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

It is known that much of the technology aimed at intensifying fluid inflow by means hydraulic fracturing involves use proppant. In order to transport and position grains in fracture, a uniform supply proppant with given concentration into ensured. The aim operation eliminate occurrence distortions injection program HF. A mathematically accurate linear increase under conditions possible only if transient correctly defined. proposed approach allows form HF work for both non-linear concentration. scientific novelty lies application new mathematical model direct calculation parameters, previously determined trial error method. during was developed. For first time, an analytical solution presented parameters main stages, including concentrations masses various types formation treatment plan maintaining correct mass distribution fractions, which facilitates implementation information systems, data transfer directly from databases. suggested improve spreadsheet forms used production, would allow applying each process without additional labour costs. obtained can be software applied design, modelling engineering support processes.