Xiaofei Qin ,Sen Lei ,Xubin Zhang, *,Chen Cao ,Feng Xin, *,Honglin Chen ,Xiaoming Zhang,Yachen Yin,Guilian Wu

1 School of Chemical Engineering and Technology,Tianjin University,Tianjin 300350,China

2 Chengdu Institute of Organic Chemistry,Chinese Academy of Sciences,Chengdu 610041,China

Keywords:Fuel additive Polyoxymethylene dimethyl ethers Kinetics HZSM-5

ABSTRACT Polyoxymethylene dimethyl ethers(CH3-O-(CH2O)n-CH3,PODEn,n ＞1)can be added to diesel to reduce air pollution caused by incomplete combustion.Driven by this need,a cost-effective and efficient synthetic route is presented and investigated by this work for the production of PODEn,which are formed from methylal and trioxane with low water content (<10 %(mass)) over HZSM-5 catalyst in a batch slurry autoclave at the temperature from 353.15 K to 393.15 K.The reaction rate laws including the PODEn and byproducts of polyoxymethylene hemiformals(HFn),polyoxymethylene glycols(MG),methanol(MeOH)and methyl formate(MF)are developed.The rate constants of propagation step(k6)and depolymerization step(k−6)are assumed independent on polymerization degree of PODEn.The rate of reaction is proportional to the content of the catalyst(Wcat) for the catalytic reaction within the scope of the study.All kinetic parameters were estimated by combining genetic algorithm and least square regression to fit experimental data well.This work is valuable for process optimization and reactor design.

1.Introduction

Diesel,as a major transportation fuel,is widely used in diesel engines to provide power which is much more efficient than spark-ignition engines.But incomplete combustion of diesel is a significant cause of serious air pollution.And regulations to control air pollution and alleviate climate change are becoming increasingly stringent across the world in recent years [1,2].To ameliorate this problem,polyoxymethylene dimethyl ethers (CH3-O-(CH2-O)n-CH3,n ＞1) is proposed to be blended with diesel fuel to reduce soot particles formation,unburned hydrocarbons and carbon monoxide emissions during combustion[3,4].

PODEnare oligomers with a different number of CH2O units and two ending groups of --O--CH3(methoxyl) and --CH3(methyl).The molecule properties are various with the different n.It is worth noting that the molecule with a degree of polymerization of 3–5,among the PODEnoligomers,are the most appropriate diesel additives in terms of reducing emissions and without any changing of the engine infrastructure[5,6].In addition to this,PODE3–5can be used in polymer recycling,polymer welding,and cleaning applications as a solvent[7].

The structure of PODEndetermines that its synthesis requires two different reactants.The one provides the methoxyl group to compose the middle aggregation unit,such as formaldehyde solution,paraformaldehyde(PF)and trioxane(TOX),and another one provides a terminal group which is composing the end of the molecule,such as methanol and methylal (PODE1).In addition to this,there are other ways to synthesize PODEn.For example,Zhang et al.[8] found an efficient catalyst that can catalytically synthesizedimethoxy dimethyl ether from dimethyl ether oxidation and PODE2selectivity was up to 60.0%.

Various routes for the production of PODEnhave been presented in recent years[9–13].Among them,methylal and PF or TOX are adopted as educts to produce PODEnin order to avoid the side reactions caused by the presence of water.Effective though these routes are,they are not economically sound because of the high price of PF or TOX.Now we have developed a process for producing PODEnbased on methanol and formaldehyde solution.Trioxane with little water is a liquid under mild conditions that are producing through a dehydrated membrane from formaldehyde solution.So hereby,an economically feasible alternative route is suggested and studied.In this route,the easy-toget and inexpensive trioxane with little water substitute high-priced paraformaldehyde or trioxane.An additional benefit is that trioxane with little water as a liquid mixture under mild conditions is more efficient by continuous feeding than TOX and PF which is a solid(T<64 °C).The small amount of water could be consumed by reacting with methylal.Consequently,large scale production of PODEnwith low cost and high efficiency is realized.

