diffusion: its onset a t fixed temperature, the drop in the slope of the constant T line, and ratio of slopes. For nth-order reaction a treatment similar to that for first-order reactions but using the nth-order rate and the generalized Thiele modulus (see Bischoff, 1967) gives for the onset of strong pore diffusion (13)
We can also show that the dividing line between regimes has a positive slope for n > 1,and negative slope for n < 1.Note that Figure 9 gives a vertical line for this transition for R = 1. In operating under strong pore diffusion the shallower T curve will give a much smaller region of instability where a temperature runaway is possible. Its size and location are found by the procedure described earlier and illustrated in Figure 9.
sponding stable points, and for finding the envelope of operating conditions which must be avoided in design. Extension to strong pore diffusion kinetics is direct. Finally, simple analytical expressions are developed for identifying unstable operating points when a rate equation for the reaction is available. Note that the treatment in this paper is limited to steadystate operations.
Nomenclature CAO= concentration of reactant in feed, mol/m3 C P =~ specific heat of the fluid per mole of entering reactant A, cal/mol K ZI = effective diffusion coefficient in a porous structure, m2/s
E = activation energy, cal/mol Eobs = observed activation energy, cal/mol -AHr = heat of reaction per mole of reactant A, cal/mol k l , k z = first-order reaction rate constant, s-1 kobs
= observed reaction rate constant
R = ideal gas law constant, cal/mol K = rate of reaction based on unit mass of catalyst, molkg of catalyst s T = temperature, K X A = fraction of reactant A converted into product T = weight time, kg of cat s/m3 feed -rA
Conclusion In adiabatic packed bed reactors we encounter two types of temperature excursions: the hot spot and the temperature runaway. The hot spot is characteristic of reactors having no recycle of fluid. I t is caused by fluid stagnancy and is localized, usually near flow obstructions. Since the adiabatic line on the conversion vs. temperature diagram is steep for operations with no fluid recycle, the temperature rise for hot spots may not be too serious, and it can be estimated directly from the conversion vs. temperature diagram. The temperature runaway results from trying to operate a reactor with large recycle at an unstable point. We show that the conversion vs. temperature chart is a convenient tool for identifying these unstable points, for finding the corre-
Literature Cited Bischoff, K. B., Chem. Eng. Sci., 22, 525 (1967). Jaffe, S.B., lnd. Eng. Chem., Process. Des. Dev., 15, 410 (1976). Konoki, K., Chem. Eng. (Jpn.),21, 408. 780 (1956). Konoki, K., Chem. Eng. (Jpn.),24, 569 (1960). Konoki, K., Chem. Eng. (Jpn.),25, 31 (1961). Levenspiel, 0.. "Chemical Reaction Engineering," 2nd ed, Chapters 8 and 14, Wiley. New York, N.Y., 1972. van Heerden, C., lnd. Eng. Chem., 45, 1242 (1953). Weisz, P. B., Prater, C. D., Adv. Catal., 6 , 143 (1954).
Received for reuieu: J u n e 1, 1976 Accepted September 15,1976
Thermodynamics of the Reaction between Sulfur Dioxide and Methane John J. Helstrom and Glenn A. Atwood' The Department of Chemical Engineering, The University of Akron, Arkon, Ohio 44325
The equilibrium composition of the reaction products for the reaction of methane and sulfur dioxide in an inert diluent are presented in this work. The compositions were calculated using data available in the literature for a total system pressure of 1 atm, reaction temperatures between 400 and 1000 K, methane to sulfur dioxide ratios from 0.1 to 2.0, sulfur dioxide concentrations of 0.003 and 0.1 atm, and various initial concentrations of H 2 0and COP.The calculations show that the equilibrium yield of elemental sulfur is maximized at methane to sulfur dioxide ratio of 2. Below 800 K, lowering the temperature increases the yield of elemental sulfur and above 800 K increasing the temperature increases the sulfur. This work is unique in that all of the likely reaction products were included as well as the seven sulfur species which are known to exist in the vapor state.
