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In this paper, the effects of pH on the mass transfer of copper extraction with hollow fiber renewal liquid membrane (HFRLM), which is a new type of l...
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Ind. Eng. Chem. Res. 2008, 47, 4256–4262

Modeling of Effect of pH on Mass Transfer of Copper(II) Extraction by Hollow Fiber Renewal Liquid Membrane Zhongqi Ren, Weidong Zhang,* Yuan Dai, Yanqiang Yang, and Zisu Hao State Key Laboratory of Chemical Resource Engineering, Beijing UniVersity of Chemical Technology, Beijing 100029, People’s Republic of China

In this paper, the effects of pH on the mass transfer of copper extraction with hollow fiber renewal liquid membrane (HFRLM), which is a new type of liquid membrane system based on the surface renewal theory, were investigated. The system of CuSO4 in acetate buffer solution + D2EHPA in kerosene + acidic aqueous solutions was used to study the effects of pH and acetate ion concentration in the feed phase and type and acidity of the stripping phase on the mass transfer performance of the HFRLM process. Results showed that the mass transfer flux and removal efficiency of copper increase with increasing pH in the feed phase, reach a maximum value at pH of 4.44, and then decrease; an addition of acetate buffer solution at a low acetate ion concentration in the feed phase is enough for maintaining the higher mass transfer flux and removal efficiency in the HFRLM process. The influence of the stripping phase on the mass transfer performance of the HFRLM process is weak in our ranges studied. The stripping phase at a low hydrogen concentration is enough for the extraction of copper by HFRLM. The mass transfer fluxes of copper ions from feed solutions with different stripping acids followed the order: Cl- > PO43- > SO42- > NO3-. And, a detailed mathematical model was developed based on the surface renewal theory. The calculated results have good agreement with experimental results. 1. Introduction Liquid membrane (LM) techniques have become an attractive removal and recovery methods of compounds from dilute aqueous solutions, such as metals and acids, due to the specific characteristics of carrying out simultaneous extraction and stripping processes in the same stage, nonequilibrium mass transfer, the uphill effect, high selectivity, the high mass transfer rate, etc.1–4 Since the end of 1960s, an emulsion liquid membrane was introduced by Li5 and a supported liquid membrane was introduced by Bloch and Finkelstein;6 liquid membrane techniques have been extensively studied for the past forty years. However, LM techniques had not been adopted for large scale industrial processes due to the lack of long-term stability and difficult operations,2,7 such as emulsification and de-emulsification steps in the emulsion liquid membrane process. Although researchers proposed many new liquid membrane compositions and liquid membrane techniques to avoid these problems,2,8–12 the issues were still not solved well. With this background, in order to avoid these problems in conventional LM, Zhang et al.4,13–15 proposed a new liquid membrane technique, called a hollow fiber renewal liquid membrane (HFRLM), which is based on the surface renewal theory and integrated the advantages of fiber membrane extraction,16 liquid film permeation,17 and other liquid membrane processes. In a HFRLM process, hydrophobic hollow fibers are used, which are prewetted with the organic phase over 48 h to make the pores fully filled with the organic phase. The feed phase is pumped through the shell side of the module. The stirred mixture of the organic and stripping phases at a high aqueous/organic volume ratio, in which the organic droplets are uniformly dispersed by stirring, is countercurrently pumped through the lumen side of the module. Due to the wetting affinity between organic phase and the walls of hydrophobic fibers, a thin organic * To whom correspondence should be addressed. Tel.: +86-1064423628. Fax: +86-10-64436781. E-mail: [email protected].

