Modelling of fixed-bed adsorption of mono-, di-, and fructooligosaccharides on a cation-exchange resin

Biochemical Engineering Journal 49 (2010) 84–88

Contents lists available at ScienceDirect

Biochemical Engineering Journal journal homepage: www.elsevier.com/locate/bej

Modelling of fixed-bed adsorption of mono-, di-, and fructooligosaccharides on a cation-exchange resin ˇ Katarína Vanková, Pavel Aˇcai, Milan Polakoviˇc ∗ Department of Chemical and Biochemical Engineering, Institute of Chemical and Environmental Engineering, Faculty of Chemical and Food Technology, Slovak University of Technology, Radlinského 9, 812 37 Bratislava, Slovak Republic

a r t i c l e

i n f o

Article history: Received 1 July 2009 Received in revised form 21 November 2009 Accepted 24 November 2009

Keywords: Bioseparations Chromatography Adsorption Mass transfer Ion-exchange Modelling

a b s t r a c t Kinetics of fixed-bed adsorption of simple saccharides (glucose, fructose, and sucrose) and fructooligosaccharides (1-kestose, 1-nystose, and 1F -fructofuranosyl nystose) on process-size particles of cation exchanger AmberliteTM CR1320Ca was investigated. A step-up method of frontal chromatography was used when several inlet concentration steps were made in the range of 0–20 g dm−3 . The obtained experimental data were fitted simultaneously using the general rate model with two estimated parameters, which were the distribution coefficient of linear adsorption isotherm and solid-phase diffusion coefficient. The contribution of individual transport phenomena to dispersion of adsorption fronts was discussed. © 2009 Elsevier B.V. All rights reserved.

1. Introduction Fructooligosaccharides (FOSs), such as 1-kestose, 1-nystose and 1F -fructofuranosyl nystose, are low-caloric, non-cariogenic, nonmutagenic compounds [1,2], whose intake is getting significant for their positive effect on human health. They stimulate adsorption of magnesium and calcium, and decrease the total cholesterol, phospholipids and triglycerides in serum [3]. Beside food such as banana, artichokes, shallot, or wheat, an important way of obtaining fructooligosaccharides is enzymatic transformation of sucrose by fructosyltransferase. The product mixture of this biotransformation contains also glucose and fructose as by-products and unreacted sucrose. A convenient way of separating these smaller saccharides from FOSs can be continuous chromatography using microporous cation-exchange resins based on sulphonated cross-linked styrene-divinylbenzene [4–9]. Water is here used as eluent. FOSs, which are less retained by the chromatographic bed, are recovered in the raffinate whereas the smaller saccharides are collected in the extract. Both outlet streams are severalfold diluted compared to the feed. The knowledge of equilibrium and kinetics of saccharide adsorption on the ion-exchange resins is

∗ Corresponding author. Tel.: +421 2 59325254; fax: +421 2 52496920. E-mail address: [email protected] (M. Polakoviˇc). 1369-703X/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.bej.2009.11.015

important for the design and optimization of the separation process. Several authors have dealt with the adsorption equilibria of saccharides on commercial and non-commercial cation-exchange resins [9–11]. They found that isotherms of fructose, glucose and sucrose were linear below the concentration of 300 g dm−3 but slightly convex above this threshold. Grambliˇcka and Polakoviˇc [12] also observed the convex character of isotherms of sucrose on four commercial Ca2+ and Na+ base ion-exchangers too but the isotherms of glucose and fructose were linear up to 400 g dm−3 . In this study, linear adsorption isotherms were also determined here for FOSs in a commercial mixture. The obtained distribution coefficients for single saccharides were used for an approximation of selectivities of individual adsorbents. The selectivities pointed out that a Ca2+ -based cation exchanger, AmberliteTM CR1320Ca, could be the most suitable adsorbent for chromatographic separation of FOSs. Quantitative characterization of fixed-bed column adsorption kinetics was most investigated for glucose/fructose mixtures [5,6]. Takahashi and Goto [13] investigated the kinetics of FOSs adsorption on analytical-size particles using elution analysis for a commercial six-component mixture. A moment method was employed to estimate the distribution coefficient, intraparticle diffusion coefficient and Peclét number for each component from its corresponding elution peak. The estimated intraparticle diffusion coefficients were of the order of magnitude 10−11 m2 s−1 .