Since the 1930's there has been an interest in the reactions of methane with sulfur or sulfur dioxide to produce hydrogen sulfide, carbon disulfide, or sulfur. Work on the last reaction has increased greatly during the past decade because of its possible utility in controlling air pollution caused by the sulfur dioxide emitted from fossil fuel power plants and ore smelting operations. However, the equilibrium compositions 148
Ind. Eng. Chem., ProcessDes. Dev., Vol. 16, No. 1, 1977
for the reduction of sulfur dioxide with methane have been calculated for only a limited number of reactant compositions and temperatures. Lepsoe (1937) presented equilibrium compositions for the reaction of hydrogen with sulfur dioxide and calculated the equilibrium constant for the reaction CH4 2,902 COS Sp HzO. Thacker and Miller (1944) provided equilibria for methane, sulfur, and CS2 but they neither
+
-
+ +
Table I. Reactions for Reduction of Sulfur Dioxide with Methane
Table 11. Sulfur Equilibrium Constants as a Function of Temperaturen K1 = exp[(166.379- 2.0 X 10-4T - 101,190.O/T 72,000.0/T2- 7.66 ln T ) / R ]
+
Kr
=
exp[(56.708- 6.667 X 10-5T - 28,281.0/T + 24,000.0/TL- 2.553 In T ) / R ]
K I = exp[(55.749- 6.667 X 10-5T - 29,874.0lT + 24,000.0/T2- 2.553 In T ) / R ] Kq = exp[(168.388 - 2.0 X 10-4T - 100,348.0/T + 72,000.0/T2- 7 66 In T ) / R ] K5 = exp[(12.26- 1.667 X 10-5T - 6615.0/T 6000.0/TL- 0.6383 In T ) / R ]
+
Ks = exp[(9.53- 8.333 X l O ? T - 5947.0/T + 3000.0/T2- 0.3192 In T ) / R ] 'The temperature, T , is in Kelvin. R is the gas constant; R = 1.9869 cal/('C mol).
stated the system pressure nor considered side reactions. Walker (1946) listed tabular data and graphs of equilibrium compositions a t 1000 K for CH4 and SO2 a t 1atm, and several ratios of SO2 to CH4 were considered. Averbukh et al. (1970) considered the pressures 0.15,0.3,0.6, and 1.0 atm and S 0 2 / CH4 ratios of 1.0,1.33,2.0, and 2.5 between 1000 and 1500 K. Vilesov and Gorbatykh (1966) provided data for the range 900 to 1600 K. The present work develops the equilibrium compositions for the methane -sulfur dioxide system between 400 and 1000 K for a S02/CH4ratio of 2.0 a t SO2 partial pressures of 0.093 and 0.1 atin along with the effect of water and carbon dioxide on the equilibrium composition. The initial SO:,/CH4 ratio is varied from 0.1 to 2.0 a t 600 K for both SO:, partial pressures and a t 700 K for SO:, a t 0.1 atm. Equilibrium Calculations The initial system that was considered contained the chemical species Sp, Ss,S4,Ss,Se,S?, Sa,SO*, H2S, COS, SQj, CHd, CO, C02, H2, 0 2 , CS2, and HzO. The concentration of these chemical species can be defined by 18 linearly independent equations which include the four atomic mass balances. The other 14 equations are the equilibrium expressions for any arbitrarily chosen set of independent chemical reactions involving the chemical species being considered. The set used in this work is listed in Table I. Reactions R1 through R6 give the equilibria of the sulfur species which will be present. Reactions R13 and R14 allow the calculation of the equilibrium concentrations of SO3 and 0 2 . The equilibrium constants for all the reactions except those involving the sulfur species S:,-Ss, as defined by R1 through R6, were calculated from the data given in the tables of thermodynamic properties tabulated by Pitzer and Brewer (1961). The sulfur equilibrium constants were found from the enthalpy and entropy data of Detry e t al. (1967),along with estimated heat capacities obtained by interpolating on a molecular weight basis between the values for S:!and SSprovided by Kelley (1964). The resulting equations are listed in Table 11. The vapor pressure for sulfur was taken from the "International Critical Tables" (1926). For gaseous reactions, two possible limiting cases are constant volume and constant pressure. Additionally, if one or more of the chemical species condenses, this must be accounted for in the mass balances. The system was solved for
