Ind. Eng. Chem. Res. 1996, 35, 3629-3636
3629
Separation between Amino Acids and Inorganic Ions through Ion Exchange: Development of a Lumped Model Stefano Melis,† Jozef Markos,‡,§ Giacomo Cao,‡ and Massimo Morbidelli*,† Laboratorium fu¨ r Technische Chemie, ETH-Zentrum, CAB C40, Universita¨ tstrasse 6, CH-8092 Zurich, Switzerland, and Dipartimento di Ingegneria Chimica e Materiali, Universita´ degli Studi di Cagliari, Piazza d’ Armi, I-09123 Cagliari, Italy
The feasibility of large-scale separation of amino acids and inorganic ions by ion exchange columns has been demonstrated by considering a prototype problem involving one amino acid (proline), sodium chloride, and chloridic acid. The optimal design and operation of such a process has been based on an appropriate mathematical model, which includes the description of multicomponent ion exchange equilibria and the simulation of inter- and intraphase transport processes. The latter is based on a new lumping approximation of the Nernst-Planck equation for the diffusion of ions. The model contains some adjustable parameters that have been estimated from binary equilibrium data and experimental binary breakthrough curves of all the involved ionic species. The model reliability has been tested by comparison with experimental effluent histories of several adsorption-elution cycles involving multicomponent mixtures. Using the model, an optimal column operation, which includes ammonia feed before regeneration, has been designed for the separation of the prototype mixture. This result has been tested experimentally at the laboratory scale. 1. Introduction Amino acids have acquired an important role in the pharmaceutical, food, and health product industries. They can be produced by selective fermentation through appropriate bacteria or, alternatively, through the hightemperature acid hydrolysis of protein-containing substrates. Both techniques usually yield to multicomponent mixtures containing amino acids, inorganic ions, and high molecular weight compounds (i.e., nonconverted proteins). Several separation steps are hence required in order to obtain amino acids in the desired pure form. Typically, high molecular weight compounds are removed by centrifugation, ultrafiltration, and adsorption on activated carbons while the removal of the inorganic ions and the extraction of the individual amino acids are carried out by chromatographic techniques. Due to the amphoteric behavior of amino acids, ion exchange chromatography offers a variety of opportunities. Two distinct driving forces may in fact be exploited: (1) differences in the ionization constants of the amino acids, which can be used for the so-called “group separation” (i.e., the fractionation of amino acids in basics, neutrals, and acidics) or for the removal of the inorganic ions (2) differences in the affinities of the individual amino acids toward the selected ion exchange resin, which can be exploited for the fractionation of amino acids within the same group. Several studies on the chromatographic separation of amino acids appeared in the literature. For example, Wang and co-workers (Yu et al., 1987) developed a model that, on the basis of the assumptions of local equilibrium and constant separation factor, was able to * Corresponding author. Fax: +41-1-6321082. † Laboratorium fu ¨ r Technische Chemie. ‡ Dipartimento di Ingegneria Chimica e Materiali. § Present address: Department of Chemical and Biochemical Engineering, Slovak Technical University, Radlinskeho 9, 812 37 Bratislava, Slovak Republik.
