Thermolysis of Hydrogen Sulfide in the Temperature Range 1350

into hydrogen and sulfur at temperatures from 1350 to 1600 K and pressures from 15 to 30 kPa ... a nominal reactor temperature of about 1800 K and a n...
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Ind. Eng. Chem. Res. 1998, 37, 2323-2332

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KINETICS, CATALYSIS, AND REACTION ENGINEERING Thermolysis of Hydrogen Sulfide in the Temperature Range 1350-1600 K William S. Harvey, Jane H. Davidson, and Edward A. Fletcher* Department of Mechanical Engineering, University of Minnesota, 111 Church Street S.E., Minneapolis, Minnesota 55455

The thermal dissociation of hydrogen sulfide gives promise of becoming an economic method to convert a hazardous waste into valuable products, conserve fossil fuels, and increase usable reserves of fossil fuels. The dissociation rates at temperatures which are attractive for an industrial process are not well-characterized. We studied the dissociation of hydrogen sulfide into hydrogen and sulfur at temperatures from 1350 to 1600 K and pressures from 15 to 30 kPa in an alumina reactor. The rate depends on the surface-to-volume ratio of the reactor. The surface reaction is the dominant contributor; the activation energy for the forward surface reaction is 194 kJ/mol. We present a global rate expression that includes surface and gasphase contributions. Introduction Sulfur, in varying amounts, is a component of all fossil fuels: coal, petroleum, and natural gas. Many gas wells, which are, of course, never used, are really hydrogen sulfide wells contaminated with natural gas. Either the sulfur must be removed from the fuel before it is burned or the oxides of sulfur must be removed from the stack gas. The sulfur which is removed during processing before combustion is usually recovered as hydrogen sulfide (H2S). Cleaning up the stack gas from the Claus units which are now used to dispose of H2S is very costly. A good method for safely disposing of hydrogen sulfide would therefore have the effect of substantially increasing our fuel reserves while reducing the cost of using them.1 It was suggested more than 20 years ago that both hydrogen and sulfur should be recovered by thermally splitting H2S in the absence of air.2 The many studies which have been made of the kinetics of thermal H2S splitting have recently been summarized in an excellent review.3 Most of these studies were carried out at temperatures ranging up to about 1200 K. At 1200 K and 100 kPa, H2S is less than 20% dissociated at equilibrium. Lower pressures and higher temperatures increase the degree of dissociation. Solar furnace studies in alumina reactors showed that yields as high as 70%, virtually 100% of theoretical, could be obtained at a nominal reactor temperature of about 1800 K and a nominal reactor pressure of 33 kPa.4,5 Although the use of sunlight as a prime source of process heat was a major objective of these previous studies, one should note that the aforementioned observations apply when other prime energy sources are used, as well.6 There is quite evidently very little agreement in the literature on the detailed kinetics or mechanisms of the * To whom correspondence should be addressed. Fax: (612) 624-1398. E-mail: [email protected].

hydrogen sulfide dissociation reaction and very little information about the reaction in the high-temperature regime which would be most useful for splitting hydrogen sulfide on a practical scale. The objective of this study was to acquire information needed for the design of reactors. What are the global rates that characterize the reaction in the temperature range above which the equilibrium dissociation is substantial (1400 K), and what effect will a practical reactor material (alumina) have on the global kinetics? Background Interpretations of past studies of the rate of decomposition of H2S have produced a wide range of activation energies, orders, and the effects of various materials, including alumina. Even the forms of the rate expressions are at variance. Darwent and Roberts7 studied the photocatalytic splitting of H2S and performed limited investigations on its thermal decomposition in a quartz vessel. From 770 to 923 K, they found the reaction to be of order 1.6 with respect to H2S with an activation energy of 104.6 kJ/mol. Over this temperature range, the “rate of reaction was strongly dependent on ... surface area”. From 923 to 970 K the reaction was second order with an activation energy of 209.6 kJ/mol. In this region the rate was independent of the surface area. Raymont2 studied a variety of catalysts: silica, cobalt molybdate, and 1% presulfided platinum, as well as an empty reactor. He found that below 1250 K the reaction was influenced by the catalyst and above 1250 K the reaction needed no catalyst to achieve equilibrium. The activation energies varied from 33 to 209 kJ/mol. Bandermann and Harder8 carried out the reaction in a tubular plug flow quartz reactor containing alumina. They measured conversions as a function of residence time, pressure, and temperature. In all cases, in the

