**4. HFSLM in engineering applications**

Compared to conventional separations, membrane separations are attractive for the processing of food, bioproducts, etc where the processed products are sensitive to temperature since most membrane separations involve no chemical, biological, or thermal changes (or moderate temperature changes) of the target component during processing. For environmental-related applications, membrane separation has developed into an important technology for separating volatile organic compounds (VOCs), e.g., acetaldehyde, BTXs, ethylene oxide, trichloroethylene, etc and other gaseous air pollutants from gas streams (Schnelle and Brown, 2002; Simmon et al., 1994).

The following works show the applications of using HFSLM and the role of facilitated transport in separation of praseodymium from nitrate solution of mixed rare earths RE(NO3)3 (Wannachod et al., 2011), separation of uranium from trisodium phosphate from monazite ores processing (Lothongkum et al., 2009) supplied by the Rare Earth Research and Development Center, Office of Atoms for Peace, Bangkok, Thailand, and separation of Cu(II) by LIX84I.

### **4.1 Effective extraction and recovery of praseodymium from mixed rare earths**

Praseodymium (Pr), one of the elements recovered from mixed rare earths (REs), is very useful, e.g., as a composition in mischmetall alloy and a core material for carbon arcs in film


therefore, much lower than ks.

coefficient in liquid membrane (km) in Eq. (6) as

where f

**4. HFSLM in engineering applications** 

(Schnelle and Brown, 2002; Simmon et al., 1994).

against t.

the concentration of stripping phase at membrane-stripping interface (Cs\*) and the concentration of target species in stripping phase (Cs). At equal flux by Eq. (9), ki is,

\* \*

3. From Eq. (5), we can ignore the third mass transfer resistance. This is attributed to the direct contact of stripping ions with the liquid membrane resulting in rapid dissolution

Pm in Eq. (5) can be substituted in terms of the distribution ratio (D) and the mass transfer

11 r 1 P k r Dk

i i lm m

Cf <sup>β</sup> V ln AP t <sup>f</sup> <sup>C</sup> <sup>β</sup> <sup>1</sup> f,0 

<sup>Q</sup> <sup>β</sup> PLNε

We can calculate the permeability coefficient from the slope of the plot between <sup>f</sup>

Compared to conventional separations, membrane separations are attractive for the processing of food, bioproducts, etc where the processed products are sensitive to temperature since most membrane separations involve no chemical, biological, or thermal changes (or moderate temperature changes) of the target component during processing. For environmental-related applications, membrane separation has developed into an important technology for separating volatile organic compounds (VOCs), e.g., acetaldehyde, BTXs, ethylene oxide, trichloroethylene, etc and other gaseous air pollutants from gas streams

The following works show the applications of using HFSLM and the role of facilitated transport in separation of praseodymium from nitrate solution of mixed rare earths RE(NO3)3 (Wannachod et al., 2011), separation of uranium from trisodium phosphate from monazite ores processing (Lothongkum et al., 2009) supplied by the Rare Earth Research and Development Center, Office of Atoms for Peace, Bangkok, Thailand, and separation of Cu(II) by LIX84I.

Praseodymium (Pr), one of the elements recovered from mixed rare earths (REs), is very useful, e.g., as a composition in mischmetall alloy and a core material for carbon arcs in film

**4.1 Effective extraction and recovery of praseodymium from mixed rare earths** 

i

and high mass transfer coefficient of the stripping phase.

In addition, from the permeability coefficient (P) by Danesi (Danesi, 1984):

Table 3 shows some applications of HFSLM and their mass transfer related.

if f ss s J k (C C ) k (C - C ) (9)

(10)

<sup>r</sup> (12)

(11)

f,0

f

<sup>C</sup> V ln C 


Table 3. Applications of HFSLM and mass transfer related

studio light and searchlights. Praseodymium produces brilliant colors in glasses and ceramics. The composition of yellow didymium glass for welding goggles derived from infrared-heat absorbed praseodymium. Currently, the selective separation and concentration of mixed rare earths are in great demand owing to their unique physical and chemical properties for advanced materials of high-technology devices. Several separation techniques are in limitations, for example, fractionation and ion exchange of REs are time consuming. Solvent extraction requires a large number of stages in series of the mixer settlers to obtain high-purity REs. Due to many advantages of HFSLM and our past successful separations of cerium(IV), trivalent and tetravalent lanthanide ions, etc by HFSLM (Pancharoen et al., 2005; Patthaveekongka et al., 2006; Ramakul et al., 2004, 2005, 2007), we again approached the HFSLM system for extraction and recovery of praseodymium from mixed rare earth solution. The system operation is shown in Fig. 3. Of three extractants, Cyanex 272 in kerosene found to be more suitable for high praseodymium recovery than Aliquat 336 and Cyanex 301 as shown in Fig. 4. Higher extraction of 92% and recovery of 78% were attained by 6-cycle continuous operation about 300 min as shown in Fig. 6.

