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Kinetics of catalytic reaction of methane and hydrogen sulphide over MoS2
~
AA PT PA LE IY DSS C L I A: GENERAL
ELSEVIER
Applied Catalysis A: General 165 (1997) 249-258
Kinetics of catalytic reaction of methane and hydrogen sulphide over MoS2 S.K. Megalofonos, N.G.
Papayannakos*
Laborato~ of Chemical Process Engineering, Department of Chemical Engineering, National Technical Universi~' of Athens, Heroon Polytechiou, 9 GR-157 73 Zografos, Athens, Greece Received 27 January 1997; received in revised form 10 June 1997: accepted 10 June 1997
Abstract
The reaction of methane and hydrogen sulphide over MoS2 catalyst has been studied in a fixed bed tubular reactor over a temperature range of 973 to 1073 K under atmospheric pressure and for space time between 0.1 and 1 s. The LangmuirHinshelwood-Hougen-Watson theory has been used to determine eighteen (18) rival kinetic models. Model discrimination has been performed by using statistical and thermodynamic constraints. According to the proposed model, the rate-controlling step is the reaction among the absorbed species CH3, H2S and S on the catalytic surface with the participation of three catalytic sites. The catalyst selectivity is also discussed. © 1997 Elsevier Science B.V.
Keywords: Hydrogen sulfide; Methane; Kinetics; Molybdenum sulfide
1. I n t r o d u c t i o n In recent times the availability of liquid fuels reserves is constantly declining. This reality has triggered research for the discovery of new solutions using other energy resources. Natural gas reserves, albeit not abundant any more world-wide, are still large enough, especially when compared with the petroleum ones, to justify efforts for the processing of natural gas and the use of methane as a raw material for the production of fuels [1]. Catalytic Steam Reforming is a widely used method today either to produce hydrogen or to give syngas as the first stage for the conversion of methane into liquid *Corresponding author. Tel.: (+30-1)7723239; fax: (+30-1) 7723155: e-mail [email protected], 0926-860X/97/$17.00 ~ 1997 Elsevier Science B,V. All rights reserved. PII S0926-860X(97)00206-8
fuels. The thereby produced syngas is converted either into methanol with the Mobil technology and then into liquid hydrocarbons or directly into hydrocarbons through the Fischer-Tropsch synthesis. In order to increase effectiveness and control over products distribution, the use of ZSM5 catalysts is combined with Co in the latter process. Besides, the use of MoS2 catalysts is under research [2]. Another promising method, but still under development, is the oxidative coupling of methane yielding oligomers that can further be processed to produce light liquid hydrocarbons. The reaction of methane with hydrogen sulphide can be considered as the first step of an alternative route to produce light hydrocarbons from methane [3]. The products of this reaction, hydrogen and carbon disulphide, can further react under different conditions
250
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
to produce light hydrocarbons: nCSz + (3n + 1)H2~-CH2n+2 + 2nH2S
In a study of homogeneous decomposition ofhydro(1)
Another way to consider the reaction of hydrogen sulphide with methane is to produce hydrogen, a valuable chemical and clean energy source, and the solvent carbon disulphide. Thus, the hydrogen sulphide produced as a by product of the hydrodesulphurization processes in refineries can be used to produce hydrogen or light hydrocarbons from methane. Natural gases containing H2S could also be considered as possible feedstocks to a process based on this reaction, It should be noted that sulphur instead of hydrogen sulphide can react with methane. Although this reaction can yield higher conversions of methane at lower temperatures, its use in a production process scheme will entail a sulphur production stage and a hydrogen production process to furnish the supplementary amount of hydrogen for the reaction, The open literature concerning the kinetic study of the methane-hydrogen sulphide reaction is very poor. Most of the papers studied deal with the kinetics and chemical reaction rates of parallel reactions taking place in the context of the methane-hydrogen sulphide reaction. Chen et al. [4] have studied the thermal decomposition of methane in the temperature range of 8501103 K. The reaction mechanism suggested by them assumes the existence of free methyl radicals in the gas phase. Chen et al. [5] who studied the same reaction, calculated a total conversion at 1000 K not overcoming the 2% in a static system for 30 rain residence time. Palmer and Hirt [6] studied the pyrolysis of methane at temperatures over 1000 K in a shock tube reactor. They argue that during the first stage of the methane pyrolysis both methyl or methylene radicals can exist, Anderson et al. [7] have studied theoretically the methane activation over MoS2 catalyst. They conclude that methane is chemisorbed on the MoS2 surface and dehydrogenated to methyl and methylen. Further dehydrogenation leads to the creation of CH and C species chemisorbed on the catalyst surface but these are unstable and have a very short life time. They also made relevant observations in a study of the FischerTropsch catalytic conversion over MoS2 [2].
gen sulphide, Kaloidas and Papayannakos [8] suggest a free radical mechanism. In accordance with their findings, hydrogen sulphide is decomposed into radicals "H and "SH which create "S radicals. They [9] also studied the heterogeneous catalytic reaction of hydrogen sulphide with MoS2 catalyst. In accordance with the suggested reaction mechanism, hydrogen sulphide is chemisorbed on the surface of the catalyst. The chemisorbed hydrogen sulphide is decomposed into S atoms which occupy an active site and hydrogen which is desorbed in the gas phase. During second stage atomic sulphur is desorbed and reacts in the gas phase to molecular Se. Kolts [10] concluded that presence of hydrogen sulphide accelerates the decomposition rate of light hydrocarbons through a free radical mechanism. Object of this paper is the study of the kinetics of the methane-hydrogen sulphide catalytic reaction by using MoS2 as a catalyst, in the temperature range of 973-1073 K and at 0.1 MPa total pressure.
2. Experimental Two coaxial c~-A1203 tubes in a down flow configuration were used as reactor. The internal diameter of the outer tube was 11.5 mm and the external diameter of the inner tube was 5.5 mm. The length of the tubes was 0.80 m. A four zone electric furnace was regulating the temperature distribution in the reactor according to the experimental requirements, using four electronic controllers. The temperature was monitored by thermocouples placed at fixed points outside the outer tube as well as inside the inner tube. One inner travelling thermocouple was also used to measure the temperature distribution along the reactor length in the course of each experiment. The accuracy of the temperature measurements was + 1 K. The H2S and C H 4 flow rates at the inlet of the reactor were measured independently using a capillary system calibrated with a bubble flowmeter. The total volumetric flow rate was measured at the reactor outlet using a bubble flowmeter. The temperatures as well as the flow rates and the pressure at the inlet of the reactor were monitored through an IBM P.C. system. The chemical composition of the gas at the inlet and outlet of the reactor was determined by a gas
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
chromatograph bearing a thermal conductivity detector and a 5.48 m Porapak-Q column. Nitrogen was used as carrier gas. The gas-chromatograph was calibrated with pure HaS, CH4 and Ha gases and with gas mixtures of CH 4 and CSa. All gases employed in the experiments were of a purity over 99.5%, with the exception of the carrier gas of the gas chromatograph the purity of which was 99.999%. The catalyst was MoSa powder of VENTRON GMBH, with a purity greater than 98%. The powder was compressed and agglomerated into particles of an average diameter, dp=0.0282 cm. The gas composition at the inlet of the reactor was double checked through the measurement of the inlet flow rates and the gas chromatography, A maximum deviation of i 2 % was observed. The input--output mass balances were tested in each experiment and their difference was found to be lesser than 3%.
