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Numerical investigation of carbon deposition behavior in Ni/Al2O3-based catalyst porous-filled solar thermochemical reactor for DRM process Hao Zhang, Yong Shuai, Songjian Pang, Ruming Pan, Bachirou Guene Lougou, and Xing Huang Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b02486 • Publication Date (Web): 09 Aug 2019 Downloaded from pubs.acs.org on August 14, 2019

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Industrial & Engineering Chemistry Research

Numerical investigation of carbon deposition behavior in Ni/Al2O3-based catalyst porous-filled solar thermochemical reactor for DRM process Hao Zhanga,b, Yong Shuaia,b*, Songjian Panga,b, Ruming Pana,b, Bachirou Guene Lougoua,b*, Xing Huangc a

Key Laboratory of Aerospace Thermophysics of MIIT, Harbin Institute of Technology, 92 West

Dazhi Street, Harbin 150001, China b

School of Energy Science and Engineering, Harbin Institute of Technology, 92 West Dazhi Street,

Harbin 150001, China c

College of Metallurgy and Energy, North China University of Science and Technology, Tangshan,

Hebei 063210, China

*

Corresponding author. 1 E-mail address: [email protected] E-mail address: [email protected] ACS Paragon Plus Environment

Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Due to the utilization of concentrated solar energy, a more complex high-temperature thermal environment will be formed inside the solar thermochemical reactor, thereby resulting in complicated behaviors of chemical reactions. This paper numerically investigates the carbon deposition behaviors inside a Ni/Al2O3-based catalyst porous-filled STR for DRM process under various operational conditions. The reaction kinetics for DRM including four side reactions are programmed via UDFs. The simulation results indicate that the optimal structural parameters of porous media for high-value syngas products with less carbon deposition are φ = 0.8 and d p = 2 mm , while the optimal feed ratio is CH4/CO2 = 1. Besides, the operating condition at vin = 100 ml/ min and Plamp = 0.7 kW has the advantage of obtaining higher conversion rate while

reducing the carbon deposition rate to some extent.

Keywords: Dry reforming of methane (DRM); Carbon deposition; Solar thermochemical reactor (STR); Porous media; Ni/Al2O3 catalyst.

TOC:

(For Table of Contents Only)

2 ACS Paragon Plus Environment

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1. Introduction Methane, the second most dangerous greenhouse gas emitted from human activities1-3 accounts for about 14% of total greenhouse gas emissions with a global warming potential of 25 times as large as CO2.4,5 Facing this increasingly serious environmental issue, the dry (CO2) reforming of methane (DRM) technology shows tremendous applicable value due to its double advantages of synthesis-gas valorization and carbon dioxide sequestration. 6,7 The syngas (mainly for H2 and CO) produced by DRM can be further processed into various products such as higher alkanes and oxygenates via Fischer-Tropsch synthesis.8 However, coke management has been the most difficult issues regarding the techno-economic feasibility and commercialization of DRM process.5,9 Theoretically, DRM can effectively convert CH4 and CO2 into syngas products with H2/CO ratio of 1 via the main reaction process (Eq. 1). However, the primary side reaction, reverse water gas shift (RWGS) reaction (Eq. 2), will result in a decrease of H2/CO ratio in the final products. As a matter of fact, DRM process belongs to a complex reaction network, rather than a stoichiometrically independent reaction.7,10 CH 4 + CO 2 → 2CO + 2H 2 , ∆H o298 = + 247.0 kJ/mol

(1)

CO 2 + H 2 → CO + H 2 O, ∆H o298 = + 41.7 kJ/mol

(2)

In this process, the C-H bonds of methane molecules are activated and broke under the effect of catalyst. Therefore, the overall reactivity of feed gas mainly depends on the catalyst activity. Currently, Ni-based catalysts are the most widely used in many industrial DRM processes because of its excellent catalytic activity and low industrial cost.11-13 However, compared with the noble metal catalysts, Ni-based catalysts tend to be more susceptible to deactivation under prolonged high-temperature reactions. The main factors leading to the deactivation of Ni-based catalysts could be listed as (1) carbon deposition; (2) sintering of active components.9,14 When the carbon is deposited, the active metal in the catalysts will be captured by the carbonaceous deposit.12 At the same time, some micropores and mesopores will be blocked by the deposit, which may severely decrease the possibility of reactants entering the active site.5 The carbon deposition and gasification reactions are given as Eq. 3 - Eq. 5.7,15 Moreover, by loading Ni nano-particle on the



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surface of support structures, such as SiC/Al2O3/MgO, a kind of catalyst with better activity can be obtained, namely supported catalyst. Due to the efficient surface and appropriate pore structure, supported catalyst has advantages of reducing carbon deposit and improving mechanical strength. Especially, the excellent thermal resistance of supports is required for extending cycle life of catalysts in some high-temperature thermal environment. CH 4 → C + 2H 2 , ∆H o298 = + 74.0 kJ/mol

(3)