In this work, the extraction equilibrium constant (Kex) obtaining from Fig. 7 was 1.98 x 10−<sup>1</sup> (Lmol-1)4. The distribution ratio (D) at Cyanex 272 concentration of 1.0-10 (%v/v) were calculated and found to be increased with the extractant concentration and agreed with Pancharoen et al., 2010. We obtained the permeability coefficients for praseodymium at Cyanex 272 concentration of 1.0-10 (%v/v) from Fig.8. The mass transfer coefficients in feed phase (ki) and in liquid membrane (km) of 0.0103 and 0.788 cm s-1, respectively were

Roles of Facilitated Transport Through HFSLM in Engineering Applications 187

**0 3 6 9 12 15 Cyanex 272 concentration (% v/v)**

**01234567 Number of cycles**

Fig. 6. The percentages of Pr(III) extraction by 10 (%v/v) Cyanex 272 and stripping against

Fig. 5. The percentage of Pr(III) extraction against Cyanex 272 concentration

**Pr(III)**

**% E % S**

the number of separation cycles

**Percentage of Pr(III) (%)**

**Percentage of extraction (%)**

obtained from Fig.9. Because km is much higher than ki, it indicates that the diffusion of praseodymium ions through the film layer between the feed phase and liquid membrane is the rate-controlling step.

Fig. 3. Schematic counter-current flow diagram for one-through-mode operation of the HFSLM system ( inlet feed solution, gear pumps, inlet pressure gauges, outlet pressure gauges, outlet flow meters, outlet stripping solution, the hollow fiber module, inlet stripping reservoir, and outlet feed solution)

Fig. 4. The percentages of the Pr(III) extraction and stripping from one-through-mode operation

obtained from Fig.9. Because km is much higher than ki, it indicates that the diffusion of praseodymium ions through the film layer between the feed phase and liquid membrane is

Fig. 3. Schematic counter-current flow diagram for one-through-mode operation of the HFSLM system ( inlet feed solution, gear pumps, inlet pressure gauges, outlet pressure gauges, outlet flow meters, outlet stripping solution, the hollow fiber

**Cyanex 301 Cyanex 272 Aliquat 336 Extractants**

Fig. 4. The percentages of the Pr(III) extraction and stripping from one-through-mode operation

module, inlet stripping reservoir, and outlet feed solution)

**% E % S**

**Percentage of Pr(III) (%)**

the rate-controlling step.

Fig. 5. The percentage of Pr(III) extraction against Cyanex 272 concentration

Fig. 6. The percentages of Pr(III) extraction by 10 (%v/v) Cyanex 272 and stripping against the number of separation cycles

Roles of Facilitated Transport Through HFSLM in Engineering Applications 189

**01234567 1/([RH]3**

**0 20 40 60 80 100 120 140 160 180 200 Time (hour)**

Fig. 10. The model prediction of dimensionless recovery concentration of Pr(III) and

**/[H<sup>+</sup> ] 3 )**

**0**

**0.1**

**0.2**

**Dimensionless concentration**

experimental results

**0.3**

**0.4**

**0.5**

Fig. 9. Plot of 1/P as a function of 1/([RH]3 / [H+]3)

**1/P (P, cm/s)**

**y = 7.6243x + 96.488**

 **= 0.8766**

**Experiment Calculation**

**R2**

Fig. 7. Extraction of Pr(III) by Cyanex 272 as a function of equilibrium [Pr3+][RH]3

Fig. 8. Plot of -Vf ln(Cf /Cf,0) of Pr(III) at different Cyanex 272 concentrations against time

**0 0.4 0.8 1.2 1.6 2 2.4**

 **(mol/l)**

**[Pr3+][RH]3**

Fig. 8. Plot of -Vf ln(Cf /Cf,0) of Pr(III) at different Cyanex 272 concentrations against time

**0 10 20 30 40 50 Time (min)**

Fig. 7. Extraction of Pr(III) by Cyanex 272 as a function of equilibrium [Pr3+][RH]3

**3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2**

**0**

**1000**

**2000**

**3000**

**4000**

**-Vf ln(Cf/Cf,0) (cm3**

**)**

**5000**

**6000**

**7000**

 **1% v/v 5% v/v 7% v/v 10% v/v** 

**8000**

**[Pr3+][H+**

**]**

**3 (mol/l)**

**R2**

 **= 0.95452**

**y = 90.333x**

**y = 108x R2**

**y = 139.33x**

**y = 165.07x**

 **= 0.95248**

 **= 0.97568**

 **= 0.99854**

 **= 0.99313**

**R2**

**R2**

**R2**

**y = 0.198x + 3.12**

Fig. 9. Plot of 1/P as a function of 1/([RH]3 / [H+]3)

Fig. 10. The model prediction of dimensionless recovery concentration of Pr(III) and experimental results

Roles of Facilitated Transport Through HFSLM in Engineering Applications 191

Fig. 12 shows percentage of uranium extraction by different extractants. We can see that D2EHPA (di (2-ethylhexyl) phosphoric acid) obtained high percentage of extraction, however its extractability abruptly decreased with time. Thus, Aliquat 336, of which its extractability followed D2EHPA and decreased slightly with time, was considered the most appropriate extractant for uranium. It can be attributed that uranium ions in trisodium phosphate solution are in [UO2(CO3)3]4- and Aliquat 336, a basic extractant, is good for cations while D2EHPA, an acidic extractant, is good for anions form of UO22+. The percentage of uranium extraction at different concentrations of Aliquat 336 is shown

> **D2EHPA Aliquat 336 TOA Cyanex 923 TBP**

**0 10 20 30 40 50 Time (min)**

stripping solution [HNO3] of 0.5 M, equal Qfeed and Qstripping solution of 100 ml/min

Fig. 12. Percentage of uranium extraction against time using different extractants of 0.1 M,

**0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 Concentration of Aliquat 336**

Fig. 13. Percentage of uranium extraction at different concentrations of Aliquat 336, stripping solution [HNO3] of 0.5 M, equal Qfeed and Qstripping solution of 100 ml/min

in Fig. 13.

