Yudong Shen ,Hao Liang ,Zuwei Liao,Binbo Jiang ,Jingdai Wang ,Yongrong Yang ,Minggang Li,Yibin Luo,Xingtian Shu

1 Zhejiang Provincial Key Laboratory of Advanced Chemical Engineering Manufacture Technology,College of Chemical and Biological Engineering,Zhejiang University,Hangzhou 310027,China

2 State Key Laboratory of Chemical Engineering,College of Chemical and Biological Engineering,Zhejiang University,Hangzhou 310027,China

3 SINOPEC Research Institute of Petroleum Processing,Beijing 100083,China

Keywords:Discrete model Pore plugging effects MTP reaction Pore network

ABSTRACT Coke is an important medium for connecting reaction and regeneration of the methanol to propylene process on the ZSM-5 catalyst.Coke grows in the meso and macro pores,it gradually worsens the diffusion inside the catalyst particle.Furthermore,pore plugging is inevitable which causes the deactivation of ZSM-5 catalyst.However,current continuum model cannot reflect the changes in pore structure with clear physical concepts.A discrete model that is verified by the carbon deposition experiments is introduced to indicate the behavior of pore plugging effects.Results show that the pore plugging has a significant effect on the performance of the catalyst.The time varying profile of effectiveness factor is obtained,indicating a regular reduction with the increase of the pore plugging effect.Spatial distributions of pore size that would significantly enhance the plugging effect are also identified.

1.Introduction

Light olefins such as ethene and propylene are the most important building blocks for the modern chemical industry,their downstream products cover almost all areas of manufacturing [1].Currently,ethene and propylene are primarily produced by catalytic cracking unit and steam cracking unit of oil refineries,where operating efficiency have been improved by various modeling and optimization tools [2–6].With the shortage of global resources,researches on renewable energy are progressing rapidly [7,8].However,due to unstable supply and the tendency of heavier crude oils,the production of olefins is under constraints.Several alternative approaches for producing light olefins have been proposed:methanol to olefin(MTO/MTP)process[9],oxidative dehydrogenation of light alkanes [10],catalytic dehydrogenation of light alkanes [11].Among these technologies,the methanol to propylene(MTP)reaction under catalytic conditions is a promising way for converting natural gas,biomass and coal into chemical products via methanol.Although the methanol feedstock is simple compared to the crude oil [12],the conversion process is not simple,it includes dozens of reactions.Current research mainly focuses on the reaction mechanism [13,14],reaction kinetics[15–18],catalyst modification [19–23] and reactor simulation[14,24].Only a few researches are focused on the coking procedure.El-Kady et al.[25]proposed a linear wedge stratification theory for the FCC catalyst deactivation.They combined the parallel pore structure model to explain catalyst inactivation behavior and pointed out that the coverage of the active site is not the main reason for the catalyst deactivation,but the pore plugging effect.Mann and Thomson [26] proposed a more specific and detailed three-region pore model,which can theoretically predict the product concentration and distribution of conversion rate.However,there are two disadvantages of the above two models:1.Monotone pore radius;2.Whether the carbonaceous precursor is a reactant,or a product is not distinguished.Therefore,Mann [27] proposed a model that combined random corrugated pore structure with carbon deposition rate.In this model,the size of the pore follows a random distribution,which allows the large-aperture pore to naturally shrink.Thus,it is more realistic than the conventional parallel pore model.Mann and Sharratt [28] introduced a twodimensional random pore network model that simplifies the pore complexity inside the catalyst.It was successfully applied to the plug flow reactor for catalytic cracking of cumene.Ye et al.[29]investigated the mass transfer and reaction in porous materials and simulated the plugging effect in the pore network during the evaporation process of mesoporous scale catalyst.The authors showed that factors such as catalyst size,pore size distribution,and pore connectivity would affect the performance of the catalyst.

MTP reaction is catalyzed by ZSM-5 catalyst,which performs well in hydrothermal stability and coke resistance.However,coke deposits are inevitable,as the coke deposits increases,the catalyst deactivated.Froment[30]classified this catalyst deactivation phenomenon into three levels:micro-,meso-and macro-level.At the micro-level,coke covers active sites and isolates these sites from reactants.At the meso-level,coke can grow to a size that is sufficient to plug the mesopores,hindering the diffusion of the reactants into the pores.At the macro-level,different reactors have different flow patterns and mass/heat transfer regimes,thereby affecting coking and deactivation of catalysts.We mainly focus on the meso-level of deactivation phenomenon in this article.