C + H 2 O → CO + H 2 , ∆H o298 = + 131.3 kJ/mol

(4)

C + CO 2 → 2CO, ∆H o298 = + 172.0 kJ/mol

(5)

According to thermodynamic calculations, the carbon deposit formed by exothermic Boudouard reaction is negligible at any temperature above 750 °C.9 Therefore, the reverse reaction of this process (Eq. 5) contributes to eliminating the carbon deposits when the operating temperature is controlled between 800-1000 °C.12 Finally, the degree of carbon deposition will be determined by the balance between the methane cracking reaction (Eq. 3), Boudouard equilibrium and carbon gasification reaction (Eq. 4).16 Many studies have investigated the thermodynamic of DRM and reported various approaches including controlling optimum operating conditions,17 changing catalyst carriers,12,18 and adding a noble metal or another transition metal11,19 for effectively inhibiting carbon deposition. To date, there is still insufficient knowledge regarding the reaction kinetics and inner reaction behaviors of the DRM process,10 especially for the porous-filled solar thermochemical reactor (STR).7,20 Xie et al.15 have numerically studied an integrated solar thermochemical energy storage system for DRM process with methane cracking reaction. The detailed numerical description for the concentration process of radiation energy and thermodynamic model of the reactor was reported. However, further discussion about carbon deposition has been lacked. Jang et al.21,22 have experimentally investigated a methane reforming (MR) process in a solar volumetric receiver-reactor. It is reported that proper adjusting of the MR time was effective to prevent the carbon deposition. Wang et al.23 and Chen et al.20,24 systematically investigated the heat transfer and thermochemical reaction in a volumetric reactor for DRM under highly concentrated solar radiation by using FVM methods coupled with thermochemical kinetics. However, the effect of carbon deposition was not


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taken into consideration. Benguerba et al.10,25 have investigated the thermochemical performance of a fixed-bed catalytic reactor with a numerical model combining Richardson and Paripatyadar kinetics,26 and Snoeck kinetics27 for analyzing carbon deposition reactions. The influence of CH4/CO2 feed ratio in addition to that of the temperature on the chemical species conversion and carbon deposition were discussed. Compared with the first thermal boundary condition, the concentrated solar irradiation generated by CSP technique will form a more complex thermoenvironment and varied composition changes of the main reactants inside the STR. 20,23,28 On the other hand, porous media has the advantage of enhancing heat and mass transfer, thereby improving the thermochemical performance.29,30 However, the effect of the porous media on carbon deposition remains uncertain. In this study, the thermochemical performance and carbon deposition behaviors in a porousfilled STR for DRM process are numerically investigated by coupling finite volume method (FVM) with DRM reaction kinetics. The concentration process of solar irradiation powered by a solar simulator is modeled and simulated by TracePro software with Monte Carlo ray tracing (MCRT) method. The incident heat flux results are numerically fitted and wrote into Fluent software as the second thermal boundary condition to calculate the heat and mass transfer characteristics. In this process, the non-Darcy effect is taken into consideration by UDFs to describe the flow resistance and pressure drop resulting from porous ceramics. Besides, local thermal equilibrium (LTE) model and discrete ordinate (DO) are adopted to solve the heat and radiation transfer problem, respectively. In addition, a complex reaction network for DRM process with RWGS, carbon cracking, carbon gasification, and Boudouard reaction is performed by UDFs. Based on these, the carbon deposition behavior inside the STR under various operating parameters and porous media properties are respectively investigated. 2. Models and methods 2.1. Physical model The schematic diagram describing the system of the Ni-based catalysis porous-filled STR coupled to the high-flux solar simulator is depicted in Figure 1. The laboratory-scale STR utilized concentrated radiation energy provided by a solar simulator as the heat source to drive the DRM reaction inside the porous zone. Note that the DRM reactions were defined as volumetric type in



this study, which was considered to only take place in the porous zone. Al2O3 porous ceramic with excellent temperature resistance and mechanical strength was filled into the reactor chamber with the aim to enlarge reaction areas and provide sufficient contact with the feed gas.28 Then, Ni nanoparticles were coated on the surface of Al2O3 support to obtain better activity and catalysis. Before entering the reaction zone, the feed gas would be dual-preheated by the heat dissipation channel and the radiant energy through the quartz window, which has the advantages of reducing heat loss and improving thermal environment.30 Besides, the multi-layer insulation structure has the advantages of minimizing heat loss and improving the overall thermal performance of STR. The detailed structural parameters and operating conditions of the solar simulator and STR for the base case simulations are listed in Table 1.

