Numerical Study of Moisture Transfer and Methane Emission in Earthen Final Covers: Effects of Ambient Conditions

Abstract

Earthen final covers (EFCs) are widely used to mitigate environmental impacts from landfills, particularly in controlling methane emissions and groundwater contamination. In this study, a one-dimensional numerical model was built to simulate the interactions of liquid water, water vapor, landfill gas, and heat, incorporating the biochemical process of methane oxidation. Parametric studies revealed that both atmospheric and waste temperatures significantly influence the soil temperature and evaporation, thereby affecting methane oxidation. Oxidation efficiency increased from 8.7% to 55.3% as atmospheric temperature rose from 5 °C to 35 °C. High waste temperatures enhanced oxidation by up to 2.9 times under cold conditions. An increase in atmospheric pressure (950–990 mbar) promoted oxygen diffusion into the cover and improved oxidation efficiency from 0.8% to 77.1%. Atmospheric relative humidity also played a critical role by affecting surface evaporation, with higher humidity promoting better water retention but limiting oxygen diffusion. The methane oxidation performance of the cover declined by 12.0% to 68.5% compared to pre-rainfall conditions. Rainfall temporarily inhibited oxidation due to moisture-induced oxygen limitation, with partial recovery after rainfall ceased. This study provided valuable insights into the complex interactions between ambient conditions and EFC performance, contributing to the optimization of landfill cover designs and methane mitigation strategies.

1. Introduction

Landfills remain a primary method for managing municipal solid waste. Methane (CH₄) emissions from landfills not only exacerbate climate change but also pose challenges for compliance with stringent regulatory standards aimed at reducing greenhouse gas emissions [1,2,3]. Earthen final covers (EFCs) have been widely adopted as an effective solution to mitigate the environmental impacts associated with landfill operations, particularly in controlling groundwater contamination and atmospheric pollution [4,5]. EFCs function by impeding the infiltration of rainwater, thereby reducing the generation of leachate and decreasing the risk of contaminants entering the groundwater system. Additionally, EFCs restrict the release of greenhouse gases, particularly CH₄, by establishing physical barriers that limit gas migration, while simultaneously promoting microbial aerobic CH₄ oxidation (MAMO) [6,7]. This process facilitates the conversion of CH₄ into less harmful substances such as carbon dioxide (CO₂) and water [8]. The performance of EFCs is influenced by a variety of factors, among which ambient conditions play a crucial role in determining their long-term efficacy in mitigating CH₄ emissions and controlling moisture transfer [9,10,11].

The performance of EFCs is not only influenced by their material composition and structural design but is also highly dependent on environmental conditions. The top of EFCs is exposed to the atmospheric environment and is significantly impacted by seasonal meteorological conditions, such as atmospheric pressure, temperature, relative humidity, and rainfall. Atmospheric pressure is commonly regarded as a key factor affecting landfill gas (LFG) emissions from the cover [12]. Field monitoring has shown a negative correlation between atmospheric pressure and CH₄ emissions [13]. Atmospheric temperature and relative humidity jointly regulate the evaporation process at the surface of EFCs, with higher temperatures and lower relative humidity accelerating surface evaporation [14]. Additionally, atmospheric temperature directly affects the soil temperature of EFCs, particularly shallow soil [15]. The optimal temperature range for MAMO is typically between 20 °C and 35 °C, with temperatures outside this range potentially causing a significant reduction in oxidation efficiency [8,16]. Rainfall directly influences the soil moisture content, thereby affecting its permeability and altering the gas composition within the cover. The CH₄ oxidation capacity of the cover soil is highly sensitive to moisture content, with the optimal range typically between 15% and 25%, as both excessively high and low moisture levels can inhibit the activity of CH₄-oxidizing bacteria [6]. Furthermore, the bottom of EFCs directly contacts the landfill waste, which influences the cover through the heat, moisture, and LFG released during the biochemical degradation of the waste [17,18]. Jafari et al. [19] reported that the temperature of landfill waste can reach up to 90 °C, creating significant temperature gradients within the cover. Liu et al. [20] demonstrated through heated column tests that the high temperatures of landfill waste altered the temperature distribution within the cover soil and significantly enhanced the movement of water vapor and evaporation. The performance of EFCs is the result of the combined effects of multiple environmental factors. However, the performance of EFCs under the complex interactions of these ambient conditions still requires further research to more thoroughly explore and understand.

