Analysis of Periodic Storage and Reduction of NOx in Catalytic

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Ind. Eng. Chem. Res. 2005, 44, 6264-6277

Analysis of Periodic Storage and Reduction of NOx in Catalytic Monoliths Manish Sharma, M. P. Harold,* and V. Balakotaiah* Department of Chemical Engineering, University of Houston, Houston, Texas 77204

A one-dimensional two-phase model of an adsorptive catalytic monolith reactor is developed and analyzed. The model simulates the generic features of NOx storage and reduction (NSR), a periodic process involving the sequential trapping on a storage component and conversion of NOx to nitrogen under lean conditions found in the exhaust of lean burn and diesel vehicles. The reactor model includes a phenomenological microkinetic model of NSR on a bifunctional storage catalyst. We examine the effects of several design and operating parameters on the reactant conversion, including cycle timing, feed flowrate, composition, and temperature. The simulations reveal complex spatio-temporal phenomena in the form of traveling concentration and temperature waves. The extent of site blocking by oxygen of NOx adsorption is an important determinant of cyclic enhancement of the NOx conversion. The model predictions are in qualitative agreement with experimental observations reported in the literature. For example, the NOx conversion exhibits a maximum at an intermediate cycle time and increases with decreasing rich pulse duty. 1. Introduction Increasingly stringent requirements for emissions from internal combustion engines require the development of advanced after-treatment systems. The vehicle catalytic converter allows a satisfactory reduction of overall engine emissions, but is subject to continuous development and improvement due to changing regulations for acceptable exhaust levels. Numerical simulation models are heavily exploited during the development stage, since they can help the engineers to investigate the behavior of the catalytic converter under different conditions and shorten the optimization process. Computer codes with varying degrees of complexity are developed and applied to assist in the design process. The optimization of geometrical dimensions, washcoat characteristics and position of the catalyst on the exhaust system of an engine, to achieve the optimal response in terms of conversion efficiency, light-off time and engine exchange process is a difficult task, due to the simultaneous oxidation and reduction chemistries and their interactions with the heat and mass transfer phenomena occurring in the converter. Lean-burn gasoline and diesel vehicles offer a higher fuel efficiency than stoichiometric gasoline vehicles. The lean fuel/air conditions of lean-burn combustion that give the higher efficiency, also produce a net-oxidizing exhaust gas containing several pollutants, including volatile organic hydrocarbons (VOCs), CO, NOx, SO2 in a mixture with O2, N2, H2O, and CO2. Diesel exhaust also includes particulate soot. The long term growth of lean-burn and diesel vehicles depends on how effectively these pollutants can be eliminated from the exhaust. While the net oxidizing exhaust benefits the catalytic oxidation of exhaust hydrocarbons and carbon monoxide, it precludes an effective chemical reduction of NOx to nitrogen. For example, Burch and co-workers1 and * Authors to whom correspondence should be addressed. Tel: (713) 743-4307 (M.P.H.); (713) 743-4318 (V.B.). Fax: (713) 743-4323. Email: [email protected] (M.P.H.); bala@ uh.edu (V.B.).

Amiridis and co-workers2,3 have shown that NOx conversion is considerably less than 100% in lean feeds. Generally, the NOx reduction (conversion) does not exceed 60%, but the absolute maximum depends on the temperature, reductant type, and precious metal loading. This is attributed to the oxygen inhibition of NOx adsorption and subsequent NO scission and N adatom recombination. Thus, the reduction of NOx to molecular nitrogen in the exhaust of these engine types is a very important technological challenge. Several approaches have been tried to improve the NOx conversion under lean conditions. One of the emerging techniques is that of NOx Storage and Reduction (NSR), and the device in which NSR is carried out is commonly referred to as the lean NOx trap (LNT). The lean NOx trap is a periodically operated adsorptive reactor and comprises of a bifunctional catalyst with deliberate periodic operation in which the air fuel ratio is altered between lean (oxygen excess) and rich (fuel excess) mixtures (Takahashi et al.4). The LNT catalyst has components for both storage (alkali earth compound) and reduction (precious metal) of NOx. During the storage phase, NOx is incorporated into the alkali earth storage component as a mixture of nitrites and nitrates through a complex set of steps that involve NO oxidation to NO2 on the precious metal (Platinum), followed by nitration of the alkali earth carbonate, among other pathways. Just before breakthrough of NOx in the reactor effluent, a net-reducing mixture is fed to the trap which is accomplished by temporary rich operation of the lean burn engine or by direct injection of reductant (fuel) into the exhaust system. During this regeneration or purge phase, the injected hydrocarbon serves the dual role of consuming the excess oxygen and of reducing the nitrites/nitrates. The NOx reduction chemistry primarily occurs on the precious metal through a selective catalytic reduction process forming a mixture of nitrogen and N2O as the N-containing products. Upon regeneration of the storage component, the feed is switched back to the netoxidizing feed and the cycle is repeated.

10.1021/ie0490785 CCC: $30.25 © 2005 American Chemical Society Published on Web 03/11/2005

Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 6265

NSR is still in the development stage due in part to challenges such as associated with fuel consumption, sulfur poisoning of the storage components (Sedlmair et al.5) and the corresponding need for effective desulfation protocols, and fuel (reductant) feed strategies that minimize the fuel penalty and reduce the precious metal content. Most studies during the past several years have examined mechanistic and kinetic aspects of NSR, and the performance of bench scale lean NOx traps. A comprehensive model of the NSR process that focuses on the interacting chemical and transport rate processes is still needed. Experimental studies of catalytic monoliths or packed powder reactors indicate that NSR holds promise (Takahashi et al.;4 Theis et al.;6 Muncrief et al.;7,8 Kabin et al.9). Theis et al.6 described results from a large study on the release of NOx from a LNT during rich purges, for different NOx trap formulations. They also suggested various mechanisms for NOx release under different conditions. Time-averaged NOx conversions exceeding 80% over a wide range of operating conditions have been reported (Muncrief et al.;7,8 Kabin et al.9). These studies show that rather fast lean/rich cycling is necessary to maximize NOx conversions; specifically, storage times of 30 s to a few minutes and regeneration times of less than 10 s. Laurent et al.10 developed a model for NOx adsorption over NOx adsorbers, which was used to predict the quantity of stored NOx. They provided data concerning kinetic and thermodynamic parameters, which were obtained by fitting the calculated extent of storage and emissions to the experimental data. Olsson et al.11 developed a microkinetic model for storage and desorption of NOx and suggested mechanisms for the process using data from flow reactor experiments. They also performed a kinetic study of NO oxidation and NOx storage on Pt/Al2O3 and Pt/BaO/Al2O3 (Olsson et al.12). Scotti et al.13 applied the NOx storage model of Olsson et al.12 and showed that further improvements are needed to fully capture the transient characteristics. Jirat et al.14 simulated the periodic switching between lean and rich combustion conditions and showed possibility to reach much improved time averaged NOx conversion on a single monolith in comparison with steady-state operation, but lower CO and hydrocarbon conversions under reducing conditions. Koci et al.15 did the modeling of catalytic monolith converters with low and high-temperature NOx storage compounds and differentiated washcoat, evaluating unknown kinetic parameters using transient experimental data. Kim et al.16 developed a lumped parameter model for Lean NOx Traps, in which the model parameters were estimated using experimental data and the model was used to predict LNT operation during lean and purge phases. There are several other studies on storage of NOx on NOx adsorbers (Sedlmair et al.;17 Cant et al.18), but these reports do not show explicitly the parameters which can directly influence the conversion during the purge phase. This paper analyzes in detail the effect of periodic switching between lean and rich combustion conditions on NOx conversion by using a one-dimensional (1-D) two-phase, model describing adsorption, desorption, and reaction of different species in a catalytic monolith. The catalytic reaction system, both reaction network and kinetics, have the main features of NOx storage and reduction. We utilize the model to examine the effects of several key operating and kinetic parameters on the conversions of the NOx and reductant, with particular

