Ind. Eng. Chem. Res. 1992,31, 1717-1730 Frank, G. T.; Sirkar, K. K. An Integrated Bioreactor-Separator: In Situ Recovery of Fermentation Products by a Novel MembraneBased Dispersion-Free Solvent Extraction Technique. Biotechnol. Bioeng. Symp. Ser. 1986,No. 17,303-316. Joshi, D. K.;Senetar, J. J.; King, C. J. Solvent Extraction for Removal of Polar-Organic Pollutants from Water. Znd. Eng. Chem. Process Des. Dev. 1984,23, 748-754. Kiani, A.; Bhave, R. R.; Sirkar, K. K. Solvent Extraction with Immobilized Interfaces in a Microporous Hydrophobic Membrane. J. Membr. Sci. 1984,20 (2),125-145. King, C. J.; Barbari, T. A.; Joshi, D. K.; Bell, N. E.; Senetar, J. J. Equilibrium Distribution Coefficient for Extraction of Organic Priority Pollutants from Water. Report No. EPA-600/S2-84-060, U.S. Environmental Protection Agency: Washington, DC, 1984. Magee, R. Personal Communication, HSMRC, NJIT, Newark, NJ, 1988. Patterson, J. W. Industrial Wastewater Treatment Technology, 2nd ed.; Butterworth Boston, MA, 1985;Chapter 20. Perry, R. H.; Chilton, C. H. Chemical Engineers’ Handbook, 5th ed.; McGraw-Hik New York, 1973;p 3-234. Prasad, R.; Sirkar, K. K. Microporous Membrane Solvent Extraction. Sep. Sci. Technol. 1987a,22 (2,3), 619-640. Prasad, R.; Sirkar, K. K. Solvent Extraction with Microporous Hydrophilic and Composite Membranes. AIChE J. 1987b,33 (2), 1057-1066. Prasad, R.; Sirkar, K. K. Dispersion-Free Solvent Extraction with Microporous Hollow-Fiber Modules. AZChE J. 1988, 34 (2), 177-188. Prasad, R.; Sirkar, K. K. Hollow Fiber Solvent Extraction of Phar-
1717
maceutical Products: A Case Study. J. Membr. Sci. 1989,47, 235-259. Prasad, R.; Sirkar, K. K. Hollow Fiber Solvent Extraction: Performances and Design. J. Membr. Sci. 1990,50,153-175. Prasad, R.; Sirkar, K. K. Membrane-Based Solvent Extraction. In Membrane Handbook; Ho, W. S. Winston, Sirkar, K. K., Eds.; Van Nostrand Reinhold New York, 1992;Chapter 41. Prasad, R.; Kiani, A.; Bhave, R. R.; Sirkar, K. K. Further Studies on Solvent Extraction with Immobilized Interfaces in a Microporous Hydrophobic Membrane. J. Membr. Sci. 1986,26 (l),74-97. Prasad, R.; Frank, G. T.; Sirkar, K. K. Nondispersive Solvent Extraction Using Microporous Membranes. AIChE Symp. Ser. 1988,84(261),42-53. Skelland, A. H. P. Diffusional Mass Transfer;Wiley: New York, 1974;pp 163-164. Treybal, R. E. Liquid Extraction, 2nd ed.; McGraw-Hik New York, 1963;Chapter 11. Wilson, E. E.A Basis for Rational Design of Heat Transfer Apparatus. Trans. ASME 1915,37,47. Yun,C. H.; Guha, A. K.; Prasad, R.; Sirkar, K. K. Novel Microporous Membrane-Based Separation Processes for Pollution Control and Waste Minimization. Presented at the 10th IUCCP Symposium on Industrial Environmental Chemistry: Waste Minimization In Industrial Processes and Remediation of Hazardous Waste; Texas A&M University: College Station, TX, Mar 24,1992. Received for review November 6, 1991 Revised manuscript received March 10, 1992 Accepted April 30,1992
Peak Compression in Stepwise pH Elution with Flow Reversal in Ion Exchange Chromatography Seung Un Kim, James A. Berninger, Qiming Yu, and Nien-Hwa L. Wang* School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907
Peak compression (increase of peak concentration and reduction of peak tailing) due to a step pH change or flow reversal has been studied theoretically and experimentally. Linear and nonlinear local equilibrium models and a detailed rate model have been used to analyze the mechanisms of peak compression. The models have been tested with L-lysine data of a cation exchange system. Peak compression, which is significant when a large difference in affinities is induced for a large dilute pulse, can achieve high resolution using relatively large sorbent particles. It is shown