Given the complex performance response behavior of EFCs under varying ambient conditions, the use of theoretical models for investigation is considered an appropriate approach. Numerous theoretical models have been developed to simulate the coupled transport of moisture and LFG within EFCs, but they are typically based on isothermal conditions, failing to account for the complex environmental factors encountered by field covers [21,22,23]. Zuo et al. [5] developed a model to study the transport of LFG in EFCs, but it neglected the effects of heat and soil moisture content. Bian et al. [9] established a non-isothermal coupled water–gas–heat transport model, but it overlooked the effects of surface evaporation and water vapor flow, thus limiting its ability to explain the role of atmospheric temperature and waste temperature in promoting moisture evaporation and transport within EFCs. Therefore, further research is needed to investigate the combined effects of atmospheric conditions and landfill waste environment on the coupled transport of moisture, gas, and heat, as well as CH₄ oxidation within EFCs.

This study aims to investigate moisture transport and evaporation, as well as CH₄ migration and oxidation, in EFCs under varying ambient conditions. A theoretical model, which can depict the coupled liquid water–vapor–LFG–heat transport in unsaturated soil under the biochemical reaction of MAMO [24], was adopted. A one-dimensional numerical model was implemented using the multi-physics software COMSOL (version 6.1). Parametric studies were conducted on ambient conditions, including ambient temperature (i.e., atmospheric temperature and landfill waste temperature), atmospheric pressure, relative humidity, and rainfall, to examine their effects on moisture transport and CH₄ emissions. The results are expected to deepen the understanding of the complex interactions between environmental factors and cover performance, providing valuable insights for optimizing cover design and improving CH₄ mitigation strategies.

2. Methods

A theoretical model capable of characterizing the coupled transport of liquid water, water vapor, LFG, and heat within EFCs was employed to investigate the effects of ambient conditions. The governing equations were derived based on the principles of mass conservation, energy conservation, and fluid transport, while incorporating the effects of vapor–liquid phase transitions and MAMO. The detailed formulation of this model is thoroughly presented in Wu et al. [24].

2.1. Governing Equation for Moisture Transfer

Moisture transport in unsaturated EFCs includes both liquid water flow and vapor flow. The governing equation for moisture transfer comprehensively incorporates the effects of liquid water flow, water vapor diffusion, LFG transport, and water production resulting from MAMO, expressed as follows [24]:

$${\displaystyle \frac{\partial \left({\rho }_l{\theta }_l+{\rho }_v{\theta }_v\right)}{\partial t}}=-\nabla \left({\rho }_l{v}_l\right)-\nabla \left({\rho }_l{v}_v+{\rho }_v{v}_g\right)+{\rho }_d{M}_{H_{2}O}{R}_w$$

(1)

where ρ_l, ρ_v, and ρ_d are liquid water density, vapor density, and dry soil density, respectively; θ_l is volumetric water content; θ_v is volumetric vapor content (volume percentage of gas in the soil); v_l, v_v, and v_g are the flow velocity of liquid water, vapor, and the LFG mixture, respectively; $M_{H_{2}O}$ is the molar mass of water; R_w is the water generation rate by MAMO per unit mass of dry soil; t is time.

The vapor density is described as follows [25]:

$${\rho }_v={\rho }_{vs}{H}_r$$

(2)

$$H_r=\mathit{exp}\left( {\displaystyle \frac{-\psi M_{H_{2}O}g}{{\gamma }_{w}RT}}\right)$$

(3)

where ρ_vs is saturated vapor density (see Supplementary File S1 (Equation (S1)) in Supplementary Materials); H_r is the relative humidity of soil; ψ is soil matric suction; g is gravitational acceleration; γ_w is the unit weight of water; R is the universal gas constant; T is temperature.

The flow velocity of vapor can be determined by the following [26]:

$$v_v=-K_{v\psi }\mathit{\nabla }\psi -K_{vT}\mathit{\nabla }T$$

(4)

where K_vψ is isothermal vapor conductivity (see Supplementary File S1 (Equation (S2))); K_vT is non-isothermal vapor conductivity (see Supplementary File S1 (Equation (S3))).

