Abstract

Numerous regression approaches to isotherm parameters estimation appear in the literature. The real insight into the proper modeling pattern can be achieved only by testing methods on a very big number of cases. Experimentally, it cannot be done in a reasonable time, so the Monte Carlo simulation method was applied. The objective of this paper is to introduce and compare numerical approaches that involve different levels of knowledge about the noise structure of the analytical method used for initial and equilibrium concentration determination. Six levels of homoscedastic noise and five types of heteroscedastic noise precision models were considered. Performance of the methods was statistically evaluated based on median percentage error and mean absolute relative error in parameter estimates. The present study showed a clear distinction between two cases. When equilibrium experiments are performed only once, for the homoscedastic case, the winning error function is ordinary least squares, while for the case of heteroscedastic noise the use of orthogonal distance regression or Margart's percent standard deviation is suggested. It was found that in case when experiments are repeated three times the simple method of weighted least squares performed as well as more complicated orthogonal distance regression method.

Highlights

  • Adsorption is a mass transfer process that plays a central role in potable water purification, wastewater treatment, both analytical and preparative chromatograph, and different types of chemical analyses as a technique for sample preconcentration and speciation of analytes

  • This study included 55 numerical simulations on the whole and they were individually subjected to the same postprocessing routine

  • Our group faced the problem of modeling the adsorption isotherms [36, 37] and the intention of this study was to single out the method of parameter estimation which is suitable for adsorption isotherms

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Summary

Introduction

Adsorption is a mass transfer process that plays a central role in potable water purification, wastewater treatment, both analytical and preparative chromatograph, and different types of chemical analyses as a technique for sample preconcentration and speciation of analytes. The predominant scientific basis for sorbent selection and design of an adsorption system is the knowledge about equilibrium partitioning between two phases often expressed in the form of adsorption isotherm. The following important factors can be estimated: capacity of the sorbent, the method of sorbent regeneration, and the product purities [1]. Adsorption isotherms are incorporated into geochemical modeling software (such as MINEQL, Visual MINTEQ, and ChemEQL) in order to understand and predict the mobility of the sorbed substances. Determination of the optimum isotherm equation and accurate estimates of the isotherm parameters are apparently important for all the mentioned purposes

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