experimentally that a dilute lysine pulse can be compressed to about 35 times its feed concentration. For multicomponent separations, compression prior to separation can give a shorter cycle time and higher product purity than linear gradient elution. Flow reversal coupled with selectivity reversal in stepwise elution allows separation to occur during both forward and reversed elution, resulting in increased column utilization. In general, optimized stepwise elution with flow reversal can give better separation than linear gradient elution. The results are useful in optimizing column design and increasing column efficiency in downstream bioprocessing. 1. Introduction Isocratic elution chromatography is rarely used for analytical and preparative purposes because of peak broadening. For separating a mixture of solutes with similar affinities, a small pulse and a long column are usually needed to achieve proper peak resolution. However, peak broadening due to mass-transfer resistances is significant for high retention solutes in isocratic elution (Snyder, 1980). The dilution causes loss of resolution in analytical chromatography and low product concentration, long cycle time, and low throughput in process scale chromatography (Jonsson, 1987). Stepwise elution, in which the solute affinity changes discontinuously in a single step, or gradient elution, in To whom correspondence should be addressed. 0888-5885/92/2631-1717$03.00/0
which the change is continuous, can effectively increase peak concentration and reduce peak tailing. The increase of peak concentration and the reduction of peak tailing is defined in this study as peak compression. The change in solute affmity is usually induced by changing pH, ionic strength, or solvent composition,depending on the specific adsorption mechanism used. For analytical chromatography, a linear gradient is usually preferred, because a gradual change in solute affinity ensures improved peak resolution. For preparative chromatography, however, stepwise elution is preferred, because it requires simpler equipment and is less costly. Flow reversal can also be used to reduce peak tailing. As shown by M y and Tondeur (19811,a mixture of small ions was separated using flow reversal, and the peak tailing was reduced. Flow reversal has long been used as a backwashing step for ion exchange in order to remove 0 1992 American Chemical Society
1718 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 Table I. References for Gradient Systems: Theoretical account for band spreading model type isotherm not considered linear ideal linear not considered ideal nonlinear not considered ideal linear no. of plates plate linear no. of plates plate linear no. of plates plate nonlinear no. of plates plate plate nonlinear no. of plates 2nd moment (axial dispersion only) moment linear lumped dispersion coeff dispersion linear dispersion nonlinear lumped dispersion coeff linear individual mass-transfer and kinet coeff rate nonlinear individual mass-transfer and kinet coeff rate
solute typea
gradient solvent solvent various general solvent salt solvent solvent salt general solvent salt salt
authors Drake (1954) Schoenmakerset al. (1978) Wankat (1990) Freiling (1955) Snyder et al. (1979) Yamamoto et al. (1983, 1987a,b) Snyder et al. (1988,1991) El Fallah and Guiochon (1991) Kang and McCoy (1989) Pitt (1976) Antia and Horvath (1989) Gibbs and Lightfootb(1986) Berninger et al.' (1991)
N/A aromatic N/A N/A N/A protein N/A alcohol protein organic acid N/A enzyme N/A "N/A indicates a reference with only theoretical work. bFeatures include sorption kinetics, axial dispersion, film mass transfer, and intraparticle diffusion. Features include aggregation and denaturation of biomolecules besides those described in note b.
