Catalytic Converters for Automobile Diesel Engines with Adsorption of

A mathematical model of a catalytic converter for automobile diesel engines that ... These are represented by all three phases of matter.1 Besides nit...
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Ind. Eng. Chem. Res. 2005, 44, 9524-9534

Catalytic Converters for Automobile Diesel Engines with Adsorption of Hydrocarbons on Zeolites David Kryl,† Petr Kocˇ ı´,† Milan Kubı´cˇ ek,‡ Milosˇ Marek,*,† Teuvo Maunula,§ and Matti Ha1 rko1 nen§ Department of Chemical Engineering and Department of Mathematics, Center for Nonlinear Dynamics of Chemical and Biological Systems, Prague Institute of Chemical Technology, Technicka´ 5, CZ-16628 Praha 6, Czech Republic, and Ecocat R&D, Typpitie 1, FIN-90650 Oulu, Finland

A mathematical model of a catalytic converter for automobile diesel engines that contains zeolites for adsorption of hydrocarbons has been developed. The model includes a description of massand heat-transfer resistance at the external surface of the monolith washcoat and internal diffusion within the catalytic washcoat layer. Kinetic parameters for adsorption and oxidation of hydrocarbons [propene (C3H6), decane (C10H22), and toluene (C6H5CH3)], CO oxidation, and NOx adsorption and reduction were evaluated on the basis of dynamic experiments. Model simulations of dynamic operation regimes illustrate the effects of the inlet flow rate, temperature and adsorption capacity on the light-off, integral conversions, and spatiotemporal concentration patterns in the monolith. The effects of varying the transport properties of the washcoat layer (effective diffusion coefficient) and washcoat thickness are also investigated. 1. Introduction It is expected that the world market for diesel engines will grow significantly in the near future because of their superior thermal efficiency, durability, and reliability in comparison to the gasoline-powered engines. However, the stringent legislation limits for the amount of pollutants in exhaust gases pose some major challenges for the diesel passenger car that cannot be met without an efficient emission control system. Unlike the spark-ignited engine operating with a stoichiometric fuel mixture, diesel engines work under air excess conditions. Such a design of the combustion process leads to significant emissions of undesirable compounds. These are represented by all three phases of matter.1 Besides nitrogen (N2) and oxygen (O2), the gaseous phase consists of carbon monoxide (CO) and hydrocarbons (HCs) derived primarily from unburned fuel, oxides of nitrogen (NOx), and oxides of sulfur (SOx). The liquid phase consisting of unburned fuel, lubricating oil, and liquid sulfates is mostly sorbed on the solid particles of dry carbon and soot. Compared to the catalytic converters used for gasoline engines, the functional requirements for a catalyst in diesel converters are quite demanding. Generally, the role of the catalyst is to minimize particulates and gaseous emissions of CO and HCs by oxidizing them to CO2 and H2O. At the same time, the catalyst must exhibit a low activity for oxidation of gaseous SO2 to SO3. Because diesel engines operate with a lean fuel mixture (air excess), and therefore work at a lower temperature than the spark-ignited engines, the catalyst has to exhibit high activity at low temperatures. The high content of oxygen also complicates the reduction of NOx.2 Until * To whom correspondence should be addressed. Tel.: +420 22044 3104. Fax: +420 23333 7335. E-mail: milos.marek@ vscht.cz. Web site: http://www.vscht.cz/monolith/. † Department of Chemical Engineering. ‡ Department of Mathematics. § Ecocat R&D.

now, NOx emissions from diesel engines have been controlled by an advanced engine calibration or exhaust gas recirculation. Because future standards will require significant reductions in the amounts of NOx emissions, a catalyst technology able to fulfill these requirements has to be further developed.3-5 Moreover, for such a system to function properly, the amount of soot has to be reduced to prevent clogging of the monolith channels6 by use of particulate filters. The ever-increasingly stringent exhaust emissions legislation requires an ever-increasing degree of efficiency of a catalytic converter. This has resulted in the need for the development of new technologies, materials, and structures of converters. Accordingly, such demands also make the experimental testing of the exhaust gas converters more complicated and expensive. Thus, to decrease the costs and design time for the development of such systems, mathematical modeling is very helpful. In general, because of a nonuniform flow distribution in the monolith structure of the catalytic converter, the system represents a spatially three-dimensional (3D) problem. However, a 3D modeling approach results in a high complexity and significant demands on the calculation time. Introduction of simplifying assumptions can reduce the problem to two or even single space dimensions. This leads to a significant model simplification, while the conformity with the real behavior of the catalytic converter is kept on an acceptable level.4,7-9 In this paper, we present the results of simulations of diesel monolithic catalytic converters by a mathematical model based on balance equations of a single monolith channel. Combined nonstationary and pseudosteady-state kinetics with the kinetic parameters fitted to experimental data have been used in the modeling equations. Two types of mathematical models have been employed to describe the catalytic converter. In the first one, the concentration gradient in the washcoat has been neglected. This approach has led to a spatially onedimensional (1D) modeling problem. The second model, in which the internal diffusion in the catalytic washcoat

10.1021/ie050249v CCC: $30.25 © 2005 American Chemical Society Published on Web 07/08/2005

Ind. Eng. Chem. Res., Vol. 44, No. 25, 2005 9525 Table 1. Reaction Schemes Employed in the Model, Including Important Adsorption and Desorption Stepsa 1 2 3 4 5 6 7 8 9 10 11

Table 3. Values of Model Parameters Used in the Simulations

CO + 1/2O2 f CO2 C3H6 + 9/2O2 f 3CO2 + 3H2O C10H22 + 31/2O2 f 10CO2 + 11H2O C6H5CH3 + 9/2O2 f 3CO2 + 3H2O C3H6 + 2NO + 7/2O2 f N2 + 3CO2 + 3H2O C10H22 + 2NO + 19/2O2 f N2 + 10CO2 + 3H2O C6H5CH3 + 2NO + 8O2 f N2 + 7CO2 + 4H2O NO + 1/2O2 h NO2 C10H22 + Zeol h C10H22‚Zeol C6H5CH3 + Zeol h C6H5CH3‚Zeol NO2 + 1/2O2 + Alu h NO3‚Alu

a The corresponding kinetic relations are given in Table 2. Zeol represents a zeolitic adsorption site, C10H22‚Zeol is adsorbed decane, and C6H5CH3‚Zeol is adsorbed toluene. Alu denotes an alumina adsorption site, and NO3‚Alu represents adsorbed NO2 in the form of a surface nitrate.

