Kinetics of Reaction between Hydrogen Sulfide and Sulfur Dioxide in

concentrations under which conditions the second reaction may be neglected. ... sulfuric acid solutions, was studied at 20-50 °C and 30-60 wt % of ac...
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Ind. Eng. Chem. Res. 2002, 41, 4707-4713

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Kinetics of Reaction between Hydrogen Sulfide and Sulfur Dioxide in Sulfuric Acid Solutions Hui Wang, Ivo G. Dalla Lana, and Karl T. Chuang* Department of Chemical and Materials Engineering, University of Alberta, Edmonton, Alberta, Canada

Our earlier study showed that when H2S and concentrated sulfuric acid react, H2S is first oxidized by molecular H2SO4 and then consecutively by SO2, a product of the first oxidation step. The rate of the first reaction was measured using initial rate analysis at temperatures and acid concentrations under which conditions the second reaction may be neglected. In this study, the kinetics of the second reaction, i.e., the reaction between hydrogen sulfide and sulfur dioxide in sulfuric acid solutions, was studied at 20-50 °C and 30-60 wt % of acid concentration, under which conditions the rate of the first reaction is negligible. The second reaction follows firstorder kinetics with respect to the partial pressure of H2S in the gas phase and also to the concentration of SO2 in the solution. Changes in acid concentration do not affect the rate constant. The activation energy and the preexponential factor of the reaction at all acid concentrations studied are 59.02 kJ mol-1 and 11 900 L s-1 m-2 Pa-1, respectively. Further experiments show that the measured kinetic results also apply to the second reaction in sulfuric acid at concentrations exceeding 60 wt %. Introduction Sulfur removal and recovery is always a crucial subject in the areas of fossil fuel applications. Current technologies using adsorption, absorption, or modified Claus process, are neither economically nor environmentally justifiable, when being used for sour gases that come from isolated and remote sites and contain small amount of H2S. Reactions between H2S and sulfuric acid have shown potential to become an alternative technology that is flexible, applicable, and cheap and able to reduce gas sulfur emission to zero. Moreover, it can remove H2S and H2O simultaneously. To develop a new and efficient sulfur removal and recovery technology based on the reactions between hydrogen sulfide and sulfuric acid

H2S + H2SO4 ) S + SO2 + 2H2O

(1)

2H2S + SO2 ) 3S + 2H2O

(2)

liquid media.12 The reaction between H2S and SO2 in liquid phases has been investigated extensively. Different liquid media lead to differences not only in reaction mechanism but also in product distribution. Table 1 summarizes the product distributions of the reaction in different liquid media, indicating that the reaction in most of the organic solvents produces sulfur but that in water and alkali aqueous solutions produces either sulfur or polythionic acids or both depending on H2S/SO2 ratio and reaction temperature. Tracer studies28,29 show that either in product sulfur or in product polythionic acids, two-thirds of the sulfur atoms originate from H2S and the other one-third from SO2. The protonophilic interaction between organic solvents and SO2 seems to be a prerequisite of the reaction leading to the production of sulfur. As a result, an intermediate is formed between the solvent and SO2 and then reacts with H2S to produce sulfur and water. For example, the reaction of H2S and SO2 in the solvent of triethylamine follows the mechanism suggested by Bikbaeva and Baranovskaya7

it is essential that SO2 generated from the first reaction be consumed completely by the second reaction. To ensure maximum consumption of SO2 in process design, the kinetics of the two reactions must be known. The aim of this paper is to study the kinetics of the second reaction, eq 2, because that of the first reaction, eq 1, has been reported elsewhere.1 Hydrogen sulfide and sulfur dioxide do not react in gas phase unless moisture is present.2 Excluding water, hydrogen sulfide and sulfur dioxide will also react in solvents such as hydrocarbons,3 methanol,4,5 poly(glycol ether)s,6 and amines,7 and in the presence of solid surface8 and catalysts.9,10 The reaction between H2S and SO2 occurring in aqueous media is known as the Wackenroder reaction.11 “Liquid-phase Claus reaction” is also used to refer to reaction 2 that takes place in

(C2H5)3N‚‚‚SO2*(l) + H2S(g) 98 S(s) + H2O(l) + (C2H5)3N(l) (5)

* To whom correspondence should be addressed. Telephone: (780)492-4676.Fax: (780)492-2881.E-mail: karlt.chuang@ ualberta.ca.