The coke formation procedure in a ZSM-5 catalyst is represented in Fig.1.A two-dimensional pore network is built first.The gray squares in Fig.1 indicate the ZSM-5 catalyst,and the white channels between the squares indicate the connected pores inside the catalyst.When the channels turn black,the pores are plugged by coke.The blue channels indicate the inaccessible pores inside the deactivated catalyst.Fig.1(A),(B) and (C) represent the fresh catalyst,the partially plugged catalyst and the deactivated catalyst respectively.As the reaction progresses,coke gradually covers the surface of pores,and the fresh pores are partially plugged.As the reaction continues,the radius of pores become smaller.When the radius of the narrowest part of a pore approaches zero,it is completely plugged.If all the pores in the outermost layer are completely plugged,the catalyst is completely deactivated.

Fig.1.A schematic diagram of pore plugging.

There are two kinds of physical models to simulate the pore plugging effect:the continuum and discrete models [31].Continuum models are widely adopted in designing and optimizing the internal structure of the catalyst [32].Solving the continuum model is simple and convenient.However,drawbacks of the solution are also obvious:1.Cannot describe the non-uniformity of the active center and pore structure [33,34];2.Cannot reflect the changes in pore structure due to the pore plugging effect;3.Cannot avoid using parameters such as tortuous factor with unclear physical meanings,resulting in insufficient extensibility of the model[35].

To overcome these problems,researchers have shifted to the discrete model[28,33,36].Discrete models can accurately describe the pore network structure through the physical characteristic parameters of the pores.The constructed pore network structure is similar to the real particles.Compared to continuum models,discrete models avoid using parameters with unclear physical meanings,such as the tortuous factor.

Therefore,we will propose a discrete model that coupling mass transfer,reaction,and pore plugging processes to investigate the pore-plugging effects in the ZSM-5 catalyst of MTP reactions.

2.Modeling

The modeling steps of discrete model is as follows:first generate a suitable pore network,and then set up mass transfer and reaction equations,followed by model solution.The pore network is the basis for the entire discrete model to describe the internal structure of the catalyst particles.

The pore size of the network is divided into three types:micropore,mesopore and macropore.The micropore is represented by straight pores and Zigzag pores.The size of mesopores and macropores range from two to several hundred nanometers.Although the acidic sites of micropores generate cokes,the coke in the mesopores and macropores play a major role in the deactivation [37].Therefore,we focus on the pore plugging behavior in the mesopores.

To model this pore plugging phenomena,we choose one of our previously prepared pore-enlarging ZSM-5 catalyst as object [38].The pore size distribution of this catalyst is shown in Fig.2,where the ordinate denotes the distribution density.As can be seen from the figure,the aperture of most pores is at about 38 nm.There is also a slow and steady increase in the distribution density when the aperture is larger than 100 nm.Since the pores with larger radius are not prone to plugging,the spatial distribution of these pores plays an important role in the plugging effect.

Fig.2.Pore size distribution of ZSM-5.

2.1.Pore network

In order to make the mass transfer and reaction equations applicable to the pore network,the following assumptions are made before establishing the pore network model:

1.Mass transfer and reaction only occur inside the pores.It was assumed that the mass transfer and reaction only take place in the channel,and the nodes considered to be zero-volume particles,no mass transfer and reaction occur at the nodes.

2.The active sites of the catalyst are uniformly distributed,and the reactions in the pores occur continuously.

3.Trimethylbenzene is selected as the coke deposition precursor,and the rate of coke deposition is related to the concentration of trimethylbenzene [39].

4.Steady-state assumption.Due to the slow deactivation rate of ZSM-5 catalyst,the pore structure and pore size change little in a short time.Therefore,it is considered that the rate of diffusion and reaction is much faster than the rate of coke formation.Thus,the concentration distribution of the substances in the pore channels is supposed to remain in steady state.

