The effects of exhaust gas recirculation on NO x storage pathway

. A LNT (lean NO x trap) model coupled with EGR (exhaust gas recirculation) was developed based on the Langmuir–Hinshelwood mechanism to investigate the EGR effects on NO x adsorption pathway of LNT catalysts with temperature changed in range 150 ℃ ~550 ℃ . Both the nitrate and nitrite adsorption paths were considered for the NO x storage process in the model as well as the spillover of stored NO x between Ba and Pt sites. The data and validation for modelling were from literatures of predecessors and our previous lean-burn gasoline engine experiment * . The model quantified the contributions of both nitrate route and nitrite route to the NO x storage with change of EGR rate (0%~30%) under raw emission atmosphere from tested gasoline engine. The model captured key feature of different trends of nitrate route and nitrite route with increasing temperature (150 ℃ ~550 ℃ ) under EGR rate varying from 0% to 25%. The LNT model provided insight of reaction mechanism for interpreting the behaviour of NO x storage with change of GER rate and temperature, which contributed to improve the NO x storage capacity when mapping EGR rate for lean-burn engine and catalyst operation strategy optimization.


Introduction
Lean NOx Trap also known as NSR (NOx storage and reduction) is one of effective ways to reduce NOx emission of diesel and lean-burn engines with good fuel economy [1]. The common LNT consisted of a noble metal (PGM specially Pt as catalyst sites for NOx oxidation and reduction) plus alkaline or alkaline-earth compounds (mostly Ba as NOx storage sites) deposited on alumina over a monolithic structure, usually cordierite [2]. NOx adsorption and reduction are based on cyclical engine operation alternating between leanburn (lean fuel, high air-to-fuel ratio A/F) and rich-burn (fuel rich, A/F<13.63/1 w/w) modes [3]. NOx is adsorbed on the catalyst surface by alkali or alkaline-earth oxides under lean-burn environment, while the adsorbed NOx is reduced during rich-burn phase to regenerate catalyst [4] [5].
Generally summarize literatus of LNT or NSR, there are five following steps to reveal the NOx storage and reduction mechanisms [6][7]: 1.NO Oxidation during lean conditions; 2. NOx adsorption on storage sites as nitrites and nitrates; 3. reductant agent evolution and byproducts reaction; 4. stored NOx release from catalyst surface to gas flow; 5. Reduction of gaseous NOx or stored NOx to N2 during the rich environment. The work about NOx adsorption process is a focus among recent LNT researches. Basically, NOx adsorption in LNT can be summarized as two parallel pathways. NO is oxidized to NO2 with precious metal catalyzing firstly, and subsequently adsorbed on NOx storage sites as nitrates involving the disproportionation reaction of NOx and formation of barium peroxide and so on, which was noted as nitrate route [8]. Another path is nitrite route, i.e., NO can be stored directly in the presence of NO and oxygen as nitrite species, then further oxidized to stable nitrates by O2 and NO2 from both gas phase and surface sites [9].
Lots of researches were done to study the difference between two pathway and respective contribution to NOx storage performance, at same boundary conditions such as inlet gas components and temperature which have a great influence on both NOx storage pathways. Morandi S et al. [10] pointed out that the nitrites possess is significantly lower stability due to thermal stability of the nitrates is significantly higher. Nova et al. [11] and Lietti et al. [8] demonstrated that the NOx disproportionation reaction did not represent the major storage route under NO and NO/O2 mixtures due to the presence of nitrites in higher amounts than nitrates during the initial NOx adsorption at low temperatures. Same conclusion can be seen in Castoldi L et al. [12] works which have confirmed participation of nitrite at 150℃, and nitrite only can be observed at the beginning of adsorption phase at 350℃. Epling W S et al. [13] revealed that the two of major components of lean-burn engine exhaust, CO2 and H2O, compete for the same NOx adsorption sites, resulting in reduction of NOx storage capacity of LNT. Lindholm A et al. [14] through the study, Influence of H2O and CO2 on NOx storage and reduction over Pt based catalysts with hydrogen as the reducing agent, has shown that H2O and CO2 of the inlet stream lead to the formation of hydroxide and carbonate species on adsorption sites. The hydroxide and carbonate species associated with the alkaline or alkaline-earth adsorption sites reduced the trapping efficiency of NOx, because it's more difficult to store NOx on Ba(OH)2 and BaCO3 than on BaO. Furthermore, Epling W S et al. [13] found that hydroxide species formed by H2O with Ba sites could be displaced by carbonate species due to its higher stability. It should be aware of that oxidation of NO to NO2 is a key initial step before NOx storage on alkaline or alkaline-earth component because NSR catalyst is more efficient to sorb NO2 compared with NO on the NOx storage sites. Auvray X P, Olsson L et al. [15] studied the inhibition effects of H2O on NO oxidation, pointed out that Pt sites are blocked by water adsorbed on it at low temperature for oxygen adsorption on Pt surface. Whereas Ren Y, Harold M P et al. [16] demonstrated that NOx storage or global NOx convection were almost impervious to H2O effects on NO oxidation.
