Ind. Eng. Chem. Res. 2005, 44, 8205-8212
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Modeling of Diesel Oxidation Catalyst Yasushi Tanaka, Takashi Hihara,† Makoto Nagata,*,† Naoto Azuma, and Akifumi Ueno Department of Materials Science, Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Hamamtsu, Shizuoka 432-8561, Japan
Optimization of hydrocarbon (HC) oxidation over a diesel oxidation catalyst (DOC) requires consideration of (i) HC gas diffusion into the catalyst layer, (ii) HC gas adsorption and desorption from catalyst sites, and (iii) kinetics of the oxidation reaction. We have already reported a brief modeling study that emphasized understanding HC storage and release from zeolitic sites within the DOC [Banno et al., SAE Tech. Pap. Ser. 2004, 2004-01-1430]. In this study, more-detailed DOC modeling was attempted, using a precise gas diffusion model and experimentally determined reaction parameters. The random pore model was used for gas diffusion calculations, to simulate the bimodal nature of the catalyst structure, which has both macroporosity between catalyst particles and microporosity within the zeolite material. HC adsorption capacity, as a function of temperature and HC concentration, was measured by temperature-programmed desorption (TPD). The rate of HC desorption rate was evaluated by changing the TPD ramping rate. The rate of HC oxidation was measured using a model gas reactor. The conversion efficiency of HC, which was calculated by computer simulation with Star-CD software, reproduced the experimental measurements well, as a function of temperature, thus validating the model. The simulation methodology was used to predict two-dimensional (2D) HC conversion efficiency profiles across radial and axial positions of the monolithic catalyst during HC combustion, and it was also applied to estimate the depth profile of adsorbed HC in the catalyst layer. Introduction A diesel oxidation catalyst (DOC) is traditionally composed of a precious-metal-dispersed-alumina catalyst coated onto the walls of a ceramic monolithic substrate. The DOC must be optimized to fit the vehicle management system and meet the regulatory emission requirements. Vincent et al.1 reported that the function of a DOC pre-cat in a diesel oxidation catalyst and catalyzed soot filter (DOC+CSF) system is primarily to catalyze fuel combustion, thus generating heat to regenerate soot that has accumulated in the CSF. On the other hand, low-temperature transient HC and CO performance is required in passenger vehicle applications, as reported by Tomazic et al.2 Here, the mechanism by which zeolite improves transient HC and CO performance is relatively well-understood. Combustion on the catalyst starts with the diffusion of gases into the catalyst through micropores and macropores in the catalyst layer, followed by adsorption on the catalyst surface during cold-start mode and by desorption at elevated temperatures where HC and CO might be oxidized into CO2 and H2O on the catalytically active sites, as reported by Higashiyama et al.,3 Kim et al.,4 Nakano et al.,5 Seo et al.,6 and Jime´nez et al.7 For this application, the adsorption quantity, desorption temperature, and catalyst light-off performance must be balanced. Nakano et al.5 and Nagata et al.8 reported that the HC light-off temperature must be lower than the HC desorption temperature to obtain high performance. Even with a low light-off temperature, too much * To whom correspondence should be addressed. Tel.: 81-55-967-9605. Fax: 81-55-966-1768. E-mail: makoto.nagata@ ne-chemcat.co.jp. † Currently with N. E. Chemcat Corporation, 678 Ipponmatsu, Numazu, Shizuoka, Japan.