3. Results and Discussion 3.1. Proposed kinetic models and reaction paths
In the technical kinetic study of the methanehydrogen sulphide reaction, it is assumed that two chemical reactions are taking place: The hydrogen sulphide-methane reaction to carbon disulphide and hydrogen and the catalytic decomposition of hydrogen sulphide to sulphur and hydrogen. Although not favoured thermodynamically, the latter is a very rapid one. The reaction rate of the catalytic decomposition of hydrogen sulphide proposed by Kaloidas and Papayannakos [10] was considered, as it concerns the same catalytic system and the same operating conditions. The methane dimerization reaction is of no interest for the purposes of the present study as it is a slow reaction [5,11] and not favouredthermodynamically [12], and thus was not taken into account along with the rest of the reactions taking place in the gas phase, The homogeneous, hydrogen sulphide-methane thermal reaction was studied experimentally in the same apparatus and it was observed that the molar fractions of the yielded hydrogen and carbon disulphide at the reactor outlet were less than the experi-
251
mental error of the analysis at the same experimental conditions for the catalytic reaction. As a consequence, the thermal reaction does not affect the catalytic results and consequently the parameter estimation of the kinetic models. The chemisorption and reaction steps considered in this study are given below. 3.1. I. Chemisorption on the catalytic surface The hydrogen sulphide molecules are chemisorbed on the surface of the catalyst so that each molecule occupies an active site.
H2S + ®v~+~-~rt2s Two possible ways can be considered for the formation and chemisorption of methylenes on the active sites. 1. The methane molecules are thermally dissociated in the gas phase creating hydrogen and methylene radicals. The former react to hydrogen while the latter are chemisorbed on the catalytic sites and each radical occupies one active site. 2. Another way postulates the chemisorption of methane on one active site, the loosening of the hydrogen-carbon bonds and the creation of gas hydrogen and chemisorbed methylenes. However, the chemical equation expressing the chemisorption mechanism as a whole is same in both cases. CH4 ÷ ®v ~- ®CHd ÷
(4
-- d) H2 2 Sulphur desorption from the catalytic surface can be considered in the following two ways. 1. Sulphur produced during the catalytic decomposition of hydrogen sulphide is desorbed from the active sites in two stages. At the first stage, the atomic sulphur-active sites bonds are loosened and atomic sulphur is desorbed in the gas phase. At a second stage, S-S bonds are created yielding molecular diatomic sulphur [10]. 2. Following another kinetic path, the chemisorbed sulphur atoms develop S-S bonds and give sulphur molecules, each one chemisorbed on two catalytic sites. These chemisorbed molecules are then desorbed in the gas phase. The chemical equation expressing the total sulphur desorption process is the same for both the above
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
252
described paths. __..1 ®s+--~S2 + ®v Each carbon disulphide molecule is considered to f~
/D(4--d)/2~ D ( 2 - v ) / 2 . p v )rs2 H2S
Ri = kRi • ~rCH4/rH2
The equation of the reaction rate for all the eighteen models derived from the above reaction paths, which are presented in more details in a previous paper [13], is given in the general form:
(1/KeqRi) • Pcsz " (PHz) (2v+d)/2 ,
[PH2s + Kps " p1/2s2 + KpcsP~c/22 + KpcHe " Pcl-h/e(H4?d)/2] c
(2)
desorb from two catalytic sites. The above mentioned sorption steps are considered to be very rapid when compared with the chemical reaction of the various species on the catalytic surface, being thus always in equilibrium,
The Langmuir-Hinshelwood-Hougen-Watson theory has been used to determine the equation of the reaction rate with the assumption that the concentration of the unsaturated sites is very low in comparison with the concentration of the saturated ones.
3.1.2. Reactions on the catalytic surface
The next section deals with the modelling of the fixed bed solid catalytic reactor, with a view to evaluate the kinetic parameters of Eq. (2) which describes mathematically the methane-hydrogen
Two catalytic reactions are taking place on the catalytic surface. The catalytic decomposition of the chemisorbed hydrogen sulphide to sulphur and hydrogen and the reaction of the chemisorbed species to produce hydrogen and carbon disulphide. For the first reaction, the loosening of the hydrogen-sulphur bonds, the creation of hydrogenhydrogen bonds and the desorption of molecular hydrogen has been proposed [9]. For the second reaction, eighteen different reaction paths can be considered with the participation of two or three active sites: 1. The reaction of either CH4 or *CH3 or "CH2 (CHd, where d=4,3 and 2) in the gas mixture with two chemisorbed sulphur atoms (v=0) or with one chemisorbed sulphur atom and one chemisorbed hydrogen sulphide ( v = l ) or with two chemisorbed hydrogen sulphide molecules (v=2) to produce chemisorbed carbon disulphide that can be further released into the gas phase as discussed before, Two catalytic active sites (c=2) participate in these steps. 2. The reaction of chemisorbed C H 4 o r *CH3 o r ° C H 2 (CHd) with two adjacent chemisorbed sulphur atoms or with one chemisorbed sulphur atom and one chemisorbed hydrogen sulphide or with two chemisorbed hydrogen sulphide molecules to produce chemisorbed carbon disulphide that can be further released into the gas phase. These reactions proceed with the participation of three catalytic sites (c=3).
sulphide reaction.
3.2. Reactor model 3.2.1. M a s s balance
A gas mixture of hydrogen sulphide and methane, of a total molar feed r a t e F t , o and molar fractions YHzS,o and YCH4,o enters a continuous flow tubular reactor with a catalyst fixed bed of w mass. Assuming plug flow in the catalyst bed, the mass balance of each chemical substance in an elementary reactor volume can be expressed through the relations: dFi -- d(Ft. yi ) = (ni,l . ZiA • R1 + ni,2 " zi,2 • Rz ) dw
(3) where iE{CH4, H2S, H2, CS2, $2} and zi, j, zi,2 denotes the stoichiometric coefficients of the reactions. The reaction rates Rj (j= 1, 2) depend on the temperature of the gas mixture surrounding the catalyst mass, the total gas pressure, the vector of the molar fractions of the chemical substancesy as well as on the vector of kinetic parameters bj = Rj = f j ( b j , T, Pt,Y). The effectiveness factor of the catalytic particles for each reaction was drawn upon a correlation of the reaction rates, the substance diffusion rate in the catalyst pores, the concentration of the chemical substance in the bulk gas surrounding the catalyst particle
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258 and the geometry of the catalyst particle [14]. The effectiveness factorcalculatedforalltheexperimental runs was practically equal to 1 which indicates that diffusion phenomena did not affect the catalytic reaction rates. External mass transfer resistances were also proved to be negligible [15]. At the outlet of the reactor the molar flow rate of the gas components is known and expressed via the relation: Fi = Ft • Yi
Finally, the mass balance is formulated in a system of five first order differential equations: 2 dFi dw - F i ' = Z ni'j'ZiJ .fj(bj, T, Pt,y) j=l dFi dw - Fi' = ~i(b, a , y )
(4)
following initial condition:for w=0: F i = Ft, o • Yi,o at the inlet of the reactor,where a denotes the vector of process conditions, T, Pt.
3.2.2. Integration of the reactor mass balances Due to the complexity of the kinetic model, the analytical solution of the above system appears inconvenient. Numerical integration along the reactor length has been adopted to solve the differential equations. The composition of the gas mixture at the reactor outlet was calculated for each of the rival kinetic models. A modified Adam's predictor corrector method was employed to integrate the equations, WI~ I
~i(b,a,y)dw
For the successful integration of the differential equations it is necessary to define the largest integration step, h, so that unstable integration conditions are avoided and precise solution is achieved [16]. The same step is selected for all the equations and its value is smaller than the smallest step required for each equation. Stiffness problems may arise when the reactions are reversible and the system can reach chemical equilibrium. To overcome these difficulties, the integration algorithm was adapted to the specific requirements of the reversible chemical reactions at equilibrium [15].
3.3. Parameter estimation
where i denotes the components CH4, H2S, H2, CS 2 and $2. The equations of this system are subject to the
P Fi(Wl+l) = Fi(wt) + /
253
For the determination of the parameters of the mathematical model i, the function of the sum of squares of the residuals for all the dependent variables is minimised [13] by using the Marquardt-Levenberg algorithm [17]. The parameters of the mathematical models were transformed so that their dependence upon temperature be taken into account and their values be positive real numbers. kRi, Kpi = exp
exp \ R . T J
Vl3wi, f3vi E RI ~ kRi, Kpi > 0
(8)
With this transformation the parameters have physical meaning; the first one represents the entropy change and the second one represents the enthalpy change, /~wi = A S i ,
~vi = A H i , ERi
(9)
Details on the procedure followed to determine the parameters kRi, Kp~, Kpcs, Kl,c. ~ of the models are presented in a recent publication [13].
