Qian Cheng,Dunyu Liu*,Jun Chen,Jing Jin,Wei Li,Shuaishuai Yu

School of Energy and Power Engineering,University of Shanghaifor Science and Technology,Shanghai200093,China

Keywords:Oxy-fuel combustion NOoxidation Sour gas compression

ABSTRACT The removal of NOfrom oxy-fuel combustion istypically incorporated in sour gas compression puri fi cation process.This process involves the oxidation of NOto NO2 at a high pressure of 1-3 MPa,followed by absorption of NO2 by water.In this pressure range,the NO conversion rates calculated using the existing kinetic constants are often higher than thoseobtained experimentally.Thisstudy aimed to achievethe regression of kinetic parameters of NOoxidation based on the existing experimental results and theoretical models.Based on threeexisting NOoxidation mechanisms,fi rst,the expressionsfor NOconversion against residence time were derived.By minimizing the mean-square errorsof NOconversion ratio,the optimum kinetic rate constants were obtained.Without considering the reverse reaction for NOoxidation,similar mean-square errors for NO conversion ratio were calculated.Considering the reverse reaction for NOoxidation based on the termolecular reaction mechanism,the minimum mean-square error for NOconversion ratio w asobtained.Thus,the optimum NO oxidation rate in the pressure range 0.1-3 MPa can be expressed as follow s:Detailed elementary reactions for N2/NO/NO2/O2 system were established to simulate the NOoxidation rate.A sensitivity analysis showed that the critical elementary reaction is 2NO+O2?2NO2.However,the simulated NO conversions at a high pressure of 10-30 bar are still higher than the experimental values and similar to those obtained from the models w ithout considering the reverse reaction for NO oxidation.

1.Introduction

Carbon capture and storage(CCS)is considered as an effective measure to mitigate CO2emission[1].CO2emission from fossil fuel combustion can be reduced by oxy-fuel combustion,one of the promising CCS technologies[2].Although fl ue gas in oxy-fuel combustion is rich in CO2,it containsimpuritiessuch as NO.To remove NOfrom fl uegas,several companies such as Air products,Linde,Air Liquide,Praxair and Alstom have developed denitration technologies.In these technologies,NOis removed after the compression process.Therefore,these technologies are know n as sour gas compression puri fi cation process.A tw ostage high-pressure scrubbing system was proposed by Air products[3-5]based on the lead chamber process.In the fi rst stage,all the SO2and a small amount of NO are removed in the form of H2SO4and HNO3,respectively.In this stage,NO is oxidized at a high pressure(1.5 MPa)to NO2,and NO2oxidizes SO2to SO3,w hich then reacts with water to form H2SO4.In the second stage,the pressure isincreased to 3 MPa to removal all the NOxas HNO2and HNO3.A w et scrubbing method w as developed by Linde;95%-99%of SO2is removed by the fl ue gas desulfurization system before entering the CO2compressor.The fl ue gas after SO2removal is compressed to 1.8 MPa[6].After the compression,NOisconverted to NO2and chemically absorbed in an ammonia solution to form ammonium nitrites.Air Liquide[7-9]developed an atmospheric scrubbing system for SO2removal and a high-pressure scrubbing system for NOremoval.In this method,a caustic solution is used to reduce the SOxconcentration to low-ppm levels.Then,fl ue gas is passed through a four-stage compression system w ith NO removal after the second(0.4 MPa)and fourth(2.4 MPa)stages as the condensates.Finally,the fl ue gas iscompressed to 3.0 MPa,and NOisremoved using the high-pressure scrubber.The reactions occurring in this process are similar to those occurring in the process proposed by Air Products.Praxair[10]designed a method named“Near-Zero Emissions”.The fl ue gas fi rst enters a compressor,and then a part of NO and SO2isremoved duringthe fl uegascondensation processascondensates such as H2SO4and HNO3.Follow ing this process,SOxand NOxare removed using tw o activated carbon beds.SOxand NOxare fi rst adsorbed onto the fi rst bed.When the fi rst activated carbon bed is almost saturated w ith impurities,a valve system sw itches the fl ue gas to the second activated carbon bed w hile the fi rst activated carbon bed is regenerated using water.Under the conditions of high pressure and activated carbon asthe catalyst,almost all NOis absorbed and removed as the corresponding acids.Alstom[11]developed the pressurized SCR,and the apparatus may be placed after direct contact condenser and in the fl ue gas compression stage.This process utilizes the reactions of NOand NO2with NH3to form N2,and in particular,NO2is believed to react faster with NH3.

