考虑表面扩散作用的页岩气瞬态流动模型

Shale gas transient flow model with effects of surface diffusion

针对甲烷气在页岩孔隙中的流动规律问题,建立了考虑孔内扩散、孔壁表面扩散、黏性滑脱流动和气体解吸附等多种流动机理的瞬态流动毛管束模型,并采用有限差分法的三层隐式差分格式离散控制方程对模型进行了数值求解。该模型考虑了"表面扩散"和吸附层对气体滑脱速度的影响,其预测产气量高于以往模型预测值。实例计算结果表明,孔壁表面扩散是页岩孔隙中不可忽略的传质方式,且表面扩散通量对总流动通量的贡献随孔径减小而增强,孔径小于5 nm孔隙中表面扩散通量占总流动通量百分比可超过50%;黏性流动通量所占百分比随孔径增大而增加,孔径大于50 nm孔隙中黏性流动通量所占百分比接近100%;孔内扩散通量相比于表面扩散通量和黏性流动通量可忽略不计。

This paper proposed a transient flow model for shale-gas in organic-rich shale, which involved the pore molecular diffusion, surface diffusion, slip flow, and gas adsorption and desorption phenomenon during shale-gas production. The three layer discretization format of finite difference method was used to discretize the governing equations. The predicated gas production from the proposed model is larger than that from other published models because of the consideration of surface flux and the effect of adsorption layer on slip flow flux. Numerical results show that the surface diffusion cannot be ignored, whose contribution for total flux is increasing with the pore diameter decreasing. For the given values of model parameters, the surface diffusion flux of Ф 5 nm pore covers over 50% of total flux. The viscous flux is becoming increasing with raising pore diameter; the flux percentage of viscous flux almost reaches 100% if the pore diameter is over 50 nm. However, the pore diffusion flux is extensively less than the surface diffusion flux and viscous slip flux, which can be negligible.