ХИМИЧЕСКАЯ ФИЗИКА,, 2014, том 33, № 10, с. 29-35
КИНЕТИКА И МЕХАНИЗМ ХИМИЧЕСКИХ РЕАКЦИЙ, КАТАЛИЗ
UDC 541.128.13
NUMERICAL SIMULATION OF CATALYTIC COMBUSTION OF METHANE USING WASHCOAT MODEL AND EXTERNAL SURFACE MODEL:
A COMPARISON STUDY
© 2014 Yang Du1*, Pei Wen Wang1, 2*, Wei Dong Shen2, Jia Feng Xu1 2
department of Military Petroleum Supply Engineering, Logistical Engineering University, Chongqing 401311, China 2Key Laboratory of Special Power Supply of PLA, Chongqing Communication Institute, Chongqing 400035, China
*E-mail: 13594199055@139.com Received 18.11.2013
This paper presents a comparison study of numerical simulation of catalytic combustion of methane on Pt catalyst using two different physical models. The external surface model and the washcoat model were employed. The simulations were conducted in a two-dimensional monolith reactor with detail surface kinetics. The agreement of simulation results of the washcoat model with the measured data is good. However, in contrast to experimental data, the external surface method will produce a lower result of conversion of CH4 at low temperature due to the neglecting of the larger inner surface of the washcoat. Moreover, the effects of specific surface area and pore size of washcoat on reaction rate were discussed. It can be concluded that the washcoat model would provide a more realistic result and can enrich the contents of numerical simulation of catalytic reaction.
Keywords: washcoat, catalytic combustion, mass transfer, porous media, physical model.
DOI: 10.7868/S0207401X14100033
INTRODUCTION
Monolithic reactor is widely used in diverse areas including power generation applications [1—3], steam reforming chemistry [4—7], complete catalytic oxidation ofvolatile organic compounds [8, 9] and emission control of automotive exhaust gases [10—12] due to its high geometric surface area, low pressure drop and good mechanical strength and high resistance to dust. It has been well recognized that methane is most difficult to oxidize among various fuels in the presence of catalyst or not, thus it has been a subject of great interest and studied extensively [1]. Numerical simulation of catalytic reaction has made remarkable progress with the development of computational science [11, 13, 14]. Over the years, a number of experimental and numerical investigations were conducted to improve our understanding of catalytic combustion and several models were developed [15, 16]. However, due to the complexity of the physical and chemical phenomena involved and their interactions, the reaction in monolithic reactor still remain a very complex system from the modeling viewpoint. To simplify the model, many researchers neglect some important aspects of the combustion processes. For example, in most of the studies, the diffusion of reactants into the thin wash-coat in modeling of monolithic reactors was neglected
and the reactions were assumed to take place on the external surface of the washcoat [9, 11].
Actually, although the washcoat is very thin (10—100 |m), the inner surface is tens of thousands of times larger than the external surface of washcoat. There are few literature available concerned the comparison of the washcoat model and external surface model [1, 10]. Unfortunately, the conclusions presented in these literatures are quite opposite. Mohammad Irani et al. [4] believed that the washcoat model causes a variation up to 16% in the prediction of reaction conversion of Steam Methane Reforming (SMR) and external surface model exhibites better results both in generality and accuracy. However, other researchers [12] found that washcoat model provides better agreement with the experimental data when it is used to simulate the automotive catalytic converters.
In this work, the external surface model and the washcoat model are employed to simulate the catalytic combustion of methane on Pt catalyst with detail surface kinetics under steady state condition. The simulation results of the two different models and experimental results from literature are compared with each other. In addition, the effects of specific surface area and pore size of washcoat on reaction rate are discussed.
20 mm
\
Washcoat External surface
Symmetry Fig. 1. Physical model.
PHYSICAL AND MATHEMATICAL MODEL
Monolithic catalyst is composed of a series of parallel micro-channels, which were coated with a thin layer of washcoat. The washcoat, which has very large surface area, can be regarded as porous media. The simulation was conducted in a single-channel. The geometric structure of the reactor is shown in Fig. 1. Two different physical models in monolith reactors were employed in this work. In the first model, the reactions are assumed to take place on the external surfaces of the washcoat (hereinafter referred to as "external surface model"). And in the second one, the diffusion of chemical species to the large inner surfaces in the washcoat are taken into consideration (hereinafter referred to as "washcoat model").
The physical and chemical phenomena involved can be described by the governing equations as below [17]:
continuity equation —
dp + d ( P Uj )
dt dx i
= 0,
(1)
where p is the density, t is the time, xi is the Cartesian coordinates, ui is the Cartesian components of the velocity vector.
Momentum conservation equation —
d ( p uj) + d ( p Uj Uj) = _ dp + dxjj
d t dXj dXj d Xj'
wherep is the pressure, t j is the stress tensor. Enthalpy equation —
d( ph) + d (p Ujh) = _
dt dx dXjV dx)
(2)
N N
d TTu • , dp dP , vp , D --> h:J: ,■ + - + U,-- + > kfRf.
dx,-X jlJ dt ]dx, X 1 1
(3)
d(p Y) , d(puY)
d
d t
+ -• - - '- = -irji,j + Rj, i = 1, 2, 3, n, (4)
d XJ
dxj
where Yi is the mass fraction of the specie i in the mixture, R is the net rate of production of species due to chemical reactions, and jj is the mass flux of the specie i in the direction j, which can be calculated by the following formula:
n dYi
(5)
where D, m is the diffusion coefficient of specie i in the mixture, which can be calculated as [18]:
D _
_ 0.001T 1/5(1/MA + 1/MB)
p [E v )3+(X v )3 ]
(6)
where MA is the molar mass of species A, MB is the molar mass of species B, v is diffusional volume.
