A semi-analytic elastoplastic model predicting the onset of failure in wellbores subjected to in-situ stress and pore pressure fields is presented. The model also has sanding applications. Rock elastic behaviour is modelled as being linear, with the plastic response described by a non-associated Mohr-Coulomb strain hardening deformation theory. The pore pressure gradient is taken into account using a source solution at the wellbore Constitutive relations are calibrated using triaxial tests on Castlegate Sandstone cores. Hollow cylinder experiments, again performed with Castlegate sandstone, are used to evaluate predictions. Numerical examples illustrate how constitutive parameters influence the stress state around the wellbore and the onset of failure.


The minimum mud weight required to prevent wellbore wall failure is often estimated using elastic-brittle models, which take the formation to be linearly elastic and assume failure occurs when the peak strength of the rock is attained (Bradley l979a, 1979b). These models are, however, over conservative: the predicted minimum mud weight usually exceeds that required during drilling.

Many models estimate the minimum mud weight more precisely than elastic-brittle theory. Most are based on either non-linear elasticity or elastoplasticity. In non-linear elastic models (Santarelli 1987) the stress rate is a homogenous linear function of the deformation rate, with Young's modulus dependent on hydrostatic pressure. The main advantage of these models over those based on elastoplasticity is simplicity. Semi-analytic elasto-plastic models assume the rock is either elastic-perfectly plastic (Detournay 1986, Detournay and Fairhurst 1987, Wang and Dusseault 1991a, 1991b) or elastic with linear hardening (Morita et al. 1989) However, neither model describes the hardening sufficiently accurately and neither, therefore, are ideally suited to rock behaviour. Fully numerical models predominantly utilize the finite element method.

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