On the Wellbore Stress Change Caused by Drawdown and Depletion: An Analytical Model for a Vertical Well in a Thin Reservoir

Abstract

Summary An analytical model is presented to describe the stress change at the wall of a vertical wellbore because of drawdown and reservoir depletion. The model predicts a lower effective tangential stress and higher effective axial stress (at a given drawdown) than the popular model of Risnes, Bratli, and Horsrud (RBH) model (Risnes et al. 1982; Bratli et al. 1983; Fjær et al. 2008). The reason for this difference is that our model is valid for a finite reservoir thickness ("thin reservoir"), whereas the RBH model is constrained by the condition of an infinite reservoir thickness. We modeled the production-induced stress change in two reservoirs with different rock properties: Reservoir A has a porosity of approximately 20% and a permeability of up to 30 md; Reservoir B has a porosity of approximately 30% and a permeability of a few darcies. Calculated wellbore stress paths were combined with mechanical properties from core deformation experiments to evaluate the risk of drawdown-induced/depletion-induced shear failure. If we consider only the experimental shear-failure data collected on samples from Reservoir A for the shear-failure limit, then, according to the present model, the planned drawdown of 34 MPa will not lead to wellbore shear failure. Even after 34 MPa of depletion, a drawdown of 34 MPa can be applied safely in Reservoir A. For high-permeability Reservoir B, the model predicts that shear failure of the borehole wall will not occur in the first phase of production, when there is only a drawdown of up to 2 MPa and no depletion. Depending on the shear-failure criterion chosen, the model predicts shear failure after 25 to 42 MPa of depletion. Massive sand production was observed only after some 40 MPa of depletion, confirming that elastic-brittle models are conservative in predicting drawdown-induced or depletion-induced shear failure in a borehole, notably in high-porosity rocks. Our examples show their value in qualitative comparative analysis of shear failure and sand-production risk.