Figure 1. Schematic of the solar thermochemical system. Table 1. Structural parameters and operating conditions of the solar simulator and STR. Parameters Power of Xenon short arc lamp The first/second focal length Diameter of ellipsoidal reflector Diameter of Xenon short arc lamp (sphericity) Number of rays for simulation Total length of STR Position of porous zone Diameter of porous zone Porosity of porous media Mean cell size of porous media Inlet diameter Inlet pressure Inlet/environment temperature Inlet flow rate CH4/CO2-feed ratio

Values Various (0.5-1 kW) 55/825 mm 380 mm 3 mm 1 million 132 mm 52-112 mm 50 mm Various (0.65-0.9) Various (1.5-9.0 mm) 5 mm 1 atm 300 K Varied (10-200 ml/min) Varied (1:3-3:1)


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2.2. Numerical models 2.2.1. Thermophysical models Continuity equation:

  ∇ ⋅ ( ρ m uYi ) = −∇J i + Ri

(6)

 where ρ m is the density of mixture gases; Yi represents the mass fraction species i; the symbol J i

and Ri represent the diffusive mass flux and net production rate of the species i, respectively. Momentum equation:   ∇ ⋅ ( ρ m uu )=∇ ⋅ ( µ∇u ) − ∇pm + Sp

(7)

where pm is the pressure of mixture gases, µ is the dynamic viscosity, and Sp is the source term caused by non-Darcy effect in porous zone, which can be calculated according to the DarcyForchheimer extended model (DF model):29,31  µ Sp = − u − 0.5CF ρ m u u K

(8)

where the first item is the viscous resistance term, the second item is the inertial resistance term, K is the permeability of porous media, and CF is the inertia resistance term that can be expressed

as follows:23,31 CF =

1.75(1 − φ ) φ 2 dp

(9)

where d p is the mean cell size of porous medium. Energy equation: n  ∇ ⋅ ( ρ m cp,m uTm ) = ∇ ⋅ (λm ∇Tm − ∑ hi J i ) + Srad + Schem

(10)

i =1

where λm and cp,m are the thermal conductivity and heat capacity of mixture gases, respectively; the symbol Srad and Schem represent the radiative heat transfer source and chemical reaction term, respectively, and hi is the enthalpy of species i. Besides, mixing law is adopted to calculate the heat capacity of mixture gases:32



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n

cp,m = ∑ yi cp,i

(11)

i

where yi and cp,i are the mole fraction and heat capacity of species i, respectively. For the outlet surface, zero temperature gradient boundary condition is given:

∂Tf,out ∂Tf,out ∂Ts,out ∂Ts,out = = = = 0 ∂x ∂y ∂x ∂y

(12)

Radiative heat transfer equation:31   σT 4 σs ∇ ⋅  I (r , s ) s  + (α + σ s= + ) I (r , s ) α n 2 π 4π

 

 

∫ π I (r , s′) Φ(s, s′)dΩ′ 4

(13)

  where I is the radiative heat intensity depending on the position r and direction s , α is the  absorption coefficient, σ s is the scattering coefficient, n is the refractive index, s ′ is the

scattering direction vector, Φ is the phase function, and Ω′ is the solid angle. Based on the DO radiative method, the radiation heat obtained by the wall surface is: = qin

∫

  I s ⋅ ndΩ

(14)

  s ⋅n > 0 in

And the net radiation heat leaving from the wall is: qout = (1 − ε w )qin + n 2ε wσ Tw 4

(15)

 where n is the unit normal vector to the wall, and ε w is the emissivity of the wall.

2.2.2. Reaction kinetics As already mentioned, the reaction system of DRM belongs to a rather complex reaction network.7,10 In order to describe the chemical behavior more accurately, the reaction kinetics of DRM including four side reactions organized by Benguerba et al.10,25 were adopted in this study. The related expressions of these reaction rates were programmed into Fluent software by UDFs. Corresponding reaction rate equations are listed in Table 2. Table 2. Reaction rate equations of DRM process.10 Reproduced from ref 10 with permission from the Springer Nature, Copyright 2015. Reactions DRM26

Equations CH 4 + CO 2 → 2CO + 2H 2 ∆H o298 = + 247.0 kJ/mol

Reaction rates k1K CO2 ,1K CH4 ,1PCH4 PCO2  (PCO PH2 ) 2  r1 = 1 −   (1+K CO2 ,1PCO2 +K CH4 ,1PCH4 ) 2  K P1 (PCH4 PCO2 ) 