constant pressure by assuming ideal gas behavior and writing each atom mass balance as ALP, = ( V/Vo)A,PL where P, and PI are the partial pressures of the i t h reactant and product. ( V / V Ois) the ratio of the final to initial volumes. The standard gas equilibrium expressions, K = xPsproducts/"Psreactants were included directly. This approach introduces additional unknowns ( V / V Oand ) Plnert. The additional equations required to define the system are a pressure summation, Ptc,tal = ZP,, and an inert balance of the form above. In the present study, sulfur was found to condense a t the lower temperatures; Le., the sum of the calculated sulfur partial pressures exceeded the vapor pressure of sulfur. In this Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 1, 1977
149
Table IV. Equilibrium Reaction Products vs. Initial Methane Concentrationajbat 1 Atm and 600 K Initial Composition 0.1 0.0501 0.055 Product Composition 0.01085 0.09141 0.09994 0.09987 0.0 9998 0.2262 0.2917 0.2200 0.2200 0.2200 0.2154 0.1746 0.1700 0.1701 0.1700 0.5080 x 0.6541 X 10-1 0.5742 x 0.2073 X 0.5334 X 0.3326 x 10-l5 0.1061 X lo-" 0.4688 X 0.1199 x 10-19 0.1303 x 0.4472 X 0.1324 X 0.5501 X 0.4348 X 0.7579 X lo-"' 0.1955 X 0.1222 x 10-25 0.1353 X 0.1095 X IO-*' 0.3707 X 1.021 1.0026 1.0000 1.0001 1.0000 All concentrations are expressed in atmospheres. The composition of the initial mixture was SO2 = 0.1 atm, HzO = 0.12 atm, atm, 0 2 = 0.1 atm. The sulfur species have been combined and expressed as the partial pressure CO2 = 0.12 atm, SO2 = 6.0 X of monatomic sulfur. 0.05002
0.05006
w
a
-1
,091
I UNREACTED S G r WATER HYDROGEN SULFIDE 45 SULFUR Cb.RRION ADIOXIDE/+ S S
?
0 5 9 400.
600. 800. TEMPERATURE DEG. K
1000.
Figure 1. Equilibrium composition of the major components for the CHd-SOz system between 400 and 1000 K. The initial gas composition was 0.1 atm of Son, 0.05 atm of CH4, and 0.85 atm of inert.
L
1
;%FOGEN
SULFIDE SULFUR AS S I DIOXIDE
400.
600.
800.
1000.
TEMPERATURE DEG. K
Figure 2. Equilibrium composition of the major components for the CH4-S02 system between 400 and 1000 K. The initial gas composition was 0.003 atm of Sop, 0.0015 atm of CH4, and 0.9955 atm of inert.
case, the sulfur partial pressures were set equal to the saturated equilibrium value. The reactions R1 through R6 were dropped from the set and the amount of sulfur condensing was added to the sulfur atom balance. The set of equations was solved by the Newton-Raphson method. The atom mass balances and equilibrium expressions were written as
where the desired values of the Fi's are zero. This set of equations is shown in Table I11 neglecting R13 and R14. This procedure is very similar to one described by Caranahan et al. (1969). A solution was accepted when the residuals of the 150
Ind. Eng. Chern., Process Des. Dev., Vol. 16, No. 1, 1977
"E
21 9 .o
.04
08
m
20
INinnAL WATER ATM
Figure 3. Effect of water on the reduction of SO1 in the CHd-SO2 system at 600 K and 1atm. The initial gas compositionwas 0.003 atm of Sot, 0.0014 atm of CH4, 0.02 to 0.06 atm of Hz0, and 0.9755 to 0.9355 atm of inert.
