Ind. Eng. Chem. Fundam., Vol.
parameters in the model; L ( 0 ) is a likelihood function; T O is the probability distribution a priori; 00 is a vector of the parameter estimates a priori; COis a parameter covariance matrix a priori; u2 is the variance of the errors about the observed variable; and A* and E* are parameters determined with knowledge a priori.
Nomenclature A = preexponential constant, mol/min g a,b,b,,cu,@ = regression coefficients
C = ethylene adsorption constant E = apparent activation energy, cal/mol F0.g5 = F - distribution AH,' = standard enthalpy of adsorption of ethylene, cal/ mol h = kinetic constant, mol/min g PA,PE,PH = ethane, ethylene, and hydrogen partial pressures, atm R = gasconstant r , = measured reaction rate, mol/min g i s = computed reaction rate, mol/min g AS,' = standard entropy of adsorption of ethylene, cal/mol K s.d. = standard deviation S ' = gaseous ethylene standard entropy, cal/mol K s j = experimental variance estimate, (mol/min g)2 sr2 = residual variance estimate, (mollmin g)*
17, No. 1, 1978
17
t = Student statistic to test the partial correlation coefficients theoretical Student statistics at the 95% confidence level T = temperature, K
to.95 =
Literature Cited Boudart, M., Mears, D. E., Vannice, M. A,, lnd. Chim. Belge, 32 ( l ) , 281 (1967). Boudart, M., "Kinetics of Chemical Processes", Prentice-Hall, Englewocd Cliffs, N.J., 1968. Derouane, E. G., Pirard, J. P.. L'Homme, G. A,, Fabry-Volders,E., "Proceedings of the InternationalSymposium on the Relations between Heterogeneous and Homogeneous Catalytic Phenomena", Brussels, Belgium, Oct 23-25, 1974, Elsevier, Amsterdam, 1975. Froment, G. F., "Proceedings of the 7th European Symposium, Computer Application in Process Development", Erlangen, Apr 2-3, 1974. Himmelblau, D. M. "Process Analysis by Statistical Methods", Wiley, New York, N.Y., 1970. Kittrell, J. R., Erjavec, J., lnd. Eng. Chem. Process Des. Dev., 7, 322 (1968). Lapidus, L., Peterson, T. I., AlChEJ., 11 (5), 891 (1965). L'Homme, G. A., lnd. Chim. Belge, 35 (3), 179 (1970a). L'Homme, G. A,, Ind. Chim. Belge, 35 (4), 291 (1970b). Mears, D.E., Ind. Eng. Chem. Process Des. Dev., I O , 541 (1971). Mezaki, R . , Kittrell, J. R., Ind. Eng. Chem., 59 (5), 63 (1967). Scotting, D. J., Cowsiey, G. W., Mitchell, F. R. G., Kennery, C. N., Trans. lnst. Chem. Eng., 52 (4), 349 (1974). Wynkoop, R . , Wilhelm, R. H., Chem. Eng. Prog., 46, 300(1950).
R e c e i w d f o r reuieu' September 29,1975 Resubmitted M a r c h 28, 1977 Accepted September 26, 1977
Adsorption of Hydrogen Sulfide in a Slurry Reactor P. A. Ramachandran and J. M. Smith" Department of Chemical Engineering, University of California, Davis, California 956 16
Equilibrium and rate constants were evaluated for adsorption of H2S gas in an aqueous slurry of activated carbon particles at 25 OC.Analysis of moments of the measured response in the effluent gas stream to a step-function input of H2S was used to evaluate the constants. The adsorption rate was first order and reversible on the activated carbon for gas concentrations as large as 6 mol % H2S in helium. The capacity of carbon for H2S was rather high, corresponding to an adsorption equilibrium constant of 20.8 cm3/g. For the carbon-particle concentrations employed, mass-transfer resistance for bulk water-to-particle surface was negligible in comparison with intraparticle-diffusion resistance, for particles with a radius as low as 0.015 mm. Also, mass transfer of H2Sfrom gas bubble-to-bulk water, and adsorption at an interior site on the carbon particle, were both so rapid that neither process affected the overall adsorption rate. These results are consistent with expectations for a relatively soluble, and strongly adsorbed, substance. The conclusion are different for other adsorbates such as NO, and the relative importance of diffusional and surface adsorption processes are compared for H2S, NO, and SOP, using available data for adsorption in aqueous slurries of activated carbon. The effective intraparticle diffusivity evaluated from the experimental data indicated a tortuosity factor of 0.72. This low value suggests that surface diffusion may be a significant contribution to intraparticle mass transport of H2S in water-filled pores of activated carbon.