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2324 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998

temperature range 1090-1230 K the equilibrium conversions were achieved within 20 ms. Bishara et al.9 examined the reaction using a solar furnace, which achieved temperatures from 933 to 1073 K. They experimented with several materials: alumina, Co-Mo sulfide, and Ni-Mo sulfide. They suggest the reaction is second order and irreversible. They rationalized their conclusion using only the forward reaction, although they had achieved equilibrium during many of their runs. They reported activation energies of 6075 kJ/mol, depending on the catalyst used. When they cast the data from Bandermann and Harder8 into a second-order forward form, the activation energy was 90 kJ/mol. They also provide rate equations which express the rate per unit mass of catalyst. For alumina their reaction rate expression in (mol/h‚g of catalyst) is

r ) (2.61 × 105)e-75600/RTamCH2S2

(1)

where am is the surface area per gram of catalyst (m2/ g). The reaction rate is proportional to the surface area of catalyst, but, it appears, they did not vary the surface area in their reactor. Al-Shamma and Naman10 studied the decomposition reaction over vanadium oxide, in a reactor also containing alumina. The reactor was partially filled with glass pellets to smooth out the temperature and concentration profiles. They concluded that for the temperature range between 723 and 873 K the reaction was first order. Kaloidas and Papayannakos11 used a tubular alumina reactor at temperatures from 873 to 1133 K. They tested for a surface effect by placing a bed of crushed alumina tubing in the reactor, but the conversions were unchanged from those without the bed at comparable flow rates. They used both forward and reverse reactions in their rate equations and reported their results in terms of pressure rather than concentration. The activation energy was 195.8 kJ/mol for the forward reaction and 105.8 kJ/mol for the reverse reaction, which is consistent with the enthalpy of reaction of 90 kJ/mol for the global reaction. They suggested that the molecular reaction

H2S a HS + H

(2)

is the rate-controlling step, but Bowman and Dodge12 and Roth et al.13 found activation energies of 310 and 345 kJ/mol, respectively, for reaction 2. Kappauf et al.4 and Kappauf and Fletcher5 used a solar furnace and several different reactor designs, carrying out the reaction at temperatures from 1200 to 1800 K. They reported an activation energy of 177 kJ/ mol, deduced from the yields obtained, although the reactor was not designed for this purpose. In contrast to Kaloidas and Papayannakos,11 they suggested that alumina had a catalytic effect on the reaction. They drew this conclusion by observing that their yields could not be explained by means of a gas-phase reaction alone using data for the molecular reactions. Tesner et al.14 studied the reaction between 873 and 1473 K in electrically heated, quartz tubular reactors with an H2S-N2 mixture. They found the reaction order to be 1.08 with respect to H2S and concluded that their reactions were predominately surface reactions. Their reported activation energy was 277 kJ/mol for the gas-phase reaction and 202 kJ/mol for the surface reaction. Conversions in their reactor at 1373 K took

Figure 1. Initial reaction rate predictions from various studies. The rate expressions, activation energies, and preexponentials of the different researchers are used to predict the dissociation rate of pure H2S at a pressure of 100 kPa. The activation energies (E) found by the researchers are also shown. Predictions are plotted only for the temperature range covered by each study. The predicted thermolysis rates for this reaction vary by over 2 orders of magnitude at some temperatures. Each study in the figure reported one rate equation; separate surface and gas-phase reaction rates were not presented.

over 1 s of residence time to approach equilibrium conversion, while in the Bishara et al.9 alumina reactor at 1073 K equilibrium conversions were achieved in less than 0.25 s. Adesina et al.15 used a quartz flow reactor at temperatures between 1030 and 1070 K. They found an activation energy of 241 kJ/mol and concluded that quartz had no catalytic effect. Of these studies, only Kappauf and Fletcher5 examined global kinetics above 1500 K, where greater equilibrium yields of products are possible and where Diver and Fletcher6 suggested a reactor would run most economically. The influence of alumina on the reaction is of special interest because alumina is an inexpensive, chemically stable candidate material for a reactor at temperatures above 1500 K. Many researchers chose to use a rate equation which ignored the reverse reaction. Such rate equations seem inappropriate for our purposes inasmuch as, even at the highest temperatures of practical interest, the equilibrium composition still contains a substantial amount of H2S. Figure 1 shows predicted H2S decomposition rates and their variation with temperature at 100 kPa using the rate expressions provided by various investigators. It is evident that more hightemperature work would be helpful. Test Facility The test facility is shown in Figure 2. Hydrogen sulfide (Air Products, 99.3%) was delivered to the reactor from a tank equipped with a pressure regulator through a critical flow orifice. Typical upstream pressures were in the range 60-150 kPa, and low downstream pressures, 15-30 kPa, maintained by a vacuum pump, assured that the orifice flow would be critical. Temperature and pressure upstream of the orifice and pressure downstream were measured. The reactor was

Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2325

Figure 2. Experimental apparatus.