K. Vanková et al. / Biochemical Engineering Journal 49 (2010) 84–88 ˇ

Nomenclature a c c0 cp cp∗ dc D Ds dp DL ε Kc k KL kh kL kS L Pe Re Sc Sh r rh t u VC V0 z 

particle specific surface area (m−1 ) liquid-phase concentration (kg m−3 ) feed concentration (kg m−3 ) solid-phase concentration (kg m−3 ) solid-phase surface concentration (kg m−3 ) column inner diameter (m) diffusion coefficient (m2 s−1 ) solid-phase diffusion coefficient (m2 s−1 ) particle mean diameter (m) axial dispersion coefficient (m2 s−1 ) bed voidage (–) distribution coefficient (–) capacity factor overall mass transfer coefficient (m s−1 ) sucrose hydrolysis rate constant (s−1 ) liquid-phase mass transfer coefficient (m s−1 ) solid-phase mass transfer coefficient (m s−1 ) bed length (m) Péclet number (–) Reynolds number (–) Schmidt number (–) Sherwood number (–) radial coordinate (m) rate of sucrose hydrolysis to glucose and fructose (kg m−3 s−1 ) time (s) interstitial velocity (m s−1 ) column volume (m3 ) column hold-up volume (m3 ) axial coordinate (m) kinematic viscosity (m2 s−1 )

85

the axial dispersion coefficient, kL is the liquid-phase mass transfer coefficient, ap is the particle specific surface, cp∗ is the solid-phase surface concentration, L is the bed length, c0 is the feed concentration, which was stepwise changed in defined times. Kc is the distribution coefficient of the linear equilibrium isotherm: cp = Kc c

(2)

where cp and c are the solid- and liquid-phase concentrations, respectively. The diffusional flux in the solid-phase balance (Eqs. (3a)–(3d)) was expressed through solid-phase diffusion coefficient Ds . The solid-phase related model equations are the following: ∂cp = Ds ∂t



∂2 cp ∂r 2

+

t=0

0 ≤ r ≤ Rp

t>0

r = Rp

r=0

∂cp =0 ∂r

Ds

2 ∂cp r ∂r



cp = 0

  ∂cp = kL c − cp∗ ∂r

(3a) (3b) (3c) (3d)

where r is the radial coordinate and Rp is the particle radius. Since a small fraction of sucrose hydrolyzed in the fixed-bed during the experiment, the model for this component was extended by the kinetic term: rh = kh cp

(4)

where kh is the rate constant and rh is the rate of sucrose hydrolysis to glucose and fructose, which was added to the left-hand side of Eq. (3a). 3. Experimental 3.1. Adsorbent

The objective of this work was to study the kinetics of fixedbed single-component adsorption on true process-size particles of AmberliteTM CR1320Ca for the saccharides pertinent to FOS’s separation. A staircase method of frontal chromatography was employed in the concentration range of 0–20 g dm−3 and the adsorption process was described by the general rate model when the distribution coefficient and solid-phase diffusion coefficient were the fitted parameters. 2. Mathematical model General rate (GR) chromatography model was used to describe the frontal chromatography experiments. The GR model, which consisted from the material balances of a saccharide in the liquid (Eq. (1a)) and solid (Eq. (3a)) phases, exactly accounts for all effects contributing to curve broadening, i.e. axial dispersion and liquidand solid-phase mass transfers. The model equations characterizing the liquid phase are as follows: ε

∂c ∂2 c ∂c = −εu + εDL 2 − kL ap (1 − ε) ∂t ∂z ∂z

t=0

0≤z≤L

t>0

z=0

z=L

∂c =0 ∂z

c=0

εu (c − c0 ) = DL



c−

cp∗ Kc



(1a) (1b)

∂c ∂z

(1c) (1d)

where ε is the bed voidage, c is the liquid-phase concentration, t is the time, u is the interstitial velocity, z is the axial coordinate, DL is