To study the presented route further,the formation of PODEnfrom this route catalyzed by molecular sieve HZSM-5 was conducted in a batch stirred autoclave at a moderate methylal/trioxane ratios.Various reaction temperatures(80,100 and 120°C)and mass concentration of catalyst(3.5%and 7%)are experimented.Combined with the collected experimental data,a kinetic model is developed in this work which considers most components in the reaction system.

2.Experimental

2.1.Materials

PODE1(GC,98%(mass)) and TOX (GC,99%(mass)) are purchased from Shanghai Aladdin Bio-Chem Technology Co.,LTD.The catalyst of molecular sieve HZSM-5 is prepared by Chengdu Institute of Organic Chemistry,Chinese Academy of Sciences.Deionized water is prepared in the lab by water purification system.PODE2and PODE3are provided by Beijing Dongfang Hongsheng Research Institute and used as standard samples in quantitative analysis of PODEn.

2.2.Apparatus and experimental procedure

The kinetic experiment was performed in a titanium alloy batch autoclave with a volume of 500 ml which is shown in Fig.1.Deionized water,PODE1and TOX were loaded into the reactor,and a mechanical agitator with the double stirring paddle was used to stir the reaction mixture.The agitation speed was set at 300 r·min−1in the premixing stage.After being sealed,the autoclave was purged 5 times by a nitrogen cylinder connecting to a pressure regulator and pressurized to 0.25 MPa.After that,the up-temperature procedure was started,the temperature and pressure were monitored.Once the temperature reached the set value,the catalyst was pressed into the reactor by the pressure difference between autoclave and pressure regulator connecting to a nitrogen cylinder.The pressure was adjusted to the range of 1.0–1.1 MPa reducing the content of reactant in the gas phase at the same time.Reactions were monitored by taking samples after the addition of the catalyst (t=0 min) during the whole reaction.The agitation speed was increased to 600 r·min−1in the reaction,and it is necessary to eliminate the external diffusion effect.Samples of the liquid phase were taken for analysis with a riser pipe whose end in the reactor was capped with a metallic filter to prevent the loss of catalyst.After each sampling,the pressure of autoclave was raised to 1.0–1.1 MPa through the N2cylinder connecting to a pressure regulator in time.Sampling was done every 10 or 20 min.When the reaction is complete,the remaining catalyst was collected and dried.The mass difference of catalyst between start and end was less than 0.5%.

2.3.Analysis

The mass fractions of MeOH,MF,TOX,PODE1,HFn(n<3)and all PODEn(up to n=8) in the liquid samples were analyzed by gas chromatography(GC,Agilent 7890B)equipped with a flame ionization detector(FID).Gas chromatography was also coupled with an Agilent HP-1 column (length:30 m,diameter:0.32 mm,film:0.25 μm).Ethylene glycol diethyl ether(EGDE,GC,99.5%)was used as an internal standard.

Fig.1.Schematic of the experimental set up for kinetic investigation.

The mass correction factors of MeOH,MF,TOX,PODE1and PODE2–3were measured using standard samples.The mass correction factors of PODEnwith n ＞3 were calculated by extrapolation.It is assumed that the mass correction factors of HF2are equal to TOX,due to their identical atom number of C and O.And the mass correction factors of HF1were calculated by effective carbon number method.The mass fraction of water was quantitative analysis by Karl Fischer.The concentration of formaldehyde was determined using titration provided by GB/T 9009-2011.It is worth noting that the overall concentration of formaldehyde (WOFA) contains various forms of formaldehyde,including the formaldehyde combined with water and methanol,and the concentration of monomeric formaldehyde is very low.So,the mixture concentration of formaldehyde(WMFA)could be calculated by Eq.(1).

The total mass fraction for all components was ranged in 98%–103%.Fractions were renormalized to 100%in order to keep consistency of data in the modeling development.

