**1. Introduction**

Coal is the dominant energy source in China. With the depletion of shallow coal resources, a large number of mines in China entered deep mining, and the threat of gas disasters is extremely serious [1–3]. The hidden danger of coal and gas outburst increases, which seriously threatens the personal safety of underground workers and affects the mining efficiency of coal resources in China [4–6]. Pre-drainage of coal seam gas can effectively prevent coal and gas outburst. Efficient gas extraction plays an important role in reducing coal seam gas pressure and gas emission, as well as preventing coal– gas outburst [7–9]. Drilling negative pressure extraction is the most common method of gas extraction. Drilling spacing and extraction time are significant factors affecting the extraction effect.

With the deepening of the research on the seepage law of coal seam gas, it is realized that the migration mode of coal seam gas in coal body is not single, and there are many flow modes among coal pores, fractures, and matrix [10–13]. According to the various characteristics of coal mechanics and the migration of gas in coal, the establishment of a gassolid coupling model is the theoretical basis for the analysis of gas extraction by negative

**Citation:** Du, F.; Cui, W.; Wang, K. Study on Gas Migration Mechanism and Multi-Borehole Spacing Optimization in Coal under Negative Pressure Extraction. *Processes* **2023**, *11*, 259. https://doi.org/10.3390/ pr11010259

Academic Editor: Albert Ratner

Received: 20 December 2022 Revised: 9 January 2023 Accepted: 11 January 2023 Published: 13 January 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

pressure drilling. Zhu et al. determined the dynamic change model of permeability and porosity considering coal deformation and the Klinkenberg effect, and deduced the low permeability gas-solid coupling model [14–16]. Based on the innovative gas-solid coupling model, Cheng et al. used COMSOL Multiphysics to numerically solve the model. The migration of gas in coal under the influence of diffusion and seepage is analyzed, and the influence of negative pressure on gas migration is studied [17–19]. Li et al. simulated the gas extraction effect under different hole spacing by analyzing the mechanism of gas flow around the borehole and the superposition effect of extraction. He obtained the reasonable hole spacing of bedding gas extraction: 2r ≤ L ≤ R [20]. Zhang et al. established a coal seam gas seepage model considering the assumption of double-hole medium and the influence of stress redistribution on the seepage characteristics of coal seam gas. They studied the influence of coal seam pressure change on gas adsorption and seepage, and the improvement of gas extraction effect by overlapping the arrangement of two boreholes [21]. Chen made a more detailed study on the optimization of borehole extraction spacing and effective extraction area [22].

The study of gas migration and the effect of different borehole spacing on gas extraction have great reference value for practical engineering. The optimal design of extraction boreholes affects the safety of coal mining and the sustainable development of coal resources. [23]. In the existing research, the research results of coal permeability, porosity change, and single row multi-borehole extraction effect of negative pressure extraction gas are quite abundant, but most of them are based on a two-dimensional case. However, based on pore-fracture dual porous media, there are few studies on understanding and analyzing gas migration in coal from the perspective of a three-dimensional simulation. There are also few studies on the gas migration and extraction effect in the coal body during drilling negative pressure extraction through the three-dimensional visualization model. In order to better reveal the migration of gas in coal during the extraction process of three boreholes and the influence of different borehole spacing on effective extraction area, an innovative gas-solid coupling model was proposed based on previous studies. The model takes into account the Klinkenberg effect, coal matrix, and skeleton deformation of coal fracture outward seepage and matrix diffusion gas influx, coal matrix adsorption gas, and the desorption diffusion gas dynamic process. In order to provide a theoretical basis for further understanding of gas migration law and studying the extraction effect under the influence of the multi-hole extraction superposition effect, this research takes a coal mine as the background and uses COMSOL simulation software for three-dimensional simulation. The research intends to provide reference value for practical engineering.

#### **2. Establishment of Coalbed Gas-Solid Coupling Model**
