基于分形表征的粗糙微纳米孔隙瓦斯气体传输方程
Gas transport equation based on fractal characterization of rough micro-nano pores
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摘要: 为揭示煤体孔隙内表面粗糙微结构对瓦斯传输的影响机制，准确研究粗糙孔隙中的瓦斯气体传输规律，运用自相似特性分形理论推导出了微纳米孔隙内壁面粗糙元有效平均高度和孔隙有效半径的精确数学表达式;采用Optical Tensiometer设备对取自煤体孔隙内壁表面进行3D形貌结构量化分析，将所得关键参数代入相对粗糙度表达式求得对应值为0.352;结合流体速度滑移效应和分子扩散传输机理，推导出了粗糙微纳米孔隙中的瓦斯气体滑流修正传输方程和非连续流扩散传输方程，再通过等效转换原则推导出微纳米孔隙内的视渗透率模型;考虑到煤体纳米级孔隙难以进行精确测量表征和规避孔隙连通性对气体传输的影响，选取结构规整的纳米级圆孔阳极氧化铝薄膜作为气体流动通道载体;基于气体压差穿透实验原理，利用实验室PMI微渗透率设备进行了纳米级孔隙薄膜的渗透性实验，将实验结果所测得的渗透率数据与本文理论模型计算值进行了对比分析。研究结果表明:基于分形表征建立的粗糙微纳米孔隙瓦斯气体传输方程合理可靠，考虑孔隙粗糙度对瓦斯流动的影响是应该且必须的，以分形理论表征的孔隙相对粗糙度公式比前人所提出的孔隙粗糙度经验性公式更为精确，研究结果可为在分形拓扑领域中构建自仿射粗糙微通道的气体流动模拟研究工作中提供借鉴。Abstract: In order to reveal the effect mechanism of rough microstructures of the inner surface of coal pores on gas transport and accurately study the law of gas transport in rough pores,the precise mathematical expressions of effective average height and effective radius of rough elements in micro-nano pore were derived based on fractal theory of self-similarity. Optical Tensiometer was used to quantitatively analyze the 3D morphology and structure of inner surface wall. The key parameters obtained from analysis were substituted into the expression of relative roughness,and the cor- responding value is 0. 352. Combining with the slip flow effect of fluid velocity and molecular diffusion transport mech- anism,the modified gas slip flow transport flux equation and molecular diffusion transport flux equation of discontinu- ous flows in rough micro-nano-pore were deduced,and then the apparent permeability model in micro-nano-pore is de- veloped in rough micro-channel by the principle of equivalent conversion. Considering that it is difficult to accurately measure and characterize the nano-pore of coal,and avoid the influence of pore connectivity on gas transport,the nano- porous anodic alumina film with regular circular holes were selected as the carrier of gas flow channel. Based on the experimental principle of gas pressure differential penetration,the permeability experiment of nano-film were carried out by using PMI micro-permeability equipment,and the permeability data measured from the experimental results were compared with the calculated values of the theoretical model in this paper. Results show that the gas transport e- quation based on fractal characterization of rough pore is reasonable and reliable. The effect of pore roughness should and must be considered in gas transport. The formula of relative roughness of pore expressed by fractal theory is more accurate than the empirical formula proposed by predecessors. In the field of fractal topology,the fractal characteriza- tion of relative roughness will provide an important theoretical support for the simulation of gas flow in self-affine rough micro-channels.
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期刊类型引用(7)
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4. 刘彦伟，贾浩杰，左伟芹，韩红凯，常平，苗健，魏建平，徐鹏. 基于有效分子自由程的纳米孔隙气体传输模型. 中国矿业大学学报. 2022(01): 90-99 . 百度学术
5. 杨琪，于岩斌，程卫民，张鑫，郑磊，崔文亭，邢浩. 基于Micro-CT的受载煤岩裂隙孔隙时空演化规律. 岩石力学与工程学报. 2022(S1): 2626-2638 . 百度学术
6. 李悬. 煤矿开采中光纤瓦斯气体传感器的应用研究. 陕西煤炭. 2022(05): 121-123 . 百度学术
7. 吴兵，赵晨光，雷柏伟. 巷道摩擦风阻粗糙表面分形表征及计算方法. 中国矿业大学学报. 2021(04): 633-640 . 百度学术
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