Fractal Features of the Effective Gas Transport Coefficient for Multiscale Porous Media
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摘要: 非常规油气资源的孔隙结构及其连通性非常复杂，其孔隙尺度从毫米到纳米跨越多个量级.多孔介质中气体的输运过程不仅依赖于介质的多尺度微观结构特征，还依赖于气体的相关属性.气体在多尺度多孔介质中的输运过程包括无滑流、滑脱流和过渡流，涉及分子扩散和努森扩散等多种机制，因此很难用唯一的连续介质理论来描述气体的输运特征.大量的数据表明真实多孔介质中的内部孔隙具有分形标度特征，因此采用分形几何表征多尺度多孔介质的孔隙结构，引入孔隙分形维数和迂曲度分形维数定量表征多孔介质的微结构和弯曲流道，建立多尺度多孔介质气体输运过程的细观模型；推导了多尺度多孔介质中气体的有效渗透率和有效扩散系数，并讨论了多尺度多孔介质微结构参数和气体属性对于气体等效输运特性的定量影响.该研究不仅可以丰富渗流理论，且有利于深入理解非常规油气藏的产出机制.Abstract: The pore structures and connections in unconventional oil and gas resources are very complex, the size of which may vary several orders of magnitude from millimeter to nanometer. And gas transport process depends on both microstructure characteristics and gas properties in the multiscale porous media. As gas transport in multiscale porous media may involve multiple transport mechanisms such as no-slip and slip flow, transition flow, Knudsen and molecular diffusion, it is difficult to characterize the gas transport with continuum theory. Since it has been proven that natural pore structures indicate fractal scaling laws, fractal geometry is employed in this study to model the multiscale pore structures. The fractal dimensions are introduced to characterize the pore size distribution and tortuous flow path, and a mesoscopic model is developed to study the gas transport in multiscale porous media. The effective permeability and diffusion coefficient of multiscale porous media are derived and presented, and the effect of microstructures and gas properties on the equivalent transport properties is also discussed. This study may be helpful for the development of seepage theory and understanding the output mechanisms of unconventional oil and gas reservoirs.
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Key words:
- porous media /
- multiscale /
- fractal /
- gas transport /
- permeability /
- diffusion coefficient /
- petroleum geology
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图 1 多孔介质分形毛管束模型示意
Fig. 1. The sketch of fractal capillary bundle model of porous media
图 2 多孔介质有效渗透率和分形维数的定量关系
Fig. 2. The relationship between effective gas permeability and fractal dimensions
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