The resin used was AmberliteTM CR1320Ca (Rohm and Haas, Paris, France), which is a highly cross-linked poly(styrene)divinylbezene cation exchanger with the functional group –(SO3 − )2 Ca2+ . The particle diameter and ion-exchange capacity were 320 ␮m and 1.63 equiv L−1 , respectively. The value of specific surface area, ap = 6/dp , was calculated to be 18,750 m−1 . The resin was washed several times with double distilled water before use and was separated on a sintered-glass filter. The water content of the resin was determined by drying wet particles at 80 ◦ C until the constant weight was reached. The value of water fraction was 48.3% with a standard deviation of 0.7%. 3.2. Equipment Saccharide solutions or eluent water were pumped by peristaltic pumps Gilson (Gilson, Middleton, WI) through a six-port switching valve (Knauer, Berlin, Germany) at a flow rate of about 0.7–1 cm3 min−1 . The column was thermostated at 60 ◦ C by means of JetStream Plus II (Thermotechnic Products, Langenzersdorf, Austria). The column outlet solution was monitored by a refractive index (RI) detector (Knauer, Berlin, Germany) and was distributed into 0.5 ml fractions using the fraction-collector Frac–920 (GE Healthcare, NY, USA). All concentrations were determined by HPLC (Knauer, Berlin, Germany) using the column REZEX RSO-Oligosaccharide (Ag+ form, 200 mm × 10 mm, Phenomenex, Torrance, CA). The column temperature was maintained at 40 ◦ C by the JetStream Plus II thermostat. Redistilled water was used as the mobile phase at a flow rate of 0.3 cm3 min−1 . The amount injected by an autosampler (Gilson, Middleton, WI) was 10 ␮l and

86

K. Vanková et al. / Biochemical Engineering Journal 49 (2010) 84–88 ˇ

Table 1 Values of transport coefficients calculated from correlation equations. Solute

u (×104 m s−1 )

DL (×107 m2 s−1 )

D (m2 s−1 )

kL (×105 m s−1 )

Fructose Glucose Sucrose 1-Kestose 1-Nystose 1F -Fructofuranosyl nystose

1.38 1.38 2.09 2.11 2.05 2.11

0.84 0.84 1.52 1.29 1.25 1.29

1.61 1.61· 1.09· 0.86 0.72· 0.64

3.11 3.11 2.43 2.35 2.08 1.92

the detection was performed by a differential flow refractometer at 25 ◦ C. 3.3. Column ˝ The column Superformance 150–16 (Gotec Labor Technik, Muhltal, Germany) was packed with the resin slurry so a fixedbed with the diameter of 1.6 cm and length L = 11.6 cm was formed. The bed void volume was measured using Dextran 2000000 (Polymer Standard Service, Mainz, Germany), which did not diffuse into the resin particle pores. The concentration of the dextran was 0.8 kg m−3 . The column bed voidage ε was 0.384 with the standard deviation of 0.009 [10]. 3.4. Mobile phase Fructose, glucose and sucrose, were obtained from Microchem (Pezinok, Slovakia). 1-Kestose, 1-nystose and 1F -fructofuranosyl nystose were products of Wako (Osaka, Japan). Water, which was used to prepare saccharides solution and eluent, was double distilled and filtered through a 0.2 ␮m cellulose-nitrate filter.

where Sh is the Sherwood number calculated from the Wilson and Geankoplis correlation [15]:

3.5. Experimental procedure Fixed-bed adsorption data were obtained by frontal analysis that is based on feeding a bed with a stream having an inlet solute concentration c0 until equilibrium is reached in the whole bed, which is indicated by the outlet concentration equal to c0 . A staircase method was used when the bed was first equilibrated with pure eluent and then the feed concentration was stepwise increased. The curves were obtained by increasing the saccharide feed concentration in steps from 0 to 20 g dm−3 . 3.6. Modelling The axial dispersion coefficients, DL , and liquid-phase mass transfer coefficients, kL , of the GR model were approximated from correlation equations. The axial dispersion coefficient was calculated from the equation suggested by Chung and Wen [14]: DL =

dp u Pe

(5)

Pe =

0.2 + 0.011Re0.48 ε

(6)

Re =

dp uε 

(7)

where Pe is the Péclet number, Re is the Reynolds number, and  is the kinematic viscosity of saccharide solution which was approximated by that of water. The liquid-phase mass transfer coefficient, kL , was calculated from the equation: kL =

Sh · D dp

Fig. 1. Comparison of experimental () and model (—) frontal chromatography data for single-component adsorption of sucrose in the concentration range of 0–20 g dm−3 on the resin AmberliteTM CR1320Ca at 60 ◦ C.

