Justification for Proppant Concentration Choice During Hydraulic Fracturing

The article presents a mathematical model of linear and nonlinear increase in proppant concentration during hydraulic fracturing. For the first time, an analytical solution using direct calculation for determining the parameters of the main hydraulic fracturing stages including the transition concentrations for given masses of proppant of various types is presented. It is shown that the use of a mathematical model in the development of a processing plan provides the correct distribution of the proppant mass by fractions, which facilitates the introduction of information and analytical systems and transferring data directly from the operating program to the database. The spreadsheet forms used in the production have been elaborated, which enables to apply the mathematical model of the operating program at each hydraulic fracturing without additional labor costs. The obtained mathematical model can be applied to improve the software used in the design, modeling and engineering support of hydraulic fracturing.