S0888-5885(96)00152-2 CCC: $12.00
correctly predict the retention time of all components in a typical analytical device. On the other hand, the optimal design and operation of large-scale separation columns require more accurate mathematical models, which should include an appropriate description of both multicomponent ion exchange equilibria as well as intra- and interphase mass transfer along the column. Saunders et al. (1989) considered the uptake of phenylalanine and tyrosine on Amberlite IR252 and developed a model that combines the simulation of ion exchange equilibria through the Myers and Byington model together with a detailed description of the interand intraparticle mass transport processes. In particular, they used the Kataoka equation (Kataoka et al., 1973) for the description of the mass transfer through the external film and accounted for the Nernst-Planck mechanism for diffusion both in the particle pores and in the resin matrix. This leads to a system of PDEs involving three independent variables: column axis, particle radius, and time. Besides the mathematical complexity, the model results appeared to be quite satisfactory. It should be pointed out that all the experimental runs were conducted for binary systems at low normality values. In these conditions, the problems related to the composition dependence of the mass transfer rates are not evidenced, while they may be important in practical applications involving multicomponent systems and higher normalities. In this paper, we address the problem of separating a representative mixture containing one amino acid (proline) and two inorganic ions (i.e., sodium and chloride), and we develop a mathematical model that on the basis of the ion exchange equilibrium model proposed by Melis et al. (1995) and of a lumped description of the intraparticle mass transport, is able to determine the optimal operating conditions. Hence, we investigated first the binary equilibria of the involved species with the hydrogen ion on an acid cation exchanger (Amberlite IR120). These data were used to estimate the parameters of a multicomponent model, which combines the description of the dissocia© 1996 American Chemical Society
3630 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 Table 1. Properties of Amberlite IR120 av particle diameter (cm) total exchange capacity (mmol/g of dry resin (H+)) Fp (g of dry resin/cm3) ω (g of dry resin/g of hydrated resin)
0.07 5.49 0.57 0.45
tion equilibria in the aqueous phase with that of the ion exchange equilibria (Melis et al., 1996). About transport processes, we used the Kataoka equation to evaluate the external film resistance. Since the adopted resin is of gelular type, it was supposed that intraparticle transport occurs via solid diffusion only, according to the Nernst-Planck equation. On this basis, a lumping procedure has been applied to the mass balance PDE of the resin particle (i.e., introducing volume-averaged concentrations) so as to obtain an ODE, where electroneutrality and zero-current conditions are properly accounted for. This leads to a relatively simple mathematical model that provides a tool for the quick simulation of adsorption-elution cycles of complex multicomponent mixtures. Several binary experimental breakthrough curves were analyzed and compared to model results in order to estimate the self-diffusion coefficients of the involved components in the resin phase. With these, in order to verify the reliability of the proposed model, the simulated results were compared with the experimental data corresponding to several adsorption-elution cycles of multicomponent mixtures. Moreover, the model was used to determine the operating conditions needed for separating the representative mixture mentioned above. This was done by feeding the column with the prolineNa+-Cl- mixture until saturation was attained. At this point, the feed was switched to a moderately concentrated solution of ammonia, inducing a quick increase in the column pH, which caused the proline to be converted to the anionic form and, therefore, to be readily eluted from the column in an almost pure form. An elution cycle with concentrated hydrochloric acid was finally carried out in order to regenerate the resin to its original hydrogen form. The reliability of the designed process was confirmed experimentally at the laboratory scale. 2. Experimental Section The resin used in this work, Amberlite IR120 (Rohm & Haas), is a strong acid cation exchanger with gelular structure, constituted of a sulfonated styrene-divinylbenzene copolymer. The same procedure described in Melis et al. (1996) has been adopted for measuring the physical properties of the resin summarized in Table 1 as well as to perform the batch equilibrium experiments. The ammonia concentration was measured either by titration or through Nessler’s reagent and spectrophotometry. Experimental breakthrough curves and adsorptionelution cycles were carried out at room temperature (approximately 20 °C) in the apparatus schematically shown in Figure 1. The resin was slurry packed in a 60 cm long glass column, 1.55 cm i.d., and enclosed between two inert layers: glass rings were placed at the top of the column in order to ensure flux uniformity, while quartz wool was placed at the bottom to avoid resin entrainment. The change in resin swelling during the adsorption-elution experiments was assumed to be negligible, and a bed void fraction equal to 0.39 was measured. A three-way valve was used to switch input solutions, while a second valve at the bottom of the
Figure 1. Experimental apparatus for adsorption-elution cycles. Table 2. Operating Conditions for Experimental Adsorption-Elution Runs run 1
run 2
run 3
run 4
run 5
initial conditions C0 (proline) C0 (sodium) C0 (chloride) C0 (ammonia)
H+ 0 0 100 0
H+ 0 0 24 0
NH+ 4
0 0 20 20
H+ 0 0 46.7 0
H+ 0 0 50 0
feed cycle number duration (min) flow rate (cm3/s) Cf (proline) Cf (sodium) Cf (chloride) Cf (ammonia)
1 40 1.02 21.6 0 100 0
1 40 1.02 0 50 24 0
1&3 75 0.79 0 48.8 48.8 0
1&3 60 0.80 14.9 14 22 0
1&4 60 1.15 14.3 15.5 25.6 0
2&4 90 0.79 0 0 0 50
2&4 120 0.80 0 0 46.7 0
2&5 80 1.15 0 0 0 32.2
feed cycle number duration (min) flow rate (cm3/s) Cf (proline) Cf (sodium) Cf (chloride) Cf (ammonia) feed cycle number duration (min) flow rate (cm3/s) Cf (proline) Cf (sodium) Cf (chloride) Cf (ammonia)
3&6 80 0 0 0 50 0
column allowed the selection of the desired flow rate. Samples of the column effluent were collected at fixed time intervals, and composition was measured through the same technique used for batch equilibrium runs. The complete description of the operating conditions used in the various experimental runs is reported in Table 2. 3. Mathematical Model 3.1. Dissociation Equilibria in Aqueous Solution. Among all the species considered in this work, only proline and ammonia are characterized by dis-
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3631
from a pH measurement or, more consistently with the modeling approach, through the local electroneutrality condition:
Table 3. Model Parameters
species
dissociation constants (25 °C)
Di (cm2/s)
9.31 × pKa ) 2.0; 0.80 × 10-5 b pKb ) 10.6 sodium 1.33 × 10-5 ammonia pKn ) 4.74b 1.96 × 10-5
H+
10-5
proline
Di (cm2/s)
K hi
γi
2.3 × 2.5 × 10-7
2.08 4.88
5.0 × 10-7 8.0 × 10-7
1.32 1.0 1.15 2.86
10-6a
a Value from Patell and Turner (1980). b Values from CRC Handbook of Chemistry and Physics (1978).