(8)

Sh =

1.09 0.33 (ReSc) ε

(9)

The Schmidt number, Sc, was defined as follows: Sc =

 D

(10)

where D is the diffusion coefficient of saccharide in water approximated from the Wilke–Chang equation [16]. The values of transport coefficients for individual saccharides calculated from the above equations are summarized in Table 1. A commercial process engineering software, Athena Visual Workbench (Stewart & Associates Engineering Software, Madison, WI; www.athenavisual.com), was used for all simulation and parameter estimation tasks in this study [17]. The models were in the form of partial differential equations with time discontinuities when uni-response absolute least-squares and orthogonal collocation technique with 6 inner collocation points were used.

Table 2 Results of parameter estimation using the GR model obtained by the simultaneous fit of all data presented in Fig. 1 and Fig. 2 in Supplementary data. Solute

Kc (–)

Fructose Glucose Sucrose 1-Kestose 1-Nystose 1F -Fructofuranosyl nystose

0.524 0.293 0.181 0.127 0.112 0.035

Ds (× 1012 m2 s−1 ) ± ± ± ± ± ±

0.003 0.004 0.006 0.005 0.005 0.005

21.0 14.1 6.22 4.81 3.42 2.49

± ± ± ± ± ±

1.2 0.5 0.83 0.41 0.17 0.24

The value after the ± sign gives the standard deviation calculated from the variance–covariance matrix. For sucrose, the third fitted parameter, kh , was 8.18 × 10−5 ± 2.65 × 10−6 s−1 .

K. Vanková et al. / Biochemical Engineering Journal 49 (2010) 84–88 ˇ

87

Table 3 Contribution of individual transport phenomena to dispersion of saccharides in the chromatographic bed. uε KL ap (1 − ε)

Solute

2DL /u (×103 m)

2

Fructose Glucose Sucrose 1-Kestose 1-Nystose 1F -Fructofuranosyl nystose

1.22 1.22 1.22 1.22 1.22 1.22

1.15 0.83 1.40 1.03 1.14 0.20

The details of numerical procedures incorporated in the Athena Visual Workbench can be found in original research papers [18]. 4. Results and discussion Step-up frontal experiments were carried out in the concentration range of 0–20 g dm−3 for single-component adsorption of fructose, glucose, sucrose, 1-kestose, 1-nystose and 1F fructofuranosyl nystose on the resin AmberliteTM CR1320Ca at the operation temperature of 60 ◦ C. An illustrative result is presented in Fig. 1 for sucrose. Results for remaining saccharides are included in Fig. 2 in Supplementary data. Individual breakthrough fronts have symmetric dispersed shapes typical for linear adsorption isotherms. Staircase frontal experiments, in general, allow a separate determination of adsorption isotherms by integrating the area below the breakthrough curve. A fully equivalent procedure is to fit the full set of breakthrough curves with a model of fixed-bed adsorption. The latter approach was applied in this work for the model described in Section 2. The main goal of the application of the GR model, which accounts for the effects of individual transport phenomena on dynamics of the fixed-bed adsorption process, was to quantify intraparticle mass transfer through solid-phase diffusion coefficients of individual saccharides, Ds . The values of axial dispersion coefficient, and liquid-phase mass transfer coefficient needed for this model were taken from the correlation equations (Eqs. (5)–(10)) and are summarized in Table 1. Solid-phase diffusion coefficients and distribution coefficients of all saccharides were estimated by the simultaneous fit of the adsorption experiments data and their values are given in Table 2. Fig. 1 and Fig. 2 in Supplementary data show that a very good accuracy of the description was achieved with the GR model. For sucrose, the value of hydrolysis rate constant, kh , was estimated to be (8.18 ± 0.27) × 10−5 s−1 . The distribution coefficients of the saccharides decreased with the increasing molecular weight, i.e. in the order fructose > glucose > sucrose > 1-kestose > 1-nystose > 1F fructofuranosyl nystose. This order is the same as in a previous paper and reflects the size-exclusion effect of the resin [12]. The estimated values of Ds of saccharides were of the order of magnitude from 10−11 to 10−12 m2 s−1 . They are from about 80 to 260 times smaller than the corresponding diffusion coefficients in water (Table 1). This implies a strong restriction effect of pore walls to intraparticle diffusion of saccharides. Different values of Ds for glucose and fructose indicate that this restriction effect is not caused solely by sterical factors. Some role can be played by the structure of hydration shell of resin functional groups [19] and accessibility of non-freezable pore-water of polystyrenedivinylbenzene resins [20]. It is always important in chromatographic separations to identify the contributions of individual transport phenomena to dispersion of components, i.e. also to the spreading of breakthrough curves in frontal chromatography. In the case of linear adsorption isotherms, the van Deemter theory provides a straightforward way