A common feature of these technologies is the utilization of high pressure to promote the oxidation reaction of NO w ith O2to form NO2.Compared w ith NO,NO2can be absorbed by w ater more easily.The reaction 2NO+O2?2NO2istherate-determining step of thisprocess and the focus of this research.

The reaction of NOand O2at atmospheric pressure has been extensively studied,but the reaction NOand O2under pressurized conditions corresponding to sour gas compression puri fi cation process has been rarely studied.NOoxidation is a third-order reaction[12-14].

Different equations have been proposed for NOoxidation rate constant by Tsukahara[14]and Bodenstein[15,16].

w here k is the overall reaction rate constant(kPa-2·s-1);R is the gas constant(L·kPa·K-1·mol-1);T is Kelvin temperature(K).

Bodenstein obtained the chemical equilibrium constant Kpfor the reverse Reaction(3)at 220-550°C.The reverse reaction rate can be calculated from the chemical equilibrium constant and forward reaction rate constant using Eqs.(1)and(2).Thesepreviously reported chemical reaction rate constants are obtained at atmospheric pressure and high temperature.They may not be applicable under the high pressure and atmospheric temperature conditions.

The global reaction of NOand O2occursin the gasphase asshow n in Eq.(3).

There are some controversies about the mechanism of NOoxidation w ith O2.The follow ing three mechanisms are generally accepted[14,17].

(i)Termolecular reaction:Tw o NO molecules collide w ith one O2molecule to form a transient complex that then decomposes to tw o NO2molecules.

Based on Eyring's transition state theory and reasonable molecular properties,Gershinow itz and Eyring[18]justi fi ed that each O atom of an O2molecule is partially bound to the N atoms of tw o NOmolecules,forming NO2directly.When the reverse reaction is not considered,the rate of NO oxidation based on mechanism(i)can be expressed as Eq.(4).

w here[NO]is the concentration of NOduring the reaction;[O2]is the concentration of O2during the reaction;k is the kinetic constant.

Although the termolecular reaction has long been a classic example of a molecular reaction in Chemistry text book,in recent years,most researchers refer to the tw o-step mechanism and consider it more persuasive.

(ii)Pre-equilibrium mechanism w ith a dimer of NOasan intermediate:First,two NOmolecules polymerize to form(NO)2asshow n in Reaction(5),and then(NO)2reacts w ith O2to form NO2as shown in Reaction(6).The rate of Reaction(5)is much higher than that of Reaction(6);therefore,Reaction(6)is the ratedetermining step.

The NOoxidation rate based on mechanism(ii)can be expressed as Eq.(7)[14,19].

w here k2is the forw ard reaction rate constant for Reaction(5);k-2is the reverse reaction rate constant for Reaction(5);k3is the reaction rate constant for Reaction(6).

(iii)Pre-equilibrium mechanism with NO3as an intermediate:First,NO reacts w ith O2to generate NO3as show n in Reaction(8),and then NO3reacts w ith NO to generate NO2as show n in Reaction(9).The rate of Reaction(8)is much higher than that of Reaction(9);therefore,Reaction(9)is the rate-determining step.The NO oxidation rate based on mechanism(iii)can be expressed as Eq.(10)[20].

w here k4is the forw ard reaction rate constant for Reaction(8);k-4is thereversereaction rateconstant for Reaction(8);k5isthe reaction rate constant of Reaction(9).

NO concentration against residence time at a low pressure is w ell predicted by previous kinetic constants.However,experimental and simulation results[21,22]show that at a high pressure(1-3 MPa),the simulated NOconcentration isusually low er than the actual NOconcentration at the same residence time.The reason for the underestimation of NOconcentration at a high pressure is still not clear.This is probably because at atmospheric pressure,NOconversion isoften low,and under this condition,the role of reverse reaction is often overlooked.On the other hand,at a high pressure,the NOconversion is usually high,and theamount of generated NO2isalso higher.Under thiscondition,thereverse reaction may signi fi cantly affect the NOreaction rate.Therefore,it isimportant to calculate the reverse reaction rate for predicting NOoxidation rateat a high pressure.Moreover,overall reaction rate constants are currently obtained at atmospheric pressure(P≤0.1 MPa);it remains to be veri fi ed w hether this is also applicable to high-pressure conditions.

