Yiquan Zhao,Yao Shi,Guanghua Ye,Jing Zhang,Xuezhi Duan,Gang Qian*,Xinggui Zhou

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

Keywords:CO methanation Numerical simulation Catalyst pellet Shape effects Reaction-diffusion behavior

ABSTRACT A fundamental understanding of the effects of catalyst pellet structures and operation conditions on catalytic performance is crucial for the reactions limited by diffusion mass transfer.In this work,a numerical investigation has been carried out to understand the effect of catalyst pellet shapes(sphere,cylinder,trilobe and tetralobe) on the reaction-diffusion behaviors of CO methanation.The results reveal that the poly-lobe pellets with larger external specific surface area have shorter diffusion path,and thus result in higher effectiveness factors and CO conversion rates in comparison with the spherical and cylindrical pellets.The effects of operating conditions and pore structures on the trilobular catalyst pellet with high performance are further probed.Though lower temperature can contribute to larger effectiveness factors of pellets,it also brings about lower reaction rates,and pressure has little impact on the effectiveness factors of the pellets.The increase in porosity can reduce the pellet internal diffusion limitations effectively and there exists an optimal porosity for the methanation reaction.Finally,the height of the trilobular pellet is optimized under the given geometric volume,and the results demonstrate that the higher the trilobular catalyst,the better the reaction performance within the allowable mechanical strength range.?2021 The Chemical Industry and Engineering Society of China,and Chemical Industry Press Co.,Ltd.All rights reserved.

1.Introduction

Production of synthetic or substitute natural gas (SNG) from coal or biomass has attracted increasing attention owing to the clean nature and unbalanced reserve of natural gas,the already existing gas distribution infrastructure,the well-established and efficient end use technologies,and the opportunity of alleviating local air pollution[1-3].A critical step in SNG production is methanation of carbon oxides,which is well known for its strong exothermic nature.Thermodynamically,low temperature is favorable to the methanation reactions [4].However,the reactions are limited by chemical kinetics at such low temperature.Therefore,extensive studies have been devoted to the development of highly efficient catalysts by optimizing the catalysts’ active components[5-8],promoters [9-12],supports [13-16] and preparation methods [17-21].Considering that CO methanation process is a fast chemical reaction,industrial extruded catalyst pellets used in fixed-bed reactors are severely limited by mass transfer,which leads to a low catalyst effectiveness factor [22-24].Therefore,it is imperative to enhance the effectiveness factor and thus improve the utilization of the extruded catalyst pellets.

Generally,a catalyst pellet with higher external specific surface area (SV) will have higher effectiveness factor because of better access for the reactants to diffuse into the interior zone of the catalyst pellet[25],and this can be achieved by decreasing pellet size or employing catalyst pellets with different shapes.However,the pellet size is constrained by pressure drop of fixed bed which will increase operating costs[26].Compared with adjusting pellet size,employing shaped catalysts can contribute to higherSVand lower pressure drop simultaneously.Although the CO methanation reaction has been well known for several decades,few studies have been focused on the investigation of the pellet shape effects on the catalytic performance.

Herein,3D models of catalysts with different shapes (sphere,cylinder,trilobe and tetralobe)have been performed to understand the effect of catalyst pellet shapes on the reaction-diffusion behaviors of CO methanation at the pellet scale.The performances of the four catalyst pellets with different shapes were compared and a relationship between the pellet shape and the performance was established.Furthermore,for the trilobular catalyst with the highest performance,the influence of operating conditions,pore structures and pellet characteristic sizes on reaction-diffusion behavior of CO methanation process were investigated.

2.Computational Methodology

To analyze the reaction-diffusion behavior of CO methanation over different shaped catalysts,the detailed reaction kinetics,energy and species conservation equations were solved in COMSOL Multiphysics software,and geometric modeling and meshing were also performed in this software.

2.1.Governing equations

2.1.1.Reactions and kinetic model

Methanation reaction was first discovered by Sabatier and Senderens [27] in 1902.The two main reactions during CO methanation process are as follows:

The kinetic model used in this paper is that of Kopyscinski[28]over a commercial catalyst Ni/Al2O3in a fixed bed reactor(Eqs.(3)and(4),in which pressure is expressed in bar(1 bar=0.1 MPa)and temperature in K).