sociation equilibria. In particular, for proline we have
Pro+ / Pro( + H+
(1.1)
Pro( / Pro- + H+
(1.2)
which led to an excess of the cationic form at low values of the solution pH. Assuming ideal behavior for the aqueous phase and knowing the total “analytical” concentration of the amino acid, the concentrations of all the ionic forms are readily computed as follows:
CA+ )
CA Ka KaKb 1+ + CH+ (C +)2
(2.1)
H
C A( )
C A- )
CA CH+ Kb 1+ + Ka CH+ CA
(CH+)2 CH+ 1+ + KaKb Kb
(2.2)
(2.3)
where Ka and Kb are the equilibrium constants of the dissociation reactions 1.1 and 1.2, respectively. Similarly for ammonia by considering the dissociation equilibrium:
NH4+ + OH- / NH3 + H2O
(3)
and assuming ideal behavior for the aqueous solution, we obtain:
CNH4+ )
CNH3 )
CN Kw 1+ KnCH+ CN Kn 1+ C K w H+
(4.1)
(4.2)
where CN represents the total “analytical” ammonia concentration, Kn is the dissociation constant for the equilibrium 3, and Kw is the ionic product of water. Note that the values of all dissociation constants are summarized in Table 3. For the other compounds considered, i.e., strong electrolytes such as NaCl and HCl, complete dissociation is assumed. From the above relations, we can compute the concentrations of all species in solution, whether in molecular or ionic form, once the concentration of the hydrogen ion (CH+) is known. This can be either obtained
CA+ + CNH4+ + CNa+ + CH+ ) CA- + COH- + CCl- (5) Equation 5, when substituting eqs 2 and 4, reduces to a single nonlinear algebraic equation in the only unknown CH+, which is solved numerically. 3.2. Ion Exchange Equilibria. When a solution containing cations is contacted with a cation exchange resin, the following independent exchange reactions occur between each counterion Sνi i+ and the hydrogen ion taken as reference one:
Sνisi+ + νiHr+ / Sνiri+ + νiHs+
i ) 1, Nc - 1 (6)
where Nc is the number of counterions present in the system, νi is the charge of the ionic species Sνi i+, and subscripts r and s refer to the resin and aqueous solution, respectively. In order to quantitatively describe the exchange equilibria represented by eq 6, we used a heterogeneous model based on mass action law, which has been recently applied to the exchange equilibria of amino acids (Melis et al., 1995, 1996). In this model, the exchange reactions are considered to be governed by the mass action law, while assuming ideal behavior for both the solution and the resin phase. Deviations from the ideal behavior of the equilibria are accounted for by considering the possible heterogeneity of the resin functional groups, which results in a statistical distribution of the standard free energies of the exchange reaction. By approximating such a distribution with a discrete symmetrical distribution of only two types of functional groups, the model reduces to describe the resin as formed by two types of functional groups, both ideal but with different values of the exchange equilibrium parameters. Hence, the equilibrium constant for the exchange of the generic ith component occurring on functional groups of type j is given by
(Qj,i)(CH+)νi
(qj,i)(CH+)νi 1-νi Kj,i ) ) Fp (Ci)(Qj,H+)νi (Ci)(qj,H+)νi
(7)
where Ci and Qj,i ()Fpqj,i) are the concentrations of the species Sνi i+ in solution and on the jth type of functional groups of the resin, respectively. By introducing in eq 7, the ionic fractions
Xi )
νiCi
νiCi ) N
Nc
∑ νkCk
(8)
k)1
Yj,i )
νiqj,i
νiqj,i )
Nc
∑ νkqj,k
q0
(9)
k)1
where N is the total ionic concentration in the aqueous solution or solution normality and q0 is the total exchange capacity of the resin, the following expression is obtained:
3632 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
Kj,i )
( )
(Yj,i)(XH+)νi Fpq0 (X )(Y +)νi N j
j,H
particle is given by
1-νi
j ) 1, 2 and i ) 1, Nc - 1 (10)
Equation 10 together with the congruence conditions (the sum of the ionic fractions equal to unity) yield the ionic fractions Yj,i once the model parameters and composition of the aqueous phase are known. Finally, the overall resin composition is obtained by averaging the ionic fractions on each type of functional groups, weighted with their relative abundance. In this case, owing to the assumption of symmetrical distribution, this leads to