Table 2. Kinetic Expressions Used in the Modeling Equationsa reaction no. 1 2 3 4 5 6 7 8 9 10 11

kinetic expression R1 ) k1yCOyO2/[(1 + Ka,1,COyCO + Ka,1,CxHyyCxHy)2(1 + Ka,1,xyCO2yCxHy2)(1 + Ka,1,NOyNO0.7)T] R2 ) k2y3yO2/[(1 + X2yC3H6)(1 + Y2yCNO)] R3 ) k3yC10H22yO2/(1 + X3yC6H5CH3yO2) R4 ) k4yC6H5CH3yO2/[(1 + K4yC6H5CH3)(1 + Y4yNO)] R5 ) R2K5NOyNO/[(1 + Ka,5,O2yO2)(1 + Z5yNO)] R6 ) R3K6,NOyNO/[(1 + Ka,6,O2yO2)(1 + Z6yNO)] R7 ) R4K7,NOyNO/[(1 + Ka,7,O2yO2)(1 + Z7yNO)] R8 ) (kf8yNOyO20.5 - kb8yNO2)/(1 + Ka,8,NO + Ka,8,O2yO20.5 + Ka,8,NO2yNO2) R9 ) Ψcap,C10H22[kads 9 yC10H22(1 - ψC10H22) kdes 9 ψC10H22] R10 ) Ψcap,C6H5CH3[kads 10 yC6H5CH3(1 - ψC6H5CH3) kdes 10 ψC6H5CH3] des R11 ) Ψcap,NOx[kads 11 ψNO2(1 - ψNO2) - k11 ψNO2]

value 2800-3300 m2 m-3 698-968 J kg-1 K-1 3 × 10-7-1 × 10-6 m2 s-1 7.5-15 cm 298 K 15000-140000 h-1 (STP) 12-72 µm 0.74-0.88 0.7 3.64-9.04 W m-1 K-1 2520-5220 kg m-3 1.4-10 cm 25-100 mol m-3 15-60 mol m-3 15-60 mol m-3

processes are treated here formally as reaction steps. The values of the physical parameters employed in the models are given in Table 3. 2.1. Spatially 1D Plug-Flow Model. A spatially 1D model of a monolith channel with plug flow is represented by the following equations:

∂ck(z,t) ∂(vck) kca s )+ g (ck - ck), k ) 1, ..., K ∂t ∂z  ∂csk(z,t)

kc a

)

(ck - csk) +

s(1 - g)φs

∂t

1

J

∑νk,jRj,

sj)1

∂ψm(z,t)

)

Ψcap,m

∂t Fgcgp

Fscsp

∂T s(z,t) ∂t

J

1

νm,jψRj, ∑ j)1

m ) 1, ..., M

kha ∂T(z,t) ∂T ) -v Fcp + g (Ts - T) ∂t ∂z  s

)λ

∂2 T s ∂z

+

2

k ha g

1-

(3)

(4)

(T - T s) J

2. Mathematical Models Plug flow of the gas in the axial direction (z), external heat and mass transfer to the surface of the washcoat, adsorption and reactions in the catalytic washcoat layer, and heat accumulation and conduction in the solid phase are considered in the spatially 1D model of a monolith channel. In addition to that, an explicit description of the internal diffusion in the catalytic washcoat layer has been included in the spatially 2D model of a monolith channel. The following balances are considered in the models: (i) mass balances in the flowing gas, (ii) mass balances in the washcoat pores, (iii) mass balances on the catalytic surface, (iv) enthalpy balance of the flowing gas, and (v) enthalpy balance of the solid phase. These balances are represented by partial differential equations (PDEs): eqs 1-5 for the 1D model and eqs 9-13 for the 2D model. The respective boundary conditions are described by eqs 6-8 for the 1D model and by eqs 14-18 for the 2D model. The reactions considered in the model are given in Table 1; the respective kinetic expressions are summarized in Table 2. Note that the adsorption/desorption

(1)

k ) 1, ..., K (2)

a The corresponding reaction and adsorption/desorption steps are defined in Table 1. For details about the employed kinetic expressions, compare the following references: reaction 1,30 reactions 2-7,28 and reactions 8-11.4

layer has been considered explicitly, represents a spatially two-dimensional (2D) problem.

parameter a csp Deff ref L Tref u δ g s λs Fs σ Ψcap,C10H22 Ψcap,C6H5CH3 Ψcap,NOx

φs

∆Hr,jRj ∑ j)1

(5)

Here Rj’s are reaction rates defined in Table 2. Boundary conditions at the inlet (z ) 0) and at the outlet (z ) L) of the monolith are

T ) T in ∂T s/∂z ) 0

at z ) 0 at z ) 0 or z ) L

ck ) cin k , k ) 1, ..., K,

at z ) 0

(6) (7) (8)

2.2. Spatially 2D Model with Washcoat Diffusion. When the washcoat diffusion is considered explicitly, concentration variations in the washcoat layer are expected also in the radial (transverse) direction (r).7 Reaction and diffusion take place simultaneously in the catalytic washcoat layer. On the other hand, we can assume that there are no temperature gradients in the transverse direction within the washcoat layer and in the wall of the channel because of a low thickness of the layer and a sufficiently high heat conductivity.10

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∂(vck) kca s ∂ck(z,t) )+ g (ck|r)δ - ck), k ) 1, ..., K (9) ∂t ∂z  ∂csk(z,r,t)

)

2 s Deff k ∂ ck

+

s ∂r2

∂t

∂ψm(z,r,t)

)

1

1 

J

νk,jRj, ∑ s j)1

∑νm,jψRj,

m ) 1, ..., M (11)

kha ∂T(z,t) ∂T ) -v Fc + g (T s - T) Fcp ∂t ∂z p  Fscsp

∂T s(z,t) ∂t

s

)λ

∂2 T s

(10)

J

Ψcap,mj)1

∂t

k ) 1, ..., K

+

∂z2

k ha 1 - g a

(12)

J

δ

1-

(13)

Here Rj’s are reaction rates defined in Table 2. The coordinates z ) 0 and z ) L correspond to the monolith inlet and outlet, respectively. In the catalytic washcoat layer, r ) 0 corresponds to the wall boundary and r ) δ denotes the external surface of the washcoat. The respective boundary conditions are

T ) T in ∂T s/∂z ) 0

at z ) 0

ck ) cin k , k ) 1, ..., K, Deff k

(14)

at z ) 0 or z ) L at z ) 0

∂csk ) kc(ck - csk), k ) 1, ..., K, ∂r

(15) (16)

at r ) δ (17)

∂csk/∂r ) 0, k ) 1, ..., K, at r ) 0

eff Deff k ) Dref

x

Wm ref T Wm Tref

(19)

k

The above equation is derived from the definition of the Knudsen diffusion coefficient. In this work, CO has been selected as the reference component.