equations, the Fi's were of the same order of magnitude as the expected roundoff error. After it was determined that essentially all of the oxygen would be consumed before reduction of SO2 would take place a t 600 K in the presence of oxygen and that the equilibrium partial pressure of SO3 was very small, eq R13 and R14 were eliminated from the set which significantly reduced the time required for convergence. Discussion Table IV lists the calculated equilibrium compositions obtained for S02/CH4 ratios from 2/1 to 1/1 with oxygen present equal to the initial SO2 concentration. These data show that as the CH4 concentration is reduced from 0.1 atm toward the stochiometric amount needed for reaction with the oxygen, i.e., reactant CH4 equals 0.05 atm, the calculated sulfur partial pressure (expressed as monatomic sulfur) is lowered and approaches zero at the stochiometric ratio. At the same time, the SO2 concentration approaches its initial value, and extrapolation shows that essentially no reduction will take place a t an initial CH4 concentration of 0.05 atm. This result is predictable when the equilibrium constants of reactions R7 and R13 are compared. A t 600 K, K = 1.81 X 1014for reaction for reaction R13. Table IV also shows R7 and K = 3.68 X that the equilibrium amount of SO3 is very small in the absence of free oxygen. Over the temperature range studied, 400 to 1000 K, the equilibrium composition of elemental sulfur reached a minimum a t about 800 O F , when the initial ratio of S02/CH4 was 2.0. The composition increased slowly with increasing temperature above 800 O F and below 800 O F the composition increased with decreasing temperature. Figures 1 and 2 show the equilibrium composition of the major components in the reaction product as a function of temperature. I t is noted that
Table V. Effect of Carbon Dioxide on the Equilibrium Composition of t h e Methane-Sulfur Dioxide System a t 600 K and 1 Atma Initial Compositiond 0.12 0.18 0.24 Product Compositiond CH4 0.752 x 10-l6 0.116 X 0.157 x 10-l5 0.198 X so:! 0.506 x 0.506 X l o w 2 0.506 x 10V 0.506 x HzO 0.882 X 10-1 0.882 x 10-l 0.882 x lo-' 0.882 X 10-1 COzb 0.108 0.167 0.226 0.285 H2S 0.101 x 10-1 0.101 x 10-1 0.101 x 10-1 0.101 x 10-1 cs2 0.100 x 10-8 0.155 X loW8 0.209 x 0.264 X H2 0.296 X 0.296 X 10-5 0.296 x 0.296 X cos 0.141 X 0.218 X 0.295 X 0.371 X co 0.130 x 0.201 x 10-6 0.271 X 0.342 x S' 0.831 x 10-l 0.831 X lo-' 0.831 x 10-l 0.831 X lo-' VIVO 1.0€77 1.0177 1.0177 1.0177 The initial composition of reacting mixture was 0.1 atm S02,0.05 atm CH2,0.06 to 0.24 atm Cos, 0.79 to 0.61 atm inert. Total COSin product. Total sulfur expressed as partial pressure of monoatomic sulfur. All compositions are given in atmospheres.
