页岩气滑脱、扩散传输机理耦合新方法

针对页岩气流动计算中所用耦合机理不同的现状,且为了厘清滑脱和各种扩散之间的关系,首先采用理论分析和数学模型的方法,根据定义和微观运动机制对滑脱和各种扩散进行了分析,然后在考虑吸附层页岩气分子所占空间对气体流动影响的情况下,提出了"壁联扩散"的概念来表征克努森扩散和表面扩散的总效应,并指出壁联扩散和滑脱效应等同,由此提出了壁联扩散和滑脱效应在流动计算中可互换而不重复叠加的耦合新方法.实例验证表明,当毛细管半径从5 nm增大到2000 nm,壁联扩散和滑脱效应的质量通量相对误差较小,在绝大部分范围内都小于10%,且在整个孔径范围内两者平均值相差1.4×10~(-6)kg·m~(-2)·s~(-1),即平均值的相对误差仅为5.8%,该方法可以满足工程计算的需要.考虑到参数选取、机理数学模型有待完善等方面的影响,新方法的论证存在进一步提升的空间.壁联扩散的提出具有实际开发意义和多重研究意义,耦合新方法的提出阐明了滑脱和各种扩散之间的关系,防止了页岩纳米级孔隙中流动机理的重复叠加,能较好改变页岩气流动计算耦合方法不一致的现状,为页岩气开发定量计算指明新方向.

A new method for the transport mechanism coupling of shale gas slippage and diffusion

In view of the current status that different literature applies different coupling methods to the calculation of shale gas flow, and in order to clarify the relation between slippage and several diffusions, in this paper the slippage effect and various diffusions are analyzed first by theoretical analysis and mathematical models according to the definitions and the mechanisms of microscopic motions. Afterwards, allowing for the spatial effect of the adsorbed molecules on gas flow, the concept “wall-associated diffusion” is proposed for the first time to represent the gross effects of Knudsen diffusion and surface diffusion, and it is pointed out that wall-associated diffusion is equivalent to slippage effect. Therefore a new coupling way where wall-associated diffusion and slippage effect are replaceable and no superposition of them is needed in flow calculation, is proposed. The case study shows that when the capillary radius ranges from 5 nm to 2000 nm, the relative error between wall-associated diffusion and slippage effect mass flux is fairly small, namely less than 10% in the vast majority of the range. The difference between mean values of wall-associated diffusion and slippage effect mass flux in the whole aperture range is 1.4×10^{- 6} kg·m^-2·s^-1. That is, the relative error between the mean values is only 5.8%. Therefore, the new method satisfies the requirements for engineering calculations. Taking parameter selection, unfinished improvements in mathematical models of relevant mechanisms and other factors into account, there is some room for further promoting the verification of the proposed method. The development of wall-associated diffusion has practical significance and multiple research significance. And the new coupling way reveals the relation between slippage and diffusions, which prevents reduplicated superposition of shale gas flow mechanisms in nano-scale pores and can well change the status where the current coupling methods for shale gas flow are not consistent, thus specifying a new direction in the quantitative calculations for shale gas development.