|Abstract:|| Hydraulic fracturing is an important part of modern technologies for intensification of hydrocarbon production. Propagation of the hydraulic fracture is stipulated by a high-pressure pumping of viscous fluid, which creates pressure on fracture's walls high enough to overcome the rock closure stresses and cause the rock failure. Process of the hydraulic fracture growth is governed by several factors: flow of viscous fluid with additives in a narrow fracture's gap, elastic reaction of the fracture's walls; filtration of fluid from the fracture to the reservoir, rock failure and advance of the fracture's tip.
In the talk we discuss mathematical models of fracture propagation in a poroelastic inhomogeneous medium, model for estimation of the productivity of a horizontal multiple fractured well, and a related model for description of cerebral hemodynamics in application to modelling of arteriovenous malformations. On the base on exact and numerical solutions, we demonstrate the influence of the inhomogeneity of physical properties of the reservoir to the dynamics of fracture propagation. For a multiple fractured horizontal well we analyze the dependence of fractures positioning and geometry to the long-term production of the well. By using the model of cerebral hemodynamics, we explain some characteristic features of experimentally observed data for fluid pressure and velocity in blood vessels.(firstname.lastname@example.org)