Phenol extraction with Cyanex 923: Kinetics of the solvent impregnated resin application

Reactive & Functional Polymers 69 (2009) 264–271

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Phenol extraction with Cyanex 923: Kinetics of the solvent impregnated resin application Bernhard Burghoff *, Edwin Zondervan, Andre B. de Haan Eindhoven University of Technology, Department of Chemical Engineering and Chemistry, Den Dolech 2, 5600 MB Eindhoven, The Netherlands

a r t i c l e

i n f o

Article history: Received 23 September 2008 Received in revised form 5 January 2009 Accepted 11 January 2009 Available online 21 January 2009 Keywords: Chromatography Extraction Kinetics Particle Porous media Separations

a b s t r a c t In the present work, experimental data concerning the kinetics of phenol extraction with a solvent impregnated resin (SIR) and the description with a kinetic model are presented. Phenol is extracted from aqueous solutions with macroporous polypropylene particles impregnated with Cyanex 923. The rate determining step of the phenol extraction kinetics is identified to be a combination of the complexation between phenol and Cyanex 923 and pore diffusion of phenol inside the SIR. Thus, a model based on chemical reaction and intraparticle diffusion is used to describe the experimental data. Using a sensitivity analysis, it is observed that the diffusivity and the physical equilibrium distribution Kphys have the most pronounced influence on the kinetic model. Increasing the temperature causes an increase of the reaction rate constant and the diffusivity. The kinetic model gives a reasonable fit of the experimentally determined phenol concentration profiles. Ó 2009 Elsevier Ltd. All rights reserved.

1. Introduction Phenol frequently occurs in waste waters from resin production [1], coke plants [2] or even olive mills [3,4]. A standard operation for phenol removal is liquid–liquid extraction [5]. However, liquid–liquid extraction can suffer from significant drawbacks, such as the formation of stable emulsions or flooding and loading in conventional contactors. An alternative technology to avoid these shortcomings is the so-called solvent impregnated resin (SIR) technology, as proposed by Warshawsky [6–8]. A SIR consists of a solid polymeric support impregnated with an extractant. SIRs are a technology, which synergistically combines adsorption and extraction [9]. High capacity and selectivity as experienced in liquid–liquid extraction are merged with relatively simple equipment and mode of operation like during adsorption. Additionally, no emulsification occurs and the loss of extractant during the extraction is negligible [10]. Like in any other extraction process, also for phenol extraction the extractant plays a key role in the SIR application. In previous studies it was shown that Cyanex 923 is an effective phenol extractant [5,11,12]. Its applicability as phenol extractant in both liquid–liquid equilibrium extraction [13] and SIR extraction was also proven [14], resulting in a high overall distribution coefficient KD. In the latter study the prepared SIR consisted of macroporous polypropylene particles impregnated with Cyanex 923.

* Corresponding author. Tel.: +31 40 247 4964; fax: +31 40 246 3966. E-mail address: [email protected] (B. Burghoff). 1381-5148/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.reactfunctpolym.2009.01.005

To achieve a thorough understanding of the extraction process also the extraction kinetics need to be known. These are moreover important at a later stage for equipment and process design. The extraction kinetics can be dominated by various mechanisms, such as film diffusion, intraparticle diffusion or chemical reaction. Depending on the underlying mechanism different kinetic models can be utilized. These are on the one hand the homogeneous particle diffusion model [15,16], in which the sorbed species is assumed to be in equilibrium with the diffusing species in the pore space. In this model, chemical reaction is consequently reversible and the modeling of the diffusion terms is based on Fick’s law of diffusion [17,18]. On the other hand, the shrinking core model [19,20] describes sorption or ion exchange under the condition that the reaction is significantly faster than the diffusion. In such a case, the reaction is assumed to be irreversible and the solute will advance through a particle as a topochemical inward moving front between the reacted shell of the particle and the unreacted core [21]. However, this condition is not satisfied when the shell behind the inward moving front is not completely saturated with the extracted solute [22]. A refinement of the shrinking core model is the modified shrinking core model, which also takes incomplete saturation and reversible reactions into account. The modified shrinking core model requires a uniform distribution of the binding sites within each particle. The particles should be spherical with a constant radius throughout the extraction process, i.e. there is no expansion of the particles. Furthermore, local equilibrium between the bound and unbound species within the particle pores is required. Such an approach can be used successfully to define the

