Global kinetic modeling and analysis of Lean NOx Traps (LNT) catalysts

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Kinetics, Catalysis, and Reaction Engineering

Global kinetic modeling and analysis of Lean NOx Traps (LNT) catalysts Nishithan Balaji, Preeti Aghalayam, and Niket Kaisare Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b01435 • Publication Date (Web): 04 May 2018 Downloaded from http://pubs.acs.org on May 5, 2018

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Industrial & Engineering Chemistry Research

Global kinetic modeling and analysis of Lean NOx Traps (LNT) catalysts Nishithan Balaji, Preeti Aghalayam,∗ and Niket S. Kaisare∗ Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India. E-mail: [email protected]; [email protected]

Abstract Lean NOx traps (LNT) is an after-treatment technique used for NOx abatement in lean burn engines. The aim of this work is to develop a generic kinetic model applicable to various LNT catalyst formulations and to apply it to the design and analysis of the LNT reactor. The kinetic model of 16 reactions is proposed using Langmuir-Hinshelwood kinetics. It is validated against experiments reported in the literature, performed for a family of catalyst formulations that use Pt-group metals as the active catalyst and barium-based NOx storage, and is capable of predicting the performance with minimal modification of parameters. A kinetic analysis highlights the contribution of each reaction to the overall kinetic scheme in order to determine the important steps and qualitatively validate the model. A reactor level analysis is done by varying the operating conditions and the time scales of the lean and rich phases are optimized.

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Introduction Lean burn engines have improved fuel efficiency and reduced carbon emissions when compared to the traditional nearly-stoichiometric engines. Granger and Parvulescu 1 provided a detailed review of the various DeNOx techniques available. Selective Catalytic Reduction (SCR) and Lean NOx Traps (LNT) are commonly used after-treatment techniques in lean burn engines. SCR involves introducing a reducing agent, such as ammonia, urea or hydrocarbons, which is injected externally to reduce NOx (i.e., NO and NO2 ) in the presence of a catalyst. Additional on-board storage component that stores NOx on the catalyst during lean cycles and reduces it to benign species during rich cycles by reacting with reducing agents released in the exhaust stream. Since LNT do not require the storage of the reducing agent on-board, they are applicable in light-duty vehicles. LNT catalyst formulations consist of platinum group metals (PGM) as active catalysts, barium oxide as the NOx storage component, ceria (optionally) as the oxygen storage component and alumina that serves as a support. The engine is operated in a periodic manner; i.e., in fuel-lean mode for a particular period of time followed by fuel-rich mode using a special air-fuel mixture controller. During the lean mode, NOx that is present in the engine exhaust is stored as nitrates in the catalyst. When switched to the rich mode, reducing agents like CO and hydrocarbons from the engine exhaust react with the nitrates stored on the catalyst, trigger the release of NOx and reduce it to nitrogen (Epling et al. 2 ; Liu and Gao 3 ). The reaction mechanism for LNT consists of five major steps: NO reversible oxidation to NO2 ; adsorption of NOx as Ba(NO3 )2 ; release and reduction of NOx stored as Ba(NO3 )2 ; reduction of NOx to N2 by reaction with the reducing agents and the oxidation of the reducing agents CO and C3 H6 . Mechanistic details of the NOx storage and reduction in LNT have been analyzed in some detail in the literature (e.g. Aftab et al. 4 , Nova et al. 5 , Harold and Balakotaiah 6–10 ). Urakawa et al. 11 reported dominance of Ba(NO3 )2 species and the absence of Ba(NO2 )2 in the storage phase, while Epling et al. 12 and Watling et al. 13 , propose that NOx storage in 2


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LNT can be modelled using two types of storage sites (fast and slow storage). Mráˇcek et al. 14 reported an indirect route to NH3 and N2 O formation, via hydrolysis or decomposition of an isocyanate intermediate when CO is used as a reducing agent. Detailed models for the LNT reactions are proposed in literature by Rankovic et al. 15 , Bhatia et al. 16 , and Kota et al. 17 incorporating various effects and validating against flow reactor and other experiments. On the other hand, global kinetic models such as Shwan et al. 18 , Bhatia et al. 19 , Cao et al. 20 and Abdulhamid et al. 21 are of practical use. A well validated and relevant LHHW model that addresses the effects of CO, C3 H6 and NO on the oxidation of CO and C3 H6 in a Pt/Al2 O3 catalyst is by Voltz et al. 22 . Similarly, Koˇc´ı et al. 23 have developed a monolith model for this catalyst, while Koltsakis et al. 24 extended the model by incorporating oxygen storage kinetics on ceria. Finally, Olsson et al. 25 developed a global kinetic model for the LNT catalyst formulation Pt/Rh/BaO/Al2 O3 , with C3 H6 as the reductant. Kinetic parameters were fitted based on the results of the flow reaction experiments. Koˇc´ı et al. 26 have presented effective global kinetics for the LNT catalyst formulation Pt/Rh/BaO/Al2 O3 /Ce2 O3 with CO, H2 and C3 H6 as the reducing agents, in the presence of CO2 and H2 O, and validated it against test drive cycle data; and analyzed NOx reduction dynamics and the selectivity to form various reduction products 27 . The reducing agents in LNT are typically CO, C3 H6 and H2 . The NOx reduction products apart from N2 include NH3 and N2 O, and the selectivity depends on several factors including the type of reductant, temperature, rich phase time scale and the nature of catalyst 28 . For e.g., NH3 selectivity is high when H2 is used as a reducing agent 29 . For the case of CO and C3 H6 , NH3 formation occurs only in an indirect fashion by the formation of H2 through water gas shift and steam reforming reactions, and is likely to occur only above 623 K 27 . N2 O formation occurs due to incomplete NOx reduction, and is known to occur in other catalytic systems (such as Ag-based 30 or zeolites 31 ) as well. N2 O formation reactions are active only in the low temperature range between 423 and 473 K 28 . LNT experimental studies have included transient flow reactor 16 and Temperature Programmed Desorption 32 experiments.