Bikbaeva et al.7,26 also obtained similar mechanisms for the reaction in other solvents such as aromatic amine,

Keq

(C2H5)3N(l) + SO2(g) y\z (C2H5)3N‚‚‚SO2(l) K/eq

(C2H5)3N‚‚‚SO2(l) y\z (C2H5)3N‚‚‚SO2*(l)

(3) (4)

ktrue

SO2 becomes reactive after a definite orientation in the complex with the solvent molecule. In this case, the effective rate constant can be described by

keff )

ktrueKeqK/eq[(C2H5)3N][SO2] 1 + Keq[SO2]

10.1021/ie020275i CCC: $22.00 © 2002 American Chemical Society Published on Web 08/24/2002

(6)

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Table 1. Summary of Products Distribution of Liquid-Phase Claus Reaction liquid media

temp range

water

N/A

tolune water-alkali soln

room temp N/A

alkali-metal sulfite water-acid solution

below the dec temp of the soln N/A

colloidal aq soln of tragacanth gum liquid media butane

-5 °C temp range varying

aqueous medium diethylene glycol K benzoate-poly(ethylene glycol) dilute sulfuric acid methanol citrate-based soln water vapor methanol + sulfuric acid phosphate triethylene glycol dimethyl ether diethylene glycol methyl ether, plus 3-pyridyl carbinol as catalyst RxXO (X ) N, P, S) heterocyclic amines ammoniacal buffer solution

products or reaction routes (a) H2S + 3SO2 ) H2S4O6 (b) 2H2S + SO2 ) 3S + 2H2O when H2S/SO2 is small, (a) predominates when H2S/SO2 is large, (b) does colloidal sulfur pentathionic acid thiosulfate (passing 2H2S + SO2 mixture into solutions) 2H2S + SO2 ) 3S + 2H2O

ref Riesenfeld and Feld13 (1921)

Bary3 (1931) Deines and Grassmann14 (1934)

Udy15 (1948) Ross and Welde16 (1950); Welde17 (1951) Pagrien18 (1951) ref Dupasquier19 (1951)

N/A 20-30 °C 130 °C 14.7-36.3 °C N/A 120-130 °F N/A room temp ∼50 °C 120-160 °C 22 °C

sulfur containing 80% insoluble in CS2 water-soluble sulfur products or reaction routs mixing H2S-butane and SO2-butane solutions produces (a) S and (b) H2S5O6 when H2S/SO2 ) 2, (a) predominates when H2S/SO2 ) 1, (b) predominates increasing temp favors (b) (S2O)nH2O sulfur solid sulfur sulfur filterable sulfur elemental sulfur sulfur allotropic sulfur sulfur sulfur

Schenk and Kretschmer20 (1962) Andreev et al.21 (1970) Franckowiak et al.22 (1974) Tiwari23 (1976) Kozak4 (1980) Madenburg and Seesee24 (1980) Vilesov25 (1980) Kozak5 (1981) Donahue and Hayford (1985) Crean6 (1987)

21-60 °C N/A N/A

sulfur sulfur sulfur

Bikbaeva et al.26 (1988) Bikbaeva et al.7 (1989) Paj et al.27 (1995)

pyridine, and sulfoxides with various aliphatic and aromatic groups as the liquid media. It is obvious that eq 5 was not balanced stoichiometrically. The derivation of keff based on this equation is questionable. Volynskii11 proposed a mechanism for the reaction of H2S and SO2 in aqueous solutions. The formation of sulfur follows the steps below.

H2S + SO2 ) HSSO2H

(7)

HSSO2H ) S(OH)2 + S

(8)

S(OH)2 + H2S ) 2H2O + 2S (or S2)

(9)

The overall equation for the three steps is reaction 2. The formation of polythionic acids results from the interaction of ionized SO2 and monatomic or polyatomic sulfur, i.e.,

SO2 + H2O ) HSO3- + H+

(10)

HSO3- + S ) HS2O3-

(11)

Sx + 2HSO3- ) S(x+1)O6- + H2S

(12)

Sx + 2HS2O3- ) S(x+2)O6- + H2S

(13)

Sx + HSO3- + HS2O3- ) S(x+3)O6- + H2S (14) where, x can range from 1 to 7. Tiwari23 believed that the reaction of H2S and SO2 in dilute sulfuric acid (below 10 wt %) follows the scheme from (7) to (9). His kinetic data show that the reaction is first order with respect to both H2S and SO2, consistent with the scheme because he assumed reaction 7 to be the rate-controlling step.

