Implementation of a Fully Coupled Wellbore Stability Model for Well Drilling Design

During wellbore drilling operations and successive oil/gas production activities, both the natural stresses and the original thermodynamic equilibrium of virgin rock formations are altered, and, as a result, borehole instability phenomena can arise with time. Instability phenomena can be so severe to determine the wellbore abandonment because of its complete collapse. During the design phase of drilling operations, the adoption of a wellbore instability modeling approach is fundamental to systematically take into consideration time-dependent alterations of the initial natural equilibrium. In this paper the possibility of investigating both the stress-strain and the thermo-dynamic formation behavior through a fully coupled thermo-poro-elasto-plastic approach is discussed. The numerical solution adopted for the model implementation is presented. In the fully coupled approach, porous flow and stress-strain calculations are performed together: the whole system is discretised on one grid domain and solved simultaneously for both the thermodynamic variables (such as: temperature and pressure), and the geomechanical response (such as: displacements). This approach has the advantage of internal consistency and stability; furthermore, it preserves second order convergence of nonlinear iterations. In order to implement the plastic analysis an iteratively coupled approach was adopted in the fully coupled routine. According to the iterative coupling technique, the model basic equations (porous flow and rock deformation) and the plastic behaviour equations are solved separately and sequentially at each non-linear iteration. This is achieved by the solution of two nested Newton-Raphson cycles at each time-step. The iterative coupling approach corresponds to an implicit treatment of the plastic variables, essential to preserve the stability of the elasto-plastic solution. Wellbore stability analyses are also presented to prove the effectiveness of the proposed model to investigate the potential impact of time-dependent phenomena on the well drilling design.