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Transport mechanisms and modelling in liquid membrane contactors
Separation and Purification Technology 19 (2000) 183 – 197 www.elsevier.com/locate/seppur
Transport mechanisms and modelling in liquid membrane contactors I.M. Coelhoso, M.M. Cardoso, R.M.C. Viegas, J.P.S.G. Crespo * Departamento de Quı´mica, Faculdade de Cieˆncias e Tecnologia, Uni6ersidade No6a de Lisboa, 2825 Monte de Caparica, Portugal Received 14 September 1999; received in revised form 3 January 2000; accepted 7 January 2000
Abstract This paper discusses the use of liquid membrane contactors for extraction of fermentation and pharmaceutical products using different types of carriers. It intends to emphasise the importance of understanding the transport mechanisms involved in liquid membrane extraction with different carriers and also to discuss relevant aspects of the mathematical modelling involved in these extraction processes. Using the extraction of organic acids, namely amino acids, as a case study it is shown how the supramolecular organisation of the extractant determines the solute transport mechanisms involved. Additionally, the resolution of racemic mixtures using chiral carriers is also discussed. The modelling work analyses two different aspects of extraction using membrane contactors with microporous membranes: (i) the importance of using a correct description of solute partition between the feed and the extractant phase (use of a variable partition description versus constant partition); (ii) the correct development of mass transfer correlations in hollow fibre contactors. For the development of mass transfer correlations the calculation method proposed by Wilson has been universally used. Given the currently available mathematical tools, that enable the analytical manipulation of equations and fittings with complex expressions, a new calculation methodology is discussed. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Membrane extraction; Facilitated transport; Transport mechanisms; Mass transfer correlations; Membrane contactors
1. Introduction Carrier-facilitated transport through liquid membranes has been inspired by the ability of natural systems to selectively pump ions across biological membranes. In liquid membrane systems an immiscible organic phase separates two aqueous * Corresponding author. Tel.: +351-21-2948385; fax: + 351-21-2948357. E-mail address: [email protected] (J.P.S.G. Crespo)
phases, the feed and the stripping phases. Solute transport can be enhanced if an extractant, which interacts selectively and reversibly with the solute, is added to the organic liquid membrane [1]. The first generation of synthetic carriers were the crown-ether macrocycles which selectively bind alkali metal cations. Since their discovery many carriers have been synthesised for the selective recognition of neutral, charged or zwitterionic species and applied in liquid membranes for binding studies or separation purposes [2].
1383-5866/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 3 - 5 8 6 6 ( 0 0 ) 0 0 0 5 1 - 4
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Liquid membrane extraction has received considerable attention due to the advantages of combining liquid-liquid extraction and membranes in a single operation. The potential advantages of membrane extraction processes are: 1. Small amounts of complexing agent are required due to the continuous regeneration associated with the reversible reaction. As a consequence operating costs can be reduced; 2. extraction and stripping can be carried out simultaneously in one equipment, reducing investment costs; 3. backmixing effects and loss of complexing agent can be minimised when an appropriate membrane configuration is used; 4. highly selective separations are possible. This feature is most useful at low solute concentration where an excess of complexing agent is present and the complexation reaction is very efficient. This is in contrast to other separation processes, which do not usually work well at low solute concentrations. In spite of the known advantages in the use of supported liquid membranes the major drawback for industrial application regards their stability. A new type of liquid membrane configuration, the membrane contactor, with the potential to eliminate the shortcomings of supported liquid membranes while retaining its advantages is gaining importance. They have been applied to a large variety of systems including extraction of fermentation products [3– 6], pollutants [7 – 9], pharmaceutical products [10,11] and metals [12 – 15]. The advantages of membrane contactors stem from the large surface area per volume, typically between 3000 m2/m3 and 5000 m2/m3. They also present other advantages over classical extractors, such as the possibility of operating with a wide range of flow rates, no need for density differences to achieve phase separation and no emulsification, since the interface between both phases is immobilised within the membrane pores [16]. This paper discusses the use of liquid membranes for extraction of fermentation and pharmaceutical products using different types of carriers or the same carrier with a different supramolecular organisation. It is our intention to emphasise the importance of understanding the
transport mechanisms involved in liquid membrane extraction and also to discuss a few relevant aspects of the mathematical modelling involved in these extraction processes. The transport mechanisms involved in the extraction of organic acids by a quaternary ammonium salt are discussed and the effect of osmotic pressure difference, through the liquid membrane, on solute transport is evaluated. The same ammonium salt is also used for amino acid transport but under conditions where the assembling of the extractant molecules in reversed micelles is favoured. The selective transport of amino acids using these molecular aggregates in liquid membranes is presented and the transport mechanisms, considering both electrostatic and hydrophobic interactions, are discussed. Racemic mixture resolution is also an important issue for the pharmaceutical industry, as public health is involved. In many cases just one of the enantiomers presents activity, the other is inactive or may even exert an adverse secondary effect. Very recently some examples were described that evidence the possibility of using a chiral carrier agent dissolved in an organic phase [17,18]. Several carriers, such as cyclodextrins [19], tartaric acid derivatives [20] and crown ethers [21] have been used. The resolution of propranolol, a b-adrenergic receptor antagonist drug, using tartaric acid derivatives is presented and discussed. The modelling work analyses two different aspects of extraction using membrane contactors with microporous membranes: (i) the importance of using a correct description of solute partition between the feed and the extractant phase (use of a variable solute partition or a constant partition); In membrane extraction processes the overall mass transfer coefficients are usually evaluated by assuming a constant partition coefficient of the solute between the two contacting phases. However, for several extraction systems, the partition coefficient may vary throughout the extraction process affecting the evaluation of the mass transfer coefficient. (ii) the correct development of mass transfer correlations;
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For development of mass transfer correlations a two-step calculation method proposed by Wilson has been universally used. Given the currently available mathematical tools that enable the analytical manipulation of equations and fittings with complex expressions, a new one-step calculation methodology is discussed. This paper uses experimental results obtained by our group during the last 8 years [22 – 33] and discusses them with a new insight, in an integrated way. It is our aim to focus attention on defined problems that were raised during these years, especially the need for a complete understanding of the mechanisms of solute transport taking into consideration the interactions established with the carrier, the knowledge about carrier organisation and structuring, and finally the importance of correct mathematical modelling of the mass transport process.
2. Materials and methods
2.1. Extraction systems The feed phase used for lactate extraction studies was a lactate solution (280 mM) obtained by dilution of sodium lactate 60% (Sigma, USA). The pH of the solutions was adjusted to 6.3 with a 0.1 M NaOH solution. The organic phase was composed of a quaternary ammonium salt carrier, Aliquat 336 (TOMAC) (Fluka, Germany) and of a hydrocarbon mixture, Shellsol A (Shell, UK), as diluent. The carrier concentration was always 30% (w/w). The stripping phase was a sodium chloride solution, with concentrations ranging from 0.28 to 4.71 M. The amino acid extraction studies were performed using the phase transfer method [34]. An aqueous solution of amino acid at 25°C was contacted with a n-heptane (spectrophotometric grade, Merck, Germany) solution containing 125 mM TOMAC as surfactant and 1.25% v/v of hexanol (99% purity, Merck, Germany) as co-surfactant. The desired pH and ionic strength in the aqueous solution were adjusted using a potassium hydroxide solution and adding potassium chloride, respectively. Phenylalanine, potassium hy-
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droxide and potassium chloride of 99% purity were also purchased from Merck (Germany) and tryptophan of 99% purity was obtained from Sigma (USA). Methanol for chromatography was supplied by Merck (Germany). Propranolol hydrochloride and tartaric acid were purchased from Aldrich Chemical (USA), boric acid from Riedel–de Hae¨n AG (Germany) and chloroform from Merck (Germany). (S,S)-din-dodecyltartrate and the free base of propranolol were prepared as described in [20]. The extraction equilibrium isotherms were determined for propranolol concentrations of 0.2, 0.5 and 5 mM in aqueous medium (demineralized water, boric acid, 0.100 M, acetate buffer, 50 mM, pH 5.2) and for (S,S)-di-n-dodecyltartrate concentrations of 2, 30 and 100 mM in chloroform, by contacting 10 ml of both organic and aqueous solutions. The samples were stirred vigorously with an Ultra-Turrax (Janke and Kunkel IKA-Labortechnik, Germany), at 24 000 rpm, for 2.5 min and at a controlled temperature of 25°C. The studies of valeric (n-pentanoic) acid extraction were carried out with a synthetic feed — 5 g/l of valeric acid in deionized water-, simulating a wastewater stream from polymer manufacturing. Amberlite LA-2 (Fluka) (10 vol%) in toluene (Merck\ 99%) (90 vol%) was chosen as extraction system according to previous studies [35].
2.2. Membrane contactor studies Liquid-Cel laboratory hollow-fibre modules with Celgard® membranes from Hoechst Celanese were used throughout these studies. Each module has 2.5 cm of internal diameter, contains 2100 hydrophobic polypropylene fibres, 16 cm long, with a nominal internal diameter of 240 mm, nominal thickness of 30 mm, porosity of 0.3 and a nominal pore size of 0.05 mm. Each module provides an effective area of 0.23 m2. The aqueous feed phase was pumped through the lumen of the fibres while the organic phase flowed in the shell side of the module. Magnetically driven gear pumps were used. To monitor both the aqueous and organic flow rates during the experiments flow meters were used. Due to the hydrophobic nature of the fibres a slight overpres-
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sure (0.2 bar) was applied to the aqueous phase in order to stabilise the interface within the membrane. All the experiments were carried out in co-current flow. For simultaneous extraction and reextraction, two hollow fibre modules were used in series. Extraction was accomplished in the first module and the loaded organic phase that leaves this module enters the shell side of a second module, where the stripping of the solute is carried out.