The nitrites on certain temperature range are discussed in reference [17] and [10], and CO2 has inhibition effect on adsorption, H2O has little influence on both adsorption paths.
EGR is an effective way to reduce engine NOx emissions. F. Sarikoc, M. Kettner et al. [18] research studied the potential of reducing the NOx emissions in a spray guided DI gasoline engine by stratified exhaust gas recirculation (EGR). Lapuerta, M. et al. [19] research showed that low-pressure exhaust gas recirculation was more efficient than high-pressure exhaust gas recirculation to reduce NOx emissions, mainly due to the higher recirculation potential and the lower temperature of the recirculated gas. However, such a differential benefit decreased as the coolant temperature decreased, which suggests the use of high-pressure exhaust gas recirculation during the engine warm-up. It was also shown that the lean-NOx trap storage efficiency decreased more rapidly at high engine load than at medium load and that such reduction in efficiency was much faster when high-pressure exhaust gas recirculation was used than when low-pressure exhaust gas recirculation was used. Previous researches of our group were about influence of the coupling of EGR and lean-burn gasoline engine with the LNT catalyst [20]. We pointed out that the main reason of the EGR effects on LNT overall performance was the inlet components CO2\H2O concentration and ratio changed with EGR rate.
There are few researches combining CO2 and H2O to the overall level of EGR to study detailed mechanism of its effects on LNT catalyst specific work stage such as NOx storage step under raw emission atmosphere from tested gasoline engine, though lots of researches done to study the effects of inlet components CO2\H2O on NO oxidation, NOx trap efficiency and NOx convection. In addition, our preliminary experimental researches focused on the discovery of the phenomenon and overall performance of synergetic system of coupling EGR with LNT, which did not conduct deep research on the influence of EGR on LNT and the underlying detailed mechanism. Hence, a detailed lean NOx trap (LNT) adsorption model coupled with EGR was developed based on the Langmuir-Hinshelwood mechanism, and both the nitrate and nitrite adsorption pathways were considered in the model as well as the NOx spillover steps between Ba\Pt sites. In additional, raw emission compositions were as boundary conditions for the LNT-EGR model. Figure 1 showed the layout of lean-burn gasoline engine test bench with EGR and LNT aftertreatment system. A commercial LNT catalytic converter (Pt/Ba/Al2O3) made by Toyota with the volume of 1.9 L was chosen for simulation and experiment. The rate of exhaust flow was 950 L/min, and tested initial exhaust temperature was set as 350℃ which was favorable for high NOx conversion. The fixed inlet temperature of LNT can be controlled by the device 20 showed in Figure 1. The ratio of lean-burn time to rich-burn time was set as 56 s : 7 s in consideration of the balance the NOx storage capacity and slip of NOx during the switch of lean-rich condition, i.e., NOx storage sites were not saturated within the adsorption time 56s for the sake of reducing NOx release and maintaining overall NOx conversion efficiency. The AFR (Air/Fuel ratio) during lean-burn phase was 23, while the AFR for rich condition was 12.   Table 1 listed the LNT characterization paramaters, and measured raw emissions of engine under different EGR rate which were used as inlet conditions for the LNT-EGR model were shown in Table 2, the more details about the bench experiment can be found in our previous paper. [20]  Noting that there were two rows data of inlet gas composition and concentration corresponded to each EGR rate in the first column on left side, the data of above row referred to lean conditions of inlet gas composition, while the below row was belonging to rich condition. (The rest inlet gas is N2 by default)

Reactor model
The Perfectly Stirred Reactor (PSR) model is a reaction model in the CHEMKIN software to simulate the process and mechanism of NOx storage and reduction in LNTs. It is a coupled system consisting of gas phase chemical reactions and surface chemical reactions, in which chemical kinetic processes play a leading role. There are assumptions and limitations, first the mass transport from bulk gas to surface (channel wall) was infinitely fast, and the relative importance of the reaction depends only on the specific surface area of the substance. Second, the flow through reactor is characterized by a nominal residence time, which can be deduced from the flow rate and the reactor volume. Based on the above assumptions, the equations used in the PSR reactor model are listed below. Global mass conservation in the reactor volume Left side of the Equation 1 is the time-rate of change of the mass in the reactor, and the right side is the difference between the mass flow in and the mass flow out, plus the net production of species on the surface material.
is the mass density of a gas mixture (g/cm 3 ), is control volume (cm 3 ), ̇ * is the inlet mass flow rate (g/sec), ̇ is the outlet mass flow rate (g/sec).
is the surface area of the material m defined within the reactor (cm 2 ). ̇, is the molar surface production rate of the species k on the material m per unit surface area (mole/(cm 2 /sec)).
is molecular weight of the species k. K and M represent the total gasphase species and materials, respectively.
Surface species conservation equation Here Am is the surface area of the material m in the reactor and ck is the molar concentration of the surface species k (mole/cm 2 ).
The model introduced in this article is an ideal PSR reaction model. Since catalysis only reacts on the surface, there is no gas phase reaction, so the energy equation of the gas phase reaction is not discussed here.

