_Applied sciences_  
_Article_  
**Investigation of the Gas Pressure Field and Production Rate for Two Typical Proppants: Small-Sized Continuous and Large-Sized Discontinuous Proppants**  
[PERSON] 1, [PERSON] 2,*, [PERSON] 1, [PERSON] 1 and [PERSON] 1,*  
State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Xuzhou 221116, China; [EMAIL_ADDRESS] (S.Y.) School of Safety Engineering, China University of Mining and Technology, Xuzhou 221116, China Correspondence: [EMAIL_ADDRESS] (Q.C. ); [EMAIL_ADDRESS] (H.L.) **Abstract: The small-sized program is widely used in the traditional hydraulic fracturing reservoir stimulation, but the theoretical research shows that the large-sized proppant can greatly improve the fracture permeability. Although many scholars have proposed the method of using large-sized proppant, the characteristics of the pressure field change and gas drainage rate during reservoir development are still unclear after pumping large-sized proppant. In this article, to study the change regularity of the reservoir pressure field, two representative proppants are selected: the small-sized proppant and large-sized proppants. First, the Navier-Stokes equations are solved using the numerical simulation method, and the characteristics of the reservoir pressure field are finely reproduced. Then, the production rate is discussed to reveal the huge potential of large-sized proppant for the natural gas development. The results show that under the same conditions, if the particle size of the proppant increases by 5 times, then the reservoir permeability will increase by 27 times approximately, and the single well production efficiency will increase by 17-19 times in the first 3000 days. In addition, a new quantitative model is proposed to evaluate the permeability magnification of the fracture and reservoir when adopting the large-sized proppant. This study further confirms that the method of large-sized proppant proposed by the author in the earlier stage has great potential. This study is helpful for the researchers and engineers to better understand the evolution regularity of the reservoir pressure field and gas production rate in the process of oil and gas exploitation after using the large-sized proppant. **  
large-sized proppant; reservoir stimulation; permeability; evaluation model; production rate  
**1. Introduction**  
The development and utilization of natural gas (shale gas, coalbed methane, etc.) is of great significance to the sustainable development of the world [1]. Under the influence of in situ stress, the reservoir porosity and permeability are generally low [2, 3]. At present, the low reservoir permeability is the main factor restricting the development efficiency of natural gas. Hydraulic fracturing is a key technology to improve reservoir permeability [4]. Hydraulic fracturing refers to the technology that uses the high-pressure fluid, such as water or liquid nitrogen, to fracture the rock formation to form a fracture network, thereby improving the permeability of the rock formation [5]. The high pressure forces the rock rupture to form fractures and eventually form artificial fractures in the formation [6, 7, 8]. At present, hydraulic fracturing technology has been widely used in the field of reservoir stimulation and permeability enhancement of coal, shale, and tight sandstone [9, 10, 11, 12, 13]. The reservoir stimulation mainly includes three steps. For the first step, the rock is fractured using the hydraulic fracturing method. For the second step, proppant is pumped into the fracture network. Third, fracturing fluid backflow. Finally, the proppant is retained in the fracture network to support the fracture and prevent its closure. The fracture hasgood conductivity under the support of proppant, so the permeability of the reservoir will increase after hydraulic fracturing stimulation [14].