Mengke Lu,Yanqiang Tang,Wenyao Chen,Guanghua Ye,Gang Qian,Xuezhi Duan*,Weikang Yuan,Xinggui Zhou

State Key Laboratory of Chemical Engineering,East China University of Science and Technology,Shanghai 200237,China

Keywords:Direct propylene epoxidation with H2/O2Propylene oxide Safe operation Explosion limits estimation Process optimization

ABSTRACT Direct propylene epoxidation with H2and O2,an attractive process to produce propylene oxide(PO),has a potential explosion danger due to the coexistence of falmmable gases(i.e.,C3H6and H2)and oxidizer(i.e.,O2).The unknown explosion limits of the multi-component feed gas mixture make it difficult to optimize the reaction process under safe operation conditions.In this work,a distribution method is proposed and verified to be effective by comparing estimated and experimental explosion limits of more than 200 kinds of flammable gas mixture.Then,it is employed to estimate the explosion limits of the feed gas mixture,some results of which are also validated by the classic Le Chatelier's Rule and flammable resistance method.Based on the estimated explosion limits,process optimization is carried out using commercially high and inherently safe reactant concentrations to enhance reaction performance.The promising results are directly obtained through the interface called gOPT in gPROMS only by using a simple,easy-constructed and mature packed-bed reactor,such as the PO yield of 13.3%,PO selectivity of 85.1%and outlet PO fraction of 1.8%.These results can be rationalized by indepth analyses and discussion about the effects of the decision variables on the operation safety and reaction performance.The insights revealed here could shed new light on the process development of the PO production based on the estimation of the explosion limits of the multi-component feed gas mixture containing flammable gases,inert gas and O2,followed by process optimization.

1.Introduction

Propylene oxide(PO),the third largest propylene derivative,is a versatile chemical intermediate in the chemical industry[1].In consideration of economic and environmental concerns,the direct propylene epoxidation with H2and O2to PO has attracted extensive attention compared to the traditional chlorohydrin and peroxidation processes[2].For this promising process,considerable efforts have been devoted to developing highly active Au catalysts supported on Ti-containing supports[3-16],among which the Au/TS-1 bifunctional catalysts showed higher stable PO formation rate being comparable to that of ethylene oxide in the commercial plant[17].

In addition to the development and modification of the catalysts in a lab scale,the inherent process safety is another very important issue because of the wide explosion limits of C3H6and H2in O2,i.e.,2.0%-59.0%[18]and 4.0%-94.0%[19],respectively.The lack of explosion limits for the feed gas mixture of this process makes it difficult to use commercially high reactant concentration under safe operation conditions.Commonly,a large amount of inert gas(e.g.,70%)like N2is introduced to dilute reactant or very low O2fraction(e.g.,＜4%)is used,aiming to keep catalysts screening/optimization and novel catalytic membrane and porous membrane reactors testing/optimization outside the explosion regions[20-22].However,these strategies usually result in low reaction performance.Therefore,there is an urgent need to obtain the explosion limits of the feed gas mixture and then to perform the process optimization toward a targeted reaction performance.

To our knowledge,there are several reported explosion limits estimation methods[23],which are mainly for three types of gas or gas mixture:i)the empirical correlations method[24],structural group contribution model[25]and molecular-based method[26,27]for single flammable gas;ii)the classic Le Chatelier's rule[28]for gas mixture containing two or more flammable gases;iii)the calculated adiabatic flame temperatures(CAFT)method[29-32],thermal balance method[32,33]and flammable resistance method[34]for gas mixture containing flammable gas with dilutions.Notably,these methods are used to estimate explosion limits in air,and the mixture itself does not contain oxidizer,indicating no explosion danger of the mixture itself.For multicomponent gas mixture containing not only multiple flammable gases and inert gas,but also oxidizer(e.g.,the feed gas mixture in this case:C3H6,H2,N2and O2),the C3H6,H2and N2mixture may explode in O2during the pre-mixing operation.How to estimate its explosion limits in O2and further determine whether the feed gas mixture is explosive or not?Hence,it is necessary to develop an alternative estimation method for this kind of multi-component gas mixture.