Reaction mechanism
Based on the CHEMKIN which is the standard for modeling and simulating gas-phase and surface chemistry through specific development, the gas phase, surface phase and thermodynamics files developed by data from experiments and simulations of predecessors and our previous lean-burn gasoline engine experiment were rewritten for the NOx adsorption process of the LNT-EGR model. A modification LNT model based on Chatterjee D et al. [21][22] [23] research was built. The detailed reactions involved in the mechanism and the related chemical kinetic parameters were shown in Table 3, which described NOx storage and reduction under isothermal conditions. Noting that (s) behind a specie means that Pt sites were occupied by the specie, specially Pt = Pt(s).  Table 3) in reaction R30, R32 and R33) are obtained by combining R30, R32 and R33. Then, nitrites are oxidized by NO2 in a reaction where nitrates are formed, and NO is desorbed into the gas phase [24]. As we can see from the disproportionation reaction, consumption of every three molecules of NO2 released one molecule of NO. As for Equations 3.3 & 3.4 involving the formation of barium peroxide and NO are the global reactions of reactions R31, R6, R9, R12, R13, R43 and R44. Barium surface can be oxidized by NO2 involving the formation of barium peroxide and NO which is released in the gas phase [24]. Then BaO(O) is involved in the NO2 adsorption for the formation of nitrates. Nitrate route: reaction involving the formation of barium peroxide While the global reactions of nitrite route [25] which is in parallel to nitrate route are presented in Equations 4 and 5 [9]. NO can be directly adsorbed as nitrite on Ba sites with help of Pt showed in Equation 4, then Ba(NO2)2 are further oxidized to stable nitrates by the spilled over oxygen from Pt sites showed in Equation 5. The global reaction 4 and 5 can be derived by elementary reaction R11, R12, R13, R33, R34, R35 and the reverse reaction of R41. In this study, Ba(NO3)2 site fraction and BaO-NO2 site fraction are employed to characterize two kinds of NOx adsorption pathways. It is noting that Ba(NO3)2 can be obtained from both nitrate route as indicated in Equation 3.1~3.4 and intermediate production conversion (nitrite route) showed in Equations 4~5. Therefor nitrate route can be indicated as difference between total Ba(NO3)2 site fraction and the part of Ba(NO3)2 produced by nitrite route, i.e., the BaO-NO2 site fraction in consideration of relationship of stoichiometric number showed in Equation 5. Nitrite route: The Figure 2 illustrates the overall perspective of reaction path related to NOx storage to get more intuitive understanding. There were not arrows in connecting lines between species because the reactions between these species are reversible as shown in Table 3. Table 3 also gives the forward and reverse kinetic parameters for each reaction, i.e., the values of , , and in the generalized Arrhenius expression where is the pre-exponential factor, is the temperature exponent, and the activation energy is .

Modelling Validation
There are 44 reactions in total involved in LNT-EGR kinetics model, which is comprised of several sub-model mentioned in section 3.2 including NO oxidation, oxidation of reductants CO, NH3 and H2, NOx storage including both nitrate and nitrite routes, water-gas shift reaction, water decomposition reaction, formation of NH3 and N2O, intermediate products surface isocyanate reaction, spillover process of NO2 and reduction reaction of stored NOx. These sub-models which are from different research groups' work as mentioned above were picked up here to combine final LNT-EGR model. Parameter values (pre-exponential factor, temperature exponent and the activation energy) of NO oxidation rate expressed by R1, R2, R6 and R13 are from the NOx adsorption experiments lasting long enough to show almost full NOx breakthrough conducted by Kočí P, Marek M et al. [26] Parameter values of oxidation of reductants CO, H2 and NH3 expressed by R8, R15, R19 were from the CO, H2 and HC oxidation light-off experiments based on slow temperature ramps under both lean and rich conditions at different con-centration levels conducted by Kočí P, Schejbal M et al. [27] These literature parameters values of these sub-models were used as the initial guess and followed by tuning to get a reasonable fitting for each sub-model. The Figure 3 illustrates the overall perspective of reaction path related to sub-models to get more intuitive understanding.

Fig. 3. Diagrammatic NOx storage and reduction reaction path。
After the preliminary determination of sub-model, the whole performance of LNT under different EGR rate was validated by the lean-burn gasoline engine test bench as we mention above. Considering the simulation accuracy and calculation cost, the step size for setting the simulation calculation is 0.1 s. In order to verify the accuracy of the model, the exhaust conditions of the catalyst under the different EGR rates measured in the previous experiment are used as the simulated boundary conditions of the catalyst. According to the engine exhaust components and concentrations measured by the experiment, the catalyst inlet gas concentration and other boundary conditions were obtained. For the comparative study, the EGR rates are set as 0%, 10%, 15%, 20%, 25%, 30%, respectively. Corresponding gas compositions and concentrations are shown in Table 2 as mentioned in Experiment setup. The comparison of outlet NOx slip between simulation and experiment is shown in Figure 4. It can be found that NOx slip of LNT from chemical reaction kinetics simulation has the similar trend with the experimental results. Simulation values basically can represent outlet NOx slip because of catalyst desorption, adsorption saturation and storage site limitation. As shown in Figure 4, the error between simulation and experiment is about 50ppm when the EGR is below 10%, when EGR increases up to 15% the error decreases below 30ppm, which indicated that maximum relative error between simulation and experiment is 4.5%, which is lower than 5%. The error may come from the distance between measurement point of LNT outlet and HORIBA gaseous element analyzer, LNT still has adsorption ability as engine switches into rich-burn phase, and abundant desorption has delay. Meanwhile, experimental catalyst cannot switch from lean-mode to rich-mode instantaneously, but simulation can switch immediately, so the simulation has more NOx slip because of desorption. All in all, these verify the validity of the mechanism so the LNT-EGR model can be used for further investigate.

