**2. Flow mechanisms in gas-shale matrix**

There are many types of flow mechanisms in shale matrix, including slippage effect, Fick diffusion, transition diffusion, Knudsen diffusion, surface diffusion, etc. It can be seen from the literature survey in Section 1 that different flow mechanism schemes have formed aiming at establishing a calculation model to properly characterize the nanoscale shale gas flow. There may be views that the more flow mechanisms are taken into account, the more precise the established models are. However, this is not the opinion in this chapter.

As is known, Klinkenberg [33] first discovered in 1941 the phenomenon that, when measuring the gas permeability of rock, not only the measurement result is higher than the liquid measurement value but also it has strong pressure dependence and attributed it to the slippage behavior of gas in the rock pores. Specifically, gas slippage refers to the phenomenon that the near-wall gas molecules move relative to the wall surface when flowing through the medium channels [34]. In essence, the gas slip flow results from the interaction of gas molecules and pore walls, so the gas molecules in the vicinity of walls are in motion and contribute an additional flux, which is macroscopically characterized by the non-zero gas velocities on channel walls, thus resulting in slip flow [35, 36]. The jump model assumes that the adsorbed gas molecules jump from one adsorption site to the adjacent adsorption site on the pore surface, which is considered to be suitable for the research on the surface diffusion of the adsorbed gas in shale nanopores [37]. Meanwhile, when the molecular mean free path is obviously larger than the pore diameter, the gas-wall collision dominates, and the collision between gas molecules is secondary, which is characterized by Knudsen diffusion [9, 38, 39].

In brief, both Knudsen diffusion and surface diffusion lead to non-zero moving speeds of the gas molecules around walls. Furthermore, from the viewpoint of microscopic motion mechanisms, they are both related to gas–solid interactions, which is consistent with slippage phenomenon in essence. Therefore, a new concept named "wall-associated diffusion" [40] is proposed, which characterizes the overall role of surface diffusion and Knudsen diffusion, as shown in **Figure 2**.

**Figure 2.**

*Relationship between wall-associated diffusion and slippage effect [40].*

The proposition of wall-associated diffusion has practical significance and multiple research significance as follows [40].

To begin with, in terms of mechanical mechanisms, since wall-associated diffusion describes the diffusion mechanisms of shale gas related to gas-wall interactions, it bridges the relationship between slippage effect and several types of diffusion, which prevents reduplicated superposition of shale gas flow mechanisms in nanoscale pores. This is where the practical significance lies. Besides, wall-associated diffusion can be regarded as a detailed form of slippage effect, dividing slippage effect into two distinct parts, i.e., surface diffusion and Knudsen diffusion. The two parts differ obviously in their mechanical mechanisms and motion patterns. Accordingly, the research significance of wall-associated diffusion involves not only the function of morphological descriptions but also the possibility of slip phenomenon research by different mechanical mechanisms. Lastly, another research significance is that wallassociated diffusion breaks through the limitation that the concept of slippage does not apply for high Knudsen number, with, however, the fact that wall effects still contribute to gas flow for high Knudsen number. Therefore, in extremely small nanopores, for example, where slip flow regime is not applicable, the wall-associated diffusion derived from physical morphology can well be used to explore the so-called slip phenomenon in other flow regimes apart from slip flow regime.

By virtue of the concept of wall-associated diffusion, the flow mechanism scheme used in this work is to be discussed next.

There is no doubt that all the mechanisms, such as continuum flow, slip flow, Knudsen diffusion, bulk diffusion, etc., have been studied in previous literature for the exploration of shale gas flow. However, it is a determinative flow mechanism scheme that is vital. According to the literature survey, apart from combining the Navier-Stokes solution with slip boundary condition whose deficiency has been mentioned in Section 1, there is also a trend in literature to assume a combination of certain flow mechanisms and check the consistency of the model results with experimental data. This method is favorable from an engineering point of view but meanwhile leads to the status that coincidence often exists and no commonly accepted consensus has formed currently. In this work, we discuss the issue physically. Firstly, due to the multiple advantages of wall-associated diffusion over the concept of slippage effect, slippage effect is replaced with wall-associated diffusion in the following discussion. On the one hand, the flow space in nanopores can be divided into two parts: the bulk phase region and the Knudsen layer [41]. On the other hand, the microscopic mechanical mechanisms can be divided into the gas– gas and gas-wall interactions. If a new comprehensive flow scheme, including viscous flow and bulk diffusion which belong to bulk phase flow and surface diffusion and Knudsen diffusion which are associated with gas-wall interactions causing non-zero flow velocities near pore walls, is proposed, the considerations of the division of flow space and mechanical mechanisms can be both realized.

*Mechanism, Model, and Upscaling of the Gas Flow in Shale Matrix: Revisit DOI: http://dx.doi.org/10.5772/intechopen.91821*

It should be noted that with the help of the methodology applied here, some flow mechanisms that are easily omitted are now included, such as bulk diffusion, an important diffusion process which is controlled by a mechanical mechanism obviously different from Knudsen diffusion. Furthermore, because the individual flow expressions, e.g., those for viscous flow and diffusion, were experimentally verified or developed for a limited range of conditions [27], the proposed physical flow mechanism scheme avoids unnecessary attempts to fit the mathematical models to experimental data so as to determine which flow mechanisms should be considered, laying a solid foundation for the research on the coupled flow model in nanopores discussed below.

To conclude, taking both division of mechanical mechanisms in nanopores and partition of flow space into account, viscous flow and bulk diffusion, which belong to bulk phase flow and result from gas–gas interactions, and surface diffusion and Knudsen diffusion, which are associated with gas-solid interactions and result in non-zero flow velocities near pore walls, are included in the proposed flow mechanism scheme.