film, i.e. liquid membrane layer, is developed within the lumen side of fibers as shown in Figure 1. The shear force resulting in the flowing fluid will cause the film liquid to form microdroplets on the surface of the liquid membrane layer, which will peel off from the surface of the liquid membrane layer and enter into the lumen side fluid. At the same time, the organic droplets, dispersed in the lumen side flowing fluid, will fill the surface of the liquid film. Then, the renewal of the liquid membrane is proceeding. And, the shear force results in a thin developed liquid film, even though the mass transfer resistance of the liquid membrane is usually as small as a fraction of the total resistance of the HFRLM process. The solute can be selectively transported across the liquid membrane from the feed phase to the stripping phase. The renewal effect of the liquid membrane and huge mass transfer area due to the direct contact of organic droplets and the aqueous phase in severe mixing can accelerate the mass transfer rate and greatly reduce the resistance of mass transfer within the lumen side. Furthermore, the additional organic phase in the lumen side fluid is needed only for the renewal and continuity of the liquid membrane layer, which is also an automatic and continuous replenishment of the membrane liquid to prevent the loss of the membrane liquid. The HFRLM technique has some potential advantages of long-term stability, high mass transfer rate, easy operation, etc.4,13–15 In addition, for the removal and recovery of heavy metals from industrial effluents using liquid membrane techniques, such as copper(II), chromium(VI), etc., the pH in the feed phase and the stripping phase are the key factors as many researchers mentioned. For example, Zhu et al.18 and Zuo et al.19 reported the effects of pH in the aqueous phase on the mass transfer of the hollow fiber membrane extraction processes; Gherrou et al.,20 Venkateswaran et al.,21 and Alguacil et al.22 indicated that the pH in the feed phase and the receiver phase had significant effects on the mass transfer of hollow fiber supported liquid membrane processes; also, the effects of pH in the feed phase and the receiver phase on the mass transfer of emulsion liquid

10.1021/ie0714798 CCC: $40.75  2008 American Chemical Society Published on Web 05/21/2008

Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4257

organic phase and stripping phase flows through the lumen side of the module. The transport of copper through a hollow fiber renewal liquid membrane from the feed phase to the stripping phase can be considered as five sequential steps, including diffusion of metal ions across the aqueous stagnant layer within the shell side, forward chelating reaction at the external surface of the membrane, diffusion of the metal complex through the membrane phase, renewal process of the developed liquid membrane layer, and backextraction process within the lumen side, which can be described mathematically within a differential ∆A as follows: (1a) Transport of copper ion in the shell side

Figure 1. Principle of hollow fiber renewal liquid membrane process.

S ∆NS,Cu ) kS,Cu∆A(Cf,Cu - Cms,Cu )

(4)

(1b) Counter transport of hydrogen ions in the shell side S ∆NS,H ) kS,H∆A(Cf,H - Cms,H )

(5)

(2) Forward chelating reaction at the external membrane surface

(

∆Nr ) ∆A k1 Figure 2. Concentration profiles of the copper transport in the HFRLM process.

membrane processes were studied by Chakravorty et al.,23 Reis et al.,24 and so on. In this work, CuSO4 in acetate buffer media aqueous solution + 10% D2EHPA in kerosene + acidic aqueous solutions were used to study the effects of pH and acetate ion concentration in the feed phase and type of acid and hydrogen concentration in the stripping phase on the mass transfer performance of HFRLM process. A mathematical model based on the surface renewal theory was also developed. The modeling results were also compared with experimental results. 2. Modeling of Mass Transfer

Cu

+

+ 2(HR)2 h CuR2·(HR)2 + 2H

(1)

Where, the overbar refers to organic phase and (HR)2 denotes the dimeric form of D2EHPA. The equilibrium constant, Keq,Cu, and the extraction distribution coefficient, m, are given by the following: m)

[CuR2] [Cu2+]

2

) Keq,Cu

[(H2R2)] [H+]2

(2)

The forward chelating reaction rate is expressed as26,27 2+

r1 ) k1

[Cu ][(HR)2]2 [H+]2

S 2 Cms,H +

(

)

m - k-1Cms,CuR 2·(HR)2

)

- k-1[CuR2 · (HR)2]

