Machine Learning‐Enhanced Modeling of Calcium Carbonate Nucleation in Porous Media Under Counter‐Diffusion Conditions

Abstract A counter‐diffusion reactive transport experiment was conducted to study calcium carbonate (CaCO 3 ) nucleation and growth in porous media, monitored in situ using synchrotron‐based techniques and modeled marrying the Classical and Non‐Classical Nucleation Theory in a machine learning‐enhanced 3D Lattice Boltzmann Model. By incorporating pH‐dependent saturation index thresholds for nucleation derived from free‐solutions experiments and accounting for stochastic induction times, the model attempts to probabilistically capture the nucleation timing and spatial distribution of CaCO 3 polymorphs and explores the influence of supersaturation gradients, spatial constraints, and nucleation probabilities. The model successfully captures the preferential nucleation of vaterite under high‐pH conditions, but the predicted spatial distribution of calcite nuclei deviates from experiments, revealing the limitations of using experimental data derived from nucleation studies in batch experiments, which may not directly apply to confined porous media in this study. Systematic variation of model parameters reveals that spatial and temporal sequence of polymorph formation are critically sensitive to supersaturation thresholds for nucleation. Importantly, our approach is highly flexible and can readily incorporate alternative nucleation threshold models tailored to different experimental or theoretical conditions. This adaptability is a key strength and underscores the primary contribution of this work. This study thus presents a novel reactive transport approach for simulating the nucleation of CaCO 3 polymorphs (calcite, vaterite, and amorphous calcium carbonate) in porous media. It establishes a foundation for understanding CaCO 3 nucleation and paves the way for future research on coupled precipitation, dissolution, and phase transition, bridging computational modeling with experimental insights into geochemical and environmental systems.