Effects of EGR rate on NOx storage at fixed temperature
Effects of EGR rate on NOx storage process were studied by the contributions and variation tendencies of the two different NOx adsorption pathways, i.e., nitrate route and nitrite route. The nitrate route and nitrite route are characterized by Ba(NO3)2 and BaO-NO2 site fractions, respectively. As previously mentioned, noting that nitrates are accumulated by both nitrate route as indicated in Equation 3.1~3.4 and intermediate production conversion (nitrite route) showed in Equations 4~5. The temperature was set as 350℃.
The main reason of the EGR effects on LNT overall performance is the change of concentration and ratio of inlet components CO2\H2O as mentioned in Introduction. Before the discussion of EGR effects on NOx storage pathway, it should be aware of that the combined influences of both CO2 and H2O on NOx storage and reduction are not equivalent to the individual effects of CO2 or H2O. In this paper, combined influences of both CO2 and H2O on NOx storage are discussed in the level of EGR, as a matter of convenience for analysis, the trend of CO2 and H2O concentration from raw emission under different EGR rate at 350℃ was showed in Figure 5.  EGR rates are divided into two intervals of 0%~15% and 20%~30% due to the different variation tendency of Ba(NO3)2 site fraction. When the EGR rate increases from 0% to 15%, Ba(NO3)2 site fraction decreased gradually, which indicates that increase of EGR rate shows inhibition effects on the NOx storage as Ba(NO3)2. Taking the 350 s of the adsorption stage as an example, when the EGR rate increases from 0% to 10%, Ba(NO3)2 site fraction is reduced by 6.78%, while EGR rate increased from 10% to 15%, Ba(NO3)2 site fraction is reduced by 8.58%. Therefore, inhibition of EGR on stored Ba(NO3)2 slightly aggravates with the EGR rate increase. This is because CO2 concentration of inlet increased with EGR rate as showed in Figure 5, resulting in production of BaCO3 from the reaction R29 (CO2 + BaO ↔ BaCO3) which indicated CO2 was chemisorbed on the BaO sites leaded to reduction of entire NOx storage sites. The result was in line with Epling W S et al. [13] study mentioned before. In addition, it's more difficult for NOx absorbed on BaCO3 than BaO [14] due to high thermal stability of BaCO3 , which leads to reduction of Ba(NO3)2 production as well. The effects of H2O on NOx storage process is neglected not only because its concentration of inlet decreases with EGR rate, but also H2O playes a much weaker role in NOx adsorption, which is widely reported in literatures such as reference [13]. The role of H2O is practiced not so much in NOx adsorption as in formation of NH3 and N2O through water-gas shift reaction and subsidiarity of reactions involving intermediate products such as -NCO, -H and -OH, which would be discussed later.
When the EGR rate increases within interval of 20%~30%, Ba(NO3)2 site fraction continues decreasing, maintaining range of 15%~25%, and the change amplitude significantly reduced. At moment of 150 s, when the EGR rate increased from 20% to 25% and from 25% to 30%, Ba(NO3)2 site fraction reductions are 0.18% and 0.34%, respectively. EGR still shows inhibition effect but the degree weakens. The distinctly different Ba(NO3)2 site fraction trends of the two EGR intervals of 0%~15% and 20%~30% are on account of the equilibrium limitations of reaction R29, which reveals competing adsorption mechanism of CO2, i.e., the same NOx storage sites (Ba sites) are occupied by CO2. Therefore, reduction of Ba(NO3)2 site fraction with increased EGR rate of intervals 20%~30% became less pronounced, through concentration of CO2 continuously increased with EGR rate.  When the EGR rate increases from 0% to 15%, the nitrite site fraction is reduced first and increases later in the NOx storage stage such as time interval 0s~56s, however the later increase of BaO-NO2 site fraction became more evident and stable in subsequent cycles while the first reduction of BaO-NO2 site fraction with EGR rate increasing was negligible. Hence EGR shows early slightly inhibition and later promotion on the nitrite path in the EGR interval of 0%~15%. At the 350s of the adsorption stage, the BaO-NO2 site fraction respectively increases by 4.56% and 5.6% as the EGR rate increased between the two EGR rate intervals 0%~10% and 10% ~15%, which shows positive effects of EGR on the nitrite path slightly aggravating with the increase of the EGR rate as the cycle was stabilized. There is different situation as EGR rate varies in the interval 20%~30%, the BaO-NO2 fraction marginally decreases with the increasing EGR rate in the NOx storage stage, and increases in flowing NOx reduction stage. The BaO-NO2 site fraction is reduced only by 1.08% and 0.81%, respectively for two EGR rate intervals 20%~25% and 25% ~30%, which shows the weak correlation between the BaO-NO2 site fraction and EGR rate interval 20%~30%. The high overlap of the lines group of EGR rate interval 20%~30% in Figure 7 also underlines this point. The main reason of the difference between two EGR rate intervals (0%~15% and 20%~30%) above is that the reduction of Ba sites occupied by CO2 was stabilized due to equilibrium limitations of reaction R29. In addition, it can be clearly seen that two trends of Ba(NO3)2 and BaO-NO2 site fraction are less stable in the first cycle of the simulation from Figure 6 and 7. Furthermore, both Ba(NO3)2 and BaO-NO2 site fraction of first cycle are different from the corresponding flowing cycle, Ba(NO3)2 site fraction is lower while BaO-NO2 site fraction is higher. This phenomenon indicates that nitrite route represents the major storage during the initial NOx storage in the presence of NOx and O2 mixtures under lean condition.