(3)

where k1 and k-1 are the interfacial forward reaction rate constant and interfacial backward reaction rate constant, respectively. 2.2. Mass Transfer in Hollow Fiber Module. The concentration profiles in and around a hydrophobic hollow fiber are shown in Figure 2, based on the fact that hydrophobic microporous membranes can be wetted by organic solvents, the feed phase flows through the shell side, and the mixture of the

(6)

(3a) Diffusion of copper complex across the membrane m m - CRm,CuR ∆Nm,Cu ) km,Cu∆A(Cms,CuR 2·(HR)2 2·(HR)2)

(7)

(3b) Diffusion of D2EHPA across the membrane m m ∆Nm,(HR)2 ) km,(HR)2∆A(Cms,(HR) - CRm,(HR) 2 2)

(8)

(4a) Transport of the copper complex during the renewal process of the liquid membrane R R ∆NR,Cu ) kR,Cu∆A(CRm,CuR - CTR,CuR 2·(HR)2 2·(HR)2)

(9)

(4b) Counter transport of D2EHPA during the renewal process of the liquid membrane R R ∆NR,(HR)2 ) kR,(HR)2∆A(CRm·(HR) - CTR,(HR) 2 2)

2.1. Solvent Extraction. The solvent extraction of copper with D2EHPA dissolved in kerosene from aqueous solutions can be written as follows:25–27 2+

S S 2 Cms,Cu (Cms,(HR) 2)

(10)

(5a) Transport of the copper in the lumen side T O ∆NBEx,Cu ) kBEx,Cu∆A ′ (CTR,CuR - Cst,Cu ) 2(HR)2

(11)

(5b) Counter transport of D2EHPA in the lumen side O T ∆NBEx,(HR)2 ) kBEx,(HR)2∆A ′ (CTR,(HR) - Cst,(HR) 2 2)

(12)

(5c) Counter transport of hydrogen in the lumen side T T ∆NBEx,H ) kBEx,H∆A ′ (CTR,H - Cst,H )

(13)

Within a differential cell ∆z, the mass balances in shell side and lumen side are given as S S ∆Nf, Cu ) Qf(Cf,Cu,z+∆z - Cf,Cu,z )

(14)

T T ∆Nst, Cu ) Qst(Cst,Cu,z+∆z - Cst,Cu,z )

(15)

Then, at steady state, all of these individual mass transfer rates are equal to the overall mass transfer rate, NCu: 1 1 NCu ) Nf,Cu ) Nst,Cu ) NS,Cu ) - NS,H ) Nm,Cu ) - NS,(HR)2 2 2 1 1 1 ) NR,Cu ) - NR,(HR)2 ) NBEx,Cu ) - NBEx,H ) - NBEx,(HR)2 2 2 2 (16)

4258 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008

According to the fast kinetics of the stripping process, the huge mass transfer area resulting from the direct contact between organic droplets and stripping aqueous phase, and the severe mixing arising by fluid flow, the stripping process of copper in the lumen side is very fast. Then, the individual mass transfer resistance of this step can be neglected.4,11,25,28 Assuming that the metal-complex concentration in organic droplets is equal to that in the surface of the renewal liquid membrane film based on surface renewal theory, when the stirred mixture of stripping phase and organic phase flows o through the lumen side of the module, CT,CuR 2 · (HR)2 ) R T m R CTR,CuR2 · (HR)2 ) m′CT,Cu, CRm,CuR2 · (HR)2 ) CRm,CuR2 · (HR)2, and m S Cms,CuR 2 · (HR)2 ) mCS,Cu, where m and m′ are the distribution coefficients of the extraction and backextraction processes, respectively. By combining eqs 4–16, then the mass transfer flux is

(

∆JCu ) Kf,Cu Cf,Cu -

m′ C m st,Cu

)

(17)

where the overall mass transfer coefficient, Kf,Cu, based on the feed phase is 1 1 ) + Kf,Cu kS,Cu

S 2 Cms,H + S 2 k1 Cms,(HR) 2

(

)