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Nomenclature c D Dpore dp k k+, k Kchem KD Kphys r, R Rorg Re T u V X Xe

concentration mol L1 diffusivity m2 s1 apparent pore diffusivity m2 s1 particle diameter m apparent reaction rate constant dm4 (mol s)1 reaction rate constants L (mol s)1 chemical equilibrium constant L mol1 overall distribution coefficient (mol L1) (mol L1)1 physical equilibrium constant (mol L1) (mol L1)1 radius m reaction rate mol (L s)1 Reynolds number of the packed bed – temperature K superficial velocity m s1 volume L fractional conversion – fractional conversion at SIR surface –

film thickness – void fraction of the packed bed – fraction of particle occupied by extractant Lorg LSIR1 kinematic viscosity m2 s1 density kg L1 tortuosity factor –

d

e ep m q s

Superscripts aq aqueous phase org organic phase Subscripts aq aqueous phase C complex between phenol and extractant E extractant i C, E, PhOH PhOH phenol SIR solvent impregnated resin

Greek symbols stoichiometry –

c

rate determining step of a sorption/extraction process in ion exchangers or SIRs [21,23,24]. In this investigation, a model incorporating combined diffusion and chemical reaction is used, which already proved to be reliable in different applications [9,17,18]. This model is experimentally evaluated for the phenol extraction with impregnated macroporous polypropylene particles containing Cyanex 923. The technique, which is applied to gain the necessary experimental data, is the zero length column (ZLC) method [25]. With the ZLC method axial dispersion in the bed can be avoided, as the column consists of a thin layer of particles. This column design and sufficiently high flow rates minimize the external resistance to mass transfer. Thus, the film diffusion through the laminar sublayer surrounding the particles can be neglected [9]. By applying the ZLC method, the influence of the flow rate, the initial phenol concentration and the temperature on the phenol extraction kinetics of the prepared SIR is investigated. The quality of the experimental data fit and subsequent simulations with the developed model is discussed. 2. Materials and methods 2.1. Substances The chemicals used are tri-(C6,C8)-alkylphosphine oxide (Cyanex 923) (93%, Cytec Industries Inc., Netherlands), n-hexane (P99%, Fluka AG, Switzerland) and phenol (P99%, Merck KGaA, Germany). All substances are used without further purification. The evaluated particles are semi-crystalline macro-porous polypropylene polymer MPP (VWS MPP Systems B.V., Netherlands). The properties of these particles are listed in Table 1. The MPP particles are sieved, then washed with acetone and left in a rotary evaporator (BÜCHI Rotavapor R-200, BÜCHI Labortechnik AG, Switzerland) equipped with a heating bath (BÜCHI Heating Bath B-490, BÜCHI Labortechnik AG, Switzerland) for 12 h at vacuum and 70 °C. 2.2. Resin impregnation

n-hexane solution during impregnation. After this, the n-hexane is slowly evaporated from the dispersion at 60 °C and 10 kPa. The extractant Cyanex 923 remains inside the pores. Different extractant loadings of the SIRs can be achieved this way. The prepared MPP based SIR is partially impregnated and has an extractant loading of 1.28 mol kg1 SIR. This loading is selected to avoid leaching of the extractant from the particles due to a volume increase of the extractant phase inside the pores during phenol extraction. 2.3. SIR kinetics The kinetics of impregnated MPP containing 1.28 mol pure Cyanex 923 kg1 SIR is determined in a zero length column setup [9,24], see Fig. 1. The setup consists of a Knauer Smartline 1000 pump, a Knauer Smartline UV Detector 2500 (Separations Analytical Instruments B.V., Netherlands) and an Omnifit Column (BioChem Valve/Omnifit, England). The dead volume of the setup is determined to be 4.8 mL. The column is made of borosilicate heavy wall glass. It has an inner diameter of 15 mm and a length of 150 mm. The bed length does not exceed 2 mm. The pump flows applied are 5, 10, 20 and 30 mL min1. The wavelength of the UV detector is adjusted to 285 nm to detect phenol in the aqueous solution. The temperatures, at which the measurements are performed are 25 °C and 50 °C, respectively. All kinetic experiments are performed according to the same procedure. The column is loaded with 0.2 g SIR and rinsed with demineralized water. After this, the setup is run for 240 min in

Table 1 Particle properties of MPP particles. Property

MPP

Material Porosity Density (g mL1) Surface area (m2 g1) Pore size (nm) Particle size (mm)

Semi-crystalline polypropylene 0.68 a 1.15 b 11.5 c <1000 d 0.8–1.18 (98%) b

a

Prior to impregnation of the MPP particles, Cyanex 923 is diluted with n-hexane. The dry method is used for the impregnation of the particles [27]. The particles are dispersed in the Cyanex 923/

b c d

Manufacturer’s data. Own measurement. Babic´ et al. [26]. Based on analysis of SEM images.