In thispaper,theexperimental dataof NOconcentration against residence timein the pressure range 0.1-3 MPaare review ed.Based on the three existing NOoxidation mechanisms,the expressions for NOconcentration against residence time w ere derived.By minimizing the mean-square error of NOconversion ratio betw een the calculated and experimental values at the sameresidence times,theoptimum reaction mechanism,kinetic rate constant,and expression for NOconcentration suitable for pressurized conditionswere obtained.Elementary reactions for NOoxidation w ere also obtained based on kinetic simulations.The controlling steps for NOoxidation w ere identi fi ed.This study is highly relevant for sour gas compression puri fi cation process for the oxy-fuel combustion of fl ue gas.

2.Experimental

Fig.1.High pressure experimental setup.

Experimentsw ere conducted using a cylinder reactor w ith avolume of 1 L.The experimental setup is show n in Fig.1.Gases w ere introduced into the reactor,and their fl ow rates w ere controlled using mass fl ow controllers.The gas inlet tube was kept close to the bottom of the reactor to ensure the maximum residence time.The volume of tube w as small relative to that of reactor;therefore,the residence time of a gas in the tube w as negligible.The average residence time was obtained by dividing the volume of reactor by the gas fl ow rate.

During the experiments,the NOand O2concentrations in the gas were continuously measured using a MRUdelta 2000 fl ue gas analyzer.At the beginning of the experiment,the gas w as sw itched to the bypass to measure the inlet NOconcentration.The required NOconcentration w as regulated using mass fl ow controllers w hile keeping the total gas fl ow rate constant.When the measured NOconcentration was stable for 10 min,the gas w as switched to the reactor.The pressure in the reactor wasshow n by the gas cylinder and controlled using a pressure relief valve.A change in pressure also changed the gas residence time in the reactor from 30 s at 0.1 MPa to 750 s at 2.5 MPa.The NOconcentration was continuously recorded using a computer,and the experiment was stopped after a period of stabilization.The stable NOconcentration and pressure w ere recorded for each experiment.

Table 1 show s the relevant experimental data obtained for NOoxidation at different pressures and from different sources.Different experimental systems were used.Continuous mode experiments were used by most researchers except Hui et al.[23]w ho conducted batch mode experiments.Yu[21]used differential optical absorption spectroscopy to measure NO2.The measurement of NO2w as based on itsselective absorption in the UV to near-UV band range.Ting[22]used a Testo 350XL fl ue gas analyzer to measure NOand NO2.Murciano et al.[24]used a 42-CHL fl ue gas analyzer to measure NO and NO2,but Murciano's experimental data w ere less.Hui[23]used an MRU/MGA 5 fl uegasanalyzer to measure NOand NO2.Notably,an intermittent measurement method was used by Hui et al.,and the gas w as fi rst collected in the bag.This may result in a signi fi cant error during the storage.

Table 1 Experimental conditions

Theeffect of temperatureon NOoxidation at ahigh pressurew asnot investigated.The current experimental data w ere obtained at room temperature.

3.NO Concentration against Time Based on Three Existing Mechanisms

3.1.NOconcentration against time for mechanism(i)

3.1.1.NOconcentration against time without variation of O2concentration(mechanism(i-1))

During the reaction of NOand O2,the O2concentration(3%-5%)is signi fi cantly higher than the NO concentration;thus,the changes in O2concentration can be ignored.

Eq.(11)w as obtained by the integration of Eq.(4).The NOconcentration as a function of time t can be expressed as Eq.(12)[14].

w here[NO]0is the initial NOconcentration;[NO]is the NOconcentration at time t;[O2]0is the initial O2concentration;t is residence time.

3.1.2.NOconcentration against time with variation of O2concentration(mechanism(i-2))

When the O2concentration iscloseto the NOconcentration,the variation in O2concentration cannot be ignored.The reaction rate of NO can be correlated with that of O2using Eq.(13).By integrating Eq.(13),Eq.(14)describing the relationship betw een NOand O2concentrations can be derived as follow s:

By substituting Eq.(14)into Eq.(4),the NOoxidation rate can be expressed as Eq.(15).

By integrating the differential Eq.(15),the NOconcentration against time can be obtained as Eq.(16).Thisequation issimilar to that used by Joshi et al.[25].

3.1.3.NOconcentration against time with reverse reaction(mechanism(i-3))

When the reverse reaction for NO oxidation is considered,the reaction rates of NO and NO2can be expressed as the differential Eq.(17).

w here[NO2]is the concentration of NO2during the reaction;k6is the forw ard reaction rate constant;K is the reverse reaction rate constant.