adsorbed HC can result in HC release when the temperature is increased. To improve the DOC pre-cat for DOC+CSF applications, all requirements for the DOC must be met. In addition to the traditional requirements of soluble organic fraction (SOF) combustion and HC, CO oxidation for cold-start emission control; the DOC also is required to occur ahead of the CSF, to oxidize NO for passive soot combustion and oxidize fuel for heat management of active soot regeneration. To improve transient HC and CO performance in the DOC, it is important to know the macroporosity and microporosity that defines the gas diffusion conditions in the catalyst layer, details of the HC adsorption capacity, desorption rate, HC and CO reaction rates, and especially an effective thickness of the catalyst layer. We have already reported one method for estimation of the effective catalyst layer depth, down the length of the DOC monolith, for transient HC performance.9 In this study, detailed DOC modeling was attempted, using a precise gas diffusion model and calculation parameters. For the real application, a representative group of HC species, CO, and SOF should be involved in the model. In some cases, a correlation between the oxidation of engine-derived HC and model gas evaluations using C3H6 as a model HC was confirmed. Simulations were performed using Star-CD computer software (which requires input of a geometrical model of the catalyst), gas diffusion coefficients, the HC adsorption capacity, the HC desorption rate, and the HC oxidation rate. The random pore model with input of the macroporosity within the catalyst layer and microporosity of the zeolite material was used for calculation of gas diffusion in the catalyst layer. The HC adsorption capacity in the catalyst, as a function of temperature, was measured by temperature-programmed desorption (TPD). The HC
10.1021/ie0580349 CCC: $30.25 © 2005 American Chemical Society Published on Web 09/30/2005
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desorption rate was evaluated by changing the TPD ramping rate. The HC oxidation rate was evaluated experimentally, using a model gas reactor. Finally, calculations were performed using Star-CD computer software and simulations were verified by comparing with the experimental HC conversion data from model gas evaluation tests. Also, the HC gas concentration distribution within the catalyst layer during HC adsorption mode and desorption/reaction mode was calculated. Experiments performed in this work are divided into three parts. In the first part, parameters necessary for computer simulation of HC combustion are experimentally determined. In the second part, HC conversion are calculated at various gas temperatures and compared to the experimental results. In the final part, the transient HC concentration at radial and axial positions in a cell of the monolithic catalyst, as well as the HC concentration within the catalyst layer, coated on the cell wall, are predicted by means of computer calculations, using the previously determined parameters. Theory 1. Governing Equations. The following five assumptions were applied to establish the model boundary conditions: (1) Chemical reactions occur in the catalyst layer only. (2) Adsorption and desorption occur in the catalyst layer only. (3) The physical properties of gases (such as viscosity, specific heat, density, and thermal conductivity) are constant, because the reactants and products are highly diluted. (4) The adsorption rate is very fast and controlled by the diffusion rate. (5) Bulk gas flow in the catalyst layer was assumed to be zero; thus, all heat and mass transport is assumed to occur via gas diffusion and concentration-gradientdriven diffusion. Conservation equations are applied to both the gas flow path and the catalyst layer. The continuity equation, momentum equation, species equation, and energy equation all are applied within the gas flow path. Only the species equation and energy equation are applied for the catalyst layer. The detailed equations are defined within the Star-CD computer software that is used in this study. 2. Random Pore Model. The random pore model proposed by Wakao and Smith10 was used as a gas diffusion model for calculation of the diffusion coefficient in the catalyst layer (De). This model had been originally applied to pellets prepared via the compression of porous catalyst particles. There were two pore systems in the model: micropores within the powder particle and macropore spaces between the powder particles. In this study, a washcoat layer is modeled by the macropores, which are defined by the molecular gas diffusion path, and the micropores, which are defined by Knudsen diffusion in small pores of zeolite material. The use of this model is considered to be more precise than the parallel pore model used in our previous study.9 Equation 1 shows the relationship in the random pore model between the effective diffusion coefficient (De), the
