Efficiency of Hollow Fiber Modules for Nondispersive Chemical

Nov 15, 1995 - wastewater treatment and hydrometallurgy. It was possible to achieve 2-4 orders of magnitude decrease of metal concentration in the aqu...
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Ind. Eng. Chem. Res. 1996, 35, 184-191

Efficiency of Hollow Fiber Modules for Nondispersive Chemical Extraction† Ulrich A. Daiminger, Andreas G. Geist, Walter Nitsch, and Pawel K. Plucinski* Technische Universita¨ t Mu¨ nchen, Institut fu¨ r Technische Chemie, Lichtenbergstrasse 4, 85748 Garching, Germany

In this work the efficiency of hollow fiber solvent extraction for the system Meaq/bis(2-ethylhexyl) phosphate (DEPA) in isododecane (Me ) Cd, Ni, Zn) has been studied from two points of view: wastewater treatment and hydrometallurgy. It was possible to achieve 2-4 orders of magnitude decrease of metal concentration in the aqueous phase by extraction in a single-pass flow mode. Furthermore the attainable phase ratios permit very high enrichment of metallic species (ca. 3 orders of magnitude) in the circle extraction-reextraction. Previously performed thorough studies on the kinetics and mechanism of the mass transfer in the investigated system (interfacial reaction, transport-limited process) allowed predictive modeling of hollow fiber reactive extraction. The necessary values of mass transfer coefficient were calculated using correlations existing in the literature, which were checked experimentally. The obtained results of extraction were compared with those for a pulsed sieve-plate column and an ideal mixer-settler cascade. It was shown that one module (54 cm length, 9000 fibers, or 25 cm and 31 000 fibers) can replace an extraction column of 6 m length and two to four ideal stages. Presented results indicate the use of hollow fiber modules as high performance extraction devices. Introduction Solvent extraction has been applied to separate and concentrate metallic species in hydrometallurgical processes and may be also used in wastewater treatment. Independently of the achievements in extraction chemistry, in recent years attention has been also paid to develop new high-efficiency equipment for solvent extraction (Sekine, 1992; Logsdail and Slater, 1993). One of the promising ideas is the use of microporous hollow fiber modules (HFMs) as liquid/liquid phase contactors (Kim, 1984). The basic principle of nondispersive extraction is the immobilization of the interface in the pores of hydrophobic membranes, due to wetting and appropriate applied static pressure (Kiani et al., 1984; Kim 1984). The main advantages of this method are the following: no entrainment; no flooding; very large interfacial area; the possibility to realize extreme phase ratios; independency of phase densities and interfacial tension (Dahuron and Cussler, 1988). A shortcoming of HFM extraction could be blinding with particles in the feed (prefiltration might be necessary). Several works exploring this technique for the extraction of organics (Basu et al., 1990; Hutter et al., 1994), extraction of bioproducts (Dahuron and Cussler, 1988; Ding et al., 1992), as well as extraction of metal ions (Kim, 1984; Yun et al., 1993; Alonso et al., 1994) have been published in the past decade. These works show the feasibility of HFMs as phase contactors. In addition to experimental work, studies have been made to model physical mass transfer (Prasad and Sirkar, 1988; Basu et al., 1990; Ding and Cussler, 1991) as well as reactive solvent extraction (Yun et al., 1993; Alonso et al., 1994). A reliable description of a mass transfer apparatus demands a knowledge of the mechanism of the process (the site of chemical reaction, the limiting mass transfer steps) and all kinetic (rate laws, mass transfer coefficients) and thermodynamic data (stoichiometry of the * To whom correspondence should be addressed. † Dedicated to Prof. Dr. J. Klein on the occasion of his 60th birthday.

