Theory of borehole stability when drilling through salt formations

Abstract We present a mathematical analysis of borehole stability when drilling through rock salt. First, we consider an elastic transversely isotropic medium and find the optimal mud weight as a function of the vertical overburden and horizontal tectonic stresses. Then, the Zener and Maxwell mechanical models are used to model the effects of transient and steady-state creep flow, respectively, in isotropic media. Under certain conditions such as the absence of dilatational anelasticity, the Burger model can be used to describe the steady-state flow, including transient creep effects. The type of creep is regulated by critical octahedral-stress values that depend on temperature and pressure. A typical drilling results in conditions of plane strain, whose solution is given by Kirsch's equations. In this case, the borehole is subject to minimum and maximum horizontal stresses, which differ from the vertical stress. The analysis provides expressions for the shape of the borehole-cross section, the borehole-wall closure time, and the optimal mud weight to avoid wall collapse or expansion. It is shown that an anisotropic state of tectonic stress may require mud pressures exceeding the overburden stress and that the calculation should consider the joint optimization of the shape and area of the borehole cross section.