3.Reactions and Kinetic Model

3.1.Chemical reactions

The synthetic reactions of PODEnfrom PODE1,TOX with little water catalyzed by molecular sieve HZSM-5 are quite complicated.In this reaction system,TOX is used as a source of the oxymethylene group.The way that TOX participates in the reaction varies in different literature reports in PODEnsynthesis.The one is that TOX could firstly decompose into a linear trioxane chain in the presence of acidic catalyst,after that PODEnare generating via direct incorporation of linear trioxane and transacetalization according to density functional theory(DFT)calculation[14,15].Another one is a complete decomposition of TOX to produce three formaldehyde monomers.And PODEngrowth was driven by the insertion of monomeric formaldehyde one by one,as shown in Reactions (3).This mechanism is also named the sequential addition mechanism.The reason is no significant preferred distribution of PODEn-PODEn+3observed in the experiments.However,it is observed that PODEn+1appearance after PODEnalong with reaction time[16,17].This is also observed in this experiment,so we use a sequential addition mechanism to develop a kinetic model.In this part,PODE9and PODE10are negligible given their small content(<0.1 wt%)and corresponding reaction equations are displayed as follows:

where kp,n,kd,nare the rate constants of PODEnpropagation and decomposition,respectively.k1,k−1are the rate constants of forward and reverse trioxane reaction,respectively.

Some side reactions could take place considering the presence of a small amount of water.Water reacts with the PODE1in an acidcatalyzed reaction forming MeOH and formaldehyde(FA).

The appeared MeOH could react with FA without acidcatalyzed to form the oligomers polyoxymethylene hemiformals (HFn,HO-(CH2O)n-CH3)according to Reactions(5)and(6).The HFnare mainly HF1and HF2.In addition to this,MF is formed in acidic environment according to Reaction(7).

Similarly,formaldehyde reacts with water and form poly(oxymethylene)glycols(MGn,HO-(CH2O)n-H)without acid catalyzed according to Reactions(8)and(9).

3.2.Model Equations

In this section,a mole concentrate-based model of the kinetic modeling is presented.In order to convert mass fraction (wi) into mole concentrate(Ci)by Eq.(10),we assumed that average density of the reaction mixture is 1.0 g·cm−3.Mass fraction of catalyst can be calculated by wcat=mcat/mfeed,in which mcatis catalyst mass and mcatis total mass of initial feed.

A pseudo-homogeneous model has been applied in this kinetic model.Due to similar structures and reaction mechanisms of PODEn'schain growth,we assumed that all rate constants of forward and backward reactions in Reactions (3) are equal respectively which is used for many times in the previous reports[9,17]to reduce the large number of rate constants,as shown in Eqs.(11)and(12).

In this work,the concentration of formaldehyde in the solution is measured by titration including formaldehyde of different forms.We can calculate the mixture concentration of formaldehyde (WMFA) by Eq.(1).And the WMFAalso contains two parts,monomeric formaldehyde and MGn,because Reactions(8)and(9)occur.To simplify the kinetic model,it is assumed that only Reaction 8 occurs and is in equilibrium.KMGis the equilibrium constants of Reaction (8).Additionally,it is assumed that:

(1) the rate of reaction is proportional to the content of the catalyst(Wcat)for the catalytic reaction;

(2) all reactions involved in this reaction system are following a firstorder kinetics for every component except for propagation of TOX;

(3) it is following a second-order kinetics for propagation of TOX.

Based on the analysis of chemical reactions in the last part and the assumptions we have done,we established the following kinetic model:

where Ci,kiand t are the concentration of component i in mol·L−1,the rate constants of reaction i and the time in minute,respectively.The relationship between the rate constant and temperature can be described by the Arrhenius Eq.(29),in which A is the pre-exponential factor,Eais the activation energy and R is the universal gas constant.

In order to minimize catalytic reaction fluctuations caused by repetitive samplings,the reaction time(tR)was corrected according to Eq.(30),which has been successfully used in previous research[12].

where mfeedis the mass of initial reaction mixture including PODE1,TOX and H2O,and msample,iis the mass of sampling every time.

