Modeling the reactive processes within a catalytic porous medium

Applied Mathematical Modelling 35 (2011) 1915–1925

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Modeling the reactive processes within a catalytic porous medium Seyed Ali Shahamiri, Ida Wierzba ⇑ Mechanical Engineering Dept., University of Calgary, 2500 University DR, NW, Calgary, AB, Canada T2N 1N2

a r t i c l e

i n f o

Article history: Received 1 October 2010 Accepted 11 October 2010 Available online 19 October 2010 Keywords: Modelling Catalytic combustion Methane Hydrogen Detailed chemical kinetics Packed bed

a b s t r a c t A one-dimensional modelling approach to the reactive processes within a heated homogeneously premixed fuel–air mixture in its passage through a non-adiabatic catalytically reactive porous medium is described. The main focus of this contribution was comparison of the results obtained while using different modeling approaches that include mass diffusion to solid pores versus neglecting it; single step reaction versus detailed kinetic simulation; adiabatic versus non-adiabatic reactor operation; two different approaches accounting for radiation heat transfer. This model was tailored to our experimental results so as to obtain original kinetic data for corresponding global reactions for different types of catalysts and validate at the same time the predictive approaches. Results presented relate mainly to the fuels methane and hydrogen. It was shown that the employment of an ‘effective thermal conductivity’ to account for radiation heat transfer is adequate for producing satisfactory predictions while significantly cutting computational time. The use of multi-step reaction mechanisms produces results that are in good agreement with a much wider range of experimental data and does not require experimental data beforehand. It was also shown that a single-step reaction approach can be employed providing that corresponding kinetic data are derived from sufficient experimental data that need to be available for the same reactor and operational conditions. Then such simplified approach can be used to predict reasonably well the effect of operational parameters such as the feed inlet temperature and velocity. However, the use of such kinetic data for different operating conditions can lead to significantly erroneous results. It is shown that suitable catalytic beds can oxidize more fully and at lower temperatures very lean mixtures. Some of the results of the simulation using the model developed are shown to validate well against our own experimental results. Comparison of corresponding results obtained while employing overall single step reactions showed significant deviations from those of the more comprehensive multi-step reaction mechanism approach. The implication of applying the modelling approach to some practical applications is outlined. Ó 2010 Elsevier Inc. All rights reserved.

1. Introduction It is commonly known that the rates of oxidation reactions of very lean mixtures of common gaseous-fuels in air can be increased significantly through the presence of some catalytic materials. Complete combustion in catalytic devices can be achieved at lower temperatures resulting in very low NOx and other pollutants [1,2]. It would be then possible to utilize the energy release from gaseous fuel mixtures of lower heating values that are normally considered to be un-exploitable ⇑ Corresponding author. Tel.: +1 403 220 4156; fax: +1 402 282 8406. E-mail address: [email protected] (I. Wierzba). 0307-904X/$ - see front matter Ó 2010 Elsevier Inc. All rights reserved. doi:10.1016/j.apm.2010.10.020

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Nomenclature av ac c Di;m h hl Hi k keff ki;m Mi R_ i T u Yi Sv

specific geometric surface catalytic surface area to volume ratio constant pressure specific heat diffusivity of species i convective heat transfer coefficient overall heat loss coefficient enthalpy of species i thermal conductivity effective thermal conductivity convective mass transfer coefficient of species i molar mass of species i production rate of species i temperature axial velocity mass fraction of species i surface to volume ratio of the reactor wall

Greek symbols e porosity / equivalence ratio g effectiveness factor q density Subscripts g gas phase p pellet s surface, solid