k k+1

2

(×103 m)

KL (–) Kc kS

HETP (×103 m)

0.979 0.986 0.993 0.994 0.995 0.996

2.37 2.05 2.62 2.25 2.36 1.42

to exact quantification of these contributions to the total dispersion effect, which is typically characterized through the height of equivalent theoretical plate (HETP) [21]. Eq. (11) defines the contributions of axial dispersion (first term) and mass transfer (second term) to the HETP: HETP =

2uε 2DL + u KL ap (1 − ε)

 k 2 k+1

(11)

where k = Kc (1 − ε) /ε, is the capacity factor and KL is the overall mass transfer coefficient. 1 1 1 = + KL kL Kc kS

(12)

which accounts for the mass transfer resistances of both liquid (first term) and solid phases (second term). The solid-phase mass transfer coefficient kS was approximated from the Glueckauf equation [22]: kS = 10

Ds Kc dp

(13)

Table 3 presents the contributions of axial dispersion and mass transfer to the HETP values for individual saccharides as well as the HETP values calculated from Eq. (11). The HETP values for all saccharides but 1F -fructofuranosyl nystose were approximately the same—(2–2.5) × 10−3 m, which was about 6–8-fold of the particle diameter. The lower value of HETP for 1F -fructofuranosyl nystose can be explained by that this saccharide almost does not penetrate the resin particles. As follows from the second term on the righthand side of Eq. (11), the contribution of liquid-solid mass transfer to the HETP becomes proportional to the square of distribution coefficient at low values of distribution coefficient. The first and second columns of Table 3 represent the contributions of axial dispersion and total mass transfer to the calculated HETP values. The third column gives the portion of solid-phase mass transfer on the overall mass transfer resistance. It is evident that the contribution of liquid-phase mass transfer resistance was almost negligible. This is quite common for fixed-bed adsorption when the bed length is sufficiently long [23]. In this case, another factor is low adsorption of saccharides which causes a low intraparticle flux. It is not a problem then for liquid-phase mass transfer to flatten the concentration gradient in the liquid film. The low intraparticle flux was responsible also for that the relative contribution of axial dispersion to the HETP values was about 50–60% for all saccharides but 1F -fructofuranosyl nystose when the contribution of axial dispersion is usually negligible for highly adsorbing compounds [23]. This can be well illustrated through the effect of capacity term (k/k + 1)2 , on the HETP in Eq. (11). It approaches one at high k-values. Nonetheless, a strong influence of axial dispersion due to the low permeability of the resin particles was indisputable. Acknowledgement This study was supported by Slovak Research and Development Agency APVV (LPP-0234-06).