5.There is no temperature gradient,and the temperature of the entire catalyst particles is identical,which is specified as 753 K.Due to the length scale of the porous catalyst is relatively small (Micron level) and the thermal conductivity is relatively high,to make the model simple and easy to calculate,the temperature gradient in the porous catalyst is assumed to be 0 and the temperature is constant at 753 K.

Based on the above assumptions,a 2D pore network model can be established.Fig.3 illustrates an 11 × 11 mesh example of the proposed 2D pore network.The nodes are uniformly distributed,where the internal nodes follow the Kirchhoff’s law while the external nodes follow the Robin boundary condition [40].

2.2.Mass transfer and reaction

The mass transfer and reaction simultaneously occur in the pore network,the pore size is so small that the component mass transfer is mainly driven by diffusion.Since the pore length is sufficiently long relative to the pore size (4–5 orders of magnitude),a set of mass transfer and reaction equations can be established in the pore channel by the continuity equation.We adopt a verified simple reaction kinetic model [41],which is shown in the appendix.Let’s consider the equations of mass transfer and coking kinetics.

Fig.3.A schematic diagram of two-dimensional pore network.

Mass transfer

In the pore channels,mass transfer equations are as follows:

where Ji,nis the diffusion flux of component i in pore n;rnis the radius of pore n;Riis the reaction rate per pore surface area of component i;lnis the length of pore n.

The diffusion of molecules in the ZSM-5 catalyst can be described by Fick’s law.

where Di,nis the effective diffusivity of component i in pore n,Ci,nis the concentration of component i in pore n.

Wheeler [42] proposed a widely used parallel pore model to describe the pore structure.It is assumed that the voids in the catalyst are composed of a number of cylindrical channels that are disjoint,smooth inside,have a uniform distribution of active sites and different pore sizes.As the pore model proposed by Wheeler[42] is consistent with the previous assumptions on the pore network,we adopt the parallel cross-linked pore model to calculate the effective diffusion coefficient.

Since the pore size we considered in this paper ranges from two nanometers to several hundred nanometers.Knudsen diffusion and molecular diffusion are only considered in the parallel crosslinked pore model,where the effective diffusion coefficient of component i in the pore can be expressed as:

where Di,mand Di,kare the molecular diffusivity and the Knudsen diffusivity,respectively.Di,mand Di,kcan be calculated by the following equations:

where yi,yjare the molar fraction of component i and j respectively;Di,Jis the binary diffusivity of component i in a mixture of i and j,which can be calculated by the following formula:

where Miand MJare the relative molecular masses of the components i and j,respectively;Viand VJare the molecular volumes of component i and j,respectively.The value of Viand VJcan be obtained by adding the atomic volumes of the participating reactants.There are three types of atoms involved in the reaction:C,H,and O.The atomic volume is shown in Table 1.

From Eqs.(3)–(6),the effective diffusion coefficient of component i at 753 K can be calculated.Remaining parameters of the two-dimensional network model are shown in Table 2.

Boundary conditions

For the inner nodes,Kirchhoff’s law is applied:

While for the boundary nodes,Robin boundary condition[40]is applied:

where Snis the cross section area of pore n;z is the connectivity of pore n;kiis the mass-transfer coefficient of component i in the catalyst surface film;Ci,bis the bulk concentration of component i;Ci,nis the concentration of component i at the outer node.

Coking kinetics

For a single independent pore channel,the pore radius changing rate can be represented by the coke formation rate.If the concentration and temperature of trimethylbenzene are known,the coke growth rate can be calculated as [28]:

where kcis the growth rate of coke;CTis the concentration of trimethylbenzene;n is the order of matrix;θnis the proportion of surface coked to n units,which is shown in Eq.(10):

where λ is the Poisson distribution parameter that can be calculated as:

where w is the mean coke depth,m;d is the coke size,m.The other parameters in the coking kinetics are shown in Table 3.

Table 1 The molecular volume of the component in MTP reaction

Table 2 Parameters for the two-dimensional pore network

Table 3 Parameters for reaction kinetics and coke deposition kinetics

Table 4 Characterization of catalyst structure

2.3.Model solution

The solving of the 2D pore network model mainly includes three steps:1.The generation of the pore network;2.The solution of mass transfer and reaction equations;3.The determination of pore plugging.The overall algorithm is presented inFig.4 and implemented in MATLAB software.In step 1,a twodimensional pore network of n × n nodes is constructed according to the geometric and pore parameters of the network.In the solution process of step 2,since the concentration of component i at the internal node is unknown,its initial value can be assumed as 0,and the entire pore network can be solved jointly after given the boundary conditions such as the concentration of the external node.