waste. Catalytic reactors that can be used for combustion are of monolith or packed-bed types that operate on essentially the same principles. Numerous experimental and theoretical investigations have been conducted over the years with the aim of improving the understanding of catalytic systems with most focusing on the monolith type. Various methods have been proposed for simulating the combustion process in this type of catalytic reactors [3–6], however due to the complexity of the physical and chemical phenomena involved, many of these models were developed for specific applications and over a narrow range of operating conditions. Also, most of them neglect some important aspects of the processes involved, such as the gas phase reaction activity [7] or to assume that the gas and solid phases are throughout in thermal equilibrium [8]. Moreover, the majority of models treated the surface and gas reactions as global reactions of the Arrhenius type [7–10] with the needed kinetic data obtained by matching with the relevant experimental data. However, such approaches do not predict the overall reaction rates over a sufficiently wide range of fuel–air mixture concentrations and temperatures. Recently improved models include 2-D and some 3-D treatment of the flow within the monolith and introduce multi-step reaction mechanisms [11–13] which would provide a more realistic simulation of the fuel oxidation rates. The multi-step mechanisms for gas phase reactions are rather well developed and available in the literature for different fuels over a wide range of operational conditions [13,14]. Multi-step mechanisms for catalytic surface reactions depend strongly on the chemical composition of the catalyst employed. Recently, several mechanisms were proposed for Pt catalyst at certain operating conditions [11,15,16]. However, the incorporation of multi-step mechanisms in the model resulting in a stiff system of equations of chemical reactions increases the numerical complexity of the model. Another important aspect of modelling combustion processes in a catalytic reactor is the selection of suitable models for all three major heat transfer modes. Several correlations are available for modelling convection heat transfer, that were shown to yield essentially similar results [17]. However, the radiation heat transfer from the solid to gas phases is usually taken into account using an ‘effective thermal conductivity’ concept. More superior approaches for accounting of radiation heat transfer are available (e.g. method of intensity radiation equation), but tend to contribute towards increased numerical complexity and time. In comparison with monolith type reactors there is much less information available on catalytic combustion in packed bed reactors, and there are only a few mechanisms proposed for the catalytic oxidation of lean mixtures of methane and air on Pt. Accordingly, the objective of the present contribution is to develop a model of reactive gaseous flow within a catalytic packed bed that would include improved modelling for heat transfer and consider more realistic multi-step reaction mechanisms for both simultaneous gas phase and surface reactions. Such a modelling approach is then applied to investigate the effects of changes in the key operational parameters on the fuel oxidation within the packed bed reactor, including the effects of fuel type and the presence of diluents. The approach can also be employed in combination with experimental data to derive much needed kinetic data for catalytic surface reactions when employing different catalysts and fuels.

S.A. Shahamiri, I. Wierzba / Applied Mathematical Modelling 35 (2011) 1915–1925

1917

2. Model description A schematic diagram of the packed bed being considered is shown in Fig. 1. A premixed, preheated homogeneous fuel–air mixture enters the cylindrical reactor packed with catalytic pellets. The bed is initially at a uniform temperature. The fuel and oxygen diffuse from the bulk fluid to the catalyst surface where they are adsorbed and reacted. The products formed, leave the surface via a desorption process and travel from the surface to the gas mixture via mass diffusion. A portion of the heat released due to the surface reactions increases the solid temperature, while the remainder is transferred to the gas. The heat received by the gas may be high enough to promote gas phase reactions. The three modes of heat transfer (conduction, convection and radiation) contribute jointly to the transport of heat within the reactor. The reactor is assumed to operate non-adiabatically and at atmospheric pressure. The flow within the reactor is assumed to be one-dimensional. The gas and solid are not in local thermal equilibrium. Therefore, separate energy equations are considered for each phase. Radiation heat transfer in the gas phase is considered to be negligible in comparison to the solid pellets radiation. The thermophysical properties of the gas species are functions of the local temperature and composition. The thermal conductivity of pellets is also considered to be a function of temperature. However, other properties of the solid phase such as density, specific heat and emissivity are assumed to be uniform and temperature independent since their values were considered to vary insignificantly over the range of temperatures considered [18]. The flow inside the reactor is laminar and the governing equations of continuity, energy balance for solid, energy balance for fluid, mass balance of species in the gas phase and on the catalyst surface are the following: continuity:

@ qg =@t þ @ðqg uÞ=@x ¼ 0

ð1Þ

species mass balance in gas phase:





qg @Y g;i =@t þ qg u@ðY g;i Þ=@x ¼ @ qg Di;m ð@Y g;i =@xÞ =@x þ K i;m av qg ðY s;i  Y g;i Þ=e þ Mi R_ g;i ; ði ¼ 1; . . . ; Ng Þ

