ABSTRACT:

Three non-linear elastic constitutive models accounting for both pre-peak non-linear effects and stiffness increase with confining stress are formulated and applied to stress-strain analysis around circular openings in rock. These models present extension of the constitutive equations of linear elasticity to nonlinear materials obtained by replacing classic elastic moduli K (bulk modulus), and G (shear modulus) of linear elasticity with radius-, stress-, or strain-dependent functions introduced in a form of power series. Depending on the model used, model parameters can be identified from uniaxial, hydrostatic, or triaxial compression tests.

RESUME:

Le developpement de contrainte et Ie changement de rigidite autour des excavations et trous de forage dans les geornateriaux sont etudies en introduisant des modèles d'elasticite non-lineaire pour les deformations avant l'affaiblissement (avant la rupture). Ces approches constituent des extensions d'analyses classiques, et ils sont crees en remplacent les modules de deformation (module de Young, coefficient de Poisson) par des modules qui sont fonctions de contrainte, de rayon, ou de deformation, exprimes en forme de serie. Pour les trois approches que nous presentons, ces fonctions peuvent etre quantifiees en utilisant les resultats des essais en compression hydrostatique et deviatorique

ZUSAMMENFASSUNG:

Drei nicht-lineare elastische Modelle, die nicht-lineare Spannungsspitzeneffekte sowie die Festigkeitszunahme bei zunehmender Drueckspannung beruecksichtigen, sind formuliert worden und zur Spannungs-Dehnungsanalyse im Umfeld von kreisförmiger öffnungen in Felsgestein angewendet worden. Diese Modelle stellen die Erweiterung der bestimmenden Gleichungen der linearen Elastizitatstheorie auf nicht-lineare Materialen dar, indem der klassische Elastizitatsmodul K° und der Schubmodul G° der linearen Elastizitatstheorie mit radius-, spannungs- und dehnungsabhangigen Funktion, die in der Form von Polynomen geschrieben sind, ersetzt werden. In Abhangigkeit vom verwendeten Modell können die Modellparameter aus einachsigen, hydrostatischen oder dreiachsigen Druckversuchen bestimmt werden.

1 INTRODUCTION

Exploration wells have normally been drilled vertical, but lately highly deviated and horizontal wells are becoming commonplace. This provides an opportunity for more effective exploitation of our petroleum resources, but presents new challenges for well planning and stability analysis, meaning that better analysis tools have to be used. In drilling deviated wells, we are bound to meet the following challenges, relevant to both drilling and production: - Mechanical failure of the formation - Lost circulation due to fracturing of the wellbore - Fracture stimulation through fluid injection - Thermal effects from water injection - Reservoir management and compaction issues The challenges listed above represent large expenditures because the economic consequences of borehole instability are a major drilling cost component. This is illustrated in Fig. 1. An example from this figure shows that oil companies operating on the Norwegian Shelf paid for, but never drilled, around 13 wells per year for the last 4 years. Thus, to predict stresses near a borehole is of direct economic importance for petroleum companies. Borehole stresses are controlled by rock mass material properties; the stress-strain-flow-yield behaviour of the formations around the wellbore strongly affect well stability and control responses to changes in extrinsic conditions (stress, pressure, temperature, geometry). For economic reasons, because of scale effects and the high stresses associated with deep boreholes, small- and large-scale experimental tests are of limited value. Numerical and analytical simulations of stresses and displacements around openings remain of interest, and such simulations constitute the scope of this paper. In this paper we make a contribution to providing tools for addressing some of the problems listed above. The goal of our research is to generate semi analytical (SA) models for stress analysis around openings, taking into account material non-linearities, elastoplastic (EP) behaviour and steady-state fluid flow. We prefer to avoid complex numerical methods such as finite elements (FE), if possible. Issues like thermal effects or anisotropic stresses are not considered at this time. Models developed assume that states of deviatoric deformation are superimposed on states of hydrostatic deformation. Thus, model parameters can be identified separately for hydrostatic and deviatoric states.

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