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

Abstract

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.