(T - T s) -

∫r)0∆HjRj dr ∑ g j)1

microporous zeolites are added into the washcoat layer.16 The values used in our simulations correspond to typical measured diffusivities in the γ-Al2O3-based washcoat of a catalytic monolith converter of automobile exhaust gases.17,18 The following equation for the recalculation of effective diffusivities based on the knowledge of the effective diffusion coefficient of the reference component at the reference temperature has been used in the 2D model:

(18)

2.3. Numerical Solution. Both systems of PDEs for spatially 1D and 2D models of reactors with plug flow have been solved by the finite difference method, using semi-implicit approximations of derivatives with respect to time, quasi-linearization of reaction terms, and an adaptive time-step control. The model of a catalytic monolith reactor with diffusion in the washcoat7 forms a part of the versatile software package for the dynamic simulations of interconnected reactor and reactoradsorber systems, which has been developed in our group.4,7-9,11,12 2.4. External Heat- and Mass-Transfer Coefficients. The values of mass- and heat-transfer coefficients along the monolith channel [kc(z) and kh(z), respectively] are calculated from the correlations.13 Recently, a new set of correlations for heat and mass transfer have been proposed.14 A comparison of different empirical and theoretical correlations with experimentally evaluated mass-transfer coefficients is given in the paper.15 Physical properties of the gas phase are evaluated depending on the temperature, using standard data available for air. 2.5. Diffusion Coefficients in the Washcoat. Different theoretical models applied to a bimodal pore size distribution typical for the γ-Al2O3 washcoat (macroand mesopores) can give large variations of the Deff value. The situation is even more complicated when

3. Experiments The kinetic parameters of the model have been estimated on the basis of laboratory experimental data. Four samples of metallic monoliths coated with Pt/γ-Al2O3/zeolites catalysts have been used in the experiments. The samples differed in the thickness of washcoat, the content of Pt and zeolites, the open frontal area, and the diameter of the channels. Three different series of experiments have been carried out. The composition of the outlet gas was analyzed online in all experimental series. 3.1. Light-off. In the first series of experiments, hydrothermally aged sections of catalytic monoliths (length L ) 7.5 cm, diameter σ ) 1.4 cm, channel densities of 260-300 cpsi) were placed into a thermostat to prevent temperature-gradient formation along the channels. In the course of each experiment, the temperature of the inlet gas and the monolith sample was increased at a constant rate of 10 K/min within the range of 300-800 K. The exhaust gases at the inlet of the converter have been simulated by the synthetic gas mixtures with defined compositions and flow rates. During the measurements, the space velocity of the gas was kept constant at u ) 30 000 h-1. The inlet gas used in each experiment consisted of the same amount of CO2 (6%), O2 (14%), H2O (6%), and the balance of N2 (collectively referred to as basic components) and different amounts of CO, C3H6, C10H22, C6H5CH3, and NOx (referred to as variable components); compare Table 4. The composition was kept constant within each experiment. Different concentrations of the variable components were used to focus on selected reactions. Such an approach allows the parameters of each single reaction to be evaluated separately at first, which significantly enlarges the applicability of the model. The used inlet concentrations are summarized in Table 4. 3.2. Adsorption and Desorption. The second series of measurements was focused on the adsorption and desorption processes of HC and NOx, using the same experimental arrangement as that in the first series. The experiments proceeded in several steps. First, the catalytic washcoat was purified at 673 K using an inlet gas mixture of 14% O2 in nitrogen for 10 min to remove all adsorbed HCs and NOx. Then, after cooling of the catalyst in pure N2 feed, a mixture of selected adsorbable components in nitrogen (for concentrations, compare Table 4) was introduced into the monolith at a

Ind. Eng. Chem. Res., Vol. 44, No. 25, 2005 9527 Table 4. Inlet Gas Concentrations (in ppm moles) Used in the Light-off Experiments for the Particular Reaction Subsystems (Kinetic Parameter Evaluation) and the Inlet Concentrations Used in the Parametric Simulation Studies with the Temperature Ramp (Denoted by “sim. s.”)a studied reactions

CO

C3H6

C10H22

C6H5CH3

NO

1 2 3, 9 4, 10 8, 11 9 10 2, 5 3, 6, 9 4, 7, 10 1-11 sim. s.

1200 0 0 0 0 0 0 0 0 0 1200 1500

0 80 0 0 0 0 0 80 0 0 55 80

0 0 25 0 0 45 0 0 25 0 10 15

0 0 0 45 0 0 45 0 0 40 10 15

0 0 0 0 140 0 0 140 140 140 140 200

a Other gases always present: CO (6% mol), O (14% mol), H O 2 2 2 (6% mol), and N2 (balance). For the EDC driving cycle, the real (nontrivial) course of the inlet concentrations has been used.