(

)

+

S 2 k-1 Cms,H + S 2 km,Cuk1 Cms,(HR) 2

(

)

(

(18)

and mCu ) Keq,Cu

S (Cms,H )2 +

)

S 2 k1(Cms,(HR) 2)

(19)

S 2 k-1(Cms,H +)

For the whole hollow fiber module in countercurrent flow mode, eq 17 should be integrated to obtain JCu,Exp ) Kf,Cu∆Clm,Cu

(20)

where ∆C1,Cu - ∆C2,Cu ∆C1,Cu ln ∆C2,Cu m′ out m′ in in out Cf,Cu - Cst,Cu - Cf,Cu - Cst,Cu m m ) m′ out in Cf,Cu - Cst,Cu m ln m′ in out Cf,Cu - Cst,Cu m

∆Clm,Cu )

(

) (

)

(21)

Where, ∆Clm,Cu is the logarithmic mean driving force of mass in out transfer. Cf,Cu and Cf,Cu are the inlet and outlet copper(II) in out concentration in the feed phase, respectively. Cst,Cu , Cst,Cu are the inlet and outlet copper(II) concentration in the stripping phase, respectively. If the mass transfer parameters are known, JCu and Kf,Cu can be calculated by solving the systems of eqs 4–21. 2.3. Estimation of Individual Mass Transfer Coefficients. The correlations used for estimating the individual mass transfer coefficient in the shell side, kS, as developed by Dai et al. are the following:29

( )(

kSdH dH2uS µ ) 8.58 D µLH FD

1⁄3

)

(

∑r ) R +∑r

2 Ri2 i

2

o

(23)

o

The individual mass transfer coefficient in the membrane phase, km, can be approximated according to30 Dε (24) ext ( τ d - dint)/2 where ε and τ are the porosity and tortuosity of the membrane support, respectively. dext and dint are the external and internal diameters of hollow fibers, respectively. And, the individual mass transfer coefficient, kR, can be obtained using following empirical correlation based on surface renewal theory,4,31,32 km )

( )

kR ) aD0.5S0.5 ) aD0.5

Fgu µTΦ

0.25

) aD0.25Re0.25Φ-0.25 (25)

S 2 kR,Cuk1(Cms,(HR) 2)

2

dH )

+

)

S 2 k-1(Cms,H +)

S (Cms,(HR) )2

effective length of the shell side, uS is the flow rate of the shell side, and dH is the hydraulic diameter of the shell side, defined as the cross-sectional flowing area divided by the wetted perimeter:

(22)

Where, D is the diffusivity of species in the aqueous phase, µ is the viscosity of the aqueous phase, F is the density, LH is the

where a is enhancement factor, which can be obtained by model fitting from experimental data, S is the renewal rate of liquid membrane, F is the density, µ is the viscosity of the organic phase, uT is the flow rate of lumen side, Re is the Reynolds number in the lumen side, and Φ is the holdup of organic droplets in the mixture flowing through the lumen side. 3. Experimental Section 3.1. Reagents and Solutions. The reagents included di(2ethylhexyl) phosphoric acid (D2EHPA) (Tianjin Guangfu Chemical Co. Ltd.; AR, >98.5%), copper sulfate anhydrous CuSO4 · 5H2O (Shanghai Tingxin chemical reagent plant; AR, >99.0%), acetic acid glacial and sodium acetate anhydrous (Tianjin Fuxing chemical reagent plant; AR, >99.0%), and commercial aviation kerosene (Tianjin Damao chemical reagent plant), which was washed twice with 20% (vol) H2SO4 to remove aromatics and then with deionized water three times. All other chemicals were of analytical grade and used as received except for kerosene. The feed phase was prepared by dissolving a weighed amount of CuSO4 in acetate buffer media, in which the pH was adjusted as suggested by Komasawa and Otake.27 The organic phase was prepared by dissolving 10 vol% D2EHPA in kerosene. 3.2. Apparatus and Procedure. All the experiments were conducted using the self-designed systems, and the experimental setup in one-through mode is shown in Figure 3. The used hollow fiber module is self-manufactured with small laboratory scale versions (with two 0-1 dm3 · min-1 peristaltic pumps and flow meters) that were specifically designed for the experimental purposes. The used polyvinylidene fluoride (PVDF) hollow fibers were from Tianjin Polytechnic University, and pores of these hollow fibers were prewetted with organic phase more than 48 h before each experiment. Additional information about these modules was provided in Table 1. The stirred mixture of the stripping phase and organic phase at a high w/o ratio (20:1) is pumped through the lumen side of the module. The feed phase is pumped through the shell side of the module. Both fluids were contacted in countercurrent and one-through mode. Pressure gauges and valves are present to control flow rates in order to ensure that a positive pressure

Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4259

Figure 4. Effects of pH in feed phase on the mass transfer flux and removal efficiency of copper.

4. Results and Discussion

Figure 3. Experimental setup of the HFRLM process in one-through mode. Table 1. Characteristics of the Hollow Fiber Module shell characteristics material length, L internal diameter, 2Ri outer diameter

glass 30.2 cm 1.50 cm 1.70 cm

fiber characteristics material number of fibers in module, N effective length, LH internal diameter, dint external diameter, dext, 2ro effective surface area of module, A packing density membrane porosity, ε membrane tortuosity, τ

PVDF 80 29.8 cm 814 µm 886 µm 0.0544 m2 0.387 0.82 2.0

was maintained on shell side of the module. When a stable state was arrived, aqueous samples (5 mL) were taken from outlet of lumen and shell side at preset time intervals. The copper(II) concentration of aqueous phase was analyzed with sodium diethyldithiocabamate spectrophotometric method (GB7474-87, P.R. China). And, a digital precision ionometer model PXS-450 (Shanghai Dapu Co. Ltd.) with a combined glass electrode was used for pH measurements ((0.01 pH). The meter was standardized against 4.01, 6.85, and 9.14 standard buffer solutions. The experimental mass transfer fluxes JCu of the Cu2+ across the liquid membrane from the feed phase to the stripping phase can be determined by applying the following equation: JCu,Exp )

d[Cu2+]stVst Qst∆[Cu2+]st ) A · dt A

(26)

where ∆[Cu2+]st represents the variation of the copper concentration in the stripping phase at time interval ∆t, Qst is the volumetric flow rate of stripping phase, A is the effective mass transfer area, and Vst is the volume of stripping solution. The removal efficiency of copper(II) is defined as follows: η)

in out - Cf,Cu Cf,Cu in Cf,Cu

× 100%

(27)

4.1. Distribution Equilibrium. More detailed information regarding the liquid-liquid extraction equilibria and mass transfer kinetics is required to understand and quantitatively describe the rate law, which controls the transport of metals species through HFRLM, and to exploit them for separation processes. In our previous studies,28 the pH and acetate ions concentration in the feed phase had significant influences on the extraction of copper with D2EHPA as carrier; the effects of acid type and hydrogen concentration on the stripping process were also studied in detail. 4.2. Influence of pH in the Feed Phase. In order to assess the significance of the role of pH in the feed phase during the transport process of copper through HFRLM, experiments were conducted at different pH values in the ranges of 2.5-5.5. The initial copper concentration in the feed phase is 182.5 mg · L-1, in which the pH was adjusted by acetate buffer solution that the acetate ions concentration is 0.073 mg · L-1. This small amount of buffer solution was assumed not to have any influence on the mass transfer rate of extraction process.27,33 It could maintain pH of the aqueous phase at a constant value over the initial 5% approach to the equilibrium. The stripping phase is 6.01 mol · L-1 HCl aqueous solutions. The effects of pH in the feed phase on mass transfer flux and removal efficiency of copper are shown in Figure 4. The mass transfer flux and removal efficiency increase with increasing pH, reach a maximum value at pH of 4.44, and then decrease. As shown in eq 18, the overall resistance of mass transfer increases with decreasing pH in the feed phase. In the case of lower pH (4.44), although the lower hydrogen concentration in the feed phase leads to lower overall resistance of mass transfer, the lower hydrogen concentration in the feed phase can also cause the acidic dissociation of D2EHPA in the interface between aqueous phase in the shell side and membrane phase, this is not beneficial for the transport of copper through HFRLM. Furthermore, the driving force of mass transfer caused by distribution equilibrium decreases with increasing pH in the feed phase. These all make the mass transfer flux and removal efficiency decreasing at higher pH in the feed phase. 4.3. Influence of Acetate Ion Concentration in the Feed Phase. In the extraction process with D2EHPA as solvent, when the pH in the CuSO4 aqueous solution was not adjusted with buffer media, the pH in aqueous phase would be significantly reduced, which would reduce the extraction efficiency of copper