Figure 3. Cross section of the alumina reactor. The alumina rods were inserted to increase the surface-to-volume ratio and were not present for the lower surface-to-volume runs.

mounted in an electric furnace. The gases which emerged from the reactor passed through a water-cooled hard-glass condenser, where most of the sulfur condensed and was removed from the gas stream. Small samples of the remaining gas were then taken for analysis, and the rest was pumped through an alkaline scrubber which removed the hydrogen sulfide. The hydrogen was then exhausted through the vacuum pump. The conversion of H2S was determined by measuring the molar ratio of H2 to H2S in the gas samples. The gas pressure in the sampling vessel was measured before and after the removal of H2S by a strongly alkaline solution. The outputs from an electronic pressure transducer (range 0-700 kPa, all pressure transducers calibrated to within (1 kPa) and a copper-constantin (type T, (0.4%) thermocouple upstream of the orifice were recorded by a Doric data logger ((0.05% of voltage, (0.1 K). Thermocouple reference junction temperatures were measured with a platinum resistance temperature detector in the data logger. The reactor pressure was monitored by a pressure transducer (0-101 kPa, (0.1 kPa) downstream of the orifice and upstream of the reactor. Furnace power was controlled manually with a variable power transformer. The reactor was a 99.5% alumina tube (2.5-cm o.d., 1.9-cm i.d., 76.5-cm length). Thermocouples measured the vertical temperature distribution within the reactor. A Swagelok tee at the top of the reactor provided a gastight penetration for the thermocouple assembly. A cross section of the reactor is shown in Figure 3. Five platinum/platinum-13% rhodium (type R) thermocouples were housed in a 1.25cm o.d., 1-cm i.d., 76.2-cm length 99.5% alumina tube, which ran down the center of the reactor and was closed

at the lower end to protect the thermocouples from corrosion. The space within the thermocouple sheath was filled with a fine alumina-silica sand to prevent convection currents. Heat-transfer analysis suggested that the gas temperature is within 1% of that measured by the thermocouples. The gas flowed around the thermocouple sheath and through the annular reactor. To increase the surface-to-volume ratio, we inserted 12 99.5% alumina rods (1.83-mm diameter, 45.7-cm length). The rods were cemented to the sheath with a ceramic adhesive at a location above the furnace cavity where the temperature was low. At this location we believe that any potential effect of the porous adhesive surface to the reaction rate was minimal. With the rods in place, the cross-sectional area of the reactor was reduced from 1.608 to 1.293 cm2; the surface-to-volume ratio was increased from 618 to 1307 m2/m3. The sampling apparatus was connected by a T-joint made of glass and polyethylene at the exit of the condenser. It was a 500-mL round-bottom flask equipped with a pressure transducer. The evacuated flask was allowed to fill with the quenched product gases and closed. The pressure in the flask (P2) was then measured. Then, to absorb the hydrogen sulfide, a small amount of a solution of sodium hydroxide of the same strength as that of the scrubber solution (to match vapor pressures) was injected into the sample via a septum, and the pressure of the sample was remeasured (P3). The fractional conversion, x, is defined as

x)1-

FH2S FH2So

(3)

where FH2So is the molar flow rate of H2S at the reactor inlet (mol/s) and FH2S is the molar flow rate of H2S at the exit (mol/s). The ideal gas law was used to calculate the conversion, which from the pressure measurements is given by

x)

P3 - P1 P2 - P1

(4)

where P1 is the residual pressure in the flask before the sample had been drawn. The temperature in the sample flask was measured with a copper-constantin (type T, (0.4%) thermocouple; observed variation in this temperature was insignificant. The uncertainty in the