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RWGS26

Methane cracking33

CO 2 + H 2 → CO + H 2 O, ∆H

o 298

= + 41.7 kJ/mol

r2 =

 (PCO PH2 O )  1 −  (1+K CO2 ,2 PCO2 +K H2 ,2 PH2 )  K P2 (PCO2 PH2 )  k 2 K CO2 ,2 K H2 ,2 PCO2 PH2

2

k 3 K CH4 ,3 (PCH4 -

CH 4 → C + 2H 2

r3 =

∆H o298 = + 74.0 kJ/mol

(1+K CH4 ,3 PCH4 +

k4

Boudouard reaction27

Coke gasification27

C + H 2 O → CO + H 2 ∆H

o 298

= + 131.3 kJ/mol

C + CO 2 → 2CO ∆H o298 = + 172.0 kJ/mol

K H2 O,4

r4 =

K P3 PH1.52

K H2 ,3

(

(1+K CH4 ,4 PCH4 +

PH22

) )2

PH2 O PCO ) PH2 K P 4 PH2 O K H2 O,4 PH2

+

PH1.52 K H2 ,4

)2

PCO P k5 ( 2 - CO ) K CO,5 K CO2 ,5 PCO K P5 r5 = PCO2 (1+K CO,5 PCO + )2 K CO,5 K CO2 ,5 PCO

Note that k i is the reaction rate constant; K i is the thermodynamic equilibrium constant, Pi is the partial pressure for species i . See Ref. (10) for detailed equations and parameters. 2.2.3. Fitting of irradiation density The original irradiation density data of ray concentrating process are some values related to discrete coordinates. Before adopted as the thermal boundary condition, these data have been supposed to be fitted to corresponding formula form. Figure 2 illuminates the comparison between the fitted data and original irradiation density distribution at the lamp power of 0.5 kW. The fitted method was based on Gaussian equation by using Origin software. The fitted irradiation density function related to the position x is expressed as follows:  x   qw = q0 + A × exp  −0.5 ×    0.00932  

2

  

(13)

where q0 and A are relevant coefficients; while the lamp power is 0.5 kW, q0 = 14.922 , A = 524.26 . The unit qw is kW.


600 Original data Fitting data

500

P = 0.5 kW

400 300 200 100 0 -0.06

-0.03 0.00 0.03 Center distance (m)

0.06

Figure 2. Data fitted for the ray concentrating process. 2.2.4. Model validation The validation of the fitted data has been carried out, and the adjusted R-square of the results is 0.985. Besides, the grid independence test has also been performed. More than 63 000 cells were drawn to satisfy this requirement. The convergence criterion of continuity and momentum equation was set to be 10-4, while that of species equation was set to be 10-6. In addition, the thermotransport model adopted in this study has been validated in our previous works.29 The methods to calculate the heat and mass transfer, as well as the fluid flow characteristics, have been proved to be reliable. On the other hand, with the aim to confirm the correction of chemical reaction part solely, the CH4/CO2 conversion results calculated in this study were compared with the numerical and experimental results from Benguerba et al.10, As shown in Figure 3. The same inlet flow rate and thermal boundary conditions were adopted in these cases to verify the correctness of the simulation results. Although the simulation data at few temperatures in this study have a certain deviation from that of Benguerba et al.10, a satisfactory degree of matching relation between these data are shown in general.

CH4, Present CH4, Simulation [10] CH4, Experiment [10] CO2, Present CO2, Simulation [10] CO2, Experiment [10]

100 Conversion (100 %)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Irradiation density (kW/m2)


80 60 40 20 450

500 550 600 Temperature (℃)

650


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Figure 3. Comparison of the CH4/CO2 conversion results with that from Benguerba et al.10 ( vin = 52 Nml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 ). Reproduced from ref 10 with permission from the Springer Nature, Copyright 2015. 3. Results and discussion 3.1. Effect of foam structural parameters Figure 4 illustrates the mole fraction distribution of carbon along the centerline of the STR with the variation of the material porosity from 0.65-0.9 at lamp power of 0.5 kW, flow rate of 100 ml/min, feed ratio CH4/CO2/N2 = 1:1:8, and barometric pressure of 1 atm. Note that the chemical reactions taking place inside the porous zone are defined as volumetric type, and all of the species including carbon are treated as diffusible. Accordingly, the mole fraction of carbon is defined as the ratio of carbon moles to total moles. As shown by the results, the amount of carbon deposition continues to grow with the increase in material porosity. This can be attributed to the overall rise in the temperature of porous media which results in the acceleration of the endothermic carbon formation reaction14 when the reacting medium porosity increases.20,24 However, it should be noted that the final quantity of carbon deposition is determined by multiple factors rather than a single one, especially in a complex thermal environment inside the STR.29,34 In addition, it can be seen that the simulation results in the same axial coordinate (perpendicular to the axis direction) have no obvious difference judging from the mole fraction distribution contours. Therefore, these mole fraction values along the centerline of the STR can be regarded as the average values at different positions along the axis.

Mole fraction of carbon

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0.012 0.009 0.006

φ = 0.65 φ = 0.70 φ = 0.75 φ = 0.80 φ = 0.85 φ = 0.90

0.003 0.000 0.03

0.06 0.09 Position (m)


0.12


Figure 4. Mole fraction distribution of carbon along the centerline at different porosities. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 ) The contours of carbon formation rate distribution at porosities of 0.65 and 0.9 are compared for further investigating the effect of porosity on the carbon formation inside the STR, as represented in Figure 5. Note that the chemical reactions only occur in the porous zone (0.0520.112 m) that coated with catalyst. It can be seen that the increase in the porosity causes an obvious change in the carbon formation rate distribution, which leads to the consequence that the carbon formation variation cannot be accurately described by the values along the centerline. Therefore, with the aim to describe the non-uniformity of carbon formation rates in the direction perpendicular to the axis caused by different porosities, six curves about carbon formation rate distribution along the front surface of porous media at the porosities from 0.65-0.9 are drawn and compared, as shown in Figure 6.