The catalytic reactions on the active surface can be represented by the following formula:
j = FJiMn
(7)
where j is the diffusion mass flux, Fge denotes the ratio between the catalytic surface area in the washcoat and the geometrical area of the washcoat external surface. The production rates st for each species can be expressed as:
•i = X V'kf n [Xi]V'k, '= 1' 2
Ng + Ns, (8)
k = 1
J = 1
where Ks is the total number of elementary surface reactions, v ik and v jk are the stoichiometric coefficient s, Ns is the number of adsorbed species, Ng is the number of gas phase species, Xi is the concentration of species i, f is the forward rate coefficient which can be is described by a modified Arrhenius expression by temperature and species coverage:
kk = AkT>k exp | - ET n
i= 1
N
^ik I &ik®i k exp k
RT
(9)
Here h is the enthalpy of the mixture and Tis the temperature, h is the enthalpy of each species. Viscosity, thermal conductivity, and the diffusion coefficient of the species in the mixture are determined by the composition and temperature for each species.
Species conservation equation:
Here Ak is the pre-exponential factor, pk is temperature exponent, Eak is activation energy of reaction k, ^k and sik are stoichiometric coefficients. Since the steady-state simulation is the concern of this study, the coverage of each species on the catalyst surface does not vary with time.
The Detail reaction mechanism brought forward by Deutschmann et al. [19] is adopted to describe the reaction on Pt surface, which contains 7 gas phase species (CH4, O2, H2, H2O, CO, CO2, N2), 11 surface species (h(s), O(s), OH(s), H2O(s), C(s), CO(s), CO2(s), CH3(s), CH2(s), CH(s), Pt (s)). Table 1 gives a multistep reaction mechanism.
Diffusion coefficient of reactant in the main flow can be calculated from eq. (6), but the diffusion pro-
ks Ng + Ns
Table 1. Surface reaction mechanism for methane combustion on a Pt surface
Reaction A, mol, cm, s Ea, kJ/mol sb Vb ß
H2 + 2Pt(s) ^ 2H(s) 4.60 10-2 ^Pt(s) = -1c
2H(s) ^ H2 + 2Pt(s) 3.70 10+21 67.4 £H(s) = 6
H + Pt(s) ^ H(s) 1.00 c
O2 + 2Pt(s) ^ 2O(s) 1.80 10+21 0.0 ß = - 0.5
O2 + 2Pt(s) ^ 2O(s) 2.30 10-2 c
2O(s) + Pt(s) ^ 2O(s) 3.70 10+21 213.2 £O(s) 60
O + Pt(s) ^ O(s) 1.0 c
H2O + Pt(s) ^ 2H2O(s) 0.75 c
H2O(s) ^ H2O + Pt(s) 1.0 • 10+13 40.3
OH + Pt(s) ^ OH(s) 1.0 c
OH(s) ^ OH + Pt(s) 1.0 • 10+13 192.8
O(s) + H(s)^> OH(s)+ Pt(s) 3J0 10+21 11.5
H(s) + OH(s) ^ H2O(s) + Pt(s) 3J0 10+21 17.4
OH(s) + OH(s) ^ H2O(s) + O(s) 3J0 10+21 48.2
CO + Pt(s) ^ CO(s) 8.40 10-1 ^Pt(s) = +1c
CO(s) ^ CO + Pt(s) 1.0 10+13 125.5
CO2(s) ^ CO2 + Pt(s) 1.0 10+13 20.5
CO(s) + O(s) ^ CO2(s) + Pt(s) 3J0 10+21 105.0
CH4(s) + 2Pt(s) ^ CH3(s) + H(s) 1.0 10-2 ^Pt(s) = +0.3c
CH3(s) + Pt(s) ^ CH2(s) + H(s) 3J0 10+21 20.0
CH2(s) + Pt(s) ^ CH(s) + H(s) 3J0 10+21 20.0
CH(s) + Pt(s) ^ C(s) + H(s) 3J0 10+21 20.0
C(s) + O(s) ^ CO(s) + Pt(s) 3J0 10+21 62.8
CO(s) + Pt(s) ^ C(s) + O(s) LO • 10+18 184.0
Note: c is the Sticking coefficient.
cess in the washcoat is quite different. Before the reaction occurs on the active surface of the washcoat, the reactants must trans through the small pores in the washcoat. The process may strongly influence the apparent reaction rate. The diffusion of the reactants in the washcoat can be described by two diffusion process: molecular diffusion and Knudsen diffusion. The diffusion coefficients can be calculated by employing the parallel hole model [20]:
1
D.
eff
1 + i svD D
Dk = - de v,
(10)
(11)
where Dk is Knudsen diffusion coefficient, s is total porosity of the washcoat, t is tortuosity factor. The average velocity of the molecules can be expressed as:
v =
( 8 R
VrtM
1/2
(12)
C
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