diffusion coefficient in macropores (Da), and the diffusion coefficient in micropores (Di):
De ) a2Da + i2Di +
4a(1 - a) (1/Da) - [(1 - a)2/(i2Di)]
(1)
where a is the porosity of the macropores and i is the porosity of the micropores. 3. Hydrocarbon (HC) Adsorption Equilibrium in the Presence of Water Vapor. The adsorption equilibrium of C3H6 in the presence of H2O is expressed by the Langmuir equation (eq 2):
qCeq3H6 )
q∞,C3H6Kad,C3H6PC3H6 1 + Kad,C3H6PC3H6 + KH2OPH2O
(2)
Here, qi is the adsorption amount of component i (given in units of µmol/g-cat), Ki the equilibrium constant of component i, q∞,i the saturated adsorption capacity (given in units of µmol/g-cat) of component i, Pi the partial pressure of component i (given in units of atm) in the gas phase, and ∆H the heat of adsorption. The parameters q∞,C3H6 and KC3H6 can be obtained experimentally from the TPD experiment. We assumed that the adsorption rate is very fast, compared to the diffusion rate. The adsorption rate (Ra) is expressed by eq 3:
Ra )
∂qC3H6 ∂t
)
∂qCeq3H6 ∂PC3H6 ∂PC3H6
∂t
(3)
In this study, however, qCeq3H6, which represents the equilibrium adsorption capacity for C3H6, was simply obtained from the TPD experiment directly under the conditions used for calculation and experimental verification. 4. Estimation of the Hydrocarbon (HC) Desorption Rate. The HC desorption rate was estimated by varying the TPD ramping rate. The peak top analysis method, as defined by De Jong et al.,11 was used to perform the estimation. The HC desorption rate (Rd) was assumed to follow first-order kinetics and is expressed by eq 4:
Rd ) -
∂qC3H6 ∂t
) kC3H6,dqC3H6
(4)
Here, the desorption rate constant of C3H6 (kC3H6,d) was expressed by eq 5:
(
kC3H6,d ) ν exp -
E RT
)
(5)
Because the temperature ramping rate (β) is constant within one TPD measurement, E and ν can be obtained by plotting ln(Tp2/β) and 1/Tp curve, and thus eq 6 is obtained:
ν E E ) exp RT RT2 β
(
)
(6)
Here, Tp is the peak top temperature of C3H6. 5. Estimation of Reaction Rate Coefficient. The combustion reaction of C3H6 is described by eq 7,
C3H6 + 4.5O2 f 3CO2 + 3H2O
(7)
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Figure 1. Mesh model of the 1/4 monolith unit cell used for the calculation.
and the reaction rate model assumed a LangmuirHinshelwood mechanism, as described by eq 8.
rC3H6 )
kC3H6PC3H6PO2
(8)
(1 + KC3H6PC3H6)2
Here, rC3H6 is the reaction rate of C3H6 [kmol/m3s], kC3H6 is the reaction rate constant, and PC3H6 and PO2 are the partial pressures of C3H6 and oxygen, respectively. The reaction rate was assumed to be expressed by the Arrhenius equation given in eq 9:
(
kC3H6 ) AC3H6 exp -
)
E C 3H 6 RT
(9)
Experimental Section 1. Preparation of the Catalyst. The model catalyst consisted of a mixture of platinum loaded onto γ-Al2O3 (150 g/L) and zeolite (50 g/L); this mixture was coated on 400 cpsi/6 mil cordierite substrates (NGK). A platinum concentration of 2.0 g/L was used. Here, H2PtCl6 was used as a platinum precursor and an impregnation method was adopted to prepare the catalyst. The catalyst evaluated in the model gas reactor had dimensions of 24 mm in diameter × 66 mm long. 2. Geometric Model of the Catalyst Used for Calculation. A mesh model for 1/4 of the unit cell (shown in Figure 1) was based on a scanning electron microscopy (SEM) image and the size of the catalyst cross section. It is the minimum required for the calculation. It was assumed that the coating is radially symmetric. 3. Parameter Estimation and Calculation Conditions. To calculate the De value in eq 1, mercury and nitrogen porosity measurements were obtained for both honeycomb-only and coated monoliths. The HC adsorption capacity of the catalyst was evaluated by TPD (Rigaku, TPD type-R) methods. C3H6 was used as a model HC species. Catalyst powder was set into the TPD equipment and flushed in a helium atmosphere at 600 °C for 30 min. The sample then was cooled and C3H6 adsorption was allowed for 30 min, to achieve equilibrium. An adsorption temperature condition of 100 °C and 1000 ppm C3H6 was used for the model. Helium was used as the balance gas. To study
