Analyses of Inclined Boreholes in Poroelastic Media

Solutions for the borehole problem based on Biot’s poroelasticity theory have shown that drilling through fluid saturated formations, gives rise to time-dependent stress and pore pressure fields in the vicinity of the borehole. As a natural consequence, borehole stability in such formations is of a time-dependent nature. However, existing analyses are based on two limiting cases viz., constant pore pressure and/or no flux boundary conditions at the borehole wall. Adding time dependency to the pore fluid boundary conditions can simulate realistic field conditions such as those observed during hydraulic fracturing, fluid injection or development of filter cake. Analytical solutions for inclined boreholes with time-dependent pore pressure and flux boundary conditions at the borehole wall are presented in this paper. Analysis is carried out for two special cases of the ramp-type pore pressure and linearly reducing flux boundary conditions. Analytical solutions are supplemented with asymptotic solutions for small and large time analysis. The effects of these conditions on stress concentrations near the borehole wall and their implications on borehole stability are examined in detail.