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Despite a volume of work on experiments, and mechanistic modelling of LNT, a comprehensive kinetic model that encompasses NO oxidation, NOx storage, NOx release and reduction as a whole which could be used for different catalyst formulations is not available in the literature. In this work, we develop a global kinetic model that can be used generically for a family of common LNT catalyst formulations; specifically, Pt/BaO/Al2 O3 and Pt/Rh/BaO/Al2 O3 as active catalysts with NOx storage, optionally with Ce2 O3 as the oxygen storage component. For sake of maintaining conciseness, the pathways to formation of N2 O and NH3 are not included in this work, in any case they are important over a narrow range of operating conditions only, and can be incorporated in future work. The developed kinetic model is used in detailed reactor simulations and the NOx concentrations at the outlet of the reactor are compared with the various experimental data sets taken from the literature 12,25,26 . Each of these experiments was performed using different catalyst formulations, thus a generic model that predicts these experimental observations is valuable. A kinetic analysis is then performed by analyzing the contribution of individual reactions in the overall reaction mechanism. Reactor performance is then analyzed by varying the operating conditions, and an operation chart is developed to determine optimal switching times between lean and rich phases.

Methodology Reactor modeling A monolith reactor is considered for the study here. All the channels are assumed to be uniform with a square cross section. A transient, 1D heterogeneous model, for a single channel of the monolith is used as the computational domain for the simulations. Mass and energy balances are considered for both the gas and solid phases, incorporating all the catalytic surface reactions. Transient balances are employed as the LNT operations are inherently transient. In the gas phase species balance (Eq: 1), axial diffusion is ignored and 4


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a lumped description of transverse mass transfer is used. The rate of mass transfer to the surface is balanced by the surface reaction rate (Eq: 2). Thus, ∂(v.Ykg ) ∂Ykg =− − kc (Ykg − Yks ) ∂t ∂z X 0 = kc CT (Ykg − Yks ) + νkj Rj

(1) (2)

j

In the above equations, Yk denotes the mole fraction of species k and the subscripts s and g denote the solid and gas phases, respectively. In the energy balance equations, transverse heat transfer between solid and gas phases is described using the lumped description; the axial heat conduction term is ignored in the gas phase, whereas the axial conduction and heat of reaction terms are accounted for in the solid energy balance. Thus, ∂Tg ∂Tg = −vρg Cpg + hav (Ts − Tg ) ∂t ∂z X ∂Ts ∂ 2 Ts ρ s Cps = λs 2 + hav (Tg − Ts ) − ∆Hrj Rj ∂t ∂z j

ρ g Cpg

(3) (4)

Component mass balances are employed on the catalytic surface which includes the rate of reactions of species that are involved in storage: 1 X ∂θl = νlj Rj ∂t Γi j

(5)

where Γi denotes the total storage capacity of the site i. The heat and mass transfer coefficients are calculated using the Nusselt and Sherwood number correlations. For Reynolds number greater than 2300, the Gnielinski correlation 33 is used.

NSh =

   3.66   

NRe < 2300 (6)

(f /8)(NRe −1000)(NSc ) 2/3

1+12.7(f /8)1/2 (NSc −1)

NRe > 2300

For Nusselt number correlations, the Schmidt number (NSc ) is replaced by the Prandtl 5



number (NP r ). The model equations constitute a set of differential algebraic equations (DAEs) and they are simulated using Axisuite 34 , a modular software designed specifically for catalytic aftertreatment applications. In literature, Pedlow et al. 35 has simulated Three Way Catalytic Converters using Axisuite and Simulink.

