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Propagation of a penny-shaped hydrau...

Savitski, Alexei Alexandrovich.

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Propagation of a penny-shaped hydraulic fracture in an impermeable rock.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Propagation of a penny-shaped hydraulic fracture in an impermeable rock./
Author:	Savitski, Alexei Alexandrovich.
Description:	110 p.
Notes:	Advisers: Emmanuel M. Detournay; Steven L. Crouch.
Contained By:	Dissertation Abstracts International61-09B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9989147
ISBN:	9780599959194

Propagation of a penny-shaped hydraulic fracture in an impermeable rock.
Savitski, Alexei Alexandrovich.

Propagation of a penny-shaped hydraulic fracture in an impermeable rock. - 110 p.

Advisers: Emmanuel M. Detournay; Steven L. Crouch.

Thesis (Ph.D.)--University of Minnesota, 2000.

The objectives of this research were two-fold: (i) investigate the influence of the material toughness and the fluid viscosity on fracture propagation and (ii) construct rigorous solutions for particular regimes of propagation.

ISBN: 9780599959194Subjects--Topical Terms:

1018410
Applied Mechanics.

Propagation of a penny-shaped hydraulic fracture in an impermeable rock.
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020 $a 9780599959194
035 $a (UMI)AAI9989147
035 $a AAI9989147
040 $a UMI $c UMI
100 1 $a Savitski, Alexei Alexandrovich. $3 1293417
245 1 0 $a Propagation of a penny-shaped hydraulic fracture in an impermeable rock.
300 $a 110 p.
500 $a Advisers: Emmanuel M. Detournay; Steven L. Crouch.
500 $a Source: Dissertation Abstracts International, Volume: 61-09, Section: B, page: 4866.
502 $a Thesis (Ph.D.)--University of Minnesota, 2000.
520 $a The objectives of this research were two-fold: (i) investigate the influence of the material toughness and the fluid viscosity on fracture propagation and (ii) construct rigorous solutions for particular regimes of propagation.
520 $a This thesis presents a mathematical analysis of the problem of a penny-shaped hydraulic fracture propagating in an infinite, homogeneous, impermeable elastic medium. The fracture is driven by injection of an incompressible Newtonian fluid at its center.
520 $a There are three regimes of propagation, namely, viscosity-dominated, toughness-dominated, and mixed. The physical parameter characterizing the different propagation regimes is the ratio of the energy expended in the creation of new fracture surfaces to the energy dissipated in viscous fluid flow. If this controlling parameter is small, the toughness can be neglected; if it is large, the fluid can be assumed to be inviscid. If the controlling parameter is neither small nor large, the fracture propagates in the mixed regime and both toughness and viscosity are significant. Mathematically, the controlling parameter is a certain dimensionless toughness, which depends on all the parameters of the problem.
520 $a In the course of the research, semi-analytical solutions were obtained for two limiting regimes of propagation. The solution for the zero-toughness case is characterized by a specific asymptotic behavior near the fracture tip, which is less singular than the classical square root singularity of linear elastic fracture mechanics. Explicit use of this asymptote is a key element of the solution. For the large-toughness case, the solution is given as a two-term regular asymptotic expansion with respect to a small parameter, a dimensionless viscosity that is an inverse power of the dimensionless toughness. The importance of the second term in the expansion is discussed.
520 $a By matching the derived solutions with reliable numerical results, the bounds of the regimes of propagation are estimated. From the point of view of numerical modeling, it is critical to know in which regime the fracture is propagating. This is illustrated with the numerical simulation of a penny-shaped fracture propagating in the viscosity-dominated regime.
590 $a School code: 0130.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Engineering, Civil. $3 783781
650 4 $a Engineering, Petroleum. $3 1018448
690 $a 0346
690 $a 0543
690 $a 0765
710 2 0 $a University of Minnesota. $3 676231
773 0 $t Dissertation Abstracts International $g 61-09B.
790 $a 0130
790 1 0 $a Crouch, Steven L., $e advisor
790 1 0 $a Detournay, Emmanuel M., $e advisor
791 $a Ph.D.
792 $a 2000
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9989147