2.3. Analytical methods The concentration of organic acids (lactate and valeric acid) was determined by HPLC. The column used was a Shodex SH 1011 (Showa Denko K.K., Japan) and the eluent sulphuric acid 0.01 N. A refractive index detector (Merck Hitachi, Japan) was employed. The amino acids concentration was also determined by HPLC. The column used was a Merck RP-18 (Merck, Germany) and the eluent was a solution with 75% methanol (v/v) and 25% water (v/v). A UV detector (Merck, Hitachi, Japan) at a wavelength of 257 nm was employed for phenylalanine and tryptophan quantification. The quantification of both propranolol enantiomers in the aqueous phase was done by HPLC with a UV detector (Merck, Hitachi, Japan) at a wavelength of 254 nm. A Chiralcel OD-R (Daicel, Japan) column was used and the mobile phase was 0.1 M potassium hexafluorophosphate aqueous solution: acetonitrile (60:40). The water content of the organic phases (namely the reversed micellar phase) was deter-
mined by Karl Fischer titration (Aquapal III, UK). The viscosity of the organic phases was measured by using a couette type viscometer (Brookfield, model DV-II digital, UK).
2.4. Calculation methods The software package Scientist™, from MicroMath® Scientific Software (USA), was used to perform the non-linear regression calculations. This software allies the capability of performing non-linear fittings and simultaneously solving both integral and differential equations. The least squares and the simplex algorithms were used.
3. Results and discussion
3.1. Transport mechanisms 3.1.1. Transport of lactate with free quaternary ammonium salts The transport of lactate using as carrier a quaternary ammonium salt (TOMAC) is used to illustrate the importance of understanding the mechanisms involved in solute transport across liquid membranes. The transport of lactate ions from the feed to the stripping phase is usually described as being counterbalanced by an equivalent transport of other anionic species from the stripping to the feed phase through a coupled transport mechanism (Fig. 1). The following ionexchange reaction takes place at both interfaces: Ke
La− + R+Cl− l R+La− + Cl− with the equilibrium constant, Ke, defined as: Ke =
Fig. 1. Coupled transport mechanism for the extraction and re-extraction of lactate in a liquid membrane with a quaternary ammonium salt.
(1)
[R+La−][Cl−]f [R+La−][Cl−]s = [La−]f [R+Cl−] [La−]s [R+Cl−]
(2)
where [R+La−] and [R+Cl−] are the lactateamine and the chloride-amine complexes concentrations in the organic phase, [La−]f and [Cl−]f are the lactate and chloride concentrations in the feed phase, and [La−]s and [Cl−]s are the lactate and chloride concentrations in the stripping phase. If this ion-pairing mechanism of transport is assumed, a simple mathematical model for equi-
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Table 1 Comparison of experimental and model lactate equilibrium activities: effect of initial chloride concentrationa [La−]0 (M)
[Cl−]0 (M)
[La−]f exp (M)
[La−]s exp (M)
aLa−/aLa− s f exp
aLa−/aLa− model
0.275 0.281 0.276 0.279
0.276 0.998 1.950 4.710
0.152 0.135 0.118 0.126
0.152 0.318 0.360 0.376
1.0 2.4 3.1 3.0
1.0 3.2 6.7 22.4
a
s
f
Bulk membrane, phase ratio (feed:org:strip) 3:3:1, [R+Cl−]0 =0.654 M.
librium can be developed. The equilibrium constant, Ke, of the reaction between the carrier and lactate can been determined, allowing a good prediction of equilibrium concentrations for independent extraction and stripping, for a large range of different experimental conditions. Due to the high concentrations of stripping agent employed it is more correct to use activities instead of concentrations. The activity coefficients for the species involved can be found in Robinson and Stokes [36]. For simultaneous extraction and stripping, as occurs in liquid membranes, the equilibrium lactate activity in the stripping phase can be related with the equilibrium lactate activity in the feed phase as a function of the initial lactate and chloride activities, if a ion-pairing mechanism of transport is considered: aLa− = aLa− · s
f
aCl− 0 aLa−
(3)
0
The model predicts that, if lactate is exclusively transported by an ion-pairing mechanism, the ratio of lactate activities in the stripping and in the feed phases increases with increasing initial chloride activity. However, the experimental results obtained with a bulk liquid membrane system show a large deviation between the experimental and the predicted values for the equilibrium lactate activities (Table 1). A similar behaviour was obtained by Drioli et al. for phenylalanine extraction also with TOMAC [37]. Contrary to the ion-exchange model prediction it can be concluded that it is not worthwhile to increase chloride concentration in the stripping phase above 1 M. For a bulk liquid membrane the ratio of lactate concentration in both phases remains constant for [Cl−]0 =1.95 M and for [Cl−
]0 = 4.71 M and it is only 30% higher than the value obtained with [Cl−]0 = 1M. Prediction of equilibrium was only accurate if both compartments (feed and stripping) have the same molar concentration of salts. For different molar concentration of salts, in the two compartments of the cell, the assumption that transport is exclusively accomplished by an ion-pairing mechanism is obviously not correct and thus it is necessary to consider the contribution of other mechanisms for ion transport. In order to confirm the occurrence of alternative mechanisms of transport, the osmotic pressure difference between the feed and stripping compartments was determined at the beginning and at the equilibrium of the experiments, by measuring the chloride and lactate concentrations in both compartments and using the corresponding osmotic coefficients [36]. As the osmotic pressure difference between the stripping and feed compartments is higher in the beginning of the experiment (Table 2), it has to be concluded that the amount of chloride transported from the stripping to the feed compartment is higher than the Table 2 Difference of osmotic pressure between stripping and feed compartments for different initial chloride concentrationsa [La−]0 (M)
[Cl−]0 (M)
(DP)0 (atm)
(DP)eq−exp (atm)
0.275 0.281 0.276 0.279
0.276 0.998 1.950 4.710
−0.37 32.7 88.6 292
−0.46 28.2 64.2 182
a Bulk membrane, phase ratio (feed:org:strip) 3:3:1, [R+Cl− ]0 =0.654 M.
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corresponding lactate transport in the opposite direction. Fig. 2 plots the osmotic pressure differences at equilibrium against its initial values. The deviation observed can be explained by a net transfer of chloride and sodium (to keep electroneutrality) from the stripping to the feed compartment. Transport of chloride and sodium, induced by the osmotic pressure difference, is probably associated with migration of aqueous ‘pockets’ across the liquid membrane in order to cancel the osmotic pressure difference. These results demonstrate the importance of understanding the mechanisms involved on solute transport, even from an engineering point of view: increasing the counter-ion concentration does not improve the extraction/stripping process because as salt transport increases less stripping solute becomes available to be counter transported by an ion-pairing mechanism.
3.1.2. Solute transport with re6ersed micelles The extractant used for lactate transport studies (TOMAC), can be induced to self-organise as a supramolecular aggregate, namely reversed micelles, if appropriate conditions are provided. This feature is rather interesting because the organic phase can be designed in order to promote the formation of these aggregates.
Fig. 2. Osmotic pressure difference at equilibrium versus initial osmotic pressure difference, for a bulk liquid membrane.
What would be the benefit of using a reversed micellar system? In the first place, reversed micelles provide different environments for solubilization: the reversed micellar water pool and the reversed micellar interface. Depending on the solute structure, polarity and ionisation state it may establish different types of interactions within these environments. These interactions will determine the solubilization site where the solute is hosted and the partition coefficient. This means that despite using a rather non-specific extractant, as it is the case of TOMAC, it is possible by organising these molecules as reversed micelles to obtain an extraction system able to interact in a selective way with different solutes. Additionally, if the transport of a defined solute with a reversed micellar system is essentially driven by hydrophobic interactions with the micellar interface then, an osmotic pressure difference between the feed and striping phases does not affect the solute transfer because the mechanism involved does not depend upon the concentration of a counter-ion. This feature is quite interesting for the transport of hydrophobic solutes. How can we induce the formation of TOMAC reversed micelles? Due to the high tail molecular volume of TOMAC, which has four alkyl chains (one methyl and three octyl chains), it is necessary to introduce a cosurfactant to promote the formation of a stable reversed micellar solution. The cosurfactant will decrease the packing parameter n/al defined by Mitchell and Ninham [38], where n is the volume of the hydrocarbon chain of the surfactant, l is an optimum length close to that of the fully extended chain, and a is the head group area. In this work an aliphatic alcohol, hexanol, was used to adjust this parameter by increasing the interfacial area per surfactant molecule and thus a stable reversed micellar solution was obtained. It has been found that hydrophilic amino acids are mainly solubilized in the water pool or establishing electrostatic interactions with the reversed micellar interface. The contribution of their zwitterionic forms in the solubilization process can be
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neglected. Solubilization of hydrophilic amino acids is thus mediated by the exchange of a charged amino acid with a surfactant counter ion (chloride, when TOMAC is used). Consequently, solubilization of hydrophilic and slightly hydrophobic amino acids can be described by an ion-exchange mechanism. Based on this mechanism, an extraction model can be developed and the equilibrium constant, Ke, determined for different amino acids, such as aspartic acid or phenylalanine (KeAsp2 − =0.20 90.04; KeAsp− =0.024 9 0.005; KePhe− = 0.619 0.04). Using this model it is possible to predict the amino acid equilibrium concentrations under different experimental conditions and optimise the extraction process. The solubilization of amino acids with a significant apolar moiety (such as tryptophan) can not be described by a simple ion-exchange model. Hydrophobic interactions have to be considered. Due to this contribution, the amino acid is mainly solubilized in the reversed micellar interface. The importance of the hydrophobic effect as a driving force for solubilization can be evaluated by plotting the amino acid equilibrium concentration in the aqueous phase against its initial concentration in the aqueous phase for a net charge Z = 0 (where electrostatic interactions are negligible). Transport of water and of amino acid from the aqueous phase to the reversed micellar phase was observed. If the degree of water transfer is equal to the degree of amino acid transfer then the concentration of amino acid in the aqueous phase remains constant. Using this representation (Fig. 3a), a straight line with slope 1 indicates that the amino acid transport is exclusively associated with water transfer from the aqueous phase to the reversed micellar water pool. As there are only two possible environments for amino acid solubilization in the organic phase — water pool and reversed micellar interface — , a deviation from a unitary slope means that the amino acid that was transferred is located in the micellar interface. As expected this effect is more pronounced for the extraction of triptophan. In Fig. 3b the final concentration of amino acid in the aqueous phase is plotted against the initial concentration, for phenylalanine with a net charge Z = − 0.7 and for tryptophan with a net charge
189
Z= − 0.35. The slope obtained for tryptophan deviates more from unity than the slope for phenylalanine, despite the lower charge of this amino acid. This behaviour illustrates how important is the hydrophobic character of an amino acid to promote its solubilization in the micellar interface. The different type of interactions established between amino acids and the reversed micellar interface can be explored to selectively separate amino acids with the same net charge. The results obtained show that even amino acids with very similar isoelectric points, as it is the case of phenylalanine (pI= 5.76) and tryptophan (pI= 5.88), can be effectively separated using a reversed micellar system of TOMAC/hexanol/n-heptane. Fig. 4 shows the selectivity obtained for resolution of tryptophan/phenylalanine mixtures by extraction with this reversed micellar system. This result is remarkable if we bear in mind that the extractant used is quite unspecific when used in a free, non-assembled form. The separation factor obtained is quite reasonable, especially taking into consideration that these two amino acids have very close isoelectric points and their separation by other methods is rather difficult. As hydrophobic amino acids establish strong interactions with the micellar interface their solubilization depends very much on the interface structure (curvature and bending modulus). This feature can be explored to selectively reextract amino acids present in the reversed micellar phase to a stripping aqueous phase. Reextraction with an aqueous phase with a relatively high ionic strength (for example, with a 1 M KCl aqueous solution) causes a reduction of the reversed micellar size, which leads to a squeezing-out of the amino acid from the interface. This procedure is more effective for amino acids solubilized in the micellar interface, as happens with hydrophobic amino acids, than for amino acids solubilized in the micellar water pool or near the interface. It is interesting to notice that in this case, operation with a relatively high ionic strength in the stripping phase can be explored to increase the selective transport of a hydrophobic amino acid (as tryptophan) against the transport of a less hydrophobic amino acid (as phenylalanine).
