Abstract

Theory of a modified hyperbolic stress-strain model that can account for shear-induced dilatational effects is outlined and to facilitate the application of the model in simulation studies, the influence of parameters that control the stress-strain response are graphically presented and discussed. The model is applied to simulate several triaxial tests on good-quality Athabasca oil sand samples under isothermal and non-isothermal conditions. The tests include (1) compressive failure of an oil sand sample at room temperature under drained conditions, (2) compressive failure of an oil sand sample under drained and elevated temperature conditions, and (3) temperature-induced failure of an oil sand sample resulting from the excess pore fluid pressure generated under untrained conditions.

The analyses depict the laboratory-measured relationships between shear stress and axial strain, volumetric strain (including shear-induced dilatancy) and axial strain, and pore fluid pressure and axial strain remarkably well. The findings are used to recommend stiffness properties, strength properties, and shear-induced dilatational properties within the hyperbolic constitutive stress-strain framework for modeling geomechanical response of oil sand under isothermal and elevated temperature conditions.

Introduction

All the, processes involved in fluid (oil, water, or gas) extraction or injection cause changes in the effective stress state within the reservoir formation. The geomechanical response of the reservoir, such as changes in volumetric strain and porosity, is primarily governed by changes in the effective stress which simply is the difference between changes in the total stress and pore fluid pressure in the system. Physical manifestations of the geomechanical effects in oil recovery projects are exemplified by formation fracturing(1), wellbore instability(2), sand production(3), operational-induced changes in permeability(4,5) (or permeability damage), and ground-surface deformations(6).

Although there is a widely-held acceptance of the validity of the effective stress concept in porous media(7), there is no general agreement on any unique relationship between changes in effective stress and the resulting strains for all natural deposits. Some of the difficulties in devising a unique constitutive model stem from the fact that soils generally behave in a non-linear manner where the non-linearity depends on the soil history, stress path, stress and strain level rate of loading, temperature, strength properties, hydraulic properties, creep properties, initial porosity, and particle size and gradation. The conventional constitutive models are basically composed of mathematical formulations that describe the response of ideal materials (e.g., elastoplastic obeying an associated flow rule) which are then modified to depict a particular soil response under laboratory (triaxial) test conditions.

The roots of many (at least over hundred) constitutive models available in the literature are basically founded on probably less than five rationally different concepts(8); however, because of the elegant mathematical and numerical modifications that might have been introduced in constructing these models for an intended application, a false appearance of the emergence of a new and radically different (or superior) technique for general stress-strain analyses is inadvertently given. Although the activities in the area of constitutive modeling have culminated in much deeper insight into the complex mechanisms governing the response of natural deposits, the wealth of apparently different models that have been

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