Homogenization theory with multiscale perturbation analysis for supervised learning of complex adsorption-desorption process in porous-media systems

Abstract

Engineered and natural adsorbers, which undergo both adsorption and desorption mechanisms during operations, are dominant treatment technologies to remove difficult contaminants from influent sources to safeguard supplies of potable water to local communities. The slow net adsorption, i.e. adsorption rate greater than desorption rate, of contaminants over long periods of operational time contributes to chemical clogging inside an operating adsorber which complexity continues to be difficult for engineers to quantify, particularly on the adsorption and desorption processes coexisting during their near-equilibrium concentration state which builds towards its exhaustion stage for maintenance purpose.In this study, we leverage on the homogenization theory with the multiscale perturbation analysis to develop an engineering model which encapsulates the complex adsorption-desorption mechanics in adsorbers. The desired model contributes towards the primary objective of having the required capabilities to perform predictive maintenance of adsorbers to garner operational benefits, especially for large-scale systems. The hybrid analytical approach systematically derives a unique homogenized representation which contains an unknown reaction rate parameter responsible for the adsorption-desorption processes taking place over a significantly long period of time leading to the adsorber’s exhaustion stage. Dimensional analysis is then carried out to express the reaction rate parameter as a function of the known physical parameters to predict the transient variations in an adsorber’s effluent concentration during its gradual build-up towards exhaustion.Measured data from both the literature and our own adsorber experimental runs are then acquired to train and validate the model’s predictive capability, via supervised learning methods, which yields an average error deviation of 10 % or less for the optimal training period determined. Finally, we demonstrate quantitatively how the model can be useful to engineers to estimate: (a) the timing for an operating adsorber to reach its exhaustion stage; and (b) the associated Damköhler number, adsorption and desorption coefficients and etc., responsible for the concerned adsorber’s effluent concentration profile for the varying types of contaminants removed.