A Feasible Strategy for Calculating the Required Mass Transfer Height

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A feasible strategy for calculating the required mass transfer height of a new bubbling organic liquid membrane extraction tower directly based upon the experimental kinetic data Jie Liu, Kun Huang, Huaizhi Wu, and Huizhou Liu Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b04734 • Publication Date (Web): 30 Mar 2016 Downloaded from http://pubs.acs.org on April 1, 2016

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Industrial & Engineering Chemistry Research

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A feasible strategy for calculating the required mass transfer

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height of a new bubbling organic liquid membrane extraction

3

tower directly based upon the experimental kinetic data

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Jie Liu 1,2, Kun Huang *1, Huaizhi Wu 2, Huizhou Liu 1,2

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1. CAS Key Laboratory of Green Process and Engineering, Institute of Process Engineering,

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Chinese Academy of Sciences, Beijing 100190, China

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2. CAS Key Laboratory of Bio-based Materials, Qingdao Institute of Bioenergy and Bioprocess

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Technology, Chinese Academy of Sciences, Qingdao 266101, China

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* Corresponding author: Prof. Dr. Kun HUANG Institute of Process Engineering, Chinese Academy of Sciences No.1 Bei Er Jie, Zhongguancun, Haidian District, Beijing, 100190, China. E-mail address: [email protected] Tel: (86)-(10)-82544910 Fax: (86)-(10)-62554264 14 15 16 17 18

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Abstract: Extraction and recovery of gold(I) with extremely low concentration in

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cyanide wastewater were conducted as an example aimed to develop a feasible

3

method based upon the experimental kinetic data for calculating the required mass

4

transfer height of a new bubbling organic liquid membrane extraction tower. The

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kinetic extraction equation based on curve-fitting the experimental c(t)~t data from

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single column extraction could be established to describe the quantitative relationship

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of the concentration change of gold(I) in flowing-out aqueous solution from the tower

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with the reaction time in the tower, so that the required tower height involving in axial

9

gas mixing effect could be calculated from the residence time of the aqueous solution

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passing through the tower to achieve a target equilibrating concentration. The

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influence of organic phase recycling on the calculation was discussed. Double column

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extraction experiments confirmed that the suggested calculation method obtained

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from single column extraction is reasonable. The present work is favor of

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understanding the mass transferring kinetic behaviors of target components in that

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suggested bubbling extraction tower, and highlights a feasible strategy directly from

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the experimental kinetic data to calculate the required mass transferring height of the

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tower for its structure design, optimization and scale-up, and provides fundamental

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data for future industrial application of the tower to extract and recover other heavy

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metal ions from wastewater.

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Keywords: Bubbling extraction tower; Liquid membrane extraction; Tower height;

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Calculation; Cyanide wastewater

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1 Introduction

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Industrial wastewater that contains various poisonous and cancerogenic heavy

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metal ions, such as Cr(VI), Cd(II), Cu(II), Pb(II), Zn(II) and Hg(II), is becoming one

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of the most serious pollution that harm human’s health and ecological environment in

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the earth.1 Being different from organic pollutants, heavy metal ions cannot be

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biodegraded. Therefore, discharge of heavy metal wastewater into soil and water is

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strictly prohibited in many countries. Up to now, many methods have been reported

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effective to remove heavy metal ions from industrial wastewater, such as chemical

9

precipitation,2,3

ion-exchanging,4-6

adsorption,7-10

membrane

filtration,11-14

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electrochemical treatment15-17 and bioremediation.18-20 However, none of them was

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aimed to treat the wastewater as a useful resource of heavy metals for their recovery,

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separation and reusing. The main difficult those techniques have to face is the

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processing cost and efficiency were not so satisfied due to extremely low

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concentrations of heavy metal ions in wastewater.21 In addition, those heavy metals

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after recovery could not be reused because of their lower content and coexisting with

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other impurities. Those heavy metals concentrated in precipitates, adsorbents and

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other residues might become another more serious pollution sources.

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Solvent extraction has been demonstrated being an effective technique to enrich

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and recover heavy metal ions with low concentrations and separate them between

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each other for reusing.22 However, traditional solvent extraction technique and

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equipment were not suitable or at least not economic for treating industrial wastewater 3 ACS Paragon Plus Environment


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containing extremely low concentrations of heavy metal ions. Repeated equilibrating

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operations aimed to remove heavy metal ions and decrease their final concentrations

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in the water make the processes costly, and the resulted wastewater contains

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emulsified oil or organic extractant which may cause another new pollution to the

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environment.23

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Our previous works suggested a gas bubble-supported organic liquid membrane

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extraction technique performed by a so-called bubbling extraction tower for

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liquid-liquid solvent extraction at extremely large aqueous-to-oil phase ratios for