The equilibrium constant for reaction 2NO2→2NO+O2can be expressed as Eq.(18).

where Kpis the equilibrium constant.

When equilibrium is reached,the formula-d[NO]/d t=d[NO2]/d t=0 is valid,and the follow ing Eq.(19)can be obtained based on Eq.(17).

Based on Eqs.(19)and(18),Eq.(20)can be obtained as follow s:By substituting[NO2]=[NO]0-[NO]into Eq.(17),Eq.(21)can be obtained as follows:

w here 2k6[O2]-2K,4K[NO]0,and-2K[NO]02are constants.To simplify the calculation,they are represented as a2,b2,and c2,respectively.

When b22-4a2c2＜0,Eq.(21)can be integrated to obtain Eq.(22).

Eq.(22)can be further transformed to obtain NO concentration against time as expressed by Eq.(23).

when b22-4a2c2＞0,Eq.(21)can be integrated to obtain Eq.(24).

When(2a2[NO]+b2-(b22-4a2c2)0.5)/(2a2[NO]+b2+(b22-4a2c2)0.5)＞0,Eq.(24)can be further transformed to obtain NOconcentration against time as expressed by Eq.(25).

When(2a2[NO]+b2-(b22-4a2c2)0.5)/(2a2[NO]+b2+(b22-4a2c2)0.5)＜0,Eq.(24)can be further transformed to obtain NOconcentration against time as expressed by Eq.(26).

Within theexpression,b22-4a2c2=16k6K[NO]02[O2],k6＞0 and K＞0 apply.Thismeans b22-4a2c2＞0;therefore,only Eqs.(25)and(26)hold.When a2=0,Eqs.(25)and(26)do not hold.At thistime,the NOoxidation rate can be expressed as-d[NO]/d t=b2[NO]+c2,and thisequation is only related to K and[NO]0.Obviously,this is not consistent w ith the actual situation;therefore,in the actual process,a2≠0 applies.

3.2.NOconcentration against time for mechanism(ii)

The equation of NOoxidation rate in mechanism(ii)isshow n below[14,19].

Because[O2]=[O2]0,it can beconsidered that k2k3/{k-2+k3[O2]}isaconstant in Eq.(7).Eq.(7)can be converted into thesame form asin Eq.(4).Thus,the expression of NOconcentration against time should also be the same as in mechanism(i-1).

3.3.NOconcentration against time for mechanism(iii)

The NOoxidation rate can be obtained from mechanism(iii)[20]as Eq.(10).

The expression of NOagainst residence time t can be obtained by integrating Eq.(10).

where C0is a constant,and this value can be obtained w hen residence time t=0.Because k4,k-4,and k5are all kinetic constants,1/(k4[O2])and k-4/k5are constants as w ell.

4.Regression of Rate Constants

Under pressurized conditions,the previous experimental data of NO concentration at different pressures and residence times are summarized in the data in brief,and the conversion ratio is de fi ned as Eq.(28).These data w ere used as the input to regress the chemical kinetic parameters based on the expressions of Eqs.(12),(16),(25),(26),and(27)in Section 3.Here,the mean-square error of NOconversion ratio wasused astheoptimization function.Thisfunction isde fi ned as Eq.(29),w here XNOiis the calculated NOconversion ratio at a particular residence time.This value is calculated based on the expressions stated in Section 3 and Eq.(28).XNO0iistheexperimental NOconversion ratio at aparticular residence time.Therefore,the mean-square errorσ2is a function related to kinetic constants only.By minimizing the functionσ2,the optimum kinetic rate constants can be obtained.

Fig.2.Relationship betw een reaction rateconstant 2k and mean-squareerror(variation in O2 concentration is ignored)(Mechanism(i-1)).

The NOconversion ratio XNOcan be expressed as follow s:

where[NO]0is the initial concentration.

The mean-square errorσ2can be expressed as Eq.(29).

Kinetic rate constants are calculated using the least-square method[26]and line search method.The least-square method is a standard approach in regression analysisfor the approximate solution of overdetermined systems,i.e.,sets of equations in w hich there are more equations than unknow ns.“Least squares”means that the overall solution minimizes the sum of squares of residuals made in the results of each single equation.To avoid the effect of different sample sizes,mean-square error w as used as the optimization criterion instead of the sum of squared errors.

