## 1 Introduction  
In 2020, the world's entire energy consumption was 556.63 exajoules (556.63 \(\times\) 10\({}^{18}\) joules), 83.1% of which was provided by hydrocarbons [1; 2; 3; 4], and the condition will not change dramatically in the forthcoming years [5; 6; 7]. To meet the growing energy demands of society, there is a need for continuous advancement in upstream industry technologies. These technological advancements are crucial for increasing production rates and improving the recovery factor of energy resources. By enhancing these factors, we can effectively address the increasing energy requirements of humanity. According to [PERSON] et al. (2006), the average recovery factor in the world ranges from 20% to 40%, which means that approximately 2/3 of total oil and gas reserves cannot be recovered [8]. Usually, the gas production rate in low permeable reservoirs decreases quickly. Stimulation processes are needed in coal beds, tight sandstones, and shale to accelerate recovery since permeability and porosity of the reservoir formation are some of the main factors that affect the rate of oil and gas recovery [9]. Thus, developing technologies in the oil and gas industry is needed to increase the production and recovery factor to cover human energy needs [10; 11; 12; 13]. Hydraulic fracturing is widely recognized as the primary technique for enhancing gas production rates, particularly in regions where water resources are abundant. This method entails the injection of water, sand, and chemicals into the reservoir to create and extend fractures, thereby facilitating the more efficient flow of fluids from the reservoir [14; 15; 16; 17]. In addition, proppants, e.g., treated sand, are used in hydraulic fracturing, as they lodge inside the fracture and prevent these fractures from closing [18]. Stimulation is often required for the economic viability of a hydrocarbon extraction project [19; 20; 21]. Most coalbed methane (CBM) reservoirs have low permeability, below 10 mD, impeding gas flow from coal to the wellbore [22]. In hydraulic fracturing, various types of power fluids can be used, e.g., water, oil, foam, acid, or cryogenic fluid. The most common is slick water [23] with friction-reducing additives. With low-viscosity slick water, the fracture expands more in length than width, and chemical additives avoid corrosion and bacterial growth. Moreover, water is often the most economical, and furthermore, this water can be recycled [24; 25], reducing makeup volume in further stimulation jobs or stages. However, total water consumption is still very high, and low-viscosity water does not transport proppant agents easily. Oil-based fluid was the first implemented in hydraulic fracturing with high viscosity [23]. This type of fluid can be applied in colder regions, where water freezing is a concern [26]; however, oil-based fluid is more expensive and involves higher safety and ecological damage risks [23]. Cryogenic fracturing technology overcomes many of these problems with minimal ecologic damage [27; 28; 29; 30]. Cryogenic fracturing can replace traditional hydraulic fracturing processes [31], with the principal mode of rock breakage being thermal shock [32; 33]. As cold liquid nitrogen is injected into the hot formation, heat, due to the laws of thermodynamics, will move from the formation to nitrogen; consequently, sudden cooling occurs in the formation. During this heat transfer and rock cooling, enormous thermal stresses develop over very short distances, often exceeding rock strength, resulting in fracturing. The greater the temperature difference, it is anticipated that cryogenic fracturing performance will also increase [34; 35]. The emulsification issue of injected fluid with reservoir fluid is also avoided with cryogenic fracturing, as liquid nitrogen is more compatible [36]. While solids contract with reduced temperature, water inside the formation converts to ice and expands in volume, thereby expanding the cracks [37; 38; 39; 40].