Introduction It has been found that slurry adsorbers and reactors may be used effectively for removal of such gaseous pollutants as NO (Niiyama and Smith, 1976) and SO2 (Komiyama and Smith, 1975). In these three-phase systems interphase mass transport rates, as well as kinetics of the adsorption step on the solid surface, affect overall performance. The relative importance of surface kinetics and mass transfer processes depends upon the chemical system (Le., the specific adsorbate, slurry liquid, and adsorbent surface) and on the slurry conditions, such as size and concentration of the adsorbent par0019-7874/78/1017-0017$01.00/0
ticles, gas flow rate, and agitation of the liquid. In the prior investigations of NO and SO*, aqueous slurries of activated carbon were used. One objective of the present study was to determine adsorption rates for H2S in aqueous slurries of the same activated carbon. With these results it is possible to compare the relative importance of surface kinetics and the several mass transport processes for adsorbents of different solubilities in water and different adsorption capacities on the carbon. Further, activated carbon catalyzes a t low temperatures the oxidation of H2S to elemental sulfur, the most desirable form of the element from an environmental point of
0 1978 Americaii Chemical Society
18
Ind. Eng. Chem. Fundam., Vol. 17, No. 1, 1978 Exit
4,
1 Flow Regulator 2. Flow Ylsr
m, =
Jm
tnCg dt
3 , 4 Nwdle Valves 5. Four-Way Valve 6. Pyrex Adsorter 1. Ice Trap 8. Manoneter 9. T C. Cell
and
The solution of the conservation equations gives the following theoretical expressions for the moments
H e d
1
'
6
1
U
Figure 1. Schematic diagram of apparatus.
view. Adsorption rate data would be useful in analyzing the overall rate of oxidation of H2S with air in slurries. Hence, a second objective was to provide quantitative data for rates of adsorption of H2S. Breakthrough curves for H2S were measured in the gas stream leaving the slurry. The technique of moment analysis of these curves was used to determine rate constants for the mass transfer and surface adsorption processes. From the same analysis it is possible to determine the adsorption equilibrium isotherm of H2S on the activated carbon and its solubility in water. All the data were determined a t 25 "C and 1 atm pressure. Theory As indicated in Figure 1, the H2S-He stream is introduced as discrete gas bubbles through a disperser located near the bottom of the vessel. The slurry is well agitated so that the concentrations of adsorbate (HzS) and adsorbent particles are assumed to be uniform throughout the liquid. Also, it is supposed that the gas bubbles travel upward in plug flow. For a gas of even moderate solubility, such as HPS, it makes no difference whether the bubble travel is in plug flow or the bubbles have a residence time distribution corresponding to complete mixing. As shown by Niiyama and Smith (1976),the residence time of the bubbles is unimportant for a gas of moderate solubility because equilibrium between bubble and liquid is reached shortly after the bubbles leave the disperser tube. That H2S fits this requirement is demonstrated later. The theoretical development is also based upon constant-size spherical bubbles and first-order reversible adsorption a t the interior adsorption sites of the activated carbon. The overall process is assumed to occur by the following sequential steps: mass transfer of H2S from gas bubble to bulk liquid with a rate constant k L a B , mass transfer from bulk liquid to outer surface of the carbon particles according to the rate constant k,a,, intraparticle diffusion with an effective diffusivity D e , and adsorption at an interior site with rate and equilibrium constants k & and K , respectively. For these conditions the differential mass conservation equations for the adsorbate in the gas bubbles, in the liquid, and in the pores of the adsorbent particles, have been derived and solved for a pulse input of the adsorbate gas by Niiyama and Smith (1976). The results can be conveniently expressed as theoretical equations for the moments of the response curve. Equations 1-3, which define first absolute and second central moments for a pulse input also indicate how numerical values of these moments can be evaluated from the response curve (C, vs. t ) measured a t the detector.
