To characterize the geomechanical behaviour of oil sand formations under the boundary conditions generally encountered in practice, a new stress-strain constitutive model is developed. The mathematical concept used in developing this model is based on three well-established theories:

  1. the hyperbolic nonlinear elastic behaviour prior to yielding,

  2. critical-state elasto-plastic behaviour following yielding, and

  3. Mohr-Coulomb criterion at failure.

This model provides a logical unification of these three theories and thus obviates the need for making simplifying assumptions about the oil sand behaviour in analysing field problems. One of the attractive features of this model for practical applications is that it can be numerically described by using the geomechanical parameters that can be normally obtained from routine laboratory tests.


In all oil recovery projects, the formation is subjected to very harsh physical conditions which often results in the mechanical failure of the affected zones. The mechanical characteristics of the formation directly influence the aspects related to the fluid now through the formation. In the petroleum engineering practice, however, the analyses with respect the simulation or prediction of the reservoir response are commonly performed with no reference to the stress/strain behaviour of the formation. This cannot be justified unless:

  • the formation is comprised of incompressiblend well-cemented material (i.e., rock-like materials); and

  • the applied stress system to the formation, such as those due to drilling the wellbore, application of heat, or hydraulic fracturing, is below the yield strength of the formation (i.e., formation behaviour is elastic).

These conditions are generally not met in the conventional recovery projects from oil sands, consequently the errors involved in neglecting thegeomechanical aspects of the formation can be significant.

The realization of the linkage between the mechanical behaviour of the porous medium and the fluid within its pore spaces by Terzaghi (1) in 1925, gave birth to the discipline of Soil Mechanics and the practice of Geomechanical Engineering. As first pioneered by Terzaghi, central to the understanding of the behaviour of saturated porous media is the principle of effective stress which simply states that the soil (or formation) behaviour is governed by the difference between Local stress and the pore fluid pressure. All the processes involved in fluid extraction or injection cause changes in the effective stress within the reservoir. The physical manifestations of the formation response to changes in effective stress are exemplified by formation fracturing, sand inflow into the wellbore (well sanding or sand production), shearing of the well casings and pipe slucking, induced changes in the permeability characteristics via changes in porosity, and formation subsidence. In situations where the formation behaviour is deemed to affect the fluid response, it is reasonable to suspect that the observed fluid-flow patterns cannot be satisfactorily matched by methods that solely depend on the fluid-flow theories.

In Vaziri(2) the description of a fully coupled fluid now and the mechanical behaviour of its transmitting medium was provided, and in Vaziri(3) it was shown how such a model can be used effectively to understand the mechanisms of well bore instability and sand inflow into wellbores.

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