A Fully Analytical Solution of the Wellbore Stability Problem under Undrained Conditions Using a Linearised Cam-Clay Model

Abstract

This paper presents a linearised version of the Cam-Clay model fully integrated in the scope of the general theory of poroplasticity. The constitutive law which is developed in the scope of the effective plastic stress concept, only contains two plastic parameters (hardening modulus and slope of the critical state line). To be validated, the model is integrated over homogeneous stress paths (hydrostatic, drained triaxial and undrained triaxal) then compared with experimental data issued from conventional laboratory triaxial tests. In the second part, a simplified version of the model is applied to the wellbore boundary problem (vertical well) in an axisymmetric horizontal stress field and under undrained conditions. Given the linearity of the constitutive law and the a priori knowledge of the shape of the plastic region, the solution (stress, strain and pore pressure) is fully analytical. The solution shows that for an overconsolidated material (overconsolidation degree less than 2) the hoop stress is strongly relaxed in the plastic zone. The higher the compressibility of the saturating fluid, the larger the relaxation of the hoop stress. In terms of stability, the more compressible the fluid saturating the porous medium is, the more stable the well will be. Finally the larger the overconsolidation ratio is, the less stable the well will be.