where (7) and H is Henry's law constant for the adsorbate in water. The procedure is to equate eq 5 and 6 to moments calculated from the measured response curves using eq 2 and 3 or eq 10 and 11. Before this can be done corrections must be considered for the retention time and dispersion in the volumes (dead volumes) between injection point and the entrance of the gas bubbles into the liquid, and between the liquid level in the slurry and the concentration detector. Such corrections can be important for a slurry adsorber because it is necessary to have a bubble-collecting space above the slurry liquid. If the retention time and dispersion effects in the dead volumes can be described by linear processes, the measured moments a t the detector (from eq 2 and 3) are related to p 1 , and 1 1 2 , ~(from ~ eq 5 and 6) by the additive relations
+ F1,d.v. F2,D = F2,Li + F2,d.v. F1,D
= F1,Ll
~ ~
(8) (9)
The values of P1,d.v. and F2,d.v. can be experimentally evaluated from breakthrough curves (BTC) for a nearly insoluble gas (such as N2) bubbling through water alone. Then F I , L and p2,1 are obtained from eq 8 and 9. Dynamic experiments with a step input of solute gas give more accurate moments than pulse experiments for slurries and such breakthrough curves (BTC) were measured in our work. The moments defined by eq 1-3 can be obtained from these BTC by the following relations
Experimental Section Figure 1 is a schematic diagram of the apparatus. The slurry adsorber was a cylindrical Pyrex vessel, about 13 cm high and 10 cm in diameter, equipped with an impeller and eight fixed baffles. The dimensions and geometry were the same as for the apparatus used by Furusawa and Smith (1973), who evaluated mass transfer coefficients, k,as, as a function of impeller speed. The gas stream (H2S and He for adsorption runs, He for purge or desorption runs, and Nz for dead-volume correction runs) was introduced through a fritted glass disk,
Ind. Eng. Chern. Fundam., Vol. 17, No. 1, 1978
19
Table I. Operating Conditions
A. Properties of Pittsburgh Activated Carbon (Type BPL) Surface area 1050-1150 m2/g Solid phase density, p t 2.1 g/cm3 Particle density, p p 0.85 g/cm3 Particle porosity, p 0.60 Average particle radius, 0.015,0.2., 0.425 mm 13 Mean intraparticle pore radius, 8, B. Volume of Slurry, Liquid plus Particles = 1100 cm3 m, = 0.023,0.0467, 0.0865 g/cm3 C. Concentrations in Inlet Gas (in He) 3 t o 6 mol % Has For equilibrium measurements For rate measurements 3 mol % H2S For dead volume 3 mol % N2 measurements D Other operating Conditions 3.33 to 10 cm3/s (at 25 OC and Gas flow rate, Q 1atm) Impeller speed 640 f 30 rpm Temperature 25i1°C Pressure 1 atm 1.2 cm in diameter and 2.1 cm in height, and located a t the bottom of the reactor. The average height of the emerging gas bubbles was 1.4 cm above the bottom of the vessel. The height of the slurry above this location was 12 cm. The properties of the activated carbon used as adsorbent are given in Table I. The hydrogen sulfide had a specified purity of 99.6% and the helium of 99.9%.For rate studies, a gas stream containing 3 mol % H2S was introduced as a step function at zero time. Table I also shows the range of gas flow rates, the volumes of slurry liquid, and other operating conditions used in the research. Before each run, the slurry was pretreated with pure helium for a t least 14 h. The step function of HaS He was introduced by turning a four-way valve. The gas stream from the reactor outlet was passed through an ice trap to eliminate water and then was divided into two streams. One stream a t a constant rate of 50 cm3/min (at 25 "C and 1 atm) flowed through a thermal conductivity detector for determination of Has, and the other was vented. The volume of the tubing between injection point and detector, and volumes of the trap and the gas space above the slurry level in the adsorber, were minimized and estimated from dimensions of the apparatus to be about 425 cm3. Breakthrough-curve data were measured with an N2-water system for obtaining the dead volume corrections, with a Has-water system for obtaining the solubility of H2S in water, and with Has-activated carbon slurries over a range of particle sizes, gas flow rates, and slurry concentrations ( m , values). Values of the moments a t the detector were obtained from these curves using eq 10 and 11.
+
Dead Volume Corrections Nitrogen has very low solubility in water; a t 25 ' C the value of H is 63.8 (Linke, 1965). The first moment a t the detector for the Na-HzO system ( m , = 0) is, from eq 5 and 8 (12)
As (VL/Q)(l/H) is less than 5% of C(l,d.v.,the measured first moments correspond to those in the dead volumes. Such data are shown as a function of VL/Q in Figure 2. Since @l,d.v.= Vd.v,/Q,the slope of the line in Figure 2 is equal to Vd.v./VL. The corresponding value of Vd.". is 395 cm3, in comparison
I
I
I
0
1
2
I
IF1
3
4
0 VL
Q,
5
rin
Figure 2. First-moment data for Nz-water system.