2326 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998

conversion measurement ((4%) stems from the calibration uncertainty of the pressure transducers. Test Procedure The objective of the experiments was to measure the conversion at a given reactor temperature distribution, reactor pressure, and H2S flow rate. At the beginning of each experiment, the system was evacuated. The system’s pressure achieved the vapor pressure of the scrubber solution which, depending on the sump temperature, was usually 1.5-2.0 kPa. The furnace and other auxiliary equipment were then turned on. Once the furnace reached a steady temperature (reactor temperatures within (1 K for 1 min), data acquisition was initiated and the sample vessel was isolated. The system was then purged with argon. After at least five system volumes of argon gas had swept through the system, the argon flow was turned off. Then hydrogen sulfide was introduced. The reactor temperatures stabilized to within (1 K after about 15 min. The reactor was brought to the desired pressure by adjusting the globe valve upstream of the vacuum pump. Once reactor temperatures and pressures had stabilized, a sample was withdrawn: the hydrogen sulfide flow was shut off. The pressure of the sample flask was recorded before (P1) and after (P2) the sample was taken. Two milliliters of a 25% sodium hydroxide solution (identical with the scrubber composition) was then injected into the sample flask and the pressure (P3) noted. The first injection was followed by 0.5-mL injections until the sample pressure no longer changed, indicating that all H2S had been removed from the gas. Data Analysis Our objective was to be able to express the global rate of conversion of H2S, in terms of the concentrations of the major constituents, H2S, H2, and S2. In the temperature range of interest, the completed reaction is an equilibrium state which contains substantial amounts of all three components. Their concentrations are linked by the stoichiometry of the equation

H2S a H2 + 1/2S2

(5)

We have chosen to represent the reaction as follows. We regard equilibrium states as states in which the forward and reverse rates are equal to each other and assume that the rate expressions for the forward and reverse reactions do not change as the composition and extent of reaction change. We have chosen to do so because the actual reaction process involves many concurrent elementary reactions. Species such as S, H, and HS may be important in determining the mechanism of the reaction, but they are not the ones that are measured easily nor the ones that are important for our purpose. It is simpler and more useful to characterize the behavior of the reaction in terms of the concentrations of the major constituents H2S, H2, and S2. Thus formulated, if the reaction takes place entirely in the gas phase, our rate equation becomes n1 n2 n3 - k′CH C )r -dCH2S/dt ) kCH 2S 2 S2

(6)

We assume our reactor is a plug flow reactor. Care was taken in the design to ensure uniform flow, and based on the dispersion number,16 axial dispersion in

the gas flow is negligible. Aris17 showed that treating real reactors as plug flow reactors may introduce errors on the order of 5% for predicted conversions. Operating in steady state, it is thus possible to obtain the rate constant, activation energy, and order of the reaction from a one-dimensional differential volume analysis. A mass balance on H2S yields the relationship

dFH2S/dV ) -r

(7)

where r is the reaction rate (mol/m3‚s) and dV is the differential volume (m3). The conversion is 0 at the reactor inlet and may, in principle, approach its equilibrium value in the reactor. In a differential volume element,

dFH2S ) -FH2So dx

(8)

The molar flow rates of H2 (FH2) and S2 (FS2) are related via the stoichiometry and the conversion, x. Expressing eq 8 in terms of conversion, separating variables, and integrating yield

dx ∫0xr(x)

V ) FH2So

(9)

where r(x) is given by

1 - x n1 r(x) ) k CH2So 1 + 0.5x n2 x 0.5x n3 CH2So (10) k′ CH2So 1 + 0.5x 1 + 0.5x

(

)

(

)(

)

In deriving eq 10, we included the effect of changing molecular weight on the density of the gas. Equations 9 and 10 give

V ) FH2So

x ∫0x {dx/[k(CH So1 1+-0.5x )

n1

2

-

) ]} (11)

n2 x 0.5x n3 k′ CH2So CH2So 1 + 0.5x 1 + 0.5x

(

)(

which relates the conversion to the volume of the reactor in terms of the initial concentration of H2S. The equivalent volume of the reactor would be a known quantity if the reactor were truly isothermal. Since the reactor was not isothermal we used a standard technique to permit the data to be treated as if the reactor were isothermal. The technique we used was that of Hougen and Watson18 as discussed in Froment and Bischoff.19 Their equivalent volume approach assigns a corrected volume V to the reactor, which assumes that the reactor can be represented as an isothermal reactor operating at an appropriate nominal temperature T. We used the equivalent volume to determine the residence time of the element of fluid in the reactor. The unknown quantities in eq 11 are the forward and reverse reaction rate constants and the exponents on the concentration terms (orders). We assumed the ratios of the orders to be the same as the ratios of the stoichiometric coefficients. Having assumed that the rate expressions do not change during the course of the reaction implies that the ratio of the forward to reverse reaction rate constant is equal to the equilibrium constant. We began by using a first order in H2S rate equation; then we attempted to fit the data to other orders using an optimization technique. With these

Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2327

assumptions, the rate equation simplifies to n r ) -dCH2S/dt ) kCH 2S

k n n/2 CH CS kneq 2 2

(12)

and eq 11 becomes

V ) FH2So

∫0x

(

{ [(

1-x dx/ k CH2So 1 + 0.5x

x k CH2So 1 + 0.5x kneq

)( n

)

n

-

0.5x CH2So 1 + 0.5x

) ]} n/2

(13)

We integrated eq 13 numerically. Plotting the variation of the natural log of the rate constants with reciprocal temperature yields the slope -E/R, and the intercept is the natural log of the Arrhenius preexponential term. Equation 12 describes the reaction that occurs within a unit volume in the gas phase of the reactor. However, experiments suggested that the alumina surface was an important factor in determining the conversion. If, in addition, we assumed the rate to be proportional to the surface-to-volume ratio (Sv), eq 12 becomes n r ) -dCH2S/dt ) kSvCH 2S

k n SvCH Cn/2 2 S2 kneq

(14)

Equation 14 incorporates the kinetic attributes of eq 12 and includes the surface-to-volume ratio as a factor. As they were in the homogeneous rate equation (12), the concentrations are expressed in terms of the initial H2S concentration and conversion. Alternatively, as a refinement to the relatively simple method which uses an equivalent volume reactor volume, we used a more rigorous optimization technique which permits analysis of the nonisothermal reactor. The alternative technique determines concurrently the combination of activation energy, reaction order, and preexponential factors which minimize the differences between the predicted and observed conversions. We first tried, in turn, a gas-phase-only equation, a surface-only equation, and a combination of the two. We guessed initial values for the activation energy, preexponential term, and order. Within a length dl of the reactor, the conversion is determined by a modified form of eq 7:

r(x)A dl dx ) FH2So

(15)

In integrating it over the length of the reactor, we adjusted the concentration to account for temperature variations with length. We used a fourth-order polynomial to interpolate between the five measured temperatures to calculate the temperature profile in the reactor. We did a Runge-Kutta integration with a step size of 1 cm. Decreasing the step size to 0.1 cm changed the predicted conversions by less than 1%. The predicted conversions were compared to the measured conversions and the differences between the two expressed as an objective function no. of runs

S)

∑ i)1

(xpredicted,i - xmeasured,i)2

Figure 4. Variation of the measured and equilibrium conversions with temperature at 15-kPa reactor pressure. Varying the surface area of the reactor has no effect on the equilibrium conversion (shown by the dashed line) at a given temperature. The molar flow rate of H2S was increased with temperature to avoid the attainment of equilibrium so that the results would yield usable kinetic data.21

(16)

Figure 5. Variation of the measured conversion with space time at 1370 and 1420 K and 15 kPa reactor pressure. The surface-tovolume ratio has been doubled for the higher Sv reactor.

We used a direct search method to find the combination of E, k0, and n that minimized S to permit us to retain the residual at points other than the optimal location. We then used this information to estimate confidence intervals on the optimized parameters.20 Results Figure 4 summarizes the results of all the experiments performed at a nominal reactor pressure of 15 kPa. The equilibrium conversions are shown by the dashed line. The observed conversions at the corresponding nominal reactor temperatures for each of the experiments are shown by the data points. The nominal reactor volumes were about 50 cm3 for the lower surface area reactor and 40 cm3 for the increased surface area reactor. Figure 4 shows that in our samples we were sufficiently far from having achieved equilibrium so that they would supply useful kinetics information. In the pressure range over which we studied the reaction, 1530 kPa, the equilibrium conversion at 1420 K is decreased by about 12% by a doubling of the pressure. We did a number of runs at various flow rates to establish the relationship between conversion and space time, a convenient way to compare reactor performance. The space time is a simplified expression of the residence time of the gas in the reactor; it is defined as the equivalent volume divided by the inlet volumetric flow