0888-5885/96/2635-0184$12.00/0

reaction and equilibrium constants). The strategy for modeling the reactive extraction, consequently applied in our work group (Nitsch and van Schoor, 1983. Hempe, 1990. Walter et al., 1993) consists of the following steps: determination of the site of chemical reaction (stirred cell experiments (Nitsch and Kruis, 1978; Nitsch, 1984)); determination of the limiting steps of mass transfer (stirred cell experiments (Nitsch and Kruis, 1978; Nitsch, 1984)); determination of either appropriate mass transfer coefficients (Nitsch and Schuster, 1983) or rate laws; calculation of concentration profiles based on hydrodynamic and kinetic parameters. This strategy has been successfully employed for the U/HNO3 extraction (Nitsch and van Schoor, 1983), for the separation of Th4+/UO22+ (Hempe, 1990), and for the Zn/DEPA system (Walter et al., 1993) in a pulsed sieveplate column as well as for the description of the metal ion permeation through solid supported liquid membranes (Plucinski and Nitsch, 1988). The concept of our contribution concerns the feasibility of HFM for heavy metal extraction in wastewater treatment, with the aim to characterize possible and optimal operation conditions regarding the throughputs of the phases and the possible enrichment in the circle extraction-reextraction. In addition an estimation of the efficiency of the HFM should be performed with comparable measurements in a pulsed sieve plate column. Mass Transfer System Most kinetic experiments were made with the system Zn/DEPA. The extraction of zinc ions with DEPA in isododecane was selected as the test system from different reasons: zinc is a typical wastewater element (Hartinger, 1991); the phosphoric extractant is suitable also for the extraction of Cd, Cu, Ni and Pb (Grimm and Kolarik, 1974; Kolarik and Grimm, 1976; Juang and Lee, 1994). It was shown with stirred cell experiments (in a concentration range 1-100 mg/L) that for all these species transport processes were rate limiting for extraction as well as reextraction (Walter et al., 1993; Walter, 1994). © 1996 American Chemical Society

Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 185 Table 1. Equilibrium and Stoichiometry Data of Investigated Systems metal ion

n

K

Cd Cu Ni Pb Zn

2 2 2.5 2 1.5

(6.0 ( 1.5) × 10-3 (2.0 ( 0.5) × 10-3 (5.4 ( 1.1) × 10-5 0.1 ( 0,02 (5.0 ( 0.8) × 10-2

The liquid/liquid interface is the site of the chemical reaction as supported by the good agreement between experimental and calculated results. The calculations were made under the assumption that bulk reaction can be neglected (Walter, 1994). Such a kinetic behavior with a fast interfacial reaction is essential for the realization of high efficiency in the module operation. Furthermore, the chemical system Zn/DEPA is proposed by the European Working Party on Distillation, Extraction and Adsorption to be tested as a standard system for investigation of extraction equipment for reactive extraction. Figure 1. Schematic view of the locale concentration profiles in a HFM: (a) extraction; (b) reextraction.

Modeling of Mass Transfer For the investigated systems the following stoichiometries of the ion exchange have been found as presented in Table 1, which are in good agreement with literature data (Grimm and Kolarik, 1974; Walter et al., 1993; Walter, 1994):

Me2+ + n(HX)2 h MeX2(HX)2n-2 + 2H+

(1)

In eq 1 it is taken into account that DEPA dimerizes in organic solvents (Ferraro and Peppard, 1963). The equilibrium constants were determined experimentally according to

[MeX2(HX)2n-2]([H ]) [Me2+]([(HX)2])n

(2)

and are also listed in Table 1. For transport-limited mass transfer the equilibrium at the liquid/liquid interface defined by eq 2 has to be assumed (Nitsch, 1984), with the appropriate interfacial concentrations in eq 2. The schematic view of the concentration profiles of all species being involved in the mass transfer process is shown in Figure 1. The various steps of mass transfer process together with kinetic equations are listed below (the + sign corresponds to the extraction of metallic species; the sign denotes the reextraction): 1. diffusion of metal ions in the aqueous phase:

jMe,aq ) (βMe,aqA1([Me2+]aq - [Me2+]aq*)

(3)

2. diffusion of hydrogen ions in the aqueous phase:

jH,aq ) (βH,aqA1([H+]aq* - [H+]aq)

jc,m ) DoAM ( ([MeX2(HX)2n-2]o* - [MeX2(HX)2n-2]M) (5) δτ 4. diffusion of complexing agent through the membrane organic phase:

jca,m ) (

DcaAM ([(HX)2]M - [(HX)2]M*) δτ

(6)