Figure 1. Different types of active sites in the washcoat and their functions. Site S is barium oxide and site Y is platinum.

focus on the conditions giving high NOx conversion with minimal breakthrough of hydrocarbon. We show that the model predicts many of the experimentally observed trends for NSR even though we have not made an attempt to fit data a priori. 2. Reactor Model Description We consider a monolith reactor consisting of a large number of parallel channels through which the reacting fluid flows. The supported catalyst is present as a thin, porous washcoat of uniform thickness on the walls of the monolith. Convective-diffusive transport of reactants toward and of products away from the washcoat surface occur as the gas mixture flows down the channel. The feed gas consists of a mixture of several components: NOx (NO and NO2), hydrocarbon, oxygen, and inerts. We consider a chemical system that is a simplified version of the more complex NOx storage and reduction. Our intent is to capture the main features of the NSR system. The catalyst has two types of sites, S and Y, representing respectively the storage component (alkali earth compound, BaO) and catalytic component (precious metal, Pt), as shown in Figure 1. We assume that the feed NOx is NO2 since the storage component can adsorb NO2 only. [If the reactor feed has NO, it has to get oxidized to NO2 (on Pt) before it can be stored on site S (BaO) (Olsson et al.12)]. The assumption is akin to assuming that NO conversion to NO2 is very fast. It has been shown that NOx storage improves if a Pt/Alumina catalyst is placed in front of the Pt/BaO/Alumina catalyst (Olsson et al.12). Also, during the first few minutes storage of NOx occurs in the form of a reversible adsorption of NO2 (Olsson et al.;11 Scotti et al.13). On site type S the reversible storage of NO2 is depicted as

1: NO2 + S h NO2 - S On site type Y, a series of adsorption and surface reaction steps occur. Steps 2, 3, and 4 represent the reversible adsorption of C3H6, O2, and NO2

2: C3H6 + 3Y h 3CH2 - Y 3: O2 + 2Y h 2O - Y 4: NO2 + Y h NO2 - Y Here, we have assumed that adsorbed C3H6 is present as CH2 and adsorbed O2 is present as oxygen atoms on the Pt surface, as described in some of the previous studies(Olsson et al.;11 Olsson et al.12). Surface reactions 5 and 6 represent the oxidation of C3H6 and NO2 reduction, respectively:

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5: CH2 - Y + 3O - Y f 4Y + CO2 + H2O 6: 4CH2 - Y + 6NO2 - Y f 10Y + 4CO2 + 4H2O + 3N2 The dissociation of NO2 to NO is not considered here. The following simplifying assumptions are made in the development of the reactor model: (i) It is a one-dimensional, two-phase model. (ii) The washcoat is thin enough so that the gradients within the washcoat normal to the flow direction can be neglected. (iii) Heat and mass transfer coefficients are assumed to be constant, which implies fully developed flow and channel length-to-diameter ratio is large. (iv) Physical properties (such as density and viscosity) are assumed to be constant. (v) Wall and washcoat thicknesses are small compared to the channel hydraulic radius. (vi) All mixtures are dilute and volume changes are neglected. (vii) Flow in the monolith channel is laminar. (viii) Conduction and diffusion terms can be neglected in fluid phase compared to convective transport. (ix) Inerts (like nitrogen) do not adsorb on the active sites in the washcoat. (x) Reaction products desorb from the active sites as soon as they are formed, so that they do not occupy active sites. The monolith aspect ratio (axial length/diameter) is assumed to be high enough so that a model with assumption (i) can describe the solid and fluid variables with sufficient accuracy. Washcoat diffusion effects will be considered in a future study (assumption (ii)), while position dependency of the heat and mass transfer coefficients is not expected to change the results qualitatively. Assumption (iv) limits the quantitative accuracy of the model. On the other hand, it allows us to obtain results of a more general nature. Assumption (v) is usually satisfied in practice and relaxing it has no influence on the qualitative predictions. Assumption (vi) is based on the fact that typical lean burn exhaust contains about 60-70% nitrogen (inert). The volume changes that occur because of reactions on the wall, temperature changes and pressure changes, are expected to be small. Assumption (vii) can be relaxed by replacing the generalized correlations for heat and mass transfer in laminar flow by corresponding correlations for turbulent flow (if the flow is turbulent). However, under most conditions in monolith converters, this assumption is satisfied. Assumption (viii) is usually satisfied for most practical cases for both gaseous and liquid reactants when the channel length-to-diameter ratio is large. The last assumption is usually true for combustion of hydrocarbons on precious metals, since combustion products form at high temperatures and desorption rates increase with temperature, and it can be relaxed by using corresponding balance equations for products. Fluid Phase. The fluid phase species balances include accumulation, convection and interphase mass transport for the gas-phase species NO2, C3H6, and O2

( )

∂Xjm ∂Xjm 1 +u jf ) -kjc (X - Xjs) ∂t ∂Z RΩ jm j ) NO2, C3H6, O2 (1)

where Xj is the mole fraction of species j (m and s denote mixing-cup/bulk and surface), u j f is the mean fluid velocity, kjc is the mass transfer coefficient of species j, and RΩ() AΩ/PΩ), is the effective transverse (diffusion or conduction) length scale and is the ratio of channel area to channel perimeter. Also, RΩ ) Dh/4, where Dh is the channel hydraulic diameter. The energy balance for fluid phase includes the accumulation, convection and interphase heat transport terms

Ffcpf

(

)

( )

∂Tm ∂Tm 1 +u jf ) -hf (T - Ts) ∂t ∂Z RΩ m

(2)

where Tm (Ts) is the bulk (surface) temperature and hf is the heat transfer coefficient. The species balance eqs 1 and 2 neglect the mass and heat diffusion along the axial direction in the fluid phase, since the axial mass and energy Peclet numbers are typically large in catalytic monoliths. Washcoat. The balances for the reactive species taking into account accumulation, adsorption, desorption, and reaction on site types S and Y are

∂θNO2S NO2 2 ) RNO CST adS - RdeS ∂t CYT

∂θCH2Y ∂t CYT CYT

(3a)

) 3RCad3H6 - 3RCde3H6 - Rr1 - 4Rr2 (3b)

∂θOY O2 2 ) 2RO ad - 2Rde - 3Rr1 ∂t

∂θNO2Y ∂t

(3c)

NO2 2 ) RNO adY - RdeY - 6Rr2

(3d)

Rr1 ) kr1CCH2YCOY

(4)

Rr2 ) kr2CCH2YCNO2Y

(5)

[ [

NO2 NO2 2 RNO adS - RdeS ) kadS psXNO2sCvS -

2 KNO S

RCad3H6 - RCde3H6 ) kCad3H6 psXC3H6sCvY -

[

O2 O2 2 RO ad - Rde ) kad psXO2sCvY -

[

]

CNO2S

]

CCH2Y KCY3H6

]

