Analytical and hybrid-neuro-differential approaches for describing contaminant removal from aqueous systems

In this study, both analytical and hybrid-neuro-differential formulations were developed for describing the contaminant removal from wastewater by adsorption. The sorption isotherm, expressed as a straight-line equation (single segment or piecewise function) or artificial neural network (ANN), was coupled to the balance equations describing the pollutant transfer in adsorbent and wastewater phases, and their contact interface. The resulting wastewater adsorption remediation model (WARM) is valid for both batch and continuous operations, does not consider a dominant internal or external resistance to mass transfer or instantaneously equilibrated adsorbent, and has an analytical solution when a straight-line isotherm is used. The applicability of current model was tested in the analysis of two experimental datasets from literature describing the removal of the anionic dye direct red 23 (DR23) by graphene oxide (GO) and 4-nitrophenol (4NP) on calcium alginate-multiwall carbon nanotube beads (CAMCNB), where internal and external mass transfer coefficients and sorption isotherm parameters were simultaneously estimated by nonlinear regression. The analytical and hybrid-neuro-differential formulations were further compared with a numerical one where the WARM was coupled to Langmuir isotherm. Besides, the model was also used to explore different scenarios for continuous operation with all tested isotherms. It was demonstrated that the proposed formulations based on straight-line and ANN isotherms achieved a good reproduction of both dynamic and equilibrium experimental data, with similar fitness indices to that obtained with other non-linear equilibrium models.

Keywords: Analytical solution, Mass transfer, Pollutant, Wastewater.