Heat Transfer and Reaction Characteristics of Steam Methane Reforming in a Novel Composite Packed Bed Microreactor for Distributed Hydrogen Production

: The development of efﬁcient and compact reactors is an urgent need in the ﬁeld of distributed hydrogen production. Steam reforming of methane is the main method to produce hydrogen. Aiming at the problems of high heat and mass transfer resistance of the existing ﬁxed bed reactors, and the difﬁculty of replacing the wall-coated catalyst in the microreactors, a composite packed bed was proposed to meet the demand of small-scale hydrogen production. The structure consists of a multi-channel framework with high thermal conductivity, which is ﬁlled with Ni/Al 2 O 3 catalyst particles in each channel. A three-dimensional numerical model of the steam methane reforming process in the novel reactor was established using ANSYS FLUENT software. The heat transfer and reaction characteristics in the reactor were studied. Firstly, the advantages of the multi-channel skeleton in enhancing the radial heat transfer performance were veriﬁed by comparing it with the traditional randomly packed bed without the channel skeleton. Secondly, the inﬂuences of inlet velocity, inlet temperature, and heating wall temperature on the heat transfer and reaction performances in the reactor were studied, and a sensitivity factor was adopted to do the sensitivity analysis. The results show that the methane conversion rate is most sensitive to the wall temperature, while the inlet velocity and inlet temperature have less effect. Finally, the effects of two skeleton materials were studied. The results show that when the wall temperature is higher than 1200 K, there is no signiﬁcant difference between these two reactors, which indicates that the use of cordierite with a lower price, but also with a lower thermal conductivity can signiﬁcantly reduce the reactor’s cost. The conclusions can be used as a reference for the design of small-scale hydrogen production reactors.