Figure 5. Contours of carbon formation rate distribution at (a) Φ = 0.65; (b) Φ = 0.9. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 ) As depicted in Figure 6, the carbon deposition rate exhibits a symmetric distribution as a function of central axis due to the symmetrical boundary conditions. Significant impacts of porosity on the carbon formation distribution on the front surface of the porous media can be seen in Figure 6. The increase in the medium porosity aggravates the chaos degree of carbon formation. However, the advantageous effects of reducing carbon deposition in the front central area to a certain range have been observed during this process. It can be seen that the carbon formation rate in the middle area is gradually declining with the increase of porosity after φ = 0.8 , which is


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mainly affected by the temperature distribution (Figure 7) and partial pressure according to the Arrhenius Law.10,15 The temperature variation at the front porous zone (at 0.052 m) as a function of the medium porosity reasonably corresponds to the difference of carbon formation rates at the position of x = 0 in Figure 6. Further, the formation of temperature field is related to many factors like mass transfer, radiation transfer, and reaction heat. With the increase of porosity, the flow resistance and pressure drop are reducing according to Equation (8) and Equation (9). Then, the fluid flow is accelerated and the effect of radiation absorption is weakened. Accordingly, the fluid temperature in the middle area declines sharply after the porosity increases to a certain degree (Figure 7). Moreover, as shown in Figure 6, the closer to the inner wall, the smaller impact of porosity on the carbon formation rate can be observed, which is mainly due to the lower flow rate

Carbon formation rate (mol·m-3·s-1)

near the wall as well. 3.00

φ = 0.65 φ = 0.70 φ = 0.75

2.85

φ = 0.80 φ = 0.85 φ = 0.90

2.70 2.55 2.40 2.25 -0.02 -0.01 0.00 0.01 Radius (m)

0.02

Figure 6. Reaction rate distribution of carbon formation along the front surface of porous media at different porosities. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 )

890

Temperature (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


880 870 φ = 0.65 φ = 0.70 φ = 0.75

860 850 0.060

0.075 0.090 Position (m)

φ = 0.80 φ = 0.85 φ = 0.90

0.105



Figure 7. Temperature distribution along the centerline of porous media at different porosities. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 ) Figure 8 depicts the variation of CH4/CO2 conversion (100%) and mole fraction of carbon at outlet with the variation of material porosities from 0.65-0.9 while keeping other conditions unchanged. The continuous increase in CH4/CO2 conversion rates is observed with the increase in the medium porosity until the porosity reaches to 0.85. However, the sustained growth of carbon deposition appears to prevent a further increase in the chemical species conversion rate, which shows that a maximum conversion can be found with reasonably selecting porosity.24 Note that the effect of carbon formation reaction (Eq. 4 and Eq. 5) is little enough to be ignored in these cases. Figure 9 shows the variation of CH4/CO2 conversion and mole fraction of carbon at the outlet when the porosity was 0.8 at different mean cell sizes varied from 1.5-9 mm. The little change in the chemical species conversion and carbon mole fraction deposition can be observed with the increase in the mean cell size of the catalyst material, which can be ignored compared to other factors. Accordingly, under current conditions, the optimal structural parameters of porous material for higher chemical conversion and less carbon deposition are: φ = 0.8 , d p = 2 mm .

0.012

XCH4

XCO2

XC,out

60 57

0.011

54

0.010 0.009

51

0.008 0.007

Conversion (100%)

0.013


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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48 0.65 0.70 0.75 0.80 0.85 0.90 Porosity

Figure 8. Variation of CH4/CO2 conversion and mole fraction of carbon at the outlet as a function of porosity. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 , d p = 3 mm )


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XCH4

XC,out

XCO2

58.5

1.112 57.0 1.111

55.5

1.110

Conversion (100%)


1.113

54.0 2

4 6 8 Mean cell size (mm)

Figure 9. Variation of CH4/CO2 conversion and mole fraction of carbon deposition at the outlet as a function of mean cell size. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 , φ = 0.8 )

3.2. Effect of CH4/CO2 feed ratio The mole fraction distribution of carbon deposition along the centerline of the STR at different CH4/CO2 feed ratios is illustrated in Figure 10. Note that N2 is adopted as carrier gas and helps to keep the total number of moles of inlet mixture gas unchanged. It can be seen that the increase in CH4/CO2 feed accelerates to the accumulation of carbon deposition inside the STR,35 which is mainly due to the reason that the increase in CH4 component helps to improve the reaction rate of methane carking. Besides, according to the cavity receiver geometry configuration, carbon deposits tend to accumulate in the outer region of the reacting medium of the STR. 0.030 Mole fraction of carbon