As for variation of Ba(NO3)2 site fraction, nitrates are the final products of stable storage of NOx as showed in the Figure 2 (diagrammatic NOx storage routes) at 350 °C. Ba(NO3)2 site fraction of each adsorption cycle consists of residual part from last cycle and production part of current ongoing cycle except for the first cycle which has the largest quantity of fresh NOx adsorption sites. Nitrite route and nitrate route concurrently accomplish the NOx storage, but BaO-NO2 is intermediate product of the unstable nitrite route, which is in the process of continuous production and transformation. It takes long storage times to oxidize nitrites to nitrates with help of oxygen and Pt sites. Therefore, in the first adsorption cycle there is lower Ba(NO3)2 site fraction than following cycles because of the absence of residual nitrates from last cycle and less production of nitrates came from oxidized nitrites for being pressed for time. Initial instability of site fraction is attributed to the largest quantity of fresh NOx adsorption sites of first cycle mentioned above. As for the situation of BaO-NO2 site fraction can be explained by the complementary correlation between nitrate route and nitrite route mentioned before. Figure 8 shows the trend of Ba(NO3)2 and BaO-NO2 site fraction at 0% EGR rate. During the adsorption phase of each cycle, the Ba(NO3)2 site fraction shows a continuous increasing trend, i.e., NOx is continuously stored as stable nitrates through several different reaction pathways including NOx disproportionation, reaction involving the formation of barium peroxide and nitrite route expressed by Equation 4~5. It's worth noting that BaO-NO2 site fraction only increases at the beginning of each NOx adsorption phase, and the increase rate is significantly higher than the Ba(NO3)2 site fraction. During the late phase of adsorption, BaO-NO2 fraction decreases over adsorption time until the adsorption phase completed, which has confirmed the conversion process of nitrite route due to BaO-NO2 further oxidized to nitrates leading to corresponding increase of Ba(NO3)2 site fraction. Therefore, the timevarying NOx storage process under lean condition at fixed temperature (350℃) can be concluded as follows, both nitrate and nitrite storage routes proceed simultaneously and parallelly, more Ba sites are occupied though nitrite process (Equation The similar NOx storage processes under other EGR rates would not be repeated here for saving space. However, the difference of NOx storage performance with EGR changing and the contributions to NOx storage of both nitrate and nitrite route, which are expressed as ratio of NOx storage sites occupied through the two different adsorption routes, were discussed below.   For analysis of other EGR rates set, the third lean-burn cycle is selected for the rest EGR rate as 0% EGR rate did in consideration of controlling variable to minimize errors as much as possible. Figure 9 shows the time variable Ba(NO3)2 site fraction and BaO-NO2 site fraction of 10% EGR rate, the Ba(NO3)2 increases by 25.50% and the corresponding BaO-NO2 reduction was 13.55% during the third cycle. Therefore, the percentage of NOx storage sites occupied through nitrate route and the nitrite route accounts for 11.95% and 22.53%, respectively, with a view to the Ba sites consumed by CO2 (R29) and the Ba sites at inactivated state. Hence the ratio of nitrate route to the nitrite route is about 1:1.89. In the third lean-burn cycle corresponding to 15% EGR showed in Figure 10, the Ba(NO3)2 site fraction increase is 25.87%, and the corresponding BaO-NO2 fractional decrease is 12.70%. Nitrate path and nitrite path accounted for 13.17% and 29.29%, respectively. The ratio of the two routes is about 1:2.22. Similarly, the percentage of NOx storage sites occupied through nitrate route and the nitrite route under EGR rate of 20%, 25% and 30% could be calculated by the data showed in Figure 11, 12 and 13, respectively. Therefore, the respective ratios of nitrate route to the nitrite route of each EGR rate above are 1:2.92, 1:2.68 and 1:2.47.
The ratio of nitrate route to nitrite route and Ba sites occupation of two NOx storage pathways with EGR rate changing are showed in Figure 14. It's worth noting that the connection and difference between the site fraction of Ba(NO3)2 and the nitrate route. For a better understanding of the leading role of both NOx adsorption routes with EGR changing, nitrate route is separated by subtracting the Ba(NO3)2 produced by nitrite route, which is equivalent to the amount of BaO-NO2 involved in the nitrite oxidation reaction in consideration of relationship of stoichiometric number showed in Equation 5, from total Ba(NO3)2 production.