Yi )
Y1,i + Y2,i 2
K h i ) (K1,iK2,i)1/2
(12)
1/2
(13)
γi ) (K1,i/K2,i)
As discussed by Melis et al. (1995), these parameters are equivalent to the equilibrium constants of the single functional groups and are more directly representative of the original energetic distribution. 3.3. Mass Transport between Aqueous Phase and Resin Particles. The description of the transport of the ionic species from the aqueous solution to the functional groups of the resin (and vice versa) should account for both the resistance in the external film as well as for the intraparticle diffusion. The mass transfer through the external film is described through the following relation (Kataoka et al., 1973):
kf 1 - -1/3 ) 1.85Re-2/3Sc-2/3 u0
)
(14)
where u0 is the surface velocity, is the bed void fraction, kf is the mass transfer coefficient, Sc is the Schmidt number, and Re is the Reynolds number defined as:
Fdu0 µ Sc ) and Re ) FD µ(1 - )
r ) R, t > 0
(16)
kf(Ci - Ci*) ) ∂qi F ∂φ - Di + νiqi ∂r R RT ∂r
[( |
| )]
(17)
R
∂qi )0 ∂r
r ) 0, t > 0
(18)
where Ci* is the aqueous phase concentration at the surface of the resin particle, in equilibrium with the corresponding concentration in the resin phase qi*. Application of a lumping procedure to eq 16, based on taking the integral over the particle volume of both sides, yields
( |
dqi 3 ∂qi ) Di dt R ∂r
R
|)
F ∂φ + νiqi* RT ∂r
(19)
R
where qi represents the volume average resin concentration of the ith species. The flux at the resin surface in the equation above can be expressed as a function of the average and the surface resin concentrations using a second-order polynomial approximation for the concentration profiles in the resin (or equivalently considering a discretization of the r domain with a single orthogonal collocation point), as follows:
|
∂qi ∂r
) R
5 (q * - q j i) R i
(20)
On the other hand, the electrical potential gradient can be expressed as a function of qi and qi* using the zero current condition as follows:
(
∑νiDi
|
F ∂φ RT ∂r
(15)
Equation 14 was originally developed for the case of mutual exchange between two counterions, and the diffusion coefficient, D, appearing in the Schmidt number was evaluated as a complicated function of the selfdiffusivities of the two counterions and their concentration (Kataoka et al., 1973). The extension to multicomponent systems can be done by taking D equal to the self-diffusivity of the slowest counterion, which is a conservative approximation. Since the resin considered here has a gelular structure, we assume that intraparticle diffusion occurs only via surface diffusion, according to the Nernst-Planck mechanism (Helfferich, 1962). Accordingly, the mass balance equation for the counterion i in the resin
)]
where Di is the self-diffusivity in the resin while φ is the electrical potential generated by the diffusion of ions with different mobilities, F is the Faraday constant, R is the ideal gas constant, and T is the temperature. The appropriate boundary conditions are
(11)
which in turn gives the total loading (qi) when multiplied by the exchange capacity (q0). In the following, we will use as equilibrium parameters the average equilibrium constant (K h i) and the heterogeneity parameter (γi), which in this case are expressed by
(
[ (
∂qi 1 ∂ ∂qi F ∂φ ) 2 + νiqi Dir2 ∂t ∂r ∂r RT ∂r r
R
)
∂qi F ∂φ + νiqi )0 ∂r RT ∂r
)-
5 R
(21)
∑νiDi(qi* - qi) ∑νi2Diqi*
(22)
It is worth pointing out that eq 20 is identical to the expression obtained by Glueckauf (1955) for the case of pure diffusion within spheres with time-dependent boundary condition. When substituting eqs 20 and 22, eq 19 reduces to an ODE involving only volume-averaged concentrations, which provides the lumped approximation of the original PDE 16:
(
dqi 15 ) 2 Di (qi* - q j i) - νiqi* dt R
∑Di(qi* - qi) ∑νkDkqk*
)
)
15 Deff,i(qi* - q j i) (23) R2
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3633
