
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12351-1
10.1016/j.heliyon.2024.e36320
e36320
Research Article
Simulation study on the oxidation performance of low-concentration methane preheating direct current catalytic oxidation plant considering thermal radiation
Zhu Junlin a
Zheng Lixing b
Xue Xiaojun XXJ377547176@163.com
b⁎
Lu Wei a
a School of Mechanical Engineering, Guangxi University, Nanning 530000,China
b School of Electric Power, Civil Engineering and Architecture, Shanxi University, Taiyuan 030006, China
⁎ Corresponding author. XXJ377547176@163.com
17 8 2024
30 8 2024
17 8 2024
10 16 e3632023 5 2024
6 8 2024
13 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
In this study, the process of catalytic oxidation of methane considering radiative heat transfer was simulated using FLUENT computational software to study the effect of thermal radiation on the oxidation performance of the simulated device, and to investigate the extent to which radiative heat transfer affects the oxidation performance of the device under different operating conditions. The results show that the extent to which thermal radiation affects the oxidative performance of the equipment increases with increasing inlet temperature. When the intake temperature reaches 900K, its proportion is close to 45 %. At the same time, as the inlet gas temperature increases, the maximum reaction temperature of the oxidation unit is 1154 K, and the methane conversion rate reaches up to 89 %. The main factor affecting the oxidation performance of the unit at this time is radiation heat transfer. The extent to which thermal radiation affects the oxidative performance of the device diminishes with increasing inlet velocity. When the wind speed reaches 2 m/s, the proportion of radiative heat transfer is only 10 %, the maximum reaction temperature of the plant falls to 993 K, and the methane conversion rate drops to 68 %. At this time, the main factor affecting the oxidation performance of the plant is convective heat transfer. The influence of thermal radiation on oxidation performance gradually diminishes with an increase in intake velocity, and the proportion of radiative heat transfer decreases continuously. At methane concentrations above 1 %, the proportion of radiative heat transfer is less than 25 per cent, the maximum reaction temperature of the unit increases to 1087 K, and the methane conversion rises to 88 %. At this point, the main factor affecting the oxidation performance of the plant is convective heat transfer.

Keywords

Radiation heat transfer
Convection heat transfer
Numerical simulation
Methane conversion rate
==== Body
pmc Nomenclature	
Symbols	
ρ	density (kg/m3)	μi	coefficient of viscosity (J/kg)	
u	velocity (m)	L	length (mm)	
τ	dynamic viscosity (N∙s/m2)	I	radiation intensity (J/kg)	
Cj	specific heat capacity (J/kg)	T	temperature (K)	
λ	porosity (%)	Ω	solid angle in space (°)	
k	turbulent energy coefficient (J/kg)	v	thermal conductivity (W/(m∙k))	
ε	dissipation rate (%)	Y	mass fraction (%)	
ω	mole fraction (1)	W	molecular mass (Da)	
Abbreviations	
AIR	Air Skid	MD	Mixing device	
CP	circulation pump	MG	100 % methane gas	
EH	electric heater	RC	Reaction chamber	
FG-WHE	Flue gas-water heat exchanger	V1	Valve 1	
FG-OHE	Flue gas-oil heat exchanger	V2	Valve 2	
MG-WHE	Mixture gas-water heat exchanger	V3	Valve 3	
MG-OHE	Mixture gas-oil heat exchanger	V4	Valve 4	

1 Introduction

Energy is the material foundation on which human survival relies, and it is the source of power for social development and progress. After the Industrial Revolution, humans began to use a large amount of fossil energy, resulting in serious greenhouse effects, leading to problems such as rising sea levels and global warming [1]. To alleviate the process of global warming, the world is vigorously developing renewable energy sources such as solar and wind energy [2]. However, with the increasing energy demands of various countries and the fluctuation and discontinuity of renewable energy sources, the development levels of renewable energy sources in multiple countries are unbalanced, especially in many developing countries where coal remains the basis of their energy supply [3]. In addition, although new energy sources have received widespread attention and achieved rapid growth in the next decade, their energy supply is still far less than coal's. According to statistics, by 2023, the global cumulative consumption of coal reached 8.7 billion tons, while the consumption of new energy sources converted into coal equivalent was only 5.72 billion tons of standard coal [4]. It can be predicted that due to factors such as energy demand, equipment investment, and technological level, coal will still be a stable energy supply for many countries for a long time.

The coal mining process releases a large amount of coalbed gas, commonly known as gas, a type of unconventional natural gas mainly composed of CH4, with great value for utilization. According to statistics, the global coalbed gas content reaches 260 trillion cubic meters, primarily distributed in coal-rich regions such as Russia, the United States, and China [5]. However, coalbed gas is a toxic and harmful gas. If not correctly utilized and directly released into the air, it will cause serious energy waste and environmental pollution and lead to gas explosions, posing severe hazards to enterprise safety production [6]. Therefore, the effective utilization of coalbed gas is of great significance for coal enterprises regarding safety production and efficiency improvement and has attracted wide attention in the industry.