2.2. Governing Equation for Multicomponent Gas Transfer

Multicomponent gas transport in unsaturated EFCs includes both advection and diffusion in the gas phase, as well as the transport of gases dissolved in water. Additionally, the impact of MAMO must also be considered. LFG transport (CH₄, CO₂, O₂, and N₂) is modeled using the advection–diffusion equation for each gas component [24]:

$${\displaystyle \frac{\partial }{\partial t}}\left[\left(\varphi -{\theta }_l\right)c_g^k+{\theta }_l{H}_l^k\right]=-\nabla \left(v_g{c}_g^k\right)-\nabla \left(v_l{H}_l^k\right)-\nabla N_g^k\pm {\rho }_d{r}_g^k$$

(5)

where $\varphi$ is soil porosity; $c_g^k$ is the molar concentration of gas k (k = 1, 2, 3, 4 represent O₂, CO₂, N₂ and CH₄, respectively); $H_l^k$ is the molar concentration of gas k dissolved in water; $N_g^k$ is the diffusive flux of gas k in the gaseous phase; and $r_g^k$ is the amount of gas k involved in MAMO.

According to Darcy’s law, the advective velocity of the LFG mixture is determined by [27]:

$$v_g=-k_{rg}{\displaystyle \frac{k_i}{u_g}}\nabla P_g$$

(6)

where k_rg is relative gas permeability; k_i is the intrinsic permeability of soil; u_g is the viscosity of the LFG mixture; P_g is absolute gas pressure, including the vapor pressure and LFG pressure [28]:

$$P_g=P_{vs}{H}_r+{\sum }_{k=1}^4{c}_g^{k}RT$$

(7)

where P_vs is the partial pressure of saturated vapor (see Supplementary File S1 (Equation (S4))).

2.3. Governing Equation for Heat Transfer

Heat transport in unsaturated EFCs incorporates conduction, convection, and latent heat from vapor phase changes. According to energy balance, heat transport is modeled as Equation (8) considering the heat generated by MAMO [24]:

$${\displaystyle \frac{\partial }{\partial t}}\left[E\left(T-T_r\right)+\left(\varphi -{\theta }_l\right){\rho }_{v}L\right]=-\mathit{\nabla }\left(-{\lambda }_T\mathit{\nabla }T\right)-\mathit{\nabla }{Q}_{conv}-\mathit{\nabla }{Q}_{hv}+Q_{oxi}$$

(8)

where E is the heat capacity of soil; T_r is the reference temperature; L is the latent heat of vaporization of water; ${\lambda }_T$ is the thermal conductivity of soil; Q_conv is sensible heat convection; Q_hv is latent heat convection; Q_oxi is heat generation by MAMO. A detailed description of each parameter in Equation (8) can be found in the literature [24].

2.4. Microbial Aerobic CH₄ Oxidation

MAMO in EFCs may be described by the relationship as follows [24,29]:

$$\mathrm{C}{\mathrm{H}}_4+1.5{\mathrm{O}}_2\to 0.5\mathrm{C}{\mathrm{O}}_2+1.5{\mathrm{H}}_2\mathrm{O}+0.5–\mathrm{C}{\mathrm{H}}_2\mathrm{O}–+\mathrm{Heat}$$

(9)

CH₄ oxidation in EFCs can be determined by [6]

$$r_g^{{\mathrm{C}\mathrm{H}}_4}=-f_{V,T}{f}_{V,m}{V}_{max}{\displaystyle \frac{y_{{\mathrm{C}\mathrm{H}}_4}}{K_m+y_{{\mathrm{C}\mathrm{H}}_4}}}\times {\displaystyle \frac{y_{{\mathrm{O}}_2}}{K_O+y_{{\mathrm{O}}_2}}}$$

(10)

where f_V,T and f_V,m determine the effects of temperature and water content on the CH₄ oxidation rate, respectively (see Supplementary File S1 (Equations (S5) and (S6))); V_max is the maximum CH₄ oxidation rate per unit mass of dry soil; $y_{{\mathrm{O}}_2}$ and $y_{\mathrm{C}{\mathrm{H}}_4}$ are the molar fraction of O₂ and CH₄, respectively; K_m and K_o are half saturation constants for CH₄ and O₂, respectively. Based on the biochemical reaction relationships in Equation (9), the changes in O₂ consumption, CO₂ production, water generation, and heat release during the CH₄ oxidation process can be determined using (Equations (S7)–(S10)) in Supplementary File S1.