Introduction
As a green and clean energy, hydrogen plays an important role in the decarbonization of the world.The existing hydrogen supply chain involves hydrogen production, hydrogen storage, and hydrogen transportation.Due to the fact that the hydrogen molecule is within a very small size and a broad explosive range, which has intrinsic drawbacks such as easy leakage and poor safety [1], the storage and transportation of hydrogen is prone to many safety hazards and high transportation costs.The above issues have become key constraints for the development of the hydrogen [2].The distributed hydrogen production strategy [1,3,4], which adopts the local hydrogen supply method, can effectively solve the problems in hydrogen storage and transportation, and has received increasing attention in recent years.High temperature methane steam reforming is the main method for producing hydrogen in the industry [5,6].The reaction usually occurs in a tubular reactor [7].Each reaction tube is filled with catalyst particles to provide reaction active sites.However, the reactor has a large volume, a large heat and mass transfer resistance, and a slow dynamic response, which cannot meet the demands of distributed hydrogen production [8].The distributed hydrogen production system should have some unique properties that are not present in a large-scale reforming system, such as: (i) daily startup and shutdown operation ability, (ii) rapid response to load fluctuation, (iii) compactness of the device, and (iv) excellent thermal exchange [9].Therefore, the development of efficient and compact reactors has become an urgent need in the field of hydrogen production.Process intensification is a good way to develop efficient and compact reactors.Researchers have conducted a lot of work in improving the structure of the existing packed bed reactors.For example, Yang et al. [10] proposed a radial layered packed bed to weaken the wall effect and to enhance the heat transfer between the mainstream and the particles.Strangio et al. [11] and Calis et al. [12] proposed a composite stacked structure to reduce the pressure drop of the randomly packed bed reactors.Wang et al. [13,14] proposed a composite ordered stacked structure to improve the flow uniformity on the cross-section, thereby improving the heat and mass transfer performance between the mainstream and the particles.All the above studies aimed to modify the pore structure which is closely related to the flow and heat/mass transfer characteristics.On the other hand, since the methane steam reforming reaction is a strong endothermic reaction, and the reaction heat is mainly provided by the tube wall [9], the radial heat transfer performance is therefore crucial.From this point of view, methods which can quickly transfer heat from the tube wall to the bulk could be more efficient.For this reason, a thermal conductive grille was inserted into a randomly packed bed by Hu et al. [15].This novel structure combines two advantages, enhancing the radial heat transfer by thermal conduction, as well as improving the heat transfer performance between the fluid and the particles.Qian et al. [16] further studied the performance of the methane steam reforming reaction in the grille-particle composite packed bed and found that both the heat transfer and the reaction rate were improved.Additionally, the tube wall temperature was significantly reduced, which can thereby extend the life of the reaction tube and save costs.The novel grille-particle composite packed bed is an effective method to improve the efficiency of chemical reactions which makes the reactors more compact.However, existing research has mainly focused on industrial scale reactors.The high internal diffusion resistance caused by large catalyst particles restricts its application in the field of distributed hydrogen production.
Microchemical technology [17], with microreactors as their core, is another way of process intensification.Compared with large scale systems, microreactors have outstanding advantages such as fast heat and mass transfer rates, strong exothermic/endothermic isothermal operations, and rapid multiphase mixing [18][19][20].Currently, researchers have conducted many studies to confirm the feasibility and efficiency of microreactors.Chen et al. [21] proposed a microchannel reactor for methane steam reforming coupled with the catalytic heating of methane, and obtained relatively suitable operating parameters, demonstrating the feasibility of a stable and efficient operation of the reactor within a millisecond contact time.Mei et al. [22] proposed a microreactor using a microneedle-shaped fin array as a catalyst support to increase the compactness of the methane steam reforming microreactor.Numerical calculations and experimental results show that the conversion rate of this reactor is higher than that of a traditional microreactor with 12 channels.Liu et al. [23] compared the performance differences of three types of microreactors with straight tube, flat arc curved tube, and triple internal spiral barrel structures, and found that the flat arc curved tube model had the best performance.Wang et al. [24] proposed a methanol steam reforming microreactor using silicon carbide honeycomb ceramics with high thermal conductivity as a catalyst carrier.Through experiments and simulations, it was found that when silicon carbide ceramics were used as the catalyst carrier, the pressure drop in the reactor was significantly reduced, and the temperature distribution was more uniform, thereby verifying the efficiency of the reactor.Currently, most microreactors are composed of several narrow parallel channels, and catalysts are coated on the channel wall, which effectively reduces the internal diffusion resistance.However, there are shortcomings in that catalysts are difficult to replace.Therefore, motivated by the grille-particle composite packed bed used for the industrial scale and the multi-channel microreactor, a "composite packed bed microreactor" was proposed in the present paper by combining the advantages Energies 2023, 16, 4347 3 of 14 of these reactors in both scales.The reactor channel was first filled by the honeycomb manufactured by metal or ceramics, and then the catalyst particles were filled into each channel of the honeycomb to provide the reaction site.This structure is compact, and the catalyst is easy to change.
Alongside the improvement of the reactor structure, one should notice that the catalyst is actually another significant issue in the field of hydrogen production.Ni supported by Al 2 O 3 is the most commonly used catalyst due to its high activity and low cost.However, coking and sintering have been the two major issues that lead to the deactivation of a catalyst during the SRM process [25].To avoid such problems, strict operating conditions, such as a high temperature above 700 • C and a high S/C ratio within 2.5~3.0, are generally required [9].Researchers have been devoted in developing more efficient catalysts over the past years.The nature of the support (e.g., Al 2 O 3 , CeO 2 , Ca 2 O 3 , MgO, and ZrO 2 , etc.) affects the catalytic activity.Charisiou et al. [26] carried out a comparative study of Ni catalysts supported on commercially available alumina and lanthana-alumina (LaAl) carriers, and found that the use of LaAl as the support can reduce carbon deposition and improve the catalytic activity and long-term stability.ZrO 2 support modified by La 2 O 3 and CeO 2 can depress carbon formation during biogas dry reforming reactions [27].The use of promoters is also an efficient way to weaken coking and sintering.Investigations conducted using density functional theory showed that the electronic synergistic effect of Ni and Co can keep Ni active after carbon accumulation in a methane dry reforming system [28].Siahvashi et al. [29] found that during propane dry reforming reactions, alumina-supported bimetallic Mo-Ni catalysts are more stable and active compared with Co-Ni catalysts due to having a low carbon deposition.The addition of H 2 as a co-reactant can also suppress carbon formation [30].Despite these improvements, the commercial catalyst of Ni supported by Al 2 O 3 is used in the present study to make the reactor more adaptable.Coking and sintering were not considered in this study, as a high temperature and high S/C ratio were selected in the present reactor.
In this work, the heat/mass transfer characteristics and the kinetic performances in the novel composite packed bed microreactor were studied with numerical simulations.The paper is organized as follows.The structure of the multi-channel microreactor is described in Section 2. The three-dimensional numerical model is established in Section 3. The heat /mass transfer and chemical reaction characteristics in the reactor were analyzed in detail, and the results are given in Section 4. We presented our conclusions in Section 5.The present paper can provide a reference for the design of small-scale hydrogen production reactors.