**0**

**5**

**10**

**15**

**Percentage of uranium extraction (%)**

**20**

**25**

**30**

**35**

**Percentage of uranium extraction (%)**

Fig. 11. The model prediction of separation factor and experimental results

From Figs. 10 and 11, we can see that the predictions of dimensionless concentration in stripping phase and the separation factor agreed with the experimental results.

### **4.2 Enhancement of uranium separation from trisodium phosphate**

Two grades of trisodium phosphate, food and technical grades, are extensively used for various purposes. Food grade is used as an additive in cheese processing. Technical grade is used for many applications, e.g., in boiler-water treatment, testing of steel parts after pickling, industrial detergents such as degreasers for steels, and heavy-duty domestic cleaners. As trisodium phosphate is a by-product from the separation of desired rare earths in monazite processing, it is contaminated by some amount of uranium which is often found with the monazite. Uranium is a carcinogen on the other hand it is useful as a radioactive element in the front and back ends of the nuclear fuel cycle, therefore the separation method to recover uranium from trisodium phosphate is necessary. For 45-ppm-uraniumcontaminated trisodium phosphate solution, HFSLM is likely a favorable method as it can simultaneously extract the ions of very low concentration and can recover them in one single operation. Undoubtedly, the facilitated transport across the HFSLM accelerates the extraction and recovery of uranium.

Eq. 13 shows that uranium species form complex species with Aliquat 336 (tri-octyl methyl ammonium chloride: CH3R3N+Cl- ) in modified leaching and extraction of uranium from monazite (El-Nadi et al., 2005).

$$\text{I}\_2\text{[UO}\_2(\text{CO}\_3)\_i\text{]}^\text{+} \overline{\text{2(NR}\_4)^\text{\*} \text{Cl}^-} \rightleftharpoons \overline{\text{(NR}\_4)\_i\text{[UO}\_2(\text{CO}\_3)\_i^\text{\*}]} \text{+2Cl}^- + \text{CO}\_3^\text{\*}\tag{13}$$

[UO2(CO3)3]4- represents the uranium species, 4 + - 2(NR ) Cl represents general form of Aliquat 336 in liquid membrane and 2- 42 2 32 (NR ) [UO (CO ) ] represents the complex species of Aliquat 336 and uranium species in liquid membrane.

**Experiment Calculation**

**0 15 30 45 60 75 90 105 120 135 Time (hour)**

From Figs. 10 and 11, we can see that the predictions of dimensionless concentration in

Two grades of trisodium phosphate, food and technical grades, are extensively used for various purposes. Food grade is used as an additive in cheese processing. Technical grade is used for many applications, e.g., in boiler-water treatment, testing of steel parts after pickling, industrial detergents such as degreasers for steels, and heavy-duty domestic cleaners. As trisodium phosphate is a by-product from the separation of desired rare earths in monazite processing, it is contaminated by some amount of uranium which is often found with the monazite. Uranium is a carcinogen on the other hand it is useful as a radioactive element in the front and back ends of the nuclear fuel cycle, therefore the separation method to recover uranium from trisodium phosphate is necessary. For 45-ppm-uraniumcontaminated trisodium phosphate solution, HFSLM is likely a favorable method as it can simultaneously extract the ions of very low concentration and can recover them in one single operation. Undoubtedly, the facilitated transport across the HFSLM accelerates the

Eq. 13 shows that uranium species form complex species with Aliquat 336 (tri-octyl methyl ammonium chloride: CH3R3N+Cl-) in modified leaching and extraction of uranium from

> 4- 2 2 2 3 34 4 223 2 3

+ - --- [UO (CO ) ] +2(NR ) Cl (NR ) [UO (CO ) ]+2Cl +CO (13)

+ - 2(NR ) Cl represents general form of

42 2 32 (NR ) [UO (CO ) ] represents the complex species of

Fig. 11. The model prediction of separation factor and experimental results

**4.2 Enhancement of uranium separation from trisodium phosphate** 

stripping phase and the separation factor agreed with the experimental results.

**0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8**

extraction and recovery of uranium.

[UO2(CO3)3]4- represents the uranium species, 4

Aliquat 336 in liquid membrane and 2-

Aliquat 336 and uranium species in liquid membrane.

monazite (El-Nadi et al., 2005).

**Separation factor**

Fig. 12 shows percentage of uranium extraction by different extractants. We can see that D2EHPA (di (2-ethylhexyl) phosphoric acid) obtained high percentage of extraction, however its extractability abruptly decreased with time. Thus, Aliquat 336, of which its extractability followed D2EHPA and decreased slightly with time, was considered the most appropriate extractant for uranium. It can be attributed that uranium ions in trisodium phosphate solution are in [UO2(CO3)3]4- and Aliquat 336, a basic extractant, is good for cations while D2EHPA, an acidic extractant, is good for anions form of UO22+. The percentage of uranium extraction at different concentrations of Aliquat 336 is shown in Fig. 13.

