Mathematical Models for Characterizing Heavy Metals Batch and Column Adsorption: Study of Adsorption, Transport Parameters, and Numerical Computation Cost

Several investigations have been conducted to examine the adsorption behavior of heavy metal ions, primarily focusing on isotherms, kinetics, and basic mathematical models. Nevertheless, these studies often lacked comprehensive mass transfer models to assess heavy metal adsorption in both batch and continuous modes. The current study showcases the application of diverse mathematical models to characterize both batch and column adsorption of Ni(II) onto epichlorohydrin-modified Putranjiva roxburghii seeds. The batch adsorption investigation employs the pore volume and surface diffusion (PVSD) model, while continuous adsorption of Ni(II) is represented by the convective–dispersive (CD) and PVSD-CD models. These mathematical formulations involve coupled algebraic, ordinary, and partial differential equations, which are solved numerically using gPROMS. In the batch mode, the predicted concentration decay curves exhibit an excellent agreement with experimental data, facilitating estimations of pore volume ( \({D}_{\text{P}}\) $D_{\text{P}}$ ≈10^–11 m²/s) and surface diffusion ( \({D}_{\text{S}}\) $D_{\text{S}}$ ≈ 10^–13 m²/s) coefficients. Similarly, for column adsorption, the breakthrough curves estimated through a combined CD and PVSD-CD approach demonstrate a good fit with experimental data, providing values for mass transfer coefficient ( \({k}_{\text{L}}\) $k_{\text{L}}$ ≈10^–4 m/s), axial dispersion coefficient ( \({D}_{L}\) $D_L$ , \({D}_{P}\) $D_P$ , and \({D}_{S}\) $D_S$ ). The efficacy of the models in depicting Ni(II)-EPRS adsorption systems, both in batch and continuous modes, is assessed through statistical analysis. Additionally, the computational cost of simulation is evaluated across various realistic scenarios, encompassing different transport parameters, isotherm types, variables, mesh sizes, and reporting time intervals. These findings illuminate crucial aspects relevant to numerical simulation and hold promise for informing more complex adsorption operations.