4260 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008

Figure 5. Effects of acetate ion concentration in the feed phase on mass transfer flux and removal efficiency of copper.

sharply. The introduction of acetate buffer solution into the CuSO4 aqueous solution can resolve this issue.28 The buffer capacity of acetate buffer solution mainly depends on the acetate ions concentration in the aqueous solution at the given pH value. The concentration of the buffer solution in the working solution was made less than 0.25 mol · L-1 in our studies, because an addition of less than 0.30 mol · L-1 was not found to have any effect on the formulation of metal extraction equilibrium in studies of Komasawa et al.27,33 For the HFRLM process, in the case of feed aqueous solution without buffer media, the small distribution coefficient of copper between aqueous solution without buffer media and organic phase leads to low mass transfer driving force of the HFRLM process; the mass transfer flux and removal efficiency of copper are very low. As indicated in Figure 5, the acetate ion concentration has significant influence on the mass transfer flux and removal efficiency of copper. The mass transfer flux and removal efficiency increase with an increasing acetate ion concentration in the feed phase at low acetate ion concentrations. At acetate ion concentrations of 0.073 mol · L-1, the mass transfer flux and removal efficiency achieve maximum values. The pH in the aqueous solution almost could maintain a constant value of 4.4. This indicates that the acetate buffer solution at a low acetate concentration can supply enough buffer capacity in the copper transport process through HFRLM. Then, the mass transfer flux and removal efficiency decrease with an increasing acetate ion concentration (>0.073 mol · L-1), because at higher acetate ion concentrations, the buffer capacity is stronger, the Na+ concentration is also higher, Na+ will compete with Cu2+. That is, Na+ will be extracted in place of Cu2+, which does not benefit the transport of copper.28 4.4. Influence of Hydrogen Concentration in the Stripping Phase. Solvent extraction studies28 in our previous work revealed that the hydrogen concentration in the stripping phase have a significant effect on the backextraction efficiency of copper from the organic phase of D2EHPA in kerosene to HCl aqueous solution. Hydrochloric acid solutions were used as stripping phase to study the effects of hydrogen concentration in the stripping phase on the mass transfer performance of the HFRLM process in our work. The hydrogen concentration in the HCl aqueous solution was in the range of 1.0-8.0 mol · L-1. The initial copper concentration in the feed phase is 189.9 mg · L-1 at a pH of 4.44. As shown in Figure 6, the influences of hydrogen concentration in the stripping phase on the mass transfer flux and removal efficiency of copper were small. As indicated in eq 18, in the transport process of copper from the feed phase in the shell side to the stripping phase in the lumen side, the overall mass transfer resistance is related with the distribution coefficient of the extraction process, but not with that of the backextraction process. Then, the influence of the stripping phase is only on

Figure 6. Effects of H+ concentration in the stripping phase on mass transfer flux and removal efficiency of copper.

