Research Article
Geotechnical Engineering and Engineering Geology

# Mathematical model of linear and non-linear proppant concentration increase during hydraulic fracturing – a solution for sequential injection of a number of proppant types

Date submitted:
2021-05-31
Date accepted:
2022-02-24
Date published:
2022-07-13

## Abstract

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.

10.31897/PMI.2022.10

## Similar articles

Prediction of the stress-strain state and stability of the front of tunnel face at the intersection of disturbed zones of the soil mass
2022 Anatoly G. Protosenya, Alexander V. Alekseev, Pavel E. Verbilo
Identification of structural control factors of primary gold ore occurrences by method of unmanned aeromagnetic survey by the example of the Neryungrisky district of Yakutia
2022 Igor B. Movchan, Zilya I. Shaygallyamova, Alexandra A. Yakovleva
Tensor compaction of porous rocks: theory and experimental verification
2022 Ivan A. Panteleev, Vladimir Lyakhovsky, Virginiya A. Mubassarova, Vladimir I. Karev, Nikolaj I. Shevtsov, Eyal Shalev