The cases where the ratio between the ion diffusivities are equal to 2 and 5 are shown in Figure 2a,b, respectively, where the ionic fraction in the liquid phase (X) is shown as a function of dimensionless time, θ ) t(Di/R2). The obtained agreement between the complete model (i.e., eq 16) and the lumped model developed in this work (i.e., eq 23) is on the whole satisfactory. Indeed, this is similar to the results obtained in the case of Fickian diffusion using the classical Glueckauf approximation [cf. Morbidelli et al. (1982)]. For a comparison, in the same Figure 2 are also shown the results of the Glueckauf approximation where two different constant values for the diffusion coefficient are considered, i.e., those corresponding to the slowest (I) and the fastest ion (II). 3.4. Column Modeling and Parameter Estimation. The transient behavior of the ion exchange column has been simulated by means of a heterogeneous axial-dispersion model. The column is assumed isothermal, since the heat released by ion exchange reactions is usually negligible. Moreover, unidimensional flux and spherical and uniformly sized resin particles are considered. With such assumptions, the mass balance equation for species i in the aqueous phase is given by
∂Ci ∂2Ci ∂Ci 3(1 - ) ) -u0 + ED 2 - kf (Ci - Ci*) (26) ∂t ∂x R ∂x along with the Danckwerts’ boundary conditions:
x ) 0; Figure 2. Comparison between the results of the complete model (eqs 16 and 25) and different lumped approximations for (a) Dj/Di ) 5 and (b) Dj/Di ) 2: (C) complete model; (NP) lumped approximation eq 23 (Deff,i ) eq 24); I (Deff,i ) Di); II (Deff,i ) Dj.). Initial conditions: Xi ) 0.7 and qi ) 0 at t ) 0.
which can then be regarded as an extension of the classical Glueckauf approximation to the case where the Nernst-Planck diffusion mechanism is dominating. The above equation defines the effective diffusivity, Deff,i which in the general case of a multicomponent system cannot be expressed analytically. However, when only two monovalent ions are involved, the following expression is obtained:
Deff,i ) Deff,k )
DiDjq0
(24)
Diqi* + Dkqk*
In order to test the reliability of this lumping approximation, the case of a binary exchange in a batch system has been considered. For this, eq 16 (or its lumped version eq 23) is coupled with the appropriate mass balance in the bulk liquid phase, given by
( |
dCi 3R ∂qi ) Di dt R ∂r
R
|)
F ∂φ + νiqi* RT ∂r
(25)
R
where R is the ratio between the resin weight and the liquid volume, and mass transfer resistance across the external film is neglected.
∂Ci u0Cfi ) u0Ci - ED ∂x
(27)
∂Ci )0 ∂x
(28)
x ) L;
where ED represents the axial dispersion coefficient (referred to the free column section), x is the axial coordinate along the bed axis, L is the column length, and Ci* is the aqueous phase concentration locally in equilibrium with the resin. Equations 26-28 together with eqs 17 and 23 constitute a mixed algebraic differential system of equations that can be solved once the self-diffusivities (both in the liquid and in the resin phase) and the axial dispersion coefficient are known. The solution was obtained numerically by expressing the spatial derivatives according to a centrate finite different scheme and considering 50 discretization points uniformly distributed along the column. The resulting system of equations was solved using the package DDASSL (Petzold, 1991). The adopted values of the diffusivities in the liquid phase, reported in Table 3, have been obtained experimentally for the sodium, ammonia, and hydrogen ions (Slater, 1991) while estimated through the correlation of Wilke and Chang (1955) in the case of proline. The axial dispersion coefficient has been estimated according to the correlation of Chung and Wen (1968). Finally, the diffusivities in the resin phase, whose values are reported in Table 3, have been estimated by fitting binary breakthrough curves (as discussed in the next section) except for the hydrogen ion, whose value for Di has been estimated experimentally by Patell and Turner (1980).
