Application of Response Surface Methodology (RSM) for the Optimization of Chromium(III) Synergistic Extraction by Supported Liquid Membrane

In this paper, the response surface methodology (RSM) was proposed for studying the synergistic extraction of chromium(III) ions by double-carrier supported liquid membrane (DCSLM) with organophosphorus carriers (D2EHPA/Cyanex272). At first, the optimization method of “one-factor-at-a-time” was adopted for determination of the best conditions for Cr(III) extraction by SLM with only one carrier (D2EHPA). The optimum/threshold D2EHPA concentration in the membrane phase increased linearly with initial concentration of Cr(III) ions in the feed phase. After the addition the second carrier (Cyanex272), the synergistic effect was observed. The largest percentage of extraction and the shorter time was obtained. The optimization of the synergistic extraction in DCSLM system by RSM using Box–Behnken design (BBD) for three variables (concentration and proportions of the carriers, initial concentration of Cr(III), and time of the process) was studied. The statistical model was verified with the analysis of variance (ANOVA) for the response surface quadratic model. The reduced quadratic model showed that the predicted values were in agreement with those obtained experimentally, as well as the fact that the concentrations and proportions of the carriers had a significant influence on the response. The developed model was considered to be verified and can be used to predict the optimal condition for the chromium ions extraction.

1. Introduction

Heavy metals (e.g., chromium) and their compounds are among the worst water contaminants. They accumulate in the sediments and are toxic for living organisms. The highest oxidation state of chromium is +6, the lowest is −2; the +3 and +6 states are most common in chromium compounds. It is still problematic to remove chromium from wastewater efficiently [1]. On the other hand, according to the European Commission Report of 2010 [2], chromium belongs to the group of “critical elements”. This means that it is characterized by limited resources and the lack of substitutes, while being essential for economic and industrial development. Considering the above factors, it is crucial to explore and develop methods for efficient separation of chromium from aqueous solutions. There are several methods such as reduction, chemical precipitation, adsorption, ion exchange, and membrane separation that are quite popular in separation of heavy metals; however, some hope is also seen in using liquid membranes, mainly immobilized—SLM (supported liquid membrane). In the SLM, the pores of the polymer matrix fill the membrane phase. Typically, the polymer support is made of polypropylene, polyethylene, Teflon, polyamide, etc. Due to the facilitated carrier transport, the liquid membrane is the most effective technique for the selective separation of metals from aqueous solutions. The most popular types of ion metal carriers are crown ethers; organophosphorus compounds; and primary, secondary, tertiary, and quaternary ammonium salts [3]. However, in recent years, liquid membrane systems with a mixture of two extractants have become very significant in the separation of the metal ions [4,5,6,7,8]. Addition of extractant/carrier mixture in appropriate proportion into the membrane phase has a synergistic and positive effect on improving both the rate and selectivity of the separation process. However, our previous works [1,4] and experiences of authors [5,8] show that the introduction of a second carrier into the liquid membrane causes an increase in the number of variable process parameters that have a decisive impact on the efficiency of the process. It is necessary to select the most favorable proportions of both carriers and determine their correlations with the most important process parameters such as the initial concentration of transported ions, duration of the process, and membrane stability.

When many factors and interactions affect desired results, response surface methodology (RSM) is an effective tool for optimizing the process [9,10,11]. RSM, as a useful statistical and mathematical tool that is always used to develop, improve, and optimize the experimental process, which is affected by several factors. Compared with “one factor at a time” method, RSM cuts down material expense and time remarkably. In this methodology, analysis of variance (ANOVA) provides the statistical results and diagnostic checking tests that enable researchers to evaluate adequacy of the established models [11,12]. Hence, RSM not only provides the optimum level for each variable but also estimates interactions among them and their impact on one or more measured responses. [9].

Some authors [13,14,15,16] have already made successful attempts to apply this method in optimizing the metal ion separation in a liquid membrane system. Wongkaew et al. [13] studied the RSM for the separation of platinum (IV) across hollow fiber supported liquid membrane with different commercial extractants. RSM was used to qualify and estimate the influence of operating conditions (the concentration of the Pt (IV) in the feed phase and concentration of the carrier in the membrane phase) on the extraction efficiency. The predicted results were in good agreement with experimental data at a standard deviation of 1%. Liu et al. [14] used the RSM to optimization of vanadium (IV) extraction from stone coal leaching solution by the emulsion liquid membrane. All of the results revealed that RSM was successfully used to optimize the extraction process. Mesli and Belkhouche [15] also showed that the predicted values in lead recovery by liquid membrane were in good agreement with those found experimentally. Additionally, the authors proved that the carrier concentration has a significant individual effect on the response. Mondal and Saha [16] analyzed separation of hexavalent chromium from industrial effluent through the liquid membrane using the RSM. The authors found that the strip phase concentration, pH, and carrier concentration had the greatest influence on the transport of Cr(VI) ions. The comparison of experimental and predicted data by the RSM was then shown to be in good agreement.

In recent years, the results of research on the optimization of the membrane separation process using RSM have been published increasingly more often [5,6,7,13,14,15,16]. Therefore, it also seems promising to improve the extraction of chromium(III) by the RSM in the supported liquid membrane system.

This work is devoted to the optimization of the chromium(III) separation process using experimental and statistical studies. The study presents the influence of the main process parameters (i.e., the concentration of carrier or carrier mixture in the membrane phase and the initial concentration of chromium in the aqueous phase) on the possibility of separation of Cr(III) from acid solutions with a double carrier supported liquid membrane. The research was carried out using the most commonly used organophosphorus carriers of the Cr(III) ions: bis(2-ethylhexyl) phosphoric acid (D2EHPA) and bis(2,4,4-trimethyl) phosphine acid (Cyanex272) [1,4].

The optimization method of “one experimental parameter at a time” was adopted for determination of the best conditions of Cr(III) recovery, from acidic aqueous solution by SLM with only one carrier (D2EHPA). In the next step, the modelling of the process was achieved by response surface methodology (RSM) using Box–Behnken design (BBD). BBD was used because, as reported by other authors [5,12], it is a method created for estimating a quadratic model and requires only three levels for each factor and specific positioning of design points, providing strong coefficient estimates near the center of the design space. This means it is significantly easier than other DoE methods, as less time is required, and no runs are include factors outside the min/max values of the studied area. For BBD, three parameters, namely, concentration and proportions of both carriers (D2EHPA/Cyanex272), initial concentration of Cr(III), and time of the process, were considered as factors of the quadratic model to predict the optimal extraction of Cr(III).