(5)
Wl
3.4. Statistical test of the kinetic models predictor: k ui.l+l = uij + h Z
Cm • Ui.l+l_
(6)
The statistical adequacy of the kinetic models has been tested by the Fisher's criterion [171:
m=l
Sr2m F = ~ - < Ft a(Vr - re) Se.m
corrector:
k ui,l+l = uij + h ~_~ C m •/21.l+ l_m m=0
(7)
(10)
where S2m represents the lack of fit of the model r for the mth dependent variable and is calculated from the
S.K. Megalofonos, N.G. Papayannakos/Applied CatalysisA: General 165 (1997) 249-258
254
sum of squares of the residuals:
v vest
2 1,5
Sr2,m - - N-~vr(X)rm 5
(11)
,.-i- o
a n d S2,m r e p r e s e n t s t h e v a r i a n c e o f t h e d e p e n d e n t
Non ade0uate kh~,etic model~
.
~'~-1 .
v a r i a b l e m a n d is a m e a s u r e o f t h e d i s p e r s i o n c a u s e d
-1,5
b y e x p e r i m e n t a l error. F o r its e s t i m a t i o n , e x p e r i m e n t a l
-21~~ ' ~ "
,
. ~. .
.
.
~.
.
.
et~aa e , O - ~ta
. . HI
.
., .
-
. e
"~ ~ "~ ~"
~ . . . . . "_ ~ . . . . . . .
- ° .........
repetitions were effected and the variances of the
.o
J
-~"~"
.Q
;
~.~ ~e~
dependent variables throughout the experimental pro-
---o--.2
-. . . . os~
-~-..~s
c e s s w e r e c a l c u l a t e d [18].
The model which has the smallest mean squares o f r e s i d u a l s Srem f o r e v e r y d e p e n d e n t
Fig. 1. Graphical presentation of the F-test results for all kinetic
variable and
models.
Table 1 Results of the statistical and thermodynamics test for all kinetic models F-Test Fo.95(41,10) S~,m
Test table
Models
H2S
4.44E-5 H2S
6.36E-6 CS2
F-Test
Tbermod. Constraints
1 2 3 4 5 6 7 8 9 10
-2.14 -2.24 - 1.92 -2.11 -2.27 - 2.18 -2.1 2.14 -2.24 -2.25 -2.20 - 1.97 -2.17 -2.32 -2.25 -2.14 -2.22 - 1.92
-0.07 -0.86 0.47 -0.30 - 1.00 -0.80 -0.39 -0.96 -0.76 -0.32 0.28 0.42 0.01 1.35 -1.35 -1.15 -0.98 1.98
-0.57 -0.95 0.27 -0.91 - 1.41 -0.75 -1.18 -0.95 -0.96 -0.58 -0.48 -0.36 -0.39 -1.61 -1.16 -0.97 -0.89 0.27
Yes Yes No Yes Yes Yes Yes Yes Yes Yes No No No Yes Yes Yes Yes No
Yes Yes Yes Yes Yes Yes No No No Yes Yes Yes Yes Yes Yes No Yes Yes
1.82E-4
11
12 13 14 15 16 17
18
Table 2 The estimated parameters of selected kinetic models
5 14 15 16
Kinetic Models
kRi
Kps
Kpcs
Kpcr~
(moles atm/g/s)
(atm 1/2)
(atm 1/2)
(atm ~4-a~/2)
exp(ASi/R) ERi[AHi exp(ASi/R) ERi/AHi exp(ASi/R) Em/AHi exp(ASi/R) ERi/AHi
3.56× 6.06x 2.17x 5.59x 5.70× 6.67× 9.32x 3.75×
4.19× 10° 3.46x 102 9.03 x 104 2.50x 104 2.78× l08 4.34x 104 4.83 x lO-6 -3.10x 104
1.40× 10-2 1.02x l0 3 8.64x 10 i 1.75 × 10 3 2.34× 100 1.18× 103 4.76× 10 11 -4.66x 104
2.61 × 103 2.12x 10 4 6.23 x 104 8.26x 103 3.33x 10 l 3.33× 103 8.95 × 10.2 1.78x 10z
108 104 107 104 108 104 l0 3 103
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
satisfies at the same time all the thermodynamic constraints [13] is considered as the best kinetic model. From Fig. 1 and Table 1 it is observed that the model 14 can be considered as the best kinetic model for the conditions and the catalyst used in this study, although more than one models present statistical adequacy and satisfy all the thermodynamic constraints. According to the model 14 the rate-controlling step is the reaction among the chemisorbed CH3, H2S and S on the catalytic surface with the participation of three catalytic sites, The rate equation of the proposed kinetic model is derived from Eq. (2) if the parameters c, d, v are substituted for 3,3 and 1 respectively:
R14 =
kRi4 "
255
discussed elsewhere [12]. The values of the kinetic parameters are given for the initial catalyst activity• In accordance with the results of a thermodynamic study [12], no methane dimerisation products have been observed in the reactor effluent gas. C a t a l y s t s e l e c t i v i t y : The selectivity of the catalytic system has been examined by using the model 14. For low total conversions of hydrogen sulphide, sulphur is produced almost exclusively as shown in Figs. 8 and 9. Sulphur production reaches a maximum corresponding to the thermodynamic equilibrium of hydrogen sulphide decomposition and decreases drastically for larger total conversions of hydrogen sulphide where the thermodynamic equilibrium of hydrogen sulphide decomposition is shifted
. p l s2 / 2 " PH2S -- ( 1 / K e q , R , 4 ) " PCS_,"p~2] • pl/2 /~1/2 - $ 2 ~- Kpcs" - c s 2 + KpCH," (PcH4/pI{2)]
(12)
[PcI~/pl/e) _ [PH2s q-
Kps
However, some other from the rival models can be used for reactor simulation and design as shown in Fig. 1 and Table 1. As they are thermodynamically and statistically accepted and their Sr2mvalues are not far from the ones of the proposed kinetic model 14, the reaction paths they represent may be followed in a lesser extent but in parallel with the path of the prevailing model. This implies that the adsorbed species on the active sites may be of more than one forms and may follow different but thermodynamically accepted ways to reorganise and yield the reaction products. The same effect has been reported for a Pt/A1203 catalyst [13] used for the same reaction and at the same operating conditions. In Table 2, the estimated values for the parameters of the most suited kinetic models are presented Figs. 2-7 show representative experimental data Catalystand the predictedspacevalues for the proposedas model 14. bed time is calculated the ratio of the catalyst bed volume to the total volumetric flow rate at reaction conditions. A maximum hydrogen and carbon disulphide yield was obtained for YH2s,o = 0.4 - 0.6. A very good agreement of the predicted values with the experimental data is observed. The deviations are within the experimental error for the 95% of the experimental points• Catalyst deactivation w a s followed with standard experiments as given and
3
to the left of the equation with simultaneous increase of the hydrogen sulphide conversion to carbon disulphide. 0.4 t ~ 0,35 i r~T,~ody,~,,~:e,~ihb,~,~ g '\,.. . . . . ~ 0,3 ~, '. ...-" ~ i ~ "" ~ 0e5 i / , ., l - - - ,- -1t ~ / "~.= |~ y " ~ ~ 0~ ~ ] ~ o,15 / ~ t ~ o,1 t
\ ' .\
/
~ ~
t o,05 i J 0 ~0
/
. . . . 02
0,1
, . .0,4 . . . . .0,5
0,3
0,6
, , 0,8~
0,7
,~
0,9
Mole fraction of hydrogen sulphide at the reactor Inlet
Fig. 2. Mole fraction of hydrogen produced on catalyst MoS2 vs. mole fraction of hydrogen sulphide at the reactor inlet. Pt=l atma. T=1065 K. Total feed flow rate: 1 : 3 Ncm3/s, 2 : 6 Ncm3/s, 3: 12Ncm3/s
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
256
o,1
0,07 ~
g 0.09
equilibrium
Thermodynamic
0,08
o -¢'*
~" •
z"
..