2328 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 Table 1. Lower and Higher Sv Reactor Rate Equation Parametersa Arrhenius plot

optimization technique

parameter

lower 95%

best

upper 95%

lower 95%

best

upper 95%

E, lower Sv reactor (kJ/mol) k0, lower Sv reactor (1/s) E, higher Sv reactor (kJ/mol) k0, higher Sv reactor (1/s)

214 1.3 × 109 163 2.9 × 107

235 7.1 × 109 221 4 × 109

255 4.0 × 1010 280 5.5 × 1011

217 1.7 × 109 140 9.4 × 106

253 3.3 × 1010 250 4.7 × 1010

266 9.3 × 1010 272 2.5 × 1011

a

A first-order rate equation is used for both the Arrhenius plot and optimization technique.

Figure 6. Variation of the natural logarithm of the observed forward first-order rate constants with 1/T and their least-squares fitted lines. The higher Sv reactor data are not well-described by a first-order homogeneous rate equation. However, assumption of a first-order rate equation shows that the increase in Sv results in higher rate constants. Addition of the alumina rods doubled the surface-to-volume ratio.

rate at the reactor condition. Figure 5 shows the variation of conversion with space time for 1370 and 1420 K, 15 kPa runs. Longer space times result in higher conversions, ultimately approaching the equilibrium conversion. Quenching was sufficiently fast so that recombination did not lower conversions at longer space times. The conversions increase with increased surface-to-volume ratio at comparable space times. The conversion at 1420 K and a space time of 0.170 s increased from 0.16 to 0.31 when the surface-to-volume ratio was doubled. Figure 6 is an exploratory Arrhenius plot. It assumes that the forward reaction is first order and that the reaction takes place only in the gas phase. The rate coefficients used in this figure are determined from the solution of eq 13 using the equivalent volumes, measured conversions, and imposed feed rates. It is clear that the reaction rate constant increased when the surface-to-volume ratio of the reactor was doubled. The reaction, at least in part, must be taking place on the alumina surface. We therefore choose to interpret our experimental results using an overall reaction rate expression which combines homogeneous and heterogeneous contributions. This approach was attractive since homogeneous gas-phase reactions had not yet been eliminated as a contributor. The physical constraints engendered by our reactor did not permit us to conduct an experiment in which we could study the homogeneous gas-phase reaction alone. Even a quartz surface has been reported to increase the reaction rate.7 To gain some insight into the relative contributions of the homogeneous and heterogeneous reactions, we

Figure 7. Determination of the homogeneous rate constant from extrapolation of the total rate constants to zero surface area. The first-order rate constants that best fit the lower and higher Sv reactors are extrapolated to zero surface area at three temperatures. The total rate constants are calculated values from the optimization technique results in Table 1. The homogeneous rate constant is the y-intercept.

tentatively assumed that both are first order. The overall reaction rate equation takes the form

r)-

dCH2S dt

[

]

khom C C 0.5 + keq H2 S2 gas phase khet khetSvCH2S S C C 0.5 (17) keq v H2 S2 surface

) khomCH2S -

[

]

If we choose to express a total rate constant which characterizes a particular reactor having a surface-tovolume ratio Sv, eq 18 defines it as

ktot ) khom + khetSv

(18)

The activation energies and preexponential terms for calculating the first-order rate constants (ktot) observed for the lower and higher Sv reactors are presented in Table 1. Best values and upper and lower 95% confidence values are given for each of two analytical techniques.21 In Figure 7, ktot is plotted versus the surface-to-volume ratio for three temperatures. The intercepts yield an estimate of the homogeneous rate constant khom at each of the temperatures. The activation energy and preexponential for the homogeneous reaction were found from an Arrhenius plot of the homogeneous rate constants versus temperature (Figure 8). The estimate of the homogeneous rate constants by this method resulted in an activation energy of 286 kJ/ mol and a preexponential of 1.3 × 1011 (1/s). Since the homogeneous rate is a small fraction of the total rate, the homogeneous parameters are difficult to estimate precisely, but their values are not crucial for determi-

Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2329 Table 2. Recommended Rate Equation Parameters Using Combined Homogeneous and Heterogeneous Rate Equations To Describe Both Reactors reaction type

rate equation

homogeneous n kCH 2S

k CnH CSn/2 (keq)1/n 2 2

heterogeneous n kSvCH 2S a

k0

k SvCnH2CSn/2 2 (keq)1/n

E (kJ/mol)

n

1.3 × 1011 (1/s)

286

1a

1.3 × 106 (m/s)(mol/m3)0.9

194

0.1a

Assigned.