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Since the complex formation is based on intermolecular hydrogen bonding, the reaction is reversible. The stoichiometry for the reaction described by Eq. (2) is c = 1 for the forward reaction of the components PhOH and E, and c = 1 for the backward reaction of the component C. The equilibrium is expected to be on the product side C. Based on Eq. (2), the chemical equilibrium constant Kchem of the complex formation can be defined as given in

K chem ¼

Fig. 1. Zero-Length-Column setup for kinetics measurements (recycle mode).

a recycle mode. During the recycle mode the inlet and outlet tube of the setup are placed in the same glass vessel, see Fig. 1. The glass vessel contains 25 mL of demineralized water spiked with phenol. The different initial phenol concentrations, which are applied for each range of flow rates, are 0.5 g kg1 (0.0053 mol L1), 1 g kg1 (0.011 mol L1) and 2 g kg1 (0.021 mol L1). The vessel is magnetically stirred at 500 rpm in order to assure ideal mixing. During the runs the signal of the UV detector is monitored online with the program EZChrom Elite – ChromGate Version 3.1.7 (Scientific Software, Inc., USA). 3. Mathematical model The principle of the extraction of phenol with a SIR is depicted in Fig. 2. The extractant is immobilized inside the pores of a macroporous particle. During the extraction process depicted in Fig. 2, phenol (PhOH) is entering the organic extractant phase E from the aqueous phase. At first, phenol physically dissolves in the organic phase, thus establishing a physical equilibrium, which is characterized by the physical equilibrium constant Kphys, as given in

K phys ¼

corg PhOH caq PhOH

ð1Þ

Once dissolved in the organic extractant phase E, the phenol will react with the extractant and form a complex C according to Eq. (2). The reaction rate constants k+ and k are the rate constants for forward and backward reaction, respectively. k

þ

PhOH þ E () C  k

ð2Þ

þ corg k Comp  ¼ org k cPhOH  corg E

ð3Þ

The overall distribution coefficient KD depends on the concentration of physically dissolved phenol and chemically complexed phenol in the organic phase, respectively, and also on the concentration of phenol in the aqueous phase. KD can be determined as shown in

KD ¼

org corg PhOH þ c Comp

ð4Þ

caq PhOH

The model which is used to describe the kinetics of the phenol extraction process with a SIR combines intraparticle diffusion and chemical reaction. As will be shown later, the combination of these two mechanisms is valid for the described system. First, the reaction rate in the organic phase can be described according to Eq. (5), where k can be substituted by the rearranged Eq. (3). þ



org org Rorg ¼ k corg PhOH c E  k c C ¼ k

þ



org corg PhOH c E 

1 K chem

corg C

 ð5Þ

In order to describe the mass-transfer and the reaction inside the particle, a number of assumptions need to be made. According to Ma and Evans [28] and Babic´ et al. [9], cylindrical particles with a diameter to length ratio of one can be approximated as spheres with identical radii. Since the applied cylindrical MPP particles have an average length and diameter of 1 mm, this condition is satisfied [9]. Furthermore it can reliably be assumed that MPP particles are inert [9,14], i.e. no additional adsorption occurs. It is moreover assumed, that simultaneous mass transfer and chemical reaction are non-stationary in a small particle due to a finite capacity. Thus, non-stationary mass-transfer and chemical reaction can be described for each component i (i = PhOH, E, C) in the organic extractant phase according to Eq. (6), where the reaction rate of Eq. (5) is already introduced [29]

   org  @corg Di 1 @ 1 þ org org org 2 @c i i  c k c c  c r ¼ i E C PhOH K chem @t s r2 @r @r

ð6Þ

The extraction mechanism between the extractant Cyanex 923 and phenol is reversible hydrogen bonding with a 1:1 stoichiometry [30,31]. This is why ci in Eq. (6) is equal to one. The term Di

Fig. 2. SIR principle of a macroporous particle impregnated with a complexing agent E.