con
0.06
Table VI. The Effect of Carbon Dioxide on the Equilibrium Composition of the Methane Sulfur Dioxide System a t 600 K and 1 Atm" Initial Compositiond 0.12 0.18 0.24 Product Compositiond CH4 0.380 X 0.725 X 0.105 x 10-l6 0.135 X SO2 0.272 X 0.277 X 0.282 X 0.287 X H20 0.247 x 0.247 X 0.248 x 0.248 X lo-* C02h 0.614 x 10-l 0.121 0.181 0.241 H2S 0.529 X 0.525 X 0.520 X 0.516 X cs2 0.200 x 10-8 0.386 X 0.565 x 0.737 x H2 0.271 x 0.269 x 0.267 x 10W6 0.265 X cos 0.150 X 0.293 X 0.434 X 0.571 X co 0.241 X 0.471 X 0.697 x 0.920 X S' 0.218 X 0.217 X 0.215 X 0.214 x VIV(' 1.001 1.001 1.001 1.001 Initial Composition 0.003 atm SOz, 0.0015 atm CH4,0.06 to 0.24 atm COS,0.9355 to 0.7555 inert. Total COz in products. Total sulfur expressed as partial pressure of monoatomic sulfur. All compositions are given in atmospheres. cos
0.06
a t low (400 K) temperatures the amount of sulfur in the product is very close t o the initial amount of sulfur in the feed. Figure 3 shows that water tends to inhibit the reduction of SO2 with methane, especially when the ratio of water to sulfur dioxide is large. This is consistent with the laws of mass action based on reaction 7. Therefore, based on equilibrium considerations, it would appear that the reduction of sulfur dioxide in stack gases with methane would not be favorable. The predicted reduction in the amount of sulfur produced in the presence of relatively large amounts of water is consistent with the reaction of water with elemental sulfur which was used in developing the kinetic model for reduction of sulfur dioxide with hydrogen (Hsieh and Atwood, 1976). The effect of carbon dioxide on the sulfur yield is small and selected data are given in Tables V and VI. The tables also show that as the C02 concentration is increased the equilibrium ratio of S/H2S remains essentially constant, the ratio of H2S/COS decreases from about 1000 to about 300, and the ratio of H2S/CO decreases from 0.8 X lo5 to 0.3 X lo5. The largest equilibrium conversion of SO2 t o sulfur occurs near the S02/CH4 ratio of 2.0 (i.e., the stoichiometric ratio) as is shown in the Figures 4, S-1,and S-2. For higher methane concentrations the amount of H2S formed increases rapidly until for a SOJCH4 ratio of 4/3 essentially only H2S is formed. Figures 5, S-3, and S-4 also indicate that the water formed reaches a maximum a t approximately the same methane concentration which gives the largest sulfur yield and then decreases. This is consistent with the reduction of sulfur
,
UNREACTED 501
Figure 4. Equilibrium composition SOz, HzS, CH4, and S for the CH4-SO2 system at 600 K and 1atm. The initial gas composition was 0.1 atm of SOz, 0.025 to 0.1 atm of CHI, and 0.875 to 0.80 atm of inert.
dioxide first to elemental sulfur and the further reaction to hydrogen sulfide. The overall reaction for conversion of the sulfur dioxide to hydrogen sulfide is 3/4CH4 SO2 H2S 3/4CO2 f/zHzO.In this reaction only one-half mole of H2O is formed per mole of SO2 feed. For the conversion of sulfur dioxide to elemental sulfur the overall reaction is R7 in which one mole of water is formed for each mole of SO2 reduced. Based on these equations, the maximum in the water production a t the stoichiometric ratio would be expected. From these figures it is obvious that if the maximum equilibrium
+
+
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Ind. Eng. Chern., Process Des. Dev., Vol. 16, No. 1, 1977
+
151
structed. In addition, the tables also contain the concentration of those species with very small concentrations which were not included on the graphs. 4
CbRBON MONOXIDE
Literature Cited
.o
.s
1.0
1.5
2 .o
MOLES CH4 PER MOLE SO0 REACTANT
Figure 5. Equilibrium composition of H20, COz, H2, and CO for the CH4-SOz system at 600 K and 1atm. The initial gas composition was 0.1 atm of SO*, 0.025 to 0.1 atm of CH4, and 0.875 to 0.80 atm of