5. diffusion of metal complex in the bulk organic phase:

+ 2

KMe )

3. diffusion of metal complex through the membrane organic phase:

(4)

The applied membrane is hydrophobic, so it was assumed that the micropores are completely filled with the organic solvent.

jc,o ) (βc,oA2([MeX2(HX)2n-2]M - [MeX2(HX)2n-2]o) (7) 6. diffusion of complexing agent in the bulk of organic phase:

jca,o ) (βca,oA2([(HX)2]o - [(HX)2]M)

(8)

At steady state the following equation holds from stoichiometric reasons:

1 1 1 jMe,aq ) jc,o ) jc,m ) jH,aq ) jca,o ) jca,m 2 n n

(9)

Equations 3-9 can be solved numerically according to a Newtonian method. Basing on the concept of the back flow model (Mecklenburg and Hartland, 1975), an iterative procedure has been developed for a cellwise calculation of concentration profiles in HFM. Because of laminar flow in both phases, the axial mixing term was neglected. For each time step the mass transfer balance in all cells was established and the procedure was repeated until stationary conditions were reached. The only input data are initial concentrations, flow rates, and geometry of the HFM. The mass transfer coefficients can be calculated according to known correlations (Skelland, 1974; Costello et al., 1993), so no fitting is needed. The local mass transfer coefficients

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in the HF lumen were calculated according to the analytical solution (Skelland, 1974): j)∞

∑ j)1

( ) ( ) ( ) ( )

Bj dΦj 2 dr+

Sh(x) )

∑ j)1

-βj(x/rt)

r+)1

Bj dΦj

j)∞

2

exp

2βj2 dr+

exp

r+)1

Re Sc

(10)

-βj(x/rt) Re Sc

where

8 βj ) 4(j - 1) + ; j ) 1, 2, 3, ... 3

(11)

Bj ) (-1)j-1(2.84606)βj-2/3

( )

-Bj dΦj 2 dr+

) 1.01276βj-1/3

Figure 2. Experimental setup.

r+)1

Table 2. Short Characteristics of Used Modules

The mean mass transfer coefficients in the shell side for countercurrent parallel flow modules (1-3) were calculated according to the experimental correlation (Costello et al., 1993):

Shav ) (0.53 - 0.58φ)Re0.53Sc0.33

(12)

To the best of our knowledge (Wang and Cussler, 1993) no literature correlation exists in order to calculate the values of mass transfer coefficients in the shell side of the cross flow Hoechst-Celanese modules (module 4 and 5). Therefore the modeling was only performed for parallel flow modules. In our research group currently efforts are made to establish our own correlation for the cross flow type of modules. The diffusion coefficients of metal ions in an aqueous phase were assumed to be 1.2 × 10-9 m2/s (Patil et al., 1993), and the diffusion coefficient of H+ was equal 2.6 × 10-9 m2/s (Tyrrel and Harris, 1984). For small concentration of complexing agent ([DEPA2] ) 0.05 mol/ L) the value 1.0 × 10-9 m2/s was taken after Yoshizuka et al. (1992) for DEPA diffusion and for metal complexes 1.33 × 10-10 m2/s after Fernandez et al. (1986). For the high concentration of complexing agent ([DEPA2] ) 0.50 mol/L) the values of diffusion coefficient were recalculated using the Wilke-Chang correlation (Tyrell and Harris, 1984) taking into account the measured change of the viscosity. The tortuosity factor of the polypropylene membrane was taken as 2.6 according to Prasad and Sirkar (1988). In order to compare the efficiency of HFM extraction with an ideal mixer-settler cascade, the concentrations of all species in the aqueous phase and in the organic phase after a particular number of stages were calculated based on the principle of batch simulation of a continuous countercurrent cascade (Treybal, 1963). These calculations enable the further estimation of HETS values of HFM for various conditions. On this way we avoid the application of a McCabe-Thiele diagram, which in a multidimensional problem such as reactive extraction (Chapman et al., 1975) can lead to ambiguous results.