2.5. Model Implementation

The one-dimensional numerical model used in this study was developed using the finite-element software COMSOL Multiphysics, which simulated the moisture–gas–heat coupling transport processes and CH₄ oxidation reactions within the EFC. The structure of the simulated cover is consistent with that reported by Zhan et al. [15] for the soil cover at the Jiangcungou landfill in Xi’an (34°14′34′′ N, 109°05′5′′ E). This region experiences a warm temperate semi-humid continental monsoon climate, characterized by distinct seasonal variations. As shown in Figure 1, the vegetative layer consists of a 0.3 m thick compacted loess layer with 3% compost incorporation, exposed to the atmospheric environment. The storage layer is a 0.6 m thick compacted loess layer, primarily responsible for water storage and permeability control. The bottom layer is a 0.3 m thick gravel layer, influenced by the high-temperature and high-humidity conditions of the landfill waste. The input parameters are provided in Table S1. The soil–water characteristic curve of the cover is described using the van Genuchten model, while the hydraulic conductivity is determined by the van Genuchten–Mualem model [30]. Detailed parameters for each soil layer are provided in Table S1. In the analysis of the effects of ambient temperature, atmospheric pressure, and relative humidity, transient simulations are typically performed over a 30-day period. For rainfall impact analysis, it first runs for 30 days under initial conditions to establish moisture–temperature equilibrium in the cover. The top moisture boundary condition is then modified to simulate rainfall, and transient simulations are conducted for 10 days under different rainfall durations.

In the absence of specific modifications to the parameters, the initial conditions are consistent across different analysis scenarios. The atmospheric pressure of dry air is set at 970 mbar, with the volume fractions of CH₄, CO₂, O₂, and N₂ being 0.00%, 0.03%, 21.21%, and 78.76%, respectively. Only the molar concentrations of the gases vary in response to changes in atmospheric pressure. The atmospheric relative humidity is 0.5, and the atmospheric temperature is 20 °C. Additionally, the matrix suction of the cover is assumed to be 33 kPa, corresponding to the field capacity.

In the parameter sensitivity analysis, boundary conditions remain consistent unless explicitly modified. At the top boundary, the gas concentrations are held constant, corresponding to atmospheric values, while the moisture boundary is set as an evaporation condition with the evaporation rate defined by Equation (S11) in Supplementary File S1. The heat boundary is specified as a heat flux, determined by Equation (S12) in Supplementary File S1. At the bottom boundary, the gas flux is maintained at a constant LFG inflow rate. As reported by Scheutz et al. [8], methane fluxes of approximately 85 g m⁻² d⁻¹ are representative for older landfills or sites equipped with gas collection systems. Accordingly, a constant CH₄ influx of 85 g m⁻² d⁻¹ was applied in this study, with a CH₄-to-CO₂ volume ratio of 1:1. The moisture boundary is defined as the vapor influx boundary, determined by the saturated vapor flux carried by LFG and the vapor flux driven by vapor pressure. The heat boundary is a constant value, which is set according to the target temperature.

3. Results and Discussion

3.1. Effects of Ambient Temperature

The ambient temperature, including both atmospheric temperature and waste temperature, exerts a significant impact on the soil temperature within the cover. The atmospheric temperature at the Jiangcungou landfill generally ranges between 0 °C and 35 °C, while the soil temperature at the base of the cover can reach up to 45 °C [15]. Therefore, four atmospheric temperature conditions (5 °C, 15 °C, 25 °C, and 35 °C) were selected to investigate the effects of atmospheric temperature on the transport of moisture and LFG. Meanwhile, to explore the impact of heat generated by the degradation of MSW [31], the temperature at the bottom boundary was set to two conditions: one corresponding to the atmospheric temperature (Condition A) and the other set to 45 °C (Condition B).

Figure 2 presents the temperature distribution in the cover soil profile on day 30 under different ambient temperatures. Under Condition A, the surface temperature consistently remained lower than the atmospheric temperature, with the temperature difference reaching a maximum of 2.64 °C (Figure 2d). This discrepancy was primarily attributed to the heat loss associated with surface evaporation. At an atmospheric temperature of 5 °C, the relatively low soil temperature effectively inhibited MAMO within the cover [16], with the heat released by this process having a negligible impact. Consequently, the soil temperature in the cover remained lower than the atmospheric temperature. As the atmospheric temperature rose above 15 °C, MAMO in the compost-amended vegetative layer within the top 30 cm of the cover was enhanced. The soil temperature generally increased with depth before declining at greater depths. The maximum soil temperature in the cover exceeded the atmospheric temperature, with a temperature difference of up to 1.40 °C (Figure 2c). The modeled results are consistent with the results reported by Al-Heetimi et al. [32] based on soil column experiments. However, the soil temperature in Condition B was significantly higher than Condition A, exhibiting a pronounced temperature gradient. The surface temperature could exceed the atmospheric temperature by up to 3.67 °C (Figure 2a). This was mainly due to heat transfer from the bottom boundary, which altered the soil temperature in the cover [20].

