title: Ð­ÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð³Ð¸Ð´ÑÐ¾ÑÐ°Ð·ÑÑÐ²Ð° Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ¸ Ð½Ð° Ð¿ÑÐ¸Ð¼ÐµÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¥ÐÐ
title: Ð¼Ð°Ð³Ð¸ÑÑÐµÑÑÐºÐ°Ñ Ð´Ð¸ÑÑÐµÑÑÐ°ÑÐ¸Ñ
titleType: Subtitle
Creators: name: Ð¡ÑÐµÐ¿Ð°Ð½Ð¾Ð², ÐÐ»ÐµÐºÑÐµÐ¹
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2016
Subjects: ÐÐµÑÑÑÐ½ÑÐµ Ð¸ Ð³Ð°Ð·Ð¾Ð²ÑÐµ Ð¿Ð»Ð°ÑÑÑ
Ð³Ð¸Ð´ÑÐ¾ÑÐ°Ð·ÑÑÐ² Ð¿Ð»Ð°ÑÑÐ°
Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð°Ñ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐ°
ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ ÑÐºÐ¾ÑÐ¾ÑÑÐ¸
hydraulic fracturing
modified theory
speed equation

description: Ð¦ÐµÐ»Ñ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ - ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¿Ð¾Ð´ÑÐ¾Ð´Ð°, Ð¾ÑÐ½Ð¾Ð²Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð½Ð° Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹ Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²ÐºÐµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¾ Ð³Ð¸Ð´ÑÐ¾ÑÐ°Ð·ÑÑÐ²Ðµ, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ðµ ÐºÐ¾ÑÐ¾ÑÐ¾Ð³Ð¾ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ñ Ð¿Ð¾Ð»ÑÑÐ¸ÑÑ ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾Ðµ Ð¸ ÑÐ¾ÑÐ½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¥ÐÐ Ñ Ð¼Ð¸Ð½Ð¸Ð¼Ð°Ð»ÑÐ½ÑÐ¼Ð¸ Ð²ÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½ÑÐ¼Ð¸ Ð·Ð°ÑÑÐ°ÑÐ°Ð¼Ð¸. ÐÐµÑÐ¾Ð´ Ð´Ð¾Ð»Ð¶ÐµÐ½ Ð¾Ð±ÐµÑÐ¿ÐµÑÐ¸Ð²Ð°ÑÑ ÑÐµÑÐµÐ½Ð¸Ðµ Ð² Ð³Ð»Ð¾Ð±Ð°Ð»ÑÐ½ÑÑ ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°ÑÐ°Ñ Ð±ÐµÐ· Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ Ð³Ð¸Ð¿ÐµÑÑÐ¸Ð½Ð³ÑÐ»ÑÑÐ½Ð¾Ð³Ð¾ Ð¾Ð¿ÐµÑÐ°ÑÐ¾ÑÐ° ÑÐµÐ¾ÑÐ¸Ð¸ ÑÐ¿ÑÑÐ³Ð¾ÑÑÐ¸. ÐÐ¾ÑÑÐ°Ð²Ð»ÐµÐ½Ð½Ð°Ñ ÑÐµÐ»Ñ Ð´Ð¾ÑÑÐ¸Ð³Ð°ÐµÑÑÑ Ð¿ÑÑÐµÐ¼ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐµÑÐºÐ¸ Ñ ÑÐ¸ÐºÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð½ÑÐ¼ ÑÐ¸ÑÐ»Ð¾Ð¼ ÑÐ·Ð»Ð¾Ð² Ð¸ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ ÑÐ¿ÐµÑÐ¸Ð°Ð»ÑÐ½Ð¾ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½ÑÑ ÐºÐ¾Ð½ÐµÑÐ½ÑÑ ÑÐ°Ð·Ð½Ð¾ÑÑÐµÐ¹ Ð¸ ÐºÐ²Ð°Ð´ÑÐ°ÑÑÑÐ½ÑÑ ÑÐ¾ÑÐ¼ÑÐ», ÑÑÐ¸ÑÑÐ²Ð°ÑÑÐ¸Ñ ÑÐ¿ÐµÑÐ¸ÑÐ¸ÐºÑ ÑÐ°ÑÑÐ¼Ð°ÑÑÐ¸Ð²Ð°ÐµÐ¼Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸. Ð£ÑÑÐ°Ð½Ð¾Ð²Ð»ÐµÐ½Ð¾, ÑÑÐ¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½Ð°Ñ Ð´Ð¸Ð½Ð°Ð¼Ð¸ÑÐµÑÐºÐ°Ñ ÑÐ¸ÑÑÐµÐ¼Ð° Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ ÑÐµÑÐµÐ½Ð° ÑÑÐ°Ð½Ð´Ð°ÑÑÐ½ÑÐ¼Ð¸ Ð¼ÐµÑÐ¾Ð´Ð°Ð¼Ð¸, Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼ÑÐ¼Ð¸ Ð¿ÑÐ¸ ÑÐµÑÐµÐ½Ð¸Ð¸ Ð·Ð°Ð´Ð°ÑÐ¸ ÐÐ¾ÑÐ¸ Ð´Ð»Ñ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¾Ð±ÑÐºÐ½Ð¾Ð²ÐµÐ½Ð½ÑÑ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹. ÐÐ¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð¿Ð¾Ð´ÑÐ¾Ð´ Ð¿ÑÐ¸Ð¼ÐµÐ½Ð¸Ð¼ ÐºÐ°Ðº Ðº Ð½ÑÑÑÐ¾Ð½Ð¾Ð²ÑÐºÐ¸Ð¼, ÑÐ°Ðº Ð¸ Ðº ÑÑÐ¾Ð½ÑÐ°ÑÑÐ¸Ð¼ÑÑ Ð¶Ð¸Ð´ÐºÐ¾ÑÑÑÐ¼. Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½ÑÐ¹ Ð¿Ð¾Ð´ÑÐ¾Ð´ Ð´Ð¾Ð¿ÑÑÐºÐ°ÐµÑ ÑÐ°ÑÐ¿ÑÐ¾ÑÑÑÐ°Ð½ÐµÐ½Ð¸Ðµ Ð½Ð° ÑÑÐµÑÐ¼ÐµÑÐ½ÑÐµ Ð·Ð°Ð´Ð°ÑÐ¸.
description: The objective of the work is to develop an approach based on the modified formulation of the hydraulic fracture problem, which provides stable and accurate solution to the KGD problem with minimal time expense. The approach should employ global coordinates and avoid using the inversion of the hypersingular elasticity operator. The objective is achieved by employing a mesh with a fixed number of nodes and by using specially designed finite differences and quadrature rules, which account for specific features of the problem under consideration. It is shown that the dynamic system obtained may be efficiently integrated by conventional methods used to solve the Cauchy problem for a system of ordinary differential equations. It appears that approach developed is applicable to Newtonian, as well to thinning fluids. The approach may be extended to 3D problems.