COY 2 KO Y

NO2 NO2 2 RNO adY - RdeY ) kadY psXNO2sCvY -

(6a)

(6c)

]

CNO2Y 2 KNO Y

(6b)

(6d)

Here, we have assumed first-order dependencies on the i various reacting species. Radj represents the rate of adsorption of species i on site type j, Ridej represents the rate of desorption of species i on site type j, and Rrk represents the rate of reaction k, where k ) 1 for combustion reaction and k ) 2 for NOx reduction reaction. Note that the surface rates are dependent on the partial pressures near the surface (psXis) and adsorbed concentrations. All rates are expressed in moles per washcoat volume per unit time. Each site type has

Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 6267 Table 1. List of Various Constants Used in the Model Tin ) 600 K feed NO2 (NOx) ) 500 ppm feed O2 ) 5% feed C3H6 (Reductant) ) 1.3% time of lean phase ) 70 s time of rich phase ) 10 s L ) 0.4 m u j f ) 5 m/s CST ) 500 mol/m3 CYT ) 40 mol /m3 kC3H6c ) 0.08 m/s kNO2c ) 0.12 m/s

Table 2. List of Various Kinetic Constants

kO2c ) 0.12 m/s Dh ) 2 mm δc ) 20 µm δw ) 125 µm Cpf ) 1000 J/kg/K Ff ) 0.6 kg/m3 Cpw ) 1000 J/kg/K Fw ) 1500 kg/m3 hf )100 W/m2K kw )1.5 W/(m.K) ∆Hr1 ) -667 kJ/mol

a fixed total number of active sites. Assuming that the reaction products and inerts do not occupy any active sites, we have

Site S: θNO2S + θvS ) 1

(7)

Site Y: θCH2Y + θOY + θNO2Y + θvY ) 1

(8)

where θij ) Cij/CjT () surface coverage of species i on site j). Subscript v denotes vacant sites and CjT denotes total concentration of sites of type j. The washcoat energy balance accounts for solid-phase accumulation and conduction, and heat effects due to combustion reaction, and is given by

δwFwcpw

∂Ts ∂2Ts ) δwkw 2 - hf(Ts - Tm) + δc(-∆Hr1)Rr1 ∂t ∂Z (9)

where notable parameters include δw, the wall half thickness; δc, the washcoat thickness; ∆Hr1, the heat of reaction 1; Fw, the solid (wall) density; cpw, the solid heat capacity; and kw, the solid thermal conductivity. Note that the washcoat heat capacity is lumped into the wall heat capacity term and heats of adsorption and reduction reactions are neglected. Finally, continuity of species (NO2, C3H6 and O2) flux between the bulk and the surface gives the following equations

CTmkjc(Xjm - Xjs) ) δc(Rjad - Rjde)S + δc(Rjad - Rjde)Y

j ) NO2, C3H6, O2 (10)

where CT is the bulk molar concentration. Inspection of the governing equations (1, 2, 3a-d, 7, 8, 9, 10) reveals 14 dependent variables (Xjm, Xjs, θNO2S, θvS, θjY, θvY, Tm, Ts). The corresponding initial and boundary conditions are as follows

t ) 0, Xjs(Z) ) Xj0(Z), Ts(Z) ) Ts0(Z) j ) NO2, C3H6, O2 (11) Z ) 0, Xjm(t) ) Xjin(t), Tm ) Tin(t) j ) NO2, C3H6, O2 (12) Z ) 0, L

∂Ts )0 ∂Z

(13)

3. Model Parameters We simulate the adsorptive reactor by assigning parameter values that approximate the NOx storage and reduction system. Tables 1 and 2 provide a listing of the nonkinetic and kinetic parameter values, respec-

kr1 ) 200 m3(s.mol)-1

NO2 kadS )500 (atm.s)-1

kr2 ) 1.2 m3(s.mol)-1

2 -1 kNO adY )100 000 (atm.s)

Er1 ) 90 kJ/mol

3H6 kCadY ) 5000 (atm.s)-1

Er2 ) 190 kJ/mol

2 -1 kO adY ) 5000 (atm.s)

2 ENO deS ) 160 kJ/mol NO2 EdeY ) 100 kJ/mol 3H6 ECdeY ) 170 kJ/mol O2 EdeY ) 180 kJ/mol

2 KNO )105(atm)-1 S 2 KNO )104 (atm)-1 Y

KCY3H6 )3500 (atm)-1 2 4 -1 KO Y )10 (atm)

tively. Unless otherwise stated, these are the base case values in the simulations. Some comments and justifications are as follows. The monolith channel length is 0.4 m and the inlet fluid velocity is 5 m/s, which gives a GHSV of 45 000 hr-1. The channel hydraulic diameter is 2 mm, the washcoat thickness is 20 µm, and the half wall thickness is 125 µm. During cyclic operation the lean and rich feeds are alternated according to 70 s lean feed and 10 s rich feed. NO2 and O2 concentrations are fixed at 500 ppm and 5% throughout the cycle. During the lean phase there is no C3H6 (hydrocarbon) fed whereas its concentration is fixed at 1.3% during the rich pulse. The temperature of the feed gas is fixed at 600 K, which is also the initial temperature of the monolith. The concentrations of active sites of type S (BaO) and of type Y (Pt) are based on 20% BaO and 2% Pt by weight washcoat and assuming a washcoat density of 1.5 g/cm3. We also assume that only 25% of these active sites are actually accessible to account for diffusion limitations encountered in experimental studies. The diffusivities of the three species have been used to estimate the three mass transfer coefficients, assuming an asymptotic Sherwood Number of 4

kjc )

4Dmj Dh

(14)

where kjc is the mass transfer coefficient of species j, Dmj is the diffusivity of species j and Dh is the channel hydraulic diameter. The half wall thickness of the monolith channel is assumed to be 125 µm, which gives a porosity of about 0.79 for the monolith channel, where porosity, can be approximated by

)

1 δw δw 1+ + RΩ 2RΩ

( )

2

(15)

The heat transfer coefficient is calculated assuming an asymptotic Nusselt Number of 4

hf )

4kf Dh

(16)

where kf, the thermal conductivity of fluid, is assumed to be equal to 0.05 W/(m K). The heat of combustion reaction (∆Hr1) is the about one-third the heat of combustion of propene (heat of combustion of one CH2). The kinetic parameter values (Table 2) were selected to capture the main kinetic features of NOx storage and reduction, with some taken directly from literature. The adsorption of NOx on barium (oxide or carbonate) is known to involve multiple steps and surface species. We treat the storage as a simple Langmuirian adsorptiondesorption process. For species NO2 on storage site S,

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we assume a value of 500 (atm s)-1 for the adsorption constant, 105 (atm)-1 for the adsorption equilibrium constant, and 160 kJ for activation energy. The rates of combustion and reduction reactions, and the activation energies are similar to that given by Olsson et al.11 Conventional temperature dependencies are assumed. Surface reaction rate constants (krj) follow the Arrhenius equation

ln

( ) ( krj(T2)

krj(T1)

)

)

Erj 1 1 R T 1 T2

(17)

The adsorption equilibrium constants for i on site j, follow vant Hoff’s equation

( ) Kji(T2)

( )

∆Had 1 ij 1 ln j ) R T T Ki(T1) 1 2

Kji,

(18)