Soil evaporation is highly influenced by temperature, with higher temperatures generally leading to increased evaporation rates. The surface evaporation rate of the cover showed a significant positive correlation with atmospheric temperature (Figure 3a). As the atmospheric temperature increased from 5 °C to 35 °C, the evaporation rate increased from 0.32 mm d⁻¹ to 1.30 mm d⁻¹ under Condition A and from 0.81 mm d⁻¹ to 1.50 mm d⁻¹ under Condition B. This demonstrated that the high-temperature boundary at the bottom significantly enhanced moisture transport and evaporation within the cover. However, the magnitude of this enhancement generally diminished as atmospheric temperature continued to rise. The results were consistent with the findings of Zhao et al. [14], which demonstrated through loess column evaporation experiments that high temperatures greatly increased surface evaporation. Correspondingly, as shown in Figure 3b, the water storage capacity of the cover decreased significantly with rising atmospheric temperatures. Under Condition B, characterized by a higher surface evaporation rate, the water storage capacity of the cover was significantly greater at an atmospheric temperature of 5 °C compared to that under Condition A.

The influence of ambient temperature variations on moisture migration within the cover is a highly complex process. On one hand, the biochemical degradation of landfill waste generated moisture and heat, creating a high-temperature and high-humidity environment at the base of the cover [18]. Driven by the temperature gradient, water vapor migrated upward into the cover (Equation (4)), with higher temperature gradients exerting a more pronounced influence on moisture replenishment. At low atmospheric temperatures (e.g., 5 °C), the water storage capacity of the cover under Condition B initially increased with time before subsequently decreasing (Figure S1). Meanwhile, the temperature gradient significantly enhanced MAMO within the cover under low-temperature conditions [15], and the water generated during this process contributed to partial moisture replenishment. On the other hand, the temperature gradient induced by the high-temperature boundary at the base of the cover layer significantly increased surface evaporation rates. At high atmospheric temperatures (e.g., 35 °C), the water storage capacity of the cover under Condition B was lower than that under Condition A on the 30th day.

Figure 4 illustrates the CH₄ oxidation efficiency of the cover under different environmental temperature conditions. Under Condition A, as the atmospheric temperature increased from 5 °C to 35 °C, and the CH₄ oxidation efficiency of the cover rose from 8.7% to 55.3%. This indicated a generally positive correlation between the CH₄ removal capacity of the cover and atmospheric temperature under this condition. As illustrated in Figure 2, this was primarily attributed to the increase in atmospheric temperature, which caused the temperature of the cover to approach the optimal temperature for MAMO (i.e., 33 °C, as detailed in Supplementary File S1 (Equation (S5))). The simulation results were consistent with those reported by Zhan et al. [15], who found that the CH₄ oxidation rate of the field soil cover increased with the rise in soil temperature. Under Condition B, the CH₄ oxidation efficiency ranged from 25.1% to 53.2%, which was significantly higher than that under Condition A at low atmospheric temperatures. When the atmospheric temperature was 5 °C, the CH₄ oxidation efficiency under Condition B was 2.9 times greater than that under Condition A, indicating that the high-temperature boundary at the bottom of the cover effectively enhanced MAMO during the winter. However, as the atmospheric temperature increased to 35 °C, the CH₄ oxidation efficiency under Condition A surpassed that under Condition B. This was primarily due to the high-temperature boundary at the bottom of the cover, which further elevated the soil temperature under high atmospheric temperature conditions, thereby inhibiting MAMO (Figure 2d). Bian et al. [9] developed a numerical simulation framework to investigate the influence of atmospheric temperature on MAMO in landfill covers. Their results suggested that methane oxidation efficiency is higher when atmospheric temperature ranges between 10 °C and 25 °C, which differs from the findings in our study. This discrepancy may be attributed to differences in model conceptualization, particularly the fact that the model used by Bian et al. [9] did not incorporate the effects of latent heat during moisture evaporation or surface evaporation within the cover. These processes can induce soil cooling—particularly in near-surface layers—which in turn affects MAMO. The omission of these mechanisms may lead to an overestimation of soil temperature under high atmospheric temperature scenarios, thereby altering the predicted oxidation performance. The transport and evaporation of moisture, as well as MAMO, within the soil cover are influenced by the combined effects of atmospheric temperature and landfill waste temperature. Therefore, when evaluating the performance of landfill covers, it is necessary to consider the coupled impact of climate conditions and the degree of biochemical degradation of the landfill waste [4,18].