The objective of this work is to obtain the explosion limits of the multi-component feed gas mixture,and thus enhance reaction performance under safe operation conditions by process optimization in a simple,mature and easy-constructed packed-bed reactor(PBR).Firstly,a distribution method was proposed and verified to be effective by comparing estimated explosion limits of about 200 kinds of flammable gas mixture to their corresponding experimental ones.Then,it was employed to estimate the explosion limits of the feed gas mixture,which were validated by the classic Le Chatelier's Rule and flammable resistance method.Based on the estimated explosion limits,process optimization was carried out through the interface called gOPT in gPROMS to enhance the reaction performance in the PBR by using commercially high and inherently safe reactant concentrations.Furthermore,the effects of the decision variables on the operation safety and reaction performance were studied and discussed in detail to explain the optimization results.

2.Methods

2.1.Distribution method for estimating explosion limits

The feed gas mixture contains C3H6,H2,N2and O2,and the mixture itself exists explosion danger.During the pre-mixing operation,it is important to evaluate whether the mixture is explosive or not.It is reported that researchers analyzed the gases from mines by removing air first,where O2has a small fraction and diluent remains after removing air[35],while in this work,O2has a considerable fraction in the feed gas mixture and remains after removing air.Herein,a distribution method was proposed to remove the O2firstly and then to obtain the explosion limits of the rest gases in O2,where by checking the level of removed O2fraction,whether the feed gas mixture is explosive or not can be determined.The method is schematically shown in Fig.1,which can guide the safe operation of reactor for the direct propylene epoxidation with H2and O2.

The volume fractions of flammable gas l(l=1,2,…,n),inert gas k and oxidizer were expressed as y0(l),y0(k)and y0(O),respectively,which satisfy Eq.(1).

Firstly,the oxidizer was removed and the rest flammable and inert gas mixture was normalized to 100%,where the problem was transferred into estimation of explosion limits of the normalized gas mixture in the oxidizer.The volume fractions of the normalized flammable gas l(l=1,2,…,n)and inert gas k were expressed as yN(l)and yN(k),respectively:

It is assumed that the explosion transforms the flammable and inert gases and oxidizer into products containing generated CO2and H2O with inert gas and/or oxidizer(e.g.,CO2,H2O,N2and/or O2in this case),and then the energy from explosion adiabatically heats all the products from ambient temperature to critical adiabatic flame temperature[36].Based on the principle of energy conservation,Eq.(5)can be obtained by taking the products as a one:

Fig.1.Schematic diagram of the distribution method.

where nf,np,Δhmix,Cpand ΔT are moles of flammable gases and products,combustion heat of flammable gases per mole,constant heat capacity of the products and adiabatic temperature change.For lower explosion limits,the moles of flammable gases nfis calculated by:

where n0is moles of gas mixture before explosion.The Eq.(5)for lower explosion limits of normalized gas mixture(LELmix)can be transformed into Eq.(7)by assuming that the number of moles is constant during the explosion[36]:

Then,a distribution was carried out for the normalized gas mixture,which was divided into n parts and each part contains one kind of flammable gas and inert gas,as also illustrated in Fig.1.Similarly,energy from explosion of each part of divided gas mixture(yN(i)and yN(k)i)was used to heat the products of Pi(i.e.,a part of all the products P),where Eq.(8)can be obtained:

where Δhiis combustion heat of flammable gas i per mole and LELiis lower explosion limit of the flammable gas i and inert gas mixture,which can be determined in explosion diagram of flammable gas i and inert gas mixture,as shown in Section 3.1.Meanwhile,the total explosion heat was equal to the sum of each part of explosion heat,as expressed by Eq.(9):

Combining Eqs.(4),(7),(8)and(9),the lower explosion limits of normalized gas mixture(LELmix)can be obtained:

Similarly,the upper explosion limits of normalized gas mixture(UELmix)can be calculated by:

where UELiwas upper explosion limit of the flammable gas i and inert gas mixture,which can be also determined in explosion diagram of flammable gas i and inert gas mixture.Herein,the problem of explosion limits of normalized gas mixture is transferred into the fractions of each part of the divided mixture(i.e.,yN(k)iand yN(i))and their explosion limits(i.e.,LELiand UELi),which are given and can be found in reported data,respectively.It should be noted that each part of divided gas mixture should be ignitable,or their explosion limits would not exist and thus this method is unavailable.