no.

type

no. of fibers

1 2 3 4 5

5PCM-106 5PCM-104 5PCM-105 5PCM-107 5PCM-108

2100 9000 9000 31000 31000

module diameter (cm)

module length (cm)

active interfacial area (m2)

2.5 5.1 5.1 10.0 10.0

16.0 24.1 54.6 25.0 65.0

0.08 0.49 1.11 2.2 5.5

HFM in a countercurrent and once-through mode. In the aqueous phase the pressure was held 0.2-0.5 bar higher than in the organic phase (measured at the outlet of the aqueous phase and inlet of the organic phase) regardless of the volumetric flow rates due to the use of four valves (Dahuron and Cussler, 1988). The pressure drop was measured in both phases. The HFMs used are manufactured by Hoechst Celanese (Liqui-Cel) and are specified in Table 2. All modules contain hollow fibers made of polypropylene (Celgard X-10) with an inner diameter equal to 240 µm and a membrane thickness of 30 µm. The porosity is equal to 30%, the pore size is 0.05 µm. The extractant phase is a solution of bis(2-ethylhexyl) phosphate (DEPA, Bayer A. G., for synthesis) in a technical grade isododecane (WBC-15, Biesterfeld, Germany). The aqueous phase contains the appropriate amount of metal sulfate (ACS grade). The initial pH was established by addition of sulfuric acid (Merck, p.a.). The concentration of metal ions in the aqueous phase was measured directly using atomic absorption spectroscopy (SP 9, Pye Unicam, England) or inductive coupled plasma atomic emission spectroscopy (SPECTROFLAME, Spectro, Germany); the concentration of metal ions in the organic phase was measured after reextraction with 1.0 mol/L sulfuric acid. The pH of the aqueous phase was determined with a 605 pH meter (Metrohm, Swiss). The viscosity of the organic phase was measured using an Ubbelohde viscometer (AVS/G, Schott, Germany), and the interfacial tension was evaluated at 20 ( 0.1 °C using a K 10 tensiometer (Kru¨ss, Germany). The applied pressure sensors (Burster, Germany) operate up to 10 bar and have an inaccuracy equal to 1% of the maximum value. Results and Discussion

Experimental Section The schematic view of the experimental setup is shown in Figure 2. Both phases were contacted in the

Transmembrane Pressure and Throughput. In HFM extraction both phases are separated macroscopically by the membrane; thus the specific flow rates (i.e.,

Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 187

a

b

Figure 3. Pressure drop in HFM 3: (a) total pressure drop in lumen and shell of HFM; (b) pressure drop difference between HFMs 2 and 3.

superficial velocity, the quotient of volumetric flow rate and free flow area of one phase) and their ratio can be varied independently in a broad range. It is well established (Kiani et al., 1984; Kim, 1984; Daiminger et al., 1995) that, in order to keep the interface within the pores of a hydrophobic membrane, it is necessary to maintain a higher local pressure in the aqueous phase. For the investigated system (in the concentration range 0.05 e [(DEPA)2] e 0.50 mol/L) stable operating conditions were obtained for transmembrane pressures in the range of 0.20 e ∆p e 4.0 bar. With ∆p > 4.0 bar breakthrough of the aqueous phase is to be encountered, while transmembrane pressures ∆p < 0.2 bar lead to a contamination of the aqueous phase with the organic phase. This range of operation conditions is mainly determined by the value of the interfacial tension, which depends on the concentration of surface active DEPA (Gaonkar and Neuman, 1987). For the concentration range mentioned above the value of the interfacial tension was measured to be 22-18 mN/m. Due to the countercurrent operation mode the signs of gradients of dynamic pressure drop in both phases are opposite. Thus on one end of the HFM the maximum transmembrane pressure must not exceed 4.0 bar, while on the other end the minimum transmembrane pressure has to be greater than 0.2 bar. The measured pressure drops in both phases agreed well with those predicted by the well-known HagenPoiseuille equation (Vauck and Mu¨ller (1989), see Figure 3a). The observed small discrepancy can be explained with entry effects. Such effects are to be excluded comparing the pressure drops in two modules of identical geometry