Development of the kinetic model The kinetic model which is applicable to a family of LNT catalysts containing platinum group metals as active sites, barium based NOx storage sites and ceria based oxygen sites (if present) is developed for both the lean and rich phases of operation with CO and C3 H6 as reducing agents. The reaction scheme consists of 16 reactions modeled using the LHHW kinetics, and is shown in Table 1. The key sets of reactions include oxidation reactions and direct NOx reduction reactions that take place on Pt-group metal (PGM) catalyst; storage of NOx as Ba(NO3 )2 ; reduction and release of stored NOx ; and reactions with ceria, when present. Reaction 1 denotes the reversible oxidation of NO to NO2 , which is included in most models (such as Olsson et al. 32 , Bhatia et al. 16 , etc.). The reducing agents CO and C3 H6 , when present, are oxidized by oxygen as per Reactions 2 and 3, and by NO as per Reactions 4 and 5. These reactions, catalyzed by PGM form the first set of reactions. The next sets of reactions involve barium-based NOx storage sites, with both storage and release of NOx considered. The exhaust feed contains excess of CO2 and H2 O; BaO could react with them to form BaCO3 and Ba(OH)2 , respectively. BaCO3 is more stable and therefore Ba(OH)2 is neglected here. BaO is assumed to exist as BaCO3 owing to reaction 6. BaCO3 reacts with both NO and NO2 to form Ba(NO3 )2 , as denoted by reactions 7 and 8. Although BaCO3 could form both barium nitrate and nitrite, only barium nitrate is included in our mechanism, as it is the most stable form as indicated by IR spectra studies of Miyoshi et al. 36 . The above mentioned steps form the lean phase reactions. In the rich phase, NOx stored as Ba(NO3 )2 6


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is released in the presence of CO and C3 H6 ; barium nitrate gets converted to carbonate, as shown in Reactions 9 – 12. The NOx stored as Ba(NO3 )2 can get directly reduced to N2 (Reactions 9 and 12) or released as NO (Reactions 10 and 11), on reaction with the reducing agents CO or C3 H6 . The NO thus released may also get reduced to N2 on reacting with the reducing agents on the PGM sites (i.e., Reactions 4 and 5, mentioned above). If ceria is present in the catalyst then ceria storage reactions (denoted by reactions 13 to 16) also need to be considered. For the operating temperatures exceeding 473 K N2 O formation is expected to be negligible and was therefore not considered in our model. Furthermore, as CO and C3 H6 are the primary reducing agents in diesel exhaust, we have currently ignored H2 in the exhaust feed. NH3 formation mainly occurs by the reaction of hydrogen with NO and Ba(NO3 )2 . As hydrogen is not present in the inlet, NH3 formation should occur only by the reaction of hydrogen formed by water gas shift reaction. The ammonia formation via indirect pathway is not expected to be significant. Hence, to maintain simplicity and generality of our model, the effects of H2 and NH3 are ignored in our current model. NH3 and N2 O formation studies for the corresponding temperature range will be done in our future work. Overall, the 16 reactions proposed here captures key qualitative aspects of LNT behavior found in literature. The rate parameters are fitted in this work and validated to three different sets of experimental data taken from the literature whose operating conditions and catalyst formulations are given in Table 2. The three experimental studies chosen for model fitting and validation in this work use different catalyst formulations. Pt-Rh is the active catalyst in two of the experiments (Koˇc´ı et al. 26 and Olsson et al. 25 ) whereas Rh is absent in the catalyst used by Epling et al. 12 ; and ceria is present only in the catalyst of Koˇc´ı et al. 26 . Further more the mechanisms suggested in these three cases are different. Epling et al. 12 propose two types of storage sites, Olsson et al. 25 use shrinking core model on Ba-site and Koˇc´ı et al. 26 use a very detailed model to capture the data.

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Table 1: The proposed global reaction scheme and kinetic expressions for LNT catalyst. 2 2 2 G = G1 G2 G3 , where G1 = (1 + K1 YCO + K2 YC3 H6 ) , G2 = 1 + K3 YCO YC3 H6 and G3 = (1 + K4 YN0.7O ). K1 = 2.08 × 103 exp(−3000/RT ), K2 = 2 × 105 exp(−31000/RT ), K3 = 3.98 × 102 exp(−96500/RT ), K4 = 4.79 × 105 exp(−31036/RT ).