ð2Þ

species mass balance on surface:

K i;m av qg ðY g;i  Y s;i Þ ¼ gac M i R_ s;i ;

ði ¼ 1; . . . ; Ng Þ

ð3Þ

energy balance for gas phase:





qg cg @T g =@t þ qg cg u@ðT g Þ=@x ¼ @ kg ð@T g =@xÞ =@x þ hav ðT s  T g Þ=e þ

Ng X

M j R_ g;j Hj

ð4Þ

j¼1

energy balance for solid phase:





qs cs @T s =@t ¼ @ keff ð@T s =@xÞ =@x þ hav ðT g  T s Þ=ð1  eÞ þ h1 Sv ðT amb  T s Þ þ

Ns X

ac M j gR_ s;j Hj =ð1  eÞ

ð5Þ

j¼1

The convective heat transfer and mass transfer coefficients were determined using Chilton–Colburn approach. The diffusion of species from the fluid bulk to the surface of the pellets and from there into the pores has been taken into account via a convective mass transfer coefficient [19] and an effectiveness factor, respectively. The effectiveness factor g which is a function of porosity, gas species concentration at the pellet surface, surface reaction rates and the diffusion coefficients of the gas species was estimated using Thiele’s approach [17]

g ¼ tanh U=U

ð6Þ

where U is Thiele factor and is defined as

U ¼ RðR_ s;i =De C s;i Þ1=2

ð7Þ

R is the thickness of the catalytic layer and C s;i is the concentration of the fuel on the pellet surface. R_ s;i is the rate of adsorption of fuel on the catalyst surface calculated as described in [20]. De is the effective diffusion coefficient in the pores of pellets and

Fig. 1. Schematic diagram of the reactor.

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De ¼ ðsp =ep Þ=ð1=Dk þ 1=Di;m Þ

ð8Þ

sp and ep are tortuosity and porosity of the pellets and Dk Knudsen diffusion which is Dk ¼ 9700rðT=Mi Þ1=2

ð9Þ

where r is the radius of the pores, T is temperature of pellet and M i is the molecular weight of the fuel. Heat loss to the surroundings was also included in the model. The overall heat transfer coefficient includes the thermal resistances of the boundary layer near the wall, conduction through the reactor wall and natural convection outside of the reactor [17]. The effective thermal conductivity of the pellets [20], accounts for both conduction and radiation heat transfers. This relatively simple modelling approach was selected for this contribution, because for a packed bed it yields results comparable to those obtained using the more comprehensive ‘radiation transfer equation’ approach [20,25] while being more computationally economical. The multi-step mechanisms for the gas phase and surface reactions are presented in Tables 1 and 2. They are based on mechanisms proposed in [11–16,21] with some relatively small modifications [20]. The kinetics used for single-step model have been derived based on the available experimental data and are presented in Table 3.

3. Numerical approach The governing equations for a packed bed reactor were solved using the commercial software, ‘FLUENT’ along with a number of modifying subroutines (UDF). These subroutines were developed to compute the thermo-physical properties, heat and mass transfer coefficients, species concentrations in the gas and on the surface, and the amount of heat release. The integrator CVODE [22] was also implemented into the subroutines for solving the system of equations of chemical reactions and obtaining the corresponding temporal concentrations of species at each numerical time step. FLUENT built-in chemistry sol-

Table 1 Surface reaction mechanism of oxidation of methane on Pt. Reactions

S0 or A (s1)

b

E (kJ/mol)

Adsorption reactions 1 H2 + Pt(s) + Pt(s) => H(s) + H(s) 2 O2 + Pt(s) + Pt(s) => O(s) + O(s) 3 CH4 + Pt(s) + Pt(s) => CH3(s) + H(s) 4 CH4 + O(s) +Pt(s) => CH3(s) + OH(s) 5 H2O + Pt(s) => H2O(s) 6 CO2 + Pt(s) => CO2(s) 7 CO + Pt(s) => CO(s) 8 H + Pt(s) => H(s) 9 O + Pt(s) => O(s) 10 OH + Pt(s) => OH(s)