Table 1. Model Gas Composition for Steady-State and Transient Evaluation scalar
molecular weight
concentration(s)
C3H6 CO NO CO2 O2 H2O N2
42 g 28 g 30 g 44 g 32 g 18 g 28 g
250, 500, 700, 1000 ppm 300 ppm 300 ppm 6% 10% 6% balance
the competitive adsorption of C3H6 and H2O, 3 or 6 vol % of H2O was added to the C3H6/helium treatment gas. The gas atmosphere was changed to helium only, and the C3H6 desorption was measured by increasing the temperature to 600 °C at a ramping rate of 30 °C/min. The HC desorption rate was estimated from TPD measurement data as a function of the ramping rate. Three different ramping rates were used in this experiment (15, 30, and 60 °C/min). The reaction rate coefficient for HC oxidation was estimated from laboratory reactor experiments, using a monolithic catalyst. As mentioned previously, C3H6, which shows relatively strong adsorption characteristics on the zeolite, was selected as a model HC species. To obtain the activation energy and frequency factor for the HC oxidation reaction, a steady-state ramp-down measurement was performed from 240 °C to 175 °C, and the gas composition is shown in Table 1. The space velocity (SV) was 40 000 h-1. Diffusion coefficients were calculated from the model, and only the reaction rate itself was estimated from the experiment. For experimental verification of the calculated results, catalyst performance was evaluated with 1000 ppm C3H6 and a temperature ramp rate of 15 °C/min with 30 min HC adsorption treatment prior to the ramping up. Thus, the simulated catalyst performance for C3H6 adsorption, desorption, and oxidation was compared with experimental results for both ramp-up and cooldown conditions. Exothermic heat was measured during evaluation of the catalyst performance, and such exothermic heat was also used in the calculation. The gas composition is shown in Table 1 (here, only a HC concentration of 1000 ppm was used). The temperature range was 100-300 °C, the ramping rate was 15 °C/ min, and the SV ) 40 000 h-1.
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Figure 2. Representative hydrocarbon (HC) desorption profile, as determined using temperature-programmed desorption (TPD); the propylene concentration in the adsorption step was 1000 ppm, and the ramping rate was 30 °C/min.
Figure 3. C3H6 adsorption capacity as a function of water vapor concentration; the adsorption temperature was 100 °C. Table 2. Calculation Parameters parameter diffusion coefficient HC adsorption capacity @100 °C HC oxidation rate constant exothermic heat @ 400 °C under these experimental conditions
source equation
value
eq 1 15 µmol/g-cat. eq 8 20 °C
Results and Discussion 1. Diffusion Coefficient by Random Pore Model. Using the random pore model, a diffusion coefficient was calculated from the pore size and pore volume distributions measured by both mercury and nitrogen porosimetry. According to the results of these porosity measurements, i ) 0.0314 and the mean pore size for micropores was 1.0 nm, and a ) 0.379 and the mean pore size for macropores was 44 nm. An effective diffusion coefficient (De) for the catalyst was calculated by eq 4. 2. HC Adsorption Capacity and Adsorption Constant. Propylene adsorption is impacted by competition with every other gas species, including other HC species, water vapor, CO and NO, etc. For simplicity, this experiment is limited to C3H6 adsorption in competition with water vapor. HC adsorption capacity was evaluated by TPD, as a function of C3H6 concentration, water vapor concentration, and temperature. Figure 2 shows a representative profile for C3H6 desorption, as measured by TPD. Here, the intensity of mass fragment 41 was calibrated by measuring a known concentration of
Figure 4. Propylene desorption profile, as determined by TPD, at different ramping rates: ([) 60 °C/min, (9) 30 °C/min, and (2) 15 °C/min.
Figure 5. Result of peak top analysis of propylene desorption rate: ([) 60 °C/min, (9) 30 °C/min, and (2) 15 °C/min.