Subsequently,the oxidizer fractions at the lower and upper boundaries can be calculated by Eqs.(12)and(13),respectively,

The difference between the initial oxidizer fraction(y0(O))of the gas mixture and the oxidizer fraction at the LELmixor UELmixcould be calculated by Eqs.(14)and(15),respectively,

According to the definition of the explosion limits,the gas mixture could be outside the explosion region if the initial fraction of flammable and inert gas mixture is lower than the LELmixor higher than the UELmixas following:

By combining the Eqs.(1),(12)-(15)and the inequality(16),inequality(17)was obtained:

which means that when the initial oxidizer fraction is high or low enough,the gas mixture is too lean and rich to explode,respectively.When Eq.(18)is satisfied,the lower and upper boundaries of flammable gases,inert gas and oxidizer mixture could be determined.

2.2.Reactor modeling

To describe the direct propylene epoxidation with H2and O2,a onedimensional packed-bed reactor(PBR)model was built.The mass,energy and momentum balances of the model were derived based on the following assumptions:

i)Ideal gas behavior was used.

ii)Axial mass dispersion was negligible(axial mass Peclet number estimated to be of order 1000[37]).

iii)Axial heat dispersion was negligible(axial heat Peclet number?1.0[37]).

iv)The catalyst particle size was small enough where both intraparticle mass and heat transfer limitations and external mass and heat transfer limitations from the gas bulk to the catalyst surface could be neglected[38].

The mass balance for species i was determined by:

with the boundary conditions:

where Ci(mol·m-3)is the concentration of species i;u0(m·s-1)is the superficial velocity;ρb(kg·m-3)is the bulk density of catalyst bed and r(mol·kg·s-1)is the reaction rate.

The energy balance equation in the PBR was shown:

with the boundary conditions:

where ρf(kg·m-3)is the density of fluid gas;Cp(kJ·mol-1·K-1)is the specific heat of fluid gas;T(K)is the reaction temperature;ΔH(kJ·mol-1)is the reaction heat;hw(W·m-2·K-1)is the wall heat transfer coefficients;dt(m)is the reactor diameter and Tw(K)is the wall temperature.

The reaction kinetic expressions for the propylene epoxidation with O2and H2are taken from reported data[11],which involve three main reactions,i.e.,the PO,CO2and H2O formation.The relevant kinetic rate equations are summarized in Table 1.

Moreover,the wall heat transfer coefficient(hw)(W·m-2·K-1)in the energy balance equation includes stagnant and turbulent contributions(i.e.,h0and hG),and the expressions for calculation of hwwere given by[39]:

The stagnant contribution was calculated bywhile the turbulent contribution was calculated by hG=where Re is the Reynolds number.

The other correlations of physical properties including the heat capacity of component i(CP,i),mixture heat capacity(CP),conductivity of component i(λi),mixture gas conductivity(λg),viscosity of component i(μi)and mixture viscosity(μ)can be referred to the work of Lu[40].The reactor structural parameters,catalyst properties and inlet temperature and pressure are listed in Table 2.

2.3.Process optimization

For the direct propylene epoxidation with H2and O2,PO yield is one of the important goals,which was chosen as the optimization objective.Meanwhile,the inlet partial pressures of C3H6(Pin(C3H6)),H2(Pin(H2))and O2(Pin(O2)),as well as the inlet superficial velocity(u0)were considered as the decision variables,and their lower and upper bounds of these decision variables were chosen as following:

i)The commonly used total inlet pressure of the process was 100 kPa.To avoid the explosion danger,the feed gas mixture was often made up of 10 vol% each of O2,H2,and C3H6with 70 vol% of inert gas,which inevitably leads to a low reaction performance.Therefore,the lower bounds for inlet partial pressures of C3H6,H2and O2were all set to be 10 kPa,while the upper bounds to be 100 kPa.Thus,the Pin(C3H6),Pin(H2)and Pin(O2)should satisfy inequality(22)and Eq.(23).

Table 2 Reactor structural parameters,catalyst properties and operation conditions

ii)The lower and upper bounds of superficial velocity were 0.01 and 1,respectively.

The optimization problem should satisfy several constraints,as following:

i)To avoid the explosion danger of feed gas mixture,the compositions of the feed gas should be kept outside the explosion region,which means that the inequality(17)should be satisfied.

ii)The kinetics used in the optimization are obtained below 463 K[11],thus the hotspot temperature(Th)in the reactor should be smaller than 463 K.

iii)To guarantee the commercially potential outlet PO fraction(yPO),the lower bound of outlet PO fraction was set to 1.0%,which is the lower bound for the outlet ethylene oxide fraction in gas phase epoxidation of ethylene[41].

iv)To guarantee the relatively high PO selectivity(SPO),its lower bound was set to 85%.

