Swift, versatile and a rigorous kinetic model based artificial neural network surrogate for single and multicomponent batch adsorption processes

Abstract

Rigorous and robust first principles-based Homogeneous Surface Diffusion Model (HSDM) is demonstrated for numerical simulation and estimation of surface diffusivities for single, binary and ternary systems involving dyes and pharmaceutical molecules. The current work's novelty lies in proposing a fast, reliable and efficient Artificial Neural Network (ANN) surrogate to the mechanistic HSDM. Repeated numerical integration of the model's partial differential equations during parameter estimation from batch adsorption kinetics data is highly time-consuming and is not required for the proposed approach. This ANN was trained by a small number of HSDM simulations and limited experimental batch kinetics data with different combinations of surface diffusivity (DS) values. ANNs were developed and tested against the experimentally obtained batch kinetics data for various systems. The trained ANN was able to capture the kinetics that was rigorously predicted using HSDM. A 99.9%, 98.6% and 99.3% similarity could be achieved between DS values estimated using HSDM and ANN for single, binary and ternary systems respectively. Similarly, the batch kinetics data was almost identically tracked by ANN. The computational time required for this novel ANN per simulation reduced spectacularly and was about 14 times lesser while the total parameter estimation time was about 17 times lesser than HSDM. The ANN developed for estimating parameters could be operated in reverse as well for simulating the multicomponent batch adsorption kinetics and tracking the increase in percentage removal of the solutes with time at different process conditions. Irrespective of number of components, the ANNs performances were consistent. The ratio of neurons and their total number in the hidden layers had a significant impact on the performance. Hence optimization of network parameters is essential to realize the benefits of ANN. The shortcomings of empirical kinetic models viz. Pseudo First Order model (PFO) and Pseudo Second Order model (PSO) were also demonstrated. This work demonstrates the utility of ANNS in rigorous multicomponent adsorption kinetics applications and has considerable potential in real time optimization and operation of wastewater treatment plants.