338 Ind. Eng. Chem. Fundam. 1984, 23, 338-341

Intrinsic Global Rate Constant for the High-Temperature Reaction of CaO with H2S

Howard Freund

Corporate Research Sclence Laboratories, Exxon Research and Engineering Company, Annandale, New Jersey 0880 1

With the use of a Ca-pretreated, high surface area, amorphous carbon, the CaO-H2S reaction was studied in the temperature range 1400-1700 K. Under these conditbns, the reaction was strongly porediffusion limited. After taking diffusion into account, the global intrlnslc chemical surface reaction rate constant was determined to be 4.93 f 0.81 X 10' exp[(-45500 f 7800)lRT)l g of CaO/cm'-s-atm of H,S.

Introduction The reaction of CaO with H2S is of technical interest

in both gasification (Squires, 1970; Moss et al., 1972) and fuel rich combustion systems (Moss et al., 1972; Freund and Lyon, 1982) as the principal sulfur capture reaction when CaO is used as a sulfur sorbent. Earlier TGA work by Squires et al. (1971) determined the overall kinetics of the reaction

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They observed an activation energy of 23 kcal/mol and reported overall reactivity using the expression

CaO + H2S + Cas + HzO

More recently, Simons and Rawlins (1980) have taken data from Keairns et al. (1973) and determined a global intrinsic rate constant. They determined the rate constant to be g/cm2-s-atm at T = 1144 K with an activation energy of only 10 kcal/mol.

Both the results by Simons and Rawlins and Squires et al., when extrapolated to temperatures suitable for pul- verized coal operation, T > 1400 K, imply that little con- version (<5%) of CaO would take place in residence times on the order of 1-3 s with HzS concentrations in the range 1000-3000 ppm. On the other hand, using dolomite, Freund (1981) has seen CaO conversions up to 25% at a temperature of 1338 K which then fall off a t still higher temperatures due to desurfacing of the stone. In a coal- based system, Jensen et al. (1982) reported conversions greater than 50% when Ca-containing char was exposed to 2000 ppm S species for 1 s a t 1673 K.

The present investigation resulted from an interest in coal-based systems in which the coal contained ion-ex- changeable Ca. On pyrolysis/devolatilization such mate- rials result in an intimately dispersed CaO phase throughout the carbon matrix which based on its activity does not appear to desurface as readily as limestone or dolomite. Using these CaO-impregnated carbon particles, reaction 1 was studied in the temperature regime 1400-1700K. Experimental Section

The experiments were done in a heated furnace with a 6.1 cm i.d. alumina reador. Total length of the heated zone was 35 cm, the usable length about 18 cm as configured for these experiments. The reaction gases (H,S/H,/N,) were preheated by flowing through a 2.54 cm thick alumina honeycomb (cell diameter = 0.32 cm). A 0.64 cm 0.d. water-cooled probe was positioned through the honeycomb and had an i.d. of 0.26 cm for feeding solids into the re-

o i ~ ~ - ~ ~ i ~ ~ a ~ ~ i o ~ ~ - o ~ ~ a ~ o ~ . s o ~ o

action zone. Solids were fed by vibrating a column of solids supported by a fme mesh screen (usually 100 mesh). The vertical position of the feeder could be varied to change the particle residence time. The collection probe was a 2.31 cm id., 3.81 cm 0.d. water-cooled stainless steel probe. Gas, usually N2, could be added through a sintered stain- less steel section 1.3 cm from the tip with the objective to further quench the reaction products. Gas exited from the reactor both through the collection

probe and through the bottom of the reactor. These flows were adjusted to yield isokinetic sampling. Flow from the collection probe was pulled through a quartz fiber filter outside of the furnace to separate the solids from the gas. The gas was then analyzed for H2S by first adding 02, burning the mixture to SO2 in an auxiliary furnace, and monitoring the SO, with a Thermoelectron Model 40 pulsed fluorescence analyzer. Figure 1 illustrates the ex- perimental system.

The temperature profile of the furnace was determined and used to calculate a gas temperature profile down the length of the reactor. The temperature of the gas exiting the preheater was taken to be that of the bottom of the honeycomb. Correlations on heat transfer were then used to determine the gas temperature down the reactor. An average effective temperature was then determined. This was generally within 20° of the calculated gas temperature a t a given distance from the honeycomb.