−− NO + O2 ) −* − NO2

2

CO + 21 O2 −−→ CO2

3

C3 H6 + 92 O2 −−→ 3CO2 + 3 H2 O

4

NO + CO −−→ CO2 + 21 N2

5

9 NO + C3 H6 −−→ 3CO2 + 3 H2 O + 92 N2

6

BaO + CO2 −−→ BaCO3

k6 ΓBa θBaO YCO2

7

BaCO3 + 2 NO2 + 21 O2 −−→ Ba(NO3 )2 + CO2

k7 ΓBa θBaCO3 YN O2 YO2

8

BaCO3 + 2 NO + 23 O2 −−→ Ba(NO3 )2 + CO2

k8 ΓBa θBaCO3 YN O YO2

9

Ba(NO3 )2 + 5 CO −−→ BaCO3 + N2 + 4CO2

k9 ΓBa θBa(N O3 )2 YCO

Oxidation & NO Reactions

1

YN O2 k1 YN O YO2 1− TG Keq YN O YO2 k2 YCO YO2 T G k3 YC3 H6 YO2 T G k4 YCO YN O T G k5 YC3 H6 YN O T G

NOx Storage

Reaction Rate

NOx Reduction

Reaction Step

Oxygen Storage

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1 2

10 Ba(NO3 )2 + 3 CO −−→ BaCO3 + 2 NO + 2CO2

k10 ΓBa θBa(N O3 )2 YCO

11 Ba(NO3 )2 + 13 C3 H6 −−→ BaCO3 + 2 NO + H2 O

k11 ΓBa θBa(N O3 )2 YC3 H6

12 Ba(NO3 )2 + 59 C3 H6 −−→ BaCO3 + 23 CO2 + 35 H2 O + N2

k12 ΓBa θBa(N O3 )2 YC3 H6

13 Ce2 O3 + 21 O2 −−→ 2 CeO2

k13 ΓCe θCe2 O3 YO2

14 2 CeO2 + CO −−→ Ce2 O3 + CO2

k14 ΓCe θCeO2 YCO

15 2 CeO2 + 19 C3 H6 −−→ Ce2 O3 + 31 CO2 + 31 H2 O

k15 ΓCe θCeO2 YC3 H6

16 Ce2 O3 + NO −−→ 2 CeO2 + 12 N2

k16 ΓCe θCe2 O3 YN O

The NOx and oxygen storage reactions are characterized by the maximum storage capacity Γi on barium and ceria sites, respectively. The kinetic expressions for the oxidation of CO and C3 H6 are taken from Voltz et al. 22 The same inhibition terms are used for the

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oxidation of NO and the NO reactions with the reducing agents.The kinetic expressions for the rest of the reactions are proposed and the parameters for the entire reaction scheme were fitted here. The procedure and the validation of the model against the experimental data is presented in the next section.

Results and discussions Model validation Koˇc´ı et al. 26 carried out temperature ramp experiments and LNT reactor experiments, by periodically switching between the lean and the rich phases. The experimental operating conditions are summarized in Table 2. The kinetic parameters of our model were fitted with the temperature ramp experiments performed by Koˇc´ı et al. 26 for both the lean and rich phases. Once the kinetic parameters were obtained, the performance of the kinetic model was validated by comparing with the LNT periodic experiments reported by Koˇc´ı et al. 26 at 523 K with a lean phase time scale of 300 s and a rich phase time scale of 20 s. Figure 1 and Figure 2 show the comparison of the simulation results with the experimental data using C3 H6 and CO as reducing agents, respectively. The NOx input to the LNT is 500 ppm which is shown in Figure 1 and Figure 2. The rise in NOx outlet concentration at the start of the rich phase is attributed to the fact that NOx stored as Ba(NO3 )2 desorbs as NO. In the case of C3 H6 as a reducing agent, the NOx exit concentrations are closely captured, whereas there is a slight over-prediction of NOx outlet concentration at the start of the rich phase in the case of CO as reducing agent. In spite of the surge in NOx concentration for a short period of time, the net NOx emission over the entire 320 second cycle is significantly low, and this is captured well in our simulations. Figure 3 shows the comparison of our simulation with the experimental data from Olsson et al. 25 . Since their catalyst formulation did not contain ceria, the storage capacity of ceria, ΓCe was set to zero in our simulations. CO2 is not present in the inlet feed for the experiments 9



1600

Rich

Lean

1400

Concentration of NOx, ppm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1200 NOx outlet - Simulation

1000

NOx outlet - Experiment NOx inlet

800 600 400 200 0 0

50

100

150

200

Time, s

250

300 310 320

Figure 1: Model validation by comparison of NOx profiles at the exit of the reactor with the experimental data from Koˇc´ı et al. 26 with C3 H6 used as reducing agent. The x-axis scale in the rich phase is expanded to clearly show the phenomena. [Symbols represent experimental data that is replotted from Koˇc´ı et al. 26 ] carried out by Olsson et al. 25 . However in the actual scenario CO2 is present in the feed and hence BaO was assumed to exist as BaCO3 in the model proposed by Olsson et al. 25 . We assume the storage site to be available as BaCO3 and the storage fraction of BaCO3 is taken as 1 for these simulations. Olsson et al. 25 suggested that some barium sites are not accessible at the surface and the diffusion of NOx is required to capture the dynamics, which they captured using shrinking core model. The kinetic parameters were kept exactly same as the previous case and only the NOx storage capacity, ΓBa was adjusted to match with the experimental data. The simulation results showed a good match with the experimental data in both the lean and the rich phases. Their experimental data showed a rapid increase in the outlet NOx concentration which indicates that the NOx storage capacity is significantly lower than Koˇc´ı et al. 26 . Figure 4 shows the comparison of model predictions with the experimental data from Epling et al. 12 . The active catalyst in the previous two works contained both Pt and Rh, whereas the catalyst formulation used by Epling et al. 12 had only Pt as the active metal component. Hence the parameters for the NOx storage reactions 7 and 8 were adjusted in