However, our interest in this reaction system involves comparatively higher acid concentrations under which conditions little is known regarding the reaction kinetics. One difficulty in studying this reaction system is the simultaneous behavior of the two reactions in a gasliquid system. Fortunately, when the acid concentration is low, the first reaction no longer dominates and the rate of the second reaction can be measured by providing a feed of both H2S and SO2. In this way, the kinetics of the reaction between H2S and SO2 in the appropriate acid concentration range can be obtained. Experimental Method The apparatus and the experimental procedure were nearly identical to those used in the study of the kinetics of the first reaction.1 A constant-volume reactor vessel charged with a certain volume of sulfuric acid solution was connected to a feed system. The air in the reactor was evacuated, and the solution was heated to a preset temperature. Afterward, the sulfuric acid solution was saturated with SO2. As soon as H2S was introduced into the reactor, the reaction between H2S and SO2 started, and the reaction rate was recorded as a time function of total pressure-drop in a closed batch system. Nonetheless, the different behaviors between the first reaction and the second reaction had been taken into account in this study. First, the stoichiometric behavior of the second reaction is different from that of the first reaction. In the second reaction, 3 mol of gaseous reactants, i.e., 2 mol of H2S and 1 mol of SO2, are consumed to form liquid and solid products. Second, the total pressure drop contributed by the dissolution of SO2 has to be eliminated. To do so, the acid solution was presaturated with SO2 at a selected SO2 partial pressure. When H2S was introduced, SO2 had been in equilibrium between the gas and acid (liquid) phases. Third,

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the second reaction occurs not only on the surface of solution but also on the wetted walls inside the reactor, formed due to the condensation of water vapor. To prevent vapor condensation, the reactor wall above the solution was heated to 10-15 °C higher than the temperature of the solution. Both temperatures of the gas and solution in the experiments were measured under these circumstances. However, the wall was not heated when condensation did not occur. More detailed information on the equipment, experimental procedures, and materials can be found in ref 1. Results and Discussion Selection of Acid Concentration. There are two factors that determine the choosing of acid concentration range to be used in this study. First, the acid concentration range should locate where the rate of the first reaction, eq 1, is insignificant and that of the second reaction, eq 2, can be studied separately. Our previous study1 has indicated that the first reaction occurs between H2S and molecular H2SO4 in concentrated sulfuric acid solution and becomes insignificant when the acid concentration is less than 88 wt %. Young and Molrafen30 and Miller31 also showed that the concentration and activity of molecular H2SO4, the active species for the first reaction, are very small when the acid concentration is less than 65 wt %. Thus, the acid concentration range in this study was chosen no more than 60 wt %. Second, the acid concentration should not change the reaction route. As discussed in the section of introduction, the form of dissolved SO2 will determine the path and accordingly, the products of the reaction. The molecular dissolved SO2 leads to the production of sulfur and water, without the production of polythionic acids. Gold and Tyr32 and Govindora and Gopalakrishna33 reported that dissolved SO2 in sulfuric acid solution remains in the molecular form when acid concentration is greater than 5 wt %. Therefore, the range from 5 to 60 wt % H2SO4 meets the requirement for studying the second reaction. To avoid the very dilute solution where vapor condensation occurs, this study chose the acid concentration range from 30 to 60 wt %. Reaction Rate Measurement and Calculation. Similar to the behavior during the study of the first reaction, the formation of solid sulfur from the second reaction also blocks the solution surface and the production of water dilutes the acid solution. Once the reaction commenced, the available surface area and the acid concentration could not be predicted. To ensure the reaction rate was measured under known conditions, the initial rate was obtained at time zero by plotting the slope of the pressure-drop vs time curve, i.e.

RP )

(dP dt )

t)0

(15)

The disappearance rate of both gas reactants is calculated based on RP by the following equation

RPVG dNS d ) (NH2S + NSO2) ) dt dt RT

(16)

From the stoichiometry of reaction 2, the reaction rate in terms of H2S consumption is described by

dNH2S 2 dNS rH2S,2 ) )dt 3 dt

(17)

Figure 1. Typical pressure drop vs time cures. Temperature: 25 °C. Acid concentration: 30.16 wt %. Stirring speed: 50 rpm. Run no.: pd_test3&5.

