Parameterization and prediction of environment-dependent colloid transport in saturated porous media: A physics-informed machine learning approach.

Colloid transport in porous media exhibits pronounced variability under varying solution chemistry, hydrodynamic conditions, and pore structural characteristics. Conventional advection-dispersion models typically treat transport parameters as constants, which limits their predictive capability across variable environmental conditions. This study develops a physics-informed machine learning (ML) framework to parameterize and predict colloid transport under varying environmental conditions by deriving explicit expressions for key transport parameters. Built on 98 column-scale experimental records, the method first identified the dominant environmental controls on each transport parameter through an integrated importance analysis. It then applied nonlinear fitting constrained by colloid filtration theory (CFT) to the reversible retention-release parameters and a hybrid eXtreme Gradient Boosting (XGBoost)-Python Symbolic Regression (PySR) framework to the irreversible retention parameters. The explicit expressions relate transport parameters to flow rate, ionic strength, pH, porosity, and particle-to-grain size ratio. Predictive performance was evaluated by cross-validation, comparison with literature parameters, and breakthrough curve simulation. Results show that the proposed parameterizations accurately captured environment-dependent transport parameters and reproduced breakthrough curves. Flow rate mainly controlled colloid transport through advection, whereas its indirect effect through parameter regulation was limited. Porosity influenced both transport pathways and retention related parameters, with parameter regulation playing the dominant role. pH, ionic strength, and particle-to-grain size ratio primarily controlled deposition, release, and retention capacity by modifying interfacial interactions, electrostatic repulsion, and physical straining. The proposed framework provides a physically interpretable and transferable strategy for modeling colloid transport in saturated porous media under varying environmental conditions.