For CO methanation reaction (Eq.(1))

For water gas shift (WGS) reaction (Eq.(2))

The rate equation for the CO methanation does not include the reverse reaction due to the large equilibrium constant(Keq,Meth=7.8×107bar-2at 280 °C andKeq,Meth=5.6×104bar-2at 380 °C),while the rate equation for the water gas shift includes the reverse reaction due to the small equilibrium constant(Keq,WGS=55.2 at 280°C andKeq,WGS=15.1 at 380°C).This kinetic model is valid within a temperature range of 473-673 K.

Reaction rate constants are calculated by

Adsorption constants are calculated by

In order to facilitate the calculation,transform the above formula into the following form:

where θk,j=ln(kj,Tref),θK,i=ln(Ki,Tref),andTref=598.15 K.Parameters of Eqs.(7) and (8) are listed in Table 1.The thermodynamic equilibrium constant of WGS reaction is defined as a function of temperature expressed as [29] (Eq.(9))

Table 1 Kinetic parameters estimated for the model [28]

2.1.2.Species conservation equations

For industrial methanation catalysts,the influence of diffusion within the catalysts cannot be ignored due to the large pellet size.The diffusion-reaction equation of gas phase componentiin the catalyst pellet can be expressed as

where ρcatis the density of the catalyst,Deffiandriare the effective diffusivity and reaction rate ofithspecies in the multicomponent gas phase,respectively.In the model,both Knudsen diffusion and molecular diffusion are considered and the effective diffusivity of each species is expressed as [30]

whereDi,mandDK,istand for the molecular diffusivity and Knudsen diffusivity,respectively.The ε and τ stand for porosity and the tortuosity whose values are set as ε=0.3 and τ=3.3,respectively.The molecular diffusivity is calculated by [31,32]

where υ is the so-called diffusion volume listed in Table 2.The Knudsen diffusivity is calculated by [30]

wheredpis the pore diameter of the catalyst set as 15 nm [13,34].

2.1.3.Energy conservation equations

During the methanation reaction,the reaction rate and the properties of the gas phase and catalysts change with the temperature as the methanation reaction is strongly exothermic.Therefore,it needs to solve the heat transfer equation given below in the pellet domain

where ΔHj(j=1,2) is the heat of reaction for the CO mathanation reaction and WGS reaction,respectively.λeffis the effective thermalconductivity of the catalyst defined as[λmε+λs(1-ε)] [31].λmand λsare the thermal conductivities of the gas and solid phases and the latter is considered as the thermal conductivity of alumina calculated by [35]

Table 2 Diffusion volumes used in this work [33]

Table 3 Empirical equations and mixing laws used for estimation of the properties of the reactive mixture and catalyst

The properties of the catalyst and reactive mixture required in the equations which are not described in detail above are calculated in Table 3.

2.2.Computational geometry and domain

In this paper,four kinds of catalyst pellets,that is sphere,cylinder,trilobe and tetralobe,were considered (refer to Fig.1).These four catalysts have the same volume as the BASF G1-85 catalyst which is a kind of cylindrical catalyst with a height and a diameter of 5 mm.Except for spherical catalyst,other catalysts have the same height.The geometrical characteristics of the four different pellets,i.e.volume (VPE),external surface area (SPE),characteristic size(LPE)and height(HPE),are listed in Table 4,in which the characteristic size of the catalyst pellet is defined as follows [39]:

Fig.1. Schematic diagram of the catalyst pellets with different shapes.

Table 4 Geometric properties of four catalyst pellets with different shapes

2.3.Meshing and boundary conditions

In order to ensure the accuracy and reliability of the model,the mesh sensitivity analysis was performed by comparing the average reaction rate of spherical pellet with different mesh resolutions,and the results are shown in Table 5.It can be seen that as the number of elements increases,the average reaction rate generally decreases.When the number increases to more than 64,667,the average reaction rate is no longer related to it.Therefore,the Mesh 4 settings were considered for further studies.

The operating conditions used in this study were selected based on the literatures related to methanation [40,41].An operating temperature (T0) and pressure (P0) of 573 K and 20 bar,respectively was used.The gas phase was defined as variable composition mixture containing CO,H2,CH4,H2O,CO2and N2with initial mole fractions of 0.082,0.54,0.252,0,0.02 and 0.106,respectively,in accordance with the industrial coke oven gas.The conservation equations were only solved on the catalyst pellet domain,and the concentration and temperature gradient between the outer surface of the pellet and the bulk gas were neglected.On the outer surface of the catalyst pellets,the boundary conditions were set asT=T0,ci=ci,0,and the physical properties of the solid phase were used as those of alumina material.