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Fig. 3. Amino acid equilibrium concentration in the excess aqueous phase ([Amino acid]aqf) versus initial concentration of amino acid ([Amino acid]aqi). Ionic strength, I = 0.13 the results shown are for (a) Z =0: () phenylalanine and ( ) tryptophan: (b) Z = − 0.7: () phenylalanine and Z= − 0.35 ( ) tryptophan.
The case study discussed above shows how reversed micelles can be used for selective extraction and reextraction of amino acids. The reversed
micellar system described can also be successfully used for extraction and reextraction of amino acids using two hollow fibre contactors in series.
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Fig. 4. Selectivity for the resolution of trypophane/phenylalanine mixtures with the reversed micellar system TOMAC/Hexanol/n-heptane. Ionic strength, I= 0.13.
3.1.3. Solute extraction by chiral carriers As mentioned in the introduction, chiral resolution is an important issue, not only for the chemical industry but in particular for the pharmaceutical industry. Specifically, b-blockers have received enormous clinical attention due to their efficacy in treating hypertension, ischemic heart disease and arrhythmia. Among these drugs is propranolol, where both enantiomers exercise different effects: d-propranolol is :40 times more potent than l-propranolol and appears to mediate the antiarrythmic and antihypertensive activity of the racemic mixture, whereas only lpropranolol appears to be beneficial in treating angina pectoris.
191
For resolution of racemic mixtures it is necessary to design and synthesise specific carriers with ability to recognise selectively the desired enantiomer. Hydrophobic (R,R)- and (S,S)-di-n-alkyltartrates have shown to have the property of forming a non polar organic soluble complex with boric acid, preferentially with the corresponding enantiomer of chiral b-amino-alcohols. The extraction mechanism of propranolol is depicted in Fig. 5. Chiral recognition occurs in the organic phase with the formation of a tetrahedral complex between the enantiomer of propranolol, boric acid and the corresponding tartrate enantiomer. Equilibrium studies performed by the authors for the racemic propranolol mixture in aqueous phase and the (S,S) or (R,R)-di-n-dodecyltartrate carrier in chloroform, have shown a strong dependence of the solute partition coefficient and enantioselectivity with the pH of the aqueous phase (Fig. 6a and b). These results show that by lowering the pH the dissociation equilibrium of propranolol is displaced for its charged form, favouring the selective route of extraction. For this reason at pH 4.4 (25°C) an enantiomeric excess of 9% in the extractant phase was achieved (Table 3). By increasing the pH, the uncharged form of propranolol is favoured and thus the non-selective extraction of propranolol by simple partition between the two phases is enhanced, increasing the partition coefficient but decreasing the enantioselectivity of the process. The successful enantioseparation obtained in the lower pH range, envisages a high potential for
Fig. 5. Enantioselective association of l-propanolol with (S,S)-di-n-dodecyltartrate, by formation of a borate complex.
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3.2. Kinetic modelling of extraction processes Two basic problems are discussed in this section: the importance of using a correct description of solute partition equilibrium between the feed and the extractant phase (and between the extractant and the stripping phase); and the development of adequate methodologies to obtain mass transfer correlations for extraction in liquid membrane contactors. The first problem was raised because it is quite common to see in the literature the use of constant partition coefficients to describe equilibrium, even when this represents a rather crude simplification. The second question inquires why a method which imposes so many restrictions, as is the case of the Wilson-plot methodology, is still extensively used for development of mass transfer correlations. A new calculation method is, therefore, proposed. The case study used to illustrate the partition equilibrium problem is the extraction of lactate with TOMAC, as described before. The extraction system used to discuss the development of mass transfer correlations is the extraction of valeric acid from an aqueous phase using a secondary amine, Amberlite LA-2.
Fig. 6. (a) Enantiomeric excess (%) of l-propranolol as a function of its initial concentration (c 0l ), for ( ) pH = 4.4, ( ) pH =5.2 and () pH =5.6; (b) partition coefficient (P) of l-propranolol as a function of its initial concentration (c 0l ), for ( ) pH= 4.4, ( ) pH=5.2 and () pH=5.6. The initial concentrations of (S,S)-di-n-dodecyltartrate and boric acid were 100 mM and the temperature was 25°C.
a continuous process using hollow-fibre membrane contactors. The enantiomeric excess of 9% obtained after one single theoretical stage of contact can be considered a rather good result but, to achieve an effective separation of the two enantiomers, a multi-step contact process is necessary.
3.2.1. Solute partition equilibrium Extraction of lactate was performed in a hollow fibre contactor as described in the materials and methods section. In order to increase the change in solute concentration, extraction was carried out with recirculation of the feed and organic phases through the module and back into the feed and organic reservoirs. Assuming a high degree of mixing in the vessel, the solute concentration in the vessel is equal to that entering the module, i.e. C in t . Taking into account that in a single passage through the module the change of solute concentration is rather small (experimentally confirmed) the driving-force, (Ct − C *), along the module can t be considered constant. A mass balance to the hollow fibre module and vessel can be used to determine the change in solute concentration with time: − Vaq ·
dCt = Kt · Am · (Ct − C*) t dt
(4)
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Table 3 Partition coefficients (P) for propranolol enantiomers (l and d) and enantiomeric excess (%) of l−propranolol in the organic phase at different pH pH
C0l−propranolol (mM)
4.4
0.25 1.0 2.5 5.0 10.0
6.2 3.5 3.1 2.7 2.6
4.7 2.1 1.8 1.5 1.5
1.8 6.8 7.6 9.3 9.0
5.2
0.50 1.2 2.5 3.7 5.0
20.8 15.0 13.4 12.7 12.0
9.5 5.9 4.9 4.6 4.3
2.7 4.2 5.4 5.6 6.8
5.6
0.50 1.2 2.5
43.6 37.4 28.9
20.3 14.0 10.5
1.0 1.8 2.8
Pl
where Kt is the overall mass transfer coefficient, Vaq represents the aqueous phase volume, Am the membrane transfer area, equal to 2pdilnf, where nf is the number of fibres, and Ct is the solute concentration in the tube side phase. The superscript * refers to the solute concentration in the aqueous phase, in equilibrium with the solute concentration in the shell side (organic phase). If it is assumed that the solute partition between the two phases is adequately described by a constant partition coefficient P then, integration of Eq. (4) using C *= Cs /P (where Cs is the solute t concentration in the shellside phase, obtained by mass balance) yields an analytical expression of Ct versus t with Kt as the unknown parameter. When a variable partition coefficient is considered necessary for a correct description of the solute partition equilibrium a relation between C *t and Cs has to be derived. For extraction of monovalent anions with a quaternary ammonium salt (TOMAC), this relation can be expressed as: 1 C 2s C*t = (5) Ke C 0c −Cs where Ke is the ion exchange equilibrium constant of the reaction between lactate and the carrier and C 0c is the initial carrier concentration. Fig. 7 represents the experimental equilibrium data fitted either by using the equilibrium relation (Eq. (5)) or a constant partition coefficient P.
Pd
Enantiomeric excess (%)
Eq. (4) may be integrated after substitution of the equilibrium equation, using Scientist®; an initial value is assumed for Kt, to allow iteration to start, and the model equation is solved obtaining the Ct variation with time. The calculation is iterated until the Kt value obtained minimises the sum of the squares residuals of model and experimental values of Ct versus time.
Fig. 7. Equilibrium data for the extraction of lactate with a quaternary ammonium salt [ experimental data --- constant P and — equilibrium model (Eq. (5))].
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Table 4 Comparison of the two different approaches, constant P or variable P, on the overall mass transfer coefficient evaluation Ret
Res
4 9 14 18 23 32 36
2
23
1 2 3 5 6
Kt (10−7 m/s)
Deviation (%)
Constant P
Equilibrium curve
1.56 9 0.31 1.11 9 0.22 1.50 9 0.27 1.15 9 0.29 1.46 9 0.59 1.48 9 0.38 1.04 9 0.19
1.2790.25 0.89 90.20 1.22 9 0.25 0.91 9 0.22 1.14 90.44 1.16 90.52 0.84 9 0.19
−23 −25 −23 −26 −28 −28 −24
1.84 9 0.49 0.91 9 0.07 1.46 9 0.59 1.57 9 0.37 1.49 9 0.28
1.59 9 0.56 1.14 90.44 0.74 9 0.09 1.25 9 0.36 1.26 90.26
−16 −23 −28 −26 −18
Mass transfer coefficients were thus evaluated for lactate extraction using the two mentioned approaches: 1. assuming a constant partition coefficient; 2. using the equilibrium relation between C *t and Cs. Table 4 compares the values of Kt obtained for these situations. The deviation between the calculated values for the overall mass transfer coefficients using either a constant or a variable partition coefficient varies between −16 and − 28%. This example illustrates very clearly the importance of using a correct description of the solute partition equilibrium for determination of mass transfer coefficient.