A reference temperature of 600 K was used to determine base values for parameters having a temperature dependence. One of the distinguishing features of the selective reduction of NOx on Pt is the high coverage of surface oxygen adatoms resulting from the high relative gas phase concentration of oxygen. Surface oxygen inhibits the adsorption of hydrocarbon and NO onto Pt. The inhibition is especially detrimental to NO reduction to nitrogen and accounts for the low NO conversions under lean conditions. Oxygen inhibition of the hydrocarbon oxidation is not as significant. Burch and Sullivan19 claim that it is possible for gas phase propene to react directly with the surface oxygen on platinum. The values used for the kinetic parameters and adsorption equilibrium constants for NO2, C3H6, and O2 on platinum capture the feature that during the lean phase most of the Pt sites are covered by oxygen and during the rich phase hydrocarbon adsorbs competitively with oxygen and reacts with oxygen on the platinum sites. We expand on these points later in the paper. 4. Qualitative/Analytical Considerations Before we present the numerical simulation results, we review here some qualitative and analytical results on adsorption and desorption fronts, and light-off and thermal front propagation in catalytic monoliths. We utilize the parameter values listed in Tables 1 and 2. This analysis is used to guide the numerical simulations as well as to interpret the results of simulations in a later section. For example, for the parameter values chosen, the contact time of the gas with the catalyst (fluid residence time) is 0.08 s and the ratio of the hydraulic radius (RΩ) to the mass transfer coefficient is a measure of the gas to solid mass transport time, for O2 it is equal to 0.0042 s. The ratio of these two characteristic times, reciprocal of an effective transverse Peclet number (number of transfer units) has a value of 19.05, indicating that exit conversions are not mass transfer limited. 4.1 Lean Phase Storage and Breakthrough. During the lean (adsorption and storage) phase, feed gas NO2 (NOx) and O2 are stored on the adsorption sites in the washcoat. As explained earlier, NO2 is mainly stored on site type S (barium oxide), while type Y (Pt) sites are occupied by O2 and NO2. Because O2 is in large excess of NO2 during storage and NO2 and O2 have comparable site Y adsorption equilibrium constants, O2

effectively blocks the adsorption of NO2 on Y. In order for NO2 to be reduced, it must desorb from the S sites, then adsorb on the Y sites where it reacts with adsorbed reductant (CH2 - Y). It is therefore important to understand the dynamics of the adsorption/desorption process and resulting species gas-phase concentration wave. The net rate of adsorption of any species, rjad, the difference between the rate of adsorption and the rate of desorption, is given by the following equation

[

rjad ) Rjad - Rjde ) kaj pjSCv -

Cj Kj

]

(19)

where kaj is the adsorption constant, pjS is the surface partial pressure of species j, Cv is the concentration of vacant sites, Cj is the concentration of sites occupied by species j in the washcoat and Kj is the adsorption equilibrium constant () kaj/kdj). The balance of active sites gives:

C T ) Cv +

∑Cj

(20)

where CT is the total concentration of active sites. Replacing Cj by θj, where θj ) Cj/CT, we get

∑θj + θv ) 1

(21)

If the rates of adsorption and desorption are fast (relative to reaction), active sites in the washcoat become saturated and the net rate of adsorption equals zero; this is adsorption equilibrium. Setting the righthand side of eq 19 equal to zero and using eqs 20 and 21, and solving for θje we get

θje ) Kjpjsθve )

Kjpjs 1+

(22)

∑Kipis

Equation 22 is the standard Langmuir isotherm. If we let Cj be the concentration of species j in the reactor, then to a first approximation (neglecting the mass transfer resistance, axial dispersion and assuming local equilibrium), the adsorption front can be described by the following equation

∂Cj δc ∂θje ∂Cj C +u jf + )0 ∂t ∂Z RΩ T ∂t

(23)

For the isothermal case, we can write Cj ) pj/RgT, and eq 22 can be written as

θje )

K ˆ jCj 1+

(24)

∑Kˆ iCi

where K ˆ j ) KjRT. Thus, eq 23 can be written as

[

]

δc ∂Cj K ˆ jCj ∂Cj ∂ +u jf + C )0 ∂t ∂Z RΩ T∂t 1 + K ˆ iCi

∑

(25)

When only one species is adsorbed, the above equation can be reduced to

δc ∂C ∂ K ˆC ∂C +u jf + C )0 ∂t ∂Z RΩ T∂t 1 + K ˆC

[

]

(26)


with the following initial and boundary conditions:

C(Z, 0) ) 0 C(0, t) ) Cin(t)

(27)

It follows from eq 26 that the front or the shock velocity of the adsorption wave can be estimated as (Rhee et al.20)

u jf

us ) 1+

δc K ˆ C RΩ T1 + K ˆ Cin

(28)

Using the values of constants as given in Tables 1 and 2, we calculate the shock velocity for NOx adsorption on barium to be, us ) 2.56 × 10-3 m/s and the approximate breakthrough time (L/us) to be around 155 s, which, as we report below, is similar to that found in the numerical simulations. If NOx is fed to the reactor for longer than the breakthrough time, then it leaks from the reactor and results in a decreased NOx conversion. Note that under practical conditions, the first term in the denominator of eq 28 is much smaller than the second term and the adsorption front velocity (as can be expected intuitively) is directly proportional to RΩ and inversely proportional to the product of δc and CT (storage capacity). 4.2 Rich Phase Behavior: Light-off, Hot Spot Propagation and Cascading Storage and Reduction. During the fuel rich phase, C3H6, representing the hydrocarbon (reductant), is fed to the reactor along with component NO2 (NOx), O2 (oxygen) and inert. At any point within the reactor C3H6 adsorbs on the Y sites (Pt) and undergoes an exothermic reaction with adsorbed O2, akin to catalytic combustion, resulting in an increase in the local temperature and depletion of O2. Front-end ignition (light-off) is desired in the reactor because backend ignition takes more time for propagation through the reactor length and thus consumes more hydrocarbon (Ramanathan et al.21). The criteria for front-end ignition given by Ramanathan et al.21 shows that higher values of reaction rate, inlet temperature, adiabatic temperature rise (inlet concentration), RΩ and δc favor frontend ignition. Assuming no washcoat diffusional limitations, front-end ignition criteria can be derived for this study. At steady state, eq 9 can be reduced to the following form by neglecting conduction and heat effects associated with adsorption of various species and NOx reduction reaction Rr2.

hf(Ts - Tm) - δc(-∆Hr1)Rr1 ) 0

(29)

For front-end ignition, Tm in the above equation can be replaced by Tin, the fluid inlet temperature. At ignition, the derivative of eq 29 with respect to Ts, the solid temperature, must be zero. This gives

hf ) δc(-∆Hr1)

( ) ∂Rr1 ∂Ts

(30)

For the case of Langmuir-Hinshelwood kinetics, if we assume that the rate of the surface reaction is the controlling step (equilibrated adsorption), then the rate of reaction (equation 4) is given by the following expression

2 Rr1 ) kr1KCY3H6 PC3H6KO Y PO2

(

CYT

)

NO2 2 1 + PC3H6KCY3H6 + PO2KO Y + PNO2KY

2

(31)