C3H6 (data not shown). Figure 3 shows, in the presence of water vapor, that a fraction of the C3H6 adsorption sites are occupied, thus reducing the C3H6 adsorption capacity. Here, the adsorption capacity was measured in the presence of 6% water vapor and 1000 ppm C3H6 at 100 °C for 30 min. The adsorption capacity measured was 15 µmol/g-cat (as shown in Table 2). 3. HC Desorption Rate. The HC desorption rate was calculated from C3H6 TPD data, using the peak top analysis method. The C3H6 desorption at different ramping rates is shown in Figure 4. The activation energy was estimated to be 102 500 J/mol (Figure 5), and the frequency factor in eq 5 as 4.05 × 109. 4. HC Reaction Rate. The reaction rate for C3H6 oxidation was estimated from the laboratory reactor experiments using a honeycomb catalyst. Under ideal conditions, a powder catalyst and high SV value should be used, to eliminate gas diffusion effects that can impact estimation of the mean reaction rate. However, the catalyst layer has a unique porosity structure that cannot be taken off the monolithic substrate without changing its porous structure. In this study, the reaction rate was calculated from honeycomb catalyst data and the gas diffusion factor was eliminated by the calculation using diffusion coefficients obtained from the model. In Figure 6, the HC conversion is measured at steady state from the highest temperature (240 °C) to the lowest temperature (175 °C). Using the data of Figure 6, the activation energy for C3H6 oxidation was estimated as 65 000 J mol-1 K-1 from the slope of the Arrhenius plot (Figure 7). The adsorption constant of
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Figure 6. Steady-state HC conversion at five different temperatures and four different C3H6 concentrations. Each conversion was measured by reducing the temperature from 240 °C to 175 °C. Legend is as follows: ([) 250 ppm, (9) 500 ppm, (2) 700 ppm, and (b) 1000 ppm.
Figure 8. Correlation between calculated and evaluated catalyst performance: (a) heating and (b) cooling. The C3H6 concentration is 1000 ppm, and the ramping rate is 15 °C/min. Figure 7. Arrhenius plot drawn using the data of Figure 6.
C3H6, KC3H6, was estimated from the data in this figure to be 31 853 kmol m-3 s-1. 5. Calculation Results and Experimental Verification. Three-dimensional (3D) modeling of the C3H6 oxidation down the length of a monolith channel was achieved using a geometric mesh model, the random pore model, the C3H6 adsorption capacity, the C3H6 desorption rate, and the oxidation rate. Experimental verification was also achieved under model gas reactor conditions. Model gas reactor evaluation of 1000 ppm C3H6 during both heating and cooling at a ramping rate of 15 °C/min was performed. Ideally, temperature ramping should be performed under conditions that are representative of actual evaluation modes, such as FTP and/ or ECE. However, the authors adopted a simple rampup and ramp-down protocol as a preliminary study for the purpose of constructing the model. HC adsorption pretreatment was performed on the catalyst at 100 °C for 30 min and then the catalyst temperature was ramped up. Under these conditions, ∼15 µmol/g-cat was adsorbed. A 20 °C exothermic heat of reaction at 400 °C was measured using a thermocouple at the outlet site of the catalyst. The calculation parameters are summarized in Table 2. A comparison between the calculation and experimental measurement results is shown in Figure 8. The calculated HC conversion profile agreed closely with the experimental profile for both the heating mode and the cooling mode, although some deviation was seen in the 0%-20% and 80%-95% conversion regions. This relatively close agreement validates the appropriateness of the model.