constant temperature of 383 K for 15 min. In the next step, the inlet gas was replaced by pure N2, and after 10 min, constant temperature conditions were changed to a temperature ramp increasing with the rate 10 K/min. The space velocity was kept constant at 30 000 h-1 within the experiments. 3.3. Driving Cycle. In the third experimental series, the performance of the catalytic converter has been tested under the conditions of a typical passenger car equipped by a diesel engine. The standard European Driving Cycle (EDC) for light-duty vehicles, type MVEG-B (including both urban and extra-urban driving modes),19 has been realized by two different experiment layouts. In the first case, the composition and temperature of the exhaust gas in the course of the EDC have been simulated in a laboratory with two limitations: The HC content was substituted by propene only, and the space velocity (u) was kept constant within each experiment. The measurements were repeated at three different levels of the space velocity: 47 000, 70 000, and 140 000 h-1. In the second experimental arrangement, the EDC was performed by a real diesel (compression-ignited) engine on a dynamometer. The engine of a typical passenger car was employed, and the combustion exhausts were fed into the catalytic monolith and online analyzers.20 4. Evaluation of Reactions and Adsorption and Desorption Kinetics According to the composition of the inlet gas and the catalyst used in the experiments, a system of reactions has been derived to represent the processes taking place in the monolithic converter. Because the real exhaust gas contains a very complex mixture of different HCs, three different components have been selected to represent the total HC content of the exhaust gas: propene (C3H6) for light, easy-to-oxidize (“fast”) HCs, toluene (C6H5CH3) for adsorbable aromates, and decane (C10H22) for heavy, adsorbable, and hard-to-oxidize (“slow”) HCs. Rate laws for the adsorption/desorption have been described by expressions based on nonstationary kinetics. For the remaining reactions, expressions derived

from the pseudostationary Langmuir-Hinshelwood concepts have been used. The employed reaction scheme and the corresponding rate law expressions are presented in Tables 1 and 2. The kinetic parameters have been fitted on the basis of a comparison between the measured outlet concentrations and the output data computed with the spatially 1D mathematical model. (The iterative computations with an explicit consideration of diffusion in the washcoat are still too time-demanding.) For this purpose, only the data measured in the first and second experimental series (the light-off and the adsorption/ desorption) were employed. Furthermore, only the data for the samples with the thin washcoat layer were used, to keep the assumption of negligible concentration gradients in the washcoat (spatially 1D model) satisfied as much as possible. The results from other measurements have been used for the comparison and control of the mathematical model robustness and applicability. The evaluated kinetic parameters included adsorption (storage) capacities of the catalyst with respect to individual components (Ψcap), reaction rate constants (k), inhibition constants (Ka, X, Y, and Z), and the selectivity constant KNO. An Arrhenius type of temperature dependence has been employed for the abovementioned reaction rates and the inhibition and selectivity parameters:

k ) A exp(-B/T)

(20)

In the case of reaction rate constants k, the exponential factor B corresponds to the activation energy Ea:

B ) Ea/Rg

(21)

At first, parameters of each single reaction have been estimated separately using the data obtained from experiments with the simplest inlet gas composition (i.e., the basic components plus one variable component). The resulting parameter values were then further tuned according to the results from the measurements focused on particular reaction subsystems (where also the inhibition and selectivity constants were evaluated), with the complete reaction system being considered in the final step of the data fitting. 4.1. Optimization Method. The weighted leastsquares method was then used to optimize the parameter values to fit the model to the experimental data with a sufficient precision. In the optimization, the following objective function (the weighted sum of squares of differences between the model and the experiment) is minimized by the simplex method: K

S(x b) )

exp,i sim,i - yout,k (x b)]2} ∑i ∑k {wk[yout,k

(22)

where b x represents the vector of parameters to be evaluated, i is the index of the data point in the time sequence obtained in the course of the experiment, and wk is a corresponding weight for the component k. Symbol yout denotes the outlet concentration of component k, and superscripts exp and sim indicate data obtained from the experiment and simulation, respectively. The weights have been chosen according to relative errors of measurements and with a view to the relative importance of the experiment and component.

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Figure 2. Comparison of the measured and simulated evolution of the outlet concentrations in the course of the adsorption/desorption experiment for decane (cf. step 9 in Tables 1 and 2).

Figure 1. Comparison of the measured and simulated evolution of the outlet concentrations in the course of the oxidation light-off for simple mixtures: (a) CO, reaction 1 studied; (b) C10H22, reactions 3 and 9 studied (cf. Tables 1 and 2). Rate of temperature increase ) 10 K min-1 and u ) 30 000 h-1.

Zero weight (wk ) 0) has been used in cases where the effect of the corresponding component is not considered for the parameter evaluation. The evaluated kinetic parameters are summarized in Table 5. 4.2. Comparison of Experiments and Simulations. Comparisons of the experimental data with the results obtained from the simulations using the evaluated kinetic parameters are presented in Figures 1-5. In the case of CO oxidation light-off (Figure 1a), the outlet and inlet concentrations are equal until the lightoff temperature is exceeded at the catalytic surface. The reaction rate becomes sufficiently high above this temperature, which results in a rapid outlet concentration decrease. The outlet concentration of C3H6 exhibits a similar behavior. The course of the outlet concentration of decane (Figure 1b) and toluene in the course of the light-off experiment is influenced by the storage of these components on the catalytic surface, while the storage of the lighter propene is not so significant. The HCs are stored mainly on the zeolites in the washcoat by physical adsorption.21-26 The prevailing adsorption at low temperatures leads to the relatively low outlet concentrations of both HCs under these conditions. At higher temperatures, the desorption process occurs, which causes a rapid outlet concentration rise until the combustion light-off is reached. The adsorption and desorption were also examined separately for toluene and decane (cf. Figure 2) to evaluate the maximum storage capacities Ψcap and the adsorption/desorption kinetic parameters kads,j and kdes,j. After the evaluation of individual kinetic parameters kj(T) from the simple-mixture experiments, the selectivity and inhibition parameters (Kj, Ka,j, Xj, Yj, and Zj) were evaluated from the experiments with more complex mixtures. The course of the outlet concentrations for the light-off experiment with the complete mixture is shown in Figure 3.

Figure 3. Comparison of the measured and simulated course of the outlet concentrations for light-off of the complete mixture: (a) total HCs; (b) NOx. Rate of temperature increase ) 10 K min-1, u ) 30 000 h-1, and ψC10H22(z,0) ) 0.3.