3.2.2. E6aluation of mass transfer correlations Three individual mass transfer resistances may be considered in contactor extraction processes: (1) the boundary layer resistance in the liquid phase inside in fibres (tube side); (2) the membrane resistance to solute diffusion across the liquid phase wetting the pores and (3) the boundary layer resistance in the shell side liquid phase. The overall resistance, for a hollow fibre system with the membrane wetted by the shell side fluid phase, can be expressed as:
1 1 1 1 = + + Kt · Ai kt · Ai P · km · Alm P · ks · A0
(6)
where kt, km and ks are the individual mass transfer coefficients on the tube side, membrane and shell side, respectively, and Ai, A0 and Alm are the fibres internal, external and logarithmic mean areas, respectively. In the present work a Le´ve`que type equation will be used to correlate both the tube side and the shell side mass transfer coefficients:
di l
Sht = a · Sc bt t · Rect t ·
Shs = b · Sc bs s · Recs s ·
(1/3)
(7)
dh l
(8)
where the subscripts t and s refer to the tube and shell sides, respectively, and a and b are constants. Thus, substituting these equations in Eq. (6), Kt will be expressed as a function of four unknown parameters: a; b; ct and cs, assuming bt = bs = 1/3. 1 = Kt
1 D · maq a· raq · l · d 2i +
2 aq
1/3
1 di · d · t + ct Ret dlm · P · o · Dorg
1 d 30 · P 3 · D 2org · morg b· d 3i · rorg · l 3
1/3
1 Recs s
(9)
When using the Wilson-plot methodology for development of mass transfer correlations the experimental data (C versus t) were fitted using Eq. (4) and the overall mass transfer coefficients were determined. The inverse of these coefficients were then plotted in two separate graphics, one as a function of 1/Rect (when the tube side Reynolds number is varied) and the other as a function of 1/Recs (when the shell side Reynolds number is varied). From the slopes of these two straight lines the values of a and b were taken. Table 5 shows the parameter values and the associated errors, for a 95% confidence level. It can be seen that for both tube and shell side the
I.M. Coelhoso et al. / Separation/Purification Technology 19 (2000) 183–197 0.558 91.277model describes quite well the experimental results. However, despite the high correlation coefficient (0.987), the errors associated with parameter estimation are considerably high, with errors ranging from 54 to 450%! These excessively high errors question the validity of the methodology, showing that the problem lies on the calculation method. However, it is not possible to assess its validity in most published work, because the associated errors are not usually stated. In order to reduce the errors obtained and to prevent any loss of information a single step calculation methodology was developed. Kt expressed by Eq. (9) was substituted into Eq. (4) and then, all the experimental values of C versus t were fitted directly in order to obtain the parameters a, b, ct and cs. Table 5 shows that this method produces estimated parameter values in a totally different range, showing higher exponent values for the Reynolds numbers. The errors are drastically reduced ranging from 15 to 22%. The Wilson-plot methodology has proved in the past to work satisfactorily in systems operated under steady state conditions and when the only parameter varying between the different experimental runs is the fluid velocity of each phase. Nevertheless the results presented show that this methodology has to be altered when working under transient state or when other parameters beside the fluid velocity are changing during the time course of the experimental study.
Table 5 Parameter values and errors using the Wilson-plot methodology and using a one-step calculation Method
Wilson-plot
One-step
Parameter
Value and error
% Error
ct cs a b
0.5589 1.277 0.3559 1.414 0.3059 0.164 1.4879 6.691
229 398 53.8 450
ct cs a b
0.91490.136 0.6979 0.136 0.2729 0.047 3.3649 0.739
14.9 19.5 17.3 22.0
r2
195
The major limitation of the Wilson-plot methodology stems from the fact that it involves a two-step calculation, i.e. two sequential fittings (estimation of the mass transfer coefficients followed by determination of the constants a, b, ct and cs ), leading to unnecessary loss of information and possible incoherent results. The other major drawback of this procedure is due to the fact that it cannot take into account any variation of the individual parameter’s values, either between or within experimental runs. The example used in this work is particularly well suited because during extraction of valeric acid with Amberlite LA-2 the association between the solute and the extractant changes with the solute concentration in the feed, forming different carriersolute complexes [35]. As a consequence, the partition coefficient of the solute between the feed and the organic phase changes during the extraction experiment as well as the average diffusion coefficient of the carrier-solute complexes. Therefore, the use of the Wilson-plot methodology is completely inadequate for development of mass transfer correlations in these type of systems. The drastic reduction, of roughly 20 times, on the errors associated with the estimated parameters when using the one-step methodology, and the different results obtained by these two methods, lead us to conclude that the Wilson-plot method may also be inaccurate. This conclusion can be extrapolated to other mass transfer processes and equipment and, therefore, we recommend the use of this one-step method as a general procedure. The one-step calculation method developed can be easily applied given the currently available mathematical tools that enable the analytical manipulation of equations and fittings with complex expressions.
4. Conclusions 0.987
0.997
Liquid membranes are a unique tool for selective transport of desired solutes from complex mixtures. The industrial future of liquid membranes will depend very strongly on the ability to design and synthesise selective carriers or receptors with the potential to achieve recognition of
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individual solutes. Therefore, the trend will be the development of supramolecular chemistry with the aim of obtaining very selective carriers, in some cases with the ability for chiral recognition. The first part of this paper discusses the importance of a comprehensive understanding of the carrier–solute interactions and the mechanisms involved on solute transport across liquid membranes. The first case study presented was a rather non-specific interaction between a quaternary amine ion-exchanger and lactate. It was our aim to demonstrate that when a organic phase with some permeability to water is used, the osmotic pressure difference across the liquid membrane may have to be considered for a correct description of solute transport. This situation is rather common and the analysis presented can be applied to similar systems. The other case studies presented — transport with reversed micelles and extraction with chiral selectors — show how structured fluids (as reversed micelles) can be used for selective transport by making use of electrostatic and hydrophobic interactions with the solutes, and also that chiral carriers can be synthesised to perform resolution of racemic mixtures. The case studies presented do not intend to cover the large field of facilitated transport but they illustrate the potential of this area and the importance of understanding the transport mechanisms involved. The second part of this work brings to discussion a few aspects related with modelling of transport in liquid membrane contactors. Intentionally, the two problems raised may be considered quite simple (or even trivial): how to describe solute partition between the feed and the extractant phase and how to obtain adequate mass transfer correlations in membrane contactors. The discussion presented aims to call attention to the importance of using a correct description of solute partition, specially when it is getting so common the use of constant partition coefficients, even when this is a wrong assumption. Concerning the development of mass transfer correlations a new calculation methodology was proposed. Amongst other advantages, this approach makes possible to
consider a variation of the partition coefficient and the solute-carrier diffusion coefficient, which is not possible to take into account with the Wilson-plot method, where all the variables but the Reynolds number have to be considered constant.
