基于动量方程的页岩气体扩散能力表征模型与实验研究

Characterization Model and Experimental Study of Shale Gas Diffusion Capacity Based on Momentum Equation

为揭示页岩微纳米孔隙中气体的扩散机理,针对页岩储层气体扩散能力难以定量表征的问题,基于考虑流体黏性的微分形式动量方程,建立了考虑页岩孔隙度、迂曲度和流动Kn数(气体分子平均自由程与流动特征尺度之比)的气体扩散系数新模型,将模型与自主研发的页岩近平衡态实验进行验证,进而形成了页岩气扩散系数影响因素图版。研究表明:考虑了页岩孔隙度、迂曲度等多孔介质参数和流动Kn数,新建立的扩散系数更能准确表征页岩气扩散能力,与近平衡扩散流量吻合度达90%以上;扩散系数与压力负相关,而与孔隙直径正相关,在压力低于20 MPa、孔隙直径低于10 nm或Kn数高于0.2后必须考虑上述参数变化对扩散系数的影响。该研究实现了储层条件下页岩气扩散流量的定量计算,可用于页岩表观渗透率模型的建立,为不同生产阶段页岩气扩散对产量的贡献以及调整生产制度、提高单井产量提供科学依据。

In order to reveal the mechanism of gas diffusion in micro-and nano-pores of shale,aiming at the problem that it is difficult to quantitatively characterize the gas diffusion capacity of shale reservoirs,a new gas diffusion coefficient model considering shale porosity,tortuosity and flow K n number(ratio of average free path of gas molecules to flow characteristic scale,dimensionless)is established based on differential form momentum equation considering fluid viscosity.The model was verified with the self-developed shale near equilibrium experiment,and then a chart of influencing factors of shale gas diffusion coefficient was formed.The research results show that:considering the porosity,tortuosity and other porous media parameters and flow K n number of shale gas,the newly established diffusion coefficient model can more accurately characterize the diffusion ability of shale gas,and the coincidence degree with the near equilibrium diffusion flow rate is more than 90%.Diffusion coefficient is negatively related to pressure and positively related to pore diameter.When the pressure is lower than 20 MPa,the pore diameter is lower than 10 nm or the K n number is higher than 0.2,the influence of the above parameters on the diffusion coefficient must be considered.This study realizes the quantitative calculation of shale gas diffusion flow rate under reservoir conditions,which can be used to establish shale apparent permeability model,and provide scientific basis for the contribution of shale gas diffusion to production in different production stages,adjustment of production system and improvement of single well production.