Structure of a Multi-Channel Microreactor
The structure and the dimensions of the novel composite packed bed reactor are shown in Figure 1.The heat required by the methane steam reforming reaction was provided through the outer wall of the reactor.The reaction section had an outer dimension of 31 × 31 × 100 mm, while the thickness of the skeleton was 0.5 mm, and the inner dimension of each channel was 2 × 2 mm, respectively.The catalyst particles filled into each channel were 0.4 mm, with Ni on the Al 2 O 3 matrix.The porosity of the catalyst bed was 0.4598.The particle density was 3960 kg/m 3 , the specific heat was 880 J/kg•K [7], and the thermal conductivity was 1 W/m•K, respectively [31].The Ni-Cr alloy, which can withstand a high temperature of 1400 K, was selected as the material of the skeleton.
In the subsequent analysis of the heat transfer and chemical reaction performance of the composite packed bed reactor, cross-sections with coordinates of 1.5 mm in the y direction (longitudinal section), and 5 mm, 35 mm, 65 mm, and 95 mm in the x direction (transverse cross section), were adopted as the reference surfaces, as shown in Figure 2a,b.Data of typical lines were also analyzed in the following text, whose positions are shown in Figure 3. Here, Line 1 was the closest to the symmetric boundary, while Line 6 was the closest to the heating wall.In the subsequent analysis of the heat transfer and chemical reaction performance of the composite packed bed reactor, cross-sections with coordinates of 1.5 mm in the y direction (longitudinal section), and 5 mm, 35 mm, 65 mm, and 95 mm in the x direction (transverse cross section), were adopted as the reference surfaces, as shown in Figure 2a,b.Data of typical lines were also analyzed in the following text, whose positions are shown in Figure 3. Here, Line 1 was the closest to the symmetric boundary, while Line 6 was the closest to the heating wall.

Govern Equations and Reactions Kinetic
In the novel composite packed bed, each channel was assumed to be a homogeneous porous media zone where heat/mass transfer and chemical reactions occur.The temperature between the particle and the mixture was regarded to be the same, and a local thermal equilibrium model was used.The monolith skeleton is a solid zone which only involves heat conduction.Due to the symmetry of the geometry, only a quarter of the reaction  In the subsequent analysis of the heat transfer and chemical reaction performance the composite packed bed reactor, cross-sections with coordinates of 1.5 mm in the y rection (longitudinal section), and 5 mm, 35 mm, 65 mm, and 95 mm in the x directi (transverse cross section), were adopted as the reference surfaces, as shown in Figure 2a Data of typical lines were also analyzed in the following text, whose positions are show in Figure 3. Here, Line 1 was the closest to the symmetric boundary, while Line 6 was t closest to the heating wall.

Govern Equations and Reactions Kinetic
In the novel composite packed bed, each channel was assumed to be a homogeneo porous media zone where heat/mass transfer and chemical reactions occur.The tempe ture between the particle and the mixture was regarded to be the same, and a local therm equilibrium model was used.The monolith skeleton is a solid zone which only involv heat conduction.Due to the symmetry of the geometry, only a quarter of the reacti  In the subsequent analysis of the heat transfer and chemical reaction performance of the composite packed bed reactor, cross-sections with coordinates of 1.5 mm in the y direction (longitudinal section), and 5 mm, 35 mm, 65 mm, and 95 mm in the x direction (transverse cross section), were adopted as the reference surfaces, as shown in Figure 2a,b.Data of typical lines were also analyzed in the following text, whose positions are shown in Figure 3. Here, Line 1 was the closest to the symmetric boundary, while Line 6 was the closest to the heating wall.

Govern Equations and Reactions Kinetic
In the novel composite packed bed, each channel was assumed to be a homogeneous porous media zone where heat/mass transfer and chemical reactions occur.The temperature between the particle and the mixture was regarded to be the same, and a local thermal equilibrium model was used.The monolith skeleton is a solid zone which only involves heat conduction.Due to the symmetry of the geometry, only a quarter of the reaction