0.046 0.07 (300/T) 0.15 1.36E+10 0.75 0.005 0.84 1.0 1.0 1.0

Desorptions 11 12 13 14 15 16 17 18

1.0E13 1.0E13 4.5E12 1.0E13 1.0E15 6.0E13 1.0E13 5.0E13

64.4 235.0 41.8 27.1 146.0 254.4 358.8 251.1

3.5E12 2.0E12 5.5E12 3.1E10 2.0E12 2.7E11 1.0E11 1.0E11 1.0E11 1.0E11 2.72E10 2.72E10 3.4E13 8.4E13 2.0E14 8.4E13 8.4E13 3.4E13

11.2 77.3 66.2 101.4 74.0 43.1 0.0 236.5 117.6 173.3 38.7 8.4 70.3 0.0 58.9 0.0 0.0 138.0

reactions H(s) + H(s) => Pt(s) + Pt(s) + H2 O(s) + O(s) => Pt(s) + Pt(s) + O2 H2O(s) => H2O + Pt(s) CO2(s) => CO2 + Pt(s) CO(s) => CO + Pt(s) H(s) => H + Pt(s) O(s) => O + Pt(s) OH(s) => OH + Pt(s)

Surface reactions 19 H(s) + O(s) => OH(s) + Pt(s) 20 OH(s) + Pt(s) => H(s) + O(s) 21 H(s) + OH(s) => H2O(s) + Pt(s) 22 H2O(s) + Pt(s) => H(s) + OH(s) 23 OH(s) + OH(s) => H2O(s) + O(s) 24 H2O(s) + O(s) => OH(s) + OH(s) 25 C(s) + O(s) => CO(s) + Pt(s) 26 CO(s) + Pt(s) => C(s) + O(s) 27 CO(s) + O(s) => CO2(s) + Pt(s) 28 CO2(s) + Pt(s) => CO(s) + O(s) 29 CO(s) + OH(s) => CO2(s) + H(s) 30 CO2(s) + H(s) => CO(s) + OH(s) 31 CH3(s) + Pt(s) => CH2(s) + H(s) 32 CH2(s) + H(s) => CH3(s) + Pt(s) 33 CH2(s) + Pt(s) => CH(s) + H(s) 34 CH(s) + H(s) => CH2(s) + Pt(s) 35 CH(s) + Pt(s) => C(s) + H(s) 36 C(s) + H(s) => CH(s) + Pt(s)

0.7

0.0 0.0 27.0 42.0 0.0 0.0 0.0 0.0 0.0 0.0

l

e (kJ/mol) Pt(s)

1.0

8.0

O(s)

10.0 188.0

H(s) O(s)

33.0 2.8 94.0 167.0

CO(s) H(s) O(s) O(s)

73.2

O(s)

167.0

O(s)

240

O(s)

33.0 33.0 -94.0 33.0

CO(s) CO(s) O(s) O(s)

2.8 50.0 2.8 2.8

H(s) C(s) H(s) H(s)

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S.A. Shahamiri, I. Wierzba / Applied Mathematical Modelling 35 (2011) 1915–1925 Table 2 Gas-phase reaction mechanism of oxidation of methane [16].

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

Reactions

A (mol cm s1)

b

E (kJ/mol)

O2 + H => OH + O HO2 + OH => H2O + O2 H + O2 + M => HO2 + M CH3 + O2 => CH2O + OH CHO + M => CO + H CH4 + OH => H2O + CH3 CO + OH => CO2 + H CH3 + HO2 => CH3O + OH CHO + O2 => CO + HO2 CH3 + HO2 => CH4 + O2 CH3O + O2 => CH2O + HO2 OH + OH => H2O + O HO2 + HO2 => H2O2 + O2 OH + OH + M => H2O2 + M CO + HO2 => CO2 + OH CH2O + H => CHO + H2 CH2O + OH => CHO + H2O CH2O + HO2 => CHO + H2O2 CH2O + O2 => CHO + HO2 CH3 + CH3 => C2H6 CH4 + O => OH + CH3 CH4 + HO2 => H2O2 + CH3 CH3O + CH3O => CH3OH + CH2O CH2O + CH3O => CH3OH + CHO CH3O2 + M => CH3 + O2 CH3 + O2 + M => CH3O2 + M CH3O2 + HO2 => CH3O2H + O2 CH3OH + OH => CH2OH + H2O