Figure 4. Comparison of the efficiency of HFM and pulsed sieveplate column (PSPC), PSPC: [(DEPA)2] ) 0.025 mol/L, [Zn2+]0 ) 63.0 mg/L, pH0 ) 2.8, V˙ aq ) 30 L/h, V˙ o ) 10 L/h, pulse frequency ) 0.45 s-1, amplitude ) 7.0 mm. Column characteristics: height 6.0 m; diameter 38 mm; number of plates 61; hole diameter 2 mm; number of holes 66, triangular array. HFM: [(DEPA)2] ) 0.025 mol/L, [Zn2+]0 ) 63.0 mg/L, pH0 ) 2.8, V˙ aq ) 30 L/h, V˙ o ) 10 L/h.

but different length (modules 2 and 3). Figure 3b shows the surplus of the measured pressure drop between module 2 (h ) 0.241 m) and module 3 (h ) 0.546 m), which is virtually identical to the calculated data. The shell-side pressure drops were always much smaller (510 times) than those in HF. Because of inaccuracy of the pressure sensors (0.10 bar) and small pressure drops, a similar presentation as Figure 3b for shell side is not reasonable. The maximum deviation between both values was ( 0.02 bar in the measured range of pressure drop between 0.01 and 0.10 bar (module 3). Basing on these results, it is possible to predict the feasible range of specific flow rates of both phases (stable conditions provided) for a given module length (Figure 3 in Daiminger et al. (1995)). Mass Transfer. In the first step to estimate the efficiency of HFM for reactive extraction, mass transfer experiments have been performed under the same working conditions as previously in pulsed sieve-plate extraction column (Walter, 1994). As one can easily see (Figure 4), it is possible to obtain a similar extraction efficiency in HFMs of 25 cm (module 4, Table 2) or of 54 cm active length (module 3, Table 2), as in a column of 6 m length (details of column construction see Walter et al. (1993)). This can be explained by the very high specific area of HFMs (ca. 5000 m2/m3 compared to ca. 100 m2/m3 for typical extraction column (Vauck and Mu¨ller, 1989)). Contrary to conventional extraction columns, whose operating conditions are mainly limited by the hydrodynamics (flooding, entrainment, etc.), HFM extraction is characterized by much higher flexibility of operating conditions (throughputs can be varied independently). To evaluate the performance of HFMs as extraction devices, two different initial zinc concentrations were chosen, both representing different applications. The so-called “100 ppm concept” (initial zinc concentration equals 100 mg/L) stands for environmental engineering; the “1000 ppm concept” (initial zinc concentration equals 1000 mg/L) represents hydrometallurgical applications. In both cases the main criteria were, according to their importance, high depletion of the metal ion concentration in the raffinate (at least 2 orders of magnitude), maximum possible volumetric flow rate of the aqueous raffinate phase, and enrichment of metals (into the stripping phase) via an extraction/reextraction

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Figure 7. Influence of DEPA concentration and flow rate on the exit concentration of zinc in cross flow module, V˙ o ) 3.2 L/h, pHin ) 5.1. Figure 5. Influence of the flow rate of the aqueous phase on the exit concentration of zinc (“100 ppm concept”): [(DEPA)2] ) 0.050 mol/L, module 2, V˙ o ) 1.76 L/h, pHin ) 4.9; [(DEPA)2] ) 0.050 mol/L, module 3, V˙ o ) 1.73 L/h, pHin ) 4.8.

a

b

Figure 6. Influence of the flow rate of the aqueous phase on the exit concentration: (a) cadmium, [(DEPA)2] ) 0.050 mol/L, V˙ o ) 1.8 L/h, pHin ) 5.5; (b) nickel, [(DEPA)2] ) 0.50 mol/L, V˙ o ) 1.8 L/h, pHin ) 5.5.

cycle (by variation of phase ratio and/or concentration of complexing agent). 1. Environmental Applications. The results of the experiments with initial concentration of zinc 100 mg/L are shown in Figure 5. The main features of Figure 5 are the following: high depletion of zinc concentration is possible; the increase of the aqueous flow rate results in a decrease of the efficiency of ion exchange (due to shorter contact time between both phases); longer modules allow greater throughputs for equal exit concentration of metal.