Unlike in the case of HCs, the adsorption of NOx on γ-Al2O3 in the form of surface nitrates is an activated process occurring mainly at intermediate temperatures27 (cf. reactions 8 and 11 in Table 1). At higher temperature, the surface nitrates become unstable and NOx desorption occurs. A typical evolution of the outlet NOx concentrations in the course of the temperature ramp (lean inlet gas mixture including HCs) is given in Figure 3b. The NOx desorption peak is eliminated here by the selective catalytic reduction (reactions 5-7 in Table 1). This reaction is significant only in a relatively narrow temperature window.5,11,28,29 As the extent of the selective catalytic reduction reaction decreases rapidly with increasing temperature, the outlet concentration rises back to its initial value and NOx conversion at higher temperatures is very poor. To check the applicability of the model, the EDC was simulated with the kinetic parameters kept constant after the evaluation and the results were compared with the laboratory data (a constant space velocity was used in this case). The course of the inlet gas temperature during the EDC is depicted in Figure 4. It can be seen

Ind. Eng. Chem. Res., Vol. 44, No. 25, 2005 9529 Table 5. Evaluated Reaction Kinetic Parameters (Preexponential Factors A and Exponential Factors B)a

Figure 4. Evolution of the inlet gas temperature and flow rate in the course of the EDC.

parameter

A

B (K)

k1 Ka,1,CO Ka,1,CxHy Ka,1,x Ka,1,NO k2 X2 Y2 k3 X3 Y3 k4 X4 Y4 K5,NO Ka,5,O2 Z5 K6,NO Ka,6,O2 Z6 K7,NO Ka,7,O2 Z7 kf8 kb8 Ka,8,NO Ka,8,O2 Ka,1,NO2 kads 9 kdes 9 kads 10 kdes 10 kads 11 kdes 11

8.3 × 1018 6.6 × 101 2.1 × 103 4.0 × 100 1.0 × 107 1.9 × 1020 5.0 × 104 9.0 × 104 2.1 × 1017 7.0 × 104 2.0 × 104 2.1 × 1018 1.0 × 103 1.0 × 104 5.5 × 103 7.0 × 1015 1.0 × 104 9.5 × 103 7.0 × 1015 1.0 × 102 5.5 × 103 7.0 × 1016 1.0 × 103 8.3 × 106 2.1 × 1014 2.9 × 10-8 2.6 × 10-7 6.4 × 10-7 5.0 × 100 9.0 × 103 4.5 × 100 6.0 × 105 4.5 × 104 9.0 × 108

+9.0 × 103 -9.6 × 102 -3.6 × 102 -1.2 × 104 +3.7 × 104 +1.2 × 104 -1.0 × 103 -6.0 × 102 +1.2 × 104 -1.0 × 102 -6.0 × 102 +1.25 × 104 -6.0 × 102 -6.0 × 102 0 +2.0 × 104 -5.0 × 101 0 +2.1 × 104 -5.0 × 101 0 +2.2 × 104 -6.0 × 102 +4.9 × 103 +1.7 × 104 -9.8 × 103 -1.0 × 104 -1.2 × 103 0 +6.0 × 103 0 +6.0 × 103 4.3 × 103 +1.3 × 103

a The corresponding reaction and adsorption/desorption steps are defined in Tables 1 and 2, and the temperature dependence is described by eq 20.

Figure 5. Comparison of the measured and predicted courses of outlet concentrations of propene (a) and NOx (b) during the laboratory EDC. u ) 70 000 h-1.

The overall conversion has been calculated from the equation

∫tt Fout k (t) dt Xk ) 1 - t ∫t Fink (t) dt 2

1

that the temperature of the exhaust gas entering the underfloor catalyst in a diesel passenger car is well below 200 °C (473 K) during the major part of the cycle (urban driving mode), which is quite demanding with respect to the activity of the catalyst. A comparison of the laboratory experiment and the simulation results for propene and NOx is presented in Figure 5. At the beginning (cold start), the propene outlet concentration fluctuates according to the composition of the inlet gas. When the light-off temperature is reached, the propene outlet concentration drops to zero. In the case of NOx, a low quantitative removal of this component occurs in the used sample of a catalytic monolith; hence, the outlet concentration is close to the inlet one throughout the entire cycle. 5. Simulation Results A series of simulations have been carried out with the 1D and 2D mathematical model fitted to the experimental data. The influence of specific operating conditions and a particular monolith configuration on the course of the outlet concentration and the overall (integral) conversion (Xk) of the individual components has been studied.

2

(23)

1

out Here Fin k (t) and Fk (t) represent the inlet and outlet molar flow rates of the gas component k, respectively, and t1 and t2 denote the start and end times of the simulation. For the purpose of brevity, the label k is omitted in the figures presented below in the text. Two basic situations have been studied in the simulations: the temperature ramp and the real driving cycle. In the temperature ramp case studies, the inlet gas composition was kept constant (cf. Table 4). 5.1. HC and NOx Adsorption on the Catalyst Surface. The calculated evolution of surface concentration profiles of the adsorbed decane and NOx in the course of the temperature ramp is shown in Figure 6. Because the storage of HCs is a nonactivated process, decane is readily adsorbed at lower temperatures and the surface concentration is relatively high. As the inlet gas temperature rises, the desorption becomes faster than the adsorption and the adsorbed decane molecules are released. The surface concentration of toluene exhibits a dependence similar to that of decane. However, because of a looser attachment of the toluene

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Figure 6. Evolution of the concentration profiles of adsorbed C10H22 (a) and NOx (b) in the course of the temperature ramp. Conditions: t1 ) 0 s, t2 ) 3000 s, T in(t1) ) 300 K, T in(t2) ) 800 K, u ) 30 000 h-1, 1D model, δ ) 24 µm, and L ) 7.5 cm.

Figure 8. Comparison of the different storage capacities of the washcoat for the adsorption of HC (a) and NOx (b): evolution of the outlet concentrations and the integral conversions in the course of the temperature ramp. Conditions: t1 ) 0 s, t2 ) 3000 s, T in(t1) ) 300 K, T in(t2) ) 800 K, u ) 30 000 h-1, 1D model, δ ) 24 µm, and L ) 15 cm. Here the storage capacities Ψcap,m of the reference washcoat are denoted by c.