The calculation of implicit functions during the process is based on thetrust-region-dogleg method.Thecalculation involvesthe regression of two unknown constants k and K.The step size for these two parameters is 0.0001.The mean-square errorσ2can be calculated by substituting attempted k and K values into expressions describing NO concentration against time given in Section 3 and NOconversion ratio show n in Eq.(28).A tw o-dimensional region can be de fi ned by k and K values.The optimum values can be calculated based on the minimum mean-square errorσ2.

5.Results and Discussion

Based on the reaction mechanism(i-1),the relationship betw een mean-square error and k is show n in Fig.2.As k increases,the mean-square errorσ2fi rst decreases and then increases.The smallest σ2min1=0.0096 and optimal k=0.0009 w ere obtained.When the temperature w as T=298 K,k=0.0012 and k=0.0013 w ere obtained from the equations k=1.2×103exp(530/T)/(TR)2and k=0.5exp(1468/T-10.9043),respectively.The regressed NO oxidation rate constant is low er than that calculated using the reported formulas.

Fig.3.Residual betw een the experimental and simulated values w hen the O2 concentration is ignored(mechanism(i-1)).(a):residual at different pressures,(b):residual at different residence times,and(c):residual at different NOinitial concentrations.

Fig.4.Relationship betw een reaction rate constant 2k1 and mean-square error(w ith variation in O2 concentration).

Fig.3(a),(b),and(c)show the residuals of NOconversion ratio betw een the experimental and calculated values against pressure,residence time,and initial NO concentration,respectively.Residual represents the actual value minus the simulated value.

Fig.5.Residual between the experimental and simulated values with variation in O2 concentration(mechanism(i-2)).5(a):residual at different pressures,5(b):residual at different residence times,5(c):residual at different NOinitial concentrations.

Fig.3(a)show sthat when the pressure is low,the residual isdistributed on both sidesof Xaxis.When thepressureis0.1 MPa,theactual NO conversion ratio is slightly higher than the simulated conversion ratio.As the pressure increases,the difference betw een the actual and simulated NOconversions gradually decreases.When the pressure is above 1 MPa,all the simulated NOconversion ratiosare higher than the actual ratios.Therefore,the effect of reverse reaction for NOoxidation should be considered at a high pressure.

Fig.3(b)show s the effect of reverse reaction for NOoxidation more directly.When the residence time is short,the actual experimental valuesarehigher than thesimulated values.Theresidual wasused to indicate the difference betw een the simulated and actual values.When the residence time is short,the NO conversion ratio is low,and the NO2concentration is not high either.Thus,the reverse reaction for NO oxidation is not obvious.When the residence time is long,the actual NOconversion is far below the simulated NOconversion.This is probably caused by the signi fi cant reverse reaction for NOoxidation resulting from the high NO2concentration at long residence times.

Fig.3(c)showsthe effect of NOconcentration on the residual of NO conversion ratio.Different initial concentrationsdid not signi fi cantly affect the residual of NOconversion ratio.The residual is alw ays distributed on both sides of X axis.When the initial concentration is lower,the error is generally higher.This is probably because the measurement error is ampli fi ed at low er NOconcentrations.

To understand the changes in O2concentration on NO conversion,the changes in O2concentration during the reaction w ere considered.

Based on mechanism(i-2),the changes in the mean-square error σ2min2w ith k is show n in Fig.4.Considering the changes in O2concentration during thereaction,theminimum mean-square errorσ2min2and the related kinetic rateconstant k(k=0.0009,σ2min2=0.0096)arethe same compared w ith ignoring changesin O2concentration(mechanism(i-1)).This shows that when the O2concentration(3%-5%)far exceeds the NOconcentration(＜2134 μl·L-1),the changes in O2concentration on NOconversion ratio is negligible.

Fig.5 shows the residual of NOconversion ratio against pressure,residence time,and initial concentration based on mechanism(i-2).The results shown in Figs.5 and 3 are similar,indicating that the changes in O2concentration did not signi fi cantly affect the simulation results.The predicted NO concentrations considering the variation in O2concentration are also the same asin the case of ignoring the change in O2concentration.According to the above calculation,the changes in O2concentration can be ignored to simplify thecalculation in thesubsequent calculation.The O2concentration[O2]is replaced with the initial O2concentration[O2]0(Fig.5).

For mechanism(ii),the predicted NO concentration is the same because the expression for NO oxidation rate is the same as mechanism(i-1).