References [1] J.J. Pellegrino, R.D. Noble, Enhanced transport and liquid membranes in bioseparations, Tibtechnology 8 (1990) 216. [2] L.A.J. Chrisstoffels, Carrier-facilitated transport as a mechanistic tool in supramolecular chemistry, Ph.D. Thesis, University of Twente, Enschede, The Netherlands, 1998. [3] T. Hano, M. Matsumoto, S. Venoyama, T. Ohtake, Y. Kawano, S. Miura, Separation of lactic acid from fermented broth by solvent extraction, Bioseparation 3 (1993) 321. [4] S. Schlosser, L. Kubisova, J. Martak, Pertraction of lactic acid in a hollow fibre contactor, in: Proceedings of Euromembrane’95, vol. 2, Bath, 1995, pp. 398 – 401. [5] R. Basu, K.K. Sirkar, Hollow fiber contained liquid membrane separation of citric acid, AIChE J. 37 (1991) 383. [6] L. Dahuron, E.L. Cussler, Protein extractions with hollow fibers, AIChE J. 34 (1) (1988) 130. [7] R. Basu, R. Prasad, K.K. Sirkar, Nondispersive membrane solvent back extraction of phenol, AIChE J. 36 (1990) 450. [8] C.M. Yun, R. Prasad, K.K. Sirkar, Membrane solvent removal of priority organic pollutants from aqueous waste streams, In. Eng. Chem. Res. 31 (1992) 1709. [9] C.J. Tompkins, A.S. Michaels, S.W. Peretti, Removal of p-nitrophenol from aqueous solution by membrane-supported solvent extraction, J. Memb. Sci. 75 (1992) 277. [10] R. Prasad, K.K. Sirkar, Hollow fiber solvent extraction of pharmaceutical products: a case study, J. Memb. Sci. 47 (1989) 235. [11] R. Basu, K.K. Sirkar, Pharmaceutical product recovery using a hollow fiber contained liquid membrane: a case study, J. Memb. Sci. 75 (1992) 131. [12] P.R. Alexander, R.W. Callahan, Liquid-liquid extraction and stripping of gold with microporous hollow fibers, J. Memb. Sci. 35 (1987) 57. [13] B.M. Kim, Membrane-based extraction for selective removal and recovery of metals, J. Memb. Sci. 21 (1984) 5. [14] M. Matsumoto, H. Shimauchi, K. Kondo, F. Nakashio, Kinetics of copper extraction with Kelex 100 using a hollow fiber membrane extractor, Solvent Extr. Ion Exch. 5 (2) (1987) 301. [15] A Alonso, A. Urtiaga, A. Irabien, I. Ortiz, Extraction of Cr (VI) with Aliquat 336 in hollow fiber contactors: mass
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variable distribution coefficient, J. Memb. Sci. 127 (1997) 141. I.M. Coelhoso, P. Silvestre, R.M.C. Viegas, J.P.S.G. Crespo, M.J.T. Carrondo, Membrane-based solvent extraction and stripping of lactate in hollow-fibre contactors, J. Memb. Sci. 134 (1997) 19. M.M. Cardoso, M.J. Barradas, M.J.T. Carrondo, K.-H. Kroner, J.P.S.G. Crespo, Mechanisms of amino acid partitioning in cationic reversed micelles, Bioseparation 7 (2) (1998) 65. M. Rodrı´guez, R.M.C. Viegas, S. Luque, I.M. Coelhoso, J.P.S.G. Crespo, J.R. Alvarez, Removal of valeric acid from waste waters by membrane contactors, J. Memb. Sci. 137 (1998) 45. R.M.C. Viegas, M. Rodrı´guez, S. Luque, J.R. Alvarez, I.M. Coelhoso, J.P.S.G. Crespo, Mass transfer correlations in membrane extraction: analysis of Wilson-plot methodology, J. Memb. Sci. 145 (1998) 129. M.M. Cardoso, R.M.C. Viegas, J.P.S.G. Crespo, Extraction and reextraction of phenylalanine by cationic reversed micelles in hollow fibre contactors, J. Memb. Sci. 156 (1999) 303. M.M. Cardoso, M.J. Barradas, K.-H. Kroner, J.P.S.G. Crespo, Amino acid solubilization in cationic reversed micelles: factors affecting amino acid and water transfer, J. Chem. Technol. Biotechnol. 74 (1999) 801. J.P.S.G. Crespo, I.M. Coelhoso, R.M.C. Viegas, Membrane contactors, in Encyclopedia of Separation Science, Academic Press (in press). E.B. Leodidis, T.A. Hatton, Amino acids in AOT reversed micelles. 1. Determination of interfacial partition coefficients using the phase-transfer method, J. Phys. Chem. 94 (1990) 6400. S. Luque, J.R. Alvarez, C. Pazos, J. Coca, Recovery of valeric acid from aqueous solutions by solvent extraction, Extr. Ion Exch. 13 (5) (1995) 923. R.A. Robinson, R.H. Stokes, Electrolyte solutions, Butterworths, London, second ed., 1970. R. Molinari, L. De Bartolo, E. Drioli, Coupled transport of aminoacids through supported liquid membranes, J. Memb. Sci. 73 (1992) 203. D.J. Mitchell, B.W. Ninham, J. Chem. Soc. Faraday Trans. 2 (77) (1981) 601.
Transport mechanisms and modelling in liquid membrane contactors I.M. Coelhoso, M.M. Cardoso, R.M.C. Viegas, J.P.S.G. Crespo * Departamento de Quı´mica, Faculdade de Cieˆncias e Tecnologia, Uni6ersidade No6a de Lisboa, 2825 Monte de Caparica, Portugal Received 14 September 1999; received in revised form 3 January 2000; accepted 7 January 2000
Abstract This paper discusses the use of liquid membrane contactors for extraction of fermentation and pharmaceutical products using different types of carriers. It intends to emphasise the importance of understanding the transport mechanisms involved in liquid membrane extraction with different carriers and also to discuss relevant aspects of the mathematical modelling involved in these extraction processes. Using the extraction of organic acids, namely amino acids, as a case study it is shown how the supramolecular organisation of the extractant determines the solute transport mechanisms involved. Additionally, the resolution of racemic mixtures using chiral carriers is also discussed. The modelling work analyses two different aspects of extraction using membrane contactors with microporous membranes: (i) the importance of using a correct description of solute partition between the feed and the extractant phase (use of a variable partition description versus constant partition); (ii) the correct development of mass transfer correlations in hollow fibre contactors. For the development of mass transfer correlations the calculation method proposed by Wilson has been universally used. Given the currently available mathematical tools, that enable the analytical manipulation of equations and fittings with complex expressions, a new calculation methodology is discussed. © 2000 Elsevier Science B.V. All rights reserved. Keywords: Membrane extraction; Facilitated transport; Transport mechanisms; Mass transfer correlations; Membrane contactors
1. Introduction Carrier-facilitated transport through liquid membranes has been inspired by the ability of natural systems to selectively pump ions across biological membranes. In liquid membrane systems an immiscible organic phase separates two aqueous * Corresponding author. Tel.: +351-21-2948385; fax: + 351-21-2948357. E-mail address: [email protected] (J.P.S.G. Crespo)
phases, the feed and the stripping phases. Solute transport can be enhanced if an extractant, which interacts selectively and reversibly with the solute, is added to the organic liquid membrane [1]. The first generation of synthetic carriers were the crown-ether macrocycles which selectively bind alkali metal cations. Since their discovery many carriers have been synthesised for the selective recognition of neutral, charged or zwitterionic species and applied in liquid membranes for binding studies or separation purposes [2].
1383-5866/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 1 3 8 3 - 5 8 6 6 ( 0 0 ) 0 0 0 5 1 - 4
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Liquid membrane extraction has received considerable attention due to the advantages of combining liquid-liquid extraction and membranes in a single operation. The potential advantages of membrane extraction processes are: 1. Small amounts of complexing agent are required due to the continuous regeneration associated with the reversible reaction. As a consequence operating costs can be reduced; 2. extraction and stripping can be carried out simultaneously in one equipment, reducing investment costs; 3. backmixing effects and loss of complexing agent can be minimised when an appropriate membrane configuration is used; 4. highly selective separations are possible. This feature is most useful at low solute concentration where an excess of complexing agent is present and the complexation reaction is very efficient. This is in contrast to other separation processes, which do not usually work well at low solute concentrations. In spite of the known advantages in the use of supported liquid membranes the major drawback for industrial application regards their stability. A new type of liquid membrane configuration, the membrane contactor, with the potential to eliminate the shortcomings of supported liquid membranes while retaining its advantages is gaining importance. They have been applied to a large variety of systems including extraction of fermentation products [3– 6], pollutants [7 – 9], pharmaceutical products [10,11] and metals [12 – 15]. The advantages of membrane contactors stem from the large surface area per volume, typically between 3000 m2/m3 and 5000 m2/m3. They also present other advantages over classical extractors, such as the possibility of operating with a wide range of flow rates, no need for density differences to achieve phase separation and no emulsification, since the interface between both phases is immobilised within the membrane pores [16]. This paper discusses the use of liquid membranes for extraction of fermentation and pharmaceutical products using different types of carriers or the same carrier with a different supramolecular organisation. It is our intention to emphasise the importance of understanding the
transport mechanisms involved in liquid membrane extraction and also to discuss a few relevant aspects of the mathematical modelling involved in these extraction processes. The transport mechanisms involved in the extraction of organic acids by a quaternary ammonium salt are discussed and the effect of osmotic pressure difference, through the liquid membrane, on solute transport is evaluated. The same ammonium salt is also used for amino acid transport but under conditions where the assembling of the extractant molecules in reversed micelles is favoured. The selective transport of amino acids using these molecular aggregates in liquid membranes is presented and the transport mechanisms, considering both electrostatic and hydrophobic interactions, are discussed. Racemic mixture resolution is also an important issue for the pharmaceutical industry, as public health is involved. In many cases just one of the enantiomers presents activity, the other is inactive or may even exert an adverse secondary effect. Very recently some examples were described that evidence the possibility of using a chiral carrier agent dissolved in an organic phase [17,18]. Several carriers, such as cyclodextrins [19], tartaric acid derivatives [20] and crown ethers [21] have been used. The resolution of propranolol, a b-adrenergic receptor antagonist drug, using tartaric acid derivatives is presented and discussed. The modelling work analyses two different aspects of extraction using membrane contactors with microporous membranes: (i) the importance of using a correct description of solute partition between the feed and the extractant phase (use of a variable solute partition or a constant partition); In membrane extraction processes the overall mass transfer coefficients are usually evaluated by assuming a constant partition coefficient of the solute between the two contacting phases. However, for several extraction systems, the partition coefficient may vary throughout the extraction process affecting the evaluation of the mass transfer coefficient. (ii) the correct development of mass transfer correlations;
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For development of mass transfer correlations a two-step calculation method proposed by Wilson has been universally used. Given the currently available mathematical tools that enable the analytical manipulation of equations and fittings with complex expressions, a new one-step calculation methodology is discussed. This paper uses experimental results obtained by our group during the last 8 years [22 – 33] and discusses them with a new insight, in an integrated way. It is our aim to focus attention on defined problems that were raised during these years, especially the need for a complete understanding of the mechanisms of solute transport taking into consideration the interactions established with the carrier, the knowledge about carrier organisation and structuring, and finally the importance of correct mathematical modelling of the mass transport process.
2. Materials and methods
2.1. Extraction systems The feed phase used for lactate extraction studies was a lactate solution (280 mM) obtained by dilution of sodium lactate 60% (Sigma, USA). The pH of the solutions was adjusted to 6.3 with a 0.1 M NaOH solution. The organic phase was composed of a quaternary ammonium salt carrier, Aliquat 336 (TOMAC) (Fluka, Germany) and of a hydrocarbon mixture, Shellsol A (Shell, UK), as diluent. The carrier concentration was always 30% (w/w). The stripping phase was a sodium chloride solution, with concentrations ranging from 0.28 to 4.71 M. The amino acid extraction studies were performed using the phase transfer method [34]. An aqueous solution of amino acid at 25°C was contacted with a n-heptane (spectrophotometric grade, Merck, Germany) solution containing 125 mM TOMAC as surfactant and 1.25% v/v of hexanol (99% purity, Merck, Germany) as co-surfactant. The desired pH and ionic strength in the aqueous solution were adjusted using a potassium hydroxide solution and adding potassium chloride, respectively. Phenylalanine, potassium hy-
185
droxide and potassium chloride of 99% purity were also purchased from Merck (Germany) and tryptophan of 99% purity was obtained from Sigma (USA). Methanol for chromatography was supplied by Merck (Germany). Propranolol hydrochloride and tartaric acid were purchased from Aldrich Chemical (USA), boric acid from Riedel–de Hae¨n AG (Germany) and chloroform from Merck (Germany). (S,S)-din-dodecyltartrate and the free base of propranolol were prepared as described in [20]. The extraction equilibrium isotherms were determined for propranolol concentrations of 0.2, 0.5 and 5 mM in aqueous medium (demineralized water, boric acid, 0.100 M, acetate buffer, 50 mM, pH 5.2) and for (S,S)-di-n-dodecyltartrate concentrations of 2, 30 and 100 mM in chloroform, by contacting 10 ml of both organic and aqueous solutions. The samples were stirred vigorously with an Ultra-Turrax (Janke and Kunkel IKA-Labortechnik, Germany), at 24 000 rpm, for 2.5 min and at a controlled temperature of 25°C. The studies of valeric (n-pentanoic) acid extraction were carried out with a synthetic feed — 5 g/l of valeric acid in deionized water-, simulating a wastewater stream from polymer manufacturing. Amberlite LA-2 (Fluka) (10 vol%) in toluene (Merck\ 99%) (90 vol%) was chosen as extraction system according to previous studies [35].