Govern Equations and Reactions Kinetic
In the novel composite packed bed, each channel was assumed to be a homogeneous porous media zone where heat/mass transfer and chemical reactions occur.The temperature between the particle and the mixture was regarded to be the same, and a local thermal equilibrium model was used.The monolith skeleton is a solid zone which only involves heat conduction.Due to the symmetry of the geometry, only a quarter of the reaction section was studied in the numerical model.The govern equations in the porous media zone are as follows.
Continuity equation: where ρ f delegates the fluid density, and → v is the superficial velocity vector.Momentum conservation equation: Energies 2023, 16, 4347 5 of 14 where p is the pressure of the fluid, µ is the molecular viscosity of the fluid, and the momentum source term S i denotes the pressure drop resulting from the porous media.The source term S i is calculated according to the Ergun equation [32]: where ε represents the porosity, and d p is the mean catalyst particle diameter.Energy equation: where k eff is the effective thermal conductivity of the porous media, which is calculated by the weighted mean value of the fluid and solid thermal conductivity.h i represents the standard state enthalpy of formation.
→ J i is the diffusion flux of species i defined as where, D i,m refers to the mass diffusion coefficient for the i th species in the mixture, calculated by the Wilke correlation [33] and the corresponding binary diffusion coefficients in the system [34].The heat source term S chem due to the chemical reactions is defined as: where r j and ∆H j are the reaction rate and the heat of the reaction for the j th reaction, respectively, m is the number of the reactions, and η j represents the effectiveness factor of the j th reaction, which is taken as 1 since the diameter of the catalyst is relatively small and the inner diffusion can be neglected.The reaction rate will be described in detail in the reaction kinetics.Species conservation equations: where y i refers to the mass fraction of the i th species, while η i and R i represent the effectiveness factor and the net rate of formation of i th gaseous species, respectively.Only N−1 species transport equations are solved, and the mass fraction of the N th species is obtained by The reaction system of methane steam reforming process is complex, mainly including three reactions: steam reforming reaction, steam shift reaction, and direct steam reforming [35,36] as follows: A widely used comprehensive kinetic model of the methane steam reforming reaction proposed by Xu and Froment [37] was used in this paper.The reaction rates of each reaction are listed below: where r 1 , r 2 and r 3 denote the reaction rates of the reactions, k 1 , k 2 and k 3 represent the reaction constants, K The reaction constants k j (j = 1, 2, 3) use an Arrhenius equation as: where A j and E j are the pre-exponential factor and the activation energy of the j th reaction, respectively, and R gas denotes the universal gas constant, 8.314 J•mol −1 •K −1 .The equilibrium constants of reactions K j (j = 1, 2, 3) are calculated with the following equations [38]: The adsorption coefficients of each species K i (i = CH 4 , H 2 , CO, H 2 O) are calculated as: where K 0,i and ∆H i represent the adsorption coefficients under the standard condition and absorption enthalpy, respectively.Parameters of the comprehensive kinetic model in the above equations are listed in Table 1.
Table 1.Parameters of the comprehensive kinetic model of the methane steam reforming reaction process [37].

Parameters Values Parameters Values
In this paper, the commercial software ANSYS FLUENT was used to solve the govern equations.The reaction rates were implemented through a user-defined function (UDF) of DEFINE_VR_RATE.The heat and species source terms in the energy and species conservation equations were defined on the basis of the reaction rates.

Boundary Conditions
The inlet of the reactor was set as the velocity inlet, with the velocity (v in ) varying from 0.1 m/s to 0.5 m/s, which is in the range of laminar flow.The S/C ratio was approximately 3:1, and small portions of H 2 , CO, and CO 2 were added at the inlet to ensure convergence.The outer heating wall was simplified to a wall with a constant temperature to provide heat for the reactions, which was in the range of 824 K to 1200 K. Symmetrical boundary conditions were adopted for the symmetric center.The operation pressure was set as the atmospheric pressure, and the outlet was set as the pressure outlet whose gauge pressure was zero.

Computational Mesh and Model Validation
The hexahedral mesh was employed into the computation.The mesh sizes in the radial direction and the axial direction were changed to check the influence of the mesh on the computational results.The methane conversion rate (X CH 4 ), and the hydrogen yield (Y H 2 ), calculated by the following equations [39], are two important indexes for analyzing the reaction performances where F refers to the molar flow rate of the species.Three mesh numbers, i.e., 0.14 million, 0.34 million, and 0.64 million were used, respectively.It was found that the grid number of 0.34 million was capable to obtain good results, as the methane conversion rate between 0.34 million and 0.64 million was within 1%.
To validate the reliability of the numerical model, a similar problem with methane steam reforming in a catalyst bed was restudied, which can be referred to in our previous study [40].