Fig.6 show s the relationship betw een tw o parameters(k-4/k5and 1/(k4[O2]))and mean-square errorσ2for mechanism(iii).When k-4/k5is a fi xed value,as 1/(k4[O2])increases,the mean-square errorσ2fi rst decreases and then increases.Whenσ2approaches the minimum,the change in k-4/k5slightly affectsσ2.The minimumσ2min3=0.0096 can be obtained w ith k-4/k5=9.0365 and 1/(k4[O2])=0.0161.

Fig.7 show s the residual of NOconversion ratio calculated from the reaction mechanism(iii).The results calculated based on mechanisms(iii)and(i-1)are also similar.

By comparing Figs.3,5,and 7,the simulated values calculated by three mechanisms(i-1,i-2,and iii)w ere found to be consistent.The mean-square errorsσ2min1,σ2min2,andσ2min3obtained through two reaction pathw ays are also consistent.Therefore,the reaction mechanisms(i-1,i-2),(ii),and(iii)have no obvious effect on the prediction of NO conversion.In terms of controlling steps,the second step is the rate-controlling step for NO oxidation for both mechanisms(ii)and(iii),but it does not consider the reverse reaction for NO oxidation.Therefore,the estimates for NO conversion ratio are still higher than the experimental values at a high pressure by using the three reaction mechanisms.

Because the three mechanisms do not affect the calculated meansquare errorsfor NOconversion ratio,thereversereaction for NOoxidation should be considered.

Fig.8 show sthe mean-squareerror for NOconversion ratio based on the reaction mechanism(i-3).In the calculation,the values of k6and K w ere selected in the range 0-1.The optimal k=0.0013 and K=0.0017 were obtained w hen σ2is the minimum.Here,σ2min4is 0.0055.Notably,theforward reaction rate constant for NOoxidation obtained at a high pressure is consistent with the rate constant for NOoxidation at atmospheric pressure as reported by previousstudies.When the NO2concentration is low,the effect of reverse reaction rate on NO oxidation is negligible.The value ofσ2min4is less than that ofσ2min1.This also indicates that the predicted NOconversion for the entire pressure range is more realistic w hen the reverse reaction for NOoxidation is incorporated.

The residual for NO conversion ratio based on mechanism(i-3)is shown in Fig.9.The residual is distributed more evenly on both sides of Xaxisthan that obtained by other mechanisms.In addition,the absolute values of maximum and minimum of residuals are both less than these predicted values w ithout considering the reversible reaction for NOoxidation.The residuals simulated by the forw ard and reverse reaction rate constants are also smaller than these values simulated by the overall reaction rate constant.As show n in Fig.8,the simulated results agree better w ith the experimental results regardless of the length of residence time.

Fig.9 shows some unusual points w ith large errors.This can be attributed to different experimental systems and intermittent measurements,resulting in a large error.Pearson correlation coef fi cient r[27]wasused to evaluatethelinearity of simulated and experimentalvalues.

w here Cov is covariance;Var is variance.

The range of r(XNOi,XNO0i)is between-1 and 1,and the accuracy of fi t isthe highest w hen r reaches1.The r values for different expressions and different mechanisms(i-1,i-2,iii,i-3,and Chemkin)w ere calculated as r1=0.968,r2=0.968,r3=0.968,r4=0.972,and r5=0.971,respectively.

Fig.6.Relationship between two parameters(k-4/k5 and 1/(k4[O2]))and mean-square errorσ2 based on mechanism(iii).

Fig.7.Residual betw een the experimental and simulated values base on mechanism(iii).7(a):residual at different pressures,7(b):residual at different residence times,7(c):residual at different NOinitial concentrations.

Supposing that XNOifollow sanormal distribution XNOi～ N(XNO0i,σ2),the con fi dence interval can be calculated using Eq.(31).

According to the three-sigma rule[28,29],in a normal distribution,68.27%,95.45%,and 99.73%of the values lie within one,two,and three standard deviations of the mean,respectively[30].When the deviation from the measured values exceeds tw ice the standard deviation,this value isknow n asan outlier.For n=2 based on Eq.(31),thecon fi dence intervals for different mechanisms(i-1,i-2,iii,i-3,and Chemkin)can be calculated as X1∈(XNO0i± 0.19566),X2∈(XNO0i± 0.19566),X3∈(XNO0i± 0.19566),X4∈(XNO0i± 0.14861),and X5∈(XNO0i±0.20431),respectively.The residual plots show that the number of outliers is less than 5%of total datapoints.Therefore,the regressed equations and data choices are convincing.

