0 772.0 731.4 755.9 767.0
45.0 33.1 40.5 35.2 25.8 41.3 29.4
0.450 0.316 0.295 0.302 0.388 0.293 0.481
y 10-
Nomenclature
8-
64-
- New C o r r e l a t i o n _ _ van d e r Waals Model
2-
o
10
Data f r o m S i m n i c k e t a l . ( l 9 7 7 )
20
40
60 80 1 0 0 P, atm
200
400
Figure 3. Comparison of calculated and experimental KH in hydrogen + tetralin mixtures. 1.0: 75-
Greek Symbols (Y = temperature dependent factor in eq 2 a = exponent in eq 9 0 = exponent in eq 9 y = exponent in eq 10 6 = exponent in eq 10 4 = fugacity coefficient = f/l(py) w = acentric factor il = objective function, eq 17
3-
10’: 75!-
Y
3-
10“: 75-
-
3-
-
-
__ 0
New Correlation van der W a a l s Model Data f r o m S l m n i c k e t aI (1977)
- 3 16
10
a = parameter in Soave equation a, = value of a at the critical temperature A = 10-’a,, (atm) ( ~ m ~ / g - m o l ) ~ b = parameter in Soave equation Cij = binary interaction constant for a in van der Waals one fluid model f = fugacity k . . = binary interaction constant in eq 16 I? = vaporization equilibrium ratio = y f x p = pressure R = universal gas constant T = absolute temperature T,= reduced temperature Tf T, V = volume x = mole fraction in liquid solution y = mole fraction in vapor mixture
30 50
100
300 500
P I atm
Figure 4. Comparison of calculated and experimental KT in hydrogen + tetralin mixtures.
a change in AAD of the K values by only 0.1% for the worse. Most of the kii values of methane binaries are quite small and close to zero. They can be set to be equal to zero for moat solvents without making any substantial difference. The best kij values of carbon dioxide binaries are about 0.14 for n-paraffins and 0.03 to 0.22 for other solvents. They can be set to be equal to 0.1 without making any substantial difference for most solvents. For the record, we include in Table V the physical property values that were used in our calculations for those components for which we found diverse values from different sources. For these substances we estimated values of critical temperature and pressure from Lydersen’s method (Reid et al. 1977, p 12); we calculated acentric factors from experimental vapor pressures interpolated to the reduced temperature T,= 0.7. For hydrogen we used T,= 33.19K, p , = 13.15 bar, and w = -0.22.
Subscripts c = critical state property CD = carbon dioxide H = hydrogen i = a component j = a component k = a component L = liquid M = methane S = solvent T = tetralin V = vapor Superscripts = per mole exptl = experimental calcd = calculated
-
Literature Cited Benham. A. L.; Katz, D. L. A I C M J . 1957. 3, 33. Besserer, G.J.; Roblnson, D. B. Can. J . Chem. Eng. 1973b, 18, 410. Besserer, G. J.; Roblnson, D. B. J . Chem. Eng. mte 1973a, 18, 298. Blddlscombe, D. P.; Mertln, J. F. TrenS. f8f8dJ’ SOC. 1958. 5 4 , 1310. Blerleln, J. A.; Kay, W. 8. I d . Eng. Chem. 1959. 45, 018. Boublik. T.; Fried, V.; Hala, E. “The Vapor Pressures of Pure Substances”; Elsevier: Amsterdam, 1973. Bwlss, W. L.; b u , N. T.; Reamer, H. H.; Sage, B. H. Ind. Eng. Chem. 1953, 45,210. Camln, D. L.; Rossinl, F. D., J . phvs. (2”. 1955, 59. 1173. Connoly, J. F. J . Chem. phva. 1982. 36,2897. Connoly, J. F.; Kandallc, G. A. Chem. Eng. Rog. Symp. Ser. l96S, 44,0. Davalos, J.; Anderson, W. R.; Phelps. R. E.; KMnay. A. J. J . Chem. Eng.
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Received for reuiew July 16, 1981 Accepted April 26, 1982
Funds for this research were provided by the Electric Power Research Institute through Grant RP-367.
Effect of Bulk Flow Due to Volume Change in the Gas Phase on Gas-Solid Reactions: Initially Porous Solids H. Y. Sohn” and Osvaldo A. Bascur Department of Metallurgy and Metallurgical Engineering, University of Utah, Sa# Lake City#Utah 84 7 12
The effect of bulk flow due to volume change in the gas phase on the rate of noncatalytic gas-soli reactions in porous sollds has been studied for systems in which diffusion is in the molecular regime. The model has been formulated in general terms so as to allow the incorporation of specific details of an actual system. The computed results show that the effect of bulk flow can be quite large. This effect increases with the importance of pore diffusion through the product layer in determining the overall rate of reaction. The law of additive reaction times previously proposed for reactions without volume change has been applied and found to yield a useful approximate solution also for this type of reaction systems. As a result, an approximate analytical equation for the conversion vs. time relationship incorporating chemical reaction, product layer diffusion, and external mass transfer has been obtained.
Introduction Because of the important role played by heterogeneous noncatalytic gas-solid reactions in many chemical and metallurgical processes, much research has been devoted to the subject. Recent advances due to the development 0198-4305/82/1121-0658$01.25/0
of more sophisticated mathematical models and experimental techniques have contributed to our understanding of reaction mechanisms and reactor design problems. The reader is referred to a recent monograph (Szekely et al., 1976) and review articles (Sohn, 1976a,b, 1978,1979) for 0
1982 American Chemical Society