3.2. Effects of Atmospheric Pressure

Atmospheric pressure variations can change the diffusion and advection flux of gases within the landfill soil cover, thereby influencing the MAMO [12]. The diurnal mean atmospheric pressure at Jiangcungou landfill generally ranged from 950 mbar to 990 mbar. Therefore, for the gas boundary conditions at the surface of the cover, the volumetric fractions of the air components were kept constant, while the atmospheric pressure was set between 950 mbar and 990 mbar with 10 mbar as the interval for the parametric study. The gas boundary conditions at the bottom of the cover were changed from a constant flux boundary condition to a constant pressure boundary condition, with an absolute pressure of 970 mbar. This modification was adopted to better represent the dynamic response of gas transport to surface atmospheric fluctuations, allowing the pressure gradient across the cover to reverse realistically [12]. The CH₄ and CO₂ gas ratio was set to 1:1.

LFG migration is influenced by the pressure gradient between the internal LFG pressure within the landfill and the external atmospheric pressure [9,12]. Figure 5a shows the distribution of O₂ mole fraction in the cover soil profile on day 30. As the atmospheric pressure increased from 950 mbar to 990 mbar, the depth of O₂ penetration increased from 0.19 m to 0.60 m. When the atmospheric pressure was below 970 mbar, O₂ primarily entered the cover through diffusion. The increase in atmospheric pressure enhanced the concentration gradient of O₂, thereby increasing the diffusion depth. Meanwhile, the O₂ mole fraction at different depths within the soil cover exhibited a positive correlation with atmospheric pressure. In contrast, the upward migration of CH₄ within the soil cover showed a negative correlation with atmospheric pressure, with the CH₄ mole fraction at different depths decreasing as atmospheric pressure increased (Figure 5b). The results indicated that the increase in atmospheric pressure facilitated the downward penetration of air while inhibiting the upward transport of LFG. The simulation results are consistent with the field experimental findings of Xu et al. [33], who indicated that landfill CH₄ emissions were strongly dependent on changes in atmospheric pressure, with increased pressure suppressing CH₄ emissions.

Figure 5c illustrates the temperature distribution within the cover, highlighting the impact of atmospheric pressure changes. Under the combined thermal effects of surface evaporation-induced cooling and CH₄ oxidation-generated heating in the cover soil, a typical temperature peak was observed within the shallow 0.5 m depth range under different atmospheric pressures. The depth of this temperature peak exhibited a positive correlation with atmospheric pressure, while the peak temperature displayed an initial increase followed by a decrease with rising atmospheric pressure. The temperature peak within the cover reached its maximum value (i.e., 22.3 °C) when atmospheric pressure reached 970 mbar, corresponding to the LFG pressure at the bottom. The temperature variation was closely related to the changes in gas composition induced by atmospheric pressure fluctuations. More favorable CH₄ and O₂ supply led to higher CH₄ oxidation rates, thereby releasing more heat [8]. Correspondingly, the variation in the CH₄ oxidation rate per unit mass of dry soil with depth was also significantly influenced by changes in atmospheric pressure (Figure 5d). When the atmospheric pressure remained below the LFG pressure at the bottom, both the depth of the CH₄ oxidation zone and the maximum oxidation rate increased with rising atmospheric pressure. At higher pressures (980 mbar and 990 mbar), the oxidation zone extended further, while the maximum oxidation rate decreased. Additionally, a sharp transition in CH₄ oxidation rate occurred at 0.3 m depth, primarily attributed to enhanced methanotrophic activity in the vegetative layer amended with compost [34].

