Carbonation-Front Prediction and Practical Identifiability of Transport–Reaction Parameters in Solid-Waste Backfill Materials Using Inverse Modeling

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Abstract
Carbonation in CO2-storage solid-waste backfill materials couples CO2 transport, mineral reaction, and strength evolution, making carbonation-front prediction and transport–reaction inference important for evaluating sequestration performance. This study proposes an evidence-ranked, physics-guided inverse-learning framework for carbonation-front prediction, auxiliary strength reconstruction, PDE-residual assessment, and practical-identifiability analysis. The framework represents carbonation using group-conditioned latent fields of effective CO2 concentration and remaining reactive capacity, maps latent carbonation degree to measured depth through a differentiable front operator, and reconstructs unconfined compressive strength through a supervised auxiliary head. Empirical front laws and reaction–diffusion physics-informed neural-network variants were evaluated using held-out ranking, repeated stratified splits, residual-weight sweeps, front-operator threshold and smoothing-coefficient sensitivity checks, profile-likelihood and Fisher-information diagnostics, and controlled synthetic tests. Results show that the grouped Weibull front law achieved the best short-range carbonation-depth interpolation, while the retained constant-diffusion PINN was used as a diagnostic formulation within the physics-guided family to improve auxiliary strength reconstruction and to evaluate residual consistency, front-threshold selection, parameter sharing, and inverse-parameter behavior rather than to replace the empirical depth regressor. Increasing the PDE-residual weight substantially reduced residual magnitudes, but profile-likelihood and Fisher-information diagnostics indicated strong parameter trade-offs; the fitted diffusion, reaction, depletion, and diffusion–decay quantities are therefore interpreted as effective, observation-conditional parameters rather than unique material constants. The proposed framework provides a prediction-first and attribution-aware approach for analyzing carbonation evolution in solid-waste backfill materials and supports coordinated assessment of front advancement, strength response, and transport–reaction behavior, while explicitly delimiting the generalization and physical interpretation that can be supported by sparse literature-derived observations.
Funding Information
  • Coal-Major Project (2026ZD1703500)
  • National Natural Science Foundation of China (52222404)
  • National Natural Science Foundation of China (52574165)
  • Shaanxi Provincial Key Research and Development Program (2023-LL-QY-07)

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