Chapter 8 - Soft Computing Optimization Algorithms and Their Application in Parameter Estimation of a Rigorous Adsorption Kinetics Model

Abstract

Adsorption is an economical and effective option to remove toxic pollutants present even at low concentrations in aqueous streams. Batch adsorption kinetics models predict time-variant uptake rate of solutes by the adsorbent, and this represents crucial input for adsorbent selection, specifying time of operation and adsorber design. The first principles–based homogeneous surface diffusion model (HSDM) mechanistically explains the concomitant interplay between decreasing adsorptive concentration in the liquid phase, solute loading at the interface as dictated by the usually nonlinear adsorption isotherm, and evolving adsorbate concentration within the solid as a function of time and space. The HSDM parameters, namely, the convective mass transfer coefficient and the intraparticle diffusion coefficient are often estimated by fitting the model predictions to the experimental batch kinetics data using a suitable optimization algorithm. However, in contrast to the simple pseudo-first- and second-order kinetic models that involve analytical expressions, the HSDM is computationally intensive as it requires the numerical solution of partial differential equations during each step of the optimization iterations. Hence, there is a need for an efficient optimization algorithm that does not require initial guesses and may reliably lead to the best estimates of the model parameters with less number of iterations. Conventional algorithms such as the simplex method are time-consuming and often predict suboptimal parameters depending on the initial guesses provided. Soft computing–based optimization algorithms possess potential to overcome these limitations. These algorithms often mimic nature, are intuitive to develop, and easy to execute. In this chapter, characteristic features of typical hard and soft computing algorithms are discussed. For estimating the HSDM parameters with less number of iterations and variability, a novel initial guess free soft computing algorithm termed as elephant herd optimization (EHO) algorithm was developed in-house. The HSDM parameters obtained from the EHO algorithm could be validated with results obtained from independent methods. When compared to Nelder–Mead, simulated annealing, particle swarm optimization, and genetic algorithms, the EHO could estimate the parameters with less computational effort and more precision. EHO on average required 30% lower time and 40% lesser number of iterations for estimating the parameters when compared to other algorithms. The mass transfer coefficient and intraparticle diffusivity estimated by EHO had on average about 63% and 52% smaller standard deviations, respectively, when compared to other algorithms. The detrimental effect on adsorption operation when using suboptimal HSDM parameters is highlighted. As demonstrated by EHO, there is considerable potential for new ideas and improvements to optimization algorithms so that they could be more effectively employed in wastewater treatment applications.