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


CH4/CO2=3:1 CH4/CO2=2:1 CH4/CO2=1:1 CH4/CO2=1:2 CH4/CO2=1:3

0.025 0.020 0.015 0.010 0.005 0.000 0.03


0.12

Figure 10. Mole fraction distribution of carbon along the centerline at different CH4/CO2 feed ratios. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , φ = 0.8 , d p = 3 mm )



Figure 11 represents the variation of carbon formation rate under the impact of different CH4/CO2 feed ratios, respectively. The little difference of carbon formation rate distribution along the centerline of the STR can be observed when the feed ratio is changed from 1:3 to 1:1. Besides, the carbon formation rate begins to increase sharply when the mole fraction of CH4 exceeds that of CO2.35 However, it should be acknowledged that the reaction rate distribution of carbon formation along the centerline is not representative enough to describe the carbon formation behavior of the total STR chamber since the feed ratio has a considerable impact on the reaction rate distribution inside the STR, as shown in Figure 12. Moreover, compared with the carbon formation reaction, the effect of carbon gasification is minor enough to be ignored. Carbon formation rate (mol·m-3·s-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

10 (a) 8

CH4/CO2=3:1 CH4/CO2=2:1

CH4/CO2=1:1 CH4/CO2=1:2 CH4/CO2=1:3

6 4 2 0

0.060

0.075 0.090 Position (m)

0.105

Figure 11. Reaction rate distribution of carbon formation at different CH4/CO2 feed ratios. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , φ = 0.8 , d p = 3 mm )

Figure 12. Contours of carbon formation rate distribution at (a) CH4/CO2 = 1:3; (b) CH4/CO2 = 3:1. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , φ = 0.8 , d p = 3 mm ) Figure 13 illustrates the variation of CH4/CO2 conversion, carbon mole fraction at outlet, and average carbon formation rate with the change of CH4/CO2 feed ratio. It can be seen that the


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growth trend of CO2 conversion is almost opposite to that of CH4.20 It is noteworthy that a syngas production of H2/CO = 1:1 ratio is theoretically able to be obtained at the feed ratio of CH4/CO2 ≈ 1,35 which is considered as an ideal ratio of raw material for further processing.7,13 On the contrary, excessive feed ratio will result in the decline of effective conversion rate with more carbon deposits.36 Besides, both the carbon mole fraction and average carbon formation rate represent a rising trend with the increase of feed ratio, especially for the cases of CH4/CO2 > 1. Actually, these two parameters are impossible to have the coincident variation tendency because the carbon accumulation is determined by the combined action of carbon formation rate and carbon gasification rate, which is affected by many factors including incident heat flux, temperature distribution, partial pressure, fluid density, flow rate, components of feed gas, catalyst type, and porous material. Accordingly, considering lower carbon formation and high-value syngas product of H2/CO = 1:1, the feed ratio of CH4/CO2 = 1 is regarded as the optimal feeding condition under current options. 0.030

8 80

0.025

XC,out

XCH4

RC,f

XCO2

7 70 6 60 5 50 4 40 3 2 30

0.020 0.015 0.010 0.005 0.000 0.0

0.5

1.0 1.5 2.0 2.5 Feed ratio (CH4/CO2)

3.0

1 20

Figure 13. Variation of CH4/CO2 conversion, carbon mole fraction deposition at the outlet, and average carbon formation rate with CH4/CO2 feed ratio. ( Plamp = 0.5 kW , vin = 100 ml/ min , Pin = 1 atm , φ = 0.8 , d p = 3 mm )

3.3. Effect of flow rate Analysis of carbon deposition by the mole fraction calculation approach seems inappropriate for describing the degree of carbon deposition due to the effect of inlet flow rate. Therefore, the values X C * vin are adopted to represent the accumulation of carbon inside the STR, as shown in Figure 14. The carbon deposition at low flow rate of 10 ml/min has a better distribution while that



of 50 ml/min has the highest accumulation in these cases. On one hand, the increase in flow rate has the effect of reducing fluid temperature, thereby limiting the reaction rate. On the other hand, the higher the flow rate, the higher the partial pressure, which accelerates the reaction rate at the same time. Therefore, under the combined action of these two factors, the highest carbon accumulation at the flow rate of 50 ml/min can be observed. Besides, it can be seen that the carbon deposition gradually slows down and the alleviating effect gradually declines with the increase in the flow rate from 50 to 200 ml/min. 1.5 XC * vin (ml/min)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1.2 0.9

10 ml/min 50 ml/min 100 ml/min 150 ml/min 200 ml/min

0.6 0.3 0.0 0.00

0.03


0.12

Figure 14. Accumulation of carbon inside the STR at different inlet flow rates. ( Plamp = 0.5 kW , CH 4 /CO 2 /N 2 = 1:1:8 , Pin = 1 atm , φ = 0.8 , d p = 3 mm )

As seen in Figure 15, the inlet flow rate has significant effects on the carbon formation rate distribution. Note that the carbon gasification rate is slow enough to be ignored here. It can be seen that the reaction zone of the highest carbon formation rate obviously changed with the increase in flow rate. As a matter of fact, the direct factor affecting the carbon formation rate is the temperature field inside the STR. As indicated in Figure 16, the increase in the inlet flow rate causes a more uneven temperature field, thereby leading to the variation of carbon formation rate distribution. In addition, judging from the contours, carbon deposits have the tendency of being consolidated on the inner wall under the influence of high-flux radiation heat.