Before solving the whole problem,we can use the ‘‘dsolve”function in MATLAB to convert Eq.(1) from differential algebraic equation to algebraic equation.Then use the ‘‘fsolve”function to solve equations including Eqs.(7) and (8) simultaneously to obtain the concentration of each substance at every node.Based on this result,we will obtain the substance concentration in each pore in step 3.Subsequently,the shrinking rate of the pore radius can be obtained through Eq.(9).When a pore is plugged,its connectivity will be updated so that a new concentration distribution at each node can be generated after recalculating the above steps.When the whole pores are completely plugged,namely the reactants cannot enter the catalyst particle,the algorithm ends and jumps out.Executing the procedures in Fig.4,we can obtain the profile of pore size variation,the concentration distribution of components inside the catalyst particle,as well as the profile of coke content variation.

2.4.Model verification

Fig.4.The algorithm for the two-dimensional pore network and model solving process.

This section compares the simulated results with the experimental results of the coke content on the ZSM-5 catalyst.The ZSM-5 catalyst used in the experiment is a spherical particle with a radius of 0.65 mm.In order to improve the selectivity of propylene,the catalyst needs to be subjected to steam treatment.The structural characterization results after treatment are shown in Table 4.Subsequently,the coke content experiment is carried out.The reaction conditions are as follows:3 g of catalyst,diluted with glass beads in a ratio of 1:5,at a reaction pressure of 0.1 MPa and a temperature of 753 K,methanol was separately feed,diluted with N2,and the partial pressure of methanol was 12.5 kPa,WHSV=1 h-1.Fig.5 shows the change of coke content of the ZSM-5 catalyst with time.From the figure,the simulated values are in good agreement with the experimental value,indicating that the model and the parameters can be used to quantitatively analyze the pore plugging effect.

Fig.5.Catalyst coking amount varies with time.Dash:Experimental value;Line:Calculated value.

3.Results and Discussion

3.1.Reactant and product distribution inside the catalyst particle

The particle is divided into 11 × 11 dark blue squares,whose edge length are 1.3×10-4m,as shown in Fig.6.Between the dark blue squares,there are lines of different color.The squares stand for the catalyst,while the lines illustrates the meso-pores whose size is random generated.The pore size is depicted by color.The brighter the color,the larger the pore radius.

Fig.6.Pore network structure of ZSM-5.

Before running the above proposed reaction and diffusion model in this single catalyst particle,we need to specify the boundary conditions.For ease of calculation and illustration,we assume the mass transfer resistance of the external surface is 0.Therefore,Dirichlet boundary conditions [44] are adopted:

Substituting Eq.(12) into Eq.(8) and solving the whole model,we can obtain the concentration profiles of methanol,propylene,alkane,and trimethylbenzene in a single catalyst particle of 1.56 × 10-3m in size,as shown in Fig.7.Color is also employed to differentiate the component concentration in the figure.

It can be seen from Fig.7 that the colors of methanol,propylene,alkane and trimethylbenzene do not change substantially in most central areas,indicating that the closer to the center of the catalyst,the lower the concentration of each substance.The result shows that both reactants and products are mainly concentrated in a thin region of the catalyst surface,including the coke precursors such as trimethylbenzene.Therefore,the coke will be formed in the outer surface of the catalyst preferentially.

3.2.Effect of pore plugging

Fig.8 shows the variation of pore plugging effect at the time point of(a)100th,(b)200th,(c)300th and(d)400th hours,respectively.The red pores are plugged while the white pores are not plugged yet in the figure.As is shown,the pores are first plugged in the outer region.As the reaction proceeds,the plugged pores move toward the center of the catalyst.The pore plugging effects seems unchanged after 200 hours.In order to indicate this phenomenon clearly,we define the plugging pore percentage parameter p:

where Nblockis number of plugging pores,Ntotalis the total number of pores.