The solid used in these experiments was amorphous carbon (Supelco, 120/140 mesh Carbosieve). This material was oxidized overnight in concentrated HN03 to provide ion-exchangeable sites and then soaked overnight in a 10% NaOH solution followed by an overnight soak in a 10% Ca (NO,), solution. The treated carbon was then pyro- lyzed under Nz at 1273 K for ' /z h to decompose the carboxylic sites and provide CaO crystallites in the carbon matrix. The BET surface area of the oxidized impregnated carbon was 872 m2/g and was found to contain 2.0% Ca. To obtain the surface area of the CaO, the carbon was first burned away by plasma ashing with oxygen. The resulting ash (CaO) was then analyzed for surface area, which was found to be 28 m2/g. The plasma ashing technique (Gluskoter, 1965) has been used with coals to concentrate the mineral matter and is believed not to affect the inor- ganic constituents. Surfur analyses were done on a Fisher Scientific Model 470 sulfur analyzer.

Residence Time. The particle size used in these ex- periments, 115 pm, is still small enough so that particle temperature follows that of the ambient gas via convective heat transfer (characteristic heat-up time -8.6 ms). The gas exiting from the honeycomb is in plug flow, i.e., has a uniform radial velocity profile across the reactor. It will

0 1984 American Chemical Soclety

Ind. Eng. Chem. Fundam., Vol. 23, No. 3,

Reaction Dlstsnce (Inches)

1984 339

Watercooled

Feeder

Watercoolea Collector

J Furnace Meter Meter

0,

Figure 1. Experimental system.

take time (-4 tube diameters under our conditions) to fully develop the laminar parabolic profile. Because the particles remain essentially in the centerline, it is impor- tant to know the average centerline gas velocity. Using an expression given in Bird et al. (1960) a centerline ve- locity can be obtained as a function of time and hence an average centerhe velocity can be determined. In this work we have taken this to be 1.3Va, where V,, is,the average or plug flow velocity.

Ideally in entrained flow, the gas velocity should be much greater than the particle terminal free fall velocity. However, the terminal velocity is actually larger than the centerline gas velocity and hence the carbon particles are moving relative to the gas flow. The actual particle velocity was not measured. The system is quite dilute in particles-solid feed rates were generally in the range 10-30 mg/min; the reactant gas flow rate was -2 L/min (mostly N,) or about 2.5 g/min. Because the system is so dilute the calculated particle terminal velocity has been assumed to be the particle velocity relative to the gas. By adding the particle terminal velocity to the gas velocity, a "lab" velocity is obtained. The reaction distance divided by this lab velocity yields the reaction time.

Procedure. Most experiments were done by feeding solids a t a slow enough rate so that little change in H2S concentration was observed; i.e., the reactor was in a dif- ferential mode. In those experiments in which a significant change in concentration was noted, the average concen- tration throughout the run was used in the data analysis.

Solids analysis from early experiments suggested that additional sulfur was either adsorbed or absorbed in the quench zone and beyond. Hence blank experiments were run adding the reactant gas into the quench line and af- terward determining the sulfur loading of the particles. The difference between the experimental and blank runs is considered to be the sulfur uptake as CaS in the reaction zone. The correction due to sulfur uptake in the quench line ranged typically between 15 and 30%.

Results The data are analyzed with the expression

- k'(1 - X)C, dX d t _ -

where X is the fractional conversion of CaO to Cas, k'is the apparent rate constant, and C, is the reactant gas concentration. Defining RcaO as the global rate of CaO disappearance per gram of CaO, one obtains

1 dX -dln (1-X) - = k'C, (3b) d t Rcao = - - - 1 - X dt Figure 2 shows a plot of In (1 - X ) vs. H2S concentration

a t fixed t. The figure is initially linear a t least up to a conversion of 50%, indicating the reaction has an apparent order of unity in reactant gas concentration. At conver-

. .

T = 1628 K

1 1 1 I = 0.6 sec 0 1000 2000 3000 4000 5000

W,SI (ppm)

Figure 2. Plots of In (1 - X) vs. concentration (solid circles) and reaction distance (solid squares).