impurities which are highly retained in the column prior to product elution or column regeneration (Grammont et al., 1986). There are primarily two motivations behind this work. First, an improved fundamental understanding of peak compression due to a stepwise elution can be useful for both analytical and process scale chromatography. The knowledge gained can be useful for elucidating the mechanisms in a continuous gradient system, which can be approximated as a series of step changes. Second, flow reversal and stepwise elution have potential to reduce peak tailing, increase product concentration, and reduce cycle time. The efficiency and productivity of process scale chromatography can be improved significantly with the help of models developed in this study. There are many literature examples of using stepwise or linear gradient elution to reduce peak tailing or peak dilution. Moore and Stein (1951) first developed a stepwise pH elution technique for amino acid analysis using ion exchange chroamtography. A linear gradient elution technique with changing solvent composition was first developed by Alm et al. (Alm, 1952; Alm et al., 1952), in an effort to reduce peak tailing in the analysis of a mixture of oligosaccharides in reversed-phase chromatography. Since then, stepwise or gradient elution has been a common practice for analytical chromatography. Kasche et al. (1981) also showed that pH gradient elution can improve resolution of proteins in affinity chromatography. In preparative chromatography, it was shown qualitatively that the larger the change in pH or the larger the change in solvent composition in stepwise elution, the higher the product concentration. Moreover, the product bandwidth and the cycle time decrease for proteins in hydrophobic interaction chromatography (Shaltiel, 1978). The yield of protein was quite high when stepwise pH elution was used in ion exchange chromatography (Scott et aL, 1985). In large scale production, stepwise pH elution has been successfully used in recovering amino acids from fermentation broths (Grammont et al., 1986). In the past four decades, many theories on gradient elution chromatography have been reported (Table I). Most of the gradient elution theories, however, are based on linear adsorption isotherms. At an earlier stage, only retention time was predicted by a local equilibrium model (Drake, 1954; Schoenmakers et al., 1978). Later, band broadening due to mass-transfer effects was considered through plate theories (Freiling, 1955; Snyder et al., 1979; Yamamoto et al., l983,1987a,b), moment theories (Kang and McCoy, 19891, a dispersion model (Pitt, 1976), and a detailed rate model (Gibbs and Lightfoot, 1986). Since solute concentration is usually quite low in analytical scale chromatography, the models for gradient elution with
linear isotherms work well. However, in process scale chromatography, the effects of solute competition for sorbent sites (interference effects) are important as a result of high solute concentration, and linear gradient elution theories do not apply. Since deVault's pioneering work (deVault, 1943),most of the nonlinear chromatographytheories involved isocratic elution systems either without mass-transfer effects (Helfferich and Klein, 1970; Rhee et al., 1970; Rhee and Amundson, (1982; Guiochon and Jacob, 1971; Yu and Wang, 1986; Yu, 1988; Golshan-Shirazi and Guiochon, 1988) or with mass-transfer considerations (Lee et al., 1989; Lin et al., 1989). Only recently, gradient elution theories with nonlinear isotherms were reported. Mass-transfer effects were considered through plate theories (Snyder et al., 1988,1991;El Fallah and Guiochon, 19911, a dispersion model (Antia and Horvath, 19891, and a rate model (Berninger et al., 1991). Most of the theoretical studies are focused on linear gradient elution systems, and there exists no quantitative theory for stepwise elution systems. For flow reversal systems, there have also been theoretical treatments. Bailly and Tondeur (1981) developed a nonlinear multicomponent local equilibrium theory. Yu (1988) used a multicomponent interference theory. Arve and Liapis (1988) developed a rate model to study a wash process. Gu et al. (1990) used a rate model for a displacement process with flow reversal. So far, these theories have been limited to isocratic systems. Wankat (1990) treated flow reversal for a nonisocratic system by the use of nonlinear local equilibrium theory. However, his treatment is limited to a single-component system. The detailed mechanism of peak compression in stepwise elution and flow reversal systems is not well understood. The effects of thermodynamics and mass transfer on the solute distributions in a column (column profiles) and the effluent histories cannot be predicted from the literature models. Furthermore, the experimental data reported in the literature on peak compression due to stepwise elution are insufficient for comparison with the predictions of a quantitative model. This study focuses on peak compression of amino acids due to stepwise pH elution and flow reversal in a strong cation exchanger system. An amino acid/pH/strong cation exchanger system was chosen for several reasons. Like peptides and proteins, amino acids change their charge structures and therefore their affinities in ion exchange as the solution pH changes. Primarily two forms of amino acids are present in the pH range investigated, and their affinities have been previously described as an explicit function of solution pH (Wang et al., 1989). A strong cation exchanger can maintain the same capacity over a wide pH range. Thus,the amount of amino acids adsorbed
Ind. Eng. Chem. Res., Vol. 31, No. 7,1992 1719 0
2 -
L
tn
At f
h
I
I
Figure 1. Qualitative time-distance diagram showing peak compression from At[ to Ate due to a step pH change in a h e a r isotherm system without mass-transfereffects, see text for definition of symbols. Line ABCD represents the propagation of the pH wave. In the region above the line ABCD, pH = pHf; below the line, pH = pH,. As the pH wave (ABCD) reaches the adsorbed band, it induces a speed (dZ/dt) increase and reduction of bandwidth from Lf to Le during Atr These two factors combined lead to a compressed peak.