Parametric analysis demonstrated significant atmospheric pressure effects on both CH₄ oxidation rate and efficiency in the cover system (Figure 6). While the oxidation rate exhibited a unimodal response, peaking then declining as atmospheric pressure increased from 950 mbar to 990 mbar, the oxidation efficiency showed a consistent upward trend across the entire pressure range. At low atmospheric pressure (950 mbar), the CH₄ oxidation rate was relatively low, with a corresponding low oxidation efficiency. This was primarily due to the atmospheric pressure being lower than the bottom LFG pressure, which suppressed O₂ diffusion into the cover, reducing the CH₄ oxidation rate. Consequently, the CH₄ flux entering the cover, driven by the pressure gradient, was significantly enhanced, leading to a CH₄ oxidation efficiency as low as approximately 0.8%. At elevated atmospheric pressure (990 mbar), the CH₄ oxidation rate was 1.51 times higher compared to 950 mbar conditions, while achieving 77.1% oxidation efficiency. This enhancement primarily resulted from reduced CH₄ influx due to reversed pressure gradients between atmospheric and underlying LFG pressures. Overall, dynamic changes in atmospheric pressure significantly affect the migration of LFG and MAMO within the cover. Higher atmospheric pressure typically promotes the downward migration of O₂ into the cover while inhibiting the upward transport of CH₄, leading to higher CH₄ oxidation efficiency. These analysis results are consistent with previous field monitoring data [35,36,37], highlighting the need for continuous monitoring under varying atmospheric conditions to accurately estimate CH₄ fluxes and develop effective mitigation strategies.

3.3. Effects of Atmospheric Relative Humidity

The dynamic variations in atmospheric relative humidity influence the water vapor pressure gradient between the cover soil and the air, thereby altering surface evaporation and ultimately modifying the liquid–gas transport capacity of the cover [38]. The reported daytime average relative humidity in Xi’an city was typically above 10% [39]. Therefore, the atmospheric relative humidity was set between 10% and 90% with 20% as the interval for the parametric study.

Figure 7 illustrates the impact of atmospheric relative humidity on moisture evaporation in the cover. As atmospheric relative humidity increased from 10% to 90%, the surface evaporation rate decreased from 1.17 mm d⁻¹ to 0.35 mm d⁻¹, indicating that a high-humidity atmosphere suppressed surface evaporation, thereby reducing water loss from the cover. Meanwhile, the water storage capacity of the cover increased from 283.9 mm to 309.9 mm, further confirming the enhanced water retention capacity of the soil under high-humidity conditions. The reduced vapor pressure difference between the atmosphere and the soil surface weakened the evaporation driving force, allowing liquid water to remain more easily in the soil and altering the distribution of liquid water within the cover [24,40]. Figure S2 focused on the shallow soil at a depth of 0.15 m in the cover, where the volumetric water content increased from 27.6% to 30.6% as atmospheric relative humidity rose. In arid regions with low atmospheric relative humidity, the high evaporation rates caused by low relative humidity could lead to soil cracking, significantly reducing the impermeability of the cover [41]. Therefore, fluctuations in atmospheric relative humidity should be considered in the durability assessment of cover materials.

Changes in soil moisture content alter the gas–liquid ratio in soil pores, which in turn changes the gas migration pathways and significantly impacts the distribution of gas components within the cover [42]. At a depth of 0.3 m in the cover, the volumetric concentrations of O₂ and CH₄ showed significant variations with atmospheric relative humidity (Figure 8a). As atmospheric relative humidity increased from 10% to 90%, the O₂ concentration decreased from 18.7% to 0, while CH₄ concentration rose from 0.5% to 32.8%. The results indicated that under conditions of high atmospheric relative humidity, the soil moisture content in the shallow part of the cover was elevated (Figure S2), which significantly impeded the diffusion of O₂ into the cover. This reduction in O₂ diffusion capacity led to an accumulation of CH₄ in the soil at this depth. The changes in moisture and gas distribution within the cover altered its CH₄ removal performance (Figure 8b). As atmospheric relative humidity increased from 10% to 50%, CH₄ oxidation efficiency steadily increased from 31.1% to 40.0%. However, when relative humidity exceeded 70%, CH₄ oxidation efficiency slowly declined to 38.0%. These findings indicate that moderate atmospheric relative humidity conditions provide a more favorable metabolic environment for CH₄-oxidizing bacteria, where adequate moisture maintains microbial cell activity, while non-saturated pore spaces ensure sufficient O₂ supply [9,43]. Atmospheric relative humidity influences the CH₄ removal efficiency of the cover by regulating the gas–liquid distribution in soil pores, gas diffusion capacity, and microbial metabolic activity. The impact of atmospheric relative humidity should be considered in landfill design, and a real-time monitoring system can be established during landfill operations to optimize the water–gas synergistic management of the cover.