The HC concentration distribution in the catalyst layer was calculated for the HC adsorption mode and for the HC desorption/oxidation mode. Figure 9 shows the counter diagrams of C3H6 concentration in the 1/4 unit cell of the catalyst 5 and 10 s after the start of gas flow, under a C3H6 inlet concentration of 1000 ppm at 100 °C. Just after the gas flow begins, the simulation shows that C3H6 diffuses into the catalyst layer surface and, after 10 s, C3H6 has diffused completely into all deep sites of the catalyst. The counter diagrams of C3H6 concentration in the 1/ unit cell of the catalyst during the oxidation reaction 4 under temperature ramp-up conditions are shown in Figure 10. Here, the HC concentration profiles at 150 °C (T10), 160 °C (T50), and 170 °C (T90) are shown. Simulations show that the HC concentration at the outlet begins to decrease at 150 °C (T10), because of the oxidation reaction, and becomes much lower at 170 °C (T90). In Figure 10c (170 °C (T90)), the HC concentration gradient along the gas flow direction, and desorption from the catalyst layer depth is suggested to show the higher oxidation performance. Conclusion (1) To simulate precise hydrocarbon (HC) transient performance (i.e., adsorption, desorption, and reaction), gas diffusion and reaction models were constructed. The random pore model was used to obtain precise gas diffusion coefficients. The HC adsorption capacity was obtained via temperature-programmed desorption (TPD) under the presence of water vapor. The HC desorption rate was estimated by peak top analysis from the TPD data. The oxidation reaction rate was calculated from steady-state oxidation performance profiles.
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Figure 9. Counter diagrams of C3H6 concentration at the HC adsorption mode under 1000 ppm C3H6 gas flow conditions at 100 °C: (a) 5 s from the start of gas flow and (b) 10 s from the start of gas flow.
(2) Catalyst performance (HC oxidation heat up profile and cool profile) was calculated using the previously described model and parameters and compared to the experimentally evaluated results. The calculated performance correlated well with the experimental data, and the appropriateness of the model and the method of obtaining the parameters was confirmed. (3) The HC concentration distribution in the catalyst layer was calculated for the HC adsorption mode and the HC desorption/oxidation mode. For the HC adsorption mode, HC diffusion was observed to start from the catalyst layer surface and proceed to sites deep into the catalyst layer corner. Also, a HC concentration gradient from the gas flow inlet to outlet of the catalyst was observed. For the HC desorption/oxidation mode, HC concentration decreased first from the deep sites of the catalyst layer corner. In the gas-low direction, a HC concentration gradient follows the extent of the oxidation reaction.
(4) Thus, a model of the diesel oxidation catalyst (DOC) for transient HC performance on a DOC monolith has been successfully created. The information obtained in this study shows that a uniform catalyst layer with uniform precious-metal dispersion in the catalyst layer and a high diffusion coefficient yields high catalyst performance. Ideally, a more uniform and thinner catalyst layer (i.e., a smaller quantity catalyst with uniform depth) could lead to a catalyst with less precious metal and, therefore, a lower-cost catalyst. However, the catalyst design must be optimized to meet all the engine conditions (i.e., temperature, HC concentration, and space velocity (SV) profiles). Under ideal conditions, the model defined in this study can be used to predict an optimum platinum loading, catalyst layering and morphology, and catalyst loading. These approaches could save time for catalyst development.Further detailed modeling under actual mode driving conditions, such as FTP and/or ECE, and including not only C3H6 but other hydrocarbons and CO, are under investigation.
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Figure 10. Counter diagrams of C3H6 concentration in the ramping step under 1000 ppm C3H6 and 15 °C/min ramping rate conditions: (a) 150 °C (T10), (b) 160 °C (T50), and (c) 170 °C (T90).
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Acknowledgment
Literature Cited
The authors wish to thank Dr. Stanley A. Roth (Engelhard Corporation) for his contribution and support of this study. The authors also wish to thank Mr. Kenichi Mimura (Chiyoda Advanced Solutions Corporation) for his contribution to the computer calculation in this study.
