A Semi-Analytical Poroelastic Solution to Evaluate the Stability of a Borehole Drilled Through a Porous Medium Saturated with Two Immiscible Fluids

Abstract

Conventional drilling design tends to inaccurately predict the mud density needed for borehole stability because it assumes that the porous medium is fully saturated with a single fluid while in actuality it may have two or more fluids. This paper provides a new semi-analytical poroelastic solution for the case of an inclined borehole subjected to non-hydrostatic stresses in a porous medium saturated with two immiscible fluids, namely, water and gas. The new solution is obtained under plane strain condition. The wellbore loading is decomposed into axisymmetric and deviatoric cases. The time-dependent field variables are obtained by performing the inversion of the Laplace transforms. Based on the expansion of Laplace transform solution, we derive the unsaturated poroelastic asymptotic solutions for early times and for a small radial distance from an inclined wellbore. The model is verified by analytical solutions for the limiting case of a formation saturated with a single fluid. The impact of the unsaturated poroelastic effect on pore pressure, stresses and borehole stability is investigated. Our results show that the excess pore pressure due to the poroelastic effect is generally higher for the saturated case (water) than the unsaturated case due to the large difference between the compressibility of fluid phases (water and gas). The time-dependency of the poroelastic effect causes the safe mud pressure window of both the unsaturated and saturated cases to narrow and approach the long-time poroelastic one with increasing time. The safe mud pressure window narrows with increasing initial gas saturation. The commonly used assumption that the formation is fully saturated by one fluid (such as water) tends to be conservative in predicting the mud density required for borehole stability. This new semi-analytical poroelastic solution enables the drilling engineer to more accurately estimate the time-dependent stresses and the pore pressure around a borehole, thus allowing him to design the mud weight to ensure borehole stability.