Analytical solutions for thermal-hydraulic-mechanical-chemical modeling of smectite illitization in bentonite buffers for nuclear waste disposal

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Nuclear waste is stored in canisters within underground repositories, surrounded by a buffer material like bentonite, which ensures isolation from the host rock due to its low hydraulic conductivity and high swelling potential. However, at high potassium ion concentrations and temperatures above 100 °C, bentonite transforms into illite, a low-swelling mineral. Many studies have addressed this phenomenon in different bentonites using numerical simulators. None has analytically modeled the phenomena of illitization and how changes in reactive surface area during drying cycles could influence the process. Furthermore, no analytical solutions address the impact of illitization and clay swelling on the transport of heat and chemical species such as K + in diffusion-dominant or advection-dominant systems. This study develops analytical models to predict temperature, water saturation, and potassium ion concentration evolution in the bentonite buffer and their effects on the smectite-to-illite transformation process. The developed models are the first to incorporate the effects of illitization and clay swelling on the heat and species transport in an engineered barrier system under various boundary conditions. The models are based on mass and energy balance principles, validated against existing temperature solutions, experimental and numerical simulation illitization data. Preliminary validation shows that incorporating the effect of declining reactive surface area improves illitization predictions by accounting for the reduction of interlayer smectite regions, which slows the illitization process. The models are then used to simulate multi-physics behavior in a nuclear repository, and their results are compared to numerical simulations conducted using TOUGHREACT-FLAC. Porosity reduction due to both mineral transformation and swelling affects not only fluid transport but also thermal dissipation in the buffer. Under limited K + availability, illitization becomes self-limiting, highlighting the potential buffering capacity of smectite-rich host rocks. When continuous K + supply is modeled (e.g., via feldspar dissolution), illitization proceeds for extended durations, indicating a need to evaluate mineral assemblages and groundwater chemistry during repository design. The findings highlight the models' effectiveness in predicting the evolution of temperature, potassium ion concentration, water saturation, and smectite content in the bentonite buffer, demonstrating their utility in understanding and predicting behavior in nuclear waste repositories.