The rate equation can be described by either eq 18 or eq 19

rH2S,2 ) k2a[H2S]m[SO2]n

(18)

rH2S,2 ) kP2aPH2Sm PSO2n

(19)

depending on whether the partial pressures, PH2S and PSO2, in the gas phase or the concentrations, [H2S] and [SO2], in the liquid phase of the reactants, are known. In these equations, a represents the interfacial area between gas and liquid, the same value as the cross sectional area of the cylindrical reactor in this study because the liquid surface was maintained flat in experiments. For a gas-liquid reaction, eq 19 seems to be the preferred expression since the partial pressures of the reactants are easily determined. kP2 is a global rate constant, which includes the effects of reaction temperature, reactant solubility, and acid concentration on the reaction rate. These effects sometimes compensate. For instance, rising temperature increases the reaction rate but decreases the solubility which, in turn, decreases the reaction rate. This compensation effect mainly comes from the term of SO2. H2S does not dissolve in sulfuric acid in significant quantity, as shown by curve 1 in Figure 1. Therefore, to eliminate this compensation effect, the following rate equation form was used.

rH2S,2 ) k′P2aPH2Sm[SO2]n

(20)

The reaction rate was measured at the equilibrium between PSO2 and [SO2], and the rate constant, k′P2, is only a function of temperature when acid concentration is a constant. SO2 Dissolution. SO2 dissolves significantly in sulfuric acid at all concentrations. In a closed gas-liquid batch reactor, the reaction stoichiometry results in changes in the system pressure, but the dissolution of SO2 in the acid also must be considered. Curve 1 in Figure 1 shows that the pressure-drop caused by the interaction between H2S and acid solution was negligible. H2S neither reacts nor dissolves in the dilute sulfuric acid solution to a detectable extent. Curve 2 indicates that the pressure drop caused by SO2 dissolution is significant. This contribution has to be eliminated

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Figure 2. SO2 dissolving rate in sulfuric acid solutions of 29.60 and 96.04 wt %. Temperature: 21 °C. Initial pressure of SO2: 8086.5 kPa. Stirring speed: 50 rpm. Run no.: pd_30_s1 and pd_96_s4.

by presaturated SO2 in the solution. When the equilibrium of SO2 in gas and liquid phases has been reached, the initial pressure drop may be attributed to the reaction only, as shown by curve 3. Figure 2 shows that the initial rate of SO2 dissolution is independent of acid concentration, and the same initial pressure of SO2 leads to the same initial dissolution rate. In the literature, the interaction of SO2 with either aqueous solutions or organic solvents was shown to induce the reaction of SO2 and H2S. In other words, the intermediates formed by SO2 in the solutions or in the solvents are reactive with H2S. If the dissolved SO2 remains in the molecular form, the reaction generates sulfur and water; but if some of the dissolved SO2 molecules are hydrolyzed and form HSO3-, polythionic acids are also produced. For sulfuric acid aqueous solutions, when the acid concentration is below 5 wt %, molecular SO2 and HSO3- coexist and the reaction in the solution may result in sulfur, water, and polythionic acids. However, when the acid concentration is 5 wt % or higher, the dissolved SO2 appears only in the molecular form,32,33 and accordingly, the reaction will give rise to sulfur and water but not polythionic acids. Tiwari23 erroneously ignored the forms of dissolved SO2 and the two reaction routes involved in his study. Under the acid concentration in his study (from 0.43 to 9.3 wt %), both molecular SO2 and HSO3- existed in the solution. In this case, both sulfur and polythionic acids would be produced when the solution reacted with H2S. Thus, his results are inconsistent with our measurements, where only one reaction route that leads to sulfur and water exists. Introduction of H2S. H2S was introduced into the reactor after the concentrations of SO2 present in both phases had equilibrated. Either pure H2S or an H2S/ SO2 mixture having a partial pressure of SO2 equal to the equilibrium pressure of SO2 in the reactor was introduced so as to keep the SO2 equilibrium unchanged during this introduction. An impeller was installed in the gas phase of the reactor to improve the mixing of the introduced gas and the gas already present within the reactor. To study the effect of this mixing on the rate measurement, different stirring speeds were used while the other experimental conditions were kept the same. As shown in Figure 3, the same initial rate of pressure drop was obtained when the impeller was stirred as fast as 40 rpm. The stirring speed could not

Figure 3. Effect of stirring speed. Temperature: 25 °C. Acid concentration: 30.16 wt %. Run no.: pd_st2, pd_p1, and pd_st6.

