A Semianalytical Poroelastic Solution To Evaluate the Stability of a Borehole Drilled Through a Porous Medium Saturated with Two Immiscible Fluids

Abstract

Summary Conventional drilling design assumes that the porous rock is fully saturated with a single fluid and therefore tends to inaccurately predict the mud weight needed for borehole stability because the pore space of the porous rock may actually have two or more fluids. This paper provides a new semianalytical poroelastic solution for the case of an inclined borehole subjected to nonhydrostatic stresses in a porous medium saturated with two immiscible fluids: 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. On the basis of the expansion of the Laplace-transform solution, we derive the unsaturated poroelastic asymptotic solutions for early times and for a small radial distance from an inclined wellbore. Sensitivity analyses are performed on different ratios of bulk modulus of two fluid phases to pore pressures of the unsaturated case. In addition, the comparative analyses of pore-pressure differences are made between the unsaturated and saturated cases. The impact of the unsaturated poroelastic effect on pore pressure, stresses, and borehole stability is investigated. Our results show that the excess pore pressure caused by the poroelastic effect is generally higher for the saturated case (water) than the unsaturated case because of 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. Contrary to the unsaturated case, the saturated case that assumes the formation to be saturated by one fluid (e.g., water) tends to optimistically predict a wider safe-mud-pressure window required for borehole stability. This new semianalytical poroelastic solution enables the drilling engineer to more accurately estimate the time-dependent stresses and the pore pressure around a borehole, thus allowing a mud weight design that will ensure borehole stability.