Heat Transfer Enhancement of the Novel Structure
The catalyst particles in a traditional randomly packed bed reactor are stacked in a disordered state, which is characterized by its easy operation and simple structure.However, due to the wall effect and the low thermal conductivity of the catalyst particles, the radial heat transfer in the disordered packed bed is not optimal, leading to a significant temperature difference between the bulk and the wall.Therefore, the tube to particle diameter ratio is usually restricted to 4~8 when used for a strong endothermic methane steam reforming reaction.In this paper, a novel composite particle packed bed structure with a highly conductive framework was proposed, which aimed to improve the radial heat transfer characteristics.The heat transfer characteristics of these two packed beds were calculated and compared under the same boundary conditions, with T in = 673 K, T w = 824 K, and v in ranges from 0.1 m/s to 0.5 m/s.The Nusselt number, defined as Nu = hL/k, was used to represent the heat transfer characteristics.Here, h is the average wall-fluid heat transfer coefficient, defined as h = q/(T w − T f ) in both structures.The geometric characteristic length L in both structures was taken as the catalyst particle diameter of 0.4 mm.
Figure 4 shows the variation of Nu in the randomly packed bed and the composite particle packed bed.It can be seen that in the composite particle packed bed, the Nu is much higher than that in the randomly packed bed, reaching 2~5 times of the disordered structure, thereby showing the superiority of the novel structure.Figure 5 shows the temperature distribution of the longitudinal section, which was introduced in Figure 2a, in both structures.According to Figure 5, the internal temperature of the reactor continuously attenuated from the outer wall to the center of the reactor, and the average temperature at the center of the reactor in a disordered structure was found to be significantly lower than that in a composite structure.This indicates that the presence of a skeleton can greatly enhance the radial heat transfer performance, and the heat transfer effect is superior to that of a disordered structure.In addition, it can be inferred that selecting skeleton materials with different thermal conductivities will have a certain degree of impact on reactor performance, which will be discussed in Section 4.3.
was used to represent the heat transfer characteristics.Here, h is the average wall-fluid heat transfer coefficient, defined as h = q/(Tw − Tf) in both structures.The geometric characteristic length L in both structures was taken as the catalyst particle diameter of 0.4 mm.
Figure 4 shows the variation of Nu in the randomly packed bed and the composite particle packed bed.It can be seen that in the composite particle packed bed, the Nu is much higher than that in the randomly packed bed, reaching 2~5 times of the disordered structure, thereby showing the superiority of the novel structure.Figure 5 shows the temperature distribution of the longitudinal section, which was introduced in Figure 2a, in both structures.According to Figure 5, the internal temperature of the reactor continuously attenuated from the outer wall to the center of the reactor, and the average temperature at the center of the reactor in a disordered structure was found to be significantly lower than that in a composite structure.This indicates that the presence of a skeleton can greatly enhance the radial heat transfer performance, and the heat transfer effect is superior to that of a disordered structure.In addition, it can be inferred that selecting skeleton materials with different thermal conductivities will have a certain degree of impact on reactor performance, which will be discussed in Section 4.3.

Effect of Operating Parameters on Reaction Performance
In this section, the impact of three operating parameters, namely, the inlet tempe ture Tin, the wall temperature Tw, and the inlet velocity vin, on the reaction performan were studied, and sensitivity analysis was conducted.Here, a sensitivity factor, which quantified as the ratio of the methane conversion change rate to the operating parame change rate, was used in the sensitivity analysis.
Figure 6 shows the methane conversion rate