Fig. 12. Percentage of uranium extraction against time using different extractants of 0.1 M, stripping solution [HNO3] of 0.5 M, equal Qfeed and Qstripping solution of 100 ml/min

Fig. 13. Percentage of uranium extraction at different concentrations of Aliquat 336, stripping solution [HNO3] of 0.5 M, equal Qfeed and Qstripping solution of 100 ml/min

Roles of Facilitated Transport Through HFSLM in Engineering Applications 193

**Remained in TSP**

**Remained in stripping solution**

4.53

**1234567 Number of cycles**

Fig. 15. Amount of uranium ions remained in trisodium phosphate and stripping solutions of one-module operation against the number of separation cycles by 0.1 M Aliquat 336 mixed with 0.06 M TBP, stripping solution [HNO3] of 0.5 M, equal Qfeed and Qstripping solution of

In regard to apply the hollow fiber contactor for industrial scale, the reliable mathematical models are required. The model can provide a guideline of mass transfer describing the transport mechanisms of the target species through liquid membrane, and predict the extraction efficiency. Normally, different types of the extractants, their concentration and transport mechanisms (diffusion and facilitated transport or carrier-mediated transport) play important roles on the extraction efficiency. The facilitated transport mechanism relates to the reaction flux of chemical reaction between the target species and the selected single extractant or synergistic extractant to form complex species (Bringas et al., 2009; Kittisupakorn et al., 2007; Ortiz et al., 1996). In principle, the metal-ion transport through the membrane phase occurs when the metal ions react with the selected extractant at the interface between feed phase or aqueous phase and liquid membrane phase, consequently the generated complex species diffuse through the membrane phase. In this work, we developed a mathematical model describing the effect of reaction flux on facilitated transport mechanism of copper ions through the HFSLM system because copper is used extensively in many manufacturing processes, for example, electroplating, electronic industry, hydrometallurgy, etc. Therefore, copper ions, which are toxic and nonbiodegradable, may contaminate wastewaters and cause environmental problems and health effects if no appropriate treatment is taken (Lin & Juang, 2001; Ren et al., 2007). The model was verified with the experimental extraction of copper ions in ppm level using LIX84I dissolved in kerosene by continuous counter-current flow through a single-hollow

7.92

4.35

0.22 0.87 2.17

0.38 0.9 1.73 2.73

14.46

8.07

**0**

**5**

**10**

**15**

**Amount of uranium remained in trisodium** 

100 ml*/*min

**phosphate and stripping solutions (mg/l)**

**20**

**25**

**30**

**35**

5.57

**4.3 Reaction flux model for extraction of Cu(II) with LIX84I** 

29.86

To enhance the extraction of uranium, a mixture of Aliquat 336 and TBP (tributylphosphate) showed synergistic effect as can be seen in Fig. 14. The percentage of uranium extraction using the synergistic extractant was higher than that by a single extractant of Aliquat 336 and TBP. The highest extraction of uranium from trisodium phosphate solution was obtained by a synergistic extractant of 0.1 M Aliquat 336 and 0.06 M TBP. (The extraction increased with the concentration of TBP upto 0.06 M.)

Fig. 14. Percentage of uranium extraction against single and synergistic extractants: stripping solution [HNO3] of 0.5 M, equal Qfeed and Qstripping solution of 100 ml/min

The reaction by the synergistic extractant of Aliquat 336 and TBP is proposed in this work.

$$\text{[UO}\_2(\text{CO}\_3)\_3\text{]}^{4-} + \overline{\text{2(NR}\_4)^+ \text{Cl}^-} + \text{x}\overline{\text{TBP}} \rightleftharpoons \overline{\text{(NR}\_4)\_2[\text{UO}\_2(\text{CO}\_3)\_2^{2-}] \cdot \text{TBP}\_x} + 2\text{Cl}^- + \text{CO}\_3^{2-} \tag{14}$$

From Fig. 15, by using the synergistic extractant of 0.1 M Aliquat 336 mixed with 0.06 M TBP, the stripping solution of 0.5 M HNO3 with equal flow rates of feed and stripping solutions of 100 ml/min, the percentages of extraction and stripping reached 99% (equivalent to the remaining uranium ions in trisodium phosphate solution of 0.22 ppm) and 53%, respectively by 7-cycle separation in 350 min. The percentage of uranium stripping was much lower than the percentage of extraction presuming that uranium ions accumulated in liquid membrane phase of the hollow fiber module. This is a limitation of the HFSLM applications. For higher stripping, a regular membrane service is needed. In conclusion, the remaining amount of uranium ions in trisodium phosphate solution was 0.22 ppm, which stayed within the standard value 3-ppm uranium of the technical-grade trisodium phosphate. Further study on a better stripping solution for uranium ions is recommended.

To enhance the extraction of uranium, a mixture of Aliquat 336 and TBP (tributylphosphate) showed synergistic effect as can be seen in Fig. 14. The percentage of uranium extraction using the synergistic extractant was higher than that by a single extractant of Aliquat 336 and TBP. The highest extraction of uranium from trisodium phosphate solution was obtained by a synergistic extractant of 0.1 M Aliquat 336 and 0.06 M TBP. (The extraction

**0.06 M TBP 0.1 M Aliquat 336 0.06 M TBP + 0.1 M**

**Extractants**

Fig. 14. Percentage of uranium extraction against single and synergistic extractants: stripping solution [HNO3] of 0.5 M, equal Qfeed and Qstripping solution of 100 ml/min

4 2 <sup>2</sup>

The reaction by the synergistic extractant of Aliquat 336 and TBP is proposed in this work.

