ABSTRACT:

This paper investigates possible breakdown criteria in the limit of slow and fast pressurization of a borehole, and the transition between these two bounds as the rate of pressurization varies. In this analysis, the existence of a critically oriented crack at the borehole wall, that triggers the failure process, is recognized. Two limiting cases, corresponding to an edge and a Griffith crack, are considered.

RESUME:

On presente un modèle pour predire la pression de claquage atteinte lors d'une mise en charge hydraulique d'un puits de forage, eflectuee à vitesse constante de pressurisation. On etudie la dependance de la pression de claquage vis a vis de la vitesse de pressurisation, et les limites correspondant aux conditions asymptotiques de faible et de grande vitesse de pressurisation. Deux cas limites sont traites: celui d'une fissure de bord et celui d'une fissure de Griffith.

ZUSAMMENFASSUNG:

Mit der vorliegenden Arbeit werden mögliche Bruckkriterien zwischen den Gren- Zen einer langsamen und einer schnellen Unterdrucksetzung eines Bohrloches und der Übergang zwischen diesen zwei Grenzen, wenn die Unterdrucksetzungsrate variiert, untersucht. Mit der Analyse wurde die Existenz eines kritisch orientierten Risses in der Bohrlochwand, welcher den Bruchprozeß auslöst, festgestellt. Zwei limitierende Faile, welche mit einem Kanten- und einem Griffith Riß uebereinstimmen, werden betrachtet.

1 INTRODUCTION

The breakdown pressure, Pb, the critical pressure at which tensile failure ("breakdown") is initiated at the borehole wall by fluid injection, is a crucial parameter for interpreting results of in-situ hydraulic fracturing stress tests. The breakdown pressure appears, however, to depend strongly on the pressurization rate A, i.e. Pb = Pb (A), as evidenced by laboratory experiments (Haimson and Zhao, 1991; Schmitt and Zoback, 1992,1993). Theoretical studies (Detournay and Cheng, 1992; Detournay and Carbonell, 1994; Garagash and Detournay, 1996) actually suggest that the classical breakdown criteria (Hubbert and Willis, 1957; Haimson and Fairhurst, 1967), which predict Pb to be independent of the pressurization rate A, correspond to particular asymptotic regimes of pressurization rate. Recently, the dependence of Pb on A was analyzed using a model in which a micro-crack of length λ small compared to the borehole radius and viscous flow in the crack was considered explicitly (Garagash and Detournay, 1996). Based on this solution, threshold values of the pressurization rate, A1 and Au, for the slow and fast asymptotic regimes were obtained. However, the other limiting case of practical importance needs to be considered, namely, when the length of preexisting crack is large compared to borehole radius. For the limit, the problem can be approximated by a Griffith crack. This case is of interest to interpret the reopening of large in-situ hydraulic fractures and also possibly the results of laboratory experiments carried out with small radius boreholes.

2 MATHEMATICAL FORMULATION
2.1 Governing equations

Consider a borehole with radius a in an infinite elastic domain under internal fluid pressure Pw and far-field loading characterized by isotropic and deviatoric components, Po and So, respectively. Consider also a critically oriented crack of length λ at the edge of the borehole, which is aligned with the far-field maximum compressive stress direction (sec Fig. 1a). We consider two limiting cases. The first case is characterized by a»λ; i.e. the crack is effectively a small defect at the boundary of the borehole. It can, hence, be treated as an edge crack of a half-plane subjected to a far-field loading, σ, in the direction perpendicular to the crack (sec Fig. 1b).

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