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enrichment and recovery of heavy metals from industrial wastewater.24-28 The aim of

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the suggested new technique is to disperse small volume of organic extractant by gas

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bubbles and makes hydrophobic organic extractant being covered onto the surface of

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gas bubbles to form a layer of organic liquid membrane. The liquid-liquid extraction

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process was in fact performed on the thin layer of organic extractant membrane

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covered on the surface of those dispersed gas bubbles when they pass through the

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tower, so that the organic liquid membrane could entrap and enrich the target metal

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ions in a large volume of feed aqueous solutions. In practical operation process, the

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aqueous-to-oil operation phase ratio of the bubbling extraction tower could reach

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500:1 or even more, therefore, heavy metal ions with extremely low concentration in

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wastewater can be rapidly enriched into small volume of organic phase with higher

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concentration factors. In addition, the gas bubble-supported organic liquid membrane

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can be easily destroyed on the top of the tower and phase separation between oil and 4 ACS Paragon Plus Environment

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water was fast, so that it is almost impossible to induce emulsion and axial mixing in

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tower, and therefore the content of oil in the final water flowing out of the tower could

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meet the requirements of wastewater discharging standards and would not cause

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secondary pollution any more.

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Previous works found that the tower height required for complete extraction has

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a close relationship with the mass transfer kinetics of target components during

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bubbling extraction process. We developed a method based upon the plug-flow model

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and the dual resistance model to calculate the required tower height.28 However, the

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plug-flow model and the dual resistance model are usually employed to calculate the

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mass transferring unit height in traditional rotating-disc tower and reciprocating sieve

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plate extraction tower.29 In that process, organic extractant was dispersed as tiny oil

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droplets to achieve counter-current contacting with aqueous feed solutions. In our

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suggested new bubbling extraction tower, however, extraction reaction was carried on

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the surface organic liquid membrane layer of the dispersed gas bubbles. The gas

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bubbles act only as a kind of inert distribution medium to support organic extractant

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liquid membrane and do not participate in the reactions. The mass transfer process of

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target component is in fact from the bulk aqueous phase onto the surface of organic

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liquid membrane layer. The mass transfer resistance and driving-force for such an

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organic liquid membrane extraction is very different from the traditional extraction by

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dispersed oil droplets. Therefore, the traditional plug-flow model and the dual

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resistance model may not be appropriate to calculate the real height of mass 5 ACS Paragon Plus Environment


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transferring unit in the suggested bubbling extraction tower.

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Currently, prediction of the mass transfer performances in extraction tower is still

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very difficult due to the lack of appropriate equations to estimate the mass transfer

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unit height.30 Babb et al.31 provided a method by measuring the concentration profile

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along the tower to calculate the “true” height of transfer unit. Vermeulen et al.32

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suggested that the effect of axial mixing and mass transfer coefficients based on the

7

diffusion or backflow models should be considered for the calculation of the apparent

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mass transfer unit height. Lei33 and Luo et al.34 developed a dynamic response curve

9

method based on the diffusion model to evaluate the parameters of axial mixing and

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mass transfer, and proved that method is as reliable as the concentration profile

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method. However, up to date, no effective method has been described for calculation

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of those required mass transfer parameters, including the axial dispersion coefficients

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and etcetera. Most of reported works still focused on some empirical correlations for

14

evaluation of the mass transfer unit height based on the particular needs of each

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individual system or tower. Those empirical correlations were obtained using different

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experimental methods, quite different from each other and cannot be used extensively

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due to associated limitation of experiments. Luo et al.35,36 develop a generalized

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equation, independent of the column type and experimental setup, for estimation of

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the apparent mass transfer unit height. However, the suggested method was still not

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satisfied, due to the effect from axial mixing was not introduced into the equation

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explicitly. 6 ACS Paragon Plus Environment

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The aim of present work is to develop a feasible method for calculating the

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required mass transferring height of our suggested bubbling extraction tower directly

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based upon the experimental kinetic data about the concentration changes of target

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components in flowing-out aqueous phase with the reaction time of target components

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in tower. Here, a cyanide wastewater containing extremely low concentration of

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gold(I) was employed as an example to perform the gas bubble-supported organic

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liquid membrane extraction. A kinetic equation describing the gold(I) concentration in

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aqueous solution flowing out from the tower, c(t), changing with the reaction time in

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bubbling extraction tower, t, were obtained based upon curve-fitting the experimental

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data from single column extraction when aqueous and organic phase flow through the

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tower continuously and circularly but not been discharged out of the tower. Then the

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required height of the suggested bubbling extraction tower could be calculated from

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the residence time of the aqueous solution passing through the tower to achieve a