\
"\
."
•
/° "\
~.
1
~ - - ~.
. ~.
~ ~
"X
/"
.- ~ . .
\
"~
°
ot
0,07
\
equ'J~brlum
~
l-
.~w
Thermodynamic
g 0,06 0,05
/
,
•
1
0,06 .~
'~ 0,04
o.o5
-a 0,03
,'
0,04
0,03
!
"6 o,o2
0.02 j
•-
0,01 0
I
I
0,1
02
r
0
,
I
•
0,3
I
I
r
0.4
I
r
0,5
,
0,6
J
0,7
.
I
•
0,01
I
0,8
0
0,9
,
I
0,]
Mole fraction of hydrogen sulphide at the reactor Inlet
,
I
o2
,
I
I
.
o,3 0.4
.
I
~
.
o,7
t
.
0.8
I
.
0.9
Mole fraction of hydrogen sulphide at the reactor
Fig. 3. Mole fraction of carbon disulphide produced on catalyst MoS2 vs mole fraction of hydrogen sulphide at the reactor inlet. Pt=l atma. T-1065 K. Total feed flow rate: 1 : 3 Ncm3/s, 2: 6Ncm3/s, 3: 12Ncm3/s.
I
0,5 o,6 inlet
Fig. 5. Mole fraction of carbon disulphide produced on catalyst MoS 2 vs mole fraction of hydrogen sulphide at the reactor inlet. Pt=l atma. T=1005 K. Total feed flow rate: 1:1.5 Ncm3/s, 2: 3 Ncm3/s, 3:7.5 Ncm3/s.
0,28¸ Thermodynamic
•-~ 024
equlltbrtum
0,28
]
. s --'" ~ . . . . . " " -
\ \
02 1
.-"/ /
"x
•
-~ 024
"" \
1
• "
I
~
D
0,16
2
o~[
~ ~
• .
0,08 ~" J
0,08
0,04 ~o, X 0
I
0
0,1
.
I
0,2
,
I
0,3
.
I
0,4
,
I
0,5
•
I
0,6
,
~
I
0,7
0,8
.
I
,
0,9
inlet Fig. 4. Mole fraction of hydrogen produced on catalyst MoS2 vs mole fraction of hydrogen sulphide at the reactor inlet. Pt = latma. T--1005 K. Total feed flow rate: 1:1.5 Ncm3/s, 2 : 3 Ncm3/s, 3" 7.5 Ncma/s.
0
' ' ' 't 0,4 0,6 0,8 Catalyst bed space time (s)
1
1,4
Fig. 6. Mole fraction of hydrogen produced on catalyst MoS2 vs catalyst bed space time. Pt=l atma. YH2Sin= 0.68. Reaction temperature: 1:1065 K, 2:1028 K, 3:1005 K, 4:977 K.
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
,
0,07
-
0.20
0,06
]
-~ "
0,05
2
'~
~
018
~
0,16
....... m28K
~
014
.....
-=
o12
.~
0,10
g)~, o,o4
-~
~
"a
oo8
"~ 0,03
/
~
0.06
~,
0.04
=
o,o2
~>
~- o,oi
1065
0.00
, --
0
02
---+----+
)
,
0,6 0,8 1 Catalyst bed space time |s)
1,,2
1,4
.......
0.14
.....
0.7 yH2Sin
~ 0.12 •~
"~ ~''-6
0.08
o o,
/
I
0.04
ta
/
~ 0 9 vH2SinX / I o~ / . . ' ~ I Conv,rsk,. hyd,,~,,s~p~,
.....
OlO
i
f
| 1 :
0.15
0.20
disulphide
Fig. 9. Selectivity of MoS2 catalyst with constant reaction temperature. Feed composition YH,Sin ~ ().5, Pt--l atma.
Conclusions
Eighteen kinetic models for the catalytic reaction of methane and hydrogen sulphide over MoS2 catalyst have been studied. According to the results of the statistical and thermodynamic testing and on the basis of minimum residual sum of squares the model 14 is proposed as the best one among the 18 rival models. This model indicates that the rate controlling step o f the catalytic reaction is the reaction among the chemisorbed species CH3, H2S and S on the catalytic surface with the participation of three catalytic sites. The activation energy of this step was calculated as 22600 cal/mole. The only products yielded are hydro-
o.2o 0.3 vH2Sin o.s vH2Sin
0.10
s u l p h u r and carbon
4.
0.18 0 36
0.05
T o t a l conversion of hydrogen sulphide to
,
0,4
Fig. 7. Mole fraction of carbon disulphide produced on catalyst MoS2 vs catalyst bed space time. P t = l atma. YHzSin= 0.68. Reaction temperature: 1:1065 K, 2:1028 K, 3:1005 K, 4:977 K.
~
1005K
.....
0.00
2 •~
/
K
o
257
ge .. bon
isu,p i e an
,ma. = o u n t , of
u,p.ur
~t I C,onversionof
5. Nomenclature
0.02 0.00
~ 000
,
0.05
0.10
0.15
0.20
T o t a l conversion of hydrogen sulphide to sulphur
and
carbon
disulphide
Fig. 8. Selectivity of MoS2 catalyst with constant feed composition. Reaction temperature 1065 K, Pt=l atma.
a b c Cm d
process conditions vector. kinetic parameters vector. number of catalytic sites. integration coefficient. the type of CHd chemical species participating to the surface reaction.
258 ERi
Fi Ft h AH kRg Keq.Ri Kpi
N PA Pt R RI Ri S~,m S~.m AS T t Ui,1 ui,I t v
Wr w y Yi
Zi,j
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A." General 165 (1997) 249-258
activation energy of the ith (i = 1 , 2 , . . . , 18) model forward reaction, cal/mol. molar flow rate of a reactant species i, mol/s, total molar flow rate, mol/s. integration step. enthalpy change, cal/mol, specific rate of the ith ( i = 1 , 2 , . . . , 1 8 ) model reaction. thermodynamic equilibrium constant of the ith model reaction at the gas phase[13]. inhibition parameters of the rate Eq. (2) where i = S , CS and CHd. total number of experiments. partial pressure of a reactant species A, atm. total pressure of the reactant system, atm. gas constant, cal/(mol K). real numbers. catalytic reaction rate of the ith (i = 1 2 , . . . , 18) model, mol/(s goat). experimental variance of the mth dependent variable. mean square of the mth dependent variable for rth model. entropy change, cal/(mol K). catalyst bed temperature, K, time of the catalyst operation, h. molar flow rate of a reactant species i, at the lth step. derivative of ui, l. number of hydrogen sulphide molecules participating in the surface reaction. number of parameters of the rth model. catalyst bed mass, g. chemical substances mole fractions vector. mole fraction of the ith component in the gas mixture. stoichiometric coefficient.
Greek letters .3w, fl~. parameters after transformations defined by the Eq. (8) and Eq. (9). d/'r.,,1 sum of squares of the residuals of mth dependent variable.
Symbols ®v one vacant catalytic site. ®A one catalytic site with the species A chemisorbed on it.
j
Superscript repetition.
o
Subscripts initial or feed condition.
eq
equilibrium.