The lower solid line in Figure 5 represents the German legal limit value for zinc discharge in the metal working industry equal to 2 mg/L. Provided that the exit concentration in raffinate must not exceed 2 mg/L (Hartinger, 1991), the maximum flow rate was found to be equal ca. 20 L/h. Similar depletion of metal ion concentration in the aqueous phase (ca. 2 orders of magnitude) were obtained for cadmium and nickel extraction (Figure 6). The initial metal concentration was set to 10 mg/L, because of the lower limit values for cadmium and nickel (0.1 and 0.5 mg/L, respectively (Hartinger, 1991)). It was also possible to realize (for module 3) a phase ratio well above 100 (experimentally reached p ) 112) and to realize as well complete decontamination of the aqueous phase ([Zn2+]aq,out ≈ 0.01 mg/L) for a (DEPA)2 concentration of 0.5 mol/L, with a specific flow of the aqueous phase equal to 30 m3/(m2 h) ([Zn2+]in ) 100 mg/ L, pHin ) 4.8). During the reextraction with 10 mol/L sulfuric acid (p ) 0.1) zinc sulfate precipitated in the aqueous phase (enrichment factor of zinc greater than 1000). Recently, so-called “cross flow” modules made of hollow fiber fabric have become commercially available (Hoechst-Celanese Corporation, product information, 1994). Due to a baffle construction a cross flow of the shell-side phase is enforced promising better mass transfer characteristics. Preliminary experiments demonstrate a 2-fold increase of the maximum throughput in a cross flow module if the aqueous phase is led through the shell side in comparison with the tube side for the same extraction yield. Figure 7 shows results of further experiments done in cross flow HFM with the aqueous phase flowing in the shell of the HFM for different DEPA concentrations with following results: the possible aqueous throughput is equal to ca. 40 L/h for [(DEPA)2] ) 0.050 mol/L; the increase of DEPA concentration accounts for a drastic increase of the maximum throughput (ca. 180 L/h); the obtained concentration factor in the extraction step is approximately 60 (outlet concentration in the organic phase equal to 6 g/L zinc). Basing on these results (Figures 5 and 7), it is feasible to foresee the possible maximum throughput of wastewater stream through similar yet larger HFMs. The increase of the length of cross flow module (from 25 to 65 cm modules 4 and 5) will result with ca. 2.5-fold increase of maximum throughput (see likewise Figure 5 for modules 2 and 3). The latest development of Hoechst-Celanese Corporation is a cross flow module

Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 189

Figure 8. Influence of the flow rate of the aqueous phase on the exit concentration of zinc (“1000 ppm concept”), pHin ) 4.8.

with the following specifications: diameter d ) 25 cm and length l ) 65 cm (Liqui-Cel Extra-Flow 10 in. × 28 in.). The increase of the module diameter 2.5 times (comparing to HFM 5, Table 2) will allow 6.25 times higher throughputs, i.e., V˙ aq ≈ 2.5 m3/h. This high throughput should be in any case interesting for industrial recovery of heavy metals from wastewater streams. 2. Hydrometallurgical Application. Experiments conducted with initial zinc concentration equal to 1000 mg/L (“1000 ppm concept”) are shown in Figure 8 (module 3). Also in this case it was possible to recover more than 98% of the metal in one passage for a small volumetric flow rate (i.e., long residence time of the aqueous phase equal to ca. 13 min). In this field of application the uptake of metal ions into the organic phase is strongly depending on the organic flow rate for a given concentration of complexing agent due to the limited loading capacity of the organic phase. This influence on the overall extraction yield can also be seen in Figure 8. 3. Reextraction (Stripping). In the case of the reextraction step it is not necessary to distinguish between both areas of application: environmental and hydrometallurgical. For both areas a goal of the extraction step is to reach the saturation of the organic phase with metal ions (i.e., the same initial conditions for the reextraction). Figure 9 shows the results of reextraction for different loading of the organic phase. In one passage of phases through module 3 it was possible to reextract from 50 to 80% of zinc depending on initial zinc concentration in the organic phase equal to 21 or 0.21 g/L, respectively. Under conditions which are close to technical applications as shown in Figure 7 (i.e., high maximum throughput V˙ aq ) 180 L/h and high phase ratio) the organic flow rate is small (V˙ o ) 3.2 L/h). For these conditions one can easily reextract at least 80% of zinc from the organic phase in the cross flow module (demonstrated by an experiment with module 4, [Zn2+]o,in ) 4.08 g/L and V˙ o 3.6 L/h). Modeling. The reactive extraction (simultaneous mass transfer with chemical reaction) is characterized by its complexity. To find optimum conditions for a given problem, either extensive experimental work or reliable modeling is necessary. 1. Test of Applied Correlations. In the first step the accuracy of the literature correlations (Skelland, 1974; Costello et al., 1993) to describe mass transfer was examined for the investigated system.

