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In order to further clarify the adsorption thermodynamic characteristics of CH4 and CO2 in coal, the giant canonical ensemble Monte Carlo method was used to simulate the adsorption behavior of CH4 and CO2 in coal at different temperatures and different moisture content. The results show that the adsorption capacity of CH4 and CO2 in coal molecules decreases with the increasing temperature and moisture content. By comparing the adsorption amounts of the two components, it is found that both high temperature and the presence of water molecules are not conducive to displace CH4 by CO2; the average adsorption heat of CH4 is negatively correlated with temperature and water content, and average adsorption heat of CO2 has a negative correlation with temperature and a positive correlation with water content. Water molecules are more inclined to react with CO2; the overall adsorption potential of CH4 and CO2 is negatively correlated with temperature and moisture content. When the pressure is low, the adsorption potential of CO2 increases slightly with the increasing of temperature; the adsorption entropy of CH4 and CO2 increases with the increasing of temperature and decreases with the increasing of moisture content. The influence of water on CO2 is stronger than CH4. When two components are injected, the existence of water molecules makes the whole system more stable, which is not conducive to CH4 output.

Let X1,…,Xn$$ {\mathbf{X}}_1,\dots, {\mathbf{X}}_n $$ be a sequence of independence random vectors from Np(μ,Σ)$$ {N}_p\left(\boldsymbol{\mu}, \boldsymbol{\varSigma} \right) $$ with population correlation matrix Rn$$ {\mathbf{R}}_n $$, and its sample correlation matrix is denoted as R^n=(r^ij)p×p$$ {\hat{\mathbf{R}}}_n={\left({\hat{r}}_{ij}\right)}_{p\times p} $$, where the matrix element r^ij$$ {\hat{r}}_{ij} $$ represents the Pearson correlation coefficient between the i$$ i $$ and j$$ j $$ columns of the data matrix (X1,…,Xn)′$$ {\left({\mathbf{X}}_1,\dots, {\mathbf{X}}_n\right)}^{\prime } $$. R^n$$ {\hat{\mathbf{R}}}_n $$ is an interesting part in multivariate analysis, and the likelihood ratio test (LRT) statistic used to test the complete independence of all components of X$$ \mathbf{X} $$ can be expressed as a function of R^n$$ {\hat{\mathbf{R}}}_n $$. On this basis, under the condition that the sample size n$$ n $$ and the dimension p$$ p $$ satisfy p/n→y∈(0,1]$$ p/n\to y\in \left(0,1\right] $$ as n→∞$$ n\to \infty $$, we derive the moderate deviation principle (MDP) of the LRT statistic for the hypothesis testing problem H0:Rn=Ip$$ {H}_0:{\mathbf{R}}_n={\mathbf{I}}_p $$ vs H1:Rn≠Ip$$ {H}_1:{\mathbf{R}}_n\ne {\mathbf{I}}_p $$. [ABSTRACT FROM AUTHOR]

Rock bursts are among the most severe and unpredictable hazards encountered in deep rock engineering, posing substantial threats to both construction safety and project progress. This study provides a comprehensive investigation into how moisture infiltration influences the propensity for rock bursts, aiming to establish new theoretical foundations and practical methods for their prevention. Through the analysis of meticulous laboratory mechanical experiments and sophisticated numerical simulations, we analyzed the variations in the physical and mechanical properties of rocks under different moisture conditions, with a particular focus on strength, brittleness, and energy release characteristics. The findings reveal that moisture infiltration significantly diminishes rock strength and reduces the likelihood of brittle fractures, thereby effectively mitigating the risk of rock bursts. Additionally, further research indicates that in high-moisture environments, the marked reduction in rock burst tendency is attributed to increased rock toughness and the suppression of crack propagation. This study advocates for the implementation of moisture control measures as a pre-treatment strategy for deep rock masses. This innovative approach presents a viable and effective solution to enhance engineering safety and improve construction efficiency, offering a practical method for managing rock burst risks in challenging environments. [ABSTRACT FROM AUTHOR]

As an efficient and clean energy, coalbed methane development and utilization have deep significance in promoting energy conservation and emission reduction, reducing greenhouse gas emissions. Therefore, molecular simulation was utilized to study the influence of N2/CO2 on the adsorption and diffusion of methane in coal under different gas injection methods and to elucidate the influence of varying gas injection methods on the efficiency of coalbed methane extraction, which provides a basis for the efficient development of coalbed methane. The results show that the adsorption effect of gases in coal decreases with the increase of temperature and increases with the rise of pressure, and the adsorption performance of the three gases in coal shows the law of CO2 > CH4 > N2. In addition, the injection of CO2/N2 had an obvious inhibition effect on CH4 adsorption, and the inhibition effect of CO2 was more significant, and the inhibition effect on CH4 adsorption reached the maximum when the two gases were mixture injected. In terms of diffusion, compared with separate injection, mixed injection of N2 + CO2 promotes CH4 diffusion more effectively, which can be reflected in the relative concentration distribution and velocity distribution. The injection of N2 helps to increase the porosity of coal, and the injection of CO2 and N2 + CO2 will lead to the decrease of porosity, but the mixed gas injection has less effect than the injection of CO2 alone. [ABSTRACT FROM AUTHOR]

This paper focuses on the likelihood ratio test (LRT) statistics for different hypothesis tests. Assuming that a random sample is from a normal population, we make the sample size n and the dimension p close to infinity and satisfy p < n − c for some 1 ≤ c ≤ 4. Based on this assumption, the moderate deviation principle (MDP) for the LRT will be given under the null hypothesis. The corresponding numerical simulation results are shown at the end of the paper. [ABSTRACT FROM AUTHOR]