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Figure 15. Reaction rate distribution contours of carbon formation at inlet flow rate of (a) 10 ml/min; (b) 200 ml/min. ( Plamp = 0.5 kW , CH 4 /CO 2 /N 2 = 1:1:8 , Pin = 1 atm , φ = 0.8 , d p = 3 mm )

Figure 16. Temperature distribution contours of the STR at inlet flow rate of (a) 10 ml/min; (b) 200 ml/min. ( Plamp = 0.5 kW , CH 4 /CO 2 /N 2 = 1:1:8 , Pin = 1 atm , φ = 0.8 , d p = 3 mm ) The variation of key factors including CH4 and CO2 conversion, carbon accumulation, and average carbon formation rate with the change of inlet flow rate are plotted in Figure 17. It can be observed that the CH4 conversion represents a decreasing trend with the increase in flow rate, while CO2 conversion is not sensitive to the variation of flow rate.15,24 Besides, syngas production with the ratio of H2/CO close to 1:1 is obtained when the flow rate has exceeded 50 ml/min. Although the conversion rates have global downward trend, the yield of syngas keeps rising as a function of flow rate. However, judging from the carbon deposition behavior, high flow rates (≥ 50 ml/min) have a detrimental influence on the catalyst performance. Therefore, from the perspective of low carbon accumulation and high conversion rate of methane, the flow rate of 10 ml/min can be chosen as the optimal inlet condition. On the other hand, high-value syngas



production can be obtained when the flow rate is set to be about 100 ml/min. Accordingly, both the inlet flow rate of 10 ml/min and 100 ml/min can be considered as the optimal choice based on specific needs. 1.5

2.5 100

1.2

2.0

0.9

1.5

0.6

1.0

80 60

0.3 0.0

0

XC,out*vin

XCH4

RC,f

XCO2

50 100 150 Flow rate (ml/min)

0.5 200

40

0.0 20

Figure 17. Variation of CH4/CO2 conversion, carbon accumulation, and average carbon formation rate with inlet flow rate. ( Plamp = 0.5 kW , CH 4 /CO 2 /N 2 = 1:1:8 , Pin = 1 atm , φ = 0.8 , d p = 3 mm )

3.4. Effect of lamp power Based on the simulation data of ray concentration process at lamp power varied from 0.5 kW to 1.0 kW, the corresponding incident radiation density at the front surface of the STR is fitted and plotted in Figure 18. These data were all programmed as thermal boundary conditions by UDFs in the form of Eq. 13. Moreover, Figure 19 illuminates the fluid temperature distribution along the centerline of the STR under the variation of lamp power. It is easy to understand that the reaction temperature was improved with the increase in lamp power. However, after the power exceeds 0.7 kW, the degree of temperature unevenness between the front part and the end continues to increase, which may have a significant influence on the distribution of species and reaction rates. According to the simulation data, the maximum temperature difference gets to 127.97 K when the lamp power is set to be 1.0 kW.


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1200 0.5 kW 0.6 kW 0.7 kW 0.8 kW 0.9 kW 1.0 kW

1000 800 600 400 200 0 -0.06

-0.03 0.00 0.03 Center distance (m)

0.06

Figure 18. Incident radiation density distribution at different lamp power. 1350 Temperature (K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Irradiation density (kW/m2)

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0.5 kW 0.6 kW 0.7 kW

1200

0.8 kW 0.9 kW 1.0 kW

1050 900 0.060

0.075 0.090 Position (m)

0.105

Figure 19. Temperature distribution along the centerline of the STR at different lamp power. ( vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 , φ = 0.8 , d p = 3 mm ) The effect of lamp power on the distribution of carbon formation rate is shown in Figure 20. Comparing with other factors, the variation of lamp power causes a little radial unevenness of mole fraction and reaction rate distribution. However, the increase in the lamp power has disadvantage effects of obviously raising the temperature in the central region of the front end of the porous media,30 where large amounts of carbon deposits may accumulate, as shown in Figure 20b. In addition, excessive heat flux also has the disadvantage of melting the front porous ceramic and catalyst, thereby slowing down the reaction rates and reducing the service life of catalyst materials.