' 5

i b$,= 19.6 kcallmole

l5 u 6 7 a

l I T ( x 10' K-')

Figure 3. Arrhenius plot for apparent rate constant.

Table I. Measured Rates and H,S Concentrations c, (X10'),

T, K Rc,, 5.' O m 3 1393 0.41 3.24 1483 0.48 3.04 1553 0.60 2.91 1613 0.93 2.80 1698 1.13 2.66

sions greater than 50% the uncertainty of the data pre- vents any definitive conclusion. High conversions, how- ever, alter the solid structure considerably and could lead, for example, to product layer diffusion inhibition in which the reaction order in H2S would be less than one.

Also in Figure 2 is a plot of In (1 - X) vs. reaction dis- tance at fixed H a concentration. The linearity of this plot suggests that the reaction rate is proportional to unreaded CaO. In addition, rate data can be obtained from one experimental point: Rcao is determined in eq 3b by di- viding In (1 - X) by the residence time for that run. This is the procedure used in Figure 3 in which log (Rcao/C,) is plotted against reciprocal temperature, where C, is the gas phase H,S concentration. The same gas mixture was used as the temperature was varied and hence an increase in concentration occurs as the temperature is lowered. Dividing the rate by C, accounts for this change in H2S concentration. The apparent activation energy is 19.6 kcal/mol. The data are summarized in Table I. Pore Diffusion. The surface area of the amorphous

carbon is quite high and consequently the carbon particle has a small effective diffusivity. This raises the question whether the CaO-HP reaction under the conditions in this study is diffusion controlled through the pores of the carbon matrix. One can gain considerable insight whether a reaction of a porous solid is kinetically controlled or diffusion limited by determining the effectiveness factor, 7. It measures the extent to which the entire volume of a particle is utilized for a reaction. Satterfield (1970) gives

340

an expression for a dimensionless modulus, a, from which an effectiveness factor can be determined

Ind. Eng. Chem. Fundam., Vol. 23, No. 3, 1984

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R, is the observed rate of reaction per unit particle volume, mol/(s cm3), C, is the reactant gas concentration, d is the particle diameter, and Deff is the effective diffu- sivity. Knudsen diffusion dominates within the pores of the particles because of their very small size, - 10 A. Defl can be evaluated by use of the kinetic theory expression for Knudsen diffusion (eq 5) where 0 is the particle po-

rosity, T is the absolute temperature, S is the specific surface area, pa is the apparent density of the carbon particle, and M is the molecular weight of the diffusing species. T is the tortuosity and is a measure of the geo- metrical configuration of the pores. Typical values range from 2 to 7. The tortuosity for diffusion through a ran- domly oriented system of long cylindrical pores is 3 (Satterfield, 1970); this is the value used in this analysis. The carbon in this study has a porosity of 0.4 and an apparent density of 1.2 g/cm3 (2 g/cm3 was used as the true density of the amorphous carbon).

Using typical values to obtain the modulus, a, a value of -3200 is obtained. This leads to an effectiveness factor of about 0.003! Such a small effectiveness factor strongly indicates control by pore diffusion or even by external mass transfer limitations.

If the system is not completely external mass transfer limited, the rate data can be expressed in terms of the intrinsic volumetric rate constant k,, the surface reactant concentration C,, and the effectiveness factor, q

R, = akvC, (6)

where R, is the observed rate, g of CaO/(s cm3) particle and is equal to RCaOpCaO where pCeO is the density of the CaO in the carbon particle. Implicit in this expression is the assumption that the effectiveness factor refers only to the porous carbon particle in which the CaO is distributed and all the CaO surface is available for reaction. Because pore diffusion through the support is throught to be dominant, no consideration has been given to changes in the porous structure of the CaO itself as it is converted to Cas. When q is quite small and the particles are spherical, q = 3/4, where 4 is the Thiele modulus

(7)

This leads to an expression k,, using (5), (6), and (7) Rp2d2paSr

(36)(19400)02 C: (;>'" (8) k, =

C, in eq 8 is still undetermined. C, would equal C, if there were no film diffusion limitation. We can determine C, by use of the mass transfer relationship

R, = K(C, - C,) ( 9 4

C, = C, - R,/K (9b)

where R, is the rate, g of CaO/(g of particle/s) (R, = R,/p,) and the overall mass transfer coefficient K on a

yielding

6 t \ i

! I i

2l '5 6 8

I IT (x lW, K-?)