8.70E13 6.00E13 2.30E18 3.30E11 3.94E14 1.60E07 4.76E07 1.80E13 3.00E12 3.60E12 4.00E10 1.50E09 2.50E11 3.25E22 1.50E14 2.30E10 3.40E09 3.00E12 6.00E13 8.32E43 6.92E08 1.10E13 3.00E13 6.00E11 7.24E16 1.41E16 4.60E10 1.00E13

0 0 0.8 0 0 1.8 1.2 0 0 0 0 1.1 0 2 0 1.1 1.2 0 0 9.1 1.6 0 0 0 0 0 0 0

60.3 0 0 37.4 70.3 11.6 0.29 0 0 0 8.9 0.42 5.2 0 98.7 13.7 1.9 54.7 170.7 67 35.5 103.1 0 13.8 111.1 4.6 10.9 7.1

Table 3 Kinetic data used in calculations for single-step reaction mechanism. Gas phase/surface reactions

Fuel

A (kmol, m, s)

E (kJ/mol)

Gas phase

CH4

128.9

Gas phase Cr2O3/Co3O4 Cr2O3/Co3O4 Pt Pt

H2 CH4 H2 CH4 H2

1.E7, T < 800 K 1.6E6, T P 800 K 2.9E9 3.97E2 3.05E1 4.20E2 3.62E1

95.4 52.4 22.5 50.0 22.48

ver and CHEMKIN link do not allow the inclusion of the effectiveness factor and coverage dependent kinetic parameters in the calculations of surface reaction rates while the CVODE integrator is completely flexible in this regard. The steady state solution for each condition was obtained by performing a sufficient number of iterations. Eight hundred computational cells for spatial discretization of the domain and a time step of 10 ls were used in the simulation. To validate the developed model, simulations were conducted for hydrogen and methane for the same operational conditions of the reactor that we experimentally employed previously [24]. The reactor bed has inside diameter of 28 mm and length of 50 mm. The bed porosity is 0.4. The catalyst used is polycrystalline Pt deposited on a substrate in the form of cylindrical pellets 3.2 mm long and 3.2 mm diameter made of Al2O3. The ratio of tortuosity to porosity of pellet (Eq. (8)) was 4.0 [23]. The pressure along the reactor was assumed to be 89 kPa, the same as in the experiments and the ambient temperature was 293 K. For all the cases presented the mixture approach space velocity was 7.2  104 h1. The estimated value of overall heat transfer coefficient was 280 W/m2 K. This value is in agreement with the experimental value obtained for the same reactor [24]. To validate the gas phase reaction mechanism employed, the simulations were also conducted for comparative purposes for an inert bed reactor. The ratio of catalytic surface area to the geometric surface area used in simulations was 2.31 and the catalyst site density was assumed to be 2.72  109 mol/cm2 [13]. 4. Results The results of application of the model showed the importance of proper accounting for external heat loss off the reactor, as shown in Fig. 2. It can be seen that a relatively low inlet mixture temperature of 700 K the methane conversion at the exit from the reactor when operated non-adiabatically is 42%, while it is 85% in the adiabatic reactor.

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CH4 conversion, vol%

100 80

adiaba atic non-ad diabatic

K 00 =9 n i T

Ø=0.35

60

Pt

40 K 00 =7 Tin

20 0 0.00 0

0.01

0.02

0.03

0.04

0.0 05

Distance from inlet, m Fig. 2. CH4 conversion along the bed for adiabatic and non-adiabatic reactors; Pt catalyst; multi-step reaction model.

