Mathematical Evaluation of Direct and Inverse Problem Applied in Breakthrough Models of Metal Adsorption

Abstract

The treatment of industrial effluents has great environmental and human health importance. The purification of water from polluting components, such as metals and organic compounds, can be considered one of the main applications in this field, with adsorption being one of the main treatment methods. Therefore, with the objective of describing the dynamics of the process in an adsorption column and estimating the parameters involved, in this work, an algorithm for the Method of Lines (MOL) was used in order to numerically solve the model formed by the mass balance in liquid phase, the linear driving force equation (LDF), and the Langmuir isotherm for equilibrium. In addition, a sensitivity analysis of the phenomenon was carried out in relation to the parameters and a subsequent estimation of these was made through the Monte Carlo technique via the Markov chain (MCMC). The validation algorithm was created using data from actual breakthrough curves found in the literature. The experimental data were obtained from the literature for the adsorption of Cadmium (Cd), Copper (Cu), Nickel (Ni), Zinc (Zn), and Chrome (Cr) ions. Among all the estimates, the one that had the lowest adjustment to the data was that related to zinc metal, which had an R2 equal to 0.8984. For the other metals, the correlation coefficient had a value closer to unity. This demonstrates that, in general, the estimates were good enough to represent the dynamics of adsorption.

Keywords

• parameter estimation
• adsorption
• metals