**1. Introduction**

Shale gas refers to a kind of self-generating and self-preserving natural gas, which gathers mainly in a free or adsorbed state in the organic-rich dark shale or high-carbon mud shale [1]. With vast reserves and the potential to offset the gradually depleted conventional resources worldwide and cut down carbon emissions at the same time, shale gas is playing an increasingly important role in ensuring global energy safety. Because shale matrix is characterized by various nanopores, where the gas flow is of high nonlinearity and complexity, an in-depth study of the mathematical model for the gas flow capacity in shale matrix is in urgent demand.

The mechanisms considered in different literature are listed in **Table 1**. It is obvious that opinions vary greatly on the flow mechanism scheme applied. The noteworthy aspects include the following: what the relationship among the various


#### **Table 1.**

*Different flow mechanism schemes in literature.*

#### **Figure 1.**

*A brief summary of the common methodology used in different research [11–32].*

flow mechanisms of shale gas, e.g., slippage, Fick diffusion, Knudsen diffusion, etc., is; whether there is a repeated superposition of these mechanisms for specific flow calculation; and how to deal with the relationship among the various flow mechanisms, etc. There is no clear answer to these problems in current literature.

**Figure 1** shows the common research methodology of the flow models used in different literature. It indicates that because the method of the continuum model with a boundary condition based on the molecular one is considered inconsistent and the limitations and drawbacks of first-order, second-order, and 1.5-order slip models are described, some studies, which are listed in **Figure 1**, are inclined to add related flow mechanisms linearly. Furthermore, the mathematical models of viscous flow and various types of diffusion do not fully agree with common flow cognition as these theories and models were experimentally verified or developed for a limited range of conditions [27]. For this reason, coupling coefficients are introduced to rectify this kind of limitation, so as to enhance the correspondence between the flow model and Knudsen number (Kn). Finally, because the secondhand average method, e.g., assuming the pore space of shale to be composed of a certain number of isodiametric pores regardless of the pore size distribution, is widely used in the research of shale gas flow, more explicit means, like taking the existence of various pore sizes in shale into account, should be adopted for transforming the flow model in nanopores to that in macroscopic-scale shale matrix.

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

Based on the literature survey for shale gas flow in shale matrix, we know that the flow mechanism scheme with its corresponding coupling method is very crucial and has not yet been solved. In addition, although the integration method using specific functions has been proposed to facilitate the consideration of various pore sizes in shale matrix, real shale experiments are rarely involved to realize this point with definitely determined parameters.

Firstly, in this chapter, the concept of wall-associated diffusion is presented to clarify the relationship between slippage effect and several types of diffusion. Secondly, a physically sound flow mechanism scheme, which considers both division of mechanical mechanisms in nanopores and partition of flow space, has been proposed by virtue of the proposition of wall-associated diffusion. Thirdly, the coupling coefficients corresponding to the flow mechanisms considered are deduced to comply with the basic flow regime cognition, so as to establish a new coupled flow model in nanopores. Fourthly, the pore size distribution experiments for real shale samples from a gas field are utilized to realize the upscaling transformation of the flow model in nanopores into that in the macroscopic-scale shale matrix, with definitely determined fitting parameters for the establishment of a unified model for the gas flow prediction in shale matrix. Finally, a case study is presented to show how the lab-scale results are translated into field-scale ones.