References [1] u. Preub, M. Baerns, Chem. Eng. Technol. 10 (1987) 297-305. [2l A.B. Anderson, J. Yu, J. Catal. 119 (1989) 135-145. [3] J.R. Anderson, Applied Catalysis 47 (1989) 177-196. [4] C.J. Chen, M.H. Back, R.A. Back, Can. J. Chem. 54 (1976) 3175-3184. [51 c.J. Chen, M.H. Back, R.A. Back, Can. J. Chem. 53 (1975) 3580-3590. [61 H.B. Palmer, T.J. Hirt, J. Phys. Chem. 67 (1963) 709-711. [7] A.B. Anderson, J.J. Maloney, J. Yu, J. Catal. 112 (1988) 392-400. [8] V.E. Kaloidas, N.G. Papayannakos, Chem. Eng. Science 44(11)(1989)2493-2500. [91 V.E. Kaloidas, N.G. Papayannakos, Ind. Eng. Chem. Res 30(2) (1991) 345-351. [101 J.H. Kolts, Ind. Eng. Chem. Fund. 25 (1986) 265-269. [11] K.I. Makarov, V.K. Pechik, Kinetika i Kataliz. 16(6) (1975) 1491-1500. [12] S.K. Megalofonos, N.G. Papayannakos, Int. J. Hydrogen Energy 16(5) (1991) 319-327. [13] S. Megalofonos,N.G. Papayannakos, Appl. Catal. A: General 138 (1996) 39-55. [14] G.F. Froment, K.B. Bischof, Chemical Reactor Analysis and Design, Wiley, New York, 1979. [15] S.K. Megalofonos, Ph.D Thesis, NTUA, 1995, Athens. [16] M.E. Davis, Numerical methods and modelling for chemical engineers, Wiley, New York, 1984. [17] D.W. Marquardt, J. Soc. Ind. Appl. Math. 11(2) (1963) 431-441. [181 D.M. Himmelblau, Process analysis by statistical methods, Wiley, New York, 1970.
AA PT PA LE IY DSS C L I A: GENERAL
ELSEVIER
Applied Catalysis A: General 165 (1997) 249-258
Kinetics of catalytic reaction of methane and hydrogen sulphide over MoS2 S.K. Megalofonos, N.G.
Papayannakos*
Laborato~ of Chemical Process Engineering, Department of Chemical Engineering, National Technical Universi~' of Athens, Heroon Polytechiou, 9 GR-157 73 Zografos, Athens, Greece Received 27 January 1997; received in revised form 10 June 1997: accepted 10 June 1997
Abstract
The reaction of methane and hydrogen sulphide over MoS2 catalyst has been studied in a fixed bed tubular reactor over a temperature range of 973 to 1073 K under atmospheric pressure and for space time between 0.1 and 1 s. The LangmuirHinshelwood-Hougen-Watson theory has been used to determine eighteen (18) rival kinetic models. Model discrimination has been performed by using statistical and thermodynamic constraints. According to the proposed model, the rate-controlling step is the reaction among the absorbed species CH3, H2S and S on the catalytic surface with the participation of three catalytic sites. The catalyst selectivity is also discussed. © 1997 Elsevier Science B.V.
Keywords: Hydrogen sulfide; Methane; Kinetics; Molybdenum sulfide
1. I n t r o d u c t i o n In recent times the availability of liquid fuels reserves is constantly declining. This reality has triggered research for the discovery of new solutions using other energy resources. Natural gas reserves, albeit not abundant any more world-wide, are still large enough, especially when compared with the petroleum ones, to justify efforts for the processing of natural gas and the use of methane as a raw material for the production of fuels [1]. Catalytic Steam Reforming is a widely used method today either to produce hydrogen or to give syngas as the first stage for the conversion of methane into liquid *Corresponding author. Tel.: (+30-1)7723239; fax: (+30-1) 7723155: e-mail [email protected], 0926-860X/97/$17.00 ~ 1997 Elsevier Science B,V. All rights reserved. PII S0926-860X(97)00206-8
fuels. The thereby produced syngas is converted either into methanol with the Mobil technology and then into liquid hydrocarbons or directly into hydrocarbons through the Fischer-Tropsch synthesis. In order to increase effectiveness and control over products distribution, the use of ZSM5 catalysts is combined with Co in the latter process. Besides, the use of MoS2 catalysts is under research [2]. Another promising method, but still under development, is the oxidative coupling of methane yielding oligomers that can further be processed to produce light liquid hydrocarbons. The reaction of methane with hydrogen sulphide can be considered as the first step of an alternative route to produce light hydrocarbons from methane [3]. The products of this reaction, hydrogen and carbon disulphide, can further react under different conditions
250
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
to produce light hydrocarbons: nCSz + (3n + 1)H2~-CH2n+2 + 2nH2S
In a study of homogeneous decomposition ofhydro(1)
Another way to consider the reaction of hydrogen sulphide with methane is to produce hydrogen, a valuable chemical and clean energy source, and the solvent carbon disulphide. Thus, the hydrogen sulphide produced as a by product of the hydrodesulphurization processes in refineries can be used to produce hydrogen or light hydrocarbons from methane. Natural gases containing H2S could also be considered as possible feedstocks to a process based on this reaction, It should be noted that sulphur instead of hydrogen sulphide can react with methane. Although this reaction can yield higher conversions of methane at lower temperatures, its use in a production process scheme will entail a sulphur production stage and a hydrogen production process to furnish the supplementary amount of hydrogen for the reaction, The open literature concerning the kinetic study of the methane-hydrogen sulphide reaction is very poor. Most of the papers studied deal with the kinetics and chemical reaction rates of parallel reactions taking place in the context of the methane-hydrogen sulphide reaction. Chen et al. [4] have studied the thermal decomposition of methane in the temperature range of 8501103 K. The reaction mechanism suggested by them assumes the existence of free methyl radicals in the gas phase. Chen et al. [5] who studied the same reaction, calculated a total conversion at 1000 K not overcoming the 2% in a static system for 30 rain residence time. Palmer and Hirt [6] studied the pyrolysis of methane at temperatures over 1000 K in a shock tube reactor. They argue that during the first stage of the methane pyrolysis both methyl or methylene radicals can exist, Anderson et al. [7] have studied theoretically the methane activation over MoS2 catalyst. They conclude that methane is chemisorbed on the MoS2 surface and dehydrogenated to methyl and methylen. Further dehydrogenation leads to the creation of CH and C species chemisorbed on the catalyst surface but these are unstable and have a very short life time. They also made relevant observations in a study of the FischerTropsch catalytic conversion over MoS2 [2].
gen sulphide, Kaloidas and Papayannakos [8] suggest a free radical mechanism. In accordance with their findings, hydrogen sulphide is decomposed into radicals "H and "SH which create "S radicals. They [9] also studied the heterogeneous catalytic reaction of hydrogen sulphide with MoS2 catalyst. In accordance with the suggested reaction mechanism, hydrogen sulphide is chemisorbed on the surface of the catalyst. The chemisorbed hydrogen sulphide is decomposed into S atoms which occupy an active site and hydrogen which is desorbed in the gas phase. During second stage atomic sulphur is desorbed and reacts in the gas phase to molecular Se. Kolts [10] concluded that presence of hydrogen sulphide accelerates the decomposition rate of light hydrocarbons through a free radical mechanism. Object of this paper is the study of the kinetics of the methane-hydrogen sulphide catalytic reaction by using MoS2 as a catalyst, in the temperature range of 973-1073 K and at 0.1 MPa total pressure.
2. Experimental Two coaxial c~-A1203 tubes in a down flow configuration were used as reactor. The internal diameter of the outer tube was 11.5 mm and the external diameter of the inner tube was 5.5 mm. The length of the tubes was 0.80 m. A four zone electric furnace was regulating the temperature distribution in the reactor according to the experimental requirements, using four electronic controllers. The temperature was monitored by thermocouples placed at fixed points outside the outer tube as well as inside the inner tube. One inner travelling thermocouple was also used to measure the temperature distribution along the reactor length in the course of each experiment. The accuracy of the temperature measurements was + 1 K. The H2S and C H 4 flow rates at the inlet of the reactor were measured independently using a capillary system calibrated with a bubble flowmeter. The total volumetric flow rate was measured at the reactor outlet using a bubble flowmeter. The temperatures as well as the flow rates and the pressure at the inlet of the reactor were monitored through an IBM P.C. system. The chemical composition of the gas at the inlet and outlet of the reactor was determined by a gas
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
chromatograph bearing a thermal conductivity detector and a 5.48 m Porapak-Q column. Nitrogen was used as carrier gas. The gas-chromatograph was calibrated with pure HaS, CH4 and Ha gases and with gas mixtures of CH 4 and CSa. All gases employed in the experiments were of a purity over 99.5%, with the exception of the carrier gas of the gas chromatograph the purity of which was 99.999%. The catalyst was MoSa powder of VENTRON GMBH, with a purity greater than 98%. The powder was compressed and agglomerated into particles of an average diameter, dp=0.0282 cm. The gas composition at the inlet of the reactor was double checked through the measurement of the inlet flow rates and the gas chromatography, A maximum deviation of i 2 % was observed. The input--output mass balances were tested in each experiment and their difference was found to be lesser than 3%.