Using the value of constants as given in Tables 1 and 2, and assuming inlet fractions of O2, NO2, and C3H6 to be 0.05, 0.0005, and 0.013, respectively, eqs 29 and 30 when solved together to eliminate Ts, give an inlet ignition temperature (Tin,ig) of about 500 K. [Remarks: (i) Equations 29 and 30 may also be used to determine in the (Tin, Cin) plane the boundary of front end ignition values of Tin and Cin. (ii) An ignited steady-state may exist even for Tin less than this critical value but can only be reached if the initial solid temperature is high. Multiple steady states exist whenever Tin,e < Tin < Tin,ig, where Tin,e is the inlet fluid temperature below which only an extinguished steady-state exists.]. To understand the reactor dynamics, it is helpful to estimate the characteristic thermal/temperature front propagation time, especially in comparison to the adsorption/concentration front propagation time. During the rich phase, light-off will occur at the front-end of the monolith channel and the resulting thermal front will propagate along the reactor length. For the case of front-end ignition, the time for the propagation of the thermal front (tp) can be estimated from the following expression (Ramanathan et al.22)

tp )

L (FwCpw) δw u j f (Ffcpf) RΩ

(32)

For our simulations, using the values of various constants as given in Table 1, L/u j f ) 0.08 s, (FwCpw)/(Ffcpf) ) 2500, δw/RΩ ) 0.25, we get a propagation time (tp) of 50 s. This thermal front propagation time (which is independent of solid thermal conductivity) is about onethird the NOx adsorption front propagation time (for the parameter values chosen in this study). 5. Simulation Results and Discussion We now present the detailed numerical simulations in order to elucidate the periodic adsorption and reaction and to identify the optimum conditions of operation in terms of NOx reduction. 5.1 Transient Profiles. Representative transient profiles are presented in this section. We consider a total cycle time of 80 s with a lean (storage) phase of 70 s and rich (regeneration) phase of 10 s. The lean phase feed contains 500 ppm NO2 (NOx) and 5% O2, with remainder inerts. The rich phase feed contains 1.3% C3H6 (hydrocarbon) and the same concentrations of NO2 and O2 as in the lean phase, with remainder inerts. The feed flow rate (linear velocity) and temperature are fixed at 5 m/s and 600 K, respectively. All other parameter values are provided in Tables 1 and 2. The overall reactor dynamics are determined in large part by the characteristic times of the various transport and kinetic processes and the timing of the rich and lean phases. Recall that the thermal front propagation time is about 50 s and the NO2 breakthrough time is about 155 s, whereas the gas-phase contact time, gas-solid external transport time, and the surface kinetic transport times are all considerably less than 1 s. The 10-second rich pulse time means that the hot spot will only traverse a fraction of the reactor length before the end of the pulse.

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Figure 2. Transient exit NO2, exit C3H6 and exit oxygen profiles. Feed hydrocarbon during rich phase is 1.3% and during lean phase is 0%, the feed temperature is 600 K, feed NO2 is 500 ppm and feed oxygen is 5%. Lean phase time is 70 s and rich phase time is 10 s.

On the other hand, the 70-s lean phase ensures complete trapping of the NOx. Figure 2 shows the outlet concentrations of NOx, hydrocarbon and oxygen for seven complete cycles after the monolith has reached a pseudo-steady-state. The effect of the lean/rich switching is evident in the effluent composition. During the lean phase there is negligible breakthrough of NOx and hydrocarbon whereas the oxygen concentration is at its feed value of 5%. During the rich phase two spikes of unreacted hydrocarbon appear at the outlet, while the oxygen concentration drops close to zero. There is also a notable spike in unreacted NOx. These effluent composition features reveal the essential phenomena of the adsorptive reactor and are consistent with experimental results. During the lean phase, NOx is effectively trapped with essentially no breakthrough. Upon the introduction of hydrocarbon, there is a rapid consumption of oxygen due to the exothermic oxidation reaction (C3H6 + O2). The heat generated increases the temperature and drives NO2 (NOx) off the BaO sites, which can then adsorb on vacant Pt sites, where it is reduced by hydrocarbon. A fraction of the desorbed NOx will escape the reactor unreacted. The existence of two spikes in unreacted hydrocarbon is the result of coupled nonisothermal effects and surface transients. The first spike results from competitive adsorption and reaction effects whereas the second spike is related to the relative supply of hydrocarbon and oxygen. At the start of the rich phase, the reactor is relatively cool and Pt sites are completely covered by oxygen. There is a resulting short delay before ignition of the oxidation reaction, leading to some breakthrough of unreacted hydrocarbon. The duration of this first spike is very small, thus it might not be observed experimentally. After all available oxygen and NOx are consumed, hydrocarbon breakthrough reemerges. This second spike is therefore a consequence of a stoichiometric excess of hydrocarbon being fed.

Figure 3. (a) Transient temperature profile of the reactor during the rich phase (profile plotted after every 2 s). (b) Transient temperature profile of the reactor during the lean phase (profile plotted after every 5 s). Feed hydrocarbon during rich phase is 1.3% and during lean phase is 0%, the feed temperature is 600 K, feed NO2 is 500 ppm and feed oxygen is 5%. Lean phase time is 70 s and rich phase time is 10 s.

Thermal effects play an important role in the overall reactor performance. Figure 3 shows the evolution of solid (and washcoat) temperature profiles during the rich phase (3a) and the lean phase (3b), for the same case as in Figure 2. Upon the introduction of hydrocarbon (at t ) 0 s, Figure 3a), there is a rapid light-off with a hot spot appearing near the front-end of the monolith. During the 10 s rich pulse, the hot spot moves only 20% down the length of the monolith. After the hydrocarbon pulse is stopped there is a gradual cooling of the reactor. Just before the start of the lean phase (at t ) 10 s, Figure 3b), the monolith is partially hot because of the heat generated during the previous rich phase. About 40 s into the lean phase (at t ) 50 s, Figure 3b), the temperature maximum exits out from the reactor. This is consistent with the 50 s estimate of the thermal front propagation time. A more detailed examination of the spatio-temporal temperature and surface coverage profiles helps to elucidate the reactor dynamics. Figure 4 shows the washcoat temperature (4a), space-time profiles of NO2 coverage on BaO and Pt sites (4b, 4c), and species O and CH2 coverage on Pt sites (4d, 4e) over two complete cycles after the reactor has reached a periodic state. The behavior of the reactor at the inlet is indicative of the coupled thermal and kinetic effects. The nearly discontinuous nature of the exothermic oxidation reaction is evident. Upon the introduction of hydrocarbon, ignition occurs at the front-entrance, while there is a rapid cooling when the hydrocarbon pulse is stopped (4a). During the rich pulse, there is a corresponding rapid decrease in the coverage of NO2 on BaO storage sites due to the local temperature increase (Figure 4b). Moreover, a rapid consumption of surface oxygen on Pt sites is apparent (Figure 4d). It is this period of oxygen depletion that enables the adsorption of NO2 (NOx) onto


Figure 4. (a) Reactor temperature profile. (b) Fractional coverage profile of NOx (NO2) on storage sites (BaO). (c) Fractional coverage profile of NOx (NO2) on platinum sites (Y sites). (d) Fractional coverage profile of oxygen (O) on platinum sites (Y sites). (e) Fractional coverage profile of reductant (CH2) on platinum sites (Y sites). Feed hydrocarbon during rich phase is 1.3% and during lean phase is 0%, the feed temperature is 600 K, feed NO2 is 500 ppm and feed oxygen is 5%. Lean phase time is 70 s and rich phase time is 10 s.