3634 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
Figure 5. Comparison between experimental data and model results for the binary breakthrough curve of sodium (run 2). Figure 3. Ion exchange isotherm for the system NH4+/H+ in terms of resin phase NH4+ ionic fraction, Y as a function of the corresponding ionic fraction in the aqueous phase, X.
Figure 6. Comparison between experimental data and model results for the adsorption-elution cycles of sodium in the bed saturated by ammonia (run 3). Figure 4. Comparison between experimental data and model results for the binary breakthrough curve of proline (run 1).
4. Results and Discussion The binary ion exchange equilibria of sodium and proline with respect to hydrogen have been studied, using the same resin adopted in this work, by Melis et al. (1996). The obtained values of the model equilibrium parameters are reported in Table 3. In the case of ammonia, the corresponding equilibrium behavior is illustrated in Figure 3 in terms of ionic fractions in the aqueous and in the resin phase. It is seen that ammonia is characterized by a sigmoidal isotherm, which is properly reproduced by the model, using the parameter values reported in Table 3. The experimental breakthrough for proline (run 1), whose operating conditions are reported in Table 2, is shown in Figure 4 together with the model results obtained by fitting the corresponding diffusion coefficient in the resin. It should be observed that the adopted operating conditions are such that the ionic fraction of proline in the aqueous phase is always lower than 0.2. This makes the effect of composition on the effective diffusion coefficient in the aqueous phase very small. The breakthrough curve of sodium (run 2 in Table 2) is shown in Figure 5. In this case, significant variations in the solution composition occur along the bed, which have a significant effect on the value of the diffusion coefficient. However, the model fitting is again satisfactory, thus supporting the reliability of the assumption
of slowest ion diffusivity in the aqueous phase. It is worth noting that the breakthrough curve for sodium in Figure 5 is quite steep, which also implies that the concentration profiles along the column are rather steep. This behavior, which is typical for systems exhibiting favorable equilibrium isotherms (as Na+ in this case), is also due to the self-accelerating nature of the adsorption of sodium due to the presence of the potential gradient in the Nernst-Planck equation. From eq 24 it can be seen that the effective diffusion coefficient in the resin is equal to that of sodium when the resin is saturated by H+, it increases for increasing values of the sodium loading, and finally becomes equal to that of the hydrogen ion when the resin is saturated by Na+. It is worth noting that the presence of these steep profiles along the column requires a finer discretization of the integration domain. Accordingly, the possibility of replacing the detailed particle model (eq 16) with the lumped one (eq 23) in each node of the grid has a significant effect on the computational effort. Finally, the diffusion coefficient for the ammonium ion has been estimated from the adsorption-elution curves of sodium in a bed initially saturated by ammonia (run 3 in Table 2). The adsorption-elution cycle has been repeated twice in order to test the reproducibility of the experimental data. In Figure 6, it appears that the fitting of the experimental data by the model is satisfactory. It is worth mentioning that the three values of the diffusion coefficients in the resin phase obtained above and reported in Table 3 are coherent with typical values reported in the literature for diffusion coefficients in similar conditions [cf. Slater (1991)].
Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996 3635
Figure 7. Comparison between experimental data and model predictions for the adsorption-elution cycles of a mixture containing sodium and proline (run 4); elution is performed with hydrochloric acid; (a) proline, (b) sodium.
