Optimal Extractive Separation of Chromium(VI) from Acidic Chloride and Nitrate Media by Commercial Amines: Equilibrium Modeling Through Linear Solvation Energy Relation

Abstract

Data for the extraction of chromium, Cr(VI), from aqueous acidic chloride and nitrate solutions by Alamine 300 (tertiary amine)/xylene and di-n-octyl amine (DOA)/xylene solvent systems (298 K) have been subjected to formulation of an optimization structure for an effective Cr(VI) separation. The optimization approach uses a derivative variation method to efficiently identify the optimization range through analyzing the first-order derivatives of the optimized quantity and the nonlinear deviation profile of the derivative value. The main characteristics of it are simplicity and suitability for generalization. Optimum Cr(VI) removal efficiencies, defined both experimentally and analytically, range from about 70 to 90% for Alamine 300 and from 50 to 70% for DOA, being dependent about equally strongly on the types and concentration levels of the amine, acid, and the transferred Cr(VI) species. These dependencies are rationalized in terms of the interactions that take place in the equilibrium phases. Three independent variables, i.e. the concentrations of the amine, acid, and Cr(VI), are adequate for expressing the nonlinear dependence of the optimized extraction factor (E, Z t) on the properties of relevant system. Modeling efforts based on the LSER (linear solvation energy relation) principles and the mass–action law methodology have shown considerable success. The proposed LSER-based solvation model using nine physical descriptors of the solvent and ion provides relatively reliable fits with a mean error of 9%, and satisfies established limiting behavior of the physical event. A critical comparison of the present method with the other commonly used reactive extraction methods on an efficiency basis has been carried out.

Optimization of reactive extraction of C1–C4 aliphatic monocarboxylic acids from aqueous solutions: modeling solvation effect with extended‐LSER, A‐UNIFAC and SPR

“…A survey of the literature reveals that there is gained a little insight into the problem concerning the prediction of optimum extraction field of a reactive extraction system . Multi‐objective optimization is usually used to define a global optimum point without converging to the local minimum or maximum points, wherein conflicting in nature objective functions are brought together for achieving a set of candidate solutions .…”

“…A survey of the literature reveals that there is gained a little insight into the problem concerning the prediction of optimum extraction field of a reactive extraction system. [11,24] Multi-objective optimization is usually used to define a global optimum point without converging to the local minimum or maximum points, wherein conflicting in nature objective functions are brought together for achieving a set of candidate solutions. [33,34] In such cases, the objective functions are non-linear with several local minima/maxima/saddle points within the specified bounds of the variables and quite often the convergence process is finalized without a unique solution.…”

“…The study deals with a new conceptual definition for optimum extraction as the locus of the proposed separation ratio R and synergistic enhancement SE factors being fundamentally suited for the optimal tests of reactive extraction of C1–C4 acids. To accomplish this goal, Senol's derivative variation method (DVM) was successfully applied to the description of the optimum extraction field by analyzing the variation profiles of the derivatives of the optimization factor in question. Because optimum extraction conditions are being very sensitive to the composition levels of amine, acid and diluent and the acid hydrophobicity, it is worthwhile to gain the idea of using only R and SE as separate factors of performance for building up the main optimization structure.…”

Optimal Reactive Extraction of Valeric Acid from Aqueous Solutions Using Tri- n -propyl amine/Diluent and Dibenzyl amine/Diluent Systems

“…However, the literature revealed very little insight relating to the validity of a generalized method for the prediction of optimum extraction limits pertaining to reactive extraction systems. [27][28][29] The study deals with a new conceptual definition for optimum extraction as the locus of the newly proposed separation ratio optimization factor R and synergistic enhancement factor SE being used as the optimization criteria. The goal is to determine the most suitable extract composition for the acid recovery against practically permissible optimum concentration range of the solvent mixture.…”

“…To simplify the complexity of the optimization problem, only the ranges of R and SE factors should be subjected to formulation of an optimization structure along with applying the derivative variation method described earlier by Senol. [27][28][29] This method implies that: (1) the contribution of the derivatives to the optimized property is validated by the slope analysis, and (2) the identification of the optimum conditions is governed by the range of changes in the derivative value.…”