inert. yield of elemental sulfur is to be obtained, the ratio of sulfur dioxide to methane must be near 2. Figures S-1and S-2are very similar to Figure 4 and Figures S-3 and S-4 are similar to Figure 5. All four are included in the supplementary information. The supplementary information also includes Tables S-1 through S-4 which contain the data from which Figures 4, 5 , S-1, S-2, S-3, and S-4 were con-
Averbukh, T. D.. Radivilov. A. A.. Bakina, N. P.. Zh. Prikl. Khim. (Leningrad), 43, 35 (1970). Carnahan, B., Luther, H. A., Wilkes, J. O., "Applied Numerical Methods," p 321, Wiley, New York, N.Y., 1969. Detry, D., Drowart, J., Goldfinger, P.,Keller, H.. Rickert, H., Z.fhys. Chem. (FrankfurlamMain), 55, 314 (1967). Hsieh, Y. D., Atwood, G. A,, ind. Eng. Chem., Process Des. Dev., 15, 358 (1976). Kelley, K. K.. U.S. Bur. Mines Bull. No. 584, (1964). Lepsoe, R., ind. Eng. Chem.. 30, 92 (1937). Lewis, G. N., Randall, M., revised by Pitzer, K. S., and Brewer, L., "Thermodynamics," 2d ed, McGraw-Hill, New York, N.Y., 1961. Thacker, C. M., Miller, E., ind. Eng. Chem., 36, 182 (1944). Vilesov, N. G., Gorbatykl, G. A,, Khim. Prom., 42, 187 (1966). Walker, S. W., Ind. Eng. Chem., 38, 906 (1946). Washburn, W. E., Ed., "International Critical Tables of Numerical Data, Physics, Chemistry and Technology," Vol. 1, p 53, McGraw-Hill, New York, N.Y. 1926.
Receiued for reuiecu June 14, 1976 Accepted September 27,1976 Supplementary Material Available. Seven tables and four figures of equilibrium composition data (12 pages). Ordering information
is given on any current masthead page.
COMMUNICATIONS
Effect of Catalyst Particle Size on Performance of a Trickle-Bed Reactor
This paper presents experimental data for the effect of catalyst particle size on the performance of a trickle bed reactor for hydrodesulfurization of 22% and 36% reduced Kuwait crudes. The results were correlated well by the effective catalyst wetting model of Mears (1974) but not by the holdup model of Henry and Gilbert (1973).
Introduction In a recent series of papers, Henry and Gilbert (1973), Mears (1974),Paraskos e t al. (1975),and Montagna and Shah (1975) analyzed holdup and effective wetting models for correlating data obtained in pilot scale hydroprocessing trickle bed reactors. Henry and Gilbert (1973) suggested that all the catalyst in a pilot scale trickle bed reactor is not effectively used. A pilot scale reactor, therefore, gives a poor performance when compared to a commercial reactor under equivalent reaction conditions. Henry and Gilbert (1973) attributed this to their low values of dynamic liquid holdup. Using the holdup correlation of Satterfield et al. (1969), they proposed that the performance of a trickle bed reactor which carries out a first-order reaction is given by In
cAi
a
( L )1/3( LHSV)-2/3( d ),
-2/3( u ) 113
CAo
(1)
Here C A and ~ C A are ~ the reactor inlet and outlet concentration of the reactant, L is the length of the catalyst bed, LHSV 152
Ind. Eng. Chem., Process Des. Dev., Vol. 16, No. 1 , 1977
is the liquid hourly space velocity, d, is the catalyst diameter, and u is the kinematic viscosity. Mears (1974) attributed the poor performance of the pilot scale reactor to incomplete catalyst wetting. Based on the wett6d packing area correlation of Puranik and the Vogelpohl (1974),he proposed an alternate relation for the reactor performance as
where u is the surface tension of liquid, uc is the critical value of the surface tension for the given packing, and 7 is the catalyst effectiveness factor. All other parameters in the above relation are the same as those in (1). For constant catalyst size and fluid properties, both relations 1 and 2 predict the same dependence of In ( C A ~ I C Aon J the catalyst bed length and the liquid hourly space velocity. Paraskos et al. (1975) and Montagna and Shah (1975) showed that for hydrodesulfurization and hydrocracking of various