The p value of all the time point in Fig.8 are shown in Fig.9.It can be seen from Fig.9 that as the reaction proceeds,the proportion of plugging pores increases,and the slope of the rise becomes smaller and smaller.

This is because in the initial stage,the plugging pores are mainly concentrated on the outer surface of the catalyst,where the concentration of trimethylbenzene is higher and the deposition rate is faster,leading pores more likely to plug.In the later stage,the plugging pores are mainly concentrated in the center of the catalyst,where the concentration of trimethylbenzene is low,and the deposition rate is slow,leading to a proportion of plugging pores increased steadily.

Fig.7.The concentration distribution of components in a single catalyst particle.

Fig.8.Pore plugging effect varies with time:(a) 100th hour;(b) 200th hour;(c) 300th hour;(d) 400th hour.

Fig.9.Percentage of plugging pores vary with reaction time.

To further indicate the catalyst activity,we introduce a effectiveness factor ? for the main reactant methanol.? is defined as follows:

where N denotes the number of pores;lnis the length of pore,whose value is 1.3 × 10-4m in this case;rnis the radius of pores;RMis the methanol reaction rate per unit area;CM,nis the concentration of methanol in pore n;CM,bis the outer concentration of methanol.Note that the numerator and denominator of the righthand side of the equation are actually the methanol consumption rate ratio of considering diffusion and not considering diffusion.

The variation of ? is shown in Fig.10.It can be seen that ? at the initial stage is about 0.076,indicating that the internal diffusion resistance of ZSM-5 catalyst is serious,which make it difficult for reactants diffusing into the catalyst.The decreasing rate of the effectiveness factor is fast at the first 100 hours,because of the plugging effect of the small size pores on the outer surface of the catalyst.The following 100–250 hours is a stable period,in which the large size pores start plugging.Since the coke plugging procedure is slow in this period,? performs stable.At the end of the reaction period,? will enter the next stable period due to the plugging effect of larger size pores than that of main size pores.When the outer surface of the catalyst is plugged by a certain percentage or even completely plugged,the conversion of methanol drops rapidly,and the catalyst is considered completely deactivated at this time.It is worth mentioning that the ? steep descent phenom-ena in the figure also agrees with the percolation theory [45].When the fraction of unplugged or open pores drops below a critical threshold,the previously connected open pores becomes disconnected.In this case,effective factor ? would experience a sudden change.

Fig.10.Effectiveness factor varies with reaction time.

3.3.Effect of pore spatial distribution

The above sections explored the plugging effect of catalyst,but the impact of pore network structures on catalyst performance haven’t been investigated yet.Pore network structures are mainly determined by pore spatial distribution which play an important role in catalyst property.Therefore,three types of pore network (random distribution,large size pore inside distribution and large size pore outside distribution) will be studied in this section.The effects of pore spatial distribution on product concentration and catalyst performance are investigated,and the structures of three kinds of pore spatial distributions are shown in Fig.11.

Pores are divided into two categories in Fig.11,the red lines represent the large pore with a radius of 475 nm,while the blue represents small pores of 38 nm radius.The red and blue lines counted for 25% and 75% respectively,which agrees with pore size distribution shown in Fig.2.The average concentration distribution of different substances along the catalyst radial direction under the three network structures is shown in Fig.12,where the abscissa 0 represents the center of the catalyst while 1 represents the surface layer.It is obvious that the average concentration of reactants or products under the structure of large pore outside is much higher than that of other two types.For products like propylene,alkanes and trimethylbenzene,their concentration increase at the outer surface and then decrease in the center.This is because the concentration of these products is zero at the outer surface at the beginning,and as the reaction progress,the concentration of each product increases in the region near the surface.As shown in Fig.12(a),the consumption of methanol is rapid in the area close to the surface.Correspondingly,olefin products are also preferentially generated in this area,as shown in Fig.12(b).When the pores on the outer surface are larger,the diffusion performance will be better,alkane and trimethylbenzene will continue to diffuse into the interior as the product of olefins,and the concentration keeps rising,as shown by the black lines in Fig.12(c) and (d).When the surface pores are small,the ability of material diffusion is poor,and the concentration of alkane and aromatic hydrocarbons decreases,as shown by the blue and red lines in Fig.12(c) and (d).