Pt sites and subsequent NOx reduction to occur. The net effect of the competing adsorption and reaction steps on the NO2 coverage is evident in Figure 4c. On the other hand, during the lean phase the saturation of Pt sites by the oxygen prevents the adsorption of NO2. Ignition can occur at any point along the channel, but for the particular cases studied here, it occurs at the front-end of the monolith, as seen in Figures 3a and 4a. This initiates a cascading effect along the length of the channel. The localized temperature rise increases the local rate of desorption of the sorbed species. Most notably, NO2 desorbs from storage (BaO) sites. The adsorption (storage) wave moves along the length of the reactor (Figure 4b). The desorbed NO2 is carried by the fluid and readsorbs (on vacant BaO and Pt sites) downstream in the cooler section of the channel. Note the moderate increase in NO2 coverage on the storage sites near the back-end of the monolith (Figure 4b). The NO2 that adsorbs on BaO sites will eventually desorb as the temperature wave arrives, whereas the NO2 that adsorbs on Pt sites may be reduced by adsorbed CH2. The temperature increase will also increase the rate of

desorption of species O (oxygen) from the Pt sites. Another process occurring is the depletion of species O due to the CH2 + O (hydrocarbon oxidation) reaction on Pt sites. This depletion effect frees-up sites on the Pt sites for subsequent adsorption and reduction of NO2 (NOx). When the thermal front moves down the channel, the readsorbed NO2 (on BaO) again desorbs and readsorbs even further downstream. In the process, some more NO2 is trapped and reduced on the Pt sites. This process continues until either all the NO2 is reduced or exits the monolith channel. The extent of reduction clearly depends on the available channel length to allow this sequential process of adsorption, desorption, readsorption, and reduction. If the length of the reactor available downstream is not sufficient to trap and reduce all the desorbed NO2 (NOx), then some of the NO2 will exit unreduced from the reactor. Moreover, if the duration of the rich phase is insufficient, and the pulse is stopped before unreacted NOx reaches the exit of the reactor, then some NOx may escape the reactor during the subsequent lean phase (Figure 2). Similarly, feeding

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low to high NOx conversion during a systematic variation in the hydrocarbon concentration was reported by Muncrief et al.7,8 and Kabin et al.,9 among others. They showed that the transition occurs very close to the leanrich demarcation for feed temperatures in the range 210-250 °C. Figure 5 also shows the sensitivity of the conversion vs propylene concentration to the feed temperature Tf. A main effect of a variation in Tf is on the surface reaction rates of the two main reactions, the oxidation of propylene (reaction 1), and reduction of NO2 (reaction 2). Since the rate of reaction decreases as Tf is decreased a higher reactant concentration is needed to achieve a prescribed rate (conversion). In turn, a reduced rate of propylene oxidation implies a higher coverage of oxygen and increased inhibition of the NOx reduction reaction. Another effect concerns the relative rates of the two primary reactions. The ratio of the rate constants for the propylene oxidation and NO2 reduction is given by

kr1(Tf) kr2(Tf) Figure 5. Comparison of steady state and pulsed operation in terms of NOx converion as function of feed propylene mole fraction for two different feed temperatures 600 K (crosses and diamonds) and 550 K (triangles and circles). The feed concentration for pulsed operation is the cycle-average value. During cycling ratio of lean phase time to rich phase time is 7:1. For the simulations, feed NO2 is 500 ppm and feed oxygen is 5%.

hydrocarbon to the reactor after all the stored NOx is either reduced or removed from the reactor, leads to the stoichiometric excess of hydrocarbon leaking from the reactor. 5.2 Comparison of Steady State and Cyclic Operation. The concept of an adsorptive reactor involves periodic switching of the feeds, first to capture the key reactant, then to inject the second reactant to effect reaction. Cyclic operation complicates the operation of the reactor, so the periodically operated reactor must out-perform the reactor operated at steady state by some measure to make it economically viable. In the current system this measure is the NOx conversion. Muncrief et al.7,8 and Kabin et al.9 have shown a large enhancement in the NOx conversion during rich/lean cycling. They compared the case of propylene pulsing into a continuous feed containing NO, O2, and N2 to that of a continuous feed, taking care to inject the same amount of propylene to the reactor. Under some conditions the cycle-average NOx conversion exceeded the steady-state conversion by over a factor of 5. In this section, we simulate the same type of comparison. Specifically, we examine if the same amount of hydrocarbon fed in discrete pulses will result in a time- or cycle-averaged NOx conversion that exceeds the steadystate conversion. It is noted that the hydrocarbon is needed not only to reduce the oxygen concentration by oxidation, thereby freeing up precious metal sites for NOx and hydrocarbon adsorption and reaction, but also to serve as the reductant of the NOx. Figure 5 compares the dependence of the NO2 (NOx) conversion on the reductant (C3H6) feed concentration for steady-state and cyclic operation. A wide range of reductant feed concentrations is spanned. The general trend is that the steady-state NO2 conversion increases with the feed hydrocarbon concentration, consistent with experimental observations. A sharp transition from

)

kr1(Tr) exp{(γr1 - γr2)(1 - Tr/Tf)} (33) kr2(Tr)

Since γr1 < γr2 in this system, a decrease in feed temperature results in a increase in kr1(Tf)/kr2(Tf). Thus, for a fixed propylene feed concentration, the conversion of NO2 (via surface reaction 2) decreases with a decrease in feed temperature. The combination of these effects explains why the transition from low to high NO2 conversion is more abrupt at the lower temperature (550 K in Figure 5), and occurs closer to the lean-rich demarcation (1.11% propylene in a mixture containing 5% O2). The model predicts an enhancement in the NOx conversion by cyclic operation, in agreement with the aforementioned experimental studies. The findings confirm that the oxygen site blockage is a principal requirement for significant conversion enhancements. The cyclic operation results in Figure 5 show the dependence of the cycle-averaged NOx conversion on the cycle-averaged hydrocarbon concentration. As in the case of steady state operation (Figure 5), the cycleaveraged NOx conversion is an increasing function of the hydrocarbon concentration. Moreover, there exists a critical concentration at which the conversion increases sharply. However, this transition occurs at a lower cycle-averaged value than occurs at steady state. (Note that since no hydrocarbon is fed during the lean phase of 70 s, the hydrocarbon concentration during the pulse is actually 8 times the indicated cycle-averaged concentration). For the lower value of kr1 in Figure 5, this critical concentration occurs at about 0.13% (cycleaveraged value), or a hydrocarbon pulse concentration of about 1.04%, which is close to the stoichiometric richlean value. For hydrocarbon concentrations less than the critical value, the rate of propylene oxidation is low and the oxygen is not removed from platinum sites. At a hydrocarbon feed concentration of 0.2% (600 K), the cyclic operation gives a NOx conversion of about 85% compared to the steady-state conversion of about 15%. It is interesting to note that the degree of separation between the cyclic and steady-state NOx conversions increases with a decreasing rate of propylene oxidation. The conversion enhancement effect was examined over a range of feed temperatures. Previous experimental findings of Muncrief et al.7,8 and Kabin et al.,9 among others demonstrated that there exists a temperature


Figure 7. Plot of the percent NO2 reduced vs the total cycle time. Figure 6. NO2 conversion vs feed temperature for steady state and periodic pulsing (cycling). During cycling ratio of lean phase time to rich phase time is 7:1 and feed hydrocarbon during rich phase is 1.3% and during lean phase is 0%. For the steady-state simulations, the feed reductant is 1.3% (rich steady state) and 0% (lean steady state), feed NO2 is 500 ppm and feed oxygen is 5%.