Effect of Operating Parameters on Reaction Performance
In this section, the impact of three operating parameters, namely, the inlet temperature T in , the wall temperature T w , and the inlet velocity v in , on the reaction performance were studied, and sensitivity analysis was conducted.Here, a sensitivity factor, which is quantified as the ratio of the methane conversion change rate to the operating parameter change rate, was used in the sensitivity analysis.
Figure 6 shows the methane conversion rate X CH 4 and hydrogen yield Y H 2 when T in = 673 K, v in = 0.1 m/s, 0.2 m/s, 0.5 m/s, and T w varies from 824 K to 1050 K. From Figure 6, it can be found that the temperature of the heating wall has a significant impact on X CH 4 and Y H 2 , especially when T w is lower than 1000 K. Furthermore, when v in increases to 0.5 m/s, the X CH 4 and Y H 2 have a clear decrease compared to that of v in = 0.1 m/s and 0.2 m/s.
Energies 2023, 16, 4347 9 of 14 change rate, was used in the sensitivity analysis.
Figure 6 shows the methane conversion rate Y when Tin = 673 K, vin = 0.1 m/s, 0.2 m/s, 0.5 m/s, and Tw varies from 824 K to 1050 K. From Figure 6, it can be found that the temperature of the heating wall has a significant impact on  To obtain a clear insight into the performance of the packed bed, the temperature contours, and the mass fractions of methane ( ) under the working conditions of vin =0.1 m/s and vin = 0.5 m/s at Tw = 950 K are displayed in Figures 7 and 8, respectively.From Figure 7a, it can be seen that the temperature distributions on the cross-sections are almost uniform and reach the maximum value except for x = 5 mm near the inlet.However, as indicated by Figure 7b, when the flow rate increases to 0.5 m/s, the temperature difference between the center of the packed bed and the heating wall is large.Analysis of the results of mass fraction of methane reveals that the local temperature exhibits a direct influence on the reaction rate, as shown in Figure 8. Figure 8a   To obtain a clear insight into the performance of the packed bed, the temperature contours, and the mass fractions of methane (y CH 4 ) under the working conditions of v in = 0.1 m/s and v in = 0.5 m/s at T w = 950 K are displayed in Figures 7 and 8, respectively.From Figure 7a, it can be seen that the temperature distributions on the cross-sections are almost uniform and reach the maximum value except for x = 5 mm near the inlet.However, as indicated by Figure 7b, when the flow rate increases to 0.5 m/s, the temperature difference between the center of the packed bed and the heating wall is large.Analysis of the results of mass fraction of methane reveals that the local temperature exhibits a direct influence on the reaction rate, as shown in Figure 8. Figure 8a indicates that when the local temperature is almost as high as the heating wall temperature, the methane consumption rates are also high for all six lines and reach the equilibrium state at half of the reactor length.Figure 8b shows that the methane consumption rates at different locations differ from each other and did not reach the equilibrium state until the outlet of the reactor.This is the reason for why the methane conversion rate and the hydrogen yield are similar when the inlet velocities are 0.1 m/s and 0.2 m/s, but these two values demonstrate significant decreases when the inlet velocity is 0.5 m/s.These results show the importance of the contact time between the reactant and the catalyst, which indicates that the inlet velocity should be determined by the reactor dimension and the catalytic activity.
Both the inlet velocity and the heating wall temperature affect the local temperature, and thus have an influence on the reaction performance.In order to quantify the influence of these two parameters, the sensitivity factor of X CH 4 to v in and X CH 4 to T w were calculated and compared, as listed in Table 2. From Table 2, it can be seen that the temperature of the heating wall was more remarkable than that of the inlet velocity, which indicates that a smaller change in the heating wall temperature will bring a more significant change in the methane conversion rate.temperature is almost as high as the heating wall temperature, the methane consumption rates are also high for all six lines and reach the equilibrium state at half of the reactor length.Figure 8b shows that the methane consumption rates at different locations differ from each other and did not reach the equilibrium state until the outlet of the reactor.This is the reason for why the methane conversion rate and the hydrogen yield are similar when the inlet velocities are 0.1 m/s and 0.2 m/s, but these two values demonstrate significant decreases when the inlet velocity is 0.5 m/s.These results show the importance of the contact time between the reactant and the catalyst, which indicates that the inlet velocity should be determined by the reactor dimension and the catalytic activity.
(a) (b)  Both the inlet velocity and the heating wall temperature affect the local temperature, and thus have an influence on the reaction performance.In order to quantify the influence of these two parameters, the sensitivity factor of  2. From Table 2, it can be seen that the temperature of the heating wall was more remarkable than that of the inlet velocity, which indicates that a smaller change in the heating wall temperature will bring a more significant change in the methane conversion rate.x/m  Figure 9 shows X CH 4 and Y H 2 at inlet velocities of 0.1~0.5 m/s and T in = 673 K, 1050 K at T w = 880 K, respectively.From Figure 9, it can be seen that the inlet velocity has a significant impact on the results, while the influence of T in does not seem to exhibit the same effect.However, one should note that the inlet velocity increases up to five times, while the inlet temperature changes within a certain range.Therefore, the sensitivity factor of X CH 4 to v in and X CH 4 to T in were subsequently calculated and are shown in Table 3.Here, working conditions with the largest change rate of X CH 4 was used for comparison, i.e., when T in = 673 K, the inlet speed increased from 0.1 m/s to 0.5 m/s, and when v in = 0.5 m/s, the inlet temperature increased from 673 K to 1050 K.According to the sensitivity factors, the effect of the inlet temperature in the reactor on X CH 4 was basically equivalent to the inlet velocity.