The coefficient of determination(R2)defined by Eq.(31)was used to measure the agreement between the experimental and calculated data.

where Ci,expand Ci,calare experimental and calculated concentrations,respectively.N is the number of experimental data.

3.3.Parameter estimation

The algorithm for estimating kinetic parameters is vital to get an accurate set of data.MATLAB software is used to estimate the parameters of the kinetic model.The differential equations are solved using the builtin‘ode23s’function.Then squares of errors Eq.(32)is calculated for the molar concentrate of all components in reaction system and their sum is deemed as the objective for parameter estimation.The optimum for the objective is found by the genetic algorithm.

4.Results and Discussion

The estimated parameters also known as the rate constant kiand equilibrium constant KMGat different temperatures are summarized in Table 1.

Figs.2 and 3 show good linear relations between the logarithm of the reaction rate constant and the reciprocal of the temperature of Reaction (2)–(7),which illustrates that the rate constants fit the Arrhenius equation well.Equilibrium constants of Reaction(8)could be fitted by Van't Hoff plots(see Fig.3).And Van't Hoff plots showed good linearity.

Solving the kinetic model equations using the kinetic parameters in Table 1,we simulate the process of reaction system at experimental operation conditions.The results calculated by the kinetic model are compared with the experimental data at different temperatures and reaction times,and the plots are shown in Fig.4.It is shown that model results agree well with all considered components,except for MG and HFnunder some reaction conditions.The calculated trioxane concentrations were also consistent with the gradually declining experimental data.Deviation in some temperature such as 100 °C is observed perhaps because of the errors brought by the difficult measurement of HF1and HF2using GC.So WMFAcould be calculated by Eq.(1) to avoid the deviation,because HFnand MG as different forms of formaldehyde in water and methanol would be separated.At the beginning of the reaction,the reactants could not quickly diffuse to the active site of the catalyst,which caused the experimental value of the first point to deviate a lot from the fitted value.The R2value calculated by Eq.(31) for all involved data points is 0.9759(shown in Fig.5).Based on the above two reasons,the value of R2can be considered reliable.

Fig.4 (continued).

Table 1Rate constants,activation energy values and pre-exponential factors for each reaction

Fig.2.The relationships of rate constants of Reactions(4),(5)and(6)with temperature.

Fig.3.The relationships of rate constants of Reactions(2),(3)and(7),and equilibrium constant of Reaction(8)with temperature.

Fig.4.Comparison between experimental and calculated concentrations value of all compounds at different reaction conditions and the parity plot.Conditions:(a) 353.1 5 K,PODE1/TOX mass ratio 2.113:1,H2O/TOX mass ratio 1:9;Wcat is 3.5%（mass);(b) 373.15 K,PODE1/TOX mass ratio 2.113:1,H2O/TOX mass ratio 1:9;Wcat is 3.5%（mass);(c) 393.15 K,PODE1/TOX mass ratio 2.113:1,H2O/TOX mass ratio 1:9;Wcat is 3.5%（mass);(d) 353.15 K,PODE1/TOX mass ratio 2.113:1,H2O/TOX mass ratio 1:9;Wcat is 7%（mass);(e) 373.15 K,PODE1/TOX mass ratio 2.113:1,H2O/TOX mass ratio 1:9;Wcat is 7%（mass)%;(f) 393.15 K,PODE1/TOX mass ratio 2.113:1,H2O/TOX mass ratio 1:9;Wcat is 7%（mass).

From the discussion of chemical reactions part and the analysis of the results of the kinetic model,we could appropriately describe the reaction path of the reaction system.First of all,the main reaction is the chain growth of PODEn.TOX is decomposed into three monomer formaldehydes in the presence of the HZSM-5 catalyst,and then the monomer formaldehyde is continuously inserted into PODEnvia a sequential addition mechanism forming a distribution of PODEn.Secondly,the occurrence of side reactions is caused by the presence of water except for the generation of MF.Regarding the reaction between PODE1and water,many researchers believe that the reaction occurs as shown in Reactions (33) and (34).But experimental data indicate that the concentration of methanol rises rapidly at the beginning of the experiment and is much more than the concentration of HF1.Also,the chemical equilibrium of Reaction(34)is far to the side of the products[18,19].So the reaction of Eq.(4)is more appropriate to describe the reactions of methylal and water,and the agreement between data and calculated results also verified this hypothesis.