window for which high cyclic NOx conversions can be achieved. The lower temperature limit is dictated by the ignition temperature for propylene oxidation, whereas the high-temperature limit is determined by the reversible decomposition of the barium nitrate storage compound. Figure 6 compares the sets of simulations involving the model system. For all the simulations, the initial solid temperature was same as the feed temperature. The first two sets involve steady-state operation in which the feed mixture contains 1.3% hydrocarbon, and 0% hydrocarbon, respectively. These two cases serve as the bounds of the cyclic operation during which a pulse containing 1.3% of hydrocarbon is fed for 10 s of the 80 s cycle whereas the lean phase is devoid of hydrocarbon. Obviously, the lower bound steady-state NOx conversion is 0% because the lack of hydrocarbon prevents any reduction from occurring. The dashed line in the higher bound plot (Figure 6) represents ignition, which occurs at a temperature of 500 K and is consistent with the prediction in the rich pulse analysis. The cyclic operation results show an interesting nonmonotonic dependence. Over a modest range of feed temperatures spanning 550 to 700 K the cycle-averaged NOx conversion exceeds 60%. The maximum in the cycle-averaged conversion is attributed to two primary effects. At low temperature ( 700 K), the rate of desorption of species NO2 (NOx) from BaO sites increases, thereby reducing the equilibrium NOx adsorptive capacity in the washcoat. This reduces the cycle-averaged NOx conversion. These effects are phenomenologically similar to the identified effects in the experimental system. At intermediate temperatures, both the ignition of the hydrocarbon oxidation and optimum desorption rates are achieved resulting in a moderate to high conversion of NOx. 5.3 Effect of Cycle Time Parameters. The cycle timing parameters must be tuned to achieve high NOx

conversion with minimal breakthrough of reductant. Three key parameters include the total cycle time, rich pulse duration (or duty) and lean phase duration. The pulse duty is the fraction of the total cycle during which the rich pulse is fed. The pulse intensity is a measure of the hydrocarbon concentration in the pulse while holding fixed the total amount of hydrocarbon fed per cycle. It is inversely proportional to the pulse duty. Muncrief et al. 7,8 and Kabin et al.,9 have shown that the NOx conversion achieves a maximum value at an intermediate cycle time for a fixed pulse duty, and that the conversion increases with increasing pulse intensity. In this section, we examine if the model system displays features similar to those observed experimentally. Figure 7 shows the dependence of the cycle-averaged NO2 conversion on the total cycle time with the rich pulse duty fixed at 12.5%. The NO2 conversion achieves a maximum value of about 89% at an intermediate cycle time of about 200 s. A second local maximum occurs at a cycle time of about 30 s in which the conversion achieves a value of about 97%. At very small and large cycle times (again, with the pulse duty fixed at 12.5%), the NO2 conversion decreases significantly. To the right of the 200 s maximum, the conversion decreases monotonically with the total cycle time. Obviously, large values of the total cycle time imply protracted lean phase times. A lean phase time that significantly exceeds the breakthrough time of the trap (estimated to be 155 s for a 500 ppm NO2 feed concentration) results in considerable unconverted NOx simply because of the limited NO2 (NOx) storage capacity. For very large total cycle time, the amount of NO2 trapped becomes negligible compared to the total amount of NOx fed during the lean phase and the system approaches steady state during the lean and the rich phases. The cycle-averaged NO2 conversion is approximated by a weighted average of the steady-state conversions during lean and rich phases. For the current choice of parameters, the propene fraction in the lean feed is zero so the steady-state NO2 conversion for the lean feed is also zero and the steady-state NO2 conversion for the rich feed containing 1.3% C3H6 is nearly 100%. Thus, the cycle-averaged NO2 conversion for very large cycle times is (100/8 )) 12.5%. This limit is not yet reached in Figure 7, where the highest cycle time is 800 s. For very small total cycle times, the rich phase duration is so

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Figure 8. Reactor temperature profile (a) during the lean phase, (b) during the rich phase for total cycle time of 30 s. Rich phase feed (Reductant-1.3%, Oxygen-5%, NO2-500 ppm), Lean phase feed (Reductant-0%, Oxygen-5%, NO2-500 ppm) and ratio of lean phase time to rich phase time is 7:1.

short that most of the hydrocarbon fed gets out unreacted from the reactor (similar to the first C3H6 spike in Figure 2), thus percent NO2 reduction decreases. Most of the simulated trends are consistent with experimental observations; in particular, the existence of a conversion maximum, and the large cycle time limit of the conversion. It is more difficult to compare the short cycle time behavior predicted by the model to that observed experimentally because of upstream axial dispersion (mixing) effects (due to short beds used) that led to a premature decline in the cycle-averaged conversion (Muncrief et al.7,8). Nevertheless, the utility of the model is that the limiting conversion can be predicted in the absence of the experimental anomalies. The model predicts the existence of a second local maximum occurring at small cycle time, a feature that was not observed experimentally. It is of fundamental interest to determine the causative factors for its existence. Recall that the thermal propagation time was estimated to be about 50 s. This means that cycle times below this limit may lead to insufficient cooling of the reactor during the lean phase, as was evident in the longer cycle time (see Figure 3b). Figure 8a shows a simulated reactor temperature profile just before the start of the rich phase, while Figure 8b shows the reactor temperature profile during the rich phase (cycle time is 30 s). In comparison to the cycle time of 80 s (viz. Figure 3a,b), it is clear that the monolith remains relatively hot near the exit throughout the duration of a cycle. The higher temperature is beneficial for the NO2 reduction which has a higher activation energy than that of the oxidation reaction. Moreover, because of the higher temperature downstream, there will be less oxygen inhibition of Pt. For a total cycle time of 30 s, when the rich phase commences a hot zone develops at the reactor entrance with a second zone located downstream in the reactor. NO2 which desorbs upstream gets carried away downstream where it is trapped and

Figure 9. (a) Plot of percent NO2 reduced vs the lean phase time. (b) Plot of percent unreacted reductant vs the lean phase time.

converted in the second zone. Thus, there is a range of total cycle times below ca. 70 s for which a decrease in total cycle time leads to an increase in the NO2 conversion. The effect of duration of the lean phase is examined systematically in Figure 9. In this simulation the lean phase duration is varied over a wide range, while holding the rich phase fixed at 10 s. As before, feed O2 concentration is fixed at 5% and feed NO2 is fixed at 500 ppm (0.05%) over the entire cycle, while C3H6 (hydrocarbon) concentration is 1.3% during the pulse and 0% during the lean phase. The NO2 conversion is a monotonically decreasing function of the lean phase duration. The decrease in conversion for long lean phase times simply shows the saturation of storage sites as we described in context of the long total cycle time (Figure 7). We discussed in section 5.1 that more the vacant sites available downstream of the reactor (at the end of the lean phase), the higher is the NO2 conversion. As the lean phase time is decreased the NO2 adsorption (storage) front travels a lesser distance inside the reactor before the start of the pulse, thus the reactor


has more downstream vacant sites for retrapping and reducing the NO2, which increases the NO2 conversion. As the lean phase duration is decreased to 50 s (Figure 9a), the cycle-averaged NO2 conversion increases to over 90%. Figure 9b shows the amount of unreacted reductant (C3H6) vs the lean phase time, for the same feed conditions as in 9a. As the lean phase duration increases, the cycle averaged unreacted C3H6 at the reactor exit decreases. The feed for the lean phase consists of oxygen and NO2 (along with inerts) which are stored inside the reactor. For small lean phase time less NO2 and oxygen are stored in the washcoat, thus less reductant is used up in the reactor during the pulse and more reductant leaves unreacted. Finally, note that although a small lean phase time gives higher NO2 conversion, it does not adequately utilize the adsorption capacity of the washcoat and leads to increased waste of reductant. The effect of duration of the rich phase is examined in Figure 10. To better understand the effect of the pulse duty, here we fix the total amount of hydrocarbon (C3H6) fed over a cycle by adjusting the hydrocarbon concentration in the pulse according to