2 33 <sup>4</sup> 42 2 32 x <sup>3</sup> [UO (CO ) ] 2(NR ) Cl xTBP (NR ) [UO (CO ) ] TBP 2Cl CO (14)

From Fig. 15, by using the synergistic extractant of 0.1 M Aliquat 336 mixed with 0.06 M TBP, the stripping solution of 0.5 M HNO3 with equal flow rates of feed and stripping solutions of 100 ml/min, the percentages of extraction and stripping reached 99% (equivalent to the remaining uranium ions in trisodium phosphate solution of 0.22 ppm) and 53%, respectively by 7-cycle separation in 350 min. The percentage of uranium stripping was much lower than the percentage of extraction presuming that uranium ions accumulated in liquid membrane phase of the hollow fiber module. This is a limitation of the HFSLM applications. For higher stripping, a regular membrane service is needed. In conclusion, the remaining amount of uranium ions in trisodium phosphate solution was 0.22 ppm, which stayed within the standard value 3-ppm uranium of the technical-grade trisodium phosphate. Further study on a better stripping solution for uranium ions is

**Aliquat 336**

increased with the concentration of TBP upto 0.06 M.)

**0**

recommended.

**5**

**10**

**15**

**20**

**Percentage of uranium extraction (%)**

**25**

**30**

**35**

**40**

**45**

Fig. 15. Amount of uranium ions remained in trisodium phosphate and stripping solutions of one-module operation against the number of separation cycles by 0.1 M Aliquat 336 mixed with 0.06 M TBP, stripping solution [HNO3] of 0.5 M, equal Qfeed and Qstripping solution of 100 ml*/*min

### **4.3 Reaction flux model for extraction of Cu(II) with LIX84I**

In regard to apply the hollow fiber contactor for industrial scale, the reliable mathematical models are required. The model can provide a guideline of mass transfer describing the transport mechanisms of the target species through liquid membrane, and predict the extraction efficiency. Normally, different types of the extractants, their concentration and transport mechanisms (diffusion and facilitated transport or carrier-mediated transport) play important roles on the extraction efficiency. The facilitated transport mechanism relates to the reaction flux of chemical reaction between the target species and the selected single extractant or synergistic extractant to form complex species (Bringas et al., 2009; Kittisupakorn et al., 2007; Ortiz et al., 1996). In principle, the metal-ion transport through the membrane phase occurs when the metal ions react with the selected extractant at the interface between feed phase or aqueous phase and liquid membrane phase, consequently the generated complex species diffuse through the membrane phase. In this work, we developed a mathematical model describing the effect of reaction flux on facilitated transport mechanism of copper ions through the HFSLM system because copper is used extensively in many manufacturing processes, for example, electroplating, electronic industry, hydrometallurgy, etc. Therefore, copper ions, which are toxic and nonbiodegradable, may contaminate wastewaters and cause environmental problems and health effects if no appropriate treatment is taken (Lin & Juang, 2001; Ren et al., 2007). The model was verified with the experimental extraction of copper ions in ppm level using LIX84I dissolved in kerosene by continuous counter-current flow through a single-hollow

Roles of Facilitated Transport Through HFSLM in Engineering Applications 195

Fig. 17. Schematic transport mechanism of copper ion in liquid membrane phase

following assumptions are made:

liquid membrane phase.

Fig. 18. Transport of copper ions in the hollow fiber

considered.

direction.

in Fig. 18.

The transport of copper ions through a cylindrical hollow fiber is considered in the axial direction or bulk flow direction and radial direction. In order to develop the model, the

1. The inside and outside diameters of a hollow fiber are very small. Thus, the membrane thickness is very thin; therefore the radial concentration profile of copper ions is constant. 2. Only the complex species occurring from the reaction, not copper ions, diffuse through

3. The extraction reaction is irreversible that means only the forward reaction of Eq. (15) is

4. Due to very thin membrane thickness, it is presumed that the reaction occurs only in the axial direction of the hollow fibers. Mass flux of copper ions exists in the axial

The conservation of mass for copper ion transport in the hollow fiber is considered as shown

fiber module. It is known that LIX-series compounds are the most selective extractants of high selectivity and widely used for copper ions (Breembroek et al., 1998; Campderros et al., 1998; Lin & Juang, 2001; Parhi & Sarangi, 2008; Sengupta, et al., 2007). The schematic flow diagram of the separation via HFSLM is shown in Fig. 16. The transport mechanism of copper ion in micro porous hollow fiber is presented schematically in Fig. 17. The chemical reaction at the interface between feed phase and liquid membrane phase takes place when the extractant (RH) reacts with copper ions in feed (Eq. (15)).

$$\text{Cu}^{2+}\_{\text{(aq)}} + 2\overline{\text{RH}}\_{\text{(org)}} \rightleftharpoons \overline{\text{CuR}}\_{\text{2}\_{\text{(org)}}} + 2\text{H}^{+}\_{\text{(aq)}} \tag{15}$$

(RH) is LIX84I in liquid membrane phase.

CuR is the complex species of copper ion in liquid membrane phase. 2

Fig. 16. Schematic diagram for counter-current flow of Cu(II) separation by a single-hollow fiber module (1 = feed reservoir, 2 = gear pumps, 3 = inlet pressure gauges, 4 = outlet pressure gauges, 5 = hollow fiber module, 6 = flow meters and 7 = stripping reservoir

Eq. (15) can be simplified as follows:

$$\text{BaA} + \text{bB} \xrightarrow{\text{k}\_{\text{L}}} \text{cC} + \text{dD} \tag{16}$$

where A is copper ion, B is LIX84I, C is complex species of copper ion and LIX84I, D is hydrogen ion, and a, b, c, d are stoichiometric coefficients of A, B, C and D, respectively. The reaction rate (rA) is

$$-\mathbf{r}\_{\rm A} = \mathbf{k}\_{\rm f} \mathbf{C}\_{\rm A}^{n} \tag{17}$$

kf is the forward reaction rate constant and n is the order of reaction.