3. Results and Discussion 3.1. Proposed kinetic models and reaction paths
In the technical kinetic study of the methanehydrogen sulphide reaction, it is assumed that two chemical reactions are taking place: The hydrogen sulphide-methane reaction to carbon disulphide and hydrogen and the catalytic decomposition of hydrogen sulphide to sulphur and hydrogen. Although not favoured thermodynamically, the latter is a very rapid one. The reaction rate of the catalytic decomposition of hydrogen sulphide proposed by Kaloidas and Papayannakos [10] was considered, as it concerns the same catalytic system and the same operating conditions. The methane dimerization reaction is of no interest for the purposes of the present study as it is a slow reaction [5,11] and not favouredthermodynamically [12], and thus was not taken into account along with the rest of the reactions taking place in the gas phase, The homogeneous, hydrogen sulphide-methane thermal reaction was studied experimentally in the same apparatus and it was observed that the molar fractions of the yielded hydrogen and carbon disulphide at the reactor outlet were less than the experi-
251
mental error of the analysis at the same experimental conditions for the catalytic reaction. As a consequence, the thermal reaction does not affect the catalytic results and consequently the parameter estimation of the kinetic models. The chemisorption and reaction steps considered in this study are given below. 3.1. I. Chemisorption on the catalytic surface The hydrogen sulphide molecules are chemisorbed on the surface of the catalyst so that each molecule occupies an active site.
H2S + ®v~+~-~rt2s Two possible ways can be considered for the formation and chemisorption of methylenes on the active sites. 1. The methane molecules are thermally dissociated in the gas phase creating hydrogen and methylene radicals. The former react to hydrogen while the latter are chemisorbed on the catalytic sites and each radical occupies one active site. 2. Another way postulates the chemisorption of methane on one active site, the loosening of the hydrogen-carbon bonds and the creation of gas hydrogen and chemisorbed methylenes. However, the chemical equation expressing the chemisorption mechanism as a whole is same in both cases. CH4 ÷ ®v ~- ®CHd ÷
(4
-- d) H2 2 Sulphur desorption from the catalytic surface can be considered in the following two ways. 1. Sulphur produced during the catalytic decomposition of hydrogen sulphide is desorbed from the active sites in two stages. At the first stage, the atomic sulphur-active sites bonds are loosened and atomic sulphur is desorbed in the gas phase. At a second stage, S-S bonds are created yielding molecular diatomic sulphur [10]. 2. Following another kinetic path, the chemisorbed sulphur atoms develop S-S bonds and give sulphur molecules, each one chemisorbed on two catalytic sites. These chemisorbed molecules are then desorbed in the gas phase. The chemical equation expressing the total sulphur desorption process is the same for both the above
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
252
described paths. __..1 ®s+--~S2 + ®v Each carbon disulphide molecule is considered to f~
/D(4--d)/2~ D ( 2 - v ) / 2 . p v )rs2 H2S
Ri = kRi • ~rCH4/rH2
The equation of the reaction rate for all the eighteen models derived from the above reaction paths, which are presented in more details in a previous paper [13], is given in the general form:
(1/KeqRi) • Pcsz " (PHz) (2v+d)/2 ,
[PH2s + Kps " p1/2s2 + KpcsP~c/22 + KpcHe " Pcl-h/e(H4?d)/2] c
(2)
desorb from two catalytic sites. The above mentioned sorption steps are considered to be very rapid when compared with the chemical reaction of the various species on the catalytic surface, being thus always in equilibrium,
The Langmuir-Hinshelwood-Hougen-Watson theory has been used to determine the equation of the reaction rate with the assumption that the concentration of the unsaturated sites is very low in comparison with the concentration of the saturated ones.
3.1.2. Reactions on the catalytic surface
The next section deals with the modelling of the fixed bed solid catalytic reactor, with a view to evaluate the kinetic parameters of Eq. (2) which describes mathematically the methane-hydrogen
Two catalytic reactions are taking place on the catalytic surface. The catalytic decomposition of the chemisorbed hydrogen sulphide to sulphur and hydrogen and the reaction of the chemisorbed species to produce hydrogen and carbon disulphide. For the first reaction, the loosening of the hydrogen-sulphur bonds, the creation of hydrogenhydrogen bonds and the desorption of molecular hydrogen has been proposed [9]. For the second reaction, eighteen different reaction paths can be considered with the participation of two or three active sites: 1. The reaction of either CH4 or *CH3 or "CH2 (CHd, where d=4,3 and 2) in the gas mixture with two chemisorbed sulphur atoms (v=0) or with one chemisorbed sulphur atom and one chemisorbed hydrogen sulphide ( v = l ) or with two chemisorbed hydrogen sulphide molecules (v=2) to produce chemisorbed carbon disulphide that can be further released into the gas phase as discussed before, Two catalytic active sites (c=2) participate in these steps. 2. The reaction of chemisorbed C H 4 o r *CH3 o r ° C H 2 (CHd) with two adjacent chemisorbed sulphur atoms or with one chemisorbed sulphur atom and one chemisorbed hydrogen sulphide or with two chemisorbed hydrogen sulphide molecules to produce chemisorbed carbon disulphide that can be further released into the gas phase. These reactions proceed with the participation of three catalytic sites (c=3).
sulphide reaction.
3.2. Reactor model 3.2.1. M a s s balance
A gas mixture of hydrogen sulphide and methane, of a total molar feed r a t e F t , o and molar fractions YHzS,o and YCH4,o enters a continuous flow tubular reactor with a catalyst fixed bed of w mass. Assuming plug flow in the catalyst bed, the mass balance of each chemical substance in an elementary reactor volume can be expressed through the relations: dFi -- d(Ft. yi ) = (ni,l . ZiA • R1 + ni,2 " zi,2 • Rz ) dw
(3) where iE{CH4, H2S, H2, CS2, $2} and zi, j, zi,2 denotes the stoichiometric coefficients of the reactions. The reaction rates Rj (j= 1, 2) depend on the temperature of the gas mixture surrounding the catalyst mass, the total gas pressure, the vector of the molar fractions of the chemical substancesy as well as on the vector of kinetic parameters bj = Rj = f j ( b j , T, Pt,Y). The effectiveness factor of the catalytic particles for each reaction was drawn upon a correlation of the reaction rates, the substance diffusion rate in the catalyst pores, the concentration of the chemical substance in the bulk gas surrounding the catalyst particle
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258 and the geometry of the catalyst particle [14]. The effectiveness factorcalculatedforalltheexperimental runs was practically equal to 1 which indicates that diffusion phenomena did not affect the catalytic reaction rates. External mass transfer resistances were also proved to be negligible [15]. At the outlet of the reactor the molar flow rate of the gas components is known and expressed via the relation: Fi = Ft • Yi
Finally, the mass balance is formulated in a system of five first order differential equations: 2 dFi dw - F i ' = Z ni'j'ZiJ .fj(bj, T, Pt,y) j=l dFi dw - Fi' = ~i(b, a , y )
(4)
following initial condition:for w=0: F i = Ft, o • Yi,o at the inlet of the reactor,where a denotes the vector of process conditions, T, Pt.