Figure 7. Evolution of decane concentrations in the course of the real EDC: (a) the inlet and computed outlet concentrations; (b) spatiotemporal concentration patterns of the adsorbed C10H22. Conditions: 1D model, δ ) 24 µm, L ) 15 cm, and σ ) 10 cm.

molecules to the surface, the desorption effect occurs already at lower temperatures compared to decane. The NOx storage is an activated process; therefore, the adsorption process starts only after a certain temperature is reached in the monolith (cf. Figure 6b). As in the case of HCs, the surface concentration of the adsorbed NOx is low at higher temperatures because of the high desorption rate. The adsorption/desorption effects are important particularly within the cold-start phase of the driving cycle. It can be seen from Figure 7 that without the adsorption the overall conversion of decane would be significantly lower because the light-off for C10H22 oxidation occurs only at higher temperatures (here after t ) 800 s). Thus, the decrease of the C10H22 emissions in the first part of the EDC is caused mainly by the adsorption on zeolites.

This is confirmed by the computed spatiotemporal concentration patterns of the adsorbed decane (Figure 7b). The evolution of the inlet gas temperature and flow rate during the EDC can be seen in Figure 4. 5.2. Storage Capacity of the Washcoat. The storage capacity of the catalytic surface depends on the particular washcoat composition (content of zeolites, specific active surface, etc.). A comparison of the evolution of the outlet concentrations and the overall conversions of HCs and NOx for different storage capacities of the washcoat is given in Figure 8. The employed values of capacities were Ψcap ) c/2, c, and 2c. Here c corresponds to the evaluated storage capacities (different values for each adsorbable component) of the reference sample used in laboratory experiments. For both HCs and NOx, the rates of adsorption and desorption processes increase with increasing storage capacity and the effect of desorption is shifted toward higher temperatures. For high surface storage capacities, HCs are released from the surface only at temperatures corresponding to high combustion rates (Figure 8a). A high HC storage capacity may lead to the appearance of a secondary desorption peak (cf. the curve for the capacity 2c in Figure 8a). In this case, the amount of the desorbed HC is temporarily higher than the HC oxidation rate. Anyway, with a higher HC storage capacity, more HCs are removed from the exhaust gas and a higher overall HC conversion is achieved. This is actually the major reason for adding the storage components to the catalytic washcoat in the monolithic converters of exhaust gases of both compression and spark-ignited engines.21 For a gasoline-powered engine, the converter systems consisting of interconnected monolithic reactors and adsorbers have been studied as well.12 It has been shown that the storage of

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Figure 9. Influence of the rate of temperature increase on the evolution of the outlet concentrations and overall conversions of HCs (a) and NOx (b). Temperature ramps 10, 30, and 180 K min-1 are for t1 ) 0 s and t2 ) 3000, 1000, and 167 s, respectively. Conditions: T in(t1) ) 300 K, T in(t2) ) 800 K, u ) 30 000 h-1, 1D model, δ ) 24 µm, and L ) 15 cm.

Figure 10. Comparison of the different thicknesses of the catalytic washcoat layer: evolution of the outlet concentrations and overall conversions of CO (a) and C10H22 (b) in the course of the temperature ramp. Conditions: t1 ) 0 s, t2 ) 3000 s, T in(t1) ) 300 K, T in(t2) ) 800 K, 2D model, Dref ) 5 × 10-7 m2 s-1, L ) 15 cm, and u ) 30 000 h-1.

large quantities of HCs on the surface leads to very high temperatures during the desorption, which might result in the deactivation of the catalyst. However, this is not the case of diesel converters because here the amounts of both gas-phase and surface-stored HCs are generally lower. The influence of the NOx storage capacity on the out evolution of the outlet NOx concentrations yNO in the x course of the temperature ramp can be seen in Figure 8b. The NOx conversions are practically the same for all studied storage capacities: in the case of the higher storage capacity, a larger extent of adsorption is compensated for by a larger extent of desorption (cf. Figure 8b). Because the inlet temperature in the simulation increases significantly above the temperature window for selective NOx reduction by HCs (reactions 5-7 in Table 1), the integral outlet conversions XNOx are quite low. 5.3. Rate of Increase of the Inlet Gas Temperature. The overall conversions and the courses of the outlet concentrations of HCs and NOx for three different rates of the inlet gas temperature increase are shown in Figure 9. The temperature ramps employed were 10, 30, and 180 K min-1, with the temperature range being 300-800 K. For higher rates of the temperature increase, higher temperature differences occur between the gas and catalytic surface because of external heattransfer resistance. In the presented figures, this phenomenon causes the apparent shift of the outlet concentration curves toward higher inlet temperatures. The values of the overall conversion have been calculated for the time interval corresponding to the growth of the inlet gas temperature within the given range. For the highest rate of temperature increase, the lowest temperature of the catalytic surface is reached within this time interval and the lowest integral conversion is obtained. However, considering the total amount of

emissions during the cold-start period, the fastest temperature ramp is the most advantageous because the light-off is reached within the shortest time. The high rate of temperature increase leads to a significant temperature gradient along the reactor. While the light-off temperature is reached at the front of the monolith, the rear part is still relatively cold. This fact obviously affects the surface storage processes as well. It causes the occurrence of two concentration maxima in the case of toluene (cf. Figure 9a). The first peak results from the desorption followed by the oxidation reaction at the front part of the reactor, while the second maximum corresponds to the same phenomenon occurring with a certain time delay at the rear part of the monolith. 5.4. Washcoat Thickness. The course of the outlet concentration and the overall conversion obtained using different thicknesses of the catalytic layer δ have been compared. Examples of comparisons for Dref ) 5 × 10-7 m2 s-1 are shown in Figure 10 for simulations of the temperature ramp and in Figure 11 for the case of the real engine EDC. The value of Dref corresponds to typical values measured for a nonsintered Pt/γ-Al2O3 washcoat.16-18 Because of a higher total number of active sites in the thicker washcoat layer, the catalytic reactions are faster and the storage capacities higher. The overall conversion is thus higher for higher values of δ. However, for the thickest washcoat layer used in the simulations, the conversion becomes limited by internal diffusion as significant concentration gradients are formed within the catalytic layer. The phenomenon is demonstrated in Figure 12, where the gradient of the CO gas concentration in the washcoat is depicted for δ ) 72 µm. In such cases, it is necessary to employ the 2D model with an explicit consideration of diffusion in the washcoat to obtain realistic results.

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Figure 11. Evolution of the outlet concentrations and overall conversions of HCs (a) and NOx (b) in the course of the real EDC for different thicknesses of the catalytic washcoat. Conditions: t1 ) 0 s and t2 ) 1180 s for the conversions given here, 2D model, Dref ) 5 × 10-7m2 s-1, L ) 15 cm, and σ ) 10 cm.