Figure 8. Variation of the natural logarithm of the homogeneous rate constants (obtained by extrapolation to zero Sv) with 1/T. The points plotted are from the zero surface area rate constants (khom) obtained from Figure 7 at 50 K increments from 1350 to 1550 K.

nation of the more important heterogeneous rate. It is interesting to note that the elementary reaction that forms the rate-limiting step in the homogeneous mechanism suggested by Kaloidas and Papayannakos11 and Adesina et al.15 is

H2S a HS + H

(19)

Roth et al.13 report an activation energy for this reaction of 345 kJ/mol; Bowman and Dodge12 report 310 kJ/mol. Our homogeneous activation energy of 286 kJ/mol, obtained from the extrapolation of rate constants to zero surface area, is within 8-21% of the activation energy found for the proposed rate-limiting elementary step. Our findings are not inconsistent with the notion that, in the gas phase, the splitting of H2S into H and HS is the rate-controlling step. Having established the relative unimportance of the homogeneous contribution, we optimized the parameters in the heterogeneous rate equation to produce the best agreement with the experimental results. The heterogeneous reaction is less sensitive to the gas-phase pressure; its order is less than 1. Fractional order reactions are characteristic of surface reactions. Laidler22 notes that “An order of zero (n ) 0) is frequently found in surface reactions involving a high degree of surface adsorption...” The Langmuir isotherm and Freundlich isotherms predict orders less than 1 for surface reactions. While interpretations of our observations incorporating surface isotherms might be made, a more refined analysis of the information we have would probably be ill-advised and beyond the scope of the present work. While the recommended kinetic model predicts conversions well, it is not adequate to describe

Figure 9. Predicted versus measured conversions, all runs, using combined homogeneous and heterogeneous rate equations. The lower Sv reactor results are shown as solid diamonds; the higher Sv reactor results are shown as open squares. Representative uncertainties in predicted and measured conversions are shown for low- and high-conversion runs.

the detailed kinetic mechanisms of the homogeneous and heterogeneous reactions. We assigned an order of 0.1 to the heterogeneous reaction to reflect our belief that it is of fractional order close to zero. Our recommended rate equations and kinetic parameters are summarized in Table 2. Figure 9 summarizes all of our observed conversions and compares them with the predicted values obtained with our recommended equation. Figure 9 includes both reactors. The average discrepancy between the predicted and measured conversions is 0.03 for the combined rate equation, about 8% on average. The activation energy over alumina reported by Kappauf and Fletcher5 is 177 kJ/mol. That of Kaloidas and Papayannakos11 is 195.8 kJ/mol. These activation energies are 9% lower and 1% higher, respectively, than the heterogeneous activation energy of 194 kJ/mol for the current study. Bishara et al.9 [76 kJ/mol] and AlShamma and Naman10 [32 kJ/mol] report activation energies below 100 kJ/mol for what they believed was a surface reaction. Kaloidas and Papayannakos,11 Kappauf and Fletcher,5 and the current study all carried out the reaction in smooth alumina tube reactors. Bishara et al.9 inserted into their reactor porous alumina particles with a surface-to-volume ratio roughly 10 000 times that of the alumina tube reactors. Their observed activation energy may be different from the activation energy of the reaction if the reaction rate was limited by the rate of diffusion of the reactant into the catalyst.19 If diffusion of H2S into the porous alumina is the rate-limiting mechanism, the observed activation energy is roughly half the activation energy of the reaction. If the activation energy of Bishara et al.9 is

2330 Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998

Figure 10. Variations of the measured and predicted conversions with space time. Predicted conversions are calculated assuming a reactor at 15 kPa; the reactor pressures for the measured data points were within (7% of 15 kPa. The predicted conversions are obtained by integrating the recommended rate equations, using a constant reactor temperature. The equilibrium conversions at 15 kPa are 0.45 at 1370 K, 0.51 at 1420 K, and 0.59 at 1490 K.