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target equilibrating concentration of gold(I). It was revealed that recycling and reusing

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of the organic phase has a certain influence on the c(t)~t dynamic equation and

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therefore the calculation value of tower height. The reasonability of that suggested

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calculation method was confirmed based on the experimental results from two single

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columns connecting in cascade. The present works provide a scientific basis for

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theoretical prediction of the required mass transfer height of the suggested gas

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bubble-supported organic liquid membrane extraction tower, and definitely be useful

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for its structure design, optimization and industrial scale-up in the future. 7 ACS Paragon Plus Environment


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2. Experimental

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2.1. Chemicals and reagents

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Experimental feed aqueous solutions were the wastewater of cyanide treatment

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of gold-containing ores, kindly provided by Shandong Gold Group Co., Ltd. The

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gold(I) concentration in the cyanide wastewater was 2.053 mg/L, and the initial

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aqueous pH value was between 6 and 7. Industrial-grade of methyl trioctyl

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ammonium chloride (N263) was used as the organic extractant, purchased from

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Xiamen Pioneer Technology Co., Ltd. Sec-caprylic alcohol, purchased from

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Sinopharm Chemical Reagent Co., Ltd., was used as the co-extractant. Kerosene,

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purchased from China Petrochemical Corporation, was used as the diluent to mix with

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N263 and sec-caprylic alcohol to prepare a stock organic phase used for experiments.

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The concentration of N263 and sec-caprylic alcohol in the stock organic phase were

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0.25 mol/L and 0.77 mol/L, respectively. All other chemicals were of analytical grade.

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2.2 Apparatus

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All experiments were performed at room temperature using the new bubbling

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extraction tower depicted in Figure 1. The diameter of the tower is 0.23 m, the height

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of the tower is 3.5 m.

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This new bubbling extraction tower was demonstrated successful in dispersing

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small-volume organic phase thoroughly into large-volume aqueous phase. The

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water-to-oil operation phase ratio could reach a very large value which is impossible 8 ACS Paragon Plus Environment

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to be obtained in traditional extractors. Therefore, target metal ions with extremely

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low concentration in a large volume of feed aqueous solution can be enriched at

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higher enrichment factors into the organic liquid layer covered on the surface of gas

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bubbles. Detailed description of the new bubbling extraction tower could be found in

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our previous works.28

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2.3 Procedures

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2.3.1 Single column extraction experiments

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(1) The aqueous solution did not flow in the tower but the organic phase passed through the tower circularly

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50 L of stock organic phase and 150 L of cyanide wastewater were employed for

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single column extraction experiments. Firstly, air was blown into the tower from the

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air inlet at the bottom of the tower. The volume flow rate of air, Lg , was 0.1 m3/h.

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And then, 140 L of cyanide wastewater was pumped into the tower from the feed

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aqueous solution inlet at the top of the tower. When gas bubbles were blown out from

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the top end of gas needles stably, the organic phase was pumped into the organic

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bubble film generator from the organic phase inlet at the bottom of the tower, so that

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the so-called organic bubbles, on the surface of which were covered a thin layer of

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organic extractant liquid membrane, could be blown out from the nozzles. The

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volume flow rate of the organic phase, L0 , was 40 L/h. After phase contacting, the

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organic bubbles were destroyed when they passed through the organic phase 9 ACS Paragon Plus Environment


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demulsification section, and agglomerated together to form a continuous organic bulk

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phase, and then overflowed from the loaded organic phase outlet at the top of the

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tower. The loaded organic phase was re-pumped into the organic bubble film

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generator from the organic phase inlet at the bottom of the tower.

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In those experiments, the feed aqueous solution did not flow in the tower but the

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organic phase passed through the tower circularly. Aqueous samples in the tower were

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taken at different times from the raffinate outlet.

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(2) Both the aqueous solution and organic phase passed through the tower circularly but not been discharged out of the tower

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50 L of stock organic phase and 150 L of cyanide wastewater were employed for

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single column extraction experiments. The 150 L of cyanide wastewater was pumped

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into the tower from the feed aqueous solution inlet, and passed through the tower

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circularly round and round, but not been discharged out of the tower. Other

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procedures were the same as described in the section 2.3.1 (1). The organic bubbles

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ascend along the main tower and counter-currently contact with the aqueous phase

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flowing down, so that countercurrent extraction could be achieved. The volume flow

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rate of the organic phase, L0 , was 40 L/h. The volume flow rate of the aqueous phase,

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L , was 100L/h. The volume flow rate of air, Lg , was 0.1 m3/h. Aqueous samples in

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the tower were taken at different times from the raffinate outlet.

