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Doklady Chemistry, Vol. 376, Nos. 1–3, 2001, pp. 34–37. Translated from Doklady Akademii Nauk, Vol. 376, No. 1, 2001, pp. 69–72.Original Russian Text Copyright © 2001 by Balaev, Konshenko, Spivak, Ismagilov, Dzhemilev.

In practical implementation of partial oxidation ofhydrogen sulfide, it is of prime importance to determinethe maximum allowable inlet hydrogen sulfide concen-tration, above which a thermal explosion in the reactoroccurs. For this purpose, the dependence of the ignitiontemperature on the inlet temperature should be found.In its turn, this requires one to construct a mathematicalmodel of the process that would allow for the change inthe amount (the number of moles) of the reaction mix-ture, and for the thereby induced additional heat andmass transfer. Approaches that are necessary for con-structing such models fundamentally differ from thoseneeded for formulating the standard kinetic model ofthe process.

The mechanism of catalytic partial oxidation ofhydrogen sulfide has been studied in the reaction overactivated carbon [1] and metal oxide catalysts [2, 3].Different hypotheses of the reaction mechanism havebeen put forward, the kinetics parameters of the reac-tion have been found, and various kinetic equations forthis process have been proposed.

In this study, we developed an unsteady mathemati-cal model of a fluidized-bed catalytic reactor and, onthe basis of this model, performed a computationalexperiment, thus determining the starting conditions,and the effect of the main technological parameters onthe process.

Partial oxidation of hydrogen sulfide yields waterand elemental sulfur. The process takes place at tem-peratures of

200–280°ë

and contact times of 1–4 s.Under these conditions, sulfur is produced in the formof finely divided solid particles. A part of the sulfurformed is retained in the adsorbed state on the activesurface of the catalyst and deactivates it. The other partis desorbed into the gas phase to form the species S

2

,which then polymerizes into the species S

4

,

S

6

, and S

8

[4]. All the finely divided species are in equilibrium.Three possible mechanisms of the hydrogen sulfide

oxidation were examined, which allow for (a) dissocia-

tive adsorption of oxygen, (b) hydrogen sulfide adsorp-tion, and (c) simultaneous adsorption of oxygen andhydrogen sulfide.

Collation between calculated and experimental datashowed that the scheme (a) fits the experimental datawell enough and, thus, can be used for the mathemati-cal modeling of the reactor.

The scheme (a) of the chemical reactions over ametal oxide catalyst has the form:

1)

O

2

+ [

K

]

⇔

[

KO

2

],

W

1

=

k

1

x

1

z

1

–

k

6

z

2

;

2) [

KO

2

] + [

K

] 2[

KO

],

W

2

=

k

2

z

1

z

2

;

3)

H

2

S

+ [

KO

]

H

2

O

+ [

KS

],

W

3

=

k

3

x

2

z

3

;

4) 2[

KS

] [

K

] + [

KS

2

],

W

4

=

k

4

;

5) [

KS

2

] [

K

] +

S

2

,

W

5

=

k

5

z

5

;

6) [

KS

] [

KS

]

d

,

W

d

=

k

d

z

4

;

7)

S

2

⇔

S

4

⇔

S

6

⇔

S

8

.

Here,

z

i

are the concentrations of surface complexes:

z

1

,[K];

z

2

,

[

KO

2

]

;

z

3

, [KO];

z

4

, [KS];

z

5

,

[

KS

2

];

and

x

i

arethe concentrations of the components:

x

1

, O

2

;

x

2

= H

2

S;

x

3

, H

2

O;

x

4

, the species S

2

, …,

S

8

.Of significance is that the mathematical model takes

account of the catalyst deactivation and of the changein the amount of the reaction mixture.

