Fractal theory-based permeability model of fracture networks in coals
XIA Binwei;LIAO Chuanbin;LUO Yafei;JI Kainan
煤储层裂隙是煤层气渗流的主要通道,决定了煤储层的渗透性及煤层气产能,研究裂隙结构特征与煤储层渗透性的关系对准确预测煤层气产能具有重要理论及实践意义。基于经典立方定律渗透率模型,同时考虑分形理论、裂隙网络结构特征及有效应力,构建包含复杂弯曲裂隙特征的分形渗透率模型,将分形渗透率模型与S & D(Shi-Durucan)模型相结合,建立真三轴应力作用下的裂隙煤渗透率模型。开展真三轴应力条件下的气体渗流实验,将构建的渗透率模型与试验结果及S & D模型拟合数据对比,该渗透率模型与实验结果具有良好的一致性,能够体现出三向应力加载条件下应力对渗透率变化的影响趋势,与S & D模型相比更能反映煤岩渗透率的各向异性特征。基于该渗透率模型,定量分析了煤岩裂隙结构参数对其渗透率的影响。结果表明,煤岩渗透率与孔隙率$ phi $(0.05~0.41)、分形维数Df(2.37~2.81)、最大裂隙长度lmax(3.5~8.0 cm)、比例系数β(0.010~0.065)呈正幂律关系;与迂曲度分形维数DTf(2.005~2.275),裂隙倾角θ(10°~80°)呈负幂律关系。研究成果对准确预测煤岩储层渗透率,揭示煤储层中煤层气的流动机理具有重要作用。
Fractures in coal reservoirs, which act as the major seepage pathways for coalbed methane (CBM), determine the permeability and CBM productivity of coal reservoirs. Research on the relationships between fracture structures and reservoir permeability is of great theoretical and practical significance for the accurate prediction of CBM productivity. Based on the classical cubic law-based permeability model, as well as the fractal theory, fracture network structures, and effective stress, this study built a permeability model containing complex bending fractures, which was then combined with the S & D (Shi-Durucan) model to build the permeability model of fractured coals under the action of true triaxial stresses. Then, gas seepage experiments under true triaxial stresses were conducted, followed by the comparison of the results of the final permeability model with the experimental results and the fitting data of the S & D model. As shown by the comparison results, the results of the permeability model agreed well with the experimental results and thus can reflect the trend of the influence of stress on permeability under the loading of triaxial stresses. The comparison results also indicate that the permeability model built in this study can reflect the anisotropy of coal permeability more effectively than the S & D model. Using this permeability model, this study quantitatively analyzed the effects of fracture structures of coals on coal permeability. The results indicate that the coal permeability exhibited positive power-law relationships with porosity $ phi $(0.05-0.41), fractal dimension Df (2.37-2.81), maximum fracture length lmax (3.5-8.0 cm), and proportionality coefficient β (0.010-0.065) and negative power-law relationships with tortuosity fractal dimension DTf (2.005-2.275) and fracture dip angle θ (10°-80°). The results of this study will play an important role in accurately predicting the permeability of coal reservoirs and revealing the flow mechanisms of CBM in coal reservoirs.
coalbed methane;permeability;tortuosity;fractal dimension;true triaxial stress
主办单位:煤炭科学研究总院有限公司 中国煤炭学会学术期刊工作委员会