Coalbed methane generally has three different uses based on its methane concentration. Surface-mined coalbed methane with a concentration of over 90 % is mainly used for manufacturing liquefied natural gas [7], but its reserves only account for 1 % of the total coal mine gas. Underground surface-mined coalbed methane, with concentrations generally ranging from 5 % to 90 %, accounts for about 15 % of the total coal mine gas reserves and can be used as fuel for power generation and vehicles [8]. Gas with a concentration lower than 5 % is considered low-concentration gas. It has a large reserve and fluctuating flow rate, making it difficult to utilize with conventional methods, leading to direct release into the air [9]. Therefore, if this low-concentration gas can be used effectively, it can reduce the hazards of gas accumulation and increase the revenue of coal production enterprises.

Researchers have conducted extensive studies on the expected utilization methods of gas, including concentration enrichment, auxiliary fuel utilization, and primary fuel utilization. Concentration enrichment refers to the use of gas purification technologies such as membrane separation [10], hydrate separation [11], and cryogenic separation [12] to concentrate low-concentration gas into high-concentration gas for industrial production. Auxiliary fuel utilization involves using low-concentration gas to replace air and mix with the primary fuel for combustion, reducing the consumption of the main fuel while ensuring continuous burning [13]. Primary fuel utilization is currently the most mainstream method, including porous media premixed combustion [14], regenerative reverse flow oxidation technology [15], and regenerative catalytic reverse flow oxidation technology [16]. Although porous media models have been widely used in recent years, their heat resistance still poses issues, as gas may not burn in the porous media when its concentration is low enough [17]. Regenerative reverse flow oxidation technology requires a change in the flow direction, leading to the discharge of some unreacted gas, and the methane obtained from this process is prone to explosion [18]. Regenerative catalytic reverse flow oxidation technology requires catalysts, which can lower the reaction temperature and improve safety, but the cost of catalysts must be addressed [19]. Therefore, although primary fuel utilization is widely used, many issues still need to be addressed, such as increasing the utilization rate of low-concentration gas.

Researchers have mainly studied the combustion characteristics of methane in response to the low utilization rate of low-concentration gas. Rashidian et al. [20] studied the effect of baffles on methane combustion, and found that placing baffles in the reaction chamber can effectively prevent heat dissipation during combustion, thereby increasing the temperature of the reaction chamber. Jiajin Zhang et al. [21] studied the effect of concentration, switching time, and compensation temperature on catalytic performance based on catalytic counterflow technology. Simulation results show that the feed concentration, switching time, and compensation temperature significantly impact the reactor's performance. Fernandez et al. [22] studied the effect of water adsorption during the oxidation process under different flow rates and methane concentration conditions on catalytic performance. Chen et al. [23] studied the effect of different reaction mechanisms on the catalytic performance of methane and their impact on reaction rates, flame structure, and temperature, the results showing that using kinetic models significantly influences flame stability.

There has been a lot of research on the combustion mechanisms of low-concentration gas, but only some studies have considered the impact of radiative heat transfer on combustion. Chen et al. [24] improved the single-channel methane catalytic combustion by allowing the outlet gas to flow out through the outer channel of the reactor to achieve heat exchange with the inlet at the inner channel, thus improving the thermal stability of the reactor through lateral heat exchange of the inlet gas. Choudary et al. [25] numerically simulated a multi-channel integral methane-air catalytic oxidation combustion reactor and found different temperature and component concentration distributions between channels. Kumaresh et al. [26] used CHEMKIN to calculate the overall honeycomb catalyst of methane, amd found that higher inlet temperatures and fuel equivalence ratios would shorten the combustion distance and require a shorter combustion length. Yan et al. [27] examined the effect of changing the thermal conductivity and thickness of the solid wall and gas inlet velocity on catalytic combustion. Karagiannidis et al. [28] found different pressure methane combustion heat stability regions by changing the gas inlet flow rate, wall thermal conductivity, and external heat transfer coefficient and studied the coupling of homogeneous and heterogeneous phases during the reaction process. Gavrilyuk et al. [29] and Bingue et al. [30] studied the effect of different equivalence ratios on the low-concentration gas combustion characteristics in porous medium burners, and found that the peak temperature of combustion decreased with oxygen enrichment. C.H.H wang [31] and others simulated a relatively particular catalytic oxidation combustion device, analyzing the effect of different combustion conditions on methane conversion rates under various combustion conditions. Hashemi et al. [32] studied premixed combustion in a double-layer porous medium burner, and the results showed that the higher the equivalence ratio, the higher the temperature in the combustion area. In these simulation studies on the catalytic oxidation of methane, researchers mostly ignore the effect of radiative heat transfer in the combustion process because of the complexity and uncertainty of radiative heat transfer, but it is well known that a large amount of heat generated by the combustion of methane in the oxidizing bed will make the whole oxidizing bed in a high temperature environment, and even if the combustion components are very low, but the combustion temperature can be as high as 1000 °C. Therefore, the role of radiative heat transfer must be considered in the study of the heat and mass transfer process in the regenerative oxidation bed. Meanwhile, for the shortcomings of the previously mentioned countercurrent oxidation method and porous media combustion model, a set of new methane combustion methods were designed, which effectively solved the problems of methane waste and inefficient utilization encountered by the previous researchers in the process.

