A modified creep analytical model for predicting shale wellbore closure in abandonment and CCS/CCUS applications

Resumo

Ensuring long-term well integrity remains a critical challenge in plug and abandonment (P&A) and carbon capture, utilization, and storage (CCS/CCUS) operations, particularly in clayey formations like shales that exhibit time-dependent deformation. In such environments, wellbore closure due to creep forming a geological barrier contributes to zonal isolation and long-term sealing. This study proposes a modified creep analytical model that extends the classical Barker solution, originally developed for salt formations, to capture the creep behavior of shales. The formulation adopts deviatoric stress instead of the difference between horizontal stress and wellbore pressure as the main driver of time-dependent deformation, consistent with viscoelastic/viscoplastic constitutive models relevant to salt and shale geomechanics. The stress state surrounding the wellbore right after drilling is derived using Kirsch’s elastic solution, enabling a closed-form expression of the deviatoric stress field. Next, creep behavior is activated, and a time-dependent exponential decay function, calibrated using finite element simulations in ABAQUS, is introduced to capture progressive stress relaxation during material deformation. The resulting stress field is incorporated into a semi-analytical, iterative framework for computing wellbore radius evolution over time, based on a creep law that depends on stress, temperature, and empirically defined material parameters. The model is implemented in Python within a lightweight computational framework, offering rapid, yet robust, assessments suitable for field-scale applications. Validation against numerical simulations demonstrates strong agreement, underscoring the model’s applicability for integrity evaluation and barrier design in P&A and CCS/CCUS scenarios. The proposed framework offers a computationally efficient, physically consistent approach for predicting long-term wellbore performance in creeping shale formations.