Figure 9. Influence of flow rate and loading of the organic phase on reextraction yield: (b) [Zn2+]in,o ) 210 mg/L, [(DEPA)2]tot ) 0.050 mol/L, V˙ aq ) 0.1 L/h; [H2SO4] ) 0.25 mol/L; (9) [Zn2+]in,o ) 10.5 g/L, [(DEPA)2]tot ) 0.50 mol/L, V˙ aq ) 3.6 L/h, [H2SO4] ) 2.0 mol/L; (2) [Zn2+]in,o ) 21.0 g/L, [(DEPA)2]tot ) 0.50 mol/L, V˙ aq ) 3.6 L/h, [H2SO4] ) 2.0 mol/L.

It is known from the measurements performed in the stirred cell (Walter et al., 1993; Walter, 1994) that for low zinc concentrations in the aqueous phase ([Zn2+]aq e 1 × 10-3 mol/L) related to [(DEPA)2] ) 0.025 mol/L, the mass transfer resistance is situated in the aqueous phase (Nitsch and Kruis, 1978). In batch experiments (recycling of both phases, for details see, e.g., Qi and Cussler (1985)) a straight linear dependence was shown in a semilogarithmic plot [Zn2+]aq/[Zn2+]aq,0 ) f(t) (inserts in Figure 10) up to 90% of extraction. This is valid for aqueous flow either in lumen of HF or in the shell of HFM. Thus, the assumption of limiting resistance in the aqueous phase is justified and a mass transfer coefficient can be calculated from the slope R:

[ (

R ) exp

) ]

βZn,aqnπdol V4 aq -1 Vaq Vaq,r

(13)

The experimental values of mass transfer coefficients were compared with those calculated according to eqs 10 and 12 (Figure 10). The agreement between literature and experimental data is good, justifying the validity of these correlations for description of mass transfer in a HFM. 2. Calculations of Exit Concentration. Such calculations were performed according to the scheme outlined previously (cf. section Modeling of Mass transfer). The calculated results are always shown as solid lines in Figures 5, 6, 8, and 9. As one can see there is a good agreement between experimental and calculated data for all investigated conditions (100 ppm and 1000 ppm concepts, different module lengths, various metal ions, extraction, and reextraction). Small discrepancies between measured and calculated data might stem from the assumption that membrane pores are completely filled with the organic phase. The presented model stands out for the fact that no fitting was applied; all necessary parameters are experimentally accessible. That means this model can be generally applied for all kinds of transport-limited reactive extraction in HFMs. Thus, the predictive modeling of concentration profiles in HFMs is possible and allows an easy scale-up for technical applications. 3. Number of Theoretical Stages. To estimate the number of theoretical stages in the HFM for countercurrent extraction, calculations of concentrations of all species after several stages were performed on the basis