The catalyst deactivation is brought about by a por-tion of the sulfur produced being deposited on theactive catalyst surface and blocking it. The catalystdeactivation is described by the equations

(1)

where

C

S

and are the amount of the sulfur depos-ited on the catalyst and its limit value, respectively;

G

c

and are the catalyst weight and its initial value,respectively;

W

d

is the deactivation rate,

ϕ

is the activityloss function,

M

S

is the molecular weight of sulfur, and

V

c

is the catalyst volume.

z42

dCS

dt--------- GcWdϕ , ϕ 1

CS

CS*-------,–= =

Gc Gc0 GS, GS+ CSMSV c, CS 0( ) 0,= = =

CS*

Gc0

CHEMICALTECHNOLOGY

Modeling of Partial Oxidation of Hydrogen Sulfide over Metal Oxide Catalysts

A. V. Balaev, E. V. Konshenko, S. I. Spivak, F. R. Ismagilov,and Corresponding Member of the RAS U. M. Dzhemilev

Received September 20, 2000

Institute of Petrochemistry and Catalysis, Ufa Scientific Center, Russian Academy of Sciences, pr. Oktyabrya 141, Ufa, 450075, Bashkortostan, Russia

DOKLADY CHEMISTRY Vol. 376 Nos. 1–3 2001

MODELING OF PARTIAL OXIDATION OF HYDROGEN SULFIDE 35

The change in the amount of the reaction mixture isalso caused by the sulfur deposition on the catalyst. Thedensity of the solid product is 1000 times higher thanthat of the gas; therefore, the formation of S2, …, S8 inthe gas phase noticeably decreases the reaction amount.Moreover, in a certain initial period of time, an addi-tional contribution to the decrease in the amount of thereaction mixture is made by the oxygen adsorption onthe catalyst surface.

The concentrations of the surface complexes arefound from the quasi-stationarity condition.

With regard for all the above phenomena, the math-ematical description of the partial oxidation of hydro-gen sulfide in an isothermal well-stirred reactor is givenby the set of equations

(2)

(3)

(4)

The initial conditions were t = 0: xi = and N = 1.Here, N is the amount of the reaction mixture, I is thenumber of the components, J is the number of the reac-tions, M is the number of the types of the surface com-plexes, kI1 is the constant of inhibition by hydrogen sul-fide, kI2 is the constant of inhibition by water, Wj is thereaction rate, νij and δj are the stoichiometric coeffi-cients, and Vr is the reactor volume.

Using mathematical description (1)–(4), we solvedthe inverse kinetic problem [5] of finding the kineticparameters on the basis of experimental data obtainedat the Institute of Petrochemistry and Catalysis. Below,the numerical values of the kinetic parameters are pre-sented; the dimensions of the constants ki (i = 1, 2, …,6) are 1/s; kd, g of sulfur per g of catalyst per s; the acti-vation energies Ei (i = 1, 2, …, 6), Ed, and the heats ofadsorption of hydrogen sulfide (Q1) and water (Q2),kJ/mol:

k1 = 0.523, E1 = 81.2;

k2 = 0.888, E2 = 63.6; k3 = 172, E3 = 85.8;

νmjW j

m 1=

M

∑ 0, m 1 2 … M 1,–, , ,= =

zm

m 1=

M

∑ 1,=

dxi

dt-------

Fi xiFN–( )N

---------------------------, i 1 2 … I ,, , ,= =

Fi ϕ ν ijωj,j 1=

J

∑=

1V r-----dN

dt------- FN ϕWd– ϕ δjωj,

j 1=

J

∑+= =

ωj

W j

1 kI1x2 kI2x3+ +---------------------------------------, δj ν ij.

i 1=

I

∑= =

xi0

k4 = 0.056, E4=76.6;

k5 = 0.107, E5 = 39.8; k6 = 0.0073, E6 = 90.4;

kd = 9.7 × 10–4, Ed = 116.8;

kI1 = 0.013, Q1= 52.3; kI2 = 0.039, Q2 = 51.5.