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2.3.2 Influence of organic phase recycling on single column extraction 10 ACS Paragon Plus Environment

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50 L of loaded organic phase from the single column extraction experiments in

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the section 2.3.1 (2) was re-used to investigate the influence of organic phase

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recycling on single column extraction. In this section, 150 L of cyanide wastewater

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was pumped into the tower. Both the aqueous solution and the organic phase passed

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through the tower circularly but not been discharged out of the tower. Other

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procedures were the same as described in the section 2.3.1 (2). The volume flow rate

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of the aqueous solution, L , was 100 L/h. The volume flow rate of the organic phase,

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L0 , was 40 L/h. The volume flow rate of air, Lg , was 0.1 m3/h. Aqueous samples in

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the tower were taken at different times from the raffinate outlet.

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2.3.3 Double column extraction experiments

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120 L of stock organic phase and 300 L of cyanide wastewater were employed

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for double column extraction experiments. The two single columns were connected in

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cascade for performing double column extraction experiment. The 300 L of cyanide

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wastewater was pumped into the first tower, and then flew into the second tower. At

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the same time, the 120 L of organic phase was pumped into the second tower, and

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then flew into the first tower. Both the aqueous solution and the organic phase passed

18

through the two towers circularly but not been discharged out of the towers. Other

19

procedures were the same as described in the section 2.3.1 (2). The volume flow rate

20

of the aqueous solution, L , was 100 L/h. The volume flow rate of the organic phase,

21

L0 , was 40 L/h. The volume flow rate of air, Lg , was 0.1 m3/h. Aqueous samples in

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the second tower were taken at different times from the raffinate outlet. 11 ACS Paragon Plus Environment


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2.4 Analysis

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The concentration of gold(I) in the raffinates flowing out from the bubbling

4

extraction tower was analyzed by an Agilent 7900 ICP-MS system (Agilent

5

Technologies, USA). A pH meter (pH211, HANNA, Italy) was used to determine the

6

pH values of the aqueous solutions.

7 8

3. Results and Discussion

9 10

3.1 Calculation of the tower height based on single column extraction

11

Figure 2 depicts the change of gold(I) concentration in the aqueous solution in

12

the bottom of the tower with the reaction time, when the aqueous solution in tower

13

does not flow.

14

As can be seen in Figure 2, gold(I) concentrations in aqueous solution decreased

15

rapidly within 50 minutes, and does not change any more after reaction for 70 minutes.

16

The final gold(I) concentration in aqueous solution after extraction decreases to 0.084

17

mg/L, and therefore the gold(I) concentration in the organic phase collected from

18

coalescence of dispersed organic liquid membrane on gas bubbles was 5.513 mg/L.

19

A dynamic equation to describe the change of gold(I) concentrations in the

20

aqueous solution in the bottom of the tower can be obtained by curve fitting the

21

experimental data in Figure 2:

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c(t )  0.06  1.926e0.059t

(1)

In equ.(1), c(t ) is gold(I) concentration in the aqueous solution at a certain 12 ACS Paragon Plus Environment

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1 2

3


2 reaction time of t . t is the reaction time in tower. R of the curve fitting is 0.9893.

From equ.(1), we have

dc  0.114e0.059t dt

(2)

4

Equ.(2) describes the decreasing rate of gold(I) concentration in the aqueous

5

solution with the reaction time. Here, the residence time of the aqueous feed solution

6

in tower is infinitely great, because the volume flow rate of the aqueous feed solution

7

in the tower is zero.

8

When the volume flow rate of the aqueous feed solution passing through the

9

tower is not equal to zero, the gold(I) concentration in the aqueous phase flowing-out

10

from the bottom of the tower should have a close relationship with the residence time

11

of aqueous phase in tower. Given that the initial gold(I) concentration in the feed

12

aqueous solution entering in the tower is c0 . And c1 is the concentration of gold(I)

13

in the extraction raffinate flowing out from the tower. Lo , L and Lg represent the

14

volume flow rate of the organic, aqueous phase and gas phase flowing through the

15

tower, respectively. We would have a similar dynamic equation to describe the change

16

of gold(I) concentrations in the aqueous phase flowing-out from the tower, as given in

17

equ.(1). Figure 3 depicts the change of gold(I) concentrations in the aqueous phase

18

flowing out from the bottom of tower with the reaction time in tower. The volume

19

flow rate, L , of the aqueous feed solution passing through the tower is 100 L/h.

20

As shown in Figure 3, gold(I) concentration in the aqueous raffinate flowing out

21

from the bottom of the tower decreases with prolonging the reaction time t . After 50 13 ACS Paragon Plus Environment


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Page 14 of 44

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minutes, the concentration of gold(I) in raffinate reaches its final equilibrium

2

gradually. The final gold(I) concentration in the raffinate decreases to 0.12 mg/L after

3

70 minutes of phase contacting, and the gold(I) concentration in the organic phase

4

collected from coalescence of dispersed organic liquid membrane on gas bubbles was

5

5.799 mg/L. The time 50 minutes could be thought as the residence time of the

6

aqueous phase in the tower, when the volume flow rate, L , of the aqueous feed

7

solution passing through the tower is 100 L/h.