Fig.8.Relationship between mean-square error and forward and reverse reaction rate constants(k and K)based on mechanism(i-3).

Fig.9.Residual between the experimental and simulated values when considering the reverse reaction mechanism(i-3).9(a):residual at different pressures,9(b):residual at different residence times,9(c):residual at different NO initial concentrations.

When the reverse reaction is not considered,the correlation coef ficients r obtained by different mechanisms(i-1,i-2,and iii)are the same.The highest correlation coef fi cient w as obtained w hen the reverse reaction w asconsidered(mechanism(i-3)).The correlation coeffi cient based on Chemkin fi tting is higher than that of fi tting w ithout considering the reverse reaction,but the con fi dence interval is the highest among the fi ve methods.Therefore,the regressed equation based on mechanism(i-3)is the optimum equation considering the highest correlation coef fi cient r and low est con fi dence interval±2σ.

6.Elementary Reactions Analysis

To determine which of thethree mechanismsismoreapplicable,the N2/NO/NO2/O2reaction system w as constructed using Chemkin-pro softw are,and the NO conversion w as simulated in the pressure range 1-30 bar in a w ell stirred reactor simulator.The relevant elementary reactions are show n in data in brief(Table 2).The kinetic parameters for these elementary reactions were taken from the National Institute of Standards and Technology.Among these reactions,R1-24 can be used to simulate NO conversion w ithout H2O vapor involved in the gas phase,w hereas R1-R113 can be used to simulate NOconversion w ith H2Oin the gas phase.

Fig.10 show s the residual for NOconversion ratio against pressure,residence time,and initial concentration.By comparing Figs.10 and 3,the residual under the same condition was found to be similar.The dominant reaction path is R16(2NO+O2=2NO2)w hose absolute reaction rate is far higher than others.Other elementary reactions did not affect the overall NOoxidation reaction based on the rate of production and sensitivity analyses.The kinetic rate constant for R16 used in the simulation was k=0.0012.Thisvalue is larger than k=0.009 obtained through data regression using mechanism(i-1).Therefore,the simulated NO conversions obtained by elementary reaction mechanisms are higher than those obtained through mechanism(i-1).

Fig.11 showsthat thesensitivity coef fi cientsof NOand NO2changed w ith residencetimeunder acertain condition(pressure:1.5 MPa;initial concentration:500 μl·L-1;no H2Ovapor).A negative value represents the consumption of NO,whereas a positive value represents the generation of NO.The consumption of NOincludes two main paths,R16 and R18(NO+NO2+O2=NO3+NO2).

A NO gas-phase reaction system containing H2Ovapor w as reconstructed,including all R1-113 reactions.Fig.12 showsthat the sensitivity coef fi cient of NO and NO2changed w ith residence time under a certain condition(pressure:1.5 MPa;initial concentration:500 ppm;H2Ovapor(saturated):3.5%;temperature:25°C).The sensitivity coef ficient isslightly different,and theconversion ratio of NOw ith H2Ovapor is consistent w ith that of w ithout H2Ovapor.Additionally,the concentration of NOisbelow 10 μl·L-1w hen the residence time is350 s;therefore,the change in sensitivity coef fi cient slightly affects the change in the absolute reaction rate of NO.

Fig.10.Residual betw een the experimental and simulated values calculated by Chemkin.10(a):residual at different pressures,10(b):residual at different residence times,10(c):residual at different NOinitial concentrations.

Based on the reaction scheme,there isno elemental reaction for NO and H2O,and the direct reaction is betw een NO and OH2,suggesting that the reaction betw een NO and H2O involves radical reactions which normally requireshigh temperature conditionsand are expected to be low at these low temperature conditions.Other important reactions include N2O3,N2O4and N2O5w ith H2O,w hich require secondary reactions and due to the very low concentrations of these species,the reactionsbetw een these nitrogen containing oxides with H2Oare insigni fi cant.This suggests that H2Ovapor does not affect the gas-phase oxidation of NO.How ever,the likely effects are that any HNO3and excess w ater w ill condense at the higher pressures w hen they are formed,resulting in a lowering of gas phase concentration and possibly driving the NOoxidation reaction faster[31].In addition,the experimental observation by Ting et al.[31]that theaddition of H2Oto thishigh pressure NOxsystem,resultsin a lossof gaseous NOx,but alarge amount of HNO3desorbed after depressurizing.This indicates that a physical removal mechanism is possible.How ever,due to the limitation of simulation,condensation of H2Oand HNO3,and physical absorption and desorption during compression process are not part of the reaction scheme.These aspects may need further research.