88

K. Vanková et al. / Biochemical Engineering Journal 49 (2010) 84–88 ˇ

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.bej.2009.11.015. References [1] F.R.J. Bornet, F. Brouns, Y. Tashiro, V. Duvillier, Nutritional aspects of short-chain fructooligosaccharides: natural occurrence, chemistry, physiology and health implications, Digest. Liver Dis. 34 (2) (2002) S111–S120. [2] M.J. Mabel, P.T. Sangeetha, K. Platel, K. Srinivasan, S.G. Prapulla, Physicochemical characterization of fructooligosaccharides and evaluation of their suitability as a potential sweetener for diabetics, Carbohyd. Res. 343 (2008) 56– 66. [3] J.W. Yun, Fructooligosaccharides—occurrence, preparation, and application, Enzyme Microb. Tech. 19 (2) (1996) 107–117. [4] I. Pedruzzi, E.A.B. da Silva, A.E. Rodrigues, Selection of resins, equilibrium and sorption kinetics of lactobionic acid, fructose, lactose and sorbitol, Sep. Purif. Technol. 63 (3) (2008) 600–611. [5] D.C.S. Avezedo, A.E. Rodrigues, Design methology and operation of a simulated moving bed reactor for the inversion of sucrose and glucose–fructose separation, Chem. Eng. J. 82 (2001) 95–107. [6] L. Matijasevic, D. Vasic-Racki, Separation of glucose/fructose mixtures: counter-current adsorption system, Biochem. Eng. J. 4 (2000) 101–106. [7] M.S. Coelho, D.C.S. Azevedo, J.A. Teixeira, A. Rodrigues, Dextran and fructose separation on an SMB continuous chromatographic unit, Biochem. Eng. J. 12 (3) (2002) 215–221. [8] Y.A. Beste, M. Lisso, G. Wozny, W. Arlt, Optimization of simulated moving bed plants with low efficient stationary phases: separation of fructose and glucose, J. Chromatogr. A 868 (2) (2000) 169–188. [9] J.A. Vente, H. Bosch, A.B. de Haan, P.J.T. Bussmann, Evaluation of sugar sorption isotherm measurement by frontal analysis under industrial processing conditions, J. Chromatogr. A 1066 (1–2) (2005) 71–79.

[10] D.A. Luz, A.K.O. Rodrigues, F.R.C. Silva, A.E.B. Torres, C.L. Cavalcante Jr., E.S. Brito, D.C.S. Azevedo, Adsorptive separation of fructose and glucose from an agroindustrial waste of cashew industry, Bioresour. Technol. 99 (7) (2008) 2455. [11] J. Nowak, K. Gedicke, D. Antos, W. Piatkowski, A. Seidel-Morgenstern, Synergistic effects in competitive adsorption of carbohydrates on an ion-exchange resin, J. Chromatogr. A 1164 (2007) 224–234. [12] M. Grambliˇcka, M. Polakoviˇc, Adsorption equilibria of glucose, fructose, sucrose, and fructooligosaccharides on cation exchange resin, J. Chem. Eng. Data 52 (2) (2007) 345–350. [13] Y. Takahashi, S. Goto, Continuous separation of fructooligosaccharides using an annular chromatography, Sep. Sci. Technol. 29 (10) (1994) 1311–1318. [14] S.F. Chung, C.Y. Wen, Longitudinal dispersion of liquid flowing through fixed and fluidized beds, AIChE J. 14 (1968) 857–866. [15] E.J. Wilson, C.J. Geankoplis, Liquid mass transfer at very low Reynolds numbers in packed beds, Ind. Eng. Chem. Fundamen. 5 (1) (1966) 9–14. [16] C.R. Wilke, P. Chang, Correlations of diffusion coefficients in dilute solutions, AIChE J. 1 (1955) 264–270. [17] Athena Visual Workbench. Technical Manual, Stewart & Associates Engineering Software Inc., Madison, WI, 2001. [18] W.E. Stewart, M. Caracotsios, J.P. Sorensen, Parameter estimation from multiresponse data, AIChE J. 38 (1992) 641–650. [19] E. Glueckauf, G.P. Kitt, A theoretical treatment of cation exchangers. III. The hydration of cations in polystyrene sulphonates, P. Roy. Soc. Lond. (1955) 322–341. [20] S. Baba, A. Ohta, M. Ohtsuki, T. Takizawa, T. Adachi, H. Hara, Fructooligosaccharides stimulate the absorption of magnesium from the hindgut in rats, Nutr. Res. 16 (4) (1996) 657–666. [21] J.J. Van Deemter, F.J. Zuiderweg, A. Klinkenberg, Longitudinal diffusion and resistance to mass transfer as causes of nonideality in chromatography, Chem. Eng. Sci. 5 (1956) 271–289. [22] E. Glueckauf, J.I. Coates, Theory of chromatography. Part 4. The influence of incomplete equilibrium on the front boundary of chromatogram and on the effectiveness of separation, J. Chem. Soc. (1947) 1315–1321. [23] M. Polakoviˇc, T. Gorner, F. Villiéras, P. de Donato, J.L. Bersillon, Kinetics of salicylic acid adsorption on activated carbon, Langmuir 21 (7) (2005) 2988–2996.