8

The dynamic equation describing the change of gold(I) concentrations in

9

raffinate with the reaction time t in the tower can be obtained by curve fitting the

10 11 12 13 14

15

experimental data in Figure 3:

c(t )  0.047  1.935e0.053t

(3)

Here, c(t ) is gold(I) concentration in raffintes flowing out from the tower at a 2 certain time of t. t is the reaction time. R of the curve fitting is 0.9801.

From equ.(3), we have

dc  0.103e0.053t dt

(4)

16

Compared equ.(4) with equ.(2), we can found the decreasing rate of the gold(I)

17

concentration in the raffinate flowing out from the tower also accords a relationship of

18

exponential function with the reaction time in tower. The R2 for the curve fitting are

19

between 0.98 and 0.99.

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Therefore, we can describe the concentration of gold (I) in the aqueous solution flowing out from the bottom of the tower using equ.(5): 14 ACS Paragon Plus Environment

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c(t )  a  bekt

1

(5)

2

In equ.(5), a , b and k are constant. t is the reaction time in tower when the

3

aqueous feed solution pass through the tower at a certain volume flow rate. It can be

4

expected the required residence time of aqueous solution in tower can be obtained if

5

we previously set a final concentration of gold(I) flowing out from the tower.

6

Here, the required residence time,  , corresponding to a certain value of

7

required tower height, can be calculated by substituting c1 into equ.(5), if the

8

concentration of gold(I) in the aqueous solution flowing out from the tower, c1 , is

9

known.

10 11 12 13

14 15 16

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The following we will discuss how to calculate the required tower height using the residence time  obtained in experiments. The residence time,  , of the aqueous solution in the tower can be calculated by the following equ. (6):



V L

(6)

In equ.(6), V is the volume of the tower corresponding to a required mass transferring height of the bubbling extraction tower. V can be expressed as:

V

 dt2 4

H

(7)

Where, H is a required mass transferring height involving in axial gas mixing effect in the bubbling extraction tower. dt is the tower diameter. Inducing equ.(7) into equ.(6), we have 15 ACS Paragon Plus Environment


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

1 2

4L

H

(8)

Therefore, we have

H

3 4

 d t2

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4 L  dt2

(9)

As can be seen from equ.(9), the required mass transferring height involving

5

axial gas mixing effect in the bubbling tower is only related to the residence time 

6

of aqueous solution in tower, when dt and L are known, previously.

7

dc  0 , the mass From the equ.(4), we know that when the mass transfer rate dt

8

transfer of target ions in tower are inclined to reach its equilibrium. The residence

9

time, when mass transfer of target ions in tower reached equilibrium, can be

te , and correspondingly the equilibrium concentration of target ions in

10

expressed as

11

the aqueous phase flowing out from the tower is expressed as

12

If

ce .

ce  c1 , it means that the extraction efficiency can reach a designed target

13

value, when all of the aqueous solution with a known volume flow out from the

14

extraction tower once time. The required tower height can be calculated by equ.(10):

H  He 

15

16

If

4 Lte  d t2

(10)

ce  c1 or ce  c1 ，it means that the extraction efficiency was better or

17

less than the designed target value, when all of the aqueous solution with a known

18

volume flow out from the extraction tower once time. The residence time

19

corresponding to the

c1



can be obtained by equ. (5), and the required tower height, 16 ACS Paragon Plus Environment

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1 2


involving axial gas mixing effect, can be calculated by equ. (9). Experiments were conducted in single column for continuous extraction of gold(I)

3

from an industrial cyanide wastewater. Here, we set the final concentration of gold(I),

4

c1 , in the aqueous solutions flowing out from the tower is equaling to 0.05 mg/L, and

5

suppose the extraction reach equilibrium when dt ≤0.001. Therefore, we have the

6

below calculation, as shown in Table 1.

dc

7

dc As can be seen in Table 1, when dt < 0.001, the required equilibrium time of

8

the aqueous solution in the tower, te , is 88 minutes. That is to say, the final

9

concentration of gold(I) in raffinates, ce , flowing out from the tower would reach

10

0.065 mg/L, and the tower height, H e , for mass transfer reaching equilibrium is 3.53

11

m. However, here we have

12

tower,

13

calculated by equ. (8) is 122 minutes. That means the required tower height, H ,

14

should be calculated by equ. (9), and it was 4.90 m. Therefore, if we set the final