0
Absorption Desorption
10
/
0
1
2
3
4
5
VL Q min
Figure 3. First-moment data for Has-water system.
with 425 cm3 estimated from the dimensions of the apparatus. ~ the Has-slurry The values of 11,d.v. were about 10%of p 1 , for system so that a 5% uncertainty in b1.d v. would lead to but a 1%error in w 1 , ~ Similarly . determined values of K2,d.v. were less than 1%of p2,D for the H2S-slurry system. Hence, dead vol~ neglected. ume corrections to p z , were HZS-Water System ( m ,= 0) First moments were obtained from breakthrough curves for both adsorption and desorption for C, corresponding to 3 mol % W2Sin He (C, = 1.22 X g-mol/cm3). These results along with P1,d.v.as previously measured are shown in Figure 3. The difference between p l , and ~ P l , d , v , corresponds to b i , ~and ~ , this difference should have a slope of 1/H according to eq 5. The value of H so determined from the data in Figure 3 is H = 0.487. The value reported in the literature (Linke, 1965) is H = 0.42, 14%less than our experimental result. The reason for the difference is not clear. The data in Figures 2 and 3 are reasonably consistent and define straight lines. Error in the correction factor for dead volumes could be a partial explanation but is unlikely to account for much of the difference. We used deionized water in preparing the slurries. Differences in water purity is another partial explanation. For subsequent calculations our value of H was used. First moments measured for different C, values (3 to 6% H2S in He) permitted the evaluation of the absorption isotherm. The results plotted as C, vs. CL in Figure 4 shows a linear behavior, corresponding to a constant value of H . Such first-order results are required in order to apply the moment method to analyze the data. Equation 6 for the second moment for the H2S-water system ( m , = 0) gives
20
Ind. Eng. Chem. Fundam., Vol. 17, No. 1, 1978
0 2
0
2
1
0
3
CL x 106
5
4
6
4
8
mS x I$, g:cm3
male cm3
Figure 7. First-moment data as a function of particle concentration,
Figure 4. Adsorption isotherm for HZS-water system.
m,.
-
80
E
g "
60 N -
12 10 8 6
-E 40
'h'
I
* x
"
I 2
0
20
0
2
1
CL
X
3
lo6
4
5
PiOle O3
0
0
4
8
16
12
ivL
Q 12
24
20
mid
Figure 5. Second-moment data for HZS-water system.
-'L 1 1 1 ,d Particle Radius
20
I
0'015 nm
E
0 0
1
2
3
4
5
VL 9. min
Figure 6. First-moment data for HZS-water-carbon system.
since the contribution of dead volume to second moment is negligible. If N L I > 5, the exponential terms in eq (13) are negligible (less than 1%) compared to unity. Using values for k L Q g , U g , and tg measured by Niiyama and Smith (1976) in the same adsorber and for the same operating conditions, aL1 for the H2S-water system is calculated from eq 7 to be 9.4 (cu is independent of gas flow rate). Hence, the effect of cy (or h 1 , a ~ )disappears from eq 13 indicating that the mass transfer resistance from gas bubble to bulk liquid is negligible. In other words, equilibrium is achieved between gas and liquid soon after the bubbles leave the disperser for the H2S-water system. Under these conditions eq 13 suggests that a plot of measured P2,D vs. ( V L / Q )should ~ give a straight line with a slope of 1/H2.The data points for adsorption and desorption are plotted in this way in Figure 5, along with a straight line
Figure 8. Adsorption isotherm for HzS-carbon (in aqueous slurry).
of slope equal to 1/(0.487)2,as determined from the firstmoment results. The second-moment data follow the same slope as predicted from first-moment results, but the absorption values fall below the line. Accurate second moments are difficult to determine because of the emphasis given to the tail of the BTC. In our experiments tailing was more pronounced in the absorption experiments which could explain why those points are low in Figure 5.
