A Constitutive Model For The Effective Stress-Strain Behaviour Of Oil Sands
Authors: Wan R.G. , Chan D.H. , Kosar K.M. 
Published: March 2010

Abstract
Extensive experimental data from drained triaxial tests on oil sands at different confining pressures and temperatures have led to the development of a non-associated generalized plasticity model in 3-D stress conditions. Many of the identifiable behavioral aspects such as hardening, softening, plastic volumetric expansion and contraction have been incorporated in the formulation. When implemented into the general purpose finite elements program ABAQUS, numerical results compare reasonably well with measured response. In trying to weigh merits of the model, it is interesting to note that the present study provides a consistent framework within which practical applications such as the computation of well casing oil sand formation interaction during in-situ thermal recovery of bitumen can be attempted.

Introduction
The use of in situ thermal methods such as steam injection through vertical as well as deviated well bores to deep seated oil sand reservoirs is common and relatively effective for the recovery of heavy oil and bitumen. There has been, however, numerous well casing failures reported during field injection trials. Due to the presence of two types of materials, namely shale and oil sand in the geological strata, strong stress and pore fluid gradients are created in the soil mass around the well bore. In particular, high differential shear stresses developed at the oil sand-shale interface during steam injection may cause instability and collapse of the well casing which compromises the good progress of oil production. The obvious solution to the casing deformation has been to stiffen the well easing installation, but in order to arrive at a rational and economical design, it is necessary to accurately evaluate the force distribution around the structure and deformation behavior of oil sand.
Numerical schemes such as the finite element method are readily available in several program packages, one of them being ABAQUS. Although they offer a wide range of applications which cover most common structural and geotechnical problems, it seems however, that there is no suitable geological material model which can specifically capture most of the constitutive behavioral aspects of oil sand. For that reason, the need for a comprehensive characterization of the stress-strain behavior of oil sand is fully acknowledged for a correct finite element analysis.
The deformation behavior of oil sand is governed by many factors. However, it can be conveniently considered as comprising of basically two main constituents: the pore fluids (water, bitumen, and gas) and the sand skeleton. The theoretical relationships governing the behavior of the pore fluid, as to describe gas ex-solution and other related aspects, have been first introduced by Harris and Sobkowicz(1) and subsequently extended by Byrne and Grigg(2). This paper does not treat the pore fluid response but rather focuses on the mathematical modeling of the sand skeleton as an elastic-plastic continuum.

Literature Review
The capability to realistically analyze oil sand behavior is a challenging task mainly due to its complexity and variability in response. As such, the inherent non-linear and history-dependent nature of the problem makes it necessary to resort to elaborate theories such as plasticity instead of simple linear elasticity for its modeling.