15

concentration of gold(I),

16

0.05 mg/L, an additional increase of tower height is required.



ce  c1 , the residence time of the aqueous solution in the

, corresponding to the final concentration of gold(I) in raffinates, c 1 ,

c1 , in the aqueous solutions flowing out from the tower is

17

The required tower height can also be calculated based upon our previous

18

suggested models.28 There, the required tower height, involving axial gas mixing

19

effect, was expressed as HWZ . The physic-chemical parameters required for

20

calculation are listed in Table 2, and calculated results are listed in Table 3. 17 ACS Paragon Plus Environment


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1 2

Page 18 of 44

Compared the calculated results listed in Table 1 and Table 3, we can conclude that the required tower height calculated by equ. (9) is reasonable.

3 4

3.2 Influence of organic phase recycling on calculation

5

In practical extraction process, the organic phase flowing out from the top of the

6

tower should be recycled and entered again from the bottom of the tower, because the

7

loading capacity of the organic phase does not reach its saturation only by passing

8

through the tower once time. Therefore, we conducted the experiment about the

9

influence from recycling of the organic phase on the extraction performance. The

10

organic phase used in previous single column extraction experiments was re-pumped

11

into the column to carry out the single column extraction experiment again. The initial

12

gold(I) concentration in the organic phase was 5.799 mg/L. The experimental results

13

are shown in Figure 4.

14

As shown in Figure 4, gold(I) concentration in aqueous phase decreased rapidly

15

in 80 minutes. After 80 minutes, gold(I) concentration in raffinates tent to equilibrium.

16

The final gold(I) concentration in aqueous phase reached 0.197 mg/L at the 220

17

minutes.

18

A dynamic equation for the gold(I) concentration in the aqueous phase flowing

19

out from the tower changing with the reaction time in tower can be obtained by curve

20

fitting the experiment data in Figure 4:

21

c(t )  0.135  1.742e0.044t

(11) 18

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1

As can be seen from equ.(11), the change of gold(I) concentrations with the

2

reaction time in tower also accords with the relationship of exponential function.

3

R 2 of the curve fitting is 0.9722.

4

5

Similarly, we have:

dc  0.077e0.044t dt

(12)

6

dc When dt < 0.001, the mass transferring from aqueous solution to the organic

7

liquid membrane on the surface of gas bubbles could be thought reaching the final

8

equilibrium. Correspondingly, the equilibrium time, te , of the aqueous solution in the

9

tower is 99 minutes, the equilibrium concentration, xe , is 0.157 mg/L, and the

10

equilibrium tower height H e is 3.97 m. In comparison with those calculation values

11

listed in Table 1, we found that the equilibrium concentration and the equilibrium

12

tower height, when organic phase was recycled, are higher than those corresponding

13

values when fresh organic phase was used. Therefore, it was confirmed that the more

14

times the organic phase was recycled, the longer the reaction time would be to reach

15

equilibrium, and the higher the concentration of target components would be in the

16

final aqueous phase flowing out from the tower, and the higher the required tower

17

height would be. Of course, those calculations and conclusions were based on such a

18

prerequisite that the organic phase doesn’t reach its saturated loading capacity. In our

19

experiments, the concentration of N263 in the organic phase was 0.25 mol/L, which is

20

far larger than the concentration of gold(I) in the aqueous phase. Therefore, that 19 ACS Paragon Plus Environment


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Page 20 of 44

1

prerequisite is reasonable. The required tower height can still be calculated based

2

upon the experimental c(t)~t curve, even the organic phase was loaded with a certain

3

amount of gold(I).

4 5

3.3 Demonstration in double column extraction

6

In Section 3.1, the required tower height can be calculated based upon the

7

residence time obtained from the experimental mass transferring kinetic equation for

8

gold(I) extraction in a single column. In order to demonstrate the reasonability of that

9

suggested calculation method, a pilot batch test was performed by using two single

10

columns connecting in cascade. The experimental results are depicted in Figure 5.

11

Figure 5a depicts the experimental data for the change of gold(I) concentrations in the

12

aqueous solution flowing out from the bottom of the tower with the reaction time in

13

tower. Figure 5b is the corresponding calculated values for extraction in two columns

14

connecting in cascade. Those calculated values were obtained from the experimental

15

mass transferring kinetic equation, i.e., equ.(3), for gold(I) extraction in a single

16

column.

17

As can be seen in Figure 5, the experimental data are consistent to the calculated

18

values almostly. Similar to previous discussion, a dynamic equation can be obtained

19

for the change of gold(I) concentrations in aqueous phase with the reaction time in

20

tower by curve fitting the experimental data:

21

c(t )  0.126  1.788e0.036t

(13) 20


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1

As shown in equ. (13), we notice that the change of gold(I) concentrations in

2

aqueous solution also accords with the exponential function given in equ.(5). R 2 of

3

the curve fitting is 0.9731.