For modeling the process, an unsteady two-phasemodel of a fluidized-bed catalytic reactor was elabo-rated. The model takes into consideration the heat andmass transfer in the dense phase by conduction and lon-gitudinal diffusion, and the heat and mass transfer inthe dense and bubble phases by convection and by theStefan flow [6]. The hydrodynamic and thermophysicalparameters were calculated from empirical criterionequations. The complete mathematical description ofthe process has the form:

(5)

(6)

(7)

(8)

(9)

The initial and boundary conditions were t = 0: U = U0,

yi = 0, xi = , T = T0, Θ = Θ0; l = 0: U = U0, xi = ,T = T0.

(10)

Here, xi and yi are the concentrations of the componentsin the dense and bubble phases, respectively; Wj is thereaction rate; U is the linear velocity of the gas flow; qis the fraction of the flow that passes through the densephase; µ is the Stefan flow velocity; βh and βm are theheat- and mass-transfer coefficients, respectively; ε andε0 are the porosities of the expanded and stationarybeds, respectively; D is the diffusion coefficient; at isthe thermal diffusivity; Θ, T, and Tcool are the tempera-

εq∂yi

∂t------- qU

∂yi

∂l-------+ D

∂2yi

∂l2--------- f βmSsp µ+( ) xi yi–( )+=

+ f ν ij yiδj–( )W j

C0------,

j 1=

J

∑

ε 1 q–( )∂xi

∂t------- 1 q–( )U

∂xi

∂l-------+ f βmSsp yi xi–( ),=

µ 1 q–( ) δj

W j

C0------

j 1=

J

∑–ε0

ε 1 ε–( )-------------------Udε

εdl----------,–=

εCc

Cr-----∂Θ

∂t------- qU

∂Θ∂l-------+ at

∂2Θ∂l2--------- f βhSsp µ+( ) T Θ–( )+=

+α xSx

Cr----------- Tcool Θ–( ) f ∆T j

W j

C0------,

j 1=

J

∑+

ε 1 q–( )∂T∂t------ 1 q–( )U

∂T∂l------+ f βhSsp Θ T–( ).=

xi0 xi

0

D∂yi

∂l------- qU yi xi

0–( ), at∂Θ∂l------- qU Θ T0–( ),= =

l H: at∂Θ∂l------- D

∂yi

∂l------- 0.= = =

36

DOKLADY CHEMISTRY Vol. 376 Nos. 1–3 2001

BALAEV et al.

tures of the catalyst, the gas, the cooler, respectively; T0is the inlet temperature; Cc and Cr are the specific heatsof the catalyst and the gas, respectively; l and H are theaxial coordinate and the height of the expanded bed,respectively; f is the reciprocal of the coefficient of bedexpansion; αcool and Scool are the coefficient of heattransfer through the wall of the cooler and its surfacearea, respectively; C0 is the molar density of the gas,which is determined from the equation of state of, e.g.,an ideal gas.

The sets of Eqs. (1) and (5)–(10) were numericallysolved by balance difference schemes, whose construc-tion has been described in detail in the literature [7].For calculating the Stefan flow velocity and automati-cally choosing the step of integration with respect to thetime coordinate, the algorithm was modified asreported previously [6].

With the use of the mathematical description of theprocess, a computational experiment was carried out,which gave the following results.

The dependence of the ignition temperature on theinlet temperature has been found. Figure 1 demon-strates the results of calculations at two values of theinitial catalyst temperature Θ0.

If the hydrogen sulfide concentration in the inletflow is no higher than 8 vol %, then one can dispensewith heat withdrawal and perform the process underadiabatic conditions.

At 15–17 vol % inlet hydrogen sulfide concentrations,one can ensure good heat removal and reach no lowerthan 99% conversion. For this case, Fig. 2 shows the tem-perature profiles in the dense and loose phases, and Fig. 3portrays the hydrogen sulfide concentration profiles.