Figure 7. Effects of acidic stripping type on mass transfer flux and removal efficiency of copper.

the driving force of mass transfer in the HFRLM process as shown in eq 21. Generally, the effect of the distribution coefficient of the backextraction process on the driving force is also small, due to the value of m′/m in eq 21 usually being large. Then, the effect of hydrogen concentration in the stripping phase is weak under the ranges studied. Therefore, the stripping phase at a low hydrogen concentration is enough for the extraction process of copper by HFRLM. 4.5. Influence of Acid Type of Stripping Phase. In this work, four types of inorganic acid were used as the stripping phase to study the influence of stripping phase type on the mass transfer performance in the HFRLM process. In all experiments, the hydrogen concentrations in the stripping phase remain at 6.00 mol · L-1, and the initial copper concentration in the feed solution is around 186.8 mg · L-1 at a pH of 4.44. The results are shown in Figure 7. Among those inorganic acids, the highest mass transfer flux and removal efficiency are observed for hydrochloric acid aqueous solutions, the order follows Cl- > PO43- > SO42- > NO3-, while the difference of acid type of stripping phase on mass transfer performance of HFRLM process is not large. As discussion above, the stripping phase almost have no influence on the overall mass transfer resistance of the HFRLM process, but only small influence on the mass transfer driving force caused by backextraction equilibrium. The difference of acid type on mass transfer may be caused by the diffusion resistance of copper in different anion aqueous conditions. That is, the resistance of mass transfer across the boundary layer of the stripping phase is different. The results are consistent with Molinari’s investigation,34 which indicated that the hydrochloric acid solutions had the highest extraction efficiency in their studies of amino acids transport with a supported liquid membrane. However Gherrou et al.20 indicated that the transport fluxes of silver and copper ions from feed solutions of different anionic compositions followed the order: NO3- > Cl- > SO42> PO43-, in their studies of removal of the silver and copper

Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4261

Figure 8. Comparison of experimental and calculated mass transfer fluxes of copper in the HFRLM process.

ions from acidic thiourea solutions with a supported liquid membrane containing D2EHPA as carrier. 4.6. Comparison of the Calculated and Experimental Results. The extraction equilibrium constant, KEx, is 4.41 × 10-4,35 the forward reaction rate constant, k1, is 7.54 × 10-10 m · s-1,26 the diffusivity of copper ions in aqueous solution, DCu, is 7.40 × 10-10 m2 · s-1,36 the diffusivity of hydrogen in the aqueous phase, DH, is 9.30 × 10-9 m2 · s-1,36 the diffusivity of D2EHPA in the organic phase (kerosene), D(HR)2, is 6.20 × 10-10 m2 · s-1,37 and the diffusivity of the copper-D2EHPA complex in the organic phase (kerosene), DCuR2, is 4.70 × 10-10 m2 · s-1.37 The terms m and m′ are mainly obtained from previous experimental results;28 the constant a in eq 25 is 0.005, obtained by fitting experimental data to model correlations.4 Then the modeled overall mass transfer coefficient and mass transfer flux can be calculated by the modeling above. In Figures 4–7, the modeled results are given as solid lines, which are in good agreement with experimental results under the conditions studied as shown in Figure 8. The weighted standard deviation defined as follows, is less than 10%, indicating the validity of the proposed models.



n

∑ i)1

(

)

JCu,Cal -1 JCu,Exp

2

× 100% (28) n-1 Where, n is the number of experimental data points. The subscripts “Cal” and “Exp” are the calculated and experimental values, respectively. The deviation maybe result from the accuracy of model parameters especially for m and m′, because m and m′ are functions of pH and copper concentration which are varying along the module. The values of [H+] and [(HR)2] concentration in the interface between the feed phase in the shell side and the membrane phase, which are used to determine the value of m by eq 19, are nearly impossible to measure, and the fitting values have large deviation. In the calculation processes, constant values of m and m′ are used instead of variants due to the values of m and m′ being difficult to determine. This may result in large deviation. Certainly, the modification of the model for these issues should be carried out in the future. SD )

5. Conclusions The effects of pH on the mass transfer performance of hollow fiber renewal liquid membrane (HFRLM), which is a new type of liquid membrane systems based on the surface renewal theory, were studied. The systems of CuSO4 in acetate buffer aqueous solution + 10% D2EHPA in kerosene + acidic aqueous solutions were used to study the mass transfer performance of HFRLM process.