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500


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


400

Lean

Rich

300 NOx outlet - Simulation NOx outlet - Experiment NOx inlet

200

100

0 0

50

100

150

200

250

300

310

320

Time, s

Figure 2: Model validation by comparison of NOx profiles at the exit of the reactor with the experimental data from Koˇc´ı et al. 26 with CO used as reducing agent. The x-axis scale in the rich phase is expanded to clearly show the phenomena. [Symbols represent experimental data that is replotted from Koˇc´ı et al. 26 ] our model. Since ceria is absent, ΓCe is kept as zero. With just these adjustments, the model closely predicted the experimental data from Epling et al. 12 . The authors performed only the storage phase experiments and their data indicates the presence of both the fast and slow time scale behavior, which is reliably captured by our model with the set of reactions shown in Table 1. The NO oxidation (Reactions 1 and 2) and NOx storage reactions (Reactions 6, 7 and 8) were active in this case. We performed error analysis for determining the goodness of fit for all the four cases. The R2 values exceed 0.98 for all the cases and show a close numerical match between experiments and model prediction for all the four cases. The model and experimental data were plotted on two axes, a straight line fit through the origin was obtained, and the slope of the line is found. Closeness of the slope to 1 indicates a good fit. Further error values were calculated as in Touitou et al. 37 . These values, which are provided in SI document, indicate that the model is able to reliably fit the experimental data from the three sources with minimum adjustment of parameters. In summary, the kinetic model developed in this paper forms a minimum set of global

11



Rich

Lean

500

Concentration, ppm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

400 300 NOx out - Simulation NOx in NOx out - Experiment

200 100

50

100

150

200

240 245 250

Time, s

Figure 3: Model validation by comparison of NOx profiles at the exit of the reactor with the experimental data from Olsson et al. 25 C3 H6 is used as reducing agent. The x-axis scale in the rich phase is expanded to clearly show the phenomena. [Symbols represent experimental data that is replotted from Olsson et al. 25 ] reactions that reliably capture the storage and reduction phases for a family of LNT catalysts, with a PGM active site, barium based NOx storage site and an optional ceria based oxygen storage site. The kinetic parameters for the three cases obtained in this work are tabulated in Table 3.

Kinetic Analysis The mathematical model developed in the previous section was able to reliably capture the NOx outlet profiles observed in the experimental data reported in the literature. We now perform a kinetic analysis to understand the contribution of individual reactions to the overall reaction scheme. While the results reported here are for the base case, with the operating conditions as indicated in Table 4, the qualitative understanding is valid for other conditions as well. Starting with arbitrary initial conditions, we simulated the LNT operation for five cycles with a lean period of 300 s and a rich period of 20 s. Kinetic analysis is performed in the fifth cycle, by which time periodically invariant conditions are established in the reactor. Kinetic analysis involves calculating the contribution of an individual reaction towards the fate of a particular species in the overall reaction scheme. If m is the species of interest, the

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Table 2: Operating conditions for three sets of experiments used in validation of the kinetics proposed in this work. Parameter Koˇc´ı et al. 26 GHSV (h−1 ) 30000 T(K) 523 PGM Pt/Rh Storage sites BaO/Al2 O3 /Ce2 O3 Lean Phase YCO2 0.05 YH2 O 0.05 YO2 0.07 CN O (ppm) 500 CC3 H6 (ppm) 0 CCO (ppm) 0 Rich Phase YCO2 0.05 YH2 O 0.05 YO2 0.002 CN O (ppm) 500 CC3 H6 (ppm) 3667 YCO 0.033

Epling et al. 12 25000 473 Pt BaO/Al2 O3

Olsson et al. 25 54000 593 Pt/Rh BaO/Al2 O3

0.08 0.08 0.08 250 0 0

0 0 0.08 450 900 0

— — — — — —

0 0 0 0 900 0

contribution of a particular reaction j in a group of reactions is the ratio between the rate of j th reaction and sum of all the reactions in the reaction group, i.e., |νmj Rj | κj = P i |νmi Ri |

(7)

Figure 5 indicates the contribution of NO under lean operating conditions, wherein only the storage phase reactions are active. The index κj is obtained by letting the species m ≡ NO in Eq. 7. The reactions that involve NO include reversible NO oxidation to NO2 (Reaction 1), NO storage on a Ba site (Reaction 8) and NO oxidation on ceria site (Reaction 16). Initially, when the ceria is in a reduced state (Ce2 O3 ), most of NO gets reduced to N2 ; the contribution of this reaction falls to a low value as ceria gets completely oxidized within a short period of time. In the absence of ceria, the contribution of this reaction is uniformly zero. Thereafter, both NO oxidation to NO2 and NO storage as Ba(NO3 )2 have significant 13




250 200 150 100

NOx inlet NOx outlet - Simulation NOx outlet - Experiment

50 0 100

200

300

400

500

600

Time, s

Figure 4: Model validation by comparison of NOx profiles at the exit of the reactor with the experimental data from Epling et al. 12 . [Symbols represent experimental data that is replotted from Epling et al. 12 ] 100 + BaCO3 80

