Egor Dontsov

TL;DR: In this article, a hybrid discrete-continuum numerical scheme was developed to study the behavior of a hydraulic fracture crossing natural fractures, and the simulation results for orthogonal crossing indicate three fundamental crossing scenarios, which occur for various stress ratios and friction coefficients of the natural fracture.

TL;DR: In this article, the steady flow of a Newtonian fluid mixed with spherical particles in a channel was analyzed for the purpose of modelling proppant transport with gravitational settling in hydraulic fractures. But, these solutions require the numerical solution of an integral equation, and, as a result, the development of a propperant transport model for hydraulic fracturing based on these results is not practicable.

TL;DR: A closed-form approximate solution for a penny-shaped hydraulic fracture whose behaviour is determined by an interplay of three competing physical processes that are associated with fluid viscosity, fracture toughness and fluid leak-off is developed.

TL;DR: In this paper, the authors developed a model for proppant transport in hydraulic fractures capable of capturing both gravitational settling and tip screen-out effects, while prohibiting the particles from reaching the crack tips by imposing a width restriction based on the particle size.

TL;DR: In this paper, the Implicit Level Set Algorithm (ILSA) is used to model the propagation of planar hydraulic fractures in situations when their progress is determined by an interplay of fluid viscosity, rock fracture toughness, and fluid leak-off into the formation.