In general, temperature is an imperative influencing factor in the packed bed reactor.All three parameters have an effect on the local temperature and the reaction performances.In the studied range of the present paper, changes in the heating wall temperature can maximize the methane conversion rate, while inlet temperature and inlet velocity have a similar and relatively low impact.at Tw = 880 K, respectively.From Figure 9, it can be seen that the inlet velocity has a significant impact on the results, while the influence of Tin does not seem to exhibit the same effect.However, one should note that the inlet velocity increases up to five times, while the inlet temperature changes within a certain range.Therefore, the sensitivity factor of     The above results show a good heat transfer and reaction performance of the composite packed bed, which used Ni-Cr alloy as the skeleton material.The main reason can be attributed to the high thermal conductivity of the Ni-Cr alloy.However, the price of the Ni-Cr alloy is relatively high.In order to reduce the cost of the reactor, this section will explore the impact of cordierite, which is inexpensive, but also has a low thermal conductivity, on the heat transfer and reaction performance.The thermal properties of these two materials are shown in Table 4. Figure 10 shows the temperature distributions of four cross-sections in a reactor with different skeleton materials at T w = 950 K and v in = 0.2 m/s.As shown in Figure 10, when using the Ni-Cr alloy, the internal temperature of the reactor reached the wall temperature except for the first section.When using cordierite, the radial temperature gradient in the reactor always existed, indicating that a sufficient heating effect was not achieved.Figure 11 shows the change of methane mass fraction y CH 4 along the auxiliary line direction in the two reactors when T w =950 K and v in =0.2 m/s, respectively.In the two reactors, y CH 4 in line 6 decreases the fastest while y CH 4 in line 1 decreases the slowest, which was deemed to be related to the radial temperature distribution in the reactor.In the Ni-Cr alloy reactor and the cordierite reactor, the methane mass fraction of all the lines tended to be the smallest at x = 0.05 m and x = 0.1 m, indicating that the reactors of the two materials completed the reaction at x = 0.05 m and x = 0.1 m, respectively.Based on the results in Section 4.2, it can be inferred that when the heating wall temperature is constant, the lower the inlet speed, the closer the reaction completion position will be to the reactor inlet, and the smaller the performance difference between the two reactors.Figure 10 shows the temperature distributions of four cross-sections in a reactor with different skeleton materials at Tw = 950 K and vin = 0.2 m/s.As shown in Figure 10, when using the Ni-Cr alloy, the internal temperature of the reactor reached the wall temperature except for the first section.When using cordierite, the radial temperature gradient in the reactor always existed, indicating that a sufficient heating effect was not achieved.Figure 11 shows the change of methane mass fraction   in line 1 decreases the slowest, which was deemed to be related to the radial temperature distribution in the reactor.In the Ni-Cr alloy reactor and the cordierite reactor, the methane mass fraction of all the lines tended to be the smallest at x = 0.05 m and x = 0.1 m, indicating that the reactors of the two materials completed the reaction at x = 0.05 m and x = 0.1 m, respectively.Based on the results in Section 4.2, it can be inferred that when the heating wall temperature is constant, the lower the inlet speed, the closer the reaction completion position will be to the reactor inlet, and the smaller the performance difference between the two reactors.In addition, the reaction performances of different wall temperatures Tw = 824 K~1200 K at an inlet velocity of 0.2 m/s were studied.Figure 12 shows the methane conversion In addition, the reaction performances of different wall temperatures T w = 824 K~1200 K at an inlet velocity of 0.2 m/s were studied.Figure 12 shows the methane conversion rate and hydrogen yield of the reactor with two skeleton materials.It can be seen from Figure 12 that the influence of the thermal conductivity of the skeleton material on the reactor cannot be ignored.The methane conversion rate and the hydrogen yield of the Ni-Cr alloy reactor were found to be always higher than those of the cordierite reactor.However, when the wall temperature was 1200 K, the difference in the hydrogen yield between the two reactors was only 1.38%, and there was no significant difference found in the performance, indicating that higher wall temperatures are able to reduce the impact of thermal conductivity.Therefore, in order to reduce the manufacturing costs of the reactor, it is recommended to select the cordierite (with a low price) as the skeleton material of the composite particle packed bed, when the external heat source can provide wall temperatures above 1200 K. rate and hydrogen yield of the reactor with two skeleton materials.It can be seen from Figure 12 that the influence of the thermal conductivity of the skeleton material on the reactor cannot be ignored.The methane conversion rate and the hydrogen yield of the Ni-Cr alloy reactor were found to be always higher than those of the cordierite reactor.However, when the wall temperature was 1200 K, the difference in the hydrogen yield between the two reactors was only 1.38%, and there was no significant difference found in the performance, indicating that higher wall temperatures are able to reduce the impact of thermal conductivity.Therefore, in order to reduce the manufacturing costs of the reactor, it is recommended to select the cordierite (with a low price) as the skeleton material of the composite particle packed bed, when the external heat source can provide wall temperatures above 1200 K.