Figure 13. Influence of transport properties of the washcoat (effective diffusivity Dref) on the evolution of the outlet concentrations in the course of the temperature ramp for CO (a) and the sum of HCs (b). Conditions: t1 ) 0 s, t2 ) 3000 s, T in(t1) ) 300 K, T in(t2) ) 800 K, u ) 30 000 h-1, 2D model, δ ) 72 µm, and L ) 15 cm.

Figure 12. CO concentration profile in the pores of the catalytic washcoat layer. Conditions: 2D model, T in ) 390 K, Dref ) 5 × 10-7m2 s-1, and u ) 30 000 h-1.

5.5. Effective Diffusivity. Different porous washcoat structures with different transport properties can be simulated by employing proper values of the reference diffusion coefficient Dref.16-18 The operating conditions of both the continuously increasing temperature and the real EDC were simulated for a 72-µm-thick catalytic washcoat layer. The courses of the outlet concentration and overall conversion were compared for four different values of Dref (1 × 10-6, 5 × 10-7, 3 × 10-7, and 1 × 10-7 m2 s-1). The selected simulation results are presented in Figures 13 and 14. With the decreasing values of Dref, the pore diffusion resistance increases, which leads to a lower overall reaction rate and thus to a lower conversion. The effect of this phenomenon is visible particularly for thicker catalytic layers and also close to the light-off conditions (cf. Figures 13a and 14a and the literature14). A more complicated behavior with respect to the diffusion in the catalytic washcoat layer has been studied elsewhere.7,8 Figure 13b shows the HC outlet concentration course calculated for the temperature ramp also deploying the 1D model. Because the pore concentration gradient is neglected in this model, the computation gives a result

Figure 14. Influence of transport properties of the washcoat (effective diffusivity Dref) on the performance of the catalytic converter during the real EDC. Details of the outlet concentrations of CO (a) and the sum of HCs (b) in the first part of the driving cycle (cold start). Conditions: t1 ) 0 s and t2 ) 1180 s for the conversions given here (entire EDC), 2D model, δ ) 72 µm, L ) 15 cm, and σ ) 10 cm.

independent of the Dref value. The comparison demonstrates that the 1D modeling approach (neglecting the internal diffusion) leads to a significant overestimation of the overall reaction rates and conversions for thick washcoat layers and/or washcoats exhibiting low diffusivity values (Dref).

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6. Conclusions The 1D and 2D models of a catalytic monolith converter for exhaust gases of automobile diesel engines, developed on the basis of extensive experimental data, form a helpful tool for the design of the washcoat and entire monolith. It enables, for example, one to study the effects of the added adsorption material (zeolites) on the conversion of HCs and NOx. The spatially 2D model, with explicit consideration of the internal diffusion, enables one to study the influence of the washcoat thickness on the spatiotemporal patterns of individual reacting components within the washcoat layer, monolith light-off, and overall conversions. These types of simulations, which can follow in detail the interplay between the adsorptive and reaction processes under varying inlet conditions (flow rate, temperature, and concentration), then can support the optimization of the washcoat and monolith design for individual applications. Acknowledgment This work has been partly supported by Project MSM 6046137306 of the Czech Ministry of Education and by Grant 104/05/2616 of the Czech Grant Agency. Nomenclature a ) density of the external surface area, m2 m-3 A ) preexponential factor of the kinetic constant, dimension depends on the reaction order B ) exponential factor of the kinetic constant, K c ) concentration in the bulk gas, mol m-3 cs ) concentration in the washcoat pores, mol.m-3 cp ) heat capacity, J kg-1 K-1 Deff ) effective diffusion coefficient, m2 s-1 Ea ) activation energy of the reaction, J mol-1 F ) flow rate, m3 s-1 (STP) J ) number of reactions k ) kinetic constant of the reaction kc ) mass-transfer coefficient, m s-1 kh ) heat-transfer coefficient, J m-2 K-1 s-1 K ) selectivity constant of the reaction; number of gas components Ka ) inhibition constant of the reaction L ) length of the monolith, m r ) transverse (radial) coordinate in the washcoat layer, m R ) reaction rate, mol m-3 s-1 Rg ) universal gas constant, 8.31434 J mol-1 K-1 t ) time, s T ) temperature of the bulk gas, K T s ) temperature of the solid phase, K u ) space velocity, s-1 (STP) v ) linear velocity, m s-1 X, Y, Z ) inhibition constants of the reaction y ) molar fraction of the component, 1 z ) axial coordinate of the monolith, m Greek Letters δ ) thickness of the washcoat layer, m ∆Hr ) standard reaction enthalpy, J mol-1 g ) macroscopic void fraction of the reactor s ) porosity of the washcoat φw ) volume fraction of the washcoat in the solid phase (including support) λ ) effective heat conductivity, J m-1 K-1 s-1 ν ) stoichiometric coefficient F ) effective density, kg m-3

σ ) monolith diameter, m ψ ) coverage of the surface adsorption sites, 1 Ψcap ) adsorption (storage) capacity of the washcoat, mol m-3 Subscripts and Superscripts ads ) adsorption b ) backward des ) desorption f ) forward g ) gas in ) inlet j ) index of the reaction k ) index of the gas component m ) index of the component deposited on the surface out ) outlet s ) solid phase w ) washcoat Abbreviations EDC ) European driving cycle, type MVEG-B19 HCs ) hydrocarbons PDE ) partial differential equation STP ) standard temperature and pressure (273.15 K, 101 325 Pa) SV ) space velocity