In the range of 0% ~ 20% EGR rate, the ratio of nitrate route to nitrite route drops while raises in the 20% ~ 30% EGR rate. With EGR rate changing from 0%~30%, there is slight variation of occupation of Ba sites by nitrate route whereas Ba sites occupation by nitrite route isn't at the operating temperature (350℃). Furthermore, similar trend of Ba sites occupation of both two NOx storage pathways is showed in Figure 14, which raises first and drops later. The change of ratio of nitrate route to nitrite route is decided by nitrite route to a great extent due to slight variation of occupation of Ba sites by nitrate route as showed above. Only when CO2 concentration reaches to a certa in quantity such as the amount contented in high EGR rate over 15%, its inhibition on NOx storage process begins to emerge, though the reaction R29(CO2 + BaO ↔ BaCO3) of CO2 competitive adsorption on the Ba sites and NOx storage reaction coexisted. Both nitrate and nitrite routes are unaffected by increased CO2 quantity within the range of low EGR rate due to abundant Ba sites for both NOx and CO2 adsorption. In the meantime, the amount of CO from engine exhaust raised modestly with EGR rate increase, which facilitates chemical equilibrium of reversible reaction R40 (Ba(NO3)2 + CO(S) ↔ BaO(NO2) + NO2 + CO2 + Pt(S)) shifting to the right leading to more BaO-NO2 production. Meanwhile, the reduction of water steam with EGR rate increase shifts the chemical equilibrium of reversible reaction R36(BaO(NO2) + H(S) ↔ BaO + NO + OH(S)) to left resulting more BaO-NO2 formation. Water steam reduction is not conducive to chemical equilibrium of reversible reaction R37(Ba(NO3)2 + H(S) ↔ BaO(NO2) + NO2 + OH(S)) due to both H(S) and OH(S) came from hydrolysis reaction which is reverse reaction of R14(H(S) + OH(S) ↔ H2O(S) + Pt(S)) with presence of catalyst Pt sites. Therefore, Ba sites occupation by nitrite route raises in range of 0%~20% EGR rate as well as nitrate route because of more NO2 formation through reaction R23(NO2(S) + CO(S) ↔ NO(S) + CO2 + Pt(S)) with the help of increased CO2 quantity with EGR rate increased.

Effects of EGR rate under different temperature zone
Temperature is vital for chemical reaction as is well-known. The case of variation for nitrate route and nitrite routs under different EGR rate is discussed at a fixed typical LNT operating temperature 350℃ above. Performance of EGR (0%,10%,15%,20%,25%) effects on NOx storage course at varying temperatures would be talked about below. According to actual engine operation conditions with different EGR rates, the simulations were carried out at different inlet temperatures from 150℃ to 550℃. For the sake of clearer interpretations, the numerical results were divided into three temperature zones: low temperature zone, i.e., 150°2 00℃, moderate temperature zone, i.e. 250℃~400℃, and high temperature zone, i.e. 450°5 50℃.

In low temperature zone
The time-varying variation trend of Ba(NO3)2 and BaO-NO2 site fraction under different EGR rate at low temperature zone (150℃~200℃) is showed in Figure 15.  As showed in Figure 15, the Ba(NO3)2 site fraction is no more than 0.06% in terms of simulation results while the maximum BaO-NO2 site fraction is about 25% over the whole low temperature range, which indicates that Ba(NO3)2 site fraction is far less than BaO-NO2 site fraction. Therefore, the nitrite route dominates the NOx storage at low temperature zone in a very explicit way. The primary cause is little NO2 which is essential for nitrates formation produced from NO oxidation because NO oxidation reaction R13(NO(S) + O(S) ↔ NO2(S) + Pt(S)) is kinetically limited at low temperature, especially near 150 ℃ (with about maximum 0.025% Ba(NO3)2 site fraction), which is in line with experimental results from Olsson L [28]. Note that the change of left scale of figure 15 (a) and (c) indicates that Ba(NO3)2 site fraction doubled due to increasing temperature from 150 ℃ to 200 ℃ . Meanwhile BaO-NO2 site fraction increased with temperature increasing as well through comparison of BaO-NO2 site fraction under same EGR rate but different temperatures as showed in Figure 15 (b) and (d).