3.4. Effects of Rainfall

Rainfall significantly influences the CH₄ oxidation process and LFG migration in the cover by altering soil moisture content and aeration. To analyze the impact of rainfall on the service performance of the cover, a transient simulation was conducted, with rainfall starting after 30 days under the default boundary conditions (detailed in Section 2.5). The rainfall intensity was set at 3 mm h⁻¹. The duration of rainfall was varied, with settings of 1 h, 3 h, 6 h, 12 h, and 24 h. Additionally, surface evaporation was not considered during the rainfall period.

Figure 9 illustrates the variations in volumetric water content and O₂ mole fraction at a depth of 0.15 m under different rainfall durations. During rainfall, the infiltration of water caused a rapid and significant increase in the moisture content of the shallow soil in the cover (Figure 9a). As the rainfall duration increased from 1 h to 24 h, the maximum volumetric water content at 0.15 m rose from 29.6% to 40.0%. This increase was attributed to the prolonged accumulation of water in the soil, which progressively saturated the soil. After the rainfall ended, the volumetric water content decreased due to downward water percolation, with the rate of decrease being positively correlated with the rainfall duration. Longer rainfall events led to a more extensive saturated zone, enhancing the liquid-phase permeability of the soil. Correspondingly, the diffusion of air into the cover was significantly affected by the rainfall (Figure 9b). As rainwater infiltrated and occupied soil pores, the gas conductivity of the shallow part of the cover decreased rapidly [44]. When the rainfall duration reached 3 h, the O₂ concentration at 0.15 m dropped close to zero. After the rainfall ceased, the moisture content in the shallow soil decreased due to downward percolation and surface evaporation, leading to enhanced air diffusion into the cover and a rapid recovery of O₂ concentration. The saturated state of the soil during rainfall limited air diffusion, while the residual moisture after rainfall prevented the gas concentration from recovering to pre-rainfall levels swiftly.

The significant impact of rainfall on moisture and gas distributions ultimately altered MAMO in the cover. During rainfall, the increase in moisture content in the shallow soil of the cover limited O₂ supply (Figure 9b), leading to a decline in CH₄ oxidation rate and efficiency (Figure 10). The CH₄ oxidation rate and efficiency dropped sharply at the onset of rainfall, and the extent of the decline increased with the duration of rainfall. As the rainfall duration increased from 1 h to 24 h, the methane oxidation performance of the cover declined by 12.0% to 68.5% compared to pre-rainfall conditions. After the rainfall ended, as O₂ supply in the surface soil gradually recovered, both CH₄ oxidation rate and efficiency increased, but the recovery generally did not reach pre-rainfall levels. This suggested that the elevated soil moisture continued to inhibit gas diffusion, with the inhibitory effect becoming more pronounced as the total amount of rainfall increased. When dynamically modeling LFG emissions, the effects of both rainfall and subsequent evaporation should be taken into account.

4. Conclusions

This study proposed a one-dimensional numerical model that simulated the effects of ambient conditions on the coupled transport of liquid water, vapor, LFG, and heat within EFCs. The results demonstrated that both atmospheric and landfill waste temperatures played a dominant role in regulating methane oxidation performance, mainly by controlling microbial activity and moisture dynamics. Elevated waste temperature was found to enhance oxidative capacity under cold conditions, whereas combined high atmospheric and waste temperatures were observed to inhibit microbial aerobic CH₄ oxidation due to excessive soil heating and moisture loss. Increased atmospheric pressure improved methane oxidation efficiency by promoting O₂ diffusion and restricting CH₄ emission. Atmospheric relative humidity influenced soil moisture retention, with higher humidity suppressing evaporation and improving water retention, which might create a more favorable environment for CH₄ oxidation. Rainfall was shown to significantly impact soil moisture distribution and gas transport, temporarily inhibiting O₂ supply in the shallow soil and reducing CH₄ oxidation efficiency, although recovery occurred after the rainfall event. While multiple ambient parameters interactively influence CH₄ oxidation, temperature is the most critical factor, as it directly controls microbial activity and regulates both evaporation-induced moisture loss and O₂ supply, thereby determining the peak oxidation rate and efficiency of the cover system.

This model provides a useful framework for predicting EFC behavior under interactive ambient influences and supports the design of site-specific methane mitigation strategies. However, it is important to acknowledge its limitations. The assumption of a constant methane influx and the use of a one-dimensional model represented simplifications that may not fully capture spatial heterogeneity, transient emission peaks, or complex field-scale flow pathways. The current model does not account for the effects of vegetation, such as root-mediated gas transport and water uptake, nor does it incorporate soil heterogeneity and the potential occurrence of preferential flow pathways, which may significantly influence gas migration patterns.