be too fast because of the need to maintain a flat surface on the solution. All runs were carried out at 50 rpm. Orders of Reaction with Respect to H2S and SO2. For 30 wt % sulfuric acid solution, the initial pressuredrop rate was measured at 25 °C at various random initial values of PH2S and [SO2]. The results are shown in Table 2. The linearization of eq 20 leads to

ln rH2S,2 ) ln(k′P2a) + m ln PH2S + n ln[SO2] (21) The calculated results of ln rH2S2, ln PH2S and ln[SO2] obtained from Table 2 were plotted in a 3-D diagram, as shown in Figure 4. The regressional analysis yielded values for m and n at 1.22 and 1.07, respectively. Rounding these numbers to unity suggests that the reaction could be described by second-order kinetics (first order with respect to each of the two reactants, H2S and SO2). The value of k′P2 was then calculated for each run with the following equation

k′P2 )

rH2S,2 aPH2S[SO2]

(22)

which is also shown in Table 2. The values of k′P2 thus obtained are of the same order of magnitude. The average of k′P2 is 4.40 × 10-7 L s-1 m-2 Pa-1. Effect of Interfacial Area. Because the liquid in this study was maintained flat, the surface area of the liquid is assumed the same as the interface area. Cylindrical- and conical-shaped reactor vessels were used to measure the reaction rate at different ratios of liquid volume to interfacial area. Figure 5 shows that similar values of k′P2 were obtained at different surface areas and solution volumes. Because k′P2 is based on the unit surface area, this result indicates that the reaction rate is proportional to surface area and not affected by the volume of solution; i.e., the reaction takes place at the surface but not in the bulk of the solution. Figure 1 shows that H2S does not diffuse into the solution of sulfuric acid significantly (curve 1) but reacts rapidly when the solution has been saturated with SO2 (curve 3). It is reasonable to assume that the reaction of H2S with the dissolved SO2 is much faster than the diffusion of H2S into the solution. Once the H2S molecules contact the dissolved SO2 molecules, they react so fast that no H2S molecules are present at the liquid surface preventing them from diffusing into the bulk

Ind. Eng. Chem. Res., Vol. 41, No. 19, 2002 4711 Table 2. Experimental Results for Reaction Order run no.

acid concent, wt %

VL × 104, m3

VG × 104, m3

soln temp, K

gas temp, K

a × 103, m2

PH2S, kPa

[SO2], mol L-1

RP, kPa s-1

k′P2 × 107, L s-1 m-2 Pa-1

pd_newp4 pd_newp3 pd_newp2 pd_newp1 pd_new4 pd_newp5 pd_newp6

30.1 30.1 30.1 30.1 30.1 30.1 30.1

2.00 2.00 2.00 2.00 2.00 2.00 2.00

5.88 5.88 5.88 5.88 5.88 5.88 5.88

298.15 298.15 298.15 298.15 298.15 298.15 298.15

294.15 294.15 294.15 294.15 293.15 293.15 293.15

4.42 4.42 4.42 4.42 4.42 4.42 4.42

112 101 103 82.5 83.4 73.2 62.5

0.667 0.695 0.804 0.722 1.00 1.24 1.55

-0.935 -0.896 -0.985 -0.689 -1.03 -1.13 -1.1

4.54 4.63 4.31 4.19 4.49 4.53 4.13

Figure 6. Arrhenius plot of reaction in sulfuric acid from 30 to 60 wt %. Figure 4. Reaction orders with respect to H2S and SO2. Temperature: 25 °C. Acid concentration: 30.10 wt %. Stirring speed: 50 rpm. Run no.: see Table 2.

where SO2(d) represents dissolved SO2 in sulfuric acid solutions. Many investigators11 believed that H2S and dissolved SO2 in aqueous solutions initially form thiosulfurous acid. Sulfur and water are formed through the following steps, as suggested by Volynskii11

Figure 5. Effect of surface area (A) on the reaction rate. Temeperature: 25 °C. Acid concentration: 30.16 wt %. Stirring speed: 50 rpm. Solution volume: 200, 300, 500, and 800 mL, respectively.

Steps 23, 25, 26, and 27 are either physical process or intermediate transformation, which occur relatively rapidly. Assuming the gas-liquid reaction, step 24, to be rate controlling, this mechanism would be in agreement with the kinetic results that the reaction is of first order with respect to the partial pressure of H2S and the concentration of SO2. Effect of Temperature and Acid Concentration. The reaction rates were measured at various temperatures from 21 to 50 °C and acid concentrations from 30 to 60 wt %. The rate constant for each run was calculated using eq 22. The plot of ln k′P2 against 1/T is shown in Figure 6, indicating that the relationship between temperature and k′P2 for the investigated acid concentrations fits a single Arrhenius equation. In other words, the second reaction has the activation energy (Ea ) 59.02 kJ mol-1) and preexponential factor (A0 ) 11 790), which are independent of acid concentration. This is contrary to that observed for the first reaction, in which the activation energy and preexponential factor change

solution. Generally, the reaction behavior of a gasliquid reaction is determined by the relative value of the reaction rate and the diffusion rate of reactants within the liquid phase. In this case, the diffusion rate of H2S is small compared with the reaction rate. Therefore, the reaction occurs only at the surface of the acid solution. The initial mechanism of the reaction may be described by the following

