页岩气复杂孔裂隙真实气体传输机理和数学模型

Real gas transport mechanism and mathematical model through complex nanopores and microfractures in shale gas reservoirs

基于滑脱流动和努森扩散,分别以分子之间碰撞频率和分子与壁面碰撞频率占总碰撞频率的比值作为滑脱流动和努森扩散的权重系数,进行权重叠加,建立了页岩气复杂孔裂隙气体传输模型.该模型综合考虑了滑脱效应和真实气体效应,同时还分别考虑了截面类型(圆形和矩形)和形状对气体传输的影响.用公开发表的分子模拟数据验证模型.结果表明:(1)本文模型能够合理地描述页岩气复杂孔裂隙气体传输机理,包括连续流动、滑脱流动和过渡流动;(2)页岩气孔裂隙截面类型和形状影响气体传输能力,相同截面面积,圆形截面孔裂隙气体传输能力大于矩形截面孔裂隙气体传输能力,矩形截面孔裂隙气体传输能力随纵横比增大而减小;与截面类型相比,截面形状对气体传输能力的影响更大;(3)真实气体效应提高了气体传输能力,且这种影响随压力增大而增大,随孔裂隙尺度减小而增大;(4)与圆形截面相比,真实气体效应对矩形截面气体传导率影响更大,且随矩形截面纵横比增大而增大.本文模型能为页岩气准确数值模拟奠定一些理论基础.

A model for real gas transport in complex nanopores and microfractures of shale gas reservoirs （SGRs） was proposed on the basis of the weighted superposition of slip flow and Knudsen diffusion, where the ratios of intermolecular collisions and molecules-nanopores or microfractures wall collisions to total collisions are the weighted factors of slip flow and Knudsen diffusion, respectively. The present model takes account of slip effect and real gas effect, additionally, the effect of cross-section type and shape of nanopores or microfractures on gas transport is also considered in this paper. The present model is successfully validated against existing molecular dyanmics simulations data in literature. The results show： （1） the present model is reasonable to describe all of the gas transport mechanisms known, including continuous flow, slip flow and transition flow in nanopores and microfractures of SGRs; （2） cross-section type and shape of nanopores or microfractures both affect gas transport capacity, at the same cross-sectional area, gas transport capacity of nanopores with a circular cross-section is greater than that of nanopores with a rectangular cross-section or microfractures, which decreases with an increasing aspect ratio; and the effect of cross-section shape on gas transport capacity is stronger compared to cross-section type; （3） a real gas effect improves gas transport capacity, which becomes more obvious with an increasing pressure and a decreasing size of nanopores or microfractures; （4） and compared to nanopores with a circular cross-section, the effect of real gas effect on gas transport capacity of nanopores with a rectangular cross-section or microfractures is stronger, and the effect increases with an increasing aspect ratio. The proposed model can provide some theoretical support in numerical simulation of reservoir behavior in SGRs.