Contribution, %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

+ Ce2O 3

60

NO 2 Ba(NO3)2

NO

N2

40

20

0 0

50

100

150

200

250

300

Time, s

Figure 5: Kinetic analysis for the contribution of NO during the lean (storage) phase of LNT operation. contributions towards the consumption of NO. The contribution of the latter is higher than NO oxidation up to 150 seconds and then it’s lower. We performed a similar analysis for the contribution of individual reactions in the conversion of NO2 ; we observed equal contribution of NO oxidation and NO2 storage. Its shown in Figure S-3 in SI file. This indicates that when NO is the only pollutant in the feed, the rate of formation of NO2 is closely matched by the rate at which it gets stored as Ba(NO3 )2 . Continuing with the analysis in the lean operating conditions, Figure 6 compares the contribution of NO and NO2 storage in the form of nitrates (i.e., m ≡ Ba(NO3 )2 in Eq. 7).

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Table 3: Kinetic parameters for the LNT reactions from Table 1. The units of kj0 for reactions 1 to 5 is molKm−3 s−1 and s−1 for rest of the reactions.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

kj0

Ej (kJ/mol)

5 × 106 3 × 1017 1 × 1020 2 × 1013 1 × 1012 1.9 × 105 1 × 1010 (1 × 1012 )† 5 × 106 (1 × 1010 )† 1 × 1012 1 × 108 1 × 104 1 × 104 1 × 107 2.6 × 106 2.6 × 106 5 × 107

40 40 110 10 2.1 29.9 70 (60)† 40.5 (48)† 30 20 12.1 10 70 70 60 20

Total storage capacity values (in mol/m3 ) are as follows: For Epling et al. 12 : ΓBa = 7.5, ΓCe = 0; Koˇc´ı et al. 26 : ΓBa = 39, ΓCe = 70; and Olsson et al. 25 : ΓBa = 2.5, ΓCe = 0. Equilibrium constant for reaction 1 is from Olsson et al. 25 † Parameters of the two reactions in parenthesis were refitted for Epling et al. 12

In the absence of CO and C3 H6 , Reactions 7 and 8 are the only active reactions involving Ba(NO3 )2 . The contribution of the NO storage reaction is higher than that of NO2 up to 150 seconds and is subsequently lower. Since there is no NO2 in the feed, first NO oxidizes to NO2 , followed by the storage of NO2 via Reaction 7. Between NO and NO2 , storage of NO2 is slightly faster as its rate constant is higher than that of NO storage reaction; the initial contribution of NO2 storage reaction is lower because of the time taken for the formation of NO2 via NO oxidation. Indeed, this was corroborated when we repeated the same simulation with equal amounts of NO and NO2 in the feed ( at 250 ppm each); the contribution of the NO2 storage reaction was higher for the entire lean phase. The kinetic analysis in lean phase is thus used to confirm that the model captures the qualitative features that both NO and NO2 contribute towards NOx storage, with storage of NO2 being slightly faster if NO2 is also present in the feed along with NO. 15



Table 4: Reactor geometry and operating conditions of the reactor for the kinetic and reactor analysis. The kinetic analysis is performed for the catalyst formulation of Koˇc´ı et al. 26 at the outlet of the reactor. Parameter Length (m) Diameter (m) Temperature (K) GHSV (h−1 ) YCO2 YH2 O YO2 CN O (ppm) CC3 H6 (ppm) YCO

Lean 0.15 0.12 523 30000 0.05 0.05 0.07 500 0 0

Rich

523 30000 0.05 0.05 0.002 0 1500 0.02

Next, we perform kinetic analysis for the regeneration and reduction phase reactions. With m ≡ Ba(NO3 )2 , various contributions were computed in the rich operation of LNT. Since the amount of CO in engine-out emissions is an order of magnitude higher than that of hydrocarbons, the same was reflected in the reactor inlet for the analysis (see Table 4). Figure 7 shows the relative contributions of the four reactions: Release of NO upon reaction of Ba(NO3 )2 with CO (Reaction-10) or C3 H6 (Reaction-11); and release of Ba(NO3 )2 as N2 on reduction with CO (Reaction-9) or C3 H6 (Reaction-12). We observe that CO has higher contribution than C3 H6 and the direct reduction of stored NOx to N2 is most favorable. In fact, the reaction with CO to release NO is negligible compared to the most dominant reaction. The individual contributions of CO and C3 H6 were also analyzed by turning off the other reducing agent from the reactor inlet. Even in the absence of C3 H6 , the contribution of CO-mediated release of NO (Reaction-10) is negligible. The inset plot in Figure 7 shows the relative contribution of the reactions when C3 H6 is the only reducing agent in the feed. Unlike the case with CO, we observe substantial contribution of direct release of NO on reaction between Ba(NO3 )2 and C3 H6 . Indeed, this explains the observation in Figure 1 where instantaneous NO concentration at the start of the rich phase was almost three-fold higher with C3 H6 as the reducing agent than with CO as the reducing agent. Finally, the