Figure 20. Reaction rate distribution contours of carbon formation at lamp power of (a) 0.5 kW; (b) 1.0 kW. ( vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 , φ = 0.8 , d p = 3 mm ) Figure 21a and Figure 21b depict the reaction rate distribution of carbon formation and carbon gasification along the centerline of the STR, respectively. These two reactions are accelerated with the increase in lamp power,25 but growth trends along the axis are reversed. This reaction distribution may aggravate the carbon deposition in the first half of the porous media, thereby accelerating the catalyst deactivation on the front area. Due to the high-temperature area is concentrated in the front part, the catalyst deactivation resulting from the excessive heat flux

15

(a)

12

0.5 kW 0.6 kW 0.7 kW

0.8 kW 0.9 kW 1.0 kW

9 6 3 0

0.060

0.075 0.090 Position (m)

0.105

Carbon gasification rate (mol·m-3·s-1)

density in this area must have worse impacts on the conversion rate and syngas yield. Carbon formation rate (mol·m-3·s-1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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0.08 0.06

0.5 kW 0.6 kW 0.7 kW 0.8 kW

0.9 kW 1.0 kW

(b)

0.04 0.02 0.00 0.060

0.075 0.090 Position (m)

0.105

Figure 21. Reaction rate of carbon formation (a) and gasification (b) at different lamp powers. ( vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 , φ = 0.8 , d p = 3 mm ) The CO2 conversion rate represents a steady upward trend while CH4 conversion firstly increases before to decrease with the increase in the lamp power, as shown in Figure 22. Besides, lower lamp power (≤ 0.7 kW) is more likely to obtain syngas products with H2/CO ≈ 1. On the


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other hand, it can be seen that the excessive lamp power has disadvantage effects of accelerating the carbon formation rate,14 which could be attributed to the drop in CH4 conversion. Therefore, suitable lamp power could be found with the aim to obtain high-quality syngas products in the most economical way.7,37 Currently, considering the chemical conversion and carbon deposition rate comprehensively, the power of 0.7 kW can be taken as the optimal setup for the energy input of DRM process. 8

0.06 0.05

XC,out

XCH4

RC,f

XCO2

6

0.04 0.03

80

4 60

0.02 0.01 0.00

100

2 40 0.5

0.6 0.7 0.8 0.9 Lamp power (kW)

1.0

Figure 22. Variation of CH4/CO2 conversion, carbon accumulation, and average carbon formation rate with the inlet flow rate. ( vin = 100 ml/ min , Pin = 1 atm , CH 4 /CO 2 /N 2 = 1:1:8 , φ = 0.8 , d p = 3 mm )

4. Conclusion In this study, the ray-thermal-chemical process in a porous-filled STR for DRM is numerically investigated to predict the thermochemical performances of the system. The carbon formation and gasification behaviors under different operational conditions are respectively analyzed by using FVM methods coupled with reaction kinetics of DRM. The main conclusions of this article are drawn as follows: (1) The increase of porosity obviously changes the reaction rate distribution of carbon formation in the front of porous zone and results in the increase of overall carbon deposition inside the STR. However, an appropriate increase (when φ ≤ 0.8 ) in porosity enables the improvement of CH4 and CO2 conversion, while the variation of mean cell size has little influence on the conversion rate and carbon deposition. Under



current operating conditions, the structural parameters of φ = 0.8 , d p = 2 mm are proved to be the best choice for higher conversion and less carbon deposition. (2) Excessive addition of methane in feed gas has the disadvantage of accelerating carbon deposition rate and reducing the quality of syngas products. It is more likely to obtain high-value syngas products of H2/CO = 1:1 with lower carbon deposition rate at the feed ratio of CH4/CO2 ≈ 1. (3) The inlet flow rate has a significant impact on the temperature distribution inside the STR, thereby further affecting the reaction rate distribution of carbon deposition. Besides, high flow rates contribute to improving the quality and yield of syngas products, but meanwhile, it is more likely to cause the catalyst deactivation. Based on different requirements, the highest CH4 conversion with least carbon deposition can be obtained when vin = 10 ml/ min , while the high-value syngas of H2/CO ≈ 1:1 can be gained when vin = 100 ml/ min .

(4) Carbon formation rate is greatly affected by incident radiation density. The increase of lamp power can aggravate the carbon deposition in the central and front region of the porous ceramic. Excessive lamp power (≥ 0.7 kW) can improve CO2 conversion but has the disadvantage of rapidly increasing carbon deposition rate and reducing CH4 conversion rate. Under current operating conditions, the power of 0.7 kW can be taken as the optimal option for the energy input of DRM process. Acknowledgment This work was supported by the National Natural Science Foundation of China (No.51876049) and the Natural Science Foundation of Hebei Province (No. E2018209211). References (1) Dean, J. F.; Middelburg, J. J.; Rockmann, T.; Aerts, R.; Blauw, L. G.; Egger, M. et al. Methane feedbacks to the global climate system in a warmer world. Rev. Geophys. 2018, 56, 207. (2) de Richter, R.; Ming, T. Z.; Davies, P.; Liu, W.; Caillol, S. Removal of non-CO2 greenhouse gases by large-scale atmospheric solar photocatalysis. Prog. Energ. Combust. 2017, 60, 68.


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Al2O3

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