Effect of wellbore mechanical responses on stimulation initiation treatment

Many practical applications of rock mechanics require an understanding of the stress/strain state in the vicinity of a circular opening: Wellbore stability analysis; estimation of whether natural fractures may be open or closed, and thus can be imaged; analysis of safe density for drilling mud; design of stimulation treatments; derivation of far-field stress state based on deformations observed at the wellbore wall, etc. These analyses all require the adoption of a model. A typical model adopted for this purpose is the simple 2D analytical solution. Alternative models may use numerical methods. In each type of model, the calculations show that the existence of an approximately-circular opening causes the stress state to be perturbed in the close vicinity of that opening. If the far-field stress state is not isotropic (e.g., σ1 > σ2), then the calculations result in values for the stress components that vary with both radial direction, and with radial distance. Does it matter which model is adopted? If they are equivalent, then the choice might be simply one of convenience. If the methods result in different results (they do, as shown here), then it becomes necessary to understand what these models are actually doing, rather than assuming that we know about them from long familiarity. Here, we present an evaluation of the classical analytical method, along with a comparison of that approach against numerical methods. This analysis leads to the realization 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. This conclusion has clear implications for how one might choose between the methods.