Figure 11. Predicted variations of the heterogeneous and homogeneous rates with reactor position in the low Sv reactor. The reactor pressure is 15.9 kPa; the H2S flow rate is 0.17 mol/min; and the measured conversion is 0.18. The nominal reactor temperature is 1370 K. The heterogeneous reaction rate is 8 times larger than the homogeneous rate at the entrance to the furnace (0 cm) and 3 times the homogeneous rate near the exit (25 cm).

doubled, from 76 to 152 kJ/mol, it would differ from that of the current study by 20%. Al-Shamma and Naman10

do not report specifics on the surface area or pore dimensions of their catalyst.

Ind. Eng. Chem. Res., Vol. 37, No. 6, 1998 2331

Several variables influence the conversion attainable in a reactor: space time, temperature, and surface-tovolume ratio. The effects of these variables are not easily apparent from merely examining the form of the rate equation and the values of the kinetic parameters. The recommended rate equation may be integrated to solve for predicted conversions versus space time, if a nominal reactor temperature is assumed. Figure 10 shows our predicted conversions versus space time for isothermal reactors at 1370, 1420, and 1490 K, at 15 kPa reactor pressure, as well as our observed conversions. The actual runs had a nonisothermal temperature profile and reactor pressures close to but not precisely 15 kPa. The predicted conversions increase with increasing space time and asymptotically approach equilibrium conversion at their temperature and pressure. The recommended rate equation produces physically realistic predictions as well as predicted conversions on average within 0.03 of the measured conversions. Predicted heterogeneous and homogeneous rates for a low Sv reactor are shown in Figure 11. The temperature is relatively constant in the center of the reactor. The predicted heterogeneous and homogeneous rates decrease as the conversion increases. This trend reflects the influence of the reverse reaction. The surface reaction comprises over 70% of the total rate for the lower Sv reactor. The surface rate is over 8 times larger than the homogeneous rate near the inlet, where temperature is lower, and is approximately 3 times the homogeneous rate in the center of the reactor, where the temperature is higher. This variation is exactly what one should expect in view of the higher order and activation energy of the homogeneous reaction. When Sv is increased, the fraction of the reaction that is taking place on the surface becomes larger. More than 90% of the reaction takes place on the surface for the higher Sv reactor. Conclusions The dissociation of H2S takes place predominately at the alumina surface. The global rate of dissociation of H2S is best expressed as the sum of homogeneous gas phase and heterogeneous surface contributions including terms for the reverse reactions. The surface rate per unit volume is proportional to the surface-to-volume ratio of the reactor and is much larger than the gasphase rate. The activation energy for the forward surface reaction is 194 kJ/mol. The preexponential term for the forward surface reaction is 1.3 × 106 (m/s)(mol/ m3)0.9. An assigned order of 0.1 to the surface reaction rationalizes the experimentally observed conversions. The homogeneous gas-phase activation energy for the forward reaction is 286 kJ/mol. Our homogeneous preexponential term for the forward reaction is 1.3 × 1011 (s-1) for what is assumed to be a first-order decomposition. An equation which contains contributions from the gas-phase and surface reactions predicts conversions on average within 8% of the measured conversions. Our observations suggest that solar reactors, which are well suited to provide the greatest absorption of energy at the site of a strongly endothermic reaction, should be given serious consideration. Acknowledgment This study was supported in part by the grant from the Graduate School of University of Minnesota.

Nomenclature A ) reactor cross-sectional area (m2) Ci ) concentration of species i (mol/m3) E ) Arrhenius activation energy (kJ/mol) Fi ) molar flow rate of species i (mol/s) k ) rate constant (units vary) khet ) heterogeneous rate constant (units vary) khom ) homogeneous rate constant (units vary) k0 ) preexponential factor (same units as k) keq ) equilibrium constant (mol0.5/m1.5) n ) order of the reaction in hydrogen sulfide P1 ) pressure in the sample flask before drawing the sample (kPa) P2 ) pressure in the sample flask after drawing the sample, before injection of a NaOH solution (kPa) P3 ) pressure in the sample flask after injection of a NaOH solution (kPa) r ) reaction rate (mol/s‚m3) R ) universal gas constant (8.314 J/mol‚K) S ) sum of squares of residuals Sv ) surface-to-volume ratio (m2/m3) T ) nominal reactor temperature (K) V ) reactor volume (m3) x ) conversion (molar flow rate of hydrogen produced/molar flow rate of hydrogen sulfide fed)

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Received for review January 30, 1998 Revised manuscript received March 31, 1998 Accepted April 7, 1998

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