Results showed that the pH in the feed phase had significant influence on the mass transfer of HFRLM process. The mass transfer flux and removal efficiency of copper increase with increasing pH in the feed phase, reach a maximum value at pH of 4.44, and then, decrease. The acetate buffer solution at a low acetate ion concentration could hold higher mass transfer fluxes and removal efficiency in the entire HFRLM process; the aqueous pH could remain at a constant value. The characteristics of the stripping phase within the lumen side almost have no influence on the overall resistance of mass transfer, but only have small influence on the driving forces of mass transfer under the whole range studied. Then, the stripping phase has a weak influence on the mass transfer performance of the HFRLM process. The stripping phase at a low hydrogen concentration is enough for the extraction of copper by HFRLM. The mass transfer fluxes of copper ions from feed solutions with different stripping acids followed the order: Cl- > PO43- > SO42- > NO3-. A mathematical model, derived from surface renewal theory and mass balance law, was developed for analyzing the influences of these variables on the mass transfer of HFRLM process. The modeled results have good agreement with experimental values. Acknowledgment This work was supported by the National Natural Science Foundation of China (Grant Nos. 20576008 and 20706003) and the Program for New Century Excellent Talents in University (Grant No. NCET-05-0122). The Authors gratefully acknowledge these grants. Nomenclature a ) enhancement factor in eq 25 A ) effective mass transfer area, m2 A′ ) effective mass transfer area in eq 11, m2 C ) concentration, mg · L-1 ∆Clm ) the logarithmic mean driving force of mass transfer D ) diffusivity, m2 · s-1 d ) diameter, m dH ) hydraulic diameter, m J ) mass transfer flux, mg · m-2 · s-1 k1 ) forward reaction rate constant, m · s-1 k-1 ) backward reaction rate constant, m · s-1 k ) individual mass transfer coefficient, m · s-1 Kf ) overall mass transfer coefficient base on the feed phase, m · s-1 Keq ) extraction equilibrium constant LH ) effective length of the shell side, m m ) distribution coefficient of extraction process m′ ) distribution coefficient of backextraction process n ) number of experimental data points N ) mass transfer rate, mg · s-1 Q ) volumetric flow rate, m3 · s-1 Ri ) internal radius of shell side, m r1 ) forward chelating reaction rate, mg · m-2 · s-1 ro ) radius of external fiber, m S ) surface renewal rate t ) time, s u ) velocity, m · s-1 V ) volume, m3 w/o ) aqueous/organic volume ratio Z ) position, m Greek Letters F ) density, kg · m-3 µ ) viscosity, Pa · s

4262 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 Φ ) dispersed phase holdup ε ) porosity of membrane support τ ) tortuosity of membrane support η ) removal efficiency Superscripts in ) inlet out ) outlet ext ) external int ) internal o ) organic phase R ) renewal liquid membrane phase or renewal process of liquid membrane m ) membrane phase S ) shell side T ) lumen side Subscripts BEx ) backextraction Cal ) calculated eq ) equilibrium Exp ) experimental f ) feed phase m ) membrane phase ms ) interface between aqueous phase of shell side and membrane phase r ) reaction R ) renewal liquid membrane layer or renewal process of liquid membrane Rm ) interface between renewal liquid membrane phase and membrane phase st ) stripping phase S ) shell side T ) lumen side TR ) interface between aqueous phase of lumen side and renewal liquid membrane phase

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ReceiVed for reView October 31, 2007 ReVised manuscript receiVed February 26, 2008 Accepted March 4, 2008 IE0714798