4

From Equ. (13) , we have:

dc  0.064e0.036t dt

5

6

When

(14)

dc dt < 0.001, the mass transferring could be thought reaching its final

7

equilibrium, based on which the required equilibrium time te can be calculated, and

8

the value is 116 minutes. Correspondingly, the equilibrium tower height H e is 4.65 m,

9

according to equ.(10), and the final equilibrium concentration ce is 0.153 mg/L,

10

according to equ.(13). It means if the final gold(I) concentration in the raffinate

11

flowing out from the two towers is 0.153 mg/L, the required total tower height is 4.65

12

m, if the extraction was performed in two towers connecting in cascade.

13

On the other hand, from equ.(3), we have the residence time of aqueous solution

14

in the tower is 55 minutes for a single column extraction, when the final gold(I)

15

concentration in aqueous phase flowing out from the tower decreased to 0.153 mg/L.

16

Substituted the value of the residence time in equ.(9) with 55 minutes, we have the

17

required height for a single column was 2.21 m. That is to say, the required total

18

height for two columns should be 4.42 m, if we calculate the values according to

19

equ.(3) and set the final gold(I) concentration in aqueous phase flowing out from two

20

columns is 0.153 mg/L, because the total volume of the water needed to treat in two 21 ACS Paragon Plus Environment


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1

Page 22 of 44

columns is twice the volume in a single column.

2

It was obvious that the tower height calculated by equ. (3) were almost the same

3

as the calculated tower height based on equ. (13) and equ. (14). The calculated error is

4

only 5%. Therefore, the experiments about two columns extraction in cascade further

5

confirmed that the dynamic equation obtained from the single column extraction was

6

reasonable. That is to say, the required tower height can be calculated indeed from the

7

experimental data about the change of gold(I) concentrations in the raffinate with

8

reaction time in tower, i.e. the c(t)~t kinetic equation obtained from the experimental

9

data.

10 11

4 Conclusions

12

In present work, extraction and recovery of gold(I) with extremely low

13

concentration in cyanide wastewater were conducted as a practical example aimed to

14

develop a feasible method based upon the experimental kinetic data for calculating the

15

mass transfer height of our previous suggested bubbling organic liquid membrane

16

extraction tower. The kinetic extraction equation, i.e., c(t)~t equation, could be

17

established by curve-fitting the experimental data from single column extraction to

18

describe the quantitative relationship of the change of gold(I) concentrations with the

19

reaction time in the tower. The required residence time for an aqueous solution

20

passing through the tower to achieve a certain target concentration can be calculated

21

by the c(t)~t equation, and then the required tower height to achieve complete

22

extraction can be calculated by the residence time. We considered the influence when 22 ACS Paragon Plus Environment

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1

the loaded organic phase was recycled for reusing and passing again through the

2

tower, on the change of the final gold(I) concentrations in raffinates flowing out the

3

tower and the residence time of aqueous phase in the tower. Experimental results

4

indicated that the more times the organic phase was recycled, the longer the required

5

time would be to reach equilibrium, and the higher the concentration of target

6

components would be in the final aqueous phase flowing out from the tower, and the

7

higher the required tower height would be. Double column extraction experiments

8

were conducted to demonstrate the reasonability of that suggested calculation method

9

obtained from a single column extraction. Experimental results confirmed that the

10

required mass transferring height of our suggested new bubbling extraction tower

11

could indeed be calculated based on the experimental c(t)~t curve.

12

The present work also highlights a promising strategy to investigate the

13

gas-bubble supported organic liquid membrane mass transferring behavior of targets

14

in the suggested bubbling extraction tower, directly based on experimental data about

15

the concentration change of target components in flowing-out aqueous solution with

16

the reaction time, i.e., the experimental c(t)~t curve. The work provides a scientific

17

basis for theoretical development and future industrial application of the new gas

18

bubble-supported organic liquid membrane extraction technology.

19 20 21

Acknowledgments This work was financially supported by the National Natural Science Foundation 23 ACS Paragon Plus Environment


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Page 24 of 44

1

of China (Nos. 51574213, 51074150) and the Key Project of Chinese National

2

Programs for Fundamental Research and Development (973 Programs Nos.

3

2012CBA01203, 2013CB632602).

4 5

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from synthetic and industrial Tunisian wastewater by electrocoagulation using

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aluminum electrodes. Desalination and Water Treatment 2015, 56, 2689.

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two-phase continuous extraction equipment. China Patent CN102512848B, 2014.

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Chem. Eng. J. 2008, 138, 389.