Table 1 Kinetic rate equations for the direct propylene epoxidation with O2and H2

2.4.Numerical solution

The reactor models,represented by differential algebraic equations(DAEs),were implemented in gPROMs,which was a general purpose software for modeling,simulation and optimization[42].The spatial variables in the DAEs were automatically discretized according to the user-provided options by using the built-in package of gPROMS,and the algorithm for solving the DAEs was based on a backward differentiation formula type method.Moreover,the optimization problem was also solved by the interface called gOPT in gPROMS.

2.5.Reaction performance

The reaction performance mainly includes C3H6conversion(x),PO selectivity(SPO),H2efficiency(EH),outlet PO fraction(yPO)and PO yield(Yield),which were calculated by the following equations,respectively:

3.Results and Discussion

3.1.Validation of the distribution method and estimation of explosion limits of feed gas mixture

According to the Eqs.(10)and(11)in the distribution method,the fraction of N2(yN(k)i)distributed to each part of flammable gas i is uncertain,and would it influence the estimation results?To address this issue,the effect of yN(k)ion estimation results was studied,which are shown in Table 3.Clearly,the different distributions of N2lead to slight change of estimated lower and upper explosion limits of the mixture,which is because the Eqs.(10)and(11)are always satisfied based on the energy balance regardless of the N2distribution.For simplicity,a proportional distribution can be used for N2like the third distribution strategy in Table 3,which can be described by Eqs.(33)and(34):

Moreover,the estimated results show excellent agreement with the experimental ones,indicating the reasonability of the estimation method.

Then,the proportional distribution method was employed for estimating explosion limits of about 200 combinations of CH4,C2H4,C3H6,C3H8or H2with different levels of N2[43-45],and about 20 combinations of CH4,C2H4or H2with different levels of CO2[46].The estimated results were then plotted against the corresponding experimental ones with confidence bound,as shown in Fig.2a,where the red dots is for N2as diluent and black dots for CO2as diluent.It can be found that the plot appears to be straight line with a slope of 1.0 and almost all the relative errors between estimated and experimental data are within 10%,further indicating that the distribution method can be reasonable to estimate explosion limits of the multi-flammable gases with one inert gas and applicable to different types of diluents.Notably,the detailed basic data,estimated and experimental explosion limits are summarized in Supplementary Materials.

Subsequently,the proportional distribution method was employed to estimate the explosion limits of the C3H6,H2and N2gas mixture.For the direct propylene epoxidation with H2and O2,the commonly used reaction temperature and pressure are 200 °C and 101.325 kPa,respectively.Under these conditions,the explosion limits of C3H6/N2mixture in O2and H2/N2mixture in O2are illustrated in Fig.2b,which are obtained from the literatures[18,19].Through the removal of O2,followed by the normalization and distribution of C3H6,H2and N2,the ratios of yN(N2)/[yN(C3H6)+yN(H2)]can be obtained and thus the corresponding Liand Uican be determined in Fig.2b.According to the Eq.(15)(ΔLO=0 and ΔUO=0),the initial O2fraction was made to be equal to the O2fraction at explosion limits.Then,the corresponding upper explosion limits were obtained and shown in Fig.2c,while lower explosion limits can not be obtained because the ΔLOvalues are always bigger than 0(i.e.,y0(O)＞yO_LELmix)for the current case.

Then,eight different compositions of C3H6,H2,N2and O2mixture from the upper explosion limits(Fig.2c)were selected,where the H2/C3H6ratios were 10/90,20/80,30/70,40/60,50/50,60/40,70/30 and 80/20 with each N2/O2ratio being equal to that in air(N2/O2=0.79/0.21).They were checked by the classic Le Chatelier's Rule,which is an effective method to estimate explosion limits of multiple flammable gases in air and expressed by:

where yiis the volume fraction of the component i,which considers only the flammable species[36];UELiis upper explosion limits of the component i;the UELmixis the upper explosion limit of the multiple flammable gas mixture,respectively.The used UELivalues of the H2and C3H6under 200°C and 101.325 kPa are 15.0%and 84.4%,respectively[18,47].The UELmixof the C3H6and H2mixture in air based on the different H2/C3H6volume ratios were calculated by Eq.(36),and then the air fractions(yair)under the upper explosion limits were calculated by:

Fig.2.(a)Comparison between estimated and experimental explosion limits,red dots for N2as diluent and black dots for CO2as diluent(experimental ones extracted/obtained from literatures 40-42);(b)Explosion limits of C3H6/N2mixture in O2and H2/N2mixture in O2under 101.325 kPa and 200°C(from experimental data[18,19]);(c)upper explosion limits of C3H6,H2,O2and N2mixture estimated by the proportional distribution method;(d)comparison between estimated explosion limits obtained by proportional distribution method with those obtained by Le Chatelier's Rule and flammable resistance method.

Thus,the volume fractions of C3H6,H2,N2and O2can be expressed as yC3H6UELmix/(yH2+yC3H6),yH2UELmix/(yH2+yC3H6),0.79yairand 0.21yair,respectively.These upper explosion limits estimated by the Le Chatelier's Rule were also illustrated in Fig.2d.Clearly,the points obtained by the Le Chatelier's Rule agree very well with those by the proportional distribution method.This results could imply the reasonability of the explosion limits of the multi-feed gas mixture estimated by the proportional distribution method.

Moreover,the flammable resistance method,a power tool to estimate explosion limits of complex gas mixture(i.e.,multiple flammable gases and inert gases)in air based on the principle of energy conservation[34],was also used to double check these points.The equations to calculate explosion limits and the parameters used in the calculation,such as the dimensionless heating potential of oxygen based on air(H0),the dimensionless quenching potential of diluent based on air(QD),and the dimensionless quenching potential of fuel based on air(QF),are listed in the Supplementary Materials,and the results are shown in Fig.2d.Obviously,the data obtained by the flammable resistance method are also in excellent agreement with those by the proportional distribution method,further indicating the reliability of the distribution method.

3.2.Process optimization

A one-dimensional PBR model was built in gPROMS to describe the direct epoxidation of propylene with H2and O2.At first,the C3H6conversions from the simulations were compared to those from the experiments under 18 different feed conditions for the validation of the PBR model[11],and the results are shown in Fig.3.The average relative error is found to be 4.43%,indicating that the simulation data are in good agreement with the experimental data,and thus the PBR model is reasonable.

Then,the interface called gOPT in gPROMS was used to optimize the reaction performance under safe operation conditions according to the estimated explosion limits in.This can directly give rise to optimal operation conditions(Table 4),where the initial guesses used for the decision variables are also listed in Table 4 and the as-obtained values of the constraints are showed in Table 5.It is found that the ΔUO2is lower than 0,implying that the feed gas mixture is outside the explosion region.The outlet PO fraction is 1.8%,which could be promising for the practical application according to the outlet fraction of ethylene oxide in commercial plants(i.e.,1.0%-3.0%)[41].

Fig.3.A comparison between C3H6conversions from simulations(▲)and those from experiments(●)under 18 different feed conditions.(Experiment data from the work of Oyama et al.[11]).

Table 4 Initial guesses,lower and upper bounds,and the optimal values of decision variables

Table 5 Values of constraints under optimal operation conditions

Moreover,the hotspot temperature is 462.98 K,which is slightly lower than the highest temperature(i.e.,463.00 K)for obtaining the used reaction kinetics,indicating the reliability of the optimization.The PO selectivity is 85.1%,which is slightly higher than the lower bound.The above results demonstrate that all the constraints are satisfied under the optimal operation conditions.In addition,the optimization objective,i.e.,the PO yield,of 13.3%is achieved,which is close to that(i.e.,14.7%)obtained by using microporous inert membrane packed-bed reactor in our previous work[40].Notably,this good reaction performance can be obtained in the simple,easily constructed and mature packed-bed reactor only by optimizing reaction conditions under safe operation region according to our estimated explosion limits.