3.Results and Discussion

3.1.Effects of the pellet shapes

The numerical simulations were first performed for four catalysts with different shapes(sphere,cylinder,trilobe and tetralobe)with equal pellet volumes under the same reaction conditions of 573 K and 2.0 MPa.Fig.2 displays a qualitative comparison for the effect of pellet shape on the CO concentration distribution inside the catalyst pellet.It can be observed that for each of the four shaped catalysts,the CO concentration distribution is symmetrical as a result of the symmetrical shape of the catalyst pellet.The CO concentration decreases drastically within a thin layer near the surface,and becomes low or even zero in the core of thecatalyst.This indicates that there exists strong internal diffusion limitations and a large fraction of the pellet volume is not utilized.Comparatively,the trilobular and tetralobular pellets show relatively less gradients of CO concentration than the spherical and cylindrical pellets,which is attributed to the reduction of the diffusion path length at the interior of the pellet and thus facilitating the transport of reactants for methanation reaction taking place in the pellet interior [39].

Table 5 Mesh sensitivity analysis

Fig.2. Concentration distributions of CO within the four catalyst pellets.

To assess the extent of the diffusion limitations,the effectiveness factors(η)of CO methanation defined below[42]for the four shaped catalysts are further compared.

where the effectiveness factor is the ratio of the average reaction rate calculated byR(V)dVPEto the surface reaction rate calculated byR(S)dSPE,in whichR(V)is the reaction rate inside the catalyst pellets,andR(S)is the reaction rate on the outer surface of the catalyst without considering the external diffusion resistance.As shown in Fig.3,the effectiveness factors decrease in the following order:tetralobe ＞trilobe ＞cylinder ＞sphere,which is consistent with the order of decreasing characteristic size (LPEin Table 4) for these four catalysts with the same surface CO concentration.Moreover,the average reaction rates of the four catalysts exhibit the similar trend.

Generally,for a reaction controlled by internal diffusion,the catalytic performance is related to the external specific surface area (SV) of catalyst pellets [25].Therefore,the relationship between the average reaction rate,the effectiveness factors andSVwas established and illustrated in Fig.4.As can be seen that the average reaction rate and the effectiveness factors increase withSV.It means that the main factor affecting the reaction performance of different shaped catalysts is their external specific surface area.

Fig.4 also shows that even for the poly-lobe pellets having the best performance among the shaped catalysts,their effectiveness factors are lower than 0.3 suggesting that the pellets have not been fully utilized because of the distinct diffusion limitations [25].Therefore,there is room for improvement in their catalytic performance.For catalyst pellets with a known shape,operating conditions and their structural parameters will also affect the reaction rate and effectiveness factor [4,39,43-45].Therefore,we take the trilobular catalyst pellets with relatively large characteristic size as an example to explore the influence of operating conditions(temperature and pressure) and catalyst pellet structure parameters(pore size,porosity and characteristic size)on the performance in methanation reaction.

3.2.Optimization of the trilobular catalyst

3.2.1.Effects of temperature and pressure

The influence of temperature and pressure on catalytic behavior over the above-mentioned trilobular catalyst was respectively investigated with the other conditions constant.Fig.5(a) shows the distribution of CO concentration in the cross section of trilobe at four typical temperatures under the porosity of 0.3 and pore diameter of 15 nm at 20 bar.At a low temperature of 513 K,CO distributes in the entire catalyst,and its concentration decreases gradually from the surface to the center of the catalyst,while it is not fully consumed as the concentration at the center is not zero.At high temperatures,CO concentrates in a narrow region near the pellet surface,and its concentration decreases rapidly to zero.To gain in-depth understanding of the effects of temperature,the reaction rates and diffusion rates at different temperatures are further compared.As depicted in Fig.5(b),both the surface reaction rate (Left-Y) and diffusion rate (Right-Y) at low temperatures are relatively slow and thus more CO can diffuse into the interior of the catalyst.As the temperature increases,the surface reaction rate increases exponentially,while the diffusion rate changes only a little.As a result,CO is consumed before it can diffusion inside the pellet,leading to low catalyst utilization.This is also reflected in the effectiveness factor presented in Fig.5(c),which decreases significantly with the increase of temperature.Notably,at 513 K,the effectiveness factor is higher than 0.9,but the average reaction rate of the catalyst is much low.Therefore,it is necessary to compromise the reaction rate and the utilization of the catalyst when selecting the reaction temperature in the industry.