B. Burghoff et al. / Reactive & Functional Polymers 69 (2009) 264–271

stands for the diffusivity of component i = PhOH, E, C inside the pores of the SIR particle. The constant s represents the tortuosity factor. The decrease of the solute in the aqueous phase can be described with Eq. (7), where Fick’s law of diffusion, which depends on the flux of the solute phenol through the phase interface, is applied at the outer particle surface r = R org  @caq DPhOH V SIR @cPhoh  PhOH ¼ 3ep @t s  R V aq @r r¼R

ð7Þ

The introduction of the dimensionless radius variable /, see Eq. (8), allows a straightforward scalability of the model later on

u¼

r R

ð8Þ

Using this dimensionless radius variable /, Eqs. (6) and (7) can be transformed into Eqs. (9) and (10), respectively.

   org  @corg Di 1 @ 1 þ org org org 2 @ci i ¼¼  ð9Þ c k c c  c u i E C PhOH K chem @t @u s  R2 u 2 @ u aq org  @cPhOH DPhOH V SIR @cPhOH  ð10Þ ¼ 3ep @t s  R2 V aq @ u u¼1 Due to the physical solubility of phenol in the extractant, the chemical reaction is not restricted to the interface. Instead, it will take place in the bulk of the organic phase. At the phase interface between the aqueous and the organic phase, there is merely physical equilibrium, as described by Eq. (1). Based on the latter, the boundary condition depicted in Eq. (11) can be assumed. aq corg PhOH ¼ K phys  c PhOH

ðt > 0; u ¼ 1Þ

ð11Þ

Furthermore, it is assumed that the extractant and the complex are not soluble in the aqueous phase and will remain in the SIR particle. Their diffusivities inside the SIR particle are presumed to be negligible compared to the diffusivity of the solute phenol, i.e. DC, DE = 0. This is expressed by

@corg E @u @corg E @u @corg C @u @corg C @u

267

external mass transfer resistance. This way, only the intraparticle effects have to be considered. The modeling is done using the program gPROMSÒ 3.0.3 ModelBuilder (Process Systems Enterprise Limited, United Kingdom). The fitting parameters are estimated with the Parameter Estimation tool using a heteroscedastic variance model for the experimentally determined values. 4. Results and discussion 4.1. Flow rate During the experiments, the flow rate is varied between 5, 10, 20 and 30 mL min1 – the respective superficial velocities are 4.7  104, 9.4  104, 18.7  104 and 28.3  104 m s1 – for initial phenol concentrations of the aqueous phase of 0.5 g kg1 (0.0053 mol L1), 1 g kg1 (0.011 mol L1) and 2 g kg1 (0.021 mol L1). The temperatures used are 25 °C and 50 °C. The different Reynolds numbers in the particle bed under these conditions can be calculated according to Rhodes [33] via Re = dp u/ (m(1e)), where dp is the particle diameter (1  103 m), u is the superficial velocity, m is the kinematic viscosity of the aqueous phase (approximately 0.95 m2 s1 at 25 °C and 0.64 m2 s1 at 50 °C) and e is the void fraction of the particle bed (e = 0.41). The different Reynolds numbers are determined to be below a value of 7.5. According to Rhodes [33], fully laminar conditions inside a particle bed exist for Re < 10. Thus, it can be assumed that inside the bed laminar flow conditions exist. Fig. 3 is an example of the obtained concentration profiles of phenol in the aqueous phase. As can be seen in Fig. 3, the flow rate of 30 mL min1 does not seem to result in a different phenol concentration profile than the flow rate of 20 mL min1. This observation is the same for both 25 °C and 50 °C. Thus, it can be assumed, that at a flow rate of 30 mL min1 the laminar sub-layer surrounding the particles is negligible and no film diffusion is occurring.

¼ 0 ðt > 0; u ¼ 1Þ

ð12Þ

4.2. Phenol concentration of aqueous phase

¼ 0 ðt > 0; u ¼ 0Þ

ð13Þ

¼ 0 ðt > 0; u ¼ 1Þ

ð14Þ

¼ 0 ðt > 0; u ¼ 0Þ

ð15Þ

According to Serarols et al. the initial concentration can have an influence on the kinetic properties [34]. As an example of the influence of the phenol concentration in the aqueous phase, Fig. 4 shows the respective concentration profiles at 25 °C. Apparently, the equilibrium is reached faster at higher concentrations, which means that the extraction is faster at higher concentrations. The increase of the phenol concentration seems to be the driving force for the faster phenol uptake of the SIR particles. However, even if the eventual equilibrium concentration of phenol in the aqueous phase is reached faster at higher initial solute concentrations, the equilibrium values are simultaneously increased. This is also in conformity with the observations made by Wang and Liu [35] for phenol extraction with trioctylamine/trioctylamine salt mixtures and 1-octanol/trioctylamine mixtures. This means, that the extraction time can be decreased by increasing the phenol concentration, albeit at the expense of increased residual solute concentration in the aqueous phase.

