## 1 Introduction  
Coal mine gas (coal bed methane), as a kind of power source with low pollution and a high utilization rate, has long been in high demand in our country [1; 2; 3; 4; 5]. The efficient extraction of coal mine gas has the triple benefits of coal mine disaster prevention and control, methane resource development and greenhouse gas emission reduction. Along with the continuous research on coal mine gas extraction and technology, anhydrous and permeability-enhancement technologies such as supercritical CO\({}_{2}\), nitrogen and liquid nitrogen cracking have been gradually favored and utilized by scholars in related fields [6; 7; 8; 9; 10]. The intrinsic mechanism of the anhydrous fracturing method is to achieve the purpose of destroying the coal rock structure by cleverly applying the freezing and swelling force generated in the process of ice-water phase change, thus expanding the pore space of the coal body, increasing the permeability and better promoting the extraction rate of coal bed methane [11; 12; 13]. Low-temperature anhydrous permeability enhancement is of great significance for the safe, green and sustainable development of coal and gas resources. Not all of the liquid water in coal is converted to solid ice when the coal is frozen by a low-temperature medium; due to surface adsorption and pore capillary action in the coal matrix, a certain amount of liquid water is always maintained, which is called unfrozen water [14; 15]. The unfrozen water is deposited between the ice crystals and the coal matrix in the form of water film, which has a great influence on the macroscopic properties of the frozen coal [16; 17]. As an important part of low-temperature fracturing, the melting process, compared with the freezing process, is characterized by a long time, complex pore evolution and significant changes in coal physical properties. Under low-temperature conditions, the solidification points of coals with different pore sizes are different due to the influence of surface particle energy and capillary suction. This leads to the transformation of ice within the pores of different pore sizes into water in a certain order [18; 19]. Under the impact of low-temperature liquid nitrogen, different sizes of coal pores will undergo different degrees of expansion and contraction, which leads to differences in pore structure and affects the melting process of coal. The degree of coal melting directly determines the permeability of the pores and affects the efficiency of CBM extraction. Based on the above reasons, the study of the water content and ice-water conversion process of low-temperature frozen coal pores during the melting process of the coal body is crucial for the development and optimization of low-temperature anhydrous permeability enhancement technology for coal seams. This is of great significance for realizing efficient CBM extraction and safe coal mining [20; 21]. The basis of unfrozen water research is how to accurately measure the content of unfrozen water [22; 23]. At present, there are many methods to measure the content of unfrozen water, including calorimetry, pulsed nuclear magnetic resonance [24]; differential scanning calorimetry (DSC); the frequency domain reflection method (FDR) and the time domain propagation method (TDT). Magnetic resonance (NMR) can quantitatively analyze the porosity and pore size distribution of coal and has been widely used in the field of coal and rock [13; 25]. By deriving the basic mathematical structure of the theoretical and parametric models, [PERSON] et al. [26] demonstrated that the surface effect of clay is the main cause of unfrozen water in permafrost. [PERSON] et al. [27] established a mathematical physical model for the relationship between temperature and unfrozen water content during freeze-thaw based on similar theory and obtained that each curve during freeze-thaw showed hysteresis due to the different thermodynamic potential of pore water. [PERSON] et al.