"An upscaled model of heavy metal biosorption in homogeneous porous media"
A field scale model for heavy metals biosorption in homogeneous soils is constructed while considering the influence of biofilm and heavy metals interactions at the pore scale. The biofilm processes at the mesoscale are described by the Wanner-Gujer model for biofilm growth and then upscaled using the volume averaging approach to distinguish its effective parameters at the field scale [Gaebler et. al., 2022]. A laminar and convection-dominated regime is assumed for the flow within the soil. Within the soil pores, two separately growing bacteria species are assumed in the biofilm phase. Dissolved substrates and suspended bacteria are injected in the soil at a constant rate. A generic heavy metal is assumed to be transported in the soil and diffuse within the biofilm, affecting its overall growth rate. In turn, the biofilm retains this toxic metal through biosorption, and prevents it from reaching the underground water. The resulting macroscale model is described by a stiff system of hyperbolic equations to be solved numerically by the uniformly accurate central scheme of order 2 (UCS2) and using MATLAB platform. Different simulation scenarios have been investigated by varying the biofilm growth and biosorption parameters. The upscaled model accurately capture the mesoscale biosorption processes after a rigorous mathematical derivation.
Additional authors: Maria Rosaria Mattei, Department of Mathematics and applications ‘Renato Caccioppoli’, University of Naples Federico II, Naples, Italy; Fernando G. Fermoso, Instituto de la Grasa, Spanish National Research Council (CSIC), Seville, Spain; Luigi Frunzo, Department of Mathematics and applications ‘Renato Caccioppoli’, University of Naples Federico II, Naples, Italy