Continuum and combined continuum-discontinuum analysis of wellbore mechanics and stimulation response

Abstract

Wellbore drilling and stimulation activities are interlinked processes within the task of borehole construction. Before drilling a well, the initial stress state in the rock can be defined by three principal stresses, with a typical assumption that these consist of the vertical stress (σv), the maximum horizontal stress (σH) and the minimum horizontal stress (σh). After drilling, the stress state changes around the created borehole. The fundamental engineering problem then is to calculate the stresses around the created borehole and/or at the borehole’s wall. Numerous analytical and numerical models exist to estimate the stresses around a circular hole, but these models cannot explain the observed phenomena either in the field or the lab. Attention here is focused on models that are commonly used to predict the stress state around a circular opening. These models do not account for the sequence of the physical processes, leading to an inadequate stress state estimation. This research investigates the 2D classical analytical method, along with a comparison of that approach against numerical methods. This investigation reveals that the models are not equivalent. This is not because of mathematical issues, but is due to the fact that the mechanical systems expressed by these models are not equivalent. The drilling model captures the physics of the real process which makes it possible to explain some phenomena observed in field and laboratory tests. The drilling model approach is applied for several sedimentary rock examples. The combined continuum-discontinuum method reveals its capability in calculating rock failure and deformation that is comparable to some published laboratory drilling tests. Also, the simulation results shed light into the complex fracture growth regime around the wellbore. Drilling and Hydraulic fracture simulation is carried out for Berea sandstone using both the continuum and the combined continuum-discontinuum methods. The results are in good agreement which identifies a practical engineering method for larger models. The fracturing initiates in Mode II (shear) near the circumference of the wellbore aligned with the maximum stress. At later stages, Mode I (tensile) fractures also develop and propagate the fracture parallel to the maximum horizontal stress. This fracturing mechanism continues for as long as the pressure is applied.