(1) Vincent, M. W.; Richards, P. J.; Novel-Cattin, F.; Marcelly, B.; Favre, C. Fuel additive performance evaluation for volume production application of a diesel particulate filter. SAE Tech. Pap. Ser. 2001, 2001-01-1286, 177-184. (2) Tomazic, D.; Tatur, M. M.; Thornton, M. J. Development of a diesel passenger car meeting Tier 2 emissions levels. SAE Tech. Pap. Ser. 2004, 2004-01-0581, 149-164. (3) Higashiyama, K.; Nagayama, T.; Nagano, M.; Nakagawa, S. Tominaga, S.; Murakami, K.; Hamada, I. A catalyzed hydrocarbon trap using metal-impregnated zeolite for SULEV systems. SAE Tech. Pap. Ser. 2003, 2003-01-0815, 45-51. (4) Kim, D. J.; Kim, J. W.; Yie, J. E.; Moon, H. TemperatureProgrammed Adsorption and Characteristics of Honeycomb Hydrocarbon Adsorbers. Ind. Eng. Chem. Res. 2002, 41, 6589. (5) Nakano, M.; Ogawa, H.; Itabashi, K. Zeolite based adsorbents and catalysts for environmental applications utilizing a function of hydrocarbon-adsorption. Toso Kenkyu‚Gijutsiu Hokoku 2001, 45, 29. (6) 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. (7) Jime´nez, C.; Romero, F. J.; Rolda´n, R.; Marinas, J. M.; Go´mez, J. P. Hydroisomerization of a hydrocarbon feed containing n-hexane, n-heptane and cyclohexane on zeolite-supported platinum catalysts. Appl. Catal., A 2003, 249, 175. (8) Nagata, M.; Kimura, R.; Banno, Y.; Maki, K. Observation of soot accumulation conditions in diesel particulate filter and gas flow analysis. SAE Tech. Pap. Ser. 2002, 2002-01-1013. (9) Banno, Y.; Tanaka, Y.; Hihara, T.; Nagata, M.; Kanno, Y. Pre-filter diesel oxidation catalyst development for DOC-CSF system. SAE Tech. Pap. Ser. 2004, 2004-01-1430. (10) Wakao, N.; Smith, J. M. Diffusion in catalyst pellets. Chem. Eng. Sci. 1962, 17, 825. (11) De Jong, A. M.; Niemantsverdriet, J. W. Comparative test of procedures for thermal desorption analysis. Vacuum 1990, 41, 232. (12) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th Edition; McGraw-Hill: New York, 2001.
Nomenclature t ) time [s] P ) pressure [Pa] CC3H6 ) molar concentration of C3H6 [kmol/m3] T ) temperature [K] De ) effective diffusion coefficient [m2/s] rC3H6 ) reaction term of C3H6 [kmol/m3-cat s] ∂q/∂t ) adsorption/desorption rate term [µmol/g-cat s] Da ) diffusion coefficient in the macropore [m2/s] Di ) diffusion coefficient in the micropore [m2/s] a ) porosity of the macropore i ) porosity of the micropore Kad,C3H6 ) adsorption equilibrium constant for C3H6 Kad,H2O ) adsorption equilibrium constant for H2O q∞,C3H6 ) saturated adsorption capacity for C3H6 [µmol/ g-cat] qCeq3H6 ) equilibrium adsorption capacity for C3H6 [µmol/ g-cat] PC3H6 ) partial pressure of C3H6 in the gas phase [atm] PH2O ) partial pressure of H2O in the gas phase [atm] ∆H ) adsorption heat [J/mol] Ra ) adsorption rate [µmol/g-cat s] Rd ) HC desorption rate [µmol/g-cat s] kC3H6,d ) desorption rate constant [s-1] E ) activation energy [J/mol] ν ) frequency factor [s-1] β ) ramping rate of TPD [°C/min] rC3H6 ) reaction rate of C3H6 [kmol/m3-cat s] kC3H6 ) reaction rate coefficient [kmol/m3 atm2 s] PC3H6 ) partial pressure of C3H6 [atm] PO2 ) partial pressure of O2 [atm] KC3H6 ) adsorption term constant in reaction rate equation R ) gas constant [J/mol K]
Received for review April 14, 2005 Revised manuscript received July 29, 2005 Accepted August 22, 2005 IE0580349