3.2.2. Integration of the reactor mass balances Due to the complexity of the kinetic model, the analytical solution of the above system appears inconvenient. Numerical integration along the reactor length has been adopted to solve the differential equations. The composition of the gas mixture at the reactor outlet was calculated for each of the rival kinetic models. A modified Adam's predictor corrector method was employed to integrate the equations, WI~ I
~i(b,a,y)dw
For the successful integration of the differential equations it is necessary to define the largest integration step, h, so that unstable integration conditions are avoided and precise solution is achieved [16]. The same step is selected for all the equations and its value is smaller than the smallest step required for each equation. Stiffness problems may arise when the reactions are reversible and the system can reach chemical equilibrium. To overcome these difficulties, the integration algorithm was adapted to the specific requirements of the reversible chemical reactions at equilibrium [15].
3.3. Parameter estimation
where i denotes the components CH4, H2S, H2, CS 2 and $2. The equations of this system are subject to the
P Fi(Wl+l) = Fi(wt) + /
253
For the determination of the parameters of the mathematical model i, the function of the sum of squares of the residuals for all the dependent variables is minimised [13] by using the Marquardt-Levenberg algorithm [17]. The parameters of the mathematical models were transformed so that their dependence upon temperature be taken into account and their values be positive real numbers. kRi, Kpi = exp
exp \ R . T J
Vl3wi, f3vi E RI ~ kRi, Kpi > 0
(8)
With this transformation the parameters have physical meaning; the first one represents the entropy change and the second one represents the enthalpy change, /~wi = A S i ,
~vi = A H i , ERi
(9)
Details on the procedure followed to determine the parameters kRi, Kp~, Kpcs, Kl,c. ~ of the models are presented in a recent publication [13].
(5)
Wl
3.4. Statistical test of the kinetic models predictor: k ui.l+l = uij + h Z
Cm • Ui.l+l_
(6)
The statistical adequacy of the kinetic models has been tested by the Fisher's criterion [171:
m=l
Sr2m F = ~ - < Ft a(Vr - re) Se.m
corrector:
k ui,l+l = uij + h ~_~ C m •/21.l+ l_m m=0
(7)
(10)
where S2m represents the lack of fit of the model r for the mth dependent variable and is calculated from the
S.K. Megalofonos, N.G. Papayannakos/Applied CatalysisA: General 165 (1997) 249-258
254
sum of squares of the residuals:
v vest
2 1,5
Sr2,m - - N-~vr(X)rm 5
(11)
,.-i- o
a n d S2,m r e p r e s e n t s t h e v a r i a n c e o f t h e d e p e n d e n t
Non ade0uate kh~,etic model~
.
~'~-1 .
v a r i a b l e m a n d is a m e a s u r e o f t h e d i s p e r s i o n c a u s e d
-1,5
b y e x p e r i m e n t a l error. F o r its e s t i m a t i o n , e x p e r i m e n t a l
-21~~ ' ~ "
,
. ~. .
.
.
~.
.
.
et~aa e , O - ~ta
. . HI
.
., .
-
. e
"~ ~ "~ ~"
~ . . . . . "_ ~ . . . . . . .
- ° .........
repetitions were effected and the variances of the
.o
J
-~"~"
.Q
;
~.~ ~e~
dependent variables throughout the experimental pro-
---o--.2
-. . . . os~
-~-..~s
c e s s w e r e c a l c u l a t e d [18].
The model which has the smallest mean squares o f r e s i d u a l s Srem f o r e v e r y d e p e n d e n t
Fig. 1. Graphical presentation of the F-test results for all kinetic
variable and
models.
Table 1 Results of the statistical and thermodynamics test for all kinetic models F-Test Fo.95(41,10) S~,m
Test table
Models
H2S
4.44E-5 H2S
6.36E-6 CS2
F-Test
Tbermod. Constraints
1 2 3 4 5 6 7 8 9 10
-2.14 -2.24 - 1.92 -2.11 -2.27 - 2.18 -2.1 2.14 -2.24 -2.25 -2.20 - 1.97 -2.17 -2.32 -2.25 -2.14 -2.22 - 1.92
-0.07 -0.86 0.47 -0.30 - 1.00 -0.80 -0.39 -0.96 -0.76 -0.32 0.28 0.42 0.01 1.35 -1.35 -1.15 -0.98 1.98
-0.57 -0.95 0.27 -0.91 - 1.41 -0.75 -1.18 -0.95 -0.96 -0.58 -0.48 -0.36 -0.39 -1.61 -1.16 -0.97 -0.89 0.27
Yes Yes No Yes Yes Yes Yes Yes Yes Yes No No No Yes Yes Yes Yes No
Yes Yes Yes Yes Yes Yes No No No Yes Yes Yes Yes Yes Yes No Yes Yes
1.82E-4
11
12 13 14 15 16 17
18
Table 2 The estimated parameters of selected kinetic models
5 14 15 16
Kinetic Models
kRi
Kps
Kpcs
Kpcr~
(moles atm/g/s)
(atm 1/2)
(atm 1/2)
(atm ~4-a~/2)
exp(ASi/R) ERi[AHi exp(ASi/R) ERi/AHi exp(ASi/R) Em/AHi exp(ASi/R) ERi/AHi
3.56× 6.06x 2.17x 5.59x 5.70× 6.67× 9.32x 3.75×
4.19× 10° 3.46x 102 9.03 x 104 2.50x 104 2.78× l08 4.34x 104 4.83 x lO-6 -3.10x 104
1.40× 10-2 1.02x l0 3 8.64x 10 i 1.75 × 10 3 2.34× 100 1.18× 103 4.76× 10 11 -4.66x 104
2.61 × 103 2.12x 10 4 6.23 x 104 8.26x 103 3.33x 10 l 3.33× 103 8.95 × 10.2 1.78x 10z
108 104 107 104 108 104 l0 3 103
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
satisfies at the same time all the thermodynamic constraints [13] is considered as the best kinetic model. From Fig. 1 and Table 1 it is observed that the model 14 can be considered as the best kinetic model for the conditions and the catalyst used in this study, although more than one models present statistical adequacy and satisfy all the thermodynamic constraints. According to the model 14 the rate-controlling step is the reaction among the chemisorbed CH3, H2S and S on the catalytic surface with the participation of three catalytic sites, The rate equation of the proposed kinetic model is derived from Eq. (2) if the parameters c, d, v are substituted for 3,3 and 1 respectively:
R14 =
kRi4 "
255
discussed elsewhere [12]. The values of the kinetic parameters are given for the initial catalyst activity• In accordance with the results of a thermodynamic study [12], no methane dimerisation products have been observed in the reactor effluent gas. C a t a l y s t s e l e c t i v i t y : The selectivity of the catalytic system has been examined by using the model 14. For low total conversions of hydrogen sulphide, sulphur is produced almost exclusively as shown in Figs. 8 and 9. Sulphur production reaches a maximum corresponding to the thermodynamic equilibrium of hydrogen sulphide decomposition and decreases drastically for larger total conversions of hydrogen sulphide where the thermodynamic equilibrium of hydrogen sulphide decomposition is shifted
. p l s2 / 2 " PH2S -- ( 1 / K e q , R , 4 ) " PCS_,"p~2] • pl/2 /~1/2 - $ 2 ~- Kpcs" - c s 2 + KpCH," (PcH4/pI{2)]
(12)
[PcI~/pl/e) _ [PH2s q-
Kps
However, some other from the rival models can be used for reactor simulation and design as shown in Fig. 1 and Table 1. As they are thermodynamically and statistically accepted and their Sr2mvalues are not far from the ones of the proposed kinetic model 14, the reaction paths they represent may be followed in a lesser extent but in parallel with the path of the prevailing model. This implies that the adsorbed species on the active sites may be of more than one forms and may follow different but thermodynamically accepted ways to reorganise and yield the reaction products. The same effect has been reported for a Pt/A1203 catalyst [13] used for the same reaction and at the same operating conditions. In Table 2, the estimated values for the parameters of the most suited kinetic models are presented Figs. 2-7 show representative experimental data Catalystand the predictedspacevalues for the proposedas model 14. bed time is calculated the ratio of the catalyst bed volume to the total volumetric flow rate at reaction conditions. A maximum hydrogen and carbon disulphide yield was obtained for YH2s,o = 0.4 - 0.6. A very good agreement of the predicted values with the experimental data is observed. The deviations are within the experimental error for the 95% of the experimental points• Catalyst deactivation w a s followed with standard experiments as given and
3
to the left of the equation with simultaneous increase of the hydrogen sulphide conversion to carbon disulphide. 0.4 t ~ 0,35 i r~T,~ody,~,,~:e,~ihb,~,~ g '\,.. . . . . ~ 0,3 ~, '. ...-" ~ i ~ "" ~ 0e5 i / , ., l - - - ,- -1t ~ / "~.= |~ y " ~ ~ 0~ ~ ] ~ o,15 / ~ t ~ o,1 t
\ ' .\
/
~ ~
t o,05 i J 0 ~0
/
. . . . 02
0,1
, . .0,4 . . . . .0,5
0,3
0,6
, , 0,8~
0,7
,~
0,9
Mole fraction of hydrogen sulphide at the reactor Inlet
Fig. 2. Mole fraction of hydrogen produced on catalyst MoS2 vs. mole fraction of hydrogen sulphide at the reactor inlet. Pt=l atma. T=1065 K. Total feed flow rate: 1 : 3 Ncm3/s, 2 : 6 Ncm3/s, 3: 12Ncm3/s
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
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Fig. 3. Mole fraction of carbon disulphide produced on catalyst MoS2 vs mole fraction of hydrogen sulphide at the reactor inlet. Pt=l atma. T-1065 K. Total feed flow rate: 1 : 3 Ncm3/s, 2: 6Ncm3/s, 3: 12Ncm3/s.
