Modification of the Thomas model for predicting unsymmetrical breakthrough curves using an adaptive neural-based fuzzy inference system

The Thomas equation is a popular model that has been widely used to predict breakthrough curves (BTCs) when describing the dynamic adsorption of different pollutants in a fixed-bed column system. However, BTCs commonly exhibit unsymmetrical patterns that cannot be predicted using empirical equations such as the Thomas model. Fortunately, adaptive neural-based fuzzy inference systems (ANFISs) can be used to model complex patterns found in adsorption processes in a fixed-bed column system. Consequently, a new hybrid model merging Thomas and an ANFIS was introduced to estimate the performance of BTCs, which were obtained for Cd(II) ion adsorption on ostrich bone ash-supported nanoscale zero-valent iron (nZVI). The results obtained showed that the fair performance of the Thomas model (NRMSE = 27.6% and E f = 64.6%) improved to excellent (NRMSE = 3.8% and E f = 93.8%) due to the unique strength of ANFISs in nonlinear modeling. The sensitivity analysis indicated that the initial solution pH was a more significant input variable influencing the hybrid model than the other operational factors. This approach proves the potential of this hybrid method to predict BTCs for the dynamic adsorption of Cd(II) ions by ostrich bone ash-supported nZVI particles.