Fig.13 showstherateof production of NO.Negativevaluesrepresent the consumption rate of NO.The reaction rate of R16 approaches the total reaction rate,whereas the rates of other reactions approach zero.Thisindicates that R16 is the critical elementary reaction.

By analyzing elementary reactions,the termolecular reaction mechanism may be better for NOoxidation.Themain elementary reaction for this process is R16.Other elementary reactions slightly affected the overall reaction.

Fig.11.Sensitivity coef fi cient of NOand NO2 under the following conditions:P=1.5 MPa,[NO]0=500 μl·L-1,no water vapor.

Fig.12.Sensitivity coef fi cient of NOand NO2 under the following conditions:P=1.5 MPa,[NO]0=500 μl·L-1,no water vapor.

Fig.13.Rate of production of NOfor N2/NO/NO2/O2/H2Oreaction system.

Two reactions R15 and R17 w ere also stated by mechanism(iii).In this pre-equilibrium mechanism,NO3is an intermediate,but the rate is not dominating through calculations.Therefore,mechanism(iii)may not conform.For the lack of corresponding(NO)2related kinetic parameters,the pre-equilibrium mechanism(ii)w ith the dimer of NO as an intermediate cannot be veri fi ed by elementary reaction analysis.

With respect to the derived NOoxidation rate formula,the forward and backw ard reaction rates are 3rd order and 2nd order regarding total pressure separately.Thismay explain the positive impact of higher pressure on enhancing the NOoxidation rate.The removal of NO2from gas phase by oxidation in the gas phase or by absorption into liquid phase is a potential pathway to promote NOoxidation reaction.

7.Conclusions

Based on three existing NOoxidation mechanisms,fi rst an expression for NOconversion against residence timew asderived.By minimizing themean-square error for NOconversion ratio,the optimum kinetic rate constant w as obtained.

Without considering the reverse reaction for NOoxidation,similar mean-squareerrorsof NOconversion ratio werecalculated.Considering the reverse reaction for NOoxidation based on the termolecular reaction mechanism,the minimum mean-square error for NOconversion ratio w asobtained.Therefore,theexpression for optimum NOoxidation rate is applicable in the pressure range 0.1-3 MPa.

Detailed elementary reactions for N2/NO/NO2/O2system w ere established to simulate the NOoxidation rate.The sensitivity analysis identi fi ed the critical elementary reaction as 2NO+O2?2NO2.Water vapor does not signi fi cantly affect the NOoxidation rate.However,the simulated NO conversions at a high pressure of 10-30 bar are still higher than the experimental values and similar to those obtained w ith models w ithout considering the reverse reaction for NO oxidation.

Nomenclature

a22k6[O2]-2 K

b24 K[NO]0

Cov covariance

C0constant at t=0

c2-2 K[NO]02

K reverse reaction rate constant,kPa-1·s-1

Kpchemical reaction equilibrium constant,kPa

k overall reaction rate constant,k Pa-2·s-1

k1overall reaction rate constant w ith variation of oxygen con

centration,kPa-2·s-1

k2reaction(5)forw ard reaction rate constant,k Pa-1·s-1

k-2reaction(5)Reverse reaction rate constant,s

k3The reaction rate constant for reaction(6),kPa-1·s-1

k4reaction(8)forw ard reaction rate constant,k Pa-1·s-1

k-4reaction(8)Reverse reaction rate constant,s

k5reaction(9)reaction rate constant,kPa-1·s-1

k6the forw ard reaction rate constant of Eq.(17),kPa-2·s-1

[NO] NOgas concentration during the reaction,kPa

[NO]0NOgas initial concentration,kPa

[NO2] NO2gas concentration during the reaction,kPa

n sample size

[O2] oxygen concentration during the reaction,kPa

[O2]0initial oxygen concentration,kPa

P experimental pressure,MPa

R ideal gas constant 8.314,L·kPa-1·K-1·mol-1

r Pearson correlation coef fi cient

T kelvin temperature,K

t reaction time,s

Var variance

XNONOconversion rate

XNOicalculate conversion ratio

XNO0iexperimental conversion ratio

σ root-mean-square error

σ2mean-square error betw een actual conversion ratio and calculated conversion ratio

Supplementary Material

Supplementary data to thisarticle can be found online at https://doi.org/10.1016/j.cjche.2018.06.017.