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continuous-flow operations. I&EC Fund 1963, 2, 113.

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column by concentration profiles under steady state and by a dynamic

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1

FIGURE CAPTIONS

2

Figure 1. Sketch structure of the bubbling organic liquid membrane extraction tower

3

Figure 2. The change of gold(I) concentrations in tower with the reaction time

4

(The aqueous solution did not flow in the tower but the organic phase passed through

5

the tower circularly. The volume flow rate of the organic phase, L0 , was 40 L/h. The

6

volume flow rate of air, Lg , was 0.1 m3/h. Error bars indicate 95% confidence

7

intervals.)

8

Figure 3. The change of gold(I) concentrations in the aqueous phase flowing out from

9

the bottom of tower with the reaction time in tower

10

(Both the aqueous solution and organic phase passed through the tower circularly but

11

not been discharged out of the tower. The volume flow rate of the organic phase, L0 ,

12

was 40 L/h. The volume flow rate of the aqueous phase, L , was 100L/h. And the

13

volume flow rate of air, Lg , was 0.1 m3/h. Error bars indicate 95% confidence

14

intervals.)

15

Figure 4. The change of gold(I) concentrations in the aqueous phase flowing out from

16

the tower when organic phase was reused

17

(The loaded organic phase was re-used to investigate the influence of organic phase

18

recycling on single column extraction. Both the aqueous solution and the organic

19

phase passed through the tower circularly but not been discharged out of the tower.

20

The volume flow rate of the aqueous solution, L , was 100 L/h. The volume flow rate

21

of the organic phase, L0 , was 40 L/h. The volume flow rate of air, Lg , was 0.1 m3/h. 29 ACS Paragon Plus Environment


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Page 30 of 44

1

Error bars indicate 95% confidence intervals.)

2

Figure 5. Comparison of the experimental data with the calculated values for

3

extraction by two columns connecting in cascade

4

(The experimental data for the change of gold(I) concentrations in the aqueous

5

solution flowing out from the bottom of the tower with the reaction time in tower. The

6

corresponding calculated values for extraction in two columns connecting in cascade,

7

obtained from the experimental mass transferring kinetic equation (3) for gold(I)

8

extraction in a single column. Both the aqueous solution and the organic phase passed

9

through the two towers circularly but not been discharged out of the towers. The

10

volume flow rate of the aqueous solution, L , was 100 L/h. The volume flow rate of

11

the organic phase, L0 , was 40 L/h. The volume flow rate of air, Lg , was 0.1 m3/h.

12

Error bars indicate 95% confidence intervals.)

13 14 15 16 17 18 19 20 21 22 23 24 30 ACS Paragon Plus Environment

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1


Figure 1.

2

3 4 5 6 7 8 9



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 32 of 44

1 2

Figure 2.

3

4 5 6 7 8 9 10 11 12 13 14 32 ACS Paragon Plus Environment

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1 2

Figure 3.

3

4 5 6 7 8 9 10 11 12 13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 44

1 2

Figure 4.

3

4 5 6 7 8 9 10 11 12 13


Page 35 of 44

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1 2

Figure 5.

3

4 5 6 7 8 9

10

11

12 35 ACS Paragon Plus Environment


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1

TABLE CAPTIONS

2

Table 1. Calculation results for required tower height in present work

3

Table 2. The physic-chemical parameters of the system

4

Table 3. Calculation results for required tower height based on previous models

Page 36 of 44

5

6


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1 2 3

Table 1. Calculation results for required tower height in present work

te

ce

He



H

min

mg/L

m

min

m

88

0.065

3.53

122

4.90

4

5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 44

1 2

Table 2. The physic-chemical parameters of the system

3

W

W

W

O

g

D0

DW



D

A

g/cm3

N/m

pa·s

g/cm3

m/s2

m2/s

m2/s

g/cm3

/

%

1.05

17.5 x10-3

3.0×10-3

0.87

9.81

0.16 x10-9

6.76x10-11

0.18

76

0.98

4 5


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1 2

Table 3. Calculation results for required tower height based on previous models 28

3 g

g

d vs

a

0



s

LR

D

k0

cm/s

/

cm

m2/m3

cm/s

cm/s

cm/s

m3/h

/

m/s

13.2

0.094

0.25

217

0.026

0.066

0.17

0.4

0.26

4.2×10-7

kW

K



NTU W

HTU W

HW

H WG

E GZ

Pe

H WZ

m/s

m/s

/

/

m

m

m

m2/s

/

m

9.13×10-6

1.69×10-6

30.4

3.75

0.41

1.54

1.70

1.61

1.5

5.0

4 5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 1.


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Figure 2.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 3.


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Figure 4.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5.


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A Feasible Strategy for Calculating the Required Mass Transfer Height

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