Fig.3. The effects of pellet shape on the (a) average reaction rate and (b) effectiveness factor.

Fig.4. (a) Average reaction rate and (b) effectiveness factor as a function of external specific surface area.

Fig.5. (a)Concentration distributions of CO within the trilobular pellet with different temperatures;(b)The average reaction rate,surface reaction rate and surface diffusion rate of the catalyst as a function of temperature;(c)Effectiveness factor as a function of temperature;(d)Concentration distributions of CO within the trilobular pellet with different pressures;(e) The average reaction rate,surface reaction rate and surface diffusion rate of the catalyst as a function of pressure and (f) Effectiveness factor as a function of pressure.

Fig.5(d)shows the change of CO concentration in the trilobular catalyst with pressures under the porosity of 0.3 and pore diameter of 15 nm at 573 K.It is seen that change of total pressure from 0.5 to 3.0 MPa has low impact on CO concentration distribution.For all the pressures,CO is mainly distributed on the outer layer of the catalyst.The surface reaction rate and diffusion rate at different pressures are also calculated and presented in Fig.5(e).Clearly,with the increase of pressure,the reaction rate increases slowly.Meanwhile,the diffusion rate increases slightly.Therefore,the effectiveness factor also changes a little from～0.19 to 0.28 with the pressure increasing from 0.5 to 3.0 MPa(Fig.5(f)).This means that it is not effective to reduce the diffusion restriction effect of the catalyst by adjusting the pressure.However,as CO methanation is a volume reducing reaction [4],high pressure will promote the reaction performance.

3.2.2.Effects of pore size,porosity and pellet characteristic size

Fig.6 illustrates the role of pore size and porosity of trilobular catalyst in the catalytic performance at 573 K and 2.0 MPa.The CO concentration contours in Fig.6(a) and (d) reveal that the CO concentration does not change significantly with the increase of pore diameter under the porosity of 0.3,and there exists strong gradients near the outer surface as a result of the diffusion limitations.In contrast,under the pore diameter of 15 nm,the porosity has a great impact on the distribution of CO concentration inside the pellet,and an increase in the porosity leads to a significant increase in the degree of usage of the inner surface.This difference is caused by the different dependence of reaction rate and diffusion rate on the pore diameter and porosity[26].As shown in Fig.6(b),the surface reaction rate is independent of the pore diameter,while the average reaction rate and the surface diffusion rate increase gradually with the pore diameter giving rise to a slow increase of effectiveness factor(Fig.6(c)).As for the porosity,it affects not only the effective diffusivity of the reactants in the catalyst pores,but also the density of the catalyst pellet.Hence,as the porosity increases from 0.2 to 0.8,the surface reaction rate keeps decreasing but the surface diffusion rate increases slowly.At low porosity,the surface reaction rate is far greater than the surface diffusion rate,and the catalytic process is severely restricted by internal diffusion leading to a low effectiveness factor.At high porosity,the surface reaction rate approaches the surface diffusion rate,which weakens the influence of internal diffusion restriction and generates a high effectiveness factor.

Fig.6. (a) Concentration distributions of CO within the trilobular pellet with different pore diameters;(b) The average reaction rate,surface reaction rate and surface diffusion rate of the catalyst as a function of pore diameter;(c)Effectiveness factor as a function of pore diameter;(d)Concentration distributions of CO within the trilobular pellet with different porosities;(e) The average reaction rate,surface reaction rate and surface diffusion rate of the catalyst as a function of porosity and (f) The average reaction rate and effectiveness factor as a function of porosity.

The above comparison results clearly demonstrate that the increase in porosity rather than pore diameter can reduce the internal diffusion limitations effectively and is favorable for the methanation reaction.However,as exhibited in Fig.6(f),too large porosity can induce a low average reaction rate due to the decrease in pellet density.Therefore,there is an optimal porosity in this process.

Fig.7. (a)Concentration distributions of CO within the trilobular pellet with different heights of catalyst;(b)Average reaction rate and(c)effectiveness factor as a function of catalyst height.