2.2. Membrane contactor studies Liquid-Cel laboratory hollow-fibre modules with Celgard® membranes from Hoechst Celanese were used throughout these studies. Each module has 2.5 cm of internal diameter, contains 2100 hydrophobic polypropylene fibres, 16 cm long, with a nominal internal diameter of 240 mm, nominal thickness of 30 mm, porosity of 0.3 and a nominal pore size of 0.05 mm. Each module provides an effective area of 0.23 m2. The aqueous feed phase was pumped through the lumen of the fibres while the organic phase flowed in the shell side of the module. Magnetically driven gear pumps were used. To monitor both the aqueous and organic flow rates during the experiments flow meters were used. Due to the hydrophobic nature of the fibres a slight overpres-
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sure (0.2 bar) was applied to the aqueous phase in order to stabilise the interface within the membrane. All the experiments were carried out in co-current flow. For simultaneous extraction and reextraction, two hollow fibre modules were used in series. Extraction was accomplished in the first module and the loaded organic phase that leaves this module enters the shell side of a second module, where the stripping of the solute is carried out.
2.3. Analytical methods The concentration of organic acids (lactate and valeric acid) was determined by HPLC. The column used was a Shodex SH 1011 (Showa Denko K.K., Japan) and the eluent sulphuric acid 0.01 N. A refractive index detector (Merck Hitachi, Japan) was employed. The amino acids concentration was also determined by HPLC. The column used was a Merck RP-18 (Merck, Germany) and the eluent was a solution with 75% methanol (v/v) and 25% water (v/v). A UV detector (Merck, Hitachi, Japan) at a wavelength of 257 nm was employed for phenylalanine and tryptophan quantification. The quantification of both propranolol enantiomers in the aqueous phase was done by HPLC with a UV detector (Merck, Hitachi, Japan) at a wavelength of 254 nm. A Chiralcel OD-R (Daicel, Japan) column was used and the mobile phase was 0.1 M potassium hexafluorophosphate aqueous solution: acetonitrile (60:40). The water content of the organic phases (namely the reversed micellar phase) was deter-
mined by Karl Fischer titration (Aquapal III, UK). The viscosity of the organic phases was measured by using a couette type viscometer (Brookfield, model DV-II digital, UK).
2.4. Calculation methods The software package Scientist™, from MicroMath® Scientific Software (USA), was used to perform the non-linear regression calculations. This software allies the capability of performing non-linear fittings and simultaneously solving both integral and differential equations. The least squares and the simplex algorithms were used.
3. Results and discussion
3.1. Transport mechanisms 3.1.1. Transport of lactate with free quaternary ammonium salts The transport of lactate using as carrier a quaternary ammonium salt (TOMAC) is used to illustrate the importance of understanding the mechanisms involved in solute transport across liquid membranes. The transport of lactate ions from the feed to the stripping phase is usually described as being counterbalanced by an equivalent transport of other anionic species from the stripping to the feed phase through a coupled transport mechanism (Fig. 1). The following ionexchange reaction takes place at both interfaces: Ke
La− + R+Cl− l R+La− + Cl− with the equilibrium constant, Ke, defined as: Ke =
Fig. 1. Coupled transport mechanism for the extraction and re-extraction of lactate in a liquid membrane with a quaternary ammonium salt.
(1)
[R+La−][Cl−]f [R+La−][Cl−]s = [La−]f [R+Cl−] [La−]s [R+Cl−]
(2)
where [R+La−] and [R+Cl−] are the lactateamine and the chloride-amine complexes concentrations in the organic phase, [La−]f and [Cl−]f are the lactate and chloride concentrations in the feed phase, and [La−]s and [Cl−]s are the lactate and chloride concentrations in the stripping phase. If this ion-pairing mechanism of transport is assumed, a simple mathematical model for equi-
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187
Table 1 Comparison of experimental and model lactate equilibrium activities: effect of initial chloride concentrationa [La−]0 (M)
[Cl−]0 (M)
[La−]f exp (M)
[La−]s exp (M)
aLa−/aLa− s f exp
aLa−/aLa− model
0.275 0.281 0.276 0.279
0.276 0.998 1.950 4.710
0.152 0.135 0.118 0.126
0.152 0.318 0.360 0.376
1.0 2.4 3.1 3.0
1.0 3.2 6.7 22.4
a
s
f
Bulk membrane, phase ratio (feed:org:strip) 3:3:1, [R+Cl−]0 =0.654 M.
librium can be developed. The equilibrium constant, Ke, of the reaction between the carrier and lactate can been determined, allowing a good prediction of equilibrium concentrations for independent extraction and stripping, for a large range of different experimental conditions. Due to the high concentrations of stripping agent employed it is more correct to use activities instead of concentrations. The activity coefficients for the species involved can be found in Robinson and Stokes [36]. For simultaneous extraction and stripping, as occurs in liquid membranes, the equilibrium lactate activity in the stripping phase can be related with the equilibrium lactate activity in the feed phase as a function of the initial lactate and chloride activities, if a ion-pairing mechanism of transport is considered: aLa− = aLa− · s
f
aCl− 0 aLa−
(3)
0
The model predicts that, if lactate is exclusively transported by an ion-pairing mechanism, the ratio of lactate activities in the stripping and in the feed phases increases with increasing initial chloride activity. However, the experimental results obtained with a bulk liquid membrane system show a large deviation between the experimental and the predicted values for the equilibrium lactate activities (Table 1). A similar behaviour was obtained by Drioli et al. for phenylalanine extraction also with TOMAC [37]. Contrary to the ion-exchange model prediction it can be concluded that it is not worthwhile to increase chloride concentration in the stripping phase above 1 M. For a bulk liquid membrane the ratio of lactate concentration in both phases remains constant for [Cl−]0 =1.95 M and for [Cl−
]0 = 4.71 M and it is only 30% higher than the value obtained with [Cl−]0 = 1M. Prediction of equilibrium was only accurate if both compartments (feed and stripping) have the same molar concentration of salts. For different molar concentration of salts, in the two compartments of the cell, the assumption that transport is exclusively accomplished by an ion-pairing mechanism is obviously not correct and thus it is necessary to consider the contribution of other mechanisms for ion transport. In order to confirm the occurrence of alternative mechanisms of transport, the osmotic pressure difference between the feed and stripping compartments was determined at the beginning and at the equilibrium of the experiments, by measuring the chloride and lactate concentrations in both compartments and using the corresponding osmotic coefficients [36]. As the osmotic pressure difference between the stripping and feed compartments is higher in the beginning of the experiment (Table 2), it has to be concluded that the amount of chloride transported from the stripping to the feed compartment is higher than the Table 2 Difference of osmotic pressure between stripping and feed compartments for different initial chloride concentrationsa [La−]0 (M)
[Cl−]0 (M)
(DP)0 (atm)
(DP)eq−exp (atm)
0.275 0.281 0.276 0.279
0.276 0.998 1.950 4.710
−0.37 32.7 88.6 292
−0.46 28.2 64.2 182
a Bulk membrane, phase ratio (feed:org:strip) 3:3:1, [R+Cl− ]0 =0.654 M.
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corresponding lactate transport in the opposite direction. Fig. 2 plots the osmotic pressure differences at equilibrium against its initial values. The deviation observed can be explained by a net transfer of chloride and sodium (to keep electroneutrality) from the stripping to the feed compartment. Transport of chloride and sodium, induced by the osmotic pressure difference, is probably associated with migration of aqueous ‘pockets’ across the liquid membrane in order to cancel the osmotic pressure difference. These results demonstrate the importance of understanding the mechanisms involved on solute transport, even from an engineering point of view: increasing the counter-ion concentration does not improve the extraction/stripping process because as salt transport increases less stripping solute becomes available to be counter transported by an ion-pairing mechanism.
3.1.2. Solute transport with re6ersed micelles The extractant used for lactate transport studies (TOMAC), can be induced to self-organise as a supramolecular aggregate, namely reversed micelles, if appropriate conditions are provided. This feature is rather interesting because the organic phase can be designed in order to promote the formation of these aggregates.
Fig. 2. Osmotic pressure difference at equilibrium versus initial osmotic pressure difference, for a bulk liquid membrane.