Figure 4. Arrhenius plot for pore diffusion corrected rate constant.

mass basis far a particle in a stagnant atmosphere. K can be expressed as

where the units are appropriate for eq 9a. A is a factor equal to the ratio of the molecular weights of the reactants, CaO/H,S; A = 1.65. D, is the molecular diffusion coef- ficient of H2S through N2. We can now express the rate constant in terms of observables as

I f film diffusion is neglibile, then C, >> Rm/K and C, - C . The units of k, are g of CaO/(cm3 s)/(g of H2S/cm3). This can readily be converted to a surface area basis knowing the surface area of CaO per unit volume of par- ticle. The concentration units can also be converted to pressure units. The results using the latter units are plotted in Figure 4. The rate constant obtained from the least-squares line is k = (4.93 f 0.81) X lo6 expj- [(45500f7800)/RT]) g of CaO/(cm2 s atm). Discussion

With the value of k determined, one can compute a value for the Thiele modulus to confirm that the effectiveness factor is indeed much less than unity so that the as- sumption q = 3/41 is valid. At T = 1500 K, 4 is 1450, leading to q = 0.002, similar to that obtained before using another modulus.

In pore-diffusion controlled experiments, generally the apparent activation energy (19.6 f 3.4 kcal/mol in this work) should be one-half of the intrinsic activation energy (45.5 f 7.8 kcal/mol from Figure 4) if film diffusion is negligible, i.e. C, >> (R,/K). Taking into consideration the error limits, the activation energies are indeed within a factor of 2 of each other. However, in these experiments f i b diffusion is not negligible (i.e., C, 5 (R,/K) - 0.1C ). As the temperature increases, R, increases and hence t i e term (C - R,/K) contributes to the temperature depen- dence ofk, in eq 11. Incorporating film diffusion into the analysis accounts for the more than fador of two difference between the mean values of the two activation energies.

As indicated in eq 11, determination of the rate constant involves among the variables the square of the measured rate R, and the concentration term C,. Errors in the measured rate are estimated to be 10-15%, which leads

Ind. Eng. Chem. Fundam., Vol. 23, No. 3, 1984 341

Ca-containing chars. However, it should also be applicable to CaO in general if the surface area of the material at reaction conditions can be adequately determined. Acknowledgment

Helpful discussions with Drs. Y. H. Song and W. Bartok are most appreciated. The excellent technical help of J. Pizzulli is gratefully acknowledged. Nomenclature E = actual activation energy, cal/mol E, = apparent activation energy, cal/mol C, = reactant gaseous concentration, g/cm3 C, = reactant surface concentration, g/cm3 d = particle diameter, cm Deff = effective diffusivity, cm2/s D, = molecular diffusion coefficient, cm2/s k, = intrinsic rate constant per unit particle volume, g/(cm3

k = intrinsic rate constant per unit reactant surface area, g/(s

k’ = apparent rate constant, cm3/(g s) K = overall mass transfer coefficient on mass basis, cm3/(g

M = molecular weight, g/mol Rcao = rate of CaO disappearance per unit mass of CaO, g/(s

R, = rate of CaO disappearance per unit mass of particle, g/ (s

R, = rate of CaO disappearance per unit particle volume, g/(s

R, = observed rate of reaction per unit particle volume, mol/(s

S = specific surface area, g/cm2 T = absolute temperature, K X = fractional conversion of CaO to Cas A = ratio of the molecular weights of the reactants, solid/gas q = effectiveness factor 4 = Thiele modulus

pa = apparent particle density, g/cm3 pCaO = density of CaO within carbon particle 0 = particle porosity 7 = particle tortuosity

Literature Cited

New York, 1960.

s g/cm3)

cm2 atm)

8 )

g)

g of particle)

cm3)

cm3)

= Satterfield modulus

Registry No. CaO, 1305-78-8; H2S, 7783-06-4.

Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. “Transport Phenomena”; Wiiey:

Freund, H. Combust. Scl. Techno/. 1081, 26, 83-88. Freund, H.; Lyon, R. K. Combust. Fleme 1982, 45, 191-203. Gluskoter, H. J. Fuel 1065, 44 , 285. Jensen, K.; Bartok, W.; Freund, H. ACS Symp. Ser. No. 796 1982,

Kelerns, D. L.; Archer, D. H.; Newby, R. A.; O’Nelll. E. P.; Vidt, E. J. “Evaluation of the Fluidized Bed Combustion Process, Voi. IV. FluMized Bed Oil Gasificetion/Desulfurizat~n”, EPA-65012-73-048D, MIS PB 238- 101, 1073.

Moss, 0.; Craig, J. W. T.; Tisdaii, D. AIChE Symp. Ser. 1972, 68(126),

Satterfield, C. “Mass Transfer in Heterogeneous Catalysis”; Massachusetts

Simons, 0. A.; Rawllns, W. T. Ind. Eng. 0“. Process Des. Dev. 1880,

Squires, A. M. Sclence 1070, 169, 821-828. Squires, A. M.; Graff, R. A.; Peli, M. Chem. Eng. frog. Symp. Ser. 115

335-346.

277-282.

Institute of Technology, Cambrldge, MA, 1970.

19, 565-572.

1071, 67, 23-34.

Received for review May 31, 1983 Reuised manuscript receiued January 13, 1984

Accepted January 27, 1984

to an uncertainty of 20-30% in the rate constant. Other errors and uncertainties lead to a factor of 2 in the rate constant. The bulk gas concentration is determined by the H2S/Hz/Nz mixture supplier. H2 is added to suppress the dissociation (eq 12), and other equilibria involving the

(12) decomposition of H2S. However a t 1700 K, equilibrium in a lo00 ppm H2S/5% H2 in Nz mixture predicts an H2S concentration about 25% less than lo00 ppm. The argu- ment supporting the use of the higher concentration ie that within the boundary layer as well as within the particle because of the H2S diffusion limited system, the equilib- rium in (12) will be shifted to the left and more H a formed from other sulfur species such as S2. Hence, more of the gas phase sulfur loading will be available for reaction with CaO. For these experiments, the entire gas-phase sulfur concentration has been used as the driving force for the H2S reaction.

Using a similar argument, the reverse reaction of (l), Cas + H20, which could occur as Cas formation proceeds has been neglected. H 2 0 within the high surface area carbon matrix will gasify the carbon at the temperatures in this study to form CO and Ha. The rate of gasification is sufficiently rapid to keep the H20 concentration at a low level.

Extrapolating the line in Figure 4 to the temperature regime used in Keairns (1973) leads to a value of k 100 times higher than that determined by Simons and Rawhs (1983). Squires et al. (1971) do not report an intrinsic rate constant although they determine an activation energy of 23 kcal/mol. The activation energy found in this study is 45.5 kcal/mol.

The reason for the large discrepancy between the rate constant reported herein and that by Simons and Rawlins is not apparent. It is also not clear why the activation energy in this work is substantially higher than previous studies. Diffusion effects at the low temperatures used in their studies would not be expected to be significant. One obvious difference between this work and others is the nature of the solid reactant. In previous work, limestone or pure CaO was used as the solid reactant. In this work, however, Ca-impregnated carbon was used yielding upon pyrolysis a carbon matrix of CaO crystallites. Another obvious difference is the higher temperature regime as well as the shorter residence time regime: seconds in this study, minutes and longer in earlier work. Although such dif- ferences exist between this and earlier work, the reasons for the difference in AE are not apparent to the author. One possibility is that there is a mechanism change as one goes from low temperatures to temperatures above about 1200 K. The nature of such a mechanism change would be an area for further research. Conclusion

The global intrinsic rate constant for the reaction of H2S with CaO has been established on a surface area basis as k = 4.93 f 0.81 X lo6 exp(-45500 f 7800/RT) g of CaO/(cm2 s atm H2S) over the temperature range of 1400-1700 K. This value was obtained by using CaO-im- pregnated amorphous carbon and should be applicable to

H2S + H2 + ‘/2S2