I
0,5 o,6 inlet
Fig. 5. Mole fraction of carbon disulphide produced on catalyst MoS 2 vs mole fraction of hydrogen sulphide at the reactor inlet. Pt=l atma. T=1005 K. Total feed flow rate: 1:1.5 Ncm3/s, 2: 3 Ncm3/s, 3:7.5 Ncm3/s.
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inlet Fig. 4. Mole fraction of hydrogen produced on catalyst MoS2 vs mole fraction of hydrogen sulphide at the reactor inlet. Pt = latma. T--1005 K. Total feed flow rate: 1:1.5 Ncm3/s, 2 : 3 Ncm3/s, 3" 7.5 Ncma/s.
0
' ' ' 't 0,4 0,6 0,8 Catalyst bed space time (s)
1
1,4
Fig. 6. Mole fraction of hydrogen produced on catalyst MoS2 vs catalyst bed space time. Pt=l atma. YH2Sin= 0.68. Reaction temperature: 1:1065 K, 2:1028 K, 3:1005 K, 4:977 K.
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A: General 165 (1997) 249-258
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Conclusions
Eighteen kinetic models for the catalytic reaction of methane and hydrogen sulphide over MoS2 catalyst have been studied. According to the results of the statistical and thermodynamic testing and on the basis of minimum residual sum of squares the model 14 is proposed as the best one among the 18 rival models. This model indicates that the rate controlling step o f the catalytic reaction is the reaction among the chemisorbed species CH3, H2S and S on the catalytic surface with the participation of three catalytic sites. The activation energy of this step was calculated as 22600 cal/mole. The only products yielded are hydro-
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4.
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T o t a l conversion of hydrogen sulphide to
,
0,4
Fig. 7. Mole fraction of carbon disulphide produced on catalyst MoS2 vs catalyst bed space time. P t = l atma. YHzSin= 0.68. Reaction temperature: 1:1065 K, 2:1028 K, 3:1005 K, 4:977 K.
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and
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disulphide
Fig. 8. Selectivity of MoS2 catalyst with constant feed composition. Reaction temperature 1065 K, Pt=l atma.
a b c Cm d
process conditions vector. kinetic parameters vector. number of catalytic sites. integration coefficient. the type of CHd chemical species participating to the surface reaction.
258 ERi
Fi Ft h AH kRg Keq.Ri Kpi
N PA Pt R RI Ri S~,m S~.m AS T t Ui,1 ui,I t v
Wr w y Yi
Zi,j
S.K. Megalofonos, N.G. Papayannakos/Applied Catalysis A." General 165 (1997) 249-258
activation energy of the ith (i = 1 , 2 , . . . , 18) model forward reaction, cal/mol. molar flow rate of a reactant species i, mol/s, total molar flow rate, mol/s. integration step. enthalpy change, cal/mol, specific rate of the ith ( i = 1 , 2 , . . . , 1 8 ) model reaction. thermodynamic equilibrium constant of the ith model reaction at the gas phase[13]. inhibition parameters of the rate Eq. (2) where i = S , CS and CHd. total number of experiments. partial pressure of a reactant species A, atm. total pressure of the reactant system, atm. gas constant, cal/(mol K). real numbers. catalytic reaction rate of the ith (i = 1 2 , . . . , 18) model, mol/(s goat). experimental variance of the mth dependent variable. mean square of the mth dependent variable for rth model. entropy change, cal/(mol K). catalyst bed temperature, K, time of the catalyst operation, h. molar flow rate of a reactant species i, at the lth step. derivative of ui, l. number of hydrogen sulphide molecules participating in the surface reaction. number of parameters of the rth model. catalyst bed mass, g. chemical substances mole fractions vector. mole fraction of the ith component in the gas mixture. stoichiometric coefficient.
Greek letters .3w, fl~. parameters after transformations defined by the Eq. (8) and Eq. (9). d/'r.,,1 sum of squares of the residuals of mth dependent variable.
Symbols ®v one vacant catalytic site. ®A one catalytic site with the species A chemisorbed on it.
j
Superscript repetition.
o
Subscripts initial or feed condition.
eq
equilibrium.
References [1] u. Preub, M. Baerns, Chem. Eng. Technol. 10 (1987) 297-305. [2l A.B. Anderson, J. Yu, J. Catal. 119 (1989) 135-145. [3] J.R. Anderson, Applied Catalysis 47 (1989) 177-196. [4] C.J. Chen, M.H. Back, R.A. Back, Can. J. Chem. 54 (1976) 3175-3184. [51 c.J. Chen, M.H. Back, R.A. Back, Can. J. Chem. 53 (1975) 3580-3590. [61 H.B. Palmer, T.J. Hirt, J. Phys. Chem. 67 (1963) 709-711. [7] A.B. Anderson, J.J. Maloney, J. Yu, J. Catal. 112 (1988) 392-400. [8] V.E. Kaloidas, N.G. Papayannakos, Chem. Eng. Science 44(11)(1989)2493-2500. [91 V.E. Kaloidas, N.G. Papayannakos, Ind. Eng. Chem. Res 30(2) (1991) 345-351. [101 J.H. Kolts, Ind. Eng. Chem. Fund. 25 (1986) 265-269. [11] K.I. Makarov, V.K. Pechik, Kinetika i Kataliz. 16(6) (1975) 1491-1500. [12] S.K. Megalofonos, N.G. Papayannakos, Int. J. Hydrogen Energy 16(5) (1991) 319-327. [13] S. Megalofonos,N.G. Papayannakos, Appl. Catal. A: General 138 (1996) 39-55. [14] G.F. Froment, K.B. Bischof, Chemical Reactor Analysis and Design, Wiley, New York, 1979. [15] S.K. Megalofonos, Ph.D Thesis, NTUA, 1995, Athens. [16] M.E. Davis, Numerical methods and modelling for chemical engineers, Wiley, New York, 1984. [17] D.W. Marquardt, J. Soc. Ind. Appl. Math. 11(2) (1963) 431-441. [181 D.M. Himmelblau, Process analysis by statistical methods, Wiley, New York, 1970.