Because of negligible amounts of the Ba(NO3)2 site fraction, the effects of EGR rate and temperature on the BaO-NO2 site fraction (nitrite route) are mainly discussed below. As showed in Figure 15 (b) and (d), the BaO-NO2 site fraction decreases with the increase of EGR rate at both 150℃ and 200℃ for the CO2 competitive adsorption reason as mentioned before. The increase of BaO-NO2 site fraction slows down as the EGR rate increase, which is more obvious at inlet temperature of 200℃ as showed in Figure 15 (d). This is because the consumption rate of Ba sites taken for initially appeared nitrites and negligible nitrates is stable over storage time because impacts of kinetically limitation of NO oxidation fade away with temperature increase within 150 ℃~200 ℃ , leading to reduction of NO and corresponding nitrites. As showed in Figure 15 (d) when the EGR rate increases from 0% to 10% at 200℃, the BaO-NO2 site fraction drops approximately 3.14% at 200 s. For EGR rate increases from 10% to 25% with increment 5%, the calculations of the variation degree are conducted at 200 s as well, and the corresponding decline of BaO-NO2 site fraction is about 1.86%, 1.30%, 0.98%, respectively for different EGR rate intervals. So, the inhibition degree of EGR rate on nitrite route weakens with EGR rate increased at 200℃, because CO2 adsorption competitiveness gradually reaches to saturation with incremental EGR rate.    With the increase of temperature from low temperature zone to moderate temperature zone, both of the Ba(NO3)2 and BaO-NO2 site fraction increases significantly, especially the Ba(NO3)2 site fraction. Take 10% EGR rate as an example, the maximum Ba(NO3)2 site fraction is about 40% as showed in Figure 11 (a) at 250℃. For the temperature of 300℃, 350℃ and 400℃, the maximum Ba(NO3)2 site fraction is about 95%, 70% and 25%, respectively. Visibly from Figure 16 (a)-(d) with temperature raises from 250℃ to 400℃, the Ba(NO3)2 site fraction increases first and declines later and BaO-NO2 site fraction trend changed oppositely at moderate temperature zone which is major turning point for NOx storage pathway conversion and change. Furthermore, Ba(NO3)2 site fraction increases by 24.06% under 10% EGR rate as showed in Figure 16 (b), in the adsorption phase (127~182 s). Meanwhile, BaO-NO2 site fraction decreases by 13.95%. Ba(NO3)2 can be obtained from both nitrate and nitrite routes as showed in Figure 2 (diagrammatic NOx storage routes). Therefore, at 300℃ the probabilities of nitrate path and nitrite path were 10.11% and 13.95%, respectively. And at 350℃, the probabilities of nitrate path and nitrite path were about 10.01% and 13.77%. So, the two adsorption pathways have approximately equivalent contribution to NOx storage at 300℃and 350℃.

In moderate temperature zone
The cause of nitrate route participation raises first to reach same level of BaO-NO2 site fraction and drops later is result of comprehensive effects of NO oxidation thermodynamic restriction, nitrate and nitrite thermostability and conversion between nitrites and nitrates. With temperature increasing from 250℃ to 350℃, there is an interval between kinetically limitation vanished and thermodynamic restriction appeared during which NO2 production from NO oxidation (R13 NO(S) + O(S) ↔ NO2(S) + Pt(S)) is at the highest level, which is in accordance with study of Olsson L [28]. NOx disproportionation (BaO + 3NO2 ↔ Ba(NO2)(NO3)(3.1) & Ba(NO2)(NO3) + NO2 ↔ Ba(NO3)2 + NO(3.2)) is more and more important with temperature raised within the interval (250℃~ 350℃) leading to more nitrates formation. Hence nitrate route participation raises first from 250℃ to 350℃ based on above two primary reasons. The absolute amount of nitrates which can be seen through Ba(NO3)2 site fraction value in figure 16 (b) and (c) was at very high level at 300℃ and 350℃ due to formation of barium nitrate species from nitrite species (Ba(NO2)2 + O2↔ Ba(NO3)2 (Equation5)) with Pt catalyzing is optimum in this temperature range (300℃~350℃) which is also reported by Forzatti P [29].
As the temperature subsequently raises to 400℃, reduction of nitrates generation from NO2(BaO + 3 NO2 ↔ 2 Ba(NO3)2 + NO (Equation3)) due to thermodynamics limitation of NO oxidation above 350℃ and decline of stored nitrates due to thermal instability of nitrates at high temperature like 400℃ result in decrease of Ba(NO3)2 site fraction above 350℃ of moderate temperature zone. Meanwhile the variation tendency of BaO-NO2 site fraction is opposite to Ba(NO3)2 site fraction variation for the reason of NOx storage sites (Ba sites) conservation and complementary correlation between nitrate and nitrite route mentioned before.
In additional, there are fluctuations of BaO-NO2 site fraction during the switching between rich and lean condition as showed in partial enlarged detail highlighted in red circle of figure 16 (b). These fluctuations came from the change of equilibrium and rates of reactions (BaO + 3 NO2 ↔ 2Ba(NO3)2 + NO (Equation3), BaO + 2NO + 0.5O2↔ Ba(NO2)2 (Equation4) and Ba(NO2)2 + O2↔ Ba(NO3)2 (Equation5)) which are affected greatly by local concentration of NO, NO2 and O2. The rich-lean switch leads to changes in NO, NO2 and O2 local concentrations and the ratio of arbitrary two of these species.