fiber module. It is known that LIX-series compounds are the most selective extractants of high selectivity and widely used for copper ions (Breembroek et al., 1998; Campderros et al., 1998; Lin & Juang, 2001; Parhi & Sarangi, 2008; Sengupta, et al., 2007). The schematic flow diagram of the separation via HFSLM is shown in Fig. 16. The transport mechanism of copper ion in micro porous hollow fiber is presented schematically in Fig. 17. The chemical reaction at the interface between feed phase and liquid membrane phase takes place when

Fig. 16. Schematic diagram for counter-current flow of Cu(II) separation by a single-hollow fiber module (1 = feed reservoir, 2 = gear pumps, 3 = inlet pressure gauges, 4 = outlet pressure gauges, 5 = hollow fiber module, 6 = flow meters and 7 = stripping reservoir

where A is copper ion, B is LIX84I, C is complex species of copper ion and LIX84I, D is hydrogen ion, and a, b, c, d are stoichiometric coefficients of A, B, C and D, respectively.

kf is the forward reaction rate constant and n is the order of reaction.

n

(org)

2+ <sup>+</sup> Cu + 2RH CuR + 2H (aq) (org) <sup>2</sup> (aq) (15)

kf aA bB cC dD (16)

A f A (x,t) r kC (17)

the extractant (RH) reacts with copper ions in feed (Eq. (15)).

CuR is the complex species of copper ion in liquid membrane phase. 2

(RH) is LIX84I in liquid membrane phase.

Eq. (15) can be simplified as follows:

The reaction rate (rA) is

Fig. 17. Schematic transport mechanism of copper ion in liquid membrane phase

The transport of copper ions through a cylindrical hollow fiber is considered in the axial direction or bulk flow direction and radial direction. In order to develop the model, the following assumptions are made:


The conservation of mass for copper ion transport in the hollow fiber is considered as shown in Fig. 18.

Fig. 18. Transport of copper ions in the hollow fiber

Roles of Facilitated Transport Through HFSLM in Engineering Applications 197

Qγ λ

Fig. 19. The integral concentrations of Cu(II) and separation time, O for n = 1 and ● for n = 2 The reaction rate constant of the second order is taken into consideration for a better curve fitting between the model and the experimental results, as shown in Table 4 by higher R-

**0 2 4 6 8 10 12 14 Time, min**

**Time (min)** 

<sup>Q</sup> , c f Akn <sup>γ</sup><sup>L</sup> <sup>λ</sup> <sup>β</sup> ln

0

**y = 0.393x**

 **= 0.813**

**y = 0.708x + 0.106**

 **= 0.9106**

**R2**

**R2**

**0 2 4 6 8 10 12 14 Time, min**

**Time (min)** 

, f c (1 n)k A <sup>γ</sup> <sup>Q</sup>

<sup>β</sup> C eC A (L,t) A (0,t <sup>τ</sup> ) (26)

and 1 n

**n = 1**

**n = 2**

A(0,0) <sup>λ</sup> <sup>C</sup>

Case 3: n 0, 1

Let <sup>c</sup> <sup>0</sup>

τ

A L

squared and less deviation.

<sup>Q</sup> , kAL f c <sup>α</sup>

**0**

**1/CA**

**1**

**2**

**ln (CA0/C**

**A)**

**3**

**4**

**5**

At a small segment Δx*,* the conservation of mass can be described below:

$$\mathbf{QC}\_{\mathbf{A} \ \langle \mathbf{x}, \mathbf{t} \rangle} - \mathbf{QC}\_{\mathbf{A} \ \langle \mathbf{x} + \Delta \mathbf{x}, \mathbf{t} \rangle} - \left\langle \mathbf{r}\_{\mathbf{A}} \right\rangle \Delta \mathbf{x} \mathbf{A}\_{\mathbf{c}} = \frac{\mathbf{d} \left\{ \mathbf{C}\_{\mathbf{A}} \right\}}{\mathbf{d} \mathbf{t}} \Delta \mathbf{x} \mathbf{A}\_{\mathbf{c}} \tag{18}$$

r and <sup>A</sup> C are the average values of the reaction A rate and the concentration of copper ions, respectively

Dividing Eq. (18) by xAc and taking a limit x 0, obtains

$$-\frac{\mathbf{Q}}{\mathbf{A}\_c} \frac{\partial \mathbf{C}\_{\text{A \text{ (x,t)}}}}{\partial \mathbf{x}} - \mathbf{r}\_{\text{A \text{ (x,t)}}} = \frac{\partial \mathbf{C}\_{\text{A \text{ (x,t)}}}}{\partial \mathbf{t}} \tag{19}$$

At the initial condition (t = 0), the conservation of mass in Eq. (19) is considered with regard to 3 cases of the reaction orders as follows:

Case 1: n = 0

$$\mathbf{C}\_{\text{A \{L,0\}}} = \mathbf{C}\_{\text{A \{0,0\}}} + \frac{\mathbf{k}\_{\text{f}} \mathbf{A}\_{\text{c}}}{\mathbf{Q}} \mathbf{L} \tag{20}$$

Case 2: n = 1

$$\mathbf{C}\_{\text{A (l,0)}} = \mathbf{C}\_{\text{A (0,0)}} \stackrel{\mathbf{k}\_f \mathbf{A}\_{\text{C}}}{\stackrel{\mathbf{Q}}{}} \,\tag{21}$$