Adsorption Isotherm for HzS-Water-Carbon System First moments were obtained for four concentrations (3 to 6%) of H2S in the inlet gas a t a constant m, of 0.0467 g/cm3. The values were independent of inlet gas concentrations, Cgn, which is characteristic of first-order processes. Hence, the adsorption of H2S in carbon slurry is linear over the range of concentrations used, and eq 5 and 6 are valid. Results for Cg, corresponding to 3% H2S and for various particle sizes are plotted vs. V L / Qin Figure 6. The dotted line shows k 1 , cal~ ~ culated from the K ~ , Daccording to eq 8. The data in Figure 6 establish a straight line, and particle size appears to have no effect on 111. Lines similar to those in Figure 6 were established from the data for two other values of m,. Equation 5 predicts that the slopes of these lines should be a linear function of m, and the results plotted in Figure 7 follow this prediction. The point for water ( m , = 0) is also included for comparison. From eq 5 the slope of the line in Figure 7 is equal to KIH. Using H = 0.487, the adsorption equilibrium constant calculated from this slope is 20.8 cm3/g. The linearity of the adsorption isotherm can be demonstrated from the first-moment results for different Cg, values vs. V J Q curves a t m, = 0.0467 g/cm3. From slopes of the for each Cgn,a value of K was obtained using eq 5. Then the adsorbed concentration n is given by C L K .The equilibrium liquid-phase concentrations CL corresponding to each Cg, were obtained from CL = C,JH. The resulting data points are shown in Figure 8. The straight line in the figure corresponds to K = 20.8, as determined from Figure 7. All the first-moment results used for evaluating K were obtained with carbon particles that had undergone at least one adsorption-desorption cycle. Measurements for fresh carbon
Ind. Eng. Chem. Fundam., Vol. 17, No. 1, 1978 21 80
70
60
50
-
PO
E
zN
s
Parlicle Radius 20
0.425 mm 0.2 mm a 0.015 mm
0
0.05
0.10
0.15
020
0.25
~ 2 j,m m ) 2
10
/
Figure 10. Effect of particle size on second moment.
0 0
1
3
2 VL
4
5
6
'Q , min
Figure 9. Second-moment dasa for HzS-water-carbon system.
showed a higher retention time than for treated carbon. This could be due to heterogeneity of sites. A few very active sites on the fresh carbon may cause irreversible adsorption and may not be regenerated when pure helium was passed through the slurry (at 25 "C) after an adsorption run. The adsorption equilibrium constant determined during the first adsorption run for fresh carbon was about 25 cm3/g.
Rate Parameters for HzS Slurry Second moments were obtained primarily a t a constant slurry loading of m, = 0.0467 g/cm3 for three different particle sizes, although some data were obtained at m, = 0.0865 g/cm3. The latter results were corrected to m, = 0.0467 g/cm3 by multiplying by the ratio of [m,K l)/H]*,as suggested by eq 6. All the results are shown in Figure 9 plotted as 1 2 , ( ~Q ~/ V L ) vs. V J Q , which should yield a straight line according to eq 6. The slope of the line for each particle size should be the same and equal to [(m,K + 1)/HI2,since the term e-aL1 0. Using the values of K = 20.8 cm3/g and H = 0.487 determined from the 11 results, this slope should be 16.4.The lines through the data points in Figure 8 correspond to a slope of 15, in reasonable agreement with the value from first moment data. The data points in Figure 9 scatter somewhat, as expected for second moments. Our experience indicates that ~2 results for H2S are less accurate than those for NO or for 0 2 (Niiyama and Smith, 1976). Probably this is because of the higher rate of adsorption for H2S and because its larger K means more weight is given to the somewhat uncertain tail of the response curve. According to eq 6 the intercepts in Figure 9 represent additive contributions from the three rate constants h,, De, and hads. For the smallest particle size (0.015 mm) the intercept is close to zero, indicating that the adsorption proceeded very rapidly. This meant that for the 0.015-mm particles the contributions to the second moment of liquid-to-particle and intraparticle mass transfer, and adsorption rate at an interior site, were all negligible. Specifically, this means that ha& is too large to evaluate, regardless of particle size. An approximate value of hsas can be predicted. Assuming that the particles are spherical, a , = 3m,/pp R. From this expression a , = 3.85,8.0, and 109 cm-1 for the 0.425,0.20, and 0.015-mm particles. The data and correlations for the same adsorber geometry give k , = 0.03 cm/s (Furusawa and Smith,
+