In high temperature zone
The variation tendency of Ba(NO3)2 and BaO-NO2 site fraction over time under different EGR rate at high temperature zone (450℃~550℃) is showed in Figure 17. taking notice of different scale of left and right Y axis in Figure 17 (a), (b) and (c). It can be clearly seen that Ba(NO3)2 site fraction is no more than 5% whereas BaO-NO2 site fraction maintained at a very high level, which indicates that nitrite route dominates again with temperature raises to high temperature zone as a result of the reduction of nitrates formation and nitrates pyrolysis at high temperature. As mentioned before, NO oxidation is thermodynamic limited above 350℃ [28] resulting in reduction of formation of NO2 which is crucial reactant for nitrates formation through BaO + 3 NO2 ↔ 2 Ba(NO3)2 + NO (Equation3), leading to reduction of nitrates formation. Meanwhile the degradation of thermal stability of nitrates resultes in reduction of stored nitrates through reaction R33 (NO2 + BaO(NO3) ↔ Ba(NO3)2). In addition, Ba(NO3)2 from nitrite route also decreases because last reaction step of nitrite route (Ba(NO2)2 + O2↔ Ba(NO3)2(Equation5)) is affected by thermodynamic limitation above 350℃ [29]. As EGR rate increases from 0% to 25%, both of Ba(NO3)2 and BaO-NO2 site fraction decreases in high temperature zone which is similar with tendency of low and moderate temperature zone except for the special circumstance of Ba(NO3)2 site fraction under 0% EGR rate at 150℃ and 200℃ explained before. The decline degree of Ba(NO3)2 and BaO-NO2 site fraction decreases with EGR rate increasing, because CO2 adsorption competitiveness gradually reaches to saturation with increasing EGR rate.

Conclusion
A LNT model coupled with EGR was developed based on the Langmuir-Hinshelwood mechanism to investigate the EGR effects on NOx adsorption pathway of LNT catalysts with temperature changed in range 150℃~550℃. Both the nitrate and nitrite adsorption paths were considered for the NOx storage process in the model as well as the spillover of stored NOx between Ba and Pt sites. The model quantified the contributions of both nitrate route and nitrite route to the NOx storage capacity for LNT with change of EGR rate (0%~30%) at fixed temperature under raw emission atmosphere from tested gasoline engine. At fixed inlet temperature of 350℃ set for high NOx conversion efficiency, EGR rate shows restraining effects on Ba(NO3)2 site fraction within range of 0%~30% whereas promotion effects on BaO-NO2 site fraction from 0% to 15% and inhibition effects in subsequent EGR rate 20%~30%. There is opposite tendency between Ba(NO3)2 site fraction BaO-NO2 site fraction over time in the same cycle of operation due to the complementary 0% EGR rate 10% EGR rate 15% EGR rate 20% EGR rate 25% EGR rate correlation between nitrate route and nitrite route. Furthermore, the similar trends of site fraction assorted in EGR rate interval 0%~15% were different from the similar trends of site fraction which were assorted in EGR rate interval 20%~30% for both Ba(NO3)2 site fraction and BaO-NO2 site fraction due to the equilibrium limitations of the reaction about CO2 was chemisorbed on the BaO sites which are supposed to be occupied by NOx. As for contributions of the two routes to NOx storage, in the range of 0% ~ 20% EGR rate, the ratio of nitrate route to nitrite route dropped while raised in the 20% ~ 30% EGR rate, the ratio is decided by nitrite route to a great extent due to slight variation of occupation of Ba sites by nitrate route due to great cardinal number of NO amounts from raw engine emission, thermodynamics limitation of NOx oxidation and in part thermal decomposition of stored Ba(NO3)2 at temperature of 350℃. The process of CO2 (which is major component of inlet stream in presence of EGR) competitive adsorption dynamic changed with the ratio of CO2 concentration and available NOx storage sites left. When LNT catalyst temperature varies from 150℃ to 550℃, there are new changes of NOx storage process under different EGR rate. Nitrite route dominates at low temperature zone (150℃~200℃) because there are little NO2 which is essential for nitrate route from NO oxidation kinetically limited at low temperature, especially near 150℃. With the increase of temperature from low temperature zone to moderate temperature zone (250℃~400℃), both of the Ba(NO3)2 and BaO-NO2 site fraction increases significantly, especially the Ba(NO3)2 site fraction which has a 4magnitude equal to BaO-NO2 site fraction. The cause of nitrate route participation raises first to reach same level of BaO-NO2 site fraction and drops later is result of comprehensive effects of NO oxidation thermodynamic restriction, nitrate and nitrite thermostability and conversion between nitrites and nitrates. Nitrite route dominates again with temperature raises to high temperature zone (450℃~550℃) as a result of the reduction of nitrates formation (NO oxidation was thermodynamic limited above 350℃) and the pyrolysis of nitrates at high temperature. As EGR rate increases from 0% to 25%, both of Ba(NO3)2 and BaO-NO2 site fraction decreases in high temperature zone which is similar with tendency of low and moderate temperature zone except for the special circumstance of Ba(NO3)2 site fraction under 0% EGR rate at 150℃ and 200℃ because oxygen atoms adsorption on Pt sites was blocked by adsorbed H2O on Pt sites at low temperature which retarded NO oxidation resulting in reduction of nitrates produced by NOx disproportionation (Equation 3.1 and 3.2) and reaction involving the formation of barium peroxide (Equation 3.3 and 3.4).