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100 90 NO

80

+ BaCO3

Ba(NO3 )2 70

Contribution, %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


NO2

+ BaCO3

60 50 40 30 20 10 0 0

50

100

150

200

250

300

Time,s

Figure 6: Comparison of the contribution of NO and NO2 to get stored as Ba(NO3 )2 in the lean phase of LNT operation. relative contributions of CO and C3 H6 were analyzed by using the same amount of the two reducing agents in the feed (i.e., 0.02 % ). We found that contribution of CO towards release and reduction of stored NOx to N2 is higher than that of C3 H6 . Its shown in Figure S-4 in SI file. Although we have not undertaken a formal sensitivity analysis exercise, we have examined each of the steps in turn to examine the effect on the predicted trends. Due to the compact nature of our reaction mechanism, the simulations are sensitive to all the parameters.

Reactor Analysis The objective of an optimally operated LNT is to balance the time periods of lean and rich operations to minimize the NOx slip from the reactor. At the desired optimal conditions, the NOx slip should be below a threshold (determined by regulatory norms) and nearly uniform across multiple lean-rich cycles. The NOx stored during the lean phase has to be completely removed during the rich phase and the exit concentrations of the reducing agents CO and C3 H6 have to be minimum. A longer lean phase period and a shorter rich phase period is necessary to ensure fuel efficiency.

17



100 90 80 70

+ CO

NO

+ CO

Ba(NO3 )2 + C 3H 6

N2

+ C 3H 6

60 Contribution, %

Contribution, %

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

50 40 30

100 80 60 40 20

20 0

10 0 300

305

305

310

310

315

315

Time,s

Figure 7: Kinetic analysis for the contribution of various reactions for NOx release and reduction from Ba(NO3 )2 in the rich phase of LNT operation. The amount of CO in the feed is one order of magnitude higher than C3 H6 . Inset shows the contribution of various reactions towards Ba(NO3 )2 when C3 H6 is the only reducing agent in the feed. Lean phase simulations were performed for 1000 s to study the evolution of NOx concentration at the reactor exit owing to saturation of the NOx storage sites. Figure 8 denotes the NOx evolution profile and the total storage fraction as a function of time. It has been found that the NOx evolution begins at around 200 s and the storage sites get completely saturated at 600 s after which the NOx entering and leaving the reactor becomes equal. For further analysis, the lean phase time scale is chosen as 300 s which is sufficient time for storage and the NOx slip in that period is minimal. The rich phase time scale was varied and its effect on NOx profiles was investigated over multiple cycles. The duration of the fuel rich phase of LNT cycle also needs to be chosen judiciously to avoid NOx slip. The effect of incomplete reduction of NOx in the rich phase is shown in Figure S-5 in the SI file. The discussion in the supplementary information underlines the importance of appropriately balancing the lean and rich cycle times for optimal performance of LNT. To delineate an “optimal” LNT operating region, simulations were carried by varying both the lean phase (50 to 400 s) and the rich phase time scales (2 to 30 s) for a total time period of 1 hour. The total amount of NOx , CO and C3 H6 emitted out is calculated in g. The results are plotted in the form of a contour with lean phase times on the x axis and the rich phase times

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Concentration, ppm

500 400 300 200

NOx in NOx out

100 0 0

200

400

600

800

1000

Time, s

Total Storage Fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 0.8 Ba(NO 3 ) 2

0.6

BaCO3

0.4 0.2 0 200

400

600

800

1000

Time, s

Figure 8: Analysis of reactor dynamics in lean phase for conditions in Table 4 and an operating period of 1000 seconds, showing evolution of NOx inlet and outlet profiles (top panel) and storage fraction of barium carbonate and barium nitrate (bottom panel). on the y axis and shown in Figure 9. CO concentrations are neglected as they overlapped with the outlet C3 H6 profiles. The amount of NOx emitted increases when lean cycle time is increased or the rich cycle time is decreased (solid contours). The amounts of CO and C3 H6 emitted, on the other hand were higher at lower lean cycle and higher rich cycle times. Both the contours were super imposed and the shaded region indicates the region which simultaneously yields the amount of NOx less than 4 g and the amount of hydrocarbons less than 4 g. While these limits are arbitrary, they correspond to 0.067 g/km of NOx and 0.13 g/km of NOx + HC, if the vehicle was driven for 60 km (i.e., below Euro VI limits of 0.08 g/km and 0.17 g/km, respectively).