1973). These values along with H , m,, K , p, and pp can be substituted in eq 6 to estimate the contribution of the l/k,a, term to M ~ , J * . Calculations for the largest particle size give a value of the intercept in Figure 9 of 0.56 min. This is negligible with respect to the total intercept in Figure 9. For the smaller particles this contribution would be less since a , is larger. Hence, the mass transfer resistance from bulk liquid-to-particle surface seems unimportant for all particle sizes. With contributions from both surface adsorption and mass transfer from bulk liquid-to-particle surface negligible, the intercepts in Figure 9 are due entirely to intraparticle diffusion. For these conditions, eq 6 shows that the intercept is given by
Since a , = 3m,/p,R for spherical particles, eq 14 may be written
Equation 15 shows that the intercept should be a linear function of R2, and the slope of the line establishes De. The intercepts from Figure 9 are so plotted in Figure 10. Some comments are needed here about the 0.425-111111 radius reported for the largest particles. These particles showed considerable attrition during a run. As noted originally by Niiyama and Smith (1976), the particles did not break into two more or less equal parts, but, rather, the edges were worn away causing a reduction in size. In order to account for this, the fresh particles were first pretreated by subjecting them to mild agitation in an aqueous slurry. The particles were then dried and sieved and used for an adsorption run. The reported radius of 0.425 mm is the average value determined from size measurements for pretreated particles before and after adsorption runs. From the slope in Figure 10, De was calculated cm2/s, which is of the expected magnitude. to be 1.34 X The specific numerical value is subject to some uncertainty because of inaccuracies in measuring second moments, but it gives a reasonable estimate of the effective diffusivity of H2S in liquid-filled pores. The molecular diffusivity of H2S in water cm2/s (Perry, 1963).Then the apparent at 25 "C is 1.61 X tortuosity factor, r, = /3D/De, is 0.72. Since this result is less than unity, surface diffusion as well as diffusion in the pore volume may contribute to intraparticle mass transport in this system. This possibility, while only speculative, is enhanced by the large adsorption capacity of H2S on activated carbon ( K = 20.8 cm3/g a t 25 "C).
22
Ind. Eng. Chem. Fundam., Vol. 17, No. 1, 1978
Table 11. Intraparticle Diffusion and Equilibrium Adsorption Parameters
sop
H2S04n
NO
HzS'
Effective diffusivity, D e , cm2/s 3.20 x 6.76 x 1.80 x 1.34 X 10-5 Molecular diffusivity, D , cm2/s 1.62 x 10-5 1.70 x 10-5 2.54 x 10-5 1.61 x 10-5 Apparent tortuosity, factor, T , 3.2 1.6 0.90 0.72 30 6.86 20.8 Adsorption equilibrium constant, K , cm3/g Komiyama and Smith (1975). Niiyama and Smith (1976). This work. Approximate values estimated from adsorption data that follow Freundlich isotherm.
The surface diffusivity D , may be estimated from the equation (Schneider and Smith, 1968)
De = DP/T + K p @ ,
(16)
which assumes that the adsorption-desorption process is fast with respect to diffusion. Using a tortuosity factor T for pore-volume diffusion of 3.0 the surface diffusivity is 5.8 X 10-7 crnz/s. Comparison of Adsorption of HzS, NO, a n d SO2 The kinetics of adsorption in aqueous slurries of activated carbon have been studied for H2S, NO, and SO2 in the same apparatus a t 25 "C and 1 atm total pressure. For NO the adsorption rate a t the carbon site was found (Niiyama and Smith, 1976) to be reversible and first order up to a gas concentration of 20 mol % NO in helium. The adsorption capacity of carbon for NO was relatively low, corresponding to an equilibrium constant of 6.86 cm3/(g of carbon). The rate of adsorption on the carbon sites was also low, with a rate constant, k&, of 5.8 X cm3/(s) (g of carbon). For very small particles ( R = 0.015 mm) in this system of a slightly soluble gas, the rate of the overall adsorption process was determined by the rate of adsorption a t the interior carbon sites and by the mass transfer resistance from gas bubble to bulk liquid. For larger particles, intraparticle diffusion also affected the overall rate. The situation was different for SO2, a more soluble gas. The adsorption isotherm was not linear, even at gas concentrations as low as 2.3 mol % SO2 in helium. An approximate value of the equilibrium constant for a linearized isotherm was 30 cm3/(g of carbon), indicating a higher adsorption capacity of carbon for SO2 than for NO. The adsorption rate of SO2 at the carbon sites was very rapid so that equilibrium was achieved with respect to the mass transfer steps. For most particle sizes only intraparticle diffusion affected the rate. Similar investigation of adsorption of HzS04 (Komiyama and Smith, 1975) indicated that only intraparticle diffusion affected the overall rate. The results of the present study for H2S are similar to those for SOn.The intrinsic rate of adsorption at the carbon site was found to be very fast so that the mass transfer resistances determined the overall rate in the slurry. The adsorption capacity of carbon for H2S was somewhat lower ( K = 20.8 cm3/(g of carbon)) than for SO2 and the isotherm was linear up to a gas concentration of 6 mol % H2S in helium. These results suggest a qualitative correlation between gas solubility in water and adsorption capacity and rate of adsorption on the carbon sites. For the more soluble gases (SO2 and H2S) the capacity was greater and the surface adsorption rates were so rapid that mass transfer steps controlled the overall slurry adsorption process. Since in all cases (except for the smallest particles) intraparticle diffusion in the liquid-filled pores affected the overall rate of adsorption, it is interesting to compare intraparticle diffusivities for the different systems. Table I1 shows these results along with tortuosity factors and surface diffusivities evaluated from eq 16. The apparent tortuosity factor for
H2S04 of 3.2 is a reasonable value for pore-volume diffusion and suggests that surface diffusion is unimportant. In contrast, the low values of 7 , for SO2 and HzS, combined with relatively large adsorption capacities, indicates that surface diffusion could be significant for these substances. Surface transport may not be a valid explanation for the low value of 7 , for NO. Both the rate of adsorption a t the carbon site and the adsorption capacity are low. Niiyama and Smith (1976) speculated that the reason might be related to magnetic interaction between activated carbon and NO, since both substances are paramagnetic. This interaction is possible in activated carbon because of the small radii of the micropores. Furthermore, calculation of tortuosities from eq 16 may be questionable for diffusing species that ionize and for particles with a wide range of pore sizes. Acknowledgment The financial assistance of the National Science Foundation, Grant ENG76-01153, for this work is gratefully acknowledged. Kevin Look provided valuable assistance in the experimental work. Nomenclature a~ = surface area of bubbles per unit volume of bubble- and
solid-free liquid, cm-l a, = external surface area of particles per unit volume of
bubble- and solid-free liquid, cm-1 C, = concentration of adsorbate in the gas stream leaving the reactor, mol/cm3 Cg, = concentration of adsorbate in the gas stream entering the reactor, mol/cm3 CL = concentration of adsorbate in bulk liquid, mol/cm3 D = molecular diffusivity of H2S in water, cmz/s D e = effective intraparticle diffusivity, cm2/s D , = effective surface diffusivity, defined by eq 16, cm2/s H = Henry's law constant for adsorbate in water = (Cg/ Cdequil
hads = adsorption rate constant, cm3/(g)(s) k L = bubble-to-liquid mass transfer coefficient, cm/s k , = liquid-to-particle mass transfer coefficent, cm/s K = adsorption equilibrium constant, ( n / C ~ ) ~cm3/g ~~il, L1 = height of slurry, cm m, = moment component defined by eq 1 m, = mass of carbon per unit volume of bubble- and solidfree liquid, g/cm3 n = concentration of adsorbed HzS, mol/(g of carbon) Q = gas flow rate, a t 25 "C and 1 atm, cm3/s R = radius of particles (assumed to be spherical), cm t = time, s U B = bubble velocity in vertical direction, cm/s V L = total volume of liquid in the adsorber, cm3 Greek Symbols = bubble-to-liquid rate parameter defined by eq 7 , cm-l 13 = particle porosity t B = bubble volume per unit volume of bubble- and solid-free liquid N
Ind. Eng. Chem. Fundam., Vol. p 1 , ~= ~ first
absolute moment for the slurry liquid of height
L1, s fi1,d.v.
= first absolute moment in the dead volumes, s
F ~ , D=
first absolute moment evaluated a t the detector, s
,ucg,~~ = second central moment for the slurry liquid of height
L1; F2,d.v. and F2,D are second moments in the dead volumes and evaluated a t the detector, respectively, (s)2 pp = particle density, g/cm3 T = tortuosity factor in the pore volume T , = apparent tortuosity factor
17,
No. 1,
1978
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Literature Cited Furusawa, T., Smith, J. M., Ind. Eng. Chem. Fundam., 12, 360 (1973). Komiyama, H., Smith, J. M., A./.Ch.E.J., 21, 664, 670 (1975). Linke, W. F., "Solubilities", American Chemical Society, Washington, D.C., 1965. Niiyama, H.,Smith, J. M., A./.Ch.E.J., 22, 961 (1976). Perry, J. H.,"Chemical Engineers Handbook", 4th ed, McGraw-Hill, New York, N.Y., 1963. Schneider, P., Smith, J. M. A./.Ch.f.J., 14, 886 (1968).