Conclusions
A novel composite particle packed bed structure for small-scale distributed hydrogen production using steam methane reforming reaction was proposed in this paper.The heat transfer and chemical reaction performances of the novel reactor were studied by establishing a three-dimensional computational fluid dynamics model.The main conclusions are as follows: 1. Compared to the traditional randomly packed bed, the presence of a heat conductive skeleton in the composite particle packed bed can enhance heat transfer, improve the radial heat transfer performance of the reactor, and is expected to improve the kinetic performance of the reactor.2. Temperature in the composite particle packed bed is an important factor that affects both the methane conversion rate and the hydrogen yield.The results of sensitivity analysis using sensitivity factors reveal that changes in the wall temperature can

Conclusions
A novel composite particle packed bed structure for small-scale distributed hydrogen production using steam methane reforming reaction was proposed in this paper.The heat transfer and chemical reaction performances of the novel reactor were studied by establishing a three-dimensional computational fluid dynamics model.The main conclusions are as follows: 1.
Compared to the traditional randomly packed bed, the presence of a heat conductive skeleton in the composite particle packed bed can enhance heat transfer, improve the radial heat transfer performance of the reactor, and is expected to improve the kinetic performance of the reactor.

2.
Temperature in the composite particle packed bed is an important factor that affects both the methane conversion rate and the hydrogen yield.The results of sensitivity analysis using sensitivity factors reveal that changes in the wall temperature can maximize reaction performance, while the inlet velocity and temperature have a similar and smaller impact.

3.
The higher the wall temperature, the smaller the influence of the thermal conductivity of the skeleton material on the reactor performance.When external heat sources provide wall temperatures above 1200 K, selecting cordierite, which has a low thermal conductivity, but also a low cost, as the skeleton material of the composite particle packed bed can greatly reduce the manufacturing cost of the reactor.

Figure 1 .
Figure 1.The structure and the dimensions of the novel composite packed bed reactor (the red circle refers to a single channel with its enlarged view at the bottom right).

Figure 1 .
Figure 1.The structure and the dimensions of the novel composite packed bed reactor (the red circle refers to a single channel with its enlarged view at the bottom right).

Figure 1 .
Figure 1.The structure and the dimensions of the novel composite packed bed reactor (the red circle refers to a single channel with its enlarged view at the bottom right).

Figure 1 .
Figure 1.The structure and the dimensions of the novel composite packed bed reactor (the red circle refers to a single channel with its enlarged view at the bottom right).

Figure 3 .
Figure 3. Locations of the lines.

Figure 4 .
Figure 4. Variation of Nu at different inlet velocities in both structures.

Figure 4 .Figure 5 .
Figure 4. Variation of Nu at different inlet velocities in both structures.Energies 2023, 16, x FOR PEER REVIEW 9 o

4 CH X a 2 HY 4 CH X and 2 HYvFigure 5 .
Figure 5. Temperature distribution of the longitudinal section in both structures: (a) randomly packed bed, and (b) composite particle packed bed.

4 CH X and 2 HY 4 CH X and 2 HY
, especially when Tw is lower than 1000 K. Furthermore, when vin increases to 0.5 m/s, the have a clear decrease compared to that of vin = 0.1 m/s and 0.2 m/s.

Figure 6 . 4 CH X and 2 HY
Figure 6.The

Figure 6 .
Figure 6.The X CH 4 and Y H 2 under various inlet velocities and heating wall temperatures.

to
Tw were calculated and compared, as listed in Table

Figure 8 .
Figure 8. Variations of y CH 4 along the flow direction in different lines: (a) T in = 673 K, v in = 0.1 m/s, T w = 950 K, and (b) T in = 673 K, v in = 0.5 m/s, T w = 950 K, respectively.

to
Tin were subsequently calculated and are shown in Table3.Here, working conditions with the largest change rate of 4 CH X was used for comparison, i.e., when Tin = 673 K, the inlet speed increased from 0.1 m/s to 0.5 m/s, and when vin = 0.5 m/s, the inlet temperature increased from 673 K to 1050 K.According to the sensitivity factors, the effect of the inlet temperature in the reactor on

Figure 9 . 4 CH X and 2 HY
Figure 9.The

Figure 9 .
Figure 9.The X CH 4 and Y H 2 under various inlet velocities and inlet temperatures.
line direction in the two reactors when Tw =950 K and vin =0.2 m/s, respectively.In the two reactors,

Figure 10 .Figure 10 .
Figure 10.The temperature contours of the cross-sections along the flow direction with different materials.(a) Ni-Cr alloy, and (b) cordierite.

Figure 10 .
Figure 10.The temperature contours of the cross-sections along the flow direction with different materials.(a) Ni-Cr alloy, and (b) cordierite.

Figure 11 .
Figure 11.Variations of y CH 4 along the flow direction in different locations.(a) Ni-Cr alloy, and (b) cordierite.

Figure 12 .
Figure 12.The XCH4 and YH2 reactors with different honeycomb materials.

Figure 12 .
Figure 12.The X CH4 and Y H2 reactors with different honeycomb materials.
1 , K 2 and K 3 represent the equilibrium constants of the reactions, K CH 4 , K CO , K H 2 and K H 2 O denote the adsorption coefficients, and p CH 4 , p H 2 , p CO , p CO 2 and p H2O are the partial pressures of respective certain species.

Table 2 .
Sensitivity factors of 4 CHXto vin and Tw.

Table 2 .
Sensitivity factors of X CH 4 to v in and T w .

Table 3 .
Sensitivity factors of 4 CHXto vin and Tin.

Table 3 .
Sensitivity factors of X CH 4 to v in and T in .

Table 4 .
Properties of cordierite and the Ni-Cr alloy.

Table 4 .
Properties of cordierite and the Ni-Cr alloy.