19



30 8

5 3 4

6

2

4

10

2

10 10

3

15 10

1

2

15

5

4

1

15 1

20

25 30

25

20

Total exit NOx, g

5

30

100

20

10

2

50

5

4

1

2

4 4

5

1

2

6

6

1

3

4

8

2

Desired Region

4

20

15

1

4

2

6

Total exit C3H 6, g 8

3

4

6

8

25

Rich phase time, s

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 29

150

200

250

30 35

35

300

350

400

Lean phase time, s

Figure 9: Contour showing the total amount of NOx and C3 H6 (in g) for a total operation period of 1 hour as a function of lean phase and rich phase cycle times. The shaded region simultaneously meets the requirement of NOx outlet less than 4 g and hydrocarbon outlet less than 4 g. The LNT simulations were now carried out for five cycles with a lean phase time of 250 s and a rich phase time scale of 20 s. Based on the above results, we chose a high enough value of lean phase cycle time and a corresponding rich phase cycle time to ensure that the operation is well within the shaded region. Figure 10 denotes the NOx evolution profiles and the total storage fraction curve as function of time, whereas Figure 11 denotes the corresponding evolution of reducing agents CO and C3 H6 . The NOx slip, as well as exit concentration profiles of CO and C3 H6 remain uniform after each cycle. Unlike the case of too low rich-phase time (see SI document for more discussion), the NOx stored as Ba(NO3 )2 is completely removed at the end of each rich phase with 20 s rich-phase time. These results also indicate that, from a practical viewpoint, a small amount of CO/C3 H6 slip at the end of rich phase ensures that Ba(NO3 )2 is completely reduced and LNT catalyst provides good performance. The outlet concentrations of the pollutants NOx , CO and C3 H6 are negligible for most of the LNT operation, except a narrow time window in the rich phase.

20


θBa(NO

)

1 0.5 0 600 500

NOx out, ppm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


3 2

Page 21 of 29

400 300 200 100 0 0

500

1000

Time, s

Figure 10: Reactor behaviour for 5 complete cycles of LNT with a lean phase time of 250 s and a rich phase time of 20 s.

Conclusions A kinetic model for the storage and reduction of NOx in Lean NOx Traps with 16 global reactions was developed and validated with the experimental data from literature. The developed model can be used for real time simulations where CO and C3 H6 are used as reducing agents. The model captured the experimentally observed profiles for various different catalyst formulations containing the active site (Pt or Pt/Rh on alumina), NOx storage (BaO), and with or without ceria (oxygen storage sites). The model would prove useful to analyze typical LNT catalysts under practically relevant operating conditions. Further, the model could also be used for other LNT catalysts of similar kind after relatively minor adjustments in kinetic parameters, as well as a precursor for other LNT catalyst formulations and/or to build more detailed kinetic models. Kinetic analysis was performed on the developed model and the results were found to be consistent with the past observations. Specifically, both NO and NO2 pathways are active for NOx storage as Ba(NO3 )2 in the storage (lean) phase, and both CO and C3 H6 are responsible for the release and reduction of stored NOx in the reduction (rich) phase. The direct reduction of Ba(NO3 )2 to N2 was more active than CO or C3 H6 mediated release of

21


20000 15000 10000

C3H6 Concentration, ppm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

CO Concentration, ppm


5000 0 1500

1000

500

0 0

500

1000

Time, s

Figure 11: Reactor inlet and outlet concentrations of CO and C3 H6 for the conditions of Figure 10. NO. The model shows that while in the presence of C3 H6 , reduction of Ba(NO3 )2 to N2 is somewhat more active than release of NO, in the presence of CO, the reduction pathway is at least an order of magnitude more active than release of NO. Finally, the effect of lean and rich cycle times on NOx , CO and C3 H6 emissions over multiple LNT cycles was analysed and the optimum time scales for lean and rich cycling were determined. LNT catalyst demonstrate a trade-off between higher NOx slip and lower CO/C3 H6 slip at longer lean cycles times (or shorter rich cycle times). The operation map with lean and rich cycle times shown in this work can prove of practical relevance in delineating the region of operation of LNT catalysts.

Supporting Information Error analysis comparing the model trends vs. experimental data on various catalysts; kinetic analyses for additional reactor operating conditions; and reactor analysis with inadequate rich-phase time period are included as Supporting Information.

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Nomenclature

av

Surface area to volume ratio (m2 /m3 )

C

Concentration (mol m−3 )

h

Convective heat transfer co-efficient (kJ m−2 s−1 K−1 )

CT

Total concentration (mol m−3 )

Cp

Specific heat capacity (kJ kg−1 K−1 )

E

Activation energy (J mol−1 )

f

Friction factor

GHSV

Gas hourly space velocity (h−1 )

kc

Mass transfer co-efficient (s−1 )

ko

Pre-exponential factor (s−1 )

NRe

Reynolds number

v

Velocity (ms−1 )

R

Rate of reaction (mol m−3 s)

NSc

Schmidt number

NSh

Sherwood number

t

Time (s)

T

Temperature (K)

Y

Mole fraction

z

Axial distance (m)

Greek Letters

∆Hr

Heat of reaction (kJ mol−1 )

23



Γ

Total storage capacity (mol m−3 )

λ

Thermal conductivity (kW m−1 K−1 )

ν

Stoichiometric co-efficient

ρ

Density (kg m−3 )

θ

Total storage fraction

Subscripts

g

Gas phase

j

Reaction number

k

Species

i

Storage species

s

Solid phase

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Global kinetic modeling and analysis of Lean NOx Traps (LNT) catalysts

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