Liquid-phases adsorption equilibrium of phenol onto two naturally available soils namely Kalathur soil (Kr) and Adhanur soil (Ar) were studied. The experimental data were analyzed using fourteen isotherm models, ranging from single-parametric model to multi-parametric models (up to 5 parameters) of the system. Results show that in general the accuracy of models to fit experimental data improves with the degree of freedom. To understand the mechanism involved with different types of sorbate-sorbent system as well as to find out the best fitting isotherm model, the correlation coefficients, and average percentage error and student t-test were carried out. Temkin isotherm model, Langmuir-Freundlich isotherm model and Fritz-Schlunder model as well as Baudu model were found to be the best fit models amongst the two-parametric models, three parametric models and four parametric isotherms modeling, respectively. This study brings out the need of simultaneous solution of multi-parametric equations (using relevant softwares, MATLAB, in present case) than solution of their linearized forms, which is mostly followed by contemporary investigators.

Adsorption plays an important role in water and wastewater treatment. The analysis and design of processes that involve adsorption rely on the availability of isotherms that describe these adsorption processes. Adsorption isotherms are usually estimated empirically from measurements of the adsorption process variables. Unfortunately, these measurements are usually contaminated with errors that degrade the accuracy of estimated isotherms. Therefore, these errors need to be filtered for improved isotherm estimation accuracy. Multiscale wavelet based filtering has been shown to be a powerful filtering tool. In this work, multiscale filtering is utilized to improve the estimation accuracy of the Freundlich adsorption isotherm in the presence of measurement noise in the data by developing a multiscale algorithm for the estimation of Freundlich isotherm parameters. The idea behind the algorithm is to use multiscale filtering to filter the data at different scales, use the filtered data from all scales to construct multiple isotherms and then select among all scales the isotherm that best represents the data based on a cross validation mean squares error criterion. The developed multiscale isotherm estimation algorithm is shown to outperform the conventional time-domain estimation method through a simulated example.

The optimization of adsorption-based operations requires an accurate model to represent the separation process. In the present study, single-component adsorption data of L-lysine on its imprinted polymer were fitted to Freundlich, Langmuir-type and Jovanovic-type models. L-Lysine imprinted polymer (LLIP) was prepared by free radical solution polymerization. The best estimate of the parameters of these models by regression analysis was obtained. The statistical analysis of results showed that the experimental data fit the Jovanovic-Freundlich mode, better than other models in terms off value. The best prediction of retention capacity equal to 0.186 mmol lysine per g of LLIP, which is the nearest value to the experimental data, was obtained by applying the Jovanovic model.

In this work, we consider each normal alkane as a hypothetical mixture of methyl and methylene groups, in which the interaction potential of each pair is assumed to be the average effective pair potential. Then, the LIR equation of state (EOS) is extended for such a hypothetical mixture. Also, three basic compounds, namely, propane, n-butane and cyclohexane, are used to obtain the contribution of each carbonic group in the EOS parameters. Using the calculated EOS parameters along with the modified EOS, the density of n-alkanes and their mixtures at different pressures and temperatures are calculated. The average percentage error in density is found to be less than 1.5% for both the pure normal alkanes and their binary mixtures.