Fig.13 shows the percentage of deactivated pores variation with time under the three types of pore network.It can be seen from the figure that the ratio of plugging pores under the large pore inside distribution (red) remained constant after about 150 hours,indicating the catalyst deactivation.The proportion of pore plugging is about 40%,the remaining 60% of the pores are still available and the catalyst utilization rate is low.With the large pore size outside distribution (blue),the catalyst deactivation time is about 350 hours,the overall catalyst utilization rate is approximately 50%.Compared with the large pore inside distribution,the catalyst utilization rate is increased by 10% and the inactivation time is more than doubled.In the case of random distribution (black),the complete deactivation time of catalyst is about 300 hours,the overall catalyst utilization rate is nearly 40%,which is equivalent to the inside distribution of large pores.

The above analysis shows that the closer the large pores are to the center of the catalyst,the harder the components diffuses into the interior of the catalyst,resulting in a lower overall utilization of the catalyst.To improve the overall utilization,catalyst can be appropriately reamed while maintaining strength,especially reaming the pores on the outer surface of the catalyst.In addition,reaming treatment will also extend the catalyst deactivation time and prolong the life of the catalyst.

Fig.11.Three types of pore spatial distribution.(a) Random distribution;(b) large pore inside;(c) large pore outside.

Fig.12.Average concentration of substances along catalyst radius in three types of pore spatial distribution.

Fig.13.Percent of plugging pores vary with reaction time with three types of pore spatial distribution.

4.Conclusions

The discrete model was employed to simulate the formation of carbon deposits inside the meso and macro pores of the ZSM-5 catalyst.Both the effect of the pore plugging and pore size distribution on the catalytic performance were investigated.Component distribution shows that the main reaction zone was concentrated on the outer surface of the catalyst due to the diffusion restriction.Coke formation also preferentially takes place on the outer surface,further inhibiting the diffusion of the reactants into the catalyst.Effectiveness factor was introduced to represent the catalyst activity.Modelling results show steep descent phenomena of catalyst activity,which agrees with the percolation phenomena of graph theory.Three kinds of pore size spatial distribution were calculated and compared.Results show that concentrating pores of large radius in the area near outer surface could slow down the pore plugging effect.This provides insight to the rational design of catalysts with coke resistance.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The financial support provided by the Project of National Natural Science Foundation of China (21822809 &21978256),the National Science Fund for Distinguished Young (21525627),and the Fundamental Research Funds for the Central Universities(2019XZZX004-03),and Ningxia Collaborative Innovation Center for Value Upgrading of Coal-based Synthetic Resin(2017DC57)are gratefully acknowledged.Dr.Zuwei Liao express their dedication to Prof.Xingtian Shu on the occasion of his 80th birthday.

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2020.10.038.

Nomenclature

Ci,bconcentration of component i in the gas phase,mol﹒m-3

Ci,nmolar concentration of component i,mol﹒m-3

Di,jtwo-component diffusion coefficient of components i,j,m2﹒s-1

Di,kNusen diffusion coefficient,m2﹒s-1

Di,mmolecular diffusion coefficient,m2﹒s-1

Di,ndiffusion coefficient of component i in pore n,m2﹒s-1

d coke particle size,m

Ji,ndiffusion flux of component i in pore n,mol﹒s-1﹒m-2

Kpadsorption equilibrium constant of propylene

KTadsorption equilibrium constant of trimethylbenzene

kccoke deposition rate,m2﹒s-1﹒mol-1

kimass transfer coefficient of component i on the surface of the catalyst,m﹒s-1

lnlength of pore,m

Mirelative molecular mass of component i

NC*percentage of coke deposition sites

Nfreenumber of free adsorption sites

NPr*percentage of propylene adsorption sites

NT*percentage of trimethylbenzene adsorption sites

Ntotpercentage of total adsorption sites

n cell number of 2-D pore networks

Rireaction rate per unit surface area of component i,mol﹒m-2﹒s-1

rnpore radius,m

Sncross-sectional area of the pore n,m2

Vimolecular volume of component i

w average coke deposit thickness,m

yimolar fraction of component i

z the connectivity of pore n,the initial value is 4

θncarbon surface coking depth,which is a function of the average thickness of n-coke deposits

λ Poisson distribution parameter