A multiscale model of heavy metal biosorption in porous media by one-dimensional biofilms

A homogeneous soil-based field-scale model was constructed to study the biosorption of heavy metals, incorporating the impact of biofilms and their interactions with heavy metals at the pore scale. The model assumes a laminar flow through a porous medium in an advection-dominated regime. A volume averaging method was applied to build a macroscale model by upscaling the biofilm growth process from the pore scale. The biofilm model consists of two mono-species biofilms that grow separately within the soil pores, participate in biosorption processes with toxic heavy metals, and undergo growth due to dissolved substrate consumption and suspended bacteria attachment. A Monod-like kinetic rate coupled with intraparticle diffusion was employed to model the heavy metal concentration within the biofilm. This kinetic model, based on the Langmuir isotherm, was extended to include the adsorption rate change over time, considering the saturation mechanisms. The upscaling process results in a stiff system of hyperbolic equations, which are solved numerically using an in-house code implemented on the MATLAB platform, utilizing a second-order accurate central scheme (UCS2). Various scenarios were simulated by varying the adsorption affinity constant, metal inhibition of the biofilm, metal inflow concentration, planktonic cell inflow concentration, and flow velocity. Simulations have demonstrated that biofilms can prevent toxic metals from reaching groundwater through biosorption. Increased biofilm biomass, and thus, better biosorption effectiveness, was observed with higher maximum sorption capacity, inhibition coefficients, and planktonic cell inflow concentrations. Conversely, biosorption effectiveness decreases with increasing adsorption affinity coefficients, metal inflow concentrations, and flow rates.