Methanation is an effective way to efficiently utilize product gas generated from the pyrolysis and gasification of organic solid wastes. To deeply study the heat transfer and mass transfer mechanisms in the reactor, a successful three-dimensional comprehensive model has been established. Multiphase flow behavior and heat transfer mechanisms were investigated under reference working conditions. Temperature is determined by the heat release of the reaction and the heat transfer of the gas-solid flow. The maximum temperature can reach 951 K where the catalyst gathers. In the simulation, changes in the gas inlet velocity and catalyst flow rate were made to explore their effects on CO conversion rate and temperature for optimization purposes. As the inlet gas velocity increases from 2.78 to 4.79 m/s, the CO conversion rate decreases from 81.6% to 72.4%. However, more heat is removed from the reactor, and the temperature rise increases from 78.03 to 113.49 K. When the catalyst flow rate is increased from 7.18 to 17.96 kg/(m^{2}·s), the mass of the catalyst in the reactor is increased from 0.0019 to 0.0042 kg, and the CO conversion rate is increased from 66.8% to 81.5%. However, this increases the maximum temperature in the reactor from 940.0 to 966.4 K.

With the rapid growth of population and the improvement of urban construction level, the amount of organic solid waste (OSW) has also been increasing sharply. On the whole, the OSW generally includes municipal solid waste (MSW), agricultural solid waste, and industrial solid waste [^{9} tons by 2050 [

In the process of pyrolysis and gasification, sufficient contact between gasification agents and volatile compounds in the OSW leads to less waste heat, better-quality gas products, and higher energy efficiency [^{3} were generated. Li et al. [

As the cleanest energy, the demand for natural gas is increasing [_{2} in pyrolysis and gasification products can produce natural gas through a methanation reaction [

It was found that during the methanation process in the fluidized bed, the whole reactor was almost isothermal, which could preserve the activity of the catalyst. Moreover, it was conducive to the process of heat and mass transfer [

Compared with experimental research, numerical simulation can save the steps of building reactors and speed up the efficiency of device optimization [_{4} generation. But at the same time, it also led to the reduction of gas-solid contact time so that the reaction could not be completely carried out. The influence of catalyst dosage on CO conversion rate was also very complex. More catalysts promoted the reaction [

To enhance the utilization efficiency of the OSW pyrolysis gasification syngas and solve the catalyst sintering problem caused by the hot spot phenomenon, the three-dimensional reaction model of the fluidized bed reactor was established in this study. The main contributions of this work are (a) the successful construction of a three-dimensional comprehensive model of the fluidized bed reactor to simulate the gas-solid multiphase flow, (b) the in-depth study of the heat transfer mechanism in the methanation process to solve the problem of catalyst deactivation, and (c) the understanding of the effects of gas velocity and particle flowrate on CO conversion and temperature to be further referenced for experimental optimization.

In the fluidized bed methanation reactor, the gas phase and solid phase exist simultaneously. The continuity equations, momentum equations, and energy equations of these two phases are solved, respectively.

Continuity equation for gas phase:

Continuity equation for catalyst phase:

Momentum equation for gas phase:

Momentum equation for catalyst phase:

The energy equation for gas phase:

The energy equation for catalyst phase:

More physical quantities need to be described as a result of closing the conservation equation.

Stress tensor of gas phase:

Shear viscosity of gas phase:

where,

Shear viscosity of gas phase:

The pressure of catalyst phase:

Momentum exchange coefficient:

Heat transfer coefficient:

The Kinetic theory of granular flow (KTGF) is used to obtain the properties of the solid phase, while the Gidaspow drag model is selected to describe the force between the gas and solid phases. For the sake of closing the energy equations, the heat transfer between gas and solid phases is described mathematically with the Gunn heat transfer model.

Description | Model | Reference |
---|---|---|

Turbulence model | Standard |
[ |

Momentum transfer | KTGF | [ |

Granular viscosity | Gidaspow | [ |

Granular bulk viscosity | Lun et al. | [ |

Drag coefficient | Gidaspow | [ |

Interphase heat transfer model | Gunn model | [ |

The reaction equation for CO to generate CH_{4} under the catalysis of catalyst is as follows:

According to the kinetic rate model of CO methanation proposed by Chein et al. [

where,

In _{4}, CO, H_{2}, and H_{2}O. All these kinetic parameters are given in Arrhenius function form as exhibited in

Unit | |
---|---|

Methanation can be evaluated by the conversion rate of CO. The CO conversion rate is defined as follows:

Under the quasi-stable state, the values of parameters

where,

The probability

where,

The fluidized bed reactor proposed by Liu et al. [

The mixture of the gas inlet is composed of CO, H_{2} and N_{2}. Among them, CO and H_{2} are the main reactants of the methanation reaction, and the mole fraction ratio is controlled at H_{2}:CO = 3:1, which is consistent with the best value found in the experiments [^{3} and an average diameter of 0.04 mm. At the same time, a certain amount of N_{2} is introduced for gas transmission.

Both catalyst inlet and gas inlet are set as velocity inlets, while the mixture outlet is selected as the pressure outlet. The boundary condition of the reactor wall is set as the adiabatic and no-slip wall. Before adding catalyst particles, it must be ensured that the gas flow field inside the reactor is uniform and stable. In the subsequent simulation, the Pressure-Based method is adopted to solve the control equations while the Phase Coupled SIMPLE scheme is applied to the pressure-velocity coupling. The energy equations are solved by the Second Order Upwind, and other equations are solved by the First Order Upwind. The time step is set to 1 × 10^{−4} s, and the max iterations per time step are set to 10.

In this work, different operating parameters were set to investigate the mass transfer behavior and heat transfer mechanism of the methanation process in the fluidized bed reactor. According to previous studies, we can find that the flow behavior directly affects the reaction rate and the heat transfer efficiency [

Test number | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|

Inlet gas velocity (m/s) | 2.78 | 3.45 | 4.12 | 4.79 | 3.45 | 3.45 | 3.45 |

Catalyst flowrate (kg/(m^{2}·s)) |
14.37 | 14.37 | 14.37 | 14.37 | 7.18 | 10.78 | 17.96 |

The number of meshes directly impacts the time and accuracy of the calculation. In order to select the most suitable method of meshing, three different kinds of meshes are divided as exhibited in

Name of meshes | Fine meshes | Medium meshes | Coarse meshes |
---|---|---|---|

Number of meshes | 495992 | 670733 | 1156295 |

In order to verify whether the calculation model and the reaction model are reasonable, the experimental results are compared with the simulation results. As exhibited in

In the process of simulation, the catalyst volume fraction at different heights is monitored and analyzed, as illustrated in

Comparing the values of the pressure at different heights, it is found that the pressure is inversely proportional to height. It is easy to understand that when the gas flows through the reactor, there are energy consumption terms such as resistance loss along the way, local resistance loss, and collision loss with particles. As the height reduces, more pressure is required to compensate for these losses, and the higher the pressure value will be. Meanwhile, the outlet of the reactor is set as a pressure outlet, so its pressure value is 0. In addition, the pressure fluctuation is gradually weakened during the upward flow of the gas and the catalyst. In the quasi-steady state, the pressure fluctuation range decreases from 17.7 Pa at the inlet to 4.5 Pa at the outlet.

As shown in

The probability density distribution can more intuitively reveal the distribution probability of parameters in different intervals. Select a certain number of research points equidistantly on the research object (such as cross sections) and read the parameter values (such as gas velocity) on these points. The range of parameter values is divided into 20 or 40 cells on average, and the probability of occurrence of values in each cell is counted. Finally, the probability density distribution is obtained by sorting the data.

In order to show the velocity distributions of different sections more accurately, a probability bar chart, as presented in

Since the methanation reaction is a strongly exothermic process, observing the temperature distribution inside the reactor to prevent the occurrence of hot spots is of great importance for the experiment. As shown in

Sections with heights of 175, 400, 1000, and 1780 mm were selected as research objects. As demonstrated in

Every working condition is named according to different inlet gas velocities and catalyst flowrate. For example, the working condition with an inlet gas velocity of 2.78 m/s and catalyst flowrate of 14.37 kg/(m^{2}·s) is called “2.78–14.37”. Other working conditions are named according to this method as well.

Under the quasi-stable state, the mean mass of the catalyst particles in the reactor and its variation range is shown in

In the simulation process of the methanation reaction, the inlet gases include CO, H_{2}, and N_{2}. When the gas mixture at the outlet was detected, H_{2}O and CH_{4} were found in addition to the gas components at the inlet. This indicates that the methanation reaction has occurred. By monitoring the composition of the gas mixture, the CO conversion rate can be calculated using

With the increase of inlet gas velocity, the conversion rate of CO decreases from 81.6% to 72.4%, basically showing a linear downward trend. This leads to the corresponding reduction of the product CH_{4} of the methanation reaction, during the reaction raw materials CO and H_{2} increase. The increase of catalyst flowrate leads to the increase of CO conversion rate from 66.8% to 81.5%. However, the increase rate decreases from 11.1% to 3.5% with the increase of the catalyst flowrate. In other words, too many catalyst particles cannot promote the increase of CO conversion but will lead to waste of catalyst. In comparison with

The temperature affects not only the progress of the methanation reaction but also the activity of the catalyst. Therefore, the temperature rise from the inlet to the outlet of the reactor and the maximum temperature inside the reactor are recorded. The results are plotted in

Increasing the catalyst flowrate will obviously increase the catalyst mass inside the reactor, as shown in

The fluidized bed methanation reactor can efficiently utilize pyrolysis and gasification syngas from OSW. A comprehensive model coupled with flow and heat transfer was established to explore the mechanism of mass transfer and heat transfer. The following conclusions can be drawn from the simulation results:

The pressure and catalyst volume fraction along the height show similar trends. At the bottom, the values of parameters fluctuate greatly. As the height increases, these fluctuations are gradually weakened and even eliminated. Under the quasi-steady state, the pressure fluctuation range decreases from 17.7 Pa at the section with a height of 0 mm to 4.5 Pa of 1780 mm.

The distribution of temperature is directly related to the catalyst volume fraction. Where the catalyst gathers, the reaction gives off a lot of heat, and the maximum temperature can reach 951 K. In the area where the catalyst is dispersed, the full mixing of gas and catalyst increases heat dissipation efficiency, and the maximum temperature on the cross-section decreases to 769 K.

The increase of inlet gas velocity not only reduces the residence time of the catalyst which makes the CO conversion rate decreases from 81.6% to 72.4% but also increases the instability of operation. However, when the inlet gas velocity is small, the mixing of the gas phase and the solid phase is inadequate. Insufficient heat exchange prevents the heat from being discharged from the reactor in time, and the maximum temperature in the reactor can reach 968.4 K.

The catalyst flowrate directly determines the catalyst mass remaining in the reactor. With the increase of catalyst flowrate, the CO conversion rate can be increased from 66.8% to 81.5%. However, when the flowrate is too large, the growth rate of CO conversion decreases to 3.5%. This shows that excessive catalyst flowrate is easy to brings about the waste of the catalyst.

Values of parameters under quasi-stable state [-, K, m/s]

Instantaneous values of parameters [-, K, m/s]

Probability of parameters [%]

Drag coefficient [-]

Turbulence model constant [-]

Isobaric specific heat capacity [J·(kg·K)^{−1}]

Diameter of catalyst particles [mm]

Total number of values of the parameter [-]

Count [-]

Turbulent kinetic energy generation term [kg·(m·s^{3})^{−1}]

Gravity [m^{−2}]

Radial distribution function [-]

Heat transfer coefficient between gas phase and catalyst phase []

Stress tensor invariant [-]

Nusselt number of catalyst phase [-]

Count [-]

Mass of spice i [kg]

Equilibrium constant of reaction [Pa^{2}]

Surface adsorption equilibrium constant of species i [Pa^{−1}] or [-]

Conductivity of granular temperature [W^{−1}]

Rate constant [^{−1}]

Pressure [Pa]

Partial pressure of species i [bar]

Prandtl number [-]

Pressure of catalyst phase [Pa]

Kinetic rate of reaction [mol_{cat}^{−1}^{−1}]

Reynolds number of catalyst [-]

Ideal gas constant (J·mol^{−1}·K^{−1})

Source term of mass transfer of gas phase [-]

Source term of mass transfer of catalyst phase [-]

Energy source term [W^{−3}]

Time [s]

Temperature [K]

Velocity [m^{−1}]

CO conversion rate [-]

Volume fraction [-]

Momentum exchange coefficient [-]

Density [kg^{−3}]

Stress tensor [Pa]

Shear viscosity [Pa

Gas phase laminar viscosity [Pa

Gas phase turbulent viscosity [Pa

Dissipation rate of gas turbulence [-]

Turbulent kinetic energy of gas [-]

Thermal conductivity of gas phase [W·m^{−1}·K^{−1}]

Thermal conductivity of catalyst phase [W·m^{−1}·K^{−1}]

Bulk viscosity of catalyst [Pa

Collision dissipation of energy [kg/(m·s^{3})]

Interphase energy exchange [kg^{3})^{−1}]

Constant [-]

Pseudo particle temperature [m^{2}^{−2}]

Gas phase

Catalyst phase

CH_{4}, CO, H_{2}, H_{2}O

Catalyst volume friction, temperature, gas velocity, catalyst velocity

Time of recording data

Inlet

Outlet

Gas velocity, catalyst velocity

This work was supported by the National Key Research and Development Program of China [Grant Number 2019YFC1906802].

The authors declare that they have no conflicts of interest to report regarding the present study.

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