3.3.Effect of superficial velocity

To understand the above optimization results,simulations were carried out to study the effects of the decision variables on the operation safety and reaction performance followed by detailed discussions.In fact,the direct epoxidation of propylene with H2and O2process involves some parallel and consecutive reactions,where the intermediate product PO easily undergoes side reactions of isomerization,cracking and over-oxidation[48].To achieve the high PO yield,the optimization of the reaction conditions is of crucial importance.Along this line,the effects of the superficial velocity were firstly studied with other conditions fixed,and the results are shown in Fig.4.It can be clearly seen in Fig.4a that the increase in the superficial velocity gives rise to the same ΔUO2values due to the unchanged composition of the feed gas mixture,and the similar hotspot temperatures(462.8-463.2 K)because of the slightly changed wall heat transfer coefficient(hw)under the tested superficial velocities.Moreover,there are decreased C3H6conversions but increased PO selectivities with the superficial velocity,which are most likely due to the increased space velocity and the decreased residence time leading to suppressed PO further conversion.

As shown in Fig.4b,the increase in the superficial velocity results in the decreased H2efficiency,PO outlet fraction and PO yield.As mentioned in Eq.(33),the H2efficiency can be expressed by the ratio of the PO and H2O formation rates being highly sensitive to the H2concentration.Fig.5 shows the H2concentration profiles along the reactor length.Clearly,increasing the superficial velocity leads to the increase in the H2concentration,which would lead to the decreased H2efficiency because of the higher reaction order of H2for the H2O formation than the PO formation(i.e.,0.67 and 0.54,respectively).Moreover,the decreased PO outlet fraction and PO yield depend on the degree in the effects of the superficial velocity on the PO selectivity against the C3H6conversion.Based on the above analyses,the optimal superficial velocity is determined to be 0.20 m·s-1and the corresponding PO yield to be 13.3%.

Fig.4.Effects of the superficial velocity on(a)the ΔUO2values,hotspot temperatures,PO selectivity and C3H6conversion;(b)the H2efficiency,PO outlet fraction and PO yield.Simulation conditions:Pin=100.0 kPa,Pin(C3H6)=12.34 kPa,Pin(H2)=19.23 kPa,Pin(O2)=12.57 kPa,Tin=443 K.

Fig.5.Effects of the superficial velocity on the H2concentration(CH2)along the reactor length.

3.4.Effects of inlet O2partial pressure

The inlet O2partial pressure(Pin(O2))influences not only the operation safety,but also the reaction performance.Effects of the inlet O2partial pressure were investigated with other conditions fixed,and the results are shown in Fig.6.It is found in Fig.6a that the increase in the inlet O2partial pressure leads to the increased ΔUO2,indicating the higher explosion danger of the feed gas mixture containing more O2.Meanwhile,no obvious change in the hotspot temperature is observed under the tested inlet O2partial pressures.Moreover,there are increased C3H6conversions but decreased PO selectivities with the inlet O2partial pressure,which could be due to the increased PO formation and over-oxidation rates according to the kinetics equations.

As shown in Fig.6b,the increase in the inlet O2partial pressure results in the increased H2efficiency,because the high O2concentration gives rise to higher PO formation rate than H2O formation rate.Moreover,the inlet O2partial pressure leads to higher PO outlet fraction and PO yield,depending on the degree in the effects of the inlet O2partial pressure on the PO selectivity against the C3H6conversion.To ensure the safety operation(ΔUO2≤0),reasonability of the optimization(Th≤463 K)and high reaction performance(SPO≥85%and yPO≥1.0%),the optimal O2inlet partial pressure is determined to be 12.57 kPa.

3.5.Effects of inlet C3H6and H2partial pressures

In addition to the O2concentration,the C3H6and H2concentrations are also important factors for the operation safety and reaction performance.The effects of the inlet C3H6and H2partial pressures were further investigated with other decision variables fixed.As shown in Fig.7a,the increase in the inlet C3H6partial pressure and/or the decrease in the inlet H2partial pressure lead to the decreased ΔUO2because of the wider explosion limits of H2than C3H6,but the increased hotspot temperature due to the higher reactant concentrations.Moreover,the high inlet H2partial pressure gives rise to the high C3H6conversion,but the low PO selectivity and H2efficiency,while the high inlet C3H6partial pressure leads to the high PO selectivity and H2efficiency,but the low C3H6conversion(Figs.7a and 7b).These results can be rationalized by analyzing the C3H6and H2concentrations,hotspot temperatures and the reaction kinetics.