Given this, this paper proposes a new method of utilizing low-concentration gas based on low-concentration gas direct current preheating catalytic oxidation technology: using non-reversing direct current intake mode and simultaneously preheating the entering low-concentration gas with catalytic oxidation method. In addition, an experimental apparatus was designed to measure the oxidation characteristics of methane combustion under radiation heat transfer and explore strategies to improve the methane conversion rate in low-concentration gas. The innovations of this paper are as follows: (1) This study is based on a new preheated DC catalytic oxidation method to build an experimental bench for methane combustion, and a simulation study of methane catalytic oxidation using the bench as a simulation object. (2) Using UDF programming to simulate the catalytic effect of the latest type of chalcogenide catalysts effectively solves the disadvantages of expensive precious metal catalysts and poor catalytic effect. (3) This paper focuses on the extent to which radiative heat transfer affects the catalytic oxidation process of methane as a means of promoting methane combustion utilization by enhancing or weakening the intensity of radiative heat transfer under different operating conditions. Starting from the combustion characteristics inside the reaction chamber, fully considering the combustion changes caused by radiation heat transfer based on Fluent simulation, establishing a mathematical model of the oxidation bed inside the catalytic oxidation layer, and conducting numerical analysis calculations with the instantaneous coupling method of flow, heat transfer, and combustion conditions inside the oxidation bed, to achieve the effect of increasing the utilization rate of low-concentration gas through radiation heat transfer under different operating conditions. This research is essential for the efficient use of low-concentration gas and the reduction of resource waste.

2 Experimental equipment

2.1 Low-concentration gas direct current preheating catalytic oxidation experiment equipment

The low-concentration gas preheating DC catalytic oxidation device belongs to the low-concentration methane catalytic oxidation technology, and the catalytic combustion of methane is superior to the traditional homogeneous combustion [33], which can realize the high-efficiency utilization of the low concentration of gas with methane concentration of 2 % and below. Make full use of the medium and low temperatures. The low-temperature flue gas is used to preheat and heat the low-temperature gas. At the same time, this device adopts low-temperature catalytic oxidation materials, which can effectively reduce the reaction temperature of methane catalytic oxidation and the generation of nitrogen oxides (NOx). Moreover, this set of devices has an auxiliary electric heating device and a low-concentration gas recycling system, which can save the electric load to ensure the complete reaction of low-concentration gas.

2.2 Process flow and composition

The new low-concentration gas direct current preheating catalytic oxidation experimental device is shown in Fig. 1. The unit consists of seven subsystems, namely a gas mixture subsystem, a gas source concentration monitoring and filtration subsystem, a heat exchange subsystem, an auxiliary electric heating subsystem, a catalytic oxidation subsystem, a power generation subsystem, a condensate recovery subsystem, a smoke exhaust subsystem, and an operation control and monitoring subsystem.Fig. 1 Operating principle diagram.

Fig. 1

The gas mixture subsystem provides a low-concentration methane-air mixture with a methane concentration of 1 % and air concentration of 99 % after sufficiently mixing methane and air, which is used to simulate the low-concentration methane gas generated from the ventilation of coal mines. The gas concentration monitoring and filtering subsystem monitors the methane concentration in the low-concentration gas. It filters the dust particles in the low-concentration gas to provide clean gas that meets the concentration requirements. The catalytic oxidation subsystem reacts to low-concentration gas that reaches the reaction temperature. As a source of high-temperature flue gas generation, it is equipped with a new high-activity catalyst to reduce the methane reaction temperature and prolong the service life of the heat accumulator. The power generation subsystem utilizes high-temperature and high-pressure water vapor, which the steam system produces to generate electricity. The condensate recovery subsystem recycles the spent steam and water vapor in the low-temperature flue gas from the turbine after the turbine has performed work. The condensate recovery subsystem condenses and collects the spent steam after the turbine does work, and the water vapor in the low-temperature flue gas replenishes the required amount of water in the steam bag to reduce the waste of water resources and the corrosion of the equipment. On the one hand, the flue gas exhaust subsystem realizes the circulating heating of the low-concentration gas. It improves heating efficiency by adjusting the opening and closing of the dampers and the fans' starting and stopping at the device's startup. On the other hand, it provides the flow power for the low-concentration gas/flue gas to make it smooth. The operation control and monitoring subsystem is used to monitor the status of each point of the device in real time and regulate the system according to the degree of data deviation. This paper is a simulation study based on the catalytic oxidation layer of this device.

2.3 Experimental Procedures

The working process is as follows: The experimental device needs to change the operating state of the device by changing the valve switching state, in the formal experiments before the device needs to be warmed up, at this time you need to open the valves 3 and 4, close the valves 1 and 2, and the device enters the internal circulation state. Turn on the electric heater and circulation pump to preheat the equipment. High-power heating rods inside the water tank and oil tank heat the water and oil to achieve heating of the circulating media through the water tank and oil tank. When the temperature of the reaction chamber and the circulating media reaches the reaction temperature, close valves 3 and 4 and open valves 1 and 2. At this time, open the gas mixing device, air and concentration of 100 % methane gas are into the mixing system, mixed for the concentration of 1 % of the low concentration of gas, the gas through the two-stage heat exchanger to reach the reaction temperature, in the reaction chamber with the catalyst to carry out catalytic oxidation reaction, and release a large number of high-temperature flue gas. The high-temperature flue gas heats the two-stage heat exchangers through the flue gas-oil heat exchanger and the flue gas-water heat exchanger. The heat obtained after heating is transported to the gas-preheating side with the action of the water pump and oil pump to preheat the gas that has not entered the reaction chamber. The preheated low-temperature flue gas is discharged from the lower right end of the equipment. In this way, when the equipment no longer needs the electric heater for preheating, close the electric heater, and the equipment can obtain the heat of the preheated gas from the flue gas and enter a self-sustaining operating state.

3 Model development

3.1 Physical model

The catalytic oxidation sub-system is where low-concentration methane-air mixtures react with catalysts. In this sub-system, the perovskite catalyst is applied to mesh plates through a particular process, and several plates coated with the catalyst are then placed parallelly inside a box. The low-concentration gas mixture flows in from the left end of the box. When the temperature of the gas mixture reaches the catalytic reaction temperature, the low-concentration gas will react with oxygen under the action of the catalyst, and the resulting exhaust gas will be discharged from the right end of the box. Since the entire catalytic oxidation reaction occurs inside the box, and the temperature and velocity of the low-concentration gas entering each plate are approximately equal, the physical and chemical reaction processes between each pair of plates are similar. This allows individual simulation studies on two plates to considerably shorten the simulation study time. The dimensions of the entire catalytic oxidation reactor model are 200mm × 200mm × 300 mm, with a reactor thickness of h = 1 mm and a plate spacing of d = 1.5 mm. According to the literature [34], when L/d is more significant than 1.8, the three-dimensional effects inside the oxidation layer can be disregarded, so this study uses a two-dimensional model for simulation. The specific physical model is shown in Fig. 2.Fig. 2 Physical model.

Fig. 2

To simplify the calculation, the following assumptions are made for the model.(1) it is assumed that the flow rate, air volume, and temperature of the low-concentration gas-air mixture entering each meshed perovskite catalyst plate are equal and uniformly distributed.

(2) It is assumed that the perovskite catalyst is uniformly coated on the meshed plate, and when the mixture gas passes through the meshed plate, a reaction will occur on the plate.

(3) It is assumed that the divergence effect of the gas is ignored during the reaction process, and the mixture gas in the reaction is an ideal incompressible gas [35].

(4) It is assumed that all wall radiation is diffuse reflection [36].

(5) The simulation uses CHEMKIN reaction mechanism files to calculate combustion, ignoring the production of CO gas during the reaction process [37].

3.2 Mathematical model

The simulation process includes the flow of mixed gases and the catalytic oxidation process of mixed gases with catalysts. Therefore, the catalytic reaction between mixed gases and catalysts should be considered when simulating. The gas-phase reactions of mixed gases within the catalytic oxidation layer should be considered, making the entire reaction process more realistic and the simulated data more accurate. Using FLUENT software for simulation calculation, a series of control equations are used to describe and control the entire reaction, which includes the mass conservation equation [38], momentum conservation equation [39], energy conservation equation [40], etc. The specific form of the control equations is as follows;

The mass conservation equation is given in equation (1):(1) ∂ρ∂t+∂(ρvx)∂x+∂(ρvy)∂y+∂(ρvz)∂z=0

The momentum conservation equation is shown in equation (2):(2) λ∂∂t(ρju)+∂p∂x+Rx12ρ|u|u=−∂∂x(ρjuu)+τ∂2u∂x2

where ρ is the density of the mixed gas; u is the velocity in each direction; τ is the gas's dynamic viscosity.

The energy conservation equation is shown in Equation (3):(3) λ∂∂t(ρjCjT)+∂∂x(ρjCjTu)+∂∂t(ρgCgT)+∂∂x(∑i=1nhiJiur)=λ∂∂t(ρgCgT)+∂2∂x2(keT+krT)+ξΔHwch4

where Cj is the specific heat capacity; T is the temperature; k is the heat transfer coefficient of the fluid; the last term is the internal heat source of the fluid and the portion where the mechanical energy of the fluid is converted into thermal energy due to viscous effects.

The conservation equation of gas-phase components is shown in Fig. 4:(4) ∂(ρuYk)∂x+∂(ρuYk)∂y=−∂∂x(ρYkVk,x)−∂∂y(ρYkVk,y)+wkWk

k=1,2…Kg−1

where u and v are the flow velocities on x and y; ρ denotes the gas density; Yk、 wk、 Wk and Vk,x、 Vk,y present the mass fraction, molar yield, molecular weight, and diffusion velocity in the and directions, respectively, of the gas phase [41].

Since the axial conduction at the wall has an essential influence on the combustion characteristics of low-concentration gas [42], the solid phase energy equation also needs to be considered, as shown in Equation (5):(5) ∂∂x(λk∂T∂x)+∂∂y(λk∂T∂y)=0

where λk is the thermal conductivity of the solid wall.

Due to the need to monitor the content of each component in the reaction process, component transport equations are required [43], as shown in Equation (6).(6) ∂∂t(λρgYi)+∂∂x(λρgYiu)+1r∂∂r(λρgYirv)+∂∂x(λρgYiUi)+1r∂∂r(λρgYirVi)=λωiW

where λ, ρg, Cg,v, Yi, ωi, W are the porosity of the porous medium and the density, specific heat, and thermal conductivity of the coal mine methane, respectively, as well as the components' mass fraction, molar fraction, and molecular weight.

During the catalytic oxidation reaction process, the mixed gas typically exhibits turbulent flow in the reactor, so it is necessary to use k−ε simulation model where the turbulent kinetic energy coefficient is the dissipation rate. The specific equation is shown in Equations (7), (8)):(7) ∂(ρkui)∂zi+∂(ρk)∂t+ρε+YM=∂∂zi[(μ+μiδk)∂k∂zj)]+Gk+Gb+Sk

(8) ∂(ρεui)∂zi+∂(ρε)∂t=∂∂zi[(μ+μiδε)∂ε∂zj)]+D1εk(Gk+D3Gh)−D2ρε2k+Sk

The turbulent kinetic energy coefficient k is shown in Equation (9):(9) ∂∂t(ρk)+∂∂xi(ρkui)=∂∂xj[(μ+μiσk)∂k∂xj]+Gk+Gb−ρε−YM+Sk

The dissipation rate ε is shown in Equation (10):(10) ∂∂t(ρε)+∂∂xi(ρεui)=∂∂xj[(μ+μtσε)∂k∂xj]+C1εεk(Gk+C3εGb)−C2ερε2k+S

where Gk represents the generation term of turbulent kinetic energy caused by velocity; μi represents the turbulent viscosity coefficient; Gb represents the generation term of turbulent kinetic energy caused by buoyancy; YM is the generation term of pulsatile expansion in compressible turbulent flow; D1、D2、D3 represents empirical constant; δk and are the Prandtl numbers corresponding to turbulent kinetic energy and dissipation rate ε; Sk is user-defined source terms; C1ε, C2ε, and C3ε are empirical constants, usually taken as C1ε = 1.44, C2ε = 1.92, C3ε = 1 [44].

The temperature inside the catalytic oxidation layer is relatively high during the experiment. According to Stefan-Boltzmann's law, the heat flux has a fourth power relationship with temperature. In the catalytic oxidation layer, radiation heat transfer plays a dominant role in heat transfer, which is also the essential reason to consider radiation heat transfer.

In this paper, the zonal method approach [45,46] is used to divide the closed cavity of a non-isothermal participatory medium into several surface segments and medium segments, assuming that the radiative properties and temperatures within each segment are uniform and consistent, and the energy equation is established to be solved. The heat transfer process in the model needs to be determined before studying the radiative heat transfer. Since the methane gas reacts very fast when it enters into the reaction chamber, the gas temperature is approximately equal in each uniform small segment, so the radiative heat transfer between the gas and gas is ignored, and the radiation of the gas to the oxidized bed and to the wall surface is considered, as well as the radiation effect between the wall surface and the oxidized bed.

The distance between the gas microelement segment dVi and the wall surface element segment dFj is L. The angle between the connecting line of the two segments and the normal vector of the surface segment is α. The total energy radiated by the gas segments within this angle of the microelement can be obtained is shown in Equation (11):(11) k(ri)Ib(ri)cosajdFjdVi/lj2

where k is the absorption coefficient of the gas section, m-1; Ib is the intensity of the blackbody directional radiation W/(m2• Sr).

The radiant heat flow between the walls can be expressed is shown in Equation (12):(12) Qwi−sj=Jwiwisj‾

where Jwi is the effective radiation of the wall segment. wisj‾ is the wall segment dAw the area of direct exchange of radiation.

The direct area of radiation between the walls is available according to literature [47], as shown in Equation (13):(13) wisj‾=∫Fi∫Fjcosαicosαjπlj2ekldFjdFi

Before selecting a radiation model, it is necessary to determine the optical thickness according to formula 14:(14) ε=(a+σs)L

where a is the absorption coefficient, the scattering coefficient is usually taken as 0; L is the typical distance between two opposite walls in the model [48].

To simplify the simulation calculation, the DO model is selected in this paper, which can be used for all-optical thicknesses and has very high computational accuracy. By examining the radiative heat transfer of this model, a differential element can be taken at position s and in the direction of radiation transfer s, with a cross-section of dA and a length of ds. The heat radiation transfer equation can be obtained by calculating the spectral projected radiation intensity at s and introducing Kirchhoff's law [49], as shown in Equation (15):(15) dI(s,s)sλds=s·∇Iλ=kλ(s)Ibλ(s)−kλ(s)Iλ(s,s)−σ(s)sλIλ(s,s)+σ(s)sλπ∫Iλ(s,s)ϕλ(si,s)dΩiΩi−πλ

The above equation depicts the radiant energy of a particular microelement body within the radiation field. The radiative transfer equation s the radiant energy equation in the direction of the microelement segment ds, so it is only necessary to integrate the above equation over the entire space π to obtain the radiant energy equation in the microelement body in space, which is simplified to get the equation, as shown in Equation (16):(16) σ(s)sλπ=∫Iλ(s,si)[∫Φλ(si,s)dΩΩi=π]Ωi=πdΩi=σ(s)sλHλ(s)

Hλ(s) is defined as Spectral projection radiation function, as shown in Equation (17):(17) Hλ(s)=∫Iλ(s,s)dΩΩ=π

where s is the direction vector; si is the scattering direction vector; I is the radiation intensity; Φ is the phase angle function; Ω is the solid angle in space; σs is the Boltzmann constant (5.669x10−8W/m2 K4);

3.3 Boundary conditions

Based on the previous research on catalytic oxidation simulation experiments, the boundary conditions of the model are as follows.(1) The inlet boundary conditions are set as velocity inlet boundary, and the outlet boundary conditions are set as pressure outlet boundary.

(2) Due to the turbulent state of the mixed gas in the fluid region, the turbulent model is adopted with a no-slip wall. The inlet turbulence intensity is set to 2 %.

(3) The material density of the reaction chamber is 3100 kg/m3, the specific heat capacity is 1267 J/(kg K), and the thermal conductivity is 92 W/(m K) [27].

(4) The SIMPLE algorithm with pressure-velocity coupling is chosen, using a Gradient discretization method based on the grid center and a second-order upwind discretization for the remaining terms [50].

(5) The iteration steps are set to 100,000, with residual values of 1.0E-6 in the x and y directions and 1.0E-4 for the remaining variables. The residual observer will automatically activate after the calculation starts. When the residual curve approaches or falls below the set residual value, it can be considered that the calculation result has converged, and the calculation can be stopped [51].

4 Results and discussion

4.1 Mathematical model validation

Before conducting the simulation experiment, it is necessary to validate the accuracy of the mathematical model and settings. The reaction temperatures of the oxidation bed at different inlet temperatures are summarized in Table 1. Set the entrance temperature of the simulation experiment to 800K, entrance velocity to 1 m/s, and methane concentration to 1 %. Compare the outlet gas temperature under this operating condition with the experimental results, as shown in Fig. 3.Table 1 Experimental measurements data at different temperatures.

Table 1Oxidizing bed position/mm	Inlet temperature 750k reaction temperature/k	Inlet temperature 800k reaction temperature/k	Inlet temperature 850k reaction temperature/k	
0	750	800	850	
30	761	815	878	
60	775	833	913	
90	793	854	951	
120	816	880	992	
150	847	918	1027	
180	889	963	1061	
210	933	1008	1092	
240	968	1042	1110	
270	980	1058	1122	
300	995	1068	1134	

Fig. 3 Comparison of simulated experimental data.

Fig. 3

Fig. 4 Methane combustion temperature distribution cloud at different inlet temperatures.

Fig. 4

As Fig. 4 shows, the trend of the simulated calculation results is the same as the experimental measurement results, with a temperature difference of about 20k between the two conditions, and the error is small. The experimental and simulated data increase with the increase of the position of the oxidation bed, this is because with the catalytic oxidation reaction of methane, the reaction temperature inside the oxidation bed is increasing, the more intense the oxidation reaction, the simulated reaction only considers the gas-to-surface and surface-to-surface radiative heat transfer, and other such as the gas-to-gas radiative heat transfer is not taken into account, and the real reaction is certainly more complex. So in the temperature difference between the two reactions at the end of the oxidation bed gradually becomes larger. Considering the unavoidable thermal errors in the experimental process, and referring to the published literature [52], this paper does not differ much from its conclusions, so it can be verified that the mathematical model in this paper can be used for the numerical analysis of the combustion and oxidation performance of methane in catalytic oxidation layer.

4.2 The impact of thermal radiation on the oxidative performance

To better explore the impact of thermal radiation on the oxidative performance of equipment, this paper specifies two proportion coefficients, namely the ratio K1 of convective heat transfer to total heat transfer and the ratio K2 of radiative heat transfer to total heat transfer. The total heat transfer k is determined to ascertain the dominant position of radiative and convective heat transfer in the methane combustion process. At the same time, the variation law of methane conversion rate under different operating conditions is studied to determine the impact law of oxidative performance of equipment to make effective designs for the utilization of low-concentration gas.

4.2.1 The impact of inlet temperature

The effect of thermal radiation on the oxidative performance of the device is studied at different intake temperatures with an intake air velocity of 1 m/s and a methane concentration of 1 %.

Fig. 4 shows the methane combustion temperature distribution cloud at different inlet temperatures. The inlet air temperatures are 750k, 800k, 850k.

From Fig. 5, it can be seen that as the inlet temperature increases, the maximum reaction temperature inside the oxidation bed also increases continuously. Moreover, during the temperature increase process, the growth rate in reaction temperature gradually increases, leading to a shorter time required to complete the reaction. At the same time, with the rise in the inlet air temperature, the reaction rate accelerates in the first half, and then the temperature change tends to flatten out. The higher the inlet temperature, the more pronounced this change becomes. According to Fig. 5, it can be seen that as the intake temperature increases, the temperature difference between the inlet and outlet gradually increases, indicating that the heat transfer efficiency of the entire catalytic oxidation layer is slowly growing. The total heat transfer is also increasing.Fig. 5 Temperature curve of reactions at different inlet temperatures.

Fig. 5

Fig. 6 shows the variation curves of K, K1, and K2 at different temperatures. It can be inferred that as the inlet temperature increases, the total heat transfer continues to increase. During this process, the proportion of convective heat transfer in the entire heat transfer process decreases while the proportion coefficient of radiative heat transfer significantly increases. Radiative heat transfer becomes the main reason driving the increase in total heat transfer during the heat transfer process, and the trends of change in total heat transfer coefficient and radiative heat transfer proportion coefficient are relatively consistent. Compared with Fig. 5, as the inlet temperature increases, radiative heat transfer becomes dominant in the heat transfer process, leading to a faster reaction of the entire device. When the inlet temperature exceeds 900 K, the proportion coefficient of radiative heat transfer reaches 45 %. Therefore, it is essential to consider the impact of radiative heat transfer on the oxidation performance of the device in high-temperature combustion conditions.Fig. 6 Variation curve of heat transfer coefficient at different inlet temperatures.

Fig. 6

Fig. 7 shows the curve of methane conversion rate at different inlet temperatures. It can be seen from the graph that with the increase in inlet temperature, the methane conversion rate also increases. Within a specific range, the methane conversion rate rises rapidly. This is because the reaction process of the catalyst is a chemical kinetic process, which is mainly affected by temperature. The higher the temperature, the more intense the reaction. At the same time, under the influence of radiative heat transfer, more heat is generated by the entire response, leading to a faster increase in temperature and a higher methane conversion rate. However, when the temperature is too high, the internal structure of the catalyst may be destroyed, which may lead to sintering phenomena, causing a decrease in catalyst activity, thereby affecting the progress of the reaction. This may result in a situation where the methane conversion rate decreases due to excessively high temperatures.Fig. 7 Methane conversion rate at different intake temperatures.

Fig. 7

4.2.2 The impact of inlet air flow rates

In the case of a constant inlet temperature of 800K and methane concentration of 1 %, the study investigates the effect of thermal radiation on the oxidative performance of the device under different inlet air flow rates.

Fig. 8 shows the methane combustion temperature distribution cloud at different inlet temperatures. The intake velocities are 1 m/s, 1.4 m/s, 1.6 m/s.Fig. 8 Distribution of methane combustion temperature at different inlet velocity.

Fig. 8

Fig. 9 shows that as the inlet air flow rate increases, the reaction temperature at the same oxidation bed position continuously decreases. As the reaction progresses, the temperature rises, and the oxidation reaction becomes smaller. It can be inferred from the slope of the curve that the smaller the inlet air flow rate, the faster the reaction process in the front section of the oxidation bed and the slower the process in the rear section. Furthermore, the trend becomes more pronounced as the air flow rate decreases.Fig. 9 Reaction temperature curve of the oxidation bed under different inlet air flow rates.

Fig. 9

From Fig. 10, it can be seen that as the air flow rate increases, the total heat exchange of the equipment decreases continuously, the convective heat exchange ratio coefficient also decreases constantly, and the radiative heat exchange ratio coefficient gradually decreases. However, during this process, the decreasing trend of the convective heat exchange ratio coefficient is slower than that of the radiative heat exchange ratio coefficient, indicating that under this operating condition, convective heat exchange mainly affects the oxidation performance of the equipment. In contrast, the impact of radiative heat exchange on the heat exchange capacity of the equipment diminishes rapidly with the increase of air intake volume. When the airflow rate reaches 2 m/s, the radiative heat exchange ratio coefficient is around 10 %, showing a weak influence.Fig. 10 Variation curve of heat transfer coefficient under different inlet air flow rates.

Fig. 10

Fig. 11 shows the methane conversion rate at different air flow rates. It can be seen that the higher the air flow rate, the lower the methane conversion rate. This is because, with higher air flow rates, the methane spends less time in the oxidation bed, resulting in a shorter reaction time with the catalyst. This leads to incomplete reactions as the high-speed methane gas is carried out of the oxidation bed before complete conversion. Additionally, the higher air flow rates prevent the accumulation of heat in the oxidation bed, causing most of the heat to be carried out, resulting in a decrease in temperature within the oxidation bed as the flow rate increases.Fig. 11 Methane conversion rate under different inlet air velocities.

Fig. 11

4.2.3 The impact of methane concentrations

In the case of a constant inlet temperature of 800K and methane concentration of 1 %, the study investigates the effect of thermal radiation on the oxidative performance of the device under different methane concentrations.

Fig. 12 shows the temperature distribution cloud of the oxidized bed under changing methane concentrations. Inlet methane concentrations were 0.8 %, 1 %, 1.2 %.Fig. 12 Distribution of methane combustion temperature at different inlet methane concentrations.

Fig. 12

According to Fig. 13, it can be seen that as the concentration of methane at the inlet increases, the reaction temperature at the same position in the oxidation bed gradually increases. At the same time, as the reaction continues, the oxidation reaction process becomes slower at the same methane concentration, and the later stages of the reaction process at different concentrations also gradually slow down, with minimal temperature changes.Fig. 13 Reaction temperature curve of the oxidation bed under different methane concentrations.

Fig. 13

Fig. 14 shows that as the methane concentration increases, the turbulence intensity of the entire device continuously strengthens, the heat transfer capacity constantly improves, and the total heat transfer increases. However, under this operating condition, the radiation heat transfer ratio coefficient decreases continuously as the methane concentration increases; the convection heat transfer ratio coefficient trend is consistent with the total heat transfer coefficient. Therefore, convection heat transfer is the main factor affecting the oxidation performance of the device at this time. When the methane concentration reaches above 1 %, the radiation heat transfer ratio coefficient is below 25 %; at this time, the impact of radiation heat transfer on the oxidation performance of the device is weakening, and as the methane concentration increases, this characteristic becomes more pronounced.Fig. 14 Variation curve of heat Transfer coefficient under different methane

concentrations.

Fig. 14

Fig. 15 shows the methane conversion rate at different methane concentrations in the intake. It can be seen from the graph that as the intake methane concentration increases, the methane conversion rate also increases continuously. This is because, with the rise in methane concentration, more methane molecules enter the oxidation bed per unit area, leading to a higher frequency of methane contact with the catalyst. As a result, the reaction becomes more complete, and more heat is released from the reaction; this, in turn, promotes the catalytic oxidation reaction on the oxidation bed, leading to an increase in the methane conversion rate.Fig. 15 Methane conversion rate under different inlet methane concentrations.

Fig. 15

4.3 Discussion

Both the catalytic oxidative combustion of methane and the reaction mechanism of chalcogenide catalysts are complex processes with many factors affecting their combustion. In this paper, only a part of the influencing factors are considered, which cannot completely cover all the methane combustion situations, the selection of the oxidation bed material, the thermal conductivity and the porosity are all factors affecting the methane combustion. This paper only considers the combustion process under a single condition, and does not consider the combustion situation under the interaction of different conditions. This paper ignores the gas-to-gas radiative heat transfer, which is necessary for further research compared to the simplification of the complex radiative heat transfer process.

From the results of the study, it can be seen that methane combustion based on the DC preheating catalytic oxidation method is very promising, which is conducive to achieving the effective use of low-concentration gas and avoiding the waste of resources. However, attention should still be paid to the emission problems of CO and NO in the combustion process, which still need to be further solved.

5 Conclusion

A simulation and analysis of the reaction chamber inside a new low-concentration gas preheating direct current catalytic oxidation device was conducted. A two-dimensional mathematical model was established and simulated using FLUENT software. Considering radiation heat transfer, the oxidation performance was studied, Exploring ways to improve methane conversion in low concentration gas. Experimental data was compared and verified with simulation data, with an error of around 20k in the mathematical model. The simulation results show.1) Radiative heat transfer is a major factor in the oxidative performance of the device at high ambient temperatures. When the intake temperature reaches 900K, its proportion is close to 45 %. Concurrently, the maximum reaction temperature of the oxidation device increases from 983K to 1154K as the intake temperature rises, and the methane conversion rate increases from 58 % to 89 %.

2) The effect of thermal radiation on the oxidative properties of the device diminishes at high ambient velocities. When the air velocity reaches 2 m/s, the proportion of radiant heat transfer is only 10 %, and the maximum reaction temperature of the oxidation unit decreases from 1138 K to 993 K with the increase of the inlet air velocity, resulting in a decrease of the methane conversion rate from 88 % to 68 %.

3) The effect of thermal radiation on the oxidizing performance of the equipment continued to decrease with increasing methane concentration, while the effect of convective heat transfer continued to increase. At methane concentrations above 1 %, the percentage of radiative heat transfer is less than 25 %, and the maximum reaction temperature of the oxidizer rises from 967 to 1087 K with increasing methane inhalation concentration, resulting in an increase in methane conversion from 71 to 88 %.

Data availability statement

Not applicable.

CRediT authorship contribution statement

Junlin Zhu: Writing – original draft, Validation, Software, Methodology, Formal analysis, Data curation. Lixing Zheng: Writing – review & editing, Supervision, Resources, Project administration, Funding acquisition, Conceptualization. Xiaojun Xue: Resources, Investigation, Funding acquisition. Wei Lu: Software, Resources, Project administration, Methodology.

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.

Acknowledgments

This work was supported by Shanxi Province "1331 Project" research center construction project (PT201807) and the central guidance of local science and technology development special funds (YDZX20191400002916).
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