The diffusivity of phenol in the extractant is estimated using the Wilke–Chang equation and the Hayduk–Minhas equation, as will be explained in Section 4.1. At / = 0 the phenol concentration is assumed to be zero, see

@corg PhOH ¼ 0 ðt > 0; u ¼ 0Þ @u

ð16Þ

The initial conditions are given as follows:

corg Phoh;0 corg C;0 ¼ corg E;0 ¼ caq Phoh;0

¼0 0 2:53mol=L ¼ constant

The initial phenol concentrations are approximately 0.0053, 0.011 and 0.023 mol L1. As mentioned above, in this investigation the ZLC method is applied [25,32]. The bed length is adequately low, so that axial dispersion can be neglected. Using a high flow rate, the laminar sub-layer around the particles can be neglected and thus also the

4.3. Temperature The influence of temperature on the extraction equilibrium was already discussed by MacGlashan et al. [36], Wang and Liu [35] and Wu and Liu [37]. With increasing temperature the distribution coefficient decreases, which can on the one hand be attributed to the decreasing solubility of phenol in the organic phase at increasing temperatures. On the other hand, the complexation mechanism between phenol and the extractant Cyanex 923 is based on hydro-

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1 Fig. 3. Determination of optimum flow rate for kinetics experiment (here: caq (0.0053 mol L1), (a) T = 25 °C, (b) T = 50 °C). 0 ðPhOHÞ= 0.5 g kg

gen bonding, which is an exothermic process. When the temperature is increased, the equilibrium of the exothermic complexation shifts to the reactant side, thus reducing the chemical phenol capacity of the extractant. The above mentioned decrease of phenol capacity of the extractant is confirmed in Fig. 5, where the concentration profiles of phenol in the aqueous phase at different temperatures are compared for initial phenol concentrations of 0.5 g kg1 (0.0053 mol L1) and 2 g kg1 (0.021 mol L1). The equilibrium phenol concentration in the aqueous phase at 50 °C is higher than at 25 °C, i.e. that less phenol is extracted at higher temperatures. Another observation is that for the lower initial phenol concentration the initial decrease of the phenol concentration is faster at 50 °C than at 25 °C. Such an increase of the extraction rate of phenol was already observed for other extractants [37,38]. This can on

Fig. 4. Concentration profiles at 25 °C, flow rate = 30 mL min1.

the one hand be attributed to the higher diffusivity of phenol in Cyanex 923 at 50 °C (compared to 25 °C). On the other hand, also the reaction rate between phenol and the extractant increases with increasing temperatures. As a results of the higher diffusivity and the higher reaction rate, the equilibrium is reached faster at 50 °C than at 25 °C, i.e. that the extraction is faster at increased temperatures. 4.4. Identification of rate determining step The extraction kinetics can be influenced by several mechanisms. These mechanisms are film diffusion through the laminar sub-layer surrounding the particle, intraparticle diffusion through the extractant phase immobilized inside the pores and, finally, chemical reaction of the solute with the extractant. The rate determining step of the solute extraction with a SIR can either be a single one of the above mentioned mechanisms or a combination of two or more of these mechanisms. Applying the modified shrinking core model can help to identify the rate determining step. This approach is based on Levenspiel’s conversion equations for elementary irreversible reactions [39] in gas–solid reaction systems. It was expanded by Bhandari et al. [40] in the modified shrinking core model, incorporating also reversible reactions. An extension of the model to describe combined film diffusion and reaction kinetics with reversible reactions was developed by Juang and Lin [17,18]. It has since been successfully applied in several cases [17,18,24,26]. In order to identify the rate determining step, three factors X, Y and Z are determined. The fractional conversion X is used to determine whether film diffusion control occurs. This factor X, as given in Eq. (17), depends on the solute loading of the particle qSIR PhOH ðtÞ and the initial extractant loading of the SIR qSIR E ðtÞ. In this case, the stoichiometry c equals one, Dfilm is the film diffusion coefficient, d is the film thickness and R the radius of the SIR particle

X¼

qSIR 3  c  Dfilm PhOH ðtÞ ¼ R  d  qSIR qSIR E E

Z 0

t

caq PhOH ðtÞdt

ð17Þ

The fractional conversion of the outer surface, Xe, and the equilibrium distribution ratio of the solute phenol between the SIR particle and the aqueous phase, KSIR, are needed to determine the factor Y. The values for Xe and KSIR are determined using Eqs. (18) and (19), respectively.

