Modelling poroelastic hollow cylinder experiments with realistic boundary conditions

摘要

A general poroelastic solution for axisymmetrical plane strain problems with time dependent boundary conditions is developed in Laplace domain. Time-domain results are obtained using numerical inversion of the Laplace transform. Previously published solutions can be considered as special cases of the proposed solution. In particular, we could reproduce numerical results for solid and hollow poroelastic cylinders with suddenly applied load/pressure (Rice and deary. Rev. Geophys. Space Phys. 1976; 14:227; Schmitt. Tait and Spann, Int. J. Rock Mech. Min. Sci. 1993; 30:1057; Cui and Abousleiman, ASCE J. Eng. Mech. 2001; 127:391). The new solution is used to model laboratory tests on thick-walled hollow cylinders of Berea sandstone subjected to intensive pressure drawdown. In the experiments, pressure at the inner boundary of the hollow cylinder is observed to decline exponentially with a decay constant of 3-5 1/s. It is found that solutions with idealized step-function type inner boundary conditions overestimate the induced tensile radial stresses considerably. Although basic poroelastic phenomena can be modelled properly at long time following a stepwise change in pressure, realistic time varying boundary conditions predict actual rock behaviour better at early time. Experimentally observed axial stresses can be matched but appear to require different values for a and v than are measured at long time. The proposed solution can be used to calculate the stress and pore pressure distributions around boreholes under infinite/finite boundary conditions. Prospective applications include investigating the effect of gradually changing pore pressure, modelling open-hole cavity completions, and describing the phenomenon of wellbore collapse (bridging) during oil or gas blowouts.