(C3H6)pulse ) 1.3 ×

(pulse10time)

(34)

That is, as the pulse duty is decreased the pulse intensity increases because of the adjustment in the hydrocarbon concentration. The lean phase duration is fixed at 70 s. Figure 10a shows a nonmonotonic dependence of the cycle-averaged NO2 on the pulse duration. To the right of the maximum the conversion decreases sharply with increasing pulse duration. This reaffirms the dependence of conversion on the pulse concentration (Figure 5). That is, as the pulse duration is increased the hydrocarbon concentration is decreased according to eq 34. As the hydrocarbon pulse concentration approaches around 1%, the demarcation between lean and rich, the conversion drops. To the left of the maximum, the NOx conversion decreases toward a low value as the pulse duration is decreased. Recall that the mechanism for NO2 reduction requires a local temperature rise to effect the release of NO2 from the storage sites and this temperature wave takes some time to travel the monolith and release NOx (Figure 3). A small rich pulse duration is not sufficient to increase the temperature of the monolith and, desorb and react all the NO2 during the pulse, so the NO2 conversion decreases. For a very small pulse duration, there is insufficient time for hydrocarbon to adsorb on platinum sites and ignite the monolith, thus NO2 conversion is very low and the first exit C3H6 spike of Figure 2 is very significant. Figure 10b shows the nonmonotonic behavior of exit unreacted hydrocarbon with pulse duration. For very small pulse duration, unreacted hydrocarbon is very high because there is insufficient time for hydrocarbon to react with oxygen or NO2 in the reactor. Since the total amount of hydrocarbon fed during the pulse is fixed by eq 34, increasing pulse duration gives the hydrocarbon more time to react with either NO2 or oxygen in the reactor, thus decreasing the unreacted reductant at exit. To the right of the minimum, the exit unreacted hydrocarbon increases with pulse duration. This is because the decreased hydrocarbon fraction (according to eq 34) in feed is unable to compete with oxygen for adsorption on platinum sites and react with either NO2 or oxygen.

Figure 10. (a) Plot of percent NO2 reduced vs duration of the rich pulse. (b) Plot of percent unreacted reductant vs the duration of the rich pulse.

5.4 Effect of Flow Rate (Fluid Velocity). Now we examine the effect of the fluid flow rate, or linear velocity through the monolith channel. Figure 11 shows the dependence of the cycle-averaged NO2 conversion and percent of unreacted hydrocarbon on the linear velocity. For these simulations, the lean phase duration and the rich pulse duration are fixed at 70 and 10 s, respectively. The NO2 conversion exhibits a maximum at an intermediate value of the flow rate (Figure 11a). As the velocity is increased to the right of the maximum the main effect is the breakthrough of NO2 during the lean phase. Recall that the breakthrough time is inversely proportional to the adsorption shock velocity according to (L/us). Since, the shock velocity (us) is proportional to the fluid velocity (eq 28), an increase in the flow rate decreases the NO2 breakthrough time. Thus, the fluid velocity is intimately linked with the adsorptive capacity of the reactor. At high fluid velocities, NO2 will leak during the lean phase and at the start of rich pulse there will be less reactor length

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6. Conclusions and Discussion A mathematical model of a periodically operated adsorptive reactor has been developed. The model is applied to NOx storage and reduction, an emerging technology for NOx abatement from the exhaust of lean burn and diesel vehicles. We have incorporated into the reactor model a phenomenological kinetic model that captures the main elements of the NSR chemistry. The reactor model helps to elucidate the complex spatiotemporal features of the adsorptive reactor. The simulations reveal that many of the experimentally observed NOx trap performance trends of cycle-averaged NOx conversion are predicted. The simulations also show the importance of understanding the coupling between the chemical and transport processes. In particular, the ignition and thermal propagation events are critical because the release of trapped NOx and the subsequent reduction of NOx requires the heat generated by the exothermic oxidation. Future work will focus on the incorporation of a more detailed microkinetic model of NOx storage and reduction, washcoat diffusion, and other upgrades. This will enable an evaluation of NOx trap composition, alternative reactor designs, and optimal operating policies. Acknowledgment The support of the State of Texas Advanced Technology Program (ATP) is gratefully acknowledged for this study. Nomenclature Roman Letters

Figure 11. (a) Effect of varying fluid velocity on percent NO2 conversion. (b) Effect of varying fluid velocity on percent unreacted reductant.

available for trapping and reducing the desorbed NO2, thereby decreasing the NO2 conversion. To the left of the maximum the conversion decreases slowly with decreasing velocity. This may be explained as follows. The duration of the rich pulse is fixed and at low velocities, the amount of hydrocarbon fed per unit time is less. In addition, the platinum sites are saturated with oxygen and there is an excess of oxygen. Thus, most of the hydrocarbon is consumed in the front end and there is insufficient amount to reduce the NO2 that is retrapped downstream of the monolith. Figure 11b shows that the exit unreacted hydrocarbon increases with fluid velocity. The reason is that for low velocity, the hydrocarbon gets sufficient residence time in the reactor to react with either NO2 or oxygen, thus the unreacted hydrocarbon fraction at the exit is small. As the flow velocity increases this contact time for hydrocarbon in the reactor decreases, thus increasing the effluent concentration of hydrocarbon.

C ) concentration cp ) specific heat Dm ) diffusion coefficient in the fluid phase Dh ) channel hydraulic diameter E ) activation energy h ) heat transfer coefficient ∆Had ) heat of adsorption ∆Hrxn ) heat of reaction kf ) fluid thermal conductivity kadji ) adsorption constant for species i on site j Kij ) equilibrium constant for species i on site j kjc ) mass transfer coefficient of species j kr ) reaction rate constant kw ) solid thermal conductivity L ) length of the monolith channel Nu ) Nusselt number ps ) pressure on wall surface Rg ) universal gas constant RΩ ) one-half the channel hydraulic radius Riadj ) rate of adsorption of species i on site type j Ridej ) rate of desorption of species i on site type j Rri ) rate of reaction i SN ) stoichiometric number t ) time T ) temperature u j ) average fluid velocity in the channel us ) shock velocity of adsorption wave Xj ) mole fraction of species j Z ) axial coordinate Greek Letters δc ) washcoat thickness δw ) half wall thickness γj ) dimensionless activation energy of reaction j, Ej/RTr

Ind. Eng. Chem. Res., Vol. 44, No. 16, 2005 6277 θ ) fractional active sites coverage F ) density Subscripts and superscripts NO2 ) NOx C3H6 ) reductant O2 ) oxygen f ) fluid phase in ) inlet m ) cup-mixing s ) surface T ) total v ) vacant sites S ) concentration of BaO sites Y ) concentration of Pt sites

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Received for review September 20, 2004 Revised manuscript received January 3, 2005 Accepted January 5, 2005 IE0490785

Analysis of Periodic Storage and Reduction of NOx in Catalytic

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