Xe ¼ 1 Fig. 5. Concentration profiles at 25 °C and 50 °C for caq 0 ðPhOHÞ = 0.5 g kg 1 1 (0.0053 mol L1) and caq ðPhOHÞ = 2.0 g kg (0.021 mol L ), flow rate = 0 30 mL min1.

caq PhOH ðtÞ  K SIR qSIR E

K SIR ¼

qSIR PhOH caq PhOH

ð18Þ ð19Þ

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The factor Y, which determines whether the process is particle diffusion controlled, can then be determined according to Eq. (20), in which Dpore is the apparent pore diffusivity

 2  ! X 3 X 13 1 þ2 1 Xe Xe Z t 6  Dpore  c caq ¼ PhOH ðtÞdt R2  qSIR 0 E

Y¼

Xe K SIR

ð20Þ

With Eq. (21), the chemical reaction control factor Z is determined. The parameter k represents the apparent chemical reaction rate constant

1 Z¼ K SIR

 1 ! Z X 3 k  c t aq ¼ 1 1 c ðtÞdt Xe R 0 PhOH

ð21Þ

In Fig. 6 the trends of the factors X, Y and Z as functions of the integral of the aqueous phenol concentration over time are depicted. Generally, a straight line indicates that the respective underlying mechanism is the rate determining step. This is the case for the factors Y and Z, as can be seen in Fig. 6, where Y and Z each give a straight line. Thus, for the investigated system a combination of intraparticle diffusion and chemical reaction can be expected [17,41,42]. Due to the selected high flow rate in the experiments, external mass transfer resistance and thus film diffusion can already be expected not to be the rate determining step. This is confirmed by Fig. 6, in which the graph of the factor X does not show a straight line. This determination of the rate determining step justifies the use of the combined reaction and diffusion model. A sensitivity analysis of this model is performed in order to obtain insight into which fitting parameters have a pronounced influence on the model. The selected fitting parameters are the physical equilibrium constant Kphys, the chemical equilibrium constant Kchem, the reaction rate constant k+ and the diffusivity of phenol in the extractant phase D0PhOH;Cyanex . The reason why Kphys and Kchem are selected as fitting parameters is that their values at 50 °C are not known, see paragraph 4.5. For the sensitivity analysis, a separate 5% increase of each parameter is selected. The sensitivity S(t) is then calculated with Eq. (22), in which c1 is the concentration before the increase of 5% and c2 the concentration after the increase of 5% of the respective parameter

SðtÞ ¼

c1  c2 0:05

Fig. 7. Sensitivity of model to selected model parameters.

ð22Þ

Fig. 7 illustrates that the parameters which influence the model the most are Kphys and D0PhOH;Cyanex . The reaction rate constant k+ has only minor influence as a fitting parameter. When the system approaches equilibrium, the influence of k+ decreases even further. This is the case, as k+ is a kinetic parameter, not an equilibrium parameter. The higher influence of D0PhOH;Cyanex on the simulated

concentration profiles compared to the influence of k+ is noticeable, although according to Fig. 6 both diffusion and chemical reaction are the rate determining steps. The reason why the influence of D0PhOH;Cyanex on the simulated concentration profiles is more pronounced than compared to the influence of k+ lies in the model equations. The simulated aqueous phenol concentration is described by Eq. (10), which is based on Fick’s law of diffusion and thus strongly dependent on D0PhOH;Cyanex . Additionally, according to the boundary condition Eq. (11), the simulated aqueous phase concentration is directly dependent on the physical equilibrium at the phase interface. This explains the strong influence of Kphys on the simulated concentration profiles, see Fig. 6. The influence of Kchem is becoming more pronounced towards the equilibrium. However, it is still significantly lower than the effect of Kphys and D0PhOH;Cyanex on the simulated concentration profiles. 4.5. Curve fittings Several model parameters are needed for the fitting of the experimentally determined concentration profiles with the equations derived in paragraph 3. These model parameters are listed in Table 2. The physical and chemical equilibrium constants Kphys and Kchem, respectively, have previously been calculated from liquid–liquid equilibrium extraction data for 25 °C [14], but not for 50 °C. The program used for the model calculations is gPROMSÒ 3.0.3 ModelBuilder (Process Systems Enterprise Limited, United Kingdom). The estimation of the fitting parameters is accomplished with the Parameter Estimation tool using a heteroscedastic variance model for the experimentally determined data. The diffusivity value D0PhOH;Cyanex for phenol in Cyanex 923 can be calculated by correlations like, e.g. Hayduk–Minhas or Wilke– Chang, see Table 3. However, these correlations can have high errors [43,44]. This is why the diffusivity value D0PhOH;Cyanex for phenol in Cyanex 923 is selected as additional fitting parameter. The results of the fitting parameters are listed in Table 4. The equilibrium parameters Kphys and Kchem need to be fitted for 50 °C, as the equilibrium values change with increasing temperature. The reaction rate constant k+ is also fitted for both temperatures.

