ABSTRACT: Numerical simulations of hydraulic micro-fractures are used to provide insight into techniques commonly used for stress measurement at depth. These simulations encompass initiation and propagation of hydraulic fractures from a borehole in poroelastic rock. It is shown that poroelastic effects may have a significant influence on the determination of the principal stresses in permeable rock. Specifically, it is found that (1) the breakdown pressure is not necessarily associated with the fracture initiation at a borehole, (2) the time of fracture closure can be identified from borehole pressure logs and (3) poroelastic effects can cause the borehole pressure at the time of fracture closure to markedly exceed the minimum in-situ stress


There has been a considerable effort directed towards practical development of techniques for in-situ stress measurement using hydraulic fracturing[1]. However, there have been relatively few detailed simulations of these processes [2 ,3]. A series of simulations of hydraulic fracturing tests is presented. Here it is assumed that the rock mass is a poroelastic material. This assumption requires that the following phenomena be treated as fully coupled: (1) the fluid flow in the fracture,( 2) the deformation of the rock mass, and (3) the fluid flow in the rock. Treatment of the rock in this manner is a unique feature of the simulations presented herein.

A detailed description of the numerical procedure used in these simulations can be found in Ref. 4. Its salient characteristics are as follows: (1) the finite element method is used to approximate the fully coupled poroelastic solution for deformation and fluid flow in the rock mass, (2) a finite-difference approximation is used to model the fluid flow in the fractures, and (3) a generalized Dugdale-Barenblatt fracture model is incorporated as a natural product of the solution procedure. This fracture model allows the crack length to increase or decrease through the course of the simulation so that events related to shut-in and fracture closure can be investigated.

The results of these simulations are presented in the next section. In the third section, their significance is described and discussed with reference to published experimental and field data.


Hydraulic fracturing for the purpose of stress measurement involves the following: (1) pressurization of a borehole until a fracture is initiated; (2) controlled flow of fluid into the borehole to propagate the fracture a short distance; and (3) shut-in or cessation of the flow into the borehole, followed by monitoring of the pressure decline.

Figure1 . The finite element mesh used in the simulation of a series of hydraulically driven fractures in poroelastic rock. The fracture is constrained to propagate along the x-axis. (available in full paper)

The crack-mouth-pressure (CMP) versus time curve is then used to deduce the in-situ stress state. In this section, results are presented for detailed simulations of initiation and propagation of a hydraulic fracture from a borehole in a poroelastic material.

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