Variational Principles for Hydraulic Fracturing

[+] Author and Article Information
S. H. Advani, T. S. Lee

Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015

R. H. Dean

ARCO Oil and Gas Co., Plano, TX 75075

J. Appl. Mech 59(4), 819-826 (Dec 01, 1992) (8 pages) doi:10.1115/1.2894048 History: Received March 14, 1991; Revised November 12, 1991; Online March 31, 2008


A new application of an energy rate variational principle for hydraulic fracturing processes is introduced. The formation structural, fracture mechanics, and fracture fluid flow responses are integrally coupled in this treatment. This unified principle, with various specialized forms, provides a formal framework for the study of continuum as well as discrete models. The applicability of the developed formulations is demonstrated by deriving time-explicit solutions for a penny-shaped model and comparing numerical results with corresponding responses from Lagrangian and finite element methods.

Copyright © 1992 by The American Society of Mechanical Engineers
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