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The paper describes a model to predict and analyze the time-dependent closure of a borehole drilled in a soft rock subjected to an initial isotropic stress, and the build-up of stress on a rigid casing after contact with the deforming rock. The rock behaves as a viscoplastic material characterized by a Mohr-Coulomb yield criterion and plastic potential, and by a time-dependent stress-strain deviatoric response akin to a Bingham rheology. The model formulation recognizes the particular structure of the solution, namely that the borehole is encircled by an evolving viscoplastic annulus, itself surrounded by an infinite domain, where the rock is either elastic or is unloading elastically.Noting that the solution outside the viscoplastic boundary is given explicitly by the Lamé solution, the evolution problem is formulated as an initial boundary value problem in the viscoplastic region only, but with a free boundary -the growing or shrinking interface between the viscoplastic and the elastic domains. The equations governing the mechanical fields and the evolution of viscoplastic boundary are spatially discretized on a moving mesh with a fixed

The current study shows that heating a cased borehole in low-permeability shale rock can induce plastic deformation, leading to the closure of the casing annulus and decreasing annulus connectivity. The thermally induced borehole closure is interesting for the field operation of plug and abandonment (P&A), as it potentially saves operation cost and time by avoiding cutting casing and cementing. Lab experiments and numerical simulations are implemented to investigate the thermally induced borehole closure. Pierre shale and a field shale are tested. The lab experiments are performed by heating the borehole wall in a 10-cm-OD hollow cylinder specimen. Here, a novel experimental setup is applied, allowing for measuring temperature and pore pressure at different radii inside the specimen. Both the experimental data and the post-test CT images of the rock samples indicate the rock failure by borehole heating, and under certain conditions, heating results in an annulus closure. The decrease of hydraulic conductivity through the casing annulus is observed, but this decrease is not enough to form the hydraulic-sealed annulus barrier, based on the results obtained so far. Lab-scale finite-element simulations aim to match the lab results to obtain poro-elastoplastic parameters. Then the field-scale simulations assess the formation of shale barriers by heating in field scenarios. Overall, (i) the lab experiments show that heating a borehole can increase the pore pressure in shale and hence induce rock failure; (ii) the numerical simulations match the experimental results reasonably well and indicate that the heating-induced borehole closure can sufficiently seal the casing annulus in the field-scale simulation.

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