Fig.7b also shows that the high inlet H2and/or C3H6partial pressure results in high PO outlet fraction and PO yield.To determine the maximum PO yield and the optimal values for the inlet C3H6and H2partial pressures,the contours of the four constraints(i.e.,ΔUO2=0,Th=463 K,SPO=85%and=1.0%)were drawn,as shown in Figs.7a and 7b.The direction of the arrows show the regions where the constraints are satisfied.It is noted that there is no contour for the outlet PO fraction(yPO)because the yPOvalues are higher than 1.0%in the given ranges of the inlet C3H6and H2partial pressures.Furthermore,the obtained contours were projected onto a plane,as shown in Fig.8,in which the coordinates are the inlet C3H6and H2partial pressures.It is found that when the inlet C3H6and H2partial pressures are in the shaded area,the requirements of the constraints can be met.By projecting the contours of the PO yield on the plane,the maximum PO yield(13.3%)can be determined at the intersection(the green point)of the contours of the ΔUO2values and hotspot temperatures,where the inlet C3H6and H2partial pressures are around 12.34 and 19.23 kPa,respectively.

Fig.6.Effects of the inlet O2partial pressure on(a)the ΔUO2values,hotspot temperatures,PO selectivity and C3H6conversion;(b)the H2efficiency,PO outlet fraction and PO yield.Simulation conditions:u0=0.2 m·s-1,Pin=100.0 kPa,Pin(C3H6)=12.34 kPa,Pin(H2)=19.23 kPa,Tin=443 K.

Fig.7.Effects of the inlet C3H6and H2partial pressures on(a)ΔUO2values,hotspot temperatures,PO selectivity and C3H6conversion,(b)H2efficiency,PO outlet fraction and PO yield.Simulation conditions:u0=0.2 m·s-1,Pin=100.0 kPa,Pin(O2)=12.57 kPa,Tin=443 K.

Fig.8.Contours of ΔUO2value,hotspot temperature,PO selectivity and PO yield against inlet C3H6and H2partial pressures.

4.Conclusions

In summary,we proposed a distribution method to estimate the explosion limits of multi-component feed gas mixture.The method was verified to be effective by comparing estimated and experimental explosion limits of more than 200 combinations of CH4,C2H4,C3H6,C3H8and H2with different levels of N2or CO2.Then,it was employed to estimate the explosion limits of the feed gas mixture of direct propylene epoxidation,some results with the N2/O2ratio of 0.79/0.21 were validated by the classic Le Chatelier's Rule and the flammable resistance method.Based on the estimated explosion limits,process optimization was then carried out through the interface called gOPT in gPROMS to enhance the reaction performance by using commercially high reactant concentrations under safe operation conditions.The promising reaction performance was obtained only by using a simple,easy-constructed and mature packed-bed reactor,such as the PO yield of 13.3%,PO selectivity of 85.1%and outlet PO fraction of 1.8%,which were comparable to those obtained in our reported membrane reactor.These results were explained by further studies about the effects of decision variables on the operation safety and reaction performance.The insights revealed here could shed new light on the process development of PO production based on the estimation of the explosion limits of the multi-component feed gas mixture containing flammable gases,inert gas and O2,followed by process optimization.

Nomenclature

Ciconcentration of component i,mol m-3

Cpspecific heat of fluid,kJ·mol-1·K-1

dpparticle size of catalysts,m

EHH2efficiency

L reactor length,m

LEL lower explosion limit,%

n mole number of component

Pininlet pressure,kPa

R radius of reactor,m

Rgideal gas constant,J·mol-1·K-1

rijreaction rate of component i in reaction j,mol·kg-1·s-1

SPOPO selectivity

T temperature,K

Tininlet temperature,K

t time,s

UEL upper explosion limit,%

u0superficial velocity,m·s-1

x C3H6conversion,%

y volume fraction,%

yPOoutlet PO fraction,%

z axial coordinate,m

ΔHjreaction enthalpy of reaction j,kJ·mol-1

ΔLO2difference between original O2fraction of feed gas mixture and O2fraction at LELs

ΔUO2difference between original O2fraction of feed gas mixture and O2fraction at UELs

ε void fraction of catalyst bed

μffluid viscosity,Pa·s

ρbcatalyst bulk density,kg·m-3

ρffluid density,kg·m-3

Subscripts

f fluid

i component index

j reaction index

k inert gas index

l flammable gas index

N normalized gas mixture

mix gas mixture

w wall

0 original gas mixture

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2019.01.015.