It is known that much of the technology aimed at intensifying fluid inflow by means of hydraulic fracturing involves the use of proppant. In order to transport and position grains in the fracture, a uniform supply of proppant with a given concentration into the fracturing fluid is ensured. The aim of the operation is to eliminate the occurrence of distortions in the injection program of proppant HF. A mathematically accurate linear increase of concentration under given conditions is possible only if the transient concentration is correctly defined. The proposed approach allows to correctly form a proppant HF work program for both linear and non-linear increase in proppant concentration. The scientific novelty of the work lies in application of a new mathematical model for direct calculation of injection program parameters, previously determined by trial and error method. A mathematical model of linear and non-linear increase of proppant concentration during HF was developed. For the first time, an analytical solution is presented that allows direct calculation of parameters of the main HF stages, including transient concentrations for given masses of the various types of proppant. The application of the mathematical model in formation of a treatment plan allows maintaining correct proppant mass distribution by fractions, which facilitates implementation of information and analytical systems, data transfer directly from a work program into databases. It is suggested to improve spreadsheet forms used in production, which would allow applying mathematical model of work program formation at each HF process without additional labour costs. The obtained mathematical model can be used to improve the software applied in the design, modelling and engineering support of HF processes.
At present, there is a significant number of experimental and theoretical works devoted to the study of the properties of soft soils under explosive loading and experimental methods for determining the shock adiabats of soft soils. However, the results obtained are largely contradictory, and both further research into the basic properties of soft soils and an in-depth theoretical justification of the experimental methods themselves are required. This paper presents the results of a numerical study of the impact of a superimposed explosive charge on sandy soil through a metal impactor plate. The ground is modeled by S.S. Grigoryan’s compressible medium with irreversible volumetric and shear deformations. Numerical solutions obtained using various shock adiabats known in the scientific literature are compared with experimental data. As a result, a synthesized sand shock adiabat is proposed and justified in the range from low pressures up to 1 GPa. The influence of volumetric plastic deformations and friction forces on wave processes in the ground is analyzed.