Case 3: n 0, 1

$$\mathbf{C}\_{\text{A} \ (\text{I}, \text{0})} = \left[ \mathbf{C}\_{\text{A} \ (\text{0}, \text{0})}^{\text{1} - \text{n}} + \frac{(\text{1} - \text{n})\mathbf{k}\_{\text{f}}\mathbf{A}\_{\text{c}}}{\mathbf{Q}} \mathbf{L} \right]^{\frac{1}{\text{1} - \text{n}}} \tag{22}$$

At time t (t 0), the conservation of mass in Eq. (19) in the differential form is

$$-\frac{\mathbf{Q}}{\mathbf{A}\_c} \frac{\partial \mathbf{C}\_{\text{A \text{ (x,t)}}}}{\partial \mathbf{x}} - \mathbf{\tilde{r}}\_{\text{A \text{ (x,t)}}} = \frac{\partial \mathbf{C}\_{\text{A \text{ (x,t)}}}}{\partial \mathbf{t}} \tag{23}$$

$$\begin{aligned} \text{where} \qquad \mathbf{C}\_{\text{A } \text{(x,t)}} &= \mathbf{C}\_{\text{A } \text{(x,t)}} - \mathbf{C}\_{\text{A (x,0)}}\\ \mathbf{r}\_{\text{A } \text{(x,t)}} &= \mathbf{r}\_{\text{A (x,t)}} - \mathbf{r}\_{\text{A (x,0)}} = - \left(\frac{\mathbf{k}\_{\text{f}} \mathbf{n}}{\lambda - \chi \infty}\right) \overline{\mathbf{C}}\_{\text{A (x,t)}} \end{aligned} $$

Linearize Eq. (23) by taking Laplace transforms and considering 3 cases of reaction orders, we obtain:

Case 1: n = 0

$$\mathbf{\overline{C}}\_{\text{A}}(\mathbf{l},\mathbf{t}) = \mathbf{\overline{C}}\_{\text{A}}(\mathbf{0},\mathbf{t}-\mathbf{r}\_{0}) + \mathbf{k}\_{\text{f}}(\mathbf{t}-\mathbf{r}\_{0}) - \mathbf{k}\_{\text{f}}\mathbf{t} \tag{24}$$

Case 2: n = 1

$$\overline{\mathbf{C}}\_{\text{A}}|\_{\text{(l,t)}} = \mathbf{e}^{\mathbf{a}} \overline{\mathbf{C}}\_{\text{A}}|\_{\text{(0,t-r\_0)}} \tag{25}$$

Case 3: n 0, 1

196 Mass Transfer in Chemical Engineering Processes

A (x,t) A (x Δx,t) A c c

r and <sup>A</sup> C are the average values of the reaction A rate and the concentration of copper

A (x,t) A (x,t) A (x,t)

f c

L

Q

k Ac f

1 n 1 n f c

A (x,t) A (x,t) A (x,t)

Q 

QC QC r ΔxA ΔxA

Q C C r A x t

A (L,0) A (0,0) k A CC L

A (L,0) A (0,0)

(1 n)k A CC L

Q C C r A x t

Linearize Eq. (23) by taking Laplace transforms and considering 3 cases of reaction orders,

A (L,0) A (0,0)

c

At time t (t 0), the conservation of mass in Eq. (19) in the differential form is

λ γx

At the initial condition (t = 0), the conservation of mass in Eq. (19) is considered with regard

A

dt (18)

(19)

(20)

<sup>Q</sup> C Ce (21)

1

(23)

A (L,t) A (0,t <sup>0</sup> <sup>τ</sup> ) C C k (t f 0f τ ) kt (24)

<sup>α</sup> C eC A (L,t) A (0,t <sup>τ</sup> ) (25)

0

(22)

d C

At a small segment Δx*,* the conservation of mass can be described below:

Dividing Eq. (18) by xAc and taking a limit x 0, obtains

to 3 cases of the reaction orders as follows:

c

ions, respectively

Case 1: n = 0

Case 2: n = 1

Case 3: n 0, 1

we obtain: Case 1: n = 0

Case 2: n = 1

where CCC A (x,t) A (x,t) A (x,0)

 <sup>f</sup> A (x,t) A (x,t) A (x,0) A x,t k n r rr C

$$
\overline{\mathbf{C}}\_{\text{A} \quad \text{(L,t)}} = \mathbf{e}^{\beta} \overline{\mathbf{C}}\_{\text{A} \quad \text{(0,t-r\_0)}} \tag{26}
$$

Fig. 19. The integral concentrations of Cu(II) and separation time, O for n = 1 and ● for n = 2 The reaction rate constant of the second order is taken into consideration for a better curve fitting between the model and the experimental results, as shown in Table 4 by higher Rsquared and less deviation.

Roles of Facilitated Transport Through HFSLM in Engineering Applications 199

(dissociated and undissociated forms) to diffuse through the liquid membrane phase. As a result, the efficiency and selectivity of the transport across liquid membrane markedly enhance. Factors that affect the facilitated transport and diffusion through the membrane are, for example, extractant types and properties (e.g., proton donors, electron donors), solvent characteristics, stripping types and properties, life time of membrane due to fouling, operating temperature. Many outstanding advantages of the HFSLM make it the most efficient type of membrane separation for several applications. It is worth to note that the HFSLM can simultaneously extract the target species of very low concentration and recover them in one single operation. For favorable ions (e.g., precious metals), high percentage of

Despite many advantages, at present the HFSLM is not often used in a large-scale industry because the major drawbacks of hollow fibers are not only fouling but also mechanical stability of the support. However, in regard to apply the HFSLM in industrial scale, the reliable mathematical model is required as the model can foretell the effect of mass transfer as the functions of operating parameters, membrane properties and feed properties on the separation efficiency. However, due to the limitations of applications or unclear phenomena around the membrane surface, no model so far is fully satisfactory and universally applicable. Even though, the model can help to understand and predict the operation as well as the separation performance. In case the separation of metal ions by the HFSLM, as there are several parameters involved, e.g., types of metal ions, extractants and stripping solutions, and the transport mechanisms, therefore the model probably has implications for

other metals but it may need some modifications corresponding to such parameters.

