Today, hydraulic fracturing is one of the most used methods of impact on the reservoir in order to increase the flow rate of the fluid. Holding an event involves a large number of risks that reduce its effectiveness. In order to increase the success of hydraulic fracturing, simulation results are applied in specialized simulators, which are based on various mathematical models. Most of the software products used is foreign-made. In this paper, we give a mathematical model that allows to consider the features of the process of flowing a viscous fluid with an admixture of particles in an opening hydraulic fracture. The model under consideration is an alternative to the commercial hydraulic fracturing simulators on the market with the option of rapid assessment. In the course of the computational experiment, it was found that the presence of particles in the fracturing fluid has a significant effect on the nature of the crack formation process, stopping its growth (in particular, due to clogging of the crack nose). A decrease in the concentration of particles in the injected mixture leads to a slowdown of precipitation and a continued growth of the crack. The dependence of the ultimate crack length, the feed time of the mixture, and the moment of stopping the growth on the volume content of particles was established. The paper presents the results of a numerical solution of the problem of the process of formation of hydraulic fractures when hydraulic fracturing fluid is injected into the well. Input parameters are: parameters of the elastic medium (Poisson's ratio, Young's modulus), reservoir properties of the rock, concentration and time of supply of the mixture. A comparison is made of the fracture parameters obtained during the computational experiment with the values, calculated using a foreign hydraulic fracturing simulator.
References
1. Perkins T.K., Kern L.R., Widths of hydraulic fractures, Journal of Petroleum Technology, 1961, V. 13, pp. 937–949.
2. Nordgren R.P., Propagation of a vertical hydraulic fracture, SPE-18959-PA, 1972.
3. Zheltov YU.P., Khristianovich S.A., On hydraulic fracturing of oil reservoir (In Russ.), Izvestiya Akademii nauk SSSR, 1955, no. 5, pp. 3–41.
4. Chernyy S.G. et al., Metody modelirovaniya zarozhdeniya i rasprostraneniya treshchiny (Methods for modeling crack initiation and propagation), Novosibirsk: Publ. of SB RAS, 2016, 312 p.
5. Khasanov M.M., Paderin G.V., Shel' E.V. et al., Approaches to modeling hydraulic fracturing and their development (In Russ.), Neftyanoe khozyaystvo = Oil Industry, 2017, no. 2, pp. 37–41.
6. Chesnokov Yu.G., Influence of the Reynolds number on the plane-channel turbulent flow of a fluid (In Russ.), Zhurnal tekhnicheskoy fiziki = Technical Physics. The Russian Journal of Applied Physics, 2010, V. 80, no. 12, pp. 33–39.
7. Tatosov A.V., Shlyapkin A.S., The motion of propping agent in an opening crack in hydraulic fracturing plast (In Russ.), Izv. Saratovskogo un-ta. Novaya seriya. Matematika. Mekhanika. Informatika, 2018, V. 18, no. 2, pp. 217–226, DOI: 10.18500/1816-9791-2018-18-2-217-226.
8. Karnakov P.V., Lapin V.N., Chernyy S.G., A model of hydraulic fracturing with fracture plugging mechanizm (In Russ.), Vestnik Novosibirskogo gosudarstvennogo universiteta. Ser. Informatsionnye tekhnologii, 2014, V. 12, no. 1, pp. 19–33.
