A Review of the Dynamic Mathematical Modeling of Heavy Metal Removal with the Biosorption Process

Abstract

Biosorption has great potential in removing toxic effluents from wastewater, especially heavy metal ions such as cobalt, lead, copper, mercury, cadmium, nickel and other ions. Mathematically modeling of biosorption process is essential for the economical and robust design of equipment employing the bioadsorption process. However, biosorption is a complex physicochemical process involving various transport and equilibrium processes, such as absorption, adsorption, ion exchange and surface and interfacial phenomena. The biosorption process becomes even more complex in cases of multicomponent systems and needs an extensive parametric analysis to develop a mathematical model in order to quantify metal ion recovery and the performance of the process. The biosorption process involves various process parameters, such as concentration, contact time, pH, charge, porosity, pore size, available sites, velocity and coefficients, related to activity, diffusion and dispersion. In this review paper, we describe the fundamental physical and chemical processes involved in the biosorption of heavy metals on various types of commonly employed biosorbents. The most common steady state and dynamic mathematical models to describe biosorption in batch and fixed-bed columns are summarized. Mathematical modeling of dynamic process models results in highly coupled partial differential equations. Approximate methods to study the sensitivity analysis of important parameters are suggested.

Insights into the Synergistic Removal of Copper(II), Cadmium(II), and Chromium(III) Ions Using Modified Chitosan Based on Schiff Bases-g-poly(acrylonitrile)

“…These findings show that energetically less suitable sites are formed by increasing metal ion concentration in the medium. These results are found to match with other studies. − The removal efficiency of Cu 2+ , Cd 2+ , or Cr 3+ ions on Ch-g-Sch I and Ch-g-Sch II at different initial concentrations (300–900 mg L –1 ) is shown in Figure S2. The results indicated that the removal percentage of Cu 2+ , Cd 2+ , and Cr 3+ ions using the Ch-g-PAN Schiff base decreases as the initial concentration of Cu 2+ , Cd 2+ , or Cr 3+ ions increases.…”

Comparative Assessment of Different Yeast Cell Wall-Based Mycotoxin Adsorbents Using a Model- and Bioassay-Based In Vitro Approach

“…Instead, it was adequately fitted into the FreundlichEXT model, and the relationship exhibited a biphasic isotherm shape. This could suggest that a competitive adsorption had occurred where other components in the adsorbate–adsorbent system could compete with further attachment of DON molecules to the active sites on PYCW [ 61 , 62 ]. This could result in a lower efficacy of PYCW at high DON concentrations as used in the present study.…”

Alkaline Modification of Arabica-Coffee and Theobroma-Cocoa Agroindustrial Waste for Effective Removal of Pb(II) from Aqueous Solutions

“…Pb(II) adsorption capacity q e (in mg g −1 ) and removal efficiency (%R) were determined using Equations (1) and (2), respectively [ 9 ]. where C 0 and C e (in mg·L −1 ) are the initial and equilibrium final Pb(II) concentrations, respectively, and V (in L) is the volume of solution and m (in g) is the biosorbent mass.…”

“…However, these methods have disadvantages such as the high operating costs, long operating times, and the generation of a large volume of toxic sludge [ 5 , 6 ]. In this context, the removal of contaminants using biological materials (biosorbents), such as algae, cyanobacteria, fungi, or particularly agroindustrial wastes has become an economical, ecological, and promising alternative method compared with the conventional methods mentioned above [ 7 , 8 , 9 , 10 ]. These biosorbents can be modified to improve the adsorption capacity, structural stability, and reusability.…”