What would be the benefit of using a reversed micellar system? In the first place, reversed micelles provide different environments for solubilization: the reversed micellar water pool and the reversed micellar interface. Depending on the solute structure, polarity and ionisation state it may establish different types of interactions within these environments. These interactions will determine the solubilization site where the solute is hosted and the partition coefficient. This means that despite using a rather non-specific extractant, as it is the case of TOMAC, it is possible by organising these molecules as reversed micelles to obtain an extraction system able to interact in a selective way with different solutes. Additionally, if the transport of a defined solute with a reversed micellar system is essentially driven by hydrophobic interactions with the micellar interface then, an osmotic pressure difference between the feed and striping phases does not affect the solute transfer because the mechanism involved does not depend upon the concentration of a counter-ion. This feature is quite interesting for the transport of hydrophobic solutes. How can we induce the formation of TOMAC reversed micelles? Due to the high tail molecular volume of TOMAC, which has four alkyl chains (one methyl and three octyl chains), it is necessary to introduce a cosurfactant to promote the formation of a stable reversed micellar solution. The cosurfactant will decrease the packing parameter n/al defined by Mitchell and Ninham [38], where n is the volume of the hydrocarbon chain of the surfactant, l is an optimum length close to that of the fully extended chain, and a is the head group area. In this work an aliphatic alcohol, hexanol, was used to adjust this parameter by increasing the interfacial area per surfactant molecule and thus a stable reversed micellar solution was obtained. It has been found that hydrophilic amino acids are mainly solubilized in the water pool or establishing electrostatic interactions with the reversed micellar interface. The contribution of their zwitterionic forms in the solubilization process can be
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neglected. Solubilization of hydrophilic amino acids is thus mediated by the exchange of a charged amino acid with a surfactant counter ion (chloride, when TOMAC is used). Consequently, solubilization of hydrophilic and slightly hydrophobic amino acids can be described by an ion-exchange mechanism. Based on this mechanism, an extraction model can be developed and the equilibrium constant, Ke, determined for different amino acids, such as aspartic acid or phenylalanine (KeAsp2 − =0.20 90.04; KeAsp− =0.024 9 0.005; KePhe− = 0.619 0.04). Using this model it is possible to predict the amino acid equilibrium concentrations under different experimental conditions and optimise the extraction process. The solubilization of amino acids with a significant apolar moiety (such as tryptophan) can not be described by a simple ion-exchange model. Hydrophobic interactions have to be considered. Due to this contribution, the amino acid is mainly solubilized in the reversed micellar interface. The importance of the hydrophobic effect as a driving force for solubilization can be evaluated by plotting the amino acid equilibrium concentration in the aqueous phase against its initial concentration in the aqueous phase for a net charge Z = 0 (where electrostatic interactions are negligible). Transport of water and of amino acid from the aqueous phase to the reversed micellar phase was observed. If the degree of water transfer is equal to the degree of amino acid transfer then the concentration of amino acid in the aqueous phase remains constant. Using this representation (Fig. 3a), a straight line with slope 1 indicates that the amino acid transport is exclusively associated with water transfer from the aqueous phase to the reversed micellar water pool. As there are only two possible environments for amino acid solubilization in the organic phase — water pool and reversed micellar interface — , a deviation from a unitary slope means that the amino acid that was transferred is located in the micellar interface. As expected this effect is more pronounced for the extraction of triptophan. In Fig. 3b the final concentration of amino acid in the aqueous phase is plotted against the initial concentration, for phenylalanine with a net charge Z = − 0.7 and for tryptophan with a net charge
189
Z= − 0.35. The slope obtained for tryptophan deviates more from unity than the slope for phenylalanine, despite the lower charge of this amino acid. This behaviour illustrates how important is the hydrophobic character of an amino acid to promote its solubilization in the micellar interface. The different type of interactions established between amino acids and the reversed micellar interface can be explored to selectively separate amino acids with the same net charge. The results obtained show that even amino acids with very similar isoelectric points, as it is the case of phenylalanine (pI= 5.76) and tryptophan (pI= 5.88), can be effectively separated using a reversed micellar system of TOMAC/hexanol/n-heptane. Fig. 4 shows the selectivity obtained for resolution of tryptophan/phenylalanine mixtures by extraction with this reversed micellar system. This result is remarkable if we bear in mind that the extractant used is quite unspecific when used in a free, non-assembled form. The separation factor obtained is quite reasonable, especially taking into consideration that these two amino acids have very close isoelectric points and their separation by other methods is rather difficult. As hydrophobic amino acids establish strong interactions with the micellar interface their solubilization depends very much on the interface structure (curvature and bending modulus). This feature can be explored to selectively reextract amino acids present in the reversed micellar phase to a stripping aqueous phase. Reextraction with an aqueous phase with a relatively high ionic strength (for example, with a 1 M KCl aqueous solution) causes a reduction of the reversed micellar size, which leads to a squeezing-out of the amino acid from the interface. This procedure is more effective for amino acids solubilized in the micellar interface, as happens with hydrophobic amino acids, than for amino acids solubilized in the micellar water pool or near the interface. It is interesting to notice that in this case, operation with a relatively high ionic strength in the stripping phase can be explored to increase the selective transport of a hydrophobic amino acid (as tryptophan) against the transport of a less hydrophobic amino acid (as phenylalanine).
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Fig. 3. Amino acid equilibrium concentration in the excess aqueous phase ([Amino acid]aqf) versus initial concentration of amino acid ([Amino acid]aqi). Ionic strength, I = 0.13 the results shown are for (a) Z =0: () phenylalanine and ( ) tryptophan: (b) Z = − 0.7: () phenylalanine and Z= − 0.35 ( ) tryptophan.
The case study discussed above shows how reversed micelles can be used for selective extraction and reextraction of amino acids. The reversed
micellar system described can also be successfully used for extraction and reextraction of amino acids using two hollow fibre contactors in series.
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Fig. 4. Selectivity for the resolution of trypophane/phenylalanine mixtures with the reversed micellar system TOMAC/Hexanol/n-heptane. Ionic strength, I= 0.13.
3.1.3. Solute extraction by chiral carriers As mentioned in the introduction, chiral resolution is an important issue, not only for the chemical industry but in particular for the pharmaceutical industry. Specifically, b-blockers have received enormous clinical attention due to their efficacy in treating hypertension, ischemic heart disease and arrhythmia. Among these drugs is propranolol, where both enantiomers exercise different effects: d-propranolol is :40 times more potent than l-propranolol and appears to mediate the antiarrythmic and antihypertensive activity of the racemic mixture, whereas only lpropranolol appears to be beneficial in treating angina pectoris.
191
For resolution of racemic mixtures it is necessary to design and synthesise specific carriers with ability to recognise selectively the desired enantiomer. Hydrophobic (R,R)- and (S,S)-di-n-alkyltartrates have shown to have the property of forming a non polar organic soluble complex with boric acid, preferentially with the corresponding enantiomer of chiral b-amino-alcohols. The extraction mechanism of propranolol is depicted in Fig. 5. Chiral recognition occurs in the organic phase with the formation of a tetrahedral complex between the enantiomer of propranolol, boric acid and the corresponding tartrate enantiomer. Equilibrium studies performed by the authors for the racemic propranolol mixture in aqueous phase and the (S,S) or (R,R)-di-n-dodecyltartrate carrier in chloroform, have shown a strong dependence of the solute partition coefficient and enantioselectivity with the pH of the aqueous phase (Fig. 6a and b). These results show that by lowering the pH the dissociation equilibrium of propranolol is displaced for its charged form, favouring the selective route of extraction. For this reason at pH 4.4 (25°C) an enantiomeric excess of 9% in the extractant phase was achieved (Table 3). By increasing the pH, the uncharged form of propranolol is favoured and thus the non-selective extraction of propranolol by simple partition between the two phases is enhanced, increasing the partition coefficient but decreasing the enantioselectivity of the process. The successful enantioseparation obtained in the lower pH range, envisages a high potential for
Fig. 5. Enantioselective association of l-propanolol with (S,S)-di-n-dodecyltartrate, by formation of a borate complex.
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3.2. Kinetic modelling of extraction processes Two basic problems are discussed in this section: the importance of using a correct description of solute partition equilibrium between the feed and the extractant phase (and between the extractant and the stripping phase); and the development of adequate methodologies to obtain mass transfer correlations for extraction in liquid membrane contactors. The first problem was raised because it is quite common to see in the literature the use of constant partition coefficients to describe equilibrium, even when this represents a rather crude simplification. The second question inquires why a method which imposes so many restrictions, as is the case of the Wilson-plot methodology, is still extensively used for development of mass transfer correlations. A new calculation method is, therefore, proposed. The case study used to illustrate the partition equilibrium problem is the extraction of lactate with TOMAC, as described before. The extraction system used to discuss the development of mass transfer correlations is the extraction of valeric acid from an aqueous phase using a secondary amine, Amberlite LA-2.
Fig. 6. (a) Enantiomeric excess (%) of l-propranolol as a function of its initial concentration (c 0l ), for ( ) pH = 4.4, ( ) pH =5.2 and () pH =5.6; (b) partition coefficient (P) of l-propranolol as a function of its initial concentration (c 0l ), for ( ) pH= 4.4, ( ) pH=5.2 and () pH=5.6. The initial concentrations of (S,S)-di-n-dodecyltartrate and boric acid were 100 mM and the temperature was 25°C.
a continuous process using hollow-fibre membrane contactors. The enantiomeric excess of 9% obtained after one single theoretical stage of contact can be considered a rather good result but, to achieve an effective separation of the two enantiomers, a multi-step contact process is necessary.
3.2.1. Solute partition equilibrium Extraction of lactate was performed in a hollow fibre contactor as described in the materials and methods section. In order to increase the change in solute concentration, extraction was carried out with recirculation of the feed and organic phases through the module and back into the feed and organic reservoirs. Assuming a high degree of mixing in the vessel, the solute concentration in the vessel is equal to that entering the module, i.e. C in t . Taking into account that in a single passage through the module the change of solute concentration is rather small (experimentally confirmed) the driving-force, (Ct − C *), along the module can t be considered constant. A mass balance to the hollow fibre module and vessel can be used to determine the change in solute concentration with time: − Vaq ·
dCt = Kt · Am · (Ct − C*) t dt
(4)
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193
Table 3 Partition coefficients (P) for propranolol enantiomers (l and d) and enantiomeric excess (%) of l−propranolol in the organic phase at different pH pH
C0l−propranolol (mM)
4.4
0.25 1.0 2.5 5.0 10.0
6.2 3.5 3.1 2.7 2.6
4.7 2.1 1.8 1.5 1.5
1.8 6.8 7.6 9.3 9.0
5.2
0.50 1.2 2.5 3.7 5.0
20.8 15.0 13.4 12.7 12.0
9.5 5.9 4.9 4.6 4.3
2.7 4.2 5.4 5.6 6.8
5.6
0.50 1.2 2.5
43.6 37.4 28.9
20.3 14.0 10.5
1.0 1.8 2.8
Pl
where Kt is the overall mass transfer coefficient, Vaq represents the aqueous phase volume, Am the membrane transfer area, equal to 2pdilnf, where nf is the number of fibres, and Ct is the solute concentration in the tube side phase. The superscript * refers to the solute concentration in the aqueous phase, in equilibrium with the solute concentration in the shell side (organic phase). If it is assumed that the solute partition between the two phases is adequately described by a constant partition coefficient P then, integration of Eq. (4) using C *= Cs /P (where Cs is the solute t concentration in the shellside phase, obtained by mass balance) yields an analytical expression of Ct versus t with Kt as the unknown parameter. When a variable partition coefficient is considered necessary for a correct description of the solute partition equilibrium a relation between C *t and Cs has to be derived. For extraction of monovalent anions with a quaternary ammonium salt (TOMAC), this relation can be expressed as: 1 C 2s C*t = (5) Ke C 0c −Cs where Ke is the ion exchange equilibrium constant of the reaction between lactate and the carrier and C 0c is the initial carrier concentration. Fig. 7 represents the experimental equilibrium data fitted either by using the equilibrium relation (Eq. (5)) or a constant partition coefficient P.
Pd
Enantiomeric excess (%)
Eq. (4) may be integrated after substitution of the equilibrium equation, using Scientist®; an initial value is assumed for Kt, to allow iteration to start, and the model equation is solved obtaining the Ct variation with time. The calculation is iterated until the Kt value obtained minimises the sum of the squares residuals of model and experimental values of Ct versus time.
Fig. 7. Equilibrium data for the extraction of lactate with a quaternary ammonium salt [ experimental data --- constant P and — equilibrium model (Eq. (5))].
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Table 4 Comparison of the two different approaches, constant P or variable P, on the overall mass transfer coefficient evaluation Ret
Res
4 9 14 18 23 32 36
2
23
1 2 3 5 6
Kt (10−7 m/s)
Deviation (%)
Constant P
Equilibrium curve
1.56 9 0.31 1.11 9 0.22 1.50 9 0.27 1.15 9 0.29 1.46 9 0.59 1.48 9 0.38 1.04 9 0.19
1.2790.25 0.89 90.20 1.22 9 0.25 0.91 9 0.22 1.14 90.44 1.16 90.52 0.84 9 0.19
−23 −25 −23 −26 −28 −28 −24
1.84 9 0.49 0.91 9 0.07 1.46 9 0.59 1.57 9 0.37 1.49 9 0.28
1.59 9 0.56 1.14 90.44 0.74 9 0.09 1.25 9 0.36 1.26 90.26
−16 −23 −28 −26 −18
Mass transfer coefficients were thus evaluated for lactate extraction using the two mentioned approaches: 1. assuming a constant partition coefficient; 2. using the equilibrium relation between C *t and Cs. Table 4 compares the values of Kt obtained for these situations. The deviation between the calculated values for the overall mass transfer coefficients using either a constant or a variable partition coefficient varies between −16 and − 28%. This example illustrates very clearly the importance of using a correct description of the solute partition equilibrium for determination of mass transfer coefficient.
3.2.2. E6aluation of mass transfer correlations Three individual mass transfer resistances may be considered in contactor extraction processes: (1) the boundary layer resistance in the liquid phase inside in fibres (tube side); (2) the membrane resistance to solute diffusion across the liquid phase wetting the pores and (3) the boundary layer resistance in the shell side liquid phase. The overall resistance, for a hollow fibre system with the membrane wetted by the shell side fluid phase, can be expressed as:
1 1 1 1 = + + Kt · Ai kt · Ai P · km · Alm P · ks · A0
(6)
where kt, km and ks are the individual mass transfer coefficients on the tube side, membrane and shell side, respectively, and Ai, A0 and Alm are the fibres internal, external and logarithmic mean areas, respectively. In the present work a Le´ve`que type equation will be used to correlate both the tube side and the shell side mass transfer coefficients:
di l
Sht = a · Sc bt t · Rect t ·
Shs = b · Sc bs s · Recs s ·
(1/3)
(7)
dh l
(8)
where the subscripts t and s refer to the tube and shell sides, respectively, and a and b are constants. Thus, substituting these equations in Eq. (6), Kt will be expressed as a function of four unknown parameters: a; b; ct and cs, assuming bt = bs = 1/3. 1 = Kt
1 D · maq a· raq · l · d 2i +
2 aq
1/3
1 di · d · t + ct Ret dlm · P · o · Dorg
1 d 30 · P 3 · D 2org · morg b· d 3i · rorg · l 3
1/3
1 Recs s
(9)
When using the Wilson-plot methodology for development of mass transfer correlations the experimental data (C versus t) were fitted using Eq. (4) and the overall mass transfer coefficients were determined. The inverse of these coefficients were then plotted in two separate graphics, one as a function of 1/Rect (when the tube side Reynolds number is varied) and the other as a function of 1/Recs (when the shell side Reynolds number is varied). From the slopes of these two straight lines the values of a and b were taken. Table 5 shows the parameter values and the associated errors, for a 95% confidence level. It can be seen that for both tube and shell side the
I.M. Coelhoso et al. / Separation/Purification Technology 19 (2000) 183–197 0.558 91.277model describes quite well the experimental results. However, despite the high correlation coefficient (0.987), the errors associated with parameter estimation are considerably high, with errors ranging from 54 to 450%! These excessively high errors question the validity of the methodology, showing that the problem lies on the calculation method. However, it is not possible to assess its validity in most published work, because the associated errors are not usually stated. In order to reduce the errors obtained and to prevent any loss of information a single step calculation methodology was developed. Kt expressed by Eq. (9) was substituted into Eq. (4) and then, all the experimental values of C versus t were fitted directly in order to obtain the parameters a, b, ct and cs. Table 5 shows that this method produces estimated parameter values in a totally different range, showing higher exponent values for the Reynolds numbers. The errors are drastically reduced ranging from 15 to 22%. The Wilson-plot methodology has proved in the past to work satisfactorily in systems operated under steady state conditions and when the only parameter varying between the different experimental runs is the fluid velocity of each phase. Nevertheless the results presented show that this methodology has to be altered when working under transient state or when other parameters beside the fluid velocity are changing during the time course of the experimental study.
Table 5 Parameter values and errors using the Wilson-plot methodology and using a one-step calculation Method
Wilson-plot
One-step
Parameter
Value and error
% Error
ct cs a b
0.5589 1.277 0.3559 1.414 0.3059 0.164 1.4879 6.691
229 398 53.8 450
ct cs a b
0.91490.136 0.6979 0.136 0.2729 0.047 3.3649 0.739
14.9 19.5 17.3 22.0
r2
195
The major limitation of the Wilson-plot methodology stems from the fact that it involves a two-step calculation, i.e. two sequential fittings (estimation of the mass transfer coefficients followed by determination of the constants a, b, ct and cs ), leading to unnecessary loss of information and possible incoherent results. The other major drawback of this procedure is due to the fact that it cannot take into account any variation of the individual parameter’s values, either between or within experimental runs. The example used in this work is particularly well suited because during extraction of valeric acid with Amberlite LA-2 the association between the solute and the extractant changes with the solute concentration in the feed, forming different carriersolute complexes [35]. As a consequence, the partition coefficient of the solute between the feed and the organic phase changes during the extraction experiment as well as the average diffusion coefficient of the carrier-solute complexes. Therefore, the use of the Wilson-plot methodology is completely inadequate for development of mass transfer correlations in these type of systems. The drastic reduction, of roughly 20 times, on the errors associated with the estimated parameters when using the one-step methodology, and the different results obtained by these two methods, lead us to conclude that the Wilson-plot method may also be inaccurate. This conclusion can be extrapolated to other mass transfer processes and equipment and, therefore, we recommend the use of this one-step method as a general procedure. The one-step calculation method developed can be easily applied given the currently available mathematical tools that enable the analytical manipulation of equations and fittings with complex expressions.
4. Conclusions 0.987
0.997
Liquid membranes are a unique tool for selective transport of desired solutes from complex mixtures. The industrial future of liquid membranes will depend very strongly on the ability to design and synthesise selective carriers or receptors with the potential to achieve recognition of
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individual solutes. Therefore, the trend will be the development of supramolecular chemistry with the aim of obtaining very selective carriers, in some cases with the ability for chiral recognition. The first part of this paper discusses the importance of a comprehensive understanding of the carrier–solute interactions and the mechanisms involved on solute transport across liquid membranes. The first case study presented was a rather non-specific interaction between a quaternary amine ion-exchanger and lactate. It was our aim to demonstrate that when a organic phase with some permeability to water is used, the osmotic pressure difference across the liquid membrane may have to be considered for a correct description of solute transport. This situation is rather common and the analysis presented can be applied to similar systems. The other case studies presented — transport with reversed micelles and extraction with chiral selectors — show how structured fluids (as reversed micelles) can be used for selective transport by making use of electrostatic and hydrophobic interactions with the solutes, and also that chiral carriers can be synthesised to perform resolution of racemic mixtures. The case studies presented do not intend to cover the large field of facilitated transport but they illustrate the potential of this area and the importance of understanding the transport mechanisms involved. The second part of this work brings to discussion a few aspects related with modelling of transport in liquid membrane contactors. Intentionally, the two problems raised may be considered quite simple (or even trivial): how to describe solute partition between the feed and the extractant phase and how to obtain adequate mass transfer correlations in membrane contactors. The discussion presented aims to call attention to the importance of using a correct description of solute partition, specially when it is getting so common the use of constant partition coefficients, even when this is a wrong assumption. Concerning the development of mass transfer correlations a new calculation methodology was proposed. Amongst other advantages, this approach makes possible to
consider a variation of the partition coefficient and the solute-carrier diffusion coefficient, which is not possible to take into account with the Wilson-plot method, where all the variables but the Reynolds number have to be considered constant.
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