From the results of calculation,we can know that the irreversible reaction is appropriate to describe the formation of MF which is formed in acidic environment from formaldehyde in a Tischenko reaction,and this is consistent with the gradually increasing trend of the experimental data.But this reaction is not taken into account in other kinetic models.Due to the irreversible nature of this reaction,the concentration of MF is constantly increasing,at the same time the concentration of FA is continuously decreasing.Activation energies for PODEnpropagation (Ep) and for PODEndecomposition (Ed) were 28.24 kJ·mol−1and 55.91 kJ·mol−1,respectively.And the(Ep−Ed)differences were −27.26 kJ·mol−1,validating that the reversible propagation reactions of PODEncompounds were exothermic,which is consistent with literature results [16,17].Those two reasons are making the formation of PODEnproceed toward the reverse reaction direction at very high temperatures,leading to an increase in the concentration of PODE1,which can be clearly observed from Fig.4(f).

Fig.4 (continued).

The result of parameter fitting can get the equilibrium constant of Reaction (8).The results show that the equilibrium constant is very large,which means that water and formaldehyde are easy to combine.And the value of KMGdecreases with rising temperature.Therefore,to avoid the generation of MG,the temperature should be raised during the process of produce PODEn.

Schulz–Flory equilibrium molecular size distribution is derived from the sequential propagation mechanism[20].This model is described by Eq.(36).

where wnis mass fraction of component i.NNCCHH22OO,,RRis the reacted amount of FA.NNPPOODDE1E,01,i0s iisn iitniaitli aalm aomuonutn otf oPfO PDOED1E.1.

Similar distribution of products composition also was found in this work.It should be noted that this model is derived from equilibrium state.But the plots of ln(wn/(n+1.533))with respect to n exhibited a good linear relationship,as illustrated in Fig.6,validating S-F distribution suitable for any stage of the process of the PODEngeneration.It indicated that the use of Reaction(3)is appropriate to describe the production of PODEn.

From this kinetic model,we can know that PODE1could react with H2O in the methylal and trioxane with little water.Therefore,the presence of water will reduce the content of PODE1and generate MeOH.The existence of H2O and MeOH will make the generation of HFnand MGn,reducing the content of FA.

Fig.5.Parity plot of experimental(Cexp)and calculated(Ccal)data.

5.Conclusions

As an economically sound alternative,the reaction kinetics of synthesizing PODEnfrom PODE1and TOX with little water(<10 wt%)catalyzed by molecular sieve HZSM-5 was studied in a batch-stirred autoclave.Experiments under different reaction conditions,namely reaction temperatures(80,100,and 120°C)and catalyst content(3.5 wt%and 7.0 wt%)were carried out.A kinetic model was developed in this work,and the model explicitly accounts for the formation of HFnand MG.

The rate constants of propagation step(k6)and depolymerization step (k−6) are assumed independent on polymerization degree of PODEn.Their activation energies are 28.24 kJ·mol−1for propagation(Ep)and 55.91 kJ·mol−1for depolymerization(Ed),respectively.And the (Ep−Ed) differences are −27.26 kJ·mol−1,validating that the reversible propagation reactions of PODEncompounds were exothermic.The transient molecular size distribution of PODEncompounds from TOX and PODE1with a trace of water content followed Schulz–Flory distribution model.In this reaction system,water and PODE1react to generate the MeOH and CH2O.The generation of MF from two molecules of the monomer formaldehyde is an irreversible reaction,and its activation energies are 29.74 kJ·mol−1.The rate of reaction is proportional to the content of the catalyst (Wcat) for the catalytic reaction within the scope of the study.

Acknowledgements

This research was supported by the National Key R&D Program of China(2018YFB0604900).