The effect of the radiation heat transfer model employed on methane conversion within the bed was investigated employing two different approaches, the ‘effective thermal conductivity’ and ‘radiation transfer equation’ while using a single-step chemical reaction model. As an example, the results of simulation of oxidation of the methane–air mixture of an equivalence ratio of 0.35, with Cr2O3/Co3O4 catalyst are shown in Fig. 3. It can be seen that the effect of the radiation model applied tends to be relatively small at relatively low mixture intake temperatures but becomes more noticeable at higher intake temperatures. However, the calculation time for this case when applying the ‘Radiation Transfer Equation’ model was eight times larger than when employing the ‘effective thermal conductivity model’. Accordingly, the results presented for other simulations were obtained employing the ‘effective thermal conductivity’ model for radiation heat transfer. The importance of inclusion of an effectiveness factor in Eqs. (3) and (5) can be clearly seen in Fig. 4 which shows the results of calculations of methane conversion for two cases. It can be seen that in case when the effect of the pore diffusion is neglected (i.e. g is 1.0) the methane conversion is highly overestimated as the complete conversion of methane was obtained at relatively low feed temperature of 700 K. It was found that the single-step (global) reaction approach can predict the conversion of the fuel in the reactor reasonably well provided that the corresponding experimental data obtained for the same reactor and the same operational conditions were available beforehand to derive the proper kinetic data for the global reaction. It can be seen (Figs. 5 and 6) that the simulation results for H2 and CH4 conversion over Pt and Cr2O3/Co3O4 catalysts are in very good agreement with the corresponding experimental data [24] employed in the derivation of kinetic data. This approach can be very useful for catalysts for which a multi-step reaction mechanism is not available (for example in house made catalysts of varying composition). As can be seen in Fig. 7 such approach can be effectively used to predict the effect of feed inlet velocity on the fuel conversion. If such experimental data were not available then resorting to the very time consuming calculations of employing multistep reaction mechanisms for both the gas and solid phases is justified. This is especially valid, for example, when investigating the effect of changes in equivalence ratio of the feed mixture. It can be seen in Fig. 8 that employing a single-step reaction based on kinetic data obtained for a certain equivalence ratio (0.35 in this case) to simulate the behaviour of hydrogen–air mixtures of different equivalence ratios gives very poor agreement with our corresponding experimental data. The

CH4 conversion, %

100 80

Ø = 0.35, Cr2O3/Co3O4 radiation transfer equation effective thermal conductivity

60 40 20 0 600

650

700 750 800 850 Inlet temperature, K

900

Fig. 3. Effect of radiation model on CH4 conversion as a function of inlet temperature; £ ¼ 0:35; Pt catalyst; single-step reaction model.

S.A. Shahamiri, I. Wierzba / Applied Mathematical Modelling 35 (2011) 1915–1925

Ø = 0.35, Pt

100 CH4 conversion, %

1921

η= 1.0

80

η = (tanh Φ)/Φ

60 40

▬ calc ■ exp [24]

20 0 600

650

700 750 800 850 Inlet temperature, K

900

Fig. 4. Effect of inclusion of pore diffusion in the model on the CH4 conversion as a function inlet temperature; £ ¼ 0:35; Pt catalyst; multi-step reaction model.

Ø = 0.35

100 CH4 conversion, vol %

●, ■, ▲ exp[24]

80

—

cal

60 40

Cr2O3/Co3O4

Pt

20

inert bed

0 500 600 700 800 900 1000 1100 1200 Inlet temperature, K Fig. 5. CH4 conversion as a function of inlet temperature for two different catalysts; £ ¼ 0:35; single-step reaction model.

∅=0.35

H2 conversion, vol %

100 ■, ▲ exp[24]

80 60 40

—

cal

Pt Cr2O3/Co3O4

inert bed

20 0 300

400

500

600

700

800

Inlet temperature, K Fig. 6. H2 conversion as a function of inlet temperature for two different catalysts; £ ¼ 0:35; single-step reaction model.

single-step model overestimates hydrogen conversion rates for richer mixtures and underestimates those for leaner mixtures especially for higher intake temperatures. For example, for a mixture of £ ¼ 0:5 the results of the simulation shows 100% conversion of hydrogen for the intake temperature of 300 K while the corresponding experimental value is only about 2%. Similarly, for a very lean mixture of £ ¼ 0:15 at the inlet temperature of 370 K, the predicted value is 16% yet the exper-