As noted above,although the effectiveness factor of the catalyst can be significantly increased by lowering the temperature and increasing the porosity,both of these measures may reduce the average reaction rate.To further alleviate diffusion limitations and enhance the average reaction rate,an attempt to optimize the characteristic size of the trilobular pellet was carried out under the porosity of 0.6 and pore diameter of 15 nm at 573 K and 2.0 MPa.For the trilobular pellet with a given geometric volume,its characteristic size can be tuned by changing its heightHPE[39].Fig.7(a) shows the CO concentration distributions within the four typical catalyst pellets with differentHPE.Clearly,increasing the height of the pellet gives rise to a small cross-sectional area and a reduction of the diffusion path length and thus weak diffusion limitations.As the reactants have better access to the interior of the pellet with a largerHPE,the effectiveness factor increases with the height.In addition,the average reaction rates shown in Fig.7(b) reveal that the higher the trilobular catalyst,the better the reaction performance.It should be noted that the pellet with too largeHPEmay lead to a weaker mechanical strength,which makes the pellet easier to break during handling and filling of the beds.Therefore,the diffusion limitations and mechanical strength should be compromised when designing industrial catalysts.

4.Conclusions

In summary,we have carried out numerical simulations on the CO methanation over four catalyst pellets with different shapes to probe the effects of catalyst shapes.For the four extruded catalysts,the effectiveness factors of the pellets and CO conversion rates decrease in the following order:tetralobe ＞trilobe ＞cylinder ＞sphere,which mainly results from the difference of their external specific surface area.The operating conditions and the pellet structure parameters make a great influence on the catalytic performance of catalyst pellets.Low temperature can increase the effectiveness factors of catalyst pellets,while total pressure has low little impact on the effectiveness factor of catalyst pellets.At 573 K and 2.0 MPa,the increase in porosity can reduce the internal diffusion limitations effectively,while the influence of pore diameter is much smaller.For the trilobular pellet with the same geometric volume,higher catalysts are more favorable for CO methanation reaction within the allowable mechanical strength range.The insights revealed here could guide the selection of an optimal pellet shape with proper structures and operation conditions to improve the CO methanation performance.

Nomenclature

cimolar concentration of compoundi,mol·m-3

ci,0molar concentration of compoundiin the bulk gas,mol·m-3

Cp,iheat capacity of speciesi,J·kg-1·K-1

Cp,mheat capacity of gas mixtureJ,J·kg-1·K-1

Dijbinary diffusion coefficient,m2·s-1

Di,mdiffusivity of speciesiin the mixture,m2·s-1

Dk,iKnudsen diffusivity of speciesi,m2·s-1

dppellet diameter,m

EA,jactivation energy of reaction (1),(2) (methanation and water gas shift,respectively),kJ ·mol-1

HPEheight of catalyst pellets,mm

ΔHθstandard enthalpy of reaction,kJ·mol-1

ΔHiadsorption enthalpy of speciesi,kJ·mol-1

ΔHjenthalpy of reaction (1),(2) (methanation and water gas shift,respectively),J·mol-1

Keqequilibrium constant of the water gas shift reaction

Kiadsorption constant of speciesi

pre-exponential factor of the adsorption constantKi

kjrate constant of reactionj

pre-exponential factor for rate constantkj

LPEcharacteristic size of catalyst pellet,mm

Mimolecular weight of speciesi,kg·kmol-1

Mmaverage molecular weight of gas mixture,kg·mol-1

Ngnumber of gas-phase species

Ptotal pressure,Pa

Pipartial pressure of speciesi,bar

P0operating pressure,bar

Runiversal gas constant,J·mol-1·K-1

Rjrate of reaction (1),(2) (methanation and water gas shift,respectively),mol·(kg cat)-1·s-1

rirate of disappearance or formation of speciesi,mol·(kg cat)-1·s-1

SPEexternal surface area of catalyst pellet,mm2

Ttemperature,K

Trefreference temperature,K

T0operating temperature,K

VPEvolume of catalyst pellets,mm3

Yimass fraction of speciesi

yimolar fraction of speciesi

ε void fraction or porosity

η effectiveness factor

θE,jdimensionless activation energy

θH,idimensionless heat of adsorption

λeffeffective thermal conductivity,W·m-1·K-1

λithermal conductivity of speciesi,W·m-1·K-1

λmthermal conductivity of gas mixture,W·m-1·K-1

λsthermal conductivity of the solid,W·m-1·K-1

μiviscosity of speciesi,kg·m-1·s-1

ρcatcatalyst density,kg·m-3

ρmgas mixture density,kg·m-3

ρssolid density,kg·m-3

τ catalyst tortuosity

υidiffusion volume of speciesi

Φijdimensionless parameter for the mixture ofiandj

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

This work was supported by the National Key Research and Development Program of China (2018YFB0604500) and the National Natural Science Foundation of China (21922803).