Advanced modeling of Pb and Zn reactive transport using HYDRUS-1D to refine metal sorption and leaching under dynamic conditions

• Batch experiments tended to overestimate amendment performance in column systems. • ML-enhanced batch data enabled accurate reactive transport modeling. • A nonlinear regression and ML-based conversion formula was developed. • Framework reduces need for column tests without compromising accuracy. Accurate prediction of risky metal transport in soil is essential for developing effective remediation strategies. This study presents a novel modeling approach that integrates batch and dynamic column experiments with reactive transport modeling in HYDRUS-1D to evaluate the behavior of Zn and Pb in soil amended with biochar (BCH), amorphous manganese oxide (AMO), and their mixture (BCH + AMO). Sorption parameters were initially derived from batch equilibrium experiments and fitted using the commonly applied Freundlich and Langmuir isotherms. Dynamic soil column experiments conducted under saturated flow conditions revealed marked differences in amendment performance, with the BCH + AMO mixture demonstrating the highest retention and stability for both metals. Breakthrough curves were modeled using the Thomas model, which confirmed the presence of competitive sorption and pH-dependent precipitation, particularly for Pb. Initial attempts to apply batch-derived parameters in HYDRUS-1D resulted in an overestimation of sorption (by approximately 45%), necessitating inverse optimization. To address this issue, a conversion formula based on nonlinear regression and machine learning was developed. This enabled the translation of batch-derived Freundlich parameters ( K f and n ) into values suitable for dynamic modeling ( n real ). As an innovative and added value, the resulting integrated modeling framework reduces reliance on resource-intensive column testing while maintaining accuracy in simulating contaminant transport in saturated soils. Validated in flood-prone soil, this approach shows promise for application in systems such as constructed wetlands and other environments with stable pH and redox conditions. These findings help bridge the gap between static batch data and dynamic field scenarios, providing a robust tool for rapid assessment and prediction of the metal sorption efficiency of soil amendments under real-world conditions.