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Ø = 0.35, Cr2O3/Co3O4

CH4 conversion, %

(a) 100

Tinlet, K 1000

80 60

900

40

800

20

700

0 0.5

1

3

3.5

Ø = 0.35, Cr2O3/Co3O4

(b) 100 H2 conversion, %

1.5 2 2.5 Inlet velocity, m/s

Tinlet, K

80

370

60

▬ calc ● exp [24]

350

40

330

20

310 300

0 0.5

1

1.5 2 2.5 3 Inlet velocity, m/s

3.5

Fig. 7. Effect of inlet velocity on fuel conversion; £ ¼ 0:35; Cr2O3/Co3O4 catalyst; single-step reaction model; (a) methane, (b) hydrogen.

Cr2O3/Co3O4

H2 conversion, vol. %

100

Ø=0.55

80 60

Ø=0.35

●, ■, ▲ exp[24]

40

—

cal Ø=0.15

20 0 300

320 340 360 380 Inlet temperature, K

400

Fig. 8. H2 conversion as a function of inlet temperature for different equivalence ratios; Cr2O3/Co3O4 catalyst; single-step reaction model.

imental value is 67%. Although this comparison was conducted for Cr2O3/Co3O4 catalyst the same trends can be expected for a Pt catalyst. The need for experimental data beforehand is unnecessary when employing multi-step reaction mechanisms for catalytic surface and gas-phase reactions. Fig. 9 shows a comparison between the calculated and experimental values of CH4 conversion within catalytic (Pt) and non-catalytic (inert) beds for a methane–air mixture with an equivalence ratio of 0.35, while Fig. 10 shows a similar comparison for hydrogen–air mixture. The agreement appears to be very good, validating the surface and gas-phase reaction mechanisms employed. It can be seen also the enormous effectiveness of the employment of the catalytic bed in comparison with the corresponding case of a non-catalytic bed for both fuels.

CH4 conversion, vol %

S.A. Shahamiri, I. Wierzba / Applied Mathematical Modelling 35 (2011) 1915–1925

1923

100 ■ ● exp[24] ■,

—

80

cal

60 40 inert

Pt

20 0 500

600

700

800

900

1000 1100

Inlet tem mperature, K Fig. 9. CH4 conversion as a function of inlet temperature within inert and catalytic reactors; £ ¼ 0:35; Pt catalyst; multi-step reaction model.

H2 conversion, vol %

100 80 60 Pt

inert

40 20

●

exp[24]

—

cal

0 300

400

500

600

7 700

800

Inlet temperature, K Fig. 10. H2 conversion as a function of inlet temperature within inert and catalytic reactors; £ ¼ 0:35; Pt catalyst; multi-step reaction model.

Pt

80

Ø=0.55

60 Ø =0 .3 5

CH4 conversion, vol %

100

40

Ø=0.15

20 0

500

600 700 800 Inlet temperature, K

900

Fig. 11. CH4 conversion as a function of inlet temperature for different equivalence ratios using different reaction models; solid line - multi-step reaction model; broken lines - single-step reaction model; Pt catalyst.

The comparison of the results of the simulations obtained with these two types of reaction models for both methane–air and hydrogen–air mixtures of different equivalence ratios and inlet temperatures is shown in Figs. 11 and 12, respectively. It can be seen, that the results deviate greatly, especially for hydrogen–air mixtures. Predicted results when based on using the detailed kinetic scheme produce much more realistic results.

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Pt

H2 conversion, vol %

100 80

Ø=0.55

Ø=0.35

60 40 Ø=0.15

20 0 300

320

340 360 380 Inlet temperature, K

400

Fig. 12. H2 conversion as a function of inlet temperature for different equivalence ratios using different reaction models; solid line - multi-step reaction model; broken lines - single-step reaction model; Pt catalyst.