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Conclusions The kinetics of the reaction between H2S and SO2 was measured. It was found that SO2 dissolves in sulfuric acid to form an active intermediate that participates in the reaction between H2S and SO2. The reaction was found to occur at the interface between the acid and gas phase because the diffusion of H2S into the bulk of the sulfuric acid phase is very slow. The molecular form of dissolved SO2 in aqueous sulfuric acid solutions is responsible for the formation of sulfur and water as the only products. The reaction in sulfuric acid exhibits firstorder behavior with respect to H2S and to SO2. The sulfuric acid phase merely provides a medium for the reaction, and therefore, its concentration does not affect the rate constant. Test results also show that the rate equation is applicable at the high acid concentrations. Figure 7. Comparison of the second reaction rate predicted by eq 28 with that obtained in experiments at various temperatures and acid concentrations.

concentration.1

with acid The differences may be attributed to the facts that sulfuric acid solution is involved in the first reaction as an oxidant but acts merely as a reaction medium for the second reaction. The reactant in the medium is dissolved SO2. The role that the sulfuric acid plays in the reaction also differs from that shown by the organic solvents, in which one SO2 molecule forms an intermediate with one solvent molecule, and accordingly, the concentration of the solvent was included in the kinetic equations.6,7,26 Our results suggest that the form of SO2 dissolved in sulfuric acid determines the path of the reaction. If its structure does not change, neither the reaction mechanism nor its kinetics behavior should change. Dissolved SO2 maintains its molecular form when acid concentration is in the range 30-60 wt %. This form also applies to the acid concentrations greater than 60 wt %. Therefore, the reaction mechanism and kinetics behavior exhibited in acid concentrations up to 60 wt % may be extrapolated to acid concentrations above 60 wt %. To confirm the validity of this extrapolation, runs were made to measure the initial reaction rate at acid concentrations of 90 and 96 wt %, where the solutions were presaturated with SO2. When H2S reacts with the fresh concentrated sulfuric acid, the first reaction causes the reactor pressure to drop because the produced SO2 tends to stay in the solution. However, when the solution was presaturated with SO2, the first reaction no longer causes a change in total pressure. Thus, the drop in pressure may be attributed to the second reaction. The reaction rate measured under each experimental condition was compared with the value predicted by eq 28.

rH2S,2 ) k′P2aPH2S[SO2], mol s-1

Acknowledgment The authors acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada and the Alberta Oilsands Technology and Research Authority and the beneficial discussions with Dr. Qinglin Zhang. Nomenclature a ) surface area, m2 A0 ) preexponential factor, L s-1 m-2 Pa-1 Ca ) apparent sulfuric acid concentration, wt % Ea ) activation energy, J/mol kC2 ) specific reaction rate in terms of molarity concentration kP2 ) specific reaction rate in terms of pressure of reactants k′P2 ) specific reaction rate defined by eqs 19 and 24, L s-1 m-2 Pa-1 N ) number of moles, mol P ) pressure, Pa or kPa R ) gas constant, J mol-1 K-1 RP ) pressure drop rate, kPa s-1 or Pa s-1 r ) reaction rate, mol s-1 T ) temperature, K V ) volume of gas phase, m3 t ) time, s [H2S] ) molarity concentration of H2S in solution, mol L-1 [SO2] ) molarity concentration of SO2 in solution, mol L-1 Superscripts and Subscripts d ) dissolving G ) gas L ) liquid m ) reaction order n ) reaction order P ) pressure S ) sulfur 0 ) refer to time zero or bulk area 1 ) refer to reaction 1 2 ) refer to reaction 2

(28)

Figure 7 shows that the predictions are in good agreement with the experimental data. So far, we have obtained two global rate equations respectively describing the rates of the two reactions. With these two equations, we should be able to predict the temperature and acid concentration enabling the two reactions to proceed stoichiometrically at any chosen PH2S and PSO2.

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Received for review April 15, 2002 Revised manuscript received July 9, 2002 Accepted July 9, 2002 IE020275I