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a

a

b

b

Figure 10. Estimation of mass transfer coefficient in a batch experiment: (a) in lumen of hollow fibers (insert) module 1, V˙ aq ) 126 L/h, V˙ o ) 20 L/h, Vaq ) 2.0 L, Vo ) 0.8 L, [Zn2+]in ) 100 mg/L, pHin ) 4.8, [(DEPA)2]in ) 0.05mol/L; (b) in shell of HFM module 1, V˙ aq ) 126 L/h, V˙ o ) 20 L/h, Vaq ) 2.0 L, Vo ) 0.8 L, [Zn2+]in ) 100 mg/L, pHin ) 4.8, [(DEPA)2]in ) 0.05 mol/L.

of batch simulation of an ideal continuous countercurrent cascade (Treybal, 1963). The results of the calculations are shown in Figure 11. For given conditions the number of theoretical stages varied between 2 and 4 (modules 2 and 3), which corresponds to HETS values between 13 and 25 cm approximately. Conclusions Microporous hollow fiber modules promise to be highly efficient devices for reactive solvent extraction. HFMs may be especially useful in environmental engineering due to the nondispersive phase contact and the extremely large specific interfacial area. This point of view is supported by the obtained decontamination of the aqueous streams. Small HETS values point also to applications in hydrometallurgy. In spite of small dimension of hollow fibers a large specific flow rate can be obtained, compared to conventional extraction columns. The phase ratio can be adjusted in a broad range according to the loading capacity of the organic phase and the required yield of the extraction. The scale-up of the apparatus is conceivable because the developed model shows good agreement between experimental and predicted data. It is possible to achieve similar extraction results in a short densely packed HFM compared to extraction column of 6 m length. This can be related to the high interfacial area and short diffusion paths, which prevail over the disadvantages of laminar flow.

Figure 11. Comparison of the efficiency of HFM and an ideal mixer-settler cascade, experimental conditions as in Figures 7 and 10. (a) “100 ppm concept”; (b) “1000 ppm concept”.

Preliminary experiments on reextraction (regeneration of complexing agent) show the possibility of thousandfold enrichment of zinc starting from a 100 mg/L wastewater. This, together with chemical variability (tailor-made extracting agent) of solvent extraction should favor the HFM extraction against the classical solid ion exchanger. Acknowledgment This work has been supported by the Bayerische Staatsministerium fu¨r Landesentwicklung und Umweltfragen (Grant BayFORREST, Project No. 31). The authors thank Hoechst AG for the discount on the hollow fiber modules and Bayer A. G. for supplying DEPA. Nomenclature a ) specific area, m2/m3 A ) active interfacial area (membrane area × ), m2 B ) constant (eqs 10 and 11) d ) diameter, m D ) diffusion coefficient, m2/s HETS ) height equivalent to a theoretical stage, m j ) mass transfer rate, kmol/s K ) equilibrium constant depend [units on stoichiometry of the reaction (see eq 2)] Me ) metal ion n ) stoichiometry parameter p ) phase ratio, p ) V˙ aq/V˙ o r ) radius, m Re ) Reynolds number, Re ) 4 V˙ dh‚F/Akη Sc ) Schmidt number, Sc ) η/FD Sh ) Sherwood number, Sh ) βdh/D

Ind. Eng. Chem. Res., Vol. 35, No. 1, 1996 191 V ) volume, m3 V˙ ) volumetric flow rate, m3/h x ) length, m [ ] ) concentration, mol/L; g/L R ) slope (eq 13), s-1 β ) mass transfer coefficient, m/s δ ) wall thickness, m  ) porosity η ) dynamic viscosity, N s/m2 F ) density, kg/m3 τ ) tortuosity φ ) packing density of HF Φ ) constant (eqs 10 and 11) Indices aq ) aqueous phase av ) average c ) complex ca ) complexing agent h ) hydraulic in ) initial k ) free cross section area m ) organic membrane phase M ) membrane organic/bulk organic interface (by concentrations, eqs 5-8) M ) mean membrane (as area, eqs 5 and 6) o ) bulk organic phase out ) outlet r ) tank t ) tube, i.e., lumen of HF tot ) total 1 ) total inner 2 ) total outer * ) interfacial - ) in the organic phase

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Received for review April 11, 1995 Accepted August 31, 1995X IE9502392

Abstract published in Advance ACS Abstracts, November 15, 1995. X