5. Conclusion The model developed was shown to allow the reasonable prediction of the oxidation of lean methane–air and hydrogen– air mixtures in catalytic and non-catalytic packed bed reactors. It is important to account for the external heat losses from the reactor, as the erroneous fuel conversion rate can be predicted, especially at the lower feed temperatures. The employment of an ‘effective thermal conductivity’ to account for radiation heat transfer is adequate for producing satisfactory predictions while significantly cutting computational time. The use of multi-step reaction mechanisms produces results that are in good agreement with a much wider range of experimental data and do not require experimental data beforehand. However, the surface reaction mechanism for different catalysts is often not available. In this case a single-step reaction approach can be employed providing that corresponding kinetic data are derived from sufficient experimental data that need to be available for the same reactor and operational conditions. Then such simplified approach can be used to predict reasonably well the effect of operational parameters such as the feed inlet temperature and velocity. However, the use of such kinetic data for different operating conditions can lead to significantly erroneous results. Acknowledgments The financial supports of Natural Sciences and Engineering Research Council of Canada, the Centre for Environmental Engineering Research and Education at the University of Calgary, ConocoPhillips Canada are greatly appreciated. References [1] K. Everaert, J. Baeyens, Catalytic combustion of volatile organic compounds, J. Hazard. Mater. B109 (2000) 113–139. [2] P. Forzatti, Environmental catalysis for stationary applications, Catal. Today 62 (2000) 51–65. [3] G. Gropp, E. Tronconi, Simulation of structured catalytic reactors with enhanced thermal conductivity for selective oxidation reactions, Catal. Today 69 (2001) 63–73. [4] M. Maestri, A. Beretta, G. Groppi, E. Tronconi, P. Forzatti, Comparison among structured and packed-bed reactors for the catalytic partial oxidation of CH4 at short contact times, Catal. Today 105 (2005) 709–717. [5] P. Marin, M.G.A. Hevia, S. Ordonez, F.V. Diez, Combustion of methane lean mixtures in reverse flow reactors: comparison between packed and structured catalyst beds, Catal. Today 105 (2005) 701–708. [6] C.T. Goralski Jr., L.D. Schmidt, Modeling heterogeneous and homogeneous reactions in the high-temperature catalytic combustion of methane, Chem. Eng. Sci. 54 (1999) 5791–5807. [7] F. Aube, H. Sapoundjiev, Mathematical model and numerical simulations of catalytic flow reversal reactors for industrial applications, Comput. Chem. Eng. 24 (2000) 2623–2632. [8] G. Groppi, A. Belloli, E. Tronconi, P. Forzatti, A comparison of lumped and distributed models of monolith catalytic combustors, Chem. Eng. Sci. 50 (17) (1995) 2705–2715. [9] R.E. Hayes, S.T. Kolaczkowski, W.J. Thomas, Finite-element model for a catalytic monolith reactor, Comput. Chem. Eng. 16 (7) (1992) 645–657. [10] G. Groppi, E. Tronconi, P. Forzatti, Mathematical models of catalytic applications, Catal. Rev. Sci. Eng. 41 (2) (1999) 22–254. [11] R.R. Quiceno, J. Perez Ramirez, J. Warnatz, O. Deutschmann, Modelling the high-temperature catalytic partial oxidation of methane over platinum gauze: detailed gas phase and surface chemistries coupled with 3D flow field simulation, Appl. Catal. A Gen. 303 (2000) 166–176. [12] S. Mazumder, D. Sengupta, Sub-grid scale modelling of heterogeneous chemical reactions and transport in full-scale catalytic converters, Combust. Flame 131 (2002) 85–97. [13] O. Deutschmann, L.I. Maier, U. Riedel, A.H. Stroemman, R.W. Dibble, Hydrogen assisted catalytic combustion of methane on platinum, Catal. Today 59 (2000) 141–150. [14] P. Aghalayam, Y.K. Park, N. Fernandes, V. Papavassiliou, A.B. Mhadeshwar, D.G. Vlachos, A C1 mechanism for methane oxidation on platinum, J. Catal. 213 (2003) 23–38. [15] C.P. Chou, J.Y. Chen, G.H. Evans, W.S. Winters, Numerical studies of methane catalytic combustion inside a monolith honeycomb reactor using multistep surface reactions, Combust. Sci. Technol. 150 (2000) 27–57.

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