A Poroelastic PKN Hydraulic Fracture Model Based on an Explicit Moving Mesh Algorithm

[+] Author and Article Information
E. Detournay

Schlumberger Cambridge Research, Cambridge, England

A. H.-D. Cheng

Department of Civil Engineering, University of Delaware, Newark, DE 19716

J. D. McLennan

TerraTek Inc., Salt Lake City, UT 84108

J. Energy Resour. Technol 112(4), 224-230 (Dec 01, 1990) (7 pages) doi:10.1115/1.2905762 History: Received January 25, 1990; Revised September 14, 1990; Online April 16, 2008


This paper describes the mathematical formulation of a Perkins-Kern-Nordgren (PKN) fracture model, that accounts for the existence of poroelastic effects in the reservoir. The poroelastic effects, induced by leak-off of the fracturing fluid, are treated in a manner consistent with the basic assumptions of the PKN model, by means of a transient influence function. The fracture model is formulated in a moving coordinates system and solved using an explicit finite difference technique. The numerical algorithm has the following features: fixed mesh, adaptive control of the time step, and unconstrained fracture length during shut-in. Numerical simulation with this model indicates that poroelastic processes could be responsible for a significant increase of the treatment pressure, but that they have virtually no influence on the fracture length and fracture width.

Copyright © 1990 by The American Society of Mechanical Engineers
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