Receiued for reuiew March 31,1977 Accepted November 7,1977
Reaction of Thiophene with Sodium on Alumina. A Method for Desulfurization of Volatile Fuels John L. Gerlock," Lee R. Mahoney, and T. Michael Harvey Engineering and Research Staff, Ford Motor Company, Dearborn, Michigan 48 12 1
The desulfurization of a commercial gasoline by reaction with sodium metal on alumina at atmospheric pressure in the temperature range 200-300 OC is found to be as efficient as that reported for desulfurization utilizing the bulk metal under high-pressure conditions. The results of a systematic study of the reaction of thiophene vapor with sodium on alumina reveal that reaction products and stoichiometry are strongly dependent on both the sodium content of the reagent and the reaction temperature. A reaction scheme involving the formation of ring opened mono- and disodium thiopene metallates is proposed which accounts for the main features of the reaction.
Introduction There is current interest in processes which lead to the removal of small amounts of organically bound sulfur from gasoline. (The Motor Vehicle Manufacturers Association reports the following values for gasoline sulfur as of April 1976: premium leaded, 330 ppm of S;premium unleaded, 80 ppm of S;regular leaded, 430 ppm of S; and regular unleaded, 260 ppm of S.)This interest is due to environmental concerns regarding both the generation of oxides of sulfur during the combustion of sulfur-containing fuels and, more recently, the oxidation of fuel derived sulfur dioxide to sulfuric acid in automotive exhaust via the oxidation catalyst (Sulfate Emissions, 1975). Among the desulfurization processes being considered is the direct reaction of sodium metal with sulfur compounds in fuels (Conant and Blatt, 1928a, b; Faught, 1932; Wright and Vancheri, 1961; Weinberger et al., 1970; Haskett, 1971). Reggel et al. (1976) have examined the reaction between excess sodium metal and seven different gasolines under a nitrogen atmosphere in an autoclave at 200-300 "C and report rapid desulfurization from 500 to 20 ppm of S with little or no change in the characteristics of the fuels. These workers estimate a sodium reagent cost of only 0.2 cents/gal for the complete desulfurization of 1000 ppm of S fuel and suggest that the sodium sulfide(s) so produced could be sold as such or converted back to sodium metal by electrolysis. Sternberg et al. (1974) have examined the reaction of sodium metal with petroleum residues in an autoclave under a hydrogen atmosphere a t 350 "C and report sulfur reduction from 1.65 wt% to 0.1 wt% after extended reaction times. Sodium was consumed a t the rate of 6 g-atoms/mol of sulfur removed. Under the same conditions, the model compound dibenzothiophene 0019-7874/78/1017-0023$01.00/0
is converted to biphenyl and a carbonaceous residue. The present work describes the manner in which sodium dispersed on high surface area alumina can be used to remove trace amounts of sulfur from volatile fuels a t atmospheric pressure and moderate reaction temperatures. We chose this reagent in place of the bulk metal utilized by earlier workers because most heterogeneous reactions are carried out more efficiently over high surface area reactants. The reagent, sodium on alumina or "high surface sodium", (Cross, 1932; U S . Industrial Chemical Co., 1954; National ,Distillers and Chemical Corp., 1963) has been used extensively as a polymerization-isomerization catalyst and the technology for its large-scale production is well developed (Texaco Development Corp., 1957). After initial experiments to compare the desulfurization efficiency of sodium-alumina reagent with that reported for the bulk metal for the desulfurization of commercial gasoline, we have examined the reaction between the reagent and the model compound thiophene in detail. The influence of both reagent sodium content and reaction temperature on reaction stoichiometry and product distribution have been determined. Thiophene was selected as a model compound due to its simplicity and the fact that fuel analyses (Rall et al., 1972; McKinney, 1972; Carrales, 1975) and evaluations of existing desulfurization technology suggest that sulfur containing organics within this class are among the more difficult to remove in trace quantities from gasoline fractions (Hoffman, 1973; Berger, 1974; Kellogg Go., 1974; Gasoline, 1974; Shell Oil Co., 1975). The results of the thiophene study have led to the proposal of a generalized reaction scheme which accounts for the products of the desulfurization reaction.
0 1978 American Chemical Society