is affected only by changes in the affinities due to the pH change and not by a change in the sorbent capacity. In this work, the mechanisms of peak compression and the effects of system parameters are studied theoretically and experimentally. A local equilibrium model with a linear isotherm is used to explain how the band of adsorbed solutes in the column contra& and changes in migrational velocity, resulting in peak compression (section 2.1). A local equilibrium model for nonlinear isotherm systems is used to study how peak tailing and peak fronting affect peak compression (section 2.2). A detailed rate model is used to study how mass-transfer effects counteract peak compression (section 2.3). The predictions of both models were compared with the amino acid data for systems undergoing flow reversal, or a step pH change, or both (sections4.1-4.4). The resulta show that the extent of peak compression in stepwise elution is greatest for dilute solutions; e.g., a large dilute feed pulse was compressed to 35 times ita feed concentration. Finally, strategies for stepwise pH elution with flow reversal for multicomponent separations are studied theoretically (section 4.5). The resulta show that peak compression leads to easier separations. Generally, a combination of stepwise elution and flow reversal can significantly improve the versatility and efficiency of process scale chromatography. 2. Theory 2.1. Peak Compression Due to a Step pH Change Analyzed by a Linear Local Equilibrium Theory. For systems with a linear isotherm and negligible mas-transfer effects (local equilibrium), the effluent peak compression due to a step pH change results from both the contraction and the acceleration of the adsorbed band. To aid in the analysis of peak compression, we define an enrichment factor (EF) as follows: Atf EF E A L
where Atf and Ate refer to the duration of pulse injection and the duration of peak elution, respectively. The subscripta "f" and -er refer to times before and after the step change (feed and effluent), respectively. Figure 1 shows peak compression due to step pH change in a linear isotherm system. When pH changes from pHf to pH,, a pH wave is generated and propagates through the column at a velocity U, As a pH wave passes through the adsorption
band during At,, it induces an increase of the band migration speed from Uf to U,. The band length in the column also changes from Lf to Le. The length of the adsorbed band in the column before and after the pH wave can be expressed as follows: Lf UfAtf, Le = UeAte (2) From eqs 1 and 2, we get E F = -Lf - ue (3) Le uf From this equation, it can be easily seen that peak compression is a result of increase of band migration speed (Ue/Uf)and contraction of the adsorption band (Lf/Le). Contribution of band contraction to peak cornpression can be further analyzed as follows. The band contraction occurs because the trailing wave of the band migrates faster than the leading wave during At,. The migration speed of the pH wave, U,, can be expressed as follows: Lf + U At Le + UeAt, g -u, = (4)
4
At,
Rearranging the above equation gives
Lf u, - Uf - =Le u g - ue
(5)
Substituting eq 5 into eq 3, we find that
The closer Ue approaches U,, the larger the band contraction (from eq 5) and the larger the EF (from eq 6). A parallel treatment can be found in a linear thermal system by Wankat (1990),where the thermal wave velocity can be infinite; thus there is no band contraction and peak compression is entirely due to the speed change. We will now d y z e the band concentration change due to affinity changes. As the pH wave travels through the band, the affinity of each component changes, and the concentrations in the mobile and stationary phases are thus adjusted to establish a new equilibrium condition. The assumption of local equilibrium requires that this reequilibrium be instantaneous. When buffer solution is strong enough to suppress any pH change in the mobile phase due to H+ exchange, U can be assumed to be the same as interstitial velocity do.Therefore, according to the following continuity equation, the stationary-phase concentration remains the same after the pH wave passes through.
where & and Cl,are the total solute concentrations in stationary and mobile phases, respectively (based on per packed bed volume), and x and y refer to mole fractions of a solute in mobile and stationary phases, respectively. Ayi = 0 or AC: = 0 for U , = Uo (7b) Equation 7 will also be used in the nonlinear, multicomponent local equilibrium theory in the next section. The change in affinity for a binary system is defined as . %2,f
where the separation factor, ai,ref, is
.
1720 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
and it depends on the ambient pH as follows (Wang et al., 1989): kl k2i(lO(PH-PKar)) = 1 + lo(pH-pK.,) (8c)
+
where kl and k2 are the a values at very low and high pH, respectively. The average valence, z,, of an amino acid also depends on the pH as follows (Wang et al., 1989): 21 ikl i + 27, ik2 i( 10(pH-pKai)) z,i = (8d) 21 i
+
22 i(lO‘PH-PKai))
where zli and z 2 iare the valence numbers at very low and high pH, respectively. From eqs 7b and 8a,b, we can get
Since AtfrlP = Ateqe,from eqs 1and 9, EF becomes as follows:
From eq 10, when is less than unity, i.e., a12,eis less than a1,2f(eq 8a), EF is greater than unity, and the smaller the 8, the higher the product concentration. In the limit, as B approaches zero, EF approaches l/xlf. Therefore, peak compression is greater for a more dilute feed. Since mass-transfer resistances and nonlinear isotherm effects are not considered here, eqs 6 and 10 represent upper estimates for EF. 2.2. