Multi-field Coupling Model Research Articles

Research on the cracking risk index of massive concrete based on Chemo-Thermo-Hygro-Mechanical multi-field coupling model

Building upon the intricate interplay of hydration, temperature, moisture, and mechanical forces, we introduce an innovative Chemo-Thermo-Hygro-Mechanical (C-T-H-M) multi-field coupling model tailored to massive concrete structures. This model facilitates the analysis of the cracking risk index through the application of the maximum effective energy density ratio. An exhaustive inquiry delves into the correlation between this index and factors such as structural form, failure driving force, and humidity effect in massive concrete. Findings reveal significant disparities in the cracking risk index across distinct structural configurations. By examining diverse stress scenarios and accounting for various failure driving forces, a Three parameters emerges as the chief contributor to the highest cracking risk index. Moreover, the proposed C-T-H-M model exposes a heightened surface cracking risk index in comparison with conventional Chemo-Thermo-Mechanical approaches. These observations underscore the significance of adopting a holistic perspective when assessing cracking risk indices and devising crack mitigation strategies, taking into account structural aspects, failure driving force, and humidity effect.

Experimental Investigations on the On-Site Crack Control of Pier Concrete in High-Altitude Environments

Concrete structures in high-altitude environments face many challenges. Establishing concrete crack control methods in high-altitude environments is crucial for enhancing the service capacity of concrete structures. In this study, a multi-field (hydration-temperature–humidity-constraint) coupling model was used to quantitatively assess the cracking risk of pier bodies at high altitude. On-site crack control tests were conducted on pier bodies using a micro-expansion anti-cracking agent to demonstrate the effectiveness of deformation shrinkage compensation in crack control at high altitudes. The results indicated that there was a risk of cracking in the pier body at high-altitude conditions, especially within 0.3 m from the pile cap and ±2.5 m from the center of the pier side surface. Compared with conventional piers, the micro-expansion anti-cracking agent approximately doubled the unit expansion deflection of piers at high temperatures while reducing the unit shrinkage deflection of piers by 11% to 12% at low temperatures. The concrete in conventional pier bodies was in a tension state after long-term hardening, while the concrete treated with the micro-expansive anti-cracking agent was in compression. Therefore, the deformation compensation effect of the micro-expansive anti-cracking agent was significant and reduced the risk of concrete cracking. In addition, early freezing had a significant impact on concrete strength, underscoring the importance of effective temperature control during the early stages of concrete placement in high-altitude environments.

Simulation study on additive-promoted microwave dehydration of lignite

ABSTRACT Microwave dehydration technology has been widely used in coal processing methods due to its unique advantages. Adding additives with high dielectric loss to coal can enhance the microwave absorption capacity of coal, so as to effectively improve the dehydration process. In order to understand the change and distribution of multi-fields in the microwave drying process of lignite under the action of different additives, verify the experiment and reduce the cost and number of experiments, this paper established a multi-field coupling model of electromagnetic field and heat and mass transfer of multiphase porous media based on COMSOL Multiphysics, so as to simulate the microwave drying process of lignite. The results show that the distribution areas of electromagnetic field, temperature field, and vapor in coal are basically the same, while the distribution of liquid water is just the opposite. With the enhancement of additive promotion effect, the parts with strong electromagnetic field strength increase, the hot spots of temperature field increase, the maximum temperature, and minimum temperature increase, and the water content in coal samples decreases. The promotion effect of additives on the microwave dehydration process of lignite is consistent with the experiment.

Development and performance evaluation of a novel solar mid-and-low temperature receiver/reactor with packed metal foam

Solar-driven hydrogen production from methanol decomposition (MD) is an important method of storing solar energy as clean fuels and improving the solar energy utilization efficiency. Catalyst preparation is one of the key steps, but conventional Cu-ZnO-Al2O3 particle catalysts lead to uneven reactor temperature, reducing the efficient conversion of solar energy into fuels. To alleviate this challenge, a monolithic catalyst utilizing packed foamy copper as a carrier is developed with exceptional thermal and mass transfer properties. The experimental results validate its excellent performance in hydrogen production using MD. The absolute conversion increases by an average of 12.11 % at 250 °C and further by 14.43 % at 270 °C compared to the particle catalyst. Based on these findings, a novel solar reactor is proposed, and a multi-field coupling model is built. The comparative results verify the performance advantage of the developed solar thermochemical receiver/reactor with packed metal foam-based catalyst. It maintains high conversion rates and solar-to-fuel energy efficiency, while alleviating overheating problems caused by traditional particle catalysts. Under the design conditions, the new reactor significantly improves the absolute conversion of methanol and the energy efficiency of solar-to-fuel conversion by 4.57 % and 3.00 %, respectively, resulting in 92.64 % and 67.56 %. This study provides a theoretical basis and technical solution for more stable and efficient use of mid-and-low temperature solar energy.

Research Progress of Three-dimensional Geological Modeling and Multi-field Coupling of Fractured Oil and Gas Reservoirs

Fractured oil and gas reservoirs play an important role in oil and gas exploration and development due to their complex fracture network structure. As the main fluid channel in the reservoir, fractures have a significant impact on the migration, accumulation and exploitation efficiency of oil and gas. This paper summarizes the key geological characteristics of fractured reservoirs, including fracture types, distribution rules and main controlling factors of fracture development, and discusses the influence of fractures on reservoir physical properties. Furthermore, the deterministic and stochastic modeling methods of three-dimensional geological modeling of fractured reservoirs and the latest progress of discrete fracture network modeling technology are introduced in detail. In addition, this paper also discusses in detail the application of multi-field coupling model in the numerical simulation of fluid flow in fractured reservoirs, including continuous medium model and discrete medium model, and their advantages and disadvantages in simulating fluid flow in fractured reservoirs. Finally, this paper summarizes the research progress of multi-physics coupling model of fractured reservoirs, and points out the direction and challenges of future research. Through these studies, it can provide theoretical support and technical guidance for oil and gas exploration and development, in order to achieve more effective development and management of fractured reservoirs.

Coupled Modeling of Sea Surface Launch Flow and Multi-Body Motion

To simulate the launching process of missile complex flow, movement, and constraint states, a multifield coupling model is put forward based on a computational fluid dynamics (CFD) method. In this coupled model, a CFD method is used to solve the three-dimensional compressible transient flow, and the six-degree motion of the launching platform is considered, and the virtual contact method is used to deal with the constraint states of the guideway and the slider. The active force and moment are applied to the launching platform to simulate its rolling, pitching, and heaving motions under the 5-level waves. Collision detection is carried out through the minimum clearance distance between the slider and the guideway, and the contact force is handled by a modified Herz collision model. In the problem of launching a missile from the water surface, the change characteristics of the flow field, the load response characteristics, and the relative motion laws of the missile and the launching platform during the catapulting process are investigated. The results show that the motion laws of the projectile and the launch tube in the constrained direction are the same, and the established coupling model is able to simulate the launch separation process of the missile in the constrained state. In addition, the effect of wind load on the missile ejection process is analyzed using the coupled model.

Improving thermal environment and ventilation efficiency in high-temperature excavation tunnels via an innovative heat insulation and cooling baffle

An increasing number of tunnels inevitably encounter high-temperature environments induced by elevated geotemperatures. The energy demand for ventilation and cooling in excavation tunnels increases significantly as the temperature of the surrounding rock increases, thereby hindering the sustainable exploitation of deep resources. This paper presents an optimization method for airflow organization in excavation tunnels that integrates thermal insulation and cooling (TIC) baffles. The proposed approach significantly improves the cooling effect of the auxiliary ventilation system while reducing energy consumption. This method offers the advantages of simplicity, convenience, and cost-effectiveness. A multifield coupling model using COMSOL software was developed and validated to analyze the system, and the application scenario was explored. Several ventilation scenarios were examined, highlighting that TIC baffles effectively reduce the heat release from the surrounding rock and lower the airflow temperature in personnel areas in the excavation tunnel. By implementing TIC baffles, the average airflow temperature in the excavation tunnel decreases by 1.5 °C to 1.8 °C, resulting in a saving of approximately 5.11 kW in cooling energy. Increasing the circulating water flow in the heat-exchange pipe of the TIC baffles or reducing the initial circulating water temperature can enhance the cooling capacity of the TIC baffles and lower the tunnel airflow temperature to a certain extent. The distance between the TIC baffles and surrounding rock significantly affects the airflow temperature between the left and right TIC baffles. An excessive length of TIC baffles (L > 7 m) leads to heat accumulation and high-temperature airflow in localized areas. In This study, a method for optimizing the thermal environment and saving energy in high-temperature excavation tunnels is proposed.

Borehole Stability of Natural Gas Hydrate Reservoirs

Abstract The decomposition of natural gas hydrate (NGH) due to long-term drilling may decrease the strength of reservoirs and increase the borehole failure risk. Meanwhile, the creep properties of NGH reservoirs also may give rise to engineering problems including borehole shrinkage and jamming of drilling tools in the late stage of drilling, which seriously impairs the drilling safety. A thermal-fluid-solid multi-field coupling model considering the decomposition kinetics of NGH and creep properties of reservoirs was established to explore the influence mechanism of NGH decomposition and creep properties of hydrate-bearing sediments on mechanical behaviors of boreholes. In addition, influences of drilling parameters and geomechanical properties of reservoirs on borehole stability in the drilling process of NGH reservoirs were analyzed. Research results show that creep properties of NGH deposits causes homogenization of stress distribution in different directions of NGH reservoirs around boreholes, transition of plastic zones around boreholes to a round shape, and possibly overall borehole collapse. As the horizontal geostress becomes more inhomogeneous, the borehole instability risk increases; the higher the initial pore pressure of formation is, the lower the effective geostress and the lower the borehole instability risk. The research results can provide theoretical support for safe drilling of NGH reservoirs in South China Sea and promote the early commercial exploitation of NGH resources in China.

Study on multi-field coupling characteristics of underground coal combustion and nitrogen injection parameter optimization

Underground coal fires, which are widely distributed and cause serious resource waste and environmental hazards, have become a common concern of the international community. This paper aims to reveal the mechanism of coal spontaneous combustion and the expansion law of underground coal fires. A void rate model from the goaf to the ground surface and a multi-field coupling model for underground coal fires were established. Based on which, the combustion process from the beginning of oxidation to the formation of large-scale fire of the remaining coal in goaf was analyzed. Furthermore, the evolution law of underground coal fire after nitrogen injection and the influence of different nitrogen injection parameters were analyzed. The results show that the coal spontaneous combustion can be divided into three stages: slow reaction stage (stage Ⅰ), violent combustion stage (stage Ⅱ), and stable combustion stage (stage Ⅲ), and the transformation of different stages is mainly controlled by the oxidation reaction rate of coal. To obtain the optimal parameters for nitrogen injection for fire suppression, the fire extinguishing efficiency concerning nitrogen injection time, nitrogen injection amount and nitrogen injection position, as well as the distribution law of nitrogen in rock strata were analyzed. Through range analysis, it is determined that the most effective fire extinguishing occurs with the injection rate of 0.15 m3/s in stage I, and the injection position has little influence on the fire extinguishing effect. This understanding contributes to a deeper understanding of the multi-field coupling mechanism of underground coal fires and provides a guidance for extinguishing and preventing underground coal fires.

Performance optimization for magnetoelectric antennas based on a multi-field coupling analysis model

This paper presents a multi-field coupling model for magnetoelectric (ME) antennas, encompassing a ME film, electrode layers, and a substrate featuring a cavity structure. This model accounts for the nonlinear magnetoelastic coupling within the radiation layer and employs a combined DC and AC simulation methodology to capture the antenna's radiation mechanism. Leveraging this multi-field coupling model, performance differences between the ME antenna and an ideal ME composite film are analyzed. By exploring optimization schemes based on multi-physics fields, electrode materials, and structural design, the ME antenna's radiation performance is significantly enhanced. The findings demonstrate that the complete antenna structure, with its increased thickness and cavity design, exhibits a lower resonance frequency and a higher converse ME (CME) coefficient compared to the ideal ME film. The optimal CME effect is achieved under proper external stimuli, leading to a broader 3 dB bandwidth. Expanding the cavity dimensions enhances the CME coefficient by 42% and reduces the resonance frequency due to decreased acoustic wave loss. Adopting electrode materials with higher acoustic impedance elevates the CME coefficient, yet narrows the bandwidth. Conversely, using silver (Ag) electrodes promotes a broader bandwidth. Additionally, ME antenna arrays are designed to broaden the bandwidth by 300%.

A coupled phase-field model for sulfate-induced concrete cracking

The performance of concrete will decrease when subjected to external sulfate corrosion, and numerical models are effective means to analyze the mechanism. Most models cannot efficiently consider the effect between cracks and ionic transport because crack initiation and propagation are ignored. In this paper, a coupled chemical-transport-mechanical phase-field model is developed, in which the phase-field model is applied for the first time to predicate the cracking of sulfate-eroded concrete. The chemical-transport model is established based on the law of conservation of mass and chemical kinetics. The phase-field model equivalents the discrete sharp crack surface into a regularized crack, making it convenient to couple with the chemical-transport model. The crack driving energy in the phase-field model is computed by the expansion strain, which can be obtained from the chemical-transport model. The coupling of crack propagation and ionic transport is achieved by a theoretical equation, which considers both the effects of cracking and porosity. Complex erosion cracks can be automatically tracked by solving the phase-field model. The simulation results of the multi-field coupling model proposed in this paper are in good agreement with the experimental data. More importantly, the spalling phenomenon observed in physical experiments is reproduced, which has not been reported by any other numerical models yet, and new insight into the spalling mechanism is provided.

Study on the influence of combined utilization of air-fog curtain on fully mechanized face

To address the ambiguous regulations for dust control and removal in the joint use of air curtain and fog curtain, this study developed a multi-field coupling model of airflow, dust, and droplets. By incorporating the spraying method into both traditional ventilation technology and air curtain technology, this study comparatively analyzed the dust control and removal efficiencies of these two methods under various ventilation conditions in tunnels. The spray experiment and simulated result indicated a maximum relative error of 19.9%. The simulation results demonstrated that the use of traditional ventilation technology resulted in significant dust contamination in the rear and top regions of the tunnel. Although the dust pollution was ameliorated when the pressure-suction ratio was 1.25, the dust control effect remained unsatisfactory, with the pollution distance extending 37.0m. After implementing air curtain technology, the airflow generated a spiral air curtain due to the wall attachment effect, effectively confining the majority of dust to the heading face area. When the axial flow ratio was 45%, the dust concentration at exceeding 13.0m from the heading face dropped to blow 1.0mg/m3, significantly reducing health risks for operators.

A comprehensive study in experiments combined with simulations for vanadium redox flow batteries at different temperatures

Ensuring the appropriate operation of Vanadium Redox Flow Batteries (VRFB) within a specific temperature range can enhance their efficiency, fully exploiting the advantages of renewable energy. This study employs a comprehensive approach combining experimentation and simulation to systematically investigate the impact of temperature on VRFB performance. Experimental evaluations of VRFB performance across various temperatures were conducted through charge and discharge experiments, electrochemical impedance spectroscopy, hydraulic pressure drop testing, and cycling charge and discharge trials. Additionally, a three-dimensional multi-field coupled model was developed to provide a theoretical analysis and elucidate VRFB performance under varying temperature conditions, incorporating temperature-dependent variations in the physical parameters of different components. The results suggest that in VRFB systems, an increase in temperature leads to a reduction in overpotential and pressure drop, resulting in improved system efficiency, albeit accompanied by a slight decrease in Coulombic efficiency. Furthermore, compared to ohmic overpotential and electrochemical overpotential, the impact of temperature on concentration overpotential appears to be relatively insignificant. Increasing the flow rate or temperature could contribute to a more stable degradation rate of capacity and Coulombic efficiency during the battery cycling process. Higher flow rates enhance the voltage efficiency of the battery, with the degree of improvement decreasing as temperature increases.

Comparative Study of Heat Transfer Simulation and Effects of Different Scrap Steel Preheating Methods

The materials charged into a converter comprise molten iron and scrap steel. Adjusting the ratio by increasing scrap steel and decreasing molten iron is a steelmaking raw material strategy designed specifically for China’s unique circumstances, with the goal of lowering carbon emissions. To maintain the converter tapping temperature, scrap must be preheated to provide additional heat. Current scrap preheating predominantly utilizes horizontal tunnel furnaces, resulting in high energy consumption and low efficiency. To address these issues, a three-stage shaft furnace for scrap preheating was designed, and Fluent software was used to compare and study the preheating efficiency of the new three-stage furnace against the traditional horizontal furnace under various operational conditions. Initially, a three-dimensional transient multi-field coupling model was developed for two scrap preheating scenarios, examining the effects of both furnaces on scrap surface and core temperatures across varying preheating durations and gas velocities. Simulation results indicate that, under identical gas heat consumption conditions, scrap achieves markedly higher final temperatures in the shaft furnace compared to the horizontal furnace, with scrap surface and core temperatures increasing notably with extended preheating times and higher gas velocities, albeit with a gradual decrease in heating rate as the scrap temperature rises. At a gas velocity of 9 m/s and a preheating time of 600 s, the shaft furnace achieves the highest waste heat utilization rate for scrap, with scrap averaging 325 °C higher than in the horizontal furnace, absorbing an additional 202 MJ of heat per ton. In the horizontal preheating furnace, scrap steel exhibits a heat absorption efficiency of 35%, whereas in the vertical furnace, this efficiency increases notably to 63%. In the vertical furnace, the waste heat recovery rate of scrap steel reaches 57%.

Vibration and noise mechanism of a 110 kV transformer under DC bias based on finite element method

Global energy and environmental issues are becoming increasingly problematic, and the vibration and noise problem of 110 kV transformers, which are the most widely distributed, have attracted widespread attention from both inside and outside the industry. DC bias is one of the main contributing factors to vibration noise during the normal operation of transformers. To clarify the vibration and noise mechanism of a 110 kV transformer under a DC bias, a multi-field coupling model of a 110 kV transformer was established using the finite element method. The electromagnetic, vibration, and noise characteristics during the DC bias process were compared and quantified through field circuit coupling in parallel with the power frequency of AC, harmonic, and DC power sources. It was found that a DC bias can cause significant distortions in the magnetic flux density, force, and displacement distributions of the core and winding. The contributions of the DC bias effect to the core and winding are different at Kdc = 0.85. At this point, the core approached saturation, and the increase in the core force and displacement slowed. However, the saturation of the core increased the leakage flux, and the stress and displacement of the winding increased faster. The sound field distribution characteristics of the 110 kV transformer under a DC bias are related to the force characteristics. When the DC bias coefficient was 1.25, the noise sound pressure level reached 73.6 dB.

Submarine slope stability during the exploitation of natural gas hydrate from horizontal wells

Horizontal wells have the advantages of high production, considerable access to reserves, and effective sand production control; thus, they are potential well types for hydrate exploitation. In the process of hydrate mining, the decomposition of hydrate will cause the deterioration of the mechanical properties of the reservoir, which may induce submarine landslides, especially in the case of multiple horizontal wells, and the risk of submarine landslides is further increased. Therefore, it is necessary to study the influence of the horizontal well pattern adopted for hydrate mining on the stability of submarine slopes. First, a triaxial mechanical experiment of gas hydrate-containing sediments was carried out, and the mechanical parameters of the hydrate-containing sediments were obtained. Second, a thermal-fluid-solid multifield coupling model considering the hydrate phase transition during the production process was established. Finally, on the basis of the finite element strength reduction method, a slope stability evaluation model for hydrate extraction from a horizontal well pattern was established, and the influence of hydrate extraction from horizontal wells on the stability of submarine slope was analyzed. The results show that the peak strength, elastic modulus and cohesion of gas hydrate-containing sediments increase with increasing hydrate saturation. In the process of hydrate exploitation via horizontal wells, with the reduction in well spacing and the increase in the number of production wells, the risk of slope instability increases. Wells positioned along the slope strike are more conducive to slope stability than those positioned perpendicular to the slope strike. The slope stability increases gradually as the slope dip decreases. When the number of wells is the same, the slope stability increases gradually with increasing well spacing and production pressure.

Energy transfer, conversion and mechanical regulation in graded piezoelectric semiconductor bipolar junction transistor

While the effective regulation of carrier redistribution in piezoelectric semiconductor devices by mechanical loads through piezoelectric polarized electric fields is well-studied, there is a scarcity of reported research on the influence of energy transfer and conversion characteristics in a non-thermal equilibrium state of these devices. This paper establishes a nonlinear multi-field coupling model for piezoelectric semiconductor graded bipolar junction transistor (PS-GBJT) and proposes a corresponding multi-gradient iterative algorithm. We regard the product of current and built-in electric field as the work done by electric field force on carriers. By incorporating the energy absorbed/released during carrier recombination/generation process, we observe that non-equilibrium carriers act as a medium that facilitates energy conversion between these two mechanisms. Additionally, the non-uniformly distributed doping extends the influence of space charge region throughout entire transistor. In terms of external input electrical energy, the emitter, base, and collector regions play roles of input energy, transfer energy, and output energy, respectively. The study concludes by demonstrating the regulation of energy transfer or conversion efficiency in emitter, base, and collector regions through mechanical loads, thereby altering the heating behavior of entire GBJT and reshaping its energy transfer path. This leads to the significant finding that distinct energy transfer paths fundamentally define the various operational states of GBJT. The novel insights gained from this research hold reference value for thermal design and energy management of electronic devices.

Shrinkage separation prediction of concrete-filled steel tube arch bridge: A coupling model concerning multiple factors

The shrinkage separation is one of the key factors restricting the development of concrete-filled steel tube (CFST) arch bridge. In this paper, its mechanism and evaluation method concerning multiple factors, including structure, environment, material and construction were investigated. Firstly, the hydration process of in-tube concrete was simulated using the hydration degree as a basic state parameter. Then with the consideration of energy and mass conservation, as well as the moisture and heat transmission effects, the temperature and relative humidity fields, early-age mechanical properties, basic creep, and total deformation of in-tube concrete were further calculated. On the basis, in accordance with the stress criterion and displacement coordination, a multi-field (hydro-thermo-hygro-constraint) coupling model was finally established, taking the ratio of normal stress to bonding strength at the steel-concrete interface as the shrinkage separation risk index. The simulation results obtained from the model were in good agreements with the full-scale CFST model test.

Optimization of deep acid fracturing parameters for Shunbei carbonate dissolved fault reservoirs

Abstract When encountering favorable reservoirs that have not been drilled along the wellbore trajectory of Shunbei carbonate fracture-cavity reservoirs, deep acid fracturing technology is required to communicate with favorable reservoirs and achieve production. Currently, there is no optimized method for designing deep acid fracturing parameters for Shunbei fracture-cavity reservoirs, which results in problems such as failure to communicate with favorable reservoirs after deep acid fracturing or rapid decline in production after communication. To address these issues, this paper establishes a geological feature model for fracture-cavity reservoirs based on the characteristics of Shunbei fracture-cavity reservoirs and proposes a deep acid fracturing fracture parameter optimization approach with production capacity as the goal. Using a multi-field coupled acid fracturing model that can reflect the large leakage characteristics of fracture-cavity reservoirs, the proposed fracture parameters are used to simulate and optimize the scale of pre-flushing liquid and acid liquid. The simulation results show that the desired increase in production can be achieved when the fracture diversion capacity is 30D·cm and the penetration ratio is between 0.1 and 0.3. Furthermore, this paper recommends injecting 450~900 m3 of pre-flushing liquid to communicate with favorable reservoirs (0.1≤De≤0.2), followed by the injection of 900 m3 of cross-linked acid and 450 m3 of gelled acid to construct the fracture diversion capacity through acid corrosion.

Analysis of methane diffusion on permeability rebound and recovery in coal reservoirs: Implications for deep coalbed methane-enhanced extraction

A proper understanding of the effect of methane diffusion on coal reservoir permeability rebound and recovery is essential, as coal reservoir permeability is the key parameter influencing the efficiency of coalbed methane migration and computational research on it is lacking. In this paper, the multifield coupling model for methane migration was established. Then, two parameters, the influence coefficient of diffusion on permeability rebound (DPRB) and the influence coefficient of diffusion on permeability recovery (DPRC), were proposed to quantify the effect of methane diffusion on rebound and recovery of coal reservoir permeability. Subsequently, we used COMSOL software to study the variation rules of the coal reservoir permeability rebound time, permeability recovery time, and permeability rebound value, DPRB, and DPRC for different geologic parameters. The results shown that the permeability rebound time and recovery time are proportional to the coal seam initial pressure, but inversely proportional to the initial permeability and initial diffusion coefficient. The rebound value decreases with increasing coal seam initial pressure and initial permeability, but ascends with rising initial diffusion coefficient. DPRB declines with increasing coal seam initial pressure, initial permeability, and initial diffusion coefficient, but they are all greater than 0.7, indicating that methane diffusion has a significant effect on permeability rebound. The DPRC values for different coal seam initial pressures, initial permeabilities, and initial diffusion coefficients are above 0.98, which implies that methane diffusion dominates the permeability recovery process. Finally, a conceptual model was presented to research the mechanism of diffusion influence on rebound and recovery of coal reservoir permeability, and the implications for enhanced drainage of deep coalbed methane were discussed. Therefore, the results of this paper can provide a theoretical foundation for deep coalbed methane-enhanced extraction.