煤层瓦斯运移机理的分数阶动力学模型及应用基础研究

The investigation on the mechanism of gas transport in coal seams is of practical significance to both gas disaster prevention and coalbed methane production. In order to uncover the dynamical mechanism, many researchers have been dedicated to developing different theoretical models which can more realistically characterize the gas transport processes in coal seams. However, the existing models which are based on classical Fick and Darcy laws take the pore-cleats dual porous media of coal seams as a uniformly distributed and virtual continuous media on a large scale, resulting in geat deviations from the actual situation. To overcome the disadvantage, in this proposal we will introduce the fractional calculus describing fractal media to this research field. Firstly, based on the anomalous diffusion and fractional non-Darcy flow theory, we will develop a coupled fractional dynamical model for coal deformation, desorption diffusion of adsorbed gas and seepage flow of free gas among quasi-three phase body of coal reservoir (solid coal, absorbed gas and free gas). Secondly, applying the coupled fractional dynamical model and using the methods of theoretical analysis, numerical simulation and experimental study, we will discuss the time-space dynamical characteristics of gas transport in coal cuttings and seams around boreholes, and uncover the multi-physics coupled mechanism during the process of gas transport. The aim of our work is to improve the existing theoretical models and to provide a guidance for the prevention of coal and gas outburst and improving the gas extraction rate.

研究煤层瓦斯运移机理对于防治瓦斯灾害、开发利用煤层气等具有现实意义。国内外众多学者一直致力于寻找形式比较简单且更加切合实际的理论模型，以此阐明煤层瓦斯运移的力学机理。目前的理论模型以经典Fick定律和达西定律为理论基础，将煤层孔隙-裂隙双重多孔介质看成一种大尺度上均匀分布的虚拟连续介质，与实际情况有较大误差。本项目将刻画分形介质的分数阶微积分应用到这一研究领域，基于反常扩散和分数阶非达西渗流理论，建立非均质煤层类三相体（固体煤、吸附态瓦斯、游离态瓦斯）之间的多物理场（煤体变形、吸附瓦斯的解吸扩散、游离瓦斯的渗流）耦合分数阶动力学模型。应用此模型，理论分析、数值模拟与实验研究相结合，定量分析瓦斯在煤屑和钻孔周围煤层内运移的时空动力学特征，揭示瓦斯运移过程中解吸扩散、渗流与煤体变形之间的多场耦合作用机制。本项研究旨在完善现有理论模型，为预防煤与瓦斯突出、提高煤层瓦斯抽采率等提供理论依据和指导。

煤储层是由固体煤、吸附态瓦斯、游离态瓦斯构成的类三相体，煤层瓦斯运移是一个复杂的多场耦合过程，涉及煤基质瓦斯吸附解吸、煤裂隙内瓦斯渗流以及煤体的变形，如何构建和发展切合实际情况的理论模型，揭示煤层瓦斯运移的动力学机理，是国内外学者竞相研究的热点课题之一。本项目运用分数阶微积分进行理论建模，通过数值模拟、实验验证、现场测试，将新的应用数学理论和矿业科学的基本问题结合起来，为研究煤层瓦斯运移的力学机理提供一种新思路。. 本项目建立了煤基质内瓦斯吸附解吸过程的分数阶反常扩散动力学模型、吸附解吸传热过程的分数阶热扩散模型、多尺度列席内游离瓦斯渗流的分数阶非达西模型、高地应力作用下煤体变形的分数阶损伤蠕变模型。为了验证模型的正确性，分别从贵州山脚树煤矿、宁夏石嘴山煤矿、河南跃进煤矿和平顶山矿采集不同煤样，分析了煤基质孔隙分布特征，开展了瓦斯吸附解吸实验以及煤体蠕变实验。数值模拟结果发现，分数阶模型比传统模型能够更好的拟合实验数据。反常扩散和反常热传导是非均匀煤基质内瓦斯吸附解吸的主导热动力学机理，Fick扩散模型预测瓦斯解吸量偏大，Fourier导热模型预测吸附热量偏高。分数阶非达西渗流模型考虑煤裂隙的多尺度性、非均匀孔隙与裂隙之间的质交换关系等因素，更适合描述煤裂隙内的气体流动。粘弹塑性损伤变形在煤体蠕变过程起主导作用，分数阶非线性蠕变模型能够准确预测蠕变的加速破坏阶段。. 本项目建立了钻孔周围瓦斯运移的多场耦合模型，数值模拟了瓦斯浓度分布的时空动力演化规律，定量分析了初始地应力、初始渗透率、钻孔直径、抽采压力、钻孔间距与布置方式等因素对瓦斯抽采浓度、累计瓦斯抽采量、抽采速率和有效抽采半径的影响，揭示了瓦斯运移过程的多场耦合作用机制，获得了钻孔抽采的优化参数，为煤层瓦斯抽采等工程实践提供了理论依据。