In order to test the model reliability, two multicomponent adsorption-elution runs have been considered. During the first cycle of run 4, a mixture containing sodium and proline is fed to the column initially saturated by the hydrogen ion until saturation is almost achieved. The elution of the two components is then obtained during the regeneration cycle, where a concentrated solution of chloridric acid is fed to the column. Again, the adsorption-elution cycles have been repeated twice. The comparison with the calculated results, shown in Figure 7, indicates that the model correctly predicts the column effluent history, even though some discrepancy is present during the elution phase of proline. Note also that the effluent concentration of the chloride ion is not shown, since it is excluded from the resin by the Donnan potential and therefore behaves like an inert tracer. In the above run 4, the separation between proline and sodium is not achieved. This was expected since, in order to obtain the desired separation with the given column length, an eluent able to displace only the amino acid should be used. For this reason, in run 5 we used ammonia as eluent, followed again by regeneration with hydrochloric acid. Ammonia has less affinity to the resin than sodium but, due to its dissociation reaction (eq 5), is able to induce a relevant increase in the column pH, causing proline to assume the anionic form and therefore to be readily eluted from the column. The results, shown in Figure 8, demonstrate that the separation is actually achieved and that proline is obtained in a concentrated and almost pure form at the beginning of the elution cycle. This is further demonstrated in the repeated adsorption-elution cycle, which shows that the process is reproducible. Besides, the
Figure 8. Comparison between experimental data and model predictions for the adsorption-elution cycles of a mixture containing sodium, proline, and ammonia (run 5); elution is performed with ammonia and then with hydrochloric acid; (a) proline, (b) sodium, (c) ammonia, (d) pH.
proposed mathematical model also in this case satisfactorily predicts the effluent history of all components
3636 Ind. Eng. Chem. Res., Vol. 35, No. 10, 1996
and thus provides a useful tool for the optimal design of the ion exchange process. 5. Concluding Remarks In the present work, we addressed the problem of the separation of amino acids and inorganic ions on ion exchange resins, and in particular, we investigated a prototype separation involving a representative mixture containing one amino acid, sodium, and chloride ions. A mathematical model that incorporates a recently developed model for the simulation of ion exchange equilibria and a lumped description of the intraparticle diffusion, according to a Nernst-Planck mechanism, has been developed. The model was then used to successfully correlate the experimental data relative to the binary breakthrough curves of all the involved components and further tested by comparing multicomponent adsorption-elution cycles and model predictions. The results showed that the separation of proline and sodium can be achieved by using ammonia as eluent even using a relatively short column. This indicates the possibility of separating amino acids from inorganic ions using eluents that properly affect the system pH. The developed model provides a useful tool for designing the optimal separation conditions. Acknowledgment We gratefully acknowledge the fellowship awarded to J.M. by TEMPUS Program 1125/91. Nomenclature Ci ) concentration of species i in the liquid phase (mmol/ L) d ) resin particle diameter (cm) Di ) self-diffusivity of cation i in the aqueous phase (cm2/ s) Di ) self-diffusivity of cation i in the resin phase (cm2/s) Deff,i ) binary effective diffusivity in the resin phase (cm2/ s) ED ) axial dispersion coefficient (cm2/s) F ) Faraday constant Ka ) acid dissociation constant for proline Kb ) basic dissociation constant for proline K h i ) average equilibrium constant between ion i and the reference ion (H+) Kj,i ) equilibrium constant between ion i and the reference ion on functional groups of type j Kn ) dissociation constant for ammonia Kw ) ionic product of water kf ) mass transfer coefficient across the external film (cm/ s) L ) column lenght (cm) N ) solution normality (mmol/L) Qj,i ) resin loading of ion i on functional groups of type j (mmol/L) q0 ) total ion exchange capacity of the resin (mmol/g of dry resin) qj,i ) resin loading of ion i on functional groups of type j (mmol/g of dry resin) R ) resin particle radius (cm) R ) ideal gas constant Re ) Reynolds number r ) radial coordinate along the particle (cm) Sc ) Schmidt number T ) temperature (K) t ) time (s) u0 ) surface velocity along the bed (cm/s)
x ) axial coordinate along the bed (cm) Xi ) ionic fraction of ion i in solution Yi ) overall ionic fraction of ion i in the resin Yj,i ) ionic fraction of ion i on resin functional groups of type j Greek Letters R ) ratio between resin weight and liquid volume (g of dry resin/L) γi ) heterogeneity parameter defined by eq 13 ) bed void fraction (-) θ ) tDi/R2 dimensionless time µ ) viscosity (g cm-1 s-1) νi ) charge of ion i Fp ) dry resin density (g of dry resin/L) ω ) ratio between dry and hydrated resin weights Subscripts and Superscripts f ) feed conditions r ) resin phase s ) aqueous phase * ) solution-resin interface 0 ) initial conditions
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Received for review March 18, 1996 Revised manuscript received June 12, 1996 Accepted June 14, 1996X IE960152W
X Abstract published in Advance ACS Abstracts, September 1, 1996.