The authors are highly grateful to the Royal Golden Jubilee Ph.D. Program (Grant No. PHD50K0329) under the Thailand Research Fund, the Rare Earth Research and Development Center of the Office of Atoms for Peace (Thailand), Thai Oil Public Co., Ltd., the Separation Laboratory, Department of Chemical Engineering, Chulalongkorn University, Bangkok, Thailand. Kind contributions by our research group are deeply

recovery is desirable.

**6. Acknowledgments** 

acknowledged.

**7. Nomenclature** 

A Membrane area (cm2)

BLM Bulk liquid membrane BTXs Benzene, toluene, xylenes CA Concentration of copper ions

(moles per unit volume)

(moles per unit volume)

(moles per unit volume)

AC Cross-sectional area of hollow fiber (cm2)

<CA> Average value of the concentration of copper ions

Cf,0 Initial concentration of target species in feed phase

Cf\* Concentration of target species at feed-membrane interface

Cf,in, Cf,out Concentration of target species at feed inlet and feed outlet

Cf Concentration of target species in feed phase (moles per unit volume)

The optimum separation time and separation cycles of the extraction can be estimated. The model was verified with the experimental extraction results and other literature.

Fig. 19 is a plot of the integral concentrations of Cu(II) against time to determine the reaction order (n) and the forward reaction rate constant (kf). The rate of diffusion and/or rates of chemical changes may control the kinetics of transport through liquid membrane depending on transport mechanisms (diffusion or facilitated). The reaction rate constants of first-order (n = 1) and second-order (n = 2) are 0.393 min-1 and 0.708 L/mgmin, respectively.


Table 4. R-squared and percentages of deviation for first-order and second-order reactions

The percentage of copper ion extraction is calculated by Eq. (27). The percentage of deviation is calculated by Eq. (28).

$$\% \text{ extraction} = \frac{\mathbf{C}\_{\text{f,in}} - \mathbf{C}\_{\text{f,out}}}{\mathbf{C}\_{\text{f,in}}} \times 100 \tag{27}$$

$$\text{\% deviation} = \frac{\sum\_{i=1}^{j} \left( \frac{\mathbf{C}\_{\text{Expt.}} - \mathbf{C}\_{\text{Theo.}}}{\mathbf{C}\_{\text{Expt.}}} \right)\_{\text{i}}}{\text{j}} \times 100\tag{28}$$

The optimum separation time for the prediction of separation cycles can be estimated by the model based on the optimum conditions from the plot of percentage of extraction as a function of initial concentration of the target species in feed and also feed flow rate.

In this work, at the legislation of Cu(II) concentration in waste stream of 2 mg/L, the calculated separation time is 10 min for about 15-continuous cycles. The percentage of extraction calculated from this reaction flux model is much higher than the results from other works which applied different extractants and transport mechanisms. Types of extractants and their concentrations are significant to the separation of metal ions. For example, a hard base extractant can extract both dissociated and undissociated forms in a basic or weak acidic condition but dissociated forms are high favorable. While a neutral extractant normally reacts with undissociated forms, but in an acidic condition it can react with dissociated forms. It is noteworthy to be aware that not only types of the extractants (single or synergistic), in this case LIX84I for Cu(II), but also the transport mechanism, e.g., facilitated transport mechanism attributes to the extraction efficiency. The model results are in good agreement with the experimental data at the average percentage of deviation of 2%.

### **5. Conclusions**

Facilitated transport of the solutes or target species benefits the separation process by liquid membrane with a non-equilibrium mass transfer and uphill effect. It is more drastic chemical changes of the target species with the presence of a suitable extractant or carrier (sometimes by synergistic extractant) in liquid membrane to form new complex species (dissociated and undissociated forms) to diffuse through the liquid membrane phase. As a result, the efficiency and selectivity of the transport across liquid membrane markedly enhance. Factors that affect the facilitated transport and diffusion through the membrane are, for example, extractant types and properties (e.g., proton donors, electron donors), solvent characteristics, stripping types and properties, life time of membrane due to fouling, operating temperature. Many outstanding advantages of the HFSLM make it the most efficient type of membrane separation for several applications. It is worth to note that the HFSLM can simultaneously extract the target species of very low concentration and recover them in one single operation. For favorable ions (e.g., precious metals), high percentage of recovery is desirable.

Despite many advantages, at present the HFSLM is not often used in a large-scale industry because the major drawbacks of hollow fibers are not only fouling but also mechanical stability of the support. However, in regard to apply the HFSLM in industrial scale, the reliable mathematical model is required as the model can foretell the effect of mass transfer as the functions of operating parameters, membrane properties and feed properties on the separation efficiency. However, due to the limitations of applications or unclear phenomena around the membrane surface, no model so far is fully satisfactory and universally applicable. Even though, the model can help to understand and predict the operation as well as the separation performance. In case the separation of metal ions by the HFSLM, as there are several parameters involved, e.g., types of metal ions, extractants and stripping solutions, and the transport mechanisms, therefore the model probably has implications for other metals but it may need some modifications corresponding to such parameters.