If the inlet hydrogen sulfide concentration is above25 vol %, one cannot abstract a sufficient amount of

heat; therefore, in the initial portion of the bed, a ther-mal explosion actually occurs. Figure 4 plots the tem-perature profiles in the dense and the loose phases dur-ing thermal explosion.

The mathematical model we developed is new andmost complete. The model takes into account not onlythe sulfur production in the form of S2, but also thepolymerization of this dimer into the species S4, andS8 being in thermodynamic equilibrium. The modelallows for the catalyst deactivation because of the sul-fur deposition on the active surface. The two-phasediffusion model, which takes account of the change inthe reaction volume, and of the thereby induced heatand mass transfer due to the Stefan flow, is radicallynovel.

55 70

168

171

170

169

167

166

16560 65 75 80

1

2

Ignition temperature, °C

Inlet temperature í0, °C 0.2

220

340

300

260

180

140

1000.4 0.6 0.8 1

Temperature, °C

Distance along reactor height, m

Θ

Τ

0

Fig. 1. Ignition temperature versus inlet temperature: (1)inlet hydrogen sulfide concentration 10 vol %, no heatremoval; (2) inlet hydrogen sulfide concentration 17 vol %,heat removal surface area 16 m2/m3.

Fig. 2. Temperature profiles in the dense and loose phases atthe inlet hydrogen sulfide concentration 17 vol % and theheat removal surface area 16 m2/m3.

0.2 0.6

10

8

6

4

2

0 0.4 0.8 1

x, y, vol %

Distance along reactor height, m

x

y

Fig. 3. Hydrogen sulfide concentration profiles in the denseand loose phases at the inlet hydrogen sulfide concentration17 vol % and the heat removal surface area 16 m2/m3.

DOKLADY CHEMISTRY Vol. 376 Nos. 1–3 2001

MODELING OF PARTIAL OXIDATION OF HYDROGEN SULFIDE 37

The new approaches to modeling have enabled oneto compute the ignition temperature and estimate theconditions of thermal explosion in the reactor.

REFERENCES

1. Pan Zhenglu, Hung-Shan Weng, Feng Han-Yu, andSmith J.M., AIChE J., 1984, vol. 30, no. 6,pp. 1021−1024.

2. Alkhazov, T.G. and Amirgulyan, N.S., Kinet. Katal.,1982, no. 5, pp. 1130–1134.

3. Zagoruiko, A.N. and Mokrinskii, V.V., Abstracts ofPapers, XIV Mezhdunarodnaya konferentsiya pokhimicheskim reaktoram (XIV Int. Conf. on ChemicalReactors), Tomsk, 1998, pp. 155–156.

4. Alkhazov, T.G. and Amirgulyan, N.S., Sernistyesoedineniya prirodnykh gazov i neftei (Sulfurous Com-pounds of Natural Gas and Petroleum), Moscow: Nedra,1989.

5. Spivak, S.I., Syst. Anal. Model. Simul., 1995, vol. 18/19,pp. 107–110.

6. Balaev, A.V., Drobyshevich, V.I., Gubaidullin, I.M., andMasagutov, R.M., Rasprostranenie teplovykh voln vgeterogennykh sredakh (Propagation of Heat Waves inHeterogeneous Media), Novosibirsk: Nauka, 1988,pp. 233–246.

7. Drobyshevich, V.I. and Il’in, V.P., Matematicheskoemodelirovanie khimicheskikh reaktorov (MathematicalModeling of Chemical Reactors), Novosibirsk: Nauka,1984, pp. 128–144.

0.2 0.6

450

350

300

250

200

0.4 0.8 1

Temperature, °C

Distance along reactor height, m

400

150

100

Θ

Τ

0

Fig. 4. Temperature profiles in the dense and the loosephases during thermal explosion at the inlet hydrogen sul-fide concentration 25 vol % and the heat removal surfacearea 16 m2/m3.