Table 2 Model input parameters.

Fig. 6. Identification of rate determining step of phenol extraction with a SIR 1 (0.011 mol L1), 25 °C, flow rate = 30 ml min1). (example: caq 0 ðPhOHÞ = 1 g kg

Model parameter

Value

Vaq (L) a Tortuosity factor s (–)b R (m) mSIR (kg) a qSIR (kg L1) ep (L L1)

29.8  103 6.51 ± 0.5 0.5  103 0.1876  103 1029 0.521

a b

As used in performed experiments. [9].

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Table 3 Diffusivity values D0PhOH;Cyanex calculated by Hayduk–Minhas and Wilke–Chang correlations. Diffusivity

Value at 25 °C

Value at 50 °C

D0PhOH;Cyanex Hayduk–Minhas (mPa s) D0PhOH;Cyanex Wilke–Chang (mPa s)

1.67  1011 6.36  1011

3.94  1010 2.01  1010

Table 4 Model fitting parameters. Fitting parameter

Value at 25 °C

Value at 50 °C

Kphys ((mol L1) (mol L1)1) Kchem (L mol1) k+ (L (mol s)1) D0PhOH;Cyanex (mPa s)

18.73 a 37.22 a 0.005468 2.863  1010

14.25 31.22 0.009498 5.0137  1010

a

Fig. 10. Parity plot of simulated values and experimental data at 25 °C.

Fixed [14].

It can be seen in Table 4 that the equilibrium parameters Kphys and Kchem decrease with increasing temperature. This confirms that the solubility of phenol in the extractant phase is decreasing with increasing temperature, as given in literature, see also paragraph 4.3. On the other hand, the reaction rate constant and the diffusivity increase at higher temperatures. This is the case, as the reaction rate constant generally increases with increasing temperatures [42]. Also the diffusivity generally increases with increasing temperature, as diffusivity depends on temperature and viscosity [43]. The fitted diffusivity value is higher than the diffusivities calculated by Hayduk–Minhas and Wilke–Chang. As mentioned before, this can be due to the possible high errors of these correlation methods. Figs. 8 and 9 compare the fitted and the experimentally determined concentration profiles. The model correlates the experimental data well. The coefficients of determination R2 are for each fitting higher than 0.92. Only at a low initial phenol concentration

Fig. 11. Parity plot of simulated values and experimental data at 50 °C.

of 0.5 g kg1 (0.0053 mol L1) and a temperature of 50 °C the model quite noticeably underestimates the experimental data when the concentration profile approaches the equilibrium value. According to the sensitivity analysis, Kphys has the most pronounced effect in this range of the concentration profile. This suggests that Kphys could be dependent on the phenol concentration in the aqueous phase. This has, however, not been included in the present model. The respective parity plots of the simulated concentration profiles versus experimentally determined concentrations, see Figs. 10 and 11, show a good agreement of the model with the different experimental datasets. 5. Conclusions

Fig. 8. Fitting of the kinetic concentration profiles at 25 °C, flow rate = 30 mL min1.

Fig. 9. Fitting of the kinetic concentration profiles at 50 °C, flow rate = 30 mL min1.

Increasing the system temperature results in faster phenol extraction kinetics, which is caused by the higher diffusivity due to the decreased viscosity of the extractant and a higher reaction rate constant. Nonetheless, an increased temperature during the extraction also results in higher equilibrium concentrations. With the modified shrinking core model the rate determining step of the extraction kinetics is identified as a combination of chemical reaction and intraparticle diffusion. At a flow rate of 30 mL/min, the laminar sub-layer around the particles in the ZLC is negligible, which means that film diffusion can be neglected. A sensitivity analysis of the combined diffusion and reaction model shows that the reaction rate constant k+ is not having a pronounced impact on the simulated concentration profiles. Rather the phenol diffusivity and the physical equilibrium constant Kphys have a significant influence on the simulated concentration profiles. This is due to the developed model equations and boundary conditions, which noticeably depend on the diffusivity and Kphys at the phase interface. The fitting and simulation of the data with the developed

