## 1 Introduction
The displacement processes under different pressures and temperatures are simulated by COMSOL. Subsequently, the stress field model and seepage field model were derived, and the numerical simulation of permeability evolution was carried out in COMSOL software. [PERSON] et al. [31] established a coupled finite element (FE) model of binary gas flow, diffusion, competitive sorption and permeability change to explore the effect of CO\({}_{2}\) injection on net recovery, permeability evolution and injectivity in uniform and homogeneously permeable reservoir. [PERSON] et al. [32] built a dual porosity/permeability model through accurately expressing the volumetric strain of matrix and fracture which aims to reveal the reservoir permeability evolution during the process of CO\({}_{2}\)-enhanced coalbed methane (CO\({}_{2}\)-ECBM) recovery. [PERSON] et al. [33] established a fluid-solid coupling model considering gas-water phases and \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Country** & **Project** & **Bunial Depth** & **Coal Rank** & **Permeability** & **Reference** \\  & **Project** & **(m)** & & **(md)** & **Reference** \\ \hline U.S.A & Allison Unit, San Juan Basin & 945 & Bituminous coal & 30–150 & \\  & Pump Canyon, San Juan Basin & 918 & Bituminous coal & 146–550 & [13] \\  & Tanquary Farms test site, Illinois Basin & 274 & Bituminous coal & 2–7.0 & [14] \\  & Virginia Central Appalachian Basin Coal Test & 427–671 & Bituminous coal & 5–20 & [15] \\  & Lignite Field Validation Test, Williston Basin & 335 & Lignite & 1 & [16] \\  & Black Warrior Basin Coal Test & 548 437 237 & Bituminous coal & 0.1–0.2 10–16 & [17] \\  & Marshall County project, Northern & 400–530 & Bituminous coal & 1 & [18] \\  & Appalachian Basin & & & & \\  & Buchanan County, Central Appalachian & 274–671 & Bituminous coal & 5–27 & \\  & Basin & & & & \\ Canada & FBV 4A Micro-Pilot Test, Western Canada & & & & \\  & Sedimentary Basin & & & & \\  & ARC ECBM & & & & \\  & CSEMP & 420 & Sub-Bituminous & & \\  & & coal & & & \\ Poland & RECOPOL, upper Silesian coalbasin, Poland & 1012–1076 & Bituminous coal & 0.4–1.5 & [20] \\  & Japan & Yubari field test, Ishikari Coal Basin, Japan & 890 & Bituminous coal & 1 & [21] \\  & China & Qinshui Basin ECBM 2004 & 472 & Anthracite & 12.0/0.95 & [22] \\  & Qinshui Basin ECBM 2010 & 923 & Anthracite & 0.002–0.8 & [23] \\  & APP ECBM, Ordos Basin & 560 & Bituminous coal & 0.64 & [24] \\  & Qinshui Basin multiple wells & 972 & Anthracite & 0.002–0.8 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Existing CO\({}_{2}\)-ECBM field experiments. Klinkenberg effect of CO\({}_{2}\) injection into coal seam for enhancement of gas drainage, parameters of gas pressure, gas content and gas extraction rate after coal seam CO\({}_{2}\) injection were analyzed by using COMSOL software and applied in engineering test. [PERSON] et al. [34] established an improved fully coupled gas migration model for CBM extraction. The permeability rebound and recovery times as well as rebound values are proposed to accurately quantify permeability evolution during CBM extraction. Also, the evolution of coal seam permeability under different CO\({}_{2}\) injection method is discussed. Most of the above scholars only consider a single or several physical fields in their research. In addition, many scholars [29; 32; 35] have studied the Thermal-Hydraulic-Mechanical coupling of CO\({}_{2}\)-ECBM, but most of these studies are based on deep unminable coal seams. At present, there are few numerical simulation studies on the Thermal-Hydraulic-Mechanical multi-physical coupling of shallow low-rank coal. The buried depth of the deep unminable coal seam is large. Under geological conditions of high temperature and high pressure, CO\({}_{2}\) is likely to exist in the supercritical state, so the change in its physical parameters may not be obvious. Therefore, previous studies regard fluid physical parameters as constants,which is barely acceptable.