Literature Cited (1) Heck, R. M.; Farrauto, R. J. Automobile exhaust catalysts. Appl. Catal. A 2001, 221, 443. (2) Frost, J. C.; Smedler, G. Control of NOx emissions in diesel powered light vehicles. Catal. Today 1995, 26, 207. (3) Greening, P. European vehicle legislationspresent and future. Top. Catal. 2001, 16/17, 5. (4) Kocˇ´ı, P.; Kubı´cˇek, M.; Marek, M.; Maunula, T.; Ha¨rko¨nen, M. Modelling of catalytic monolith converters with low- and hightemperature storage compounds and differentiated washcoat. Chem. Eng. J. 2004, 97, 131. (5) Burch, R.; Breen, J. P.; Meunier, F. C. A review of the selective reduction of NOx with hydrocarbons under lean-burn conditions with nonzeolitic oxide and platinum group metal catalysts. Appl. Catal. B 2002, 39, 283. (6) Christensen, H.; Rak, Z. S. A novel diesel particulate converter. Catal. Today 2002, 75, 451. (7) Kocˇ´ı, P.; Kubı´cˇek, M.; Marek, M. Modeling of Three-WayCatalyst Monolith Converters with Microkinetics and Diffusion in the Washcoat. Ind. Eng. Chem. Res. 2004, 43, 4503. (8) Kocˇ´ı, P.; Kubı´cˇek, M.; Marek, M. Multifunctional Aspects of Three-Way Catalyst: Effects of Complex Washcoat Composition. Chem. Eng. Res. Des. 2004, 82 (A2), 284. (9) Kocˇ´ı, P.; Kubı´cˇek, M.; Marek, M. Periodic forcing of threeway catalyst with diffusion in the washcoat. Catal. Today 2004, 98, 345. (10) Wanker, R.; Raupenstrauch, H.; Staudinger, G. A fully distributed model for the simulation of a catalytic combustor. Chem. Eng. Sci. 2000, 55, 4709. (11) Jira´t, J.; Sˇ teˇpa´nek, F.; Kubı´cˇek, M.; Marek, M. Nonstationary operation of a system of catalytic monolithic reactors for selective NOx reduction. Chem. Eng. Sci. 1999, 54, 2609. (12) Jira´t, J.; Kubı´cˇek, M.; Marek, M. Adsorber-reactor systems for emission treatment from mobile sources. Chem. Eng. Sci. 2001, 56, 1597. (13) Kirchner, T.; Eigenberger, G. Optimization of the cold-start behaviour of automotive catalysts using an electrically heated precatalyst. Chem. Eng. Sci. 1996, 51, 2409. (14) Ramanathan, K.; Balakotaiah, V.; West, D. H. Light-off criterion and transient analysis of catalytic monoliths. Chem. Eng. Sci. 2003, 58, 1381. (15) West, D. H.; Balakotaiah, V.; Jovanovic, Z. Experimental and theoretical investigation of the mass transfer controlled regime in catalytic monoliths. Catal. Today 2003, 88, 3. (16) Mezedur, M. M.; Kaviany, M. Effect of Pore Structure, Randomness and Size on Effective Mass Diffusivity. AIChE J. 2002, 48, 15.

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Ind. Eng. Chem. Res., Vol. 44, No. 25, 2005

(17) Hayes, R. E.; Kolaczkowski, S. T.; Li, P. K. C.; Awdry, S. Evaluating the effective diffusivity of methane in the washcoat of a honeycomb monolith. Appl. Catal. B 2000, 25, 93. (18) Zhang, F.; Hayes, R. E.; Kolaczkowski, S. T. A new technique to measure the effective diffusivity in the washcoat of a monolith reactor. Chem. Eng. Res. Des. 2004, 82 (A4), 481. (19) European driving cycle for light-duty vehicles. European Union directive 98/69/EC, 2005. http://www.dieselnet.com/standards/ eu/ld.html. (20) Maunula, T.; Suopanki, A.; Torkkell, K.; Hrknen, M. The Optimization of Light-Duty Diesel Oxidation Catalysts for Preturbo, Closed-Coupled and Underfloor Positions; SAE Technical Paper Series 2004-01-3021; SAE: Warrendale, PA, 2004. (21) Seo, H. K.; Oh, J. W.; Lee, S. C.; Sung, J. Y.; Choung, S. J. Adsorption Characteristics of HCA (Hydrocarbon Adsorber) Catalysts for Hydrocarbon and NOx Removals under Cold-Start Engine Conditions. Korean J. Chem. Eng. 2001, 18 (5), 698. (22) Koltsakis, G. C.; Stamatelos, A. M. Modeling of Hydrocarbon Trap Systems; SAE Technical Paper Series 2000-01-0654; SAE: Warrendale, PA, 2000. (23) Goralski, C. T., Jr.; Chanko, T.; Lupescu, J.; Ganti, G. Experimental and Modeling Investigation of Catalyzed Hydrocarbon Trap Performance; SAE Technical Paper Series 2000-01-0655; SAE: Warrendale, PA, 2000. (24) Kruglov, A. V.; Aris, R. Adsorption Kinetics for the Case of Step and S-Shape Isotherms. AIChE J. 1995, 41, 2393. (25) Watanabe, Y.; Asano, A.; Kondo, T.; Sakakibara, Y.; Sugiura, M. Development of a model for the lean NOx catalytic

reaction with hydrocarbon adsorption and desorption. Appl. Catal. B 2001, 31, 221. (26) Watanabe, Y.; Asano, A.; Banno, K.; Yokota, K.; Sugiura, M. Application of numerical modeling of selective NOx reduction by hydrocarbon under diesel transient conditions in consideration of hydrocarbon adsorption and desorption process. Catal. Today 2001, 69, 209. (27) Laurent, F.; Pope, C. J.; Mahzoul, H.; Delfosse, L.; Gilot, P. Modelling of NOx adsorption over NOx adsorbers. Chem. Eng. Sci. 2003, 58, 1793. (28) Ansell, G. P.; Bennett, P. S.; Cox, J. P.; Frost, J. C.; Gray, P. G.; Jones, A.-M.; Rajaram, R. R.; Walker, A. P.; Litorell, M.; Smedler, G. The development of a model capable of predicting diesel lean NOx catalyst performance under transient conditions. Appl. Catal. B 1996, 10, 183. (29) Westerberg, B.; Ku¨nkel, C.; Odenbrand, C. U. I. Transient modelling of a HC-SCR catalyst for diesel exhaust aftertreatment. Chem. Eng. J. 2003, 92, 27. (30) Voltz, S. E.; Morgan, C. R.; Leiderman, D.; Jacob, S. M. Kinetic study of carbon monoxide and propylene oxidation on platinum catalysts. Ind. Eng. Chem. Prod. Res. Dev. 1973, 12, 294.

Received for review February 25, 2005 Revised manuscript received May 5, 2005 Accepted June 6, 2005 IE050249V