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model are quite accurate, as parity plots and coefficients of determination R2 show. Acknowledgements This work is financially supported by the Technology Foundation STW. Additional support by VWS MPP Systems, Akzo Nobel Chemicals, Diosynth, INEOS Phenol, and Vitens is also acknowledged. Finally the supply of Cyanex 923 by Cytec Industries Inc., Netherlands is also gratefully acknowledged. References [1] K. Inoue, S. Nakayama, Solvent extraction of phenol with primary and tertiary amines and a quaternary ammonium compound, Solvent Extr. Ion Exc. 2 (1984) 1047–1067. [2] H. Jiang, Y. Tang, Q.-X. Guo, Separation and recycle of phenol from wastewater by liquid–liquid extraction, Sep. Sci. Technol. 38 (2003) 2579–2596. [3] M. Carmona, A. De Lucas, J.L. Valverde, B. Velasco, J.F. Rodriguez, Combined adsorption and ion exchange equilibrium of phenol on Amberlite IRA-420, Chem. Eng. J. 117 (2006) 155–160. [4] H.K. Obied, D.R. Bedgood, P.D. Prenzler, K. Robards, Effect of processing conditions, prestorage treatment, and storage conditions on the phenol content and antioxidant activity of olive mill waste, J. Agri. Food Chem. 56 (2008) 3925–3932. [5] M.T.A. Reis, O.M.F. de Freitas, M.R.C. Ismael, J.M.R. Carvalho, Recovery of phenol from aqueous solutions using liquid membranes with Cyanex 923, J. Mem. Sci. 305 (2007) 313–324. [6] A. Warshawsky, Polystyrene impregnated with b-diphenylglyoxime, a selective reagent for palladium, Talanta 21 (1974) 624–626. [7] A. Warshawsky, Polystyrenes impregnated with ethers–a polymeric reagent selective for gold, Talanta 21 (1974) 962–965. [8] A. Warshawsky, J.L. Cortina, M. Aguilar, K. Jerabek, New developments in solvent impregnated resins. An overview, in: International Solvent Extraction Conference, Barcelona, Spain, 1999, pp. 1267-1272. [9] K. Babic´, A.G.J. van der Ham, A.B. de Haan, Sorption kinetics for the removal of aldehydes from aqueous streams with extractant impregnated resins, Adsorption 14 (2008) 357–366. [10] M. Traving, H.-J. Bart, Recovery of organic acids using ion-exchangerimpregnated resins, Chem. Eng. Technol. 25 (2002) 997–1003. [11] B. Burghoff, E.L.V. Goetheer, A.B. de Haan, COSMO-RS-based extractant screening for phenol extraction as model system, Ind. Eng. Chem. Res. 47 (2008) 4263–4269. [12] A.M. Urtiaga, I. Ortiz, Extraction of phenol using trialkylphosphine oxides (Cyanex 923) in kerosene, Sep. Sci. Technol. 32 (1997) 1157–1162. [13] E.K. Watson, W.A. Rickelton, A.J. Robertson, T.J. Brown, The recovery of acetic acid, phenol and ethanol by solvent extraction with a liquid phosphine oxide, in: International Solvent Extraction Conference, Moscow, USSR, 1988, pp. 370373. [14] B. Burghoff, E.L.V. Goetheer, A.B. de Haan, Solvent impregnated resins for the removal of low concentration phenol from water, React. Funct. Polym. 68 (2008) 1314–1324. [15] J. Serarols, J. Poch, M.F. Llop, I. Villaescusa, Determination of the effective diffusion coefficient for gold(III) on a macroporous resin XAD-2 impregnated with triisobutyl phosphine sulfide, React. Funct. Polym. 41 (1999) 27–35. [16] Y. Guan, X.Y. Wu, H.F. Hu, Kinetic studies of solvent impregnated resins for sorption of spiramycin, Huagong Xuebao 42 (1991) 603–610. [17] R.-S. Juang, H.-C. Lin, Metal sorption with extractant-impregnated macroporous resins. 1. particle diffusion kinetics, J. Chem. Technol. Biot. 62 (1995) 132–140. [18] R.-S. Juang, H.-C. Lin, Metal sorption with extractant-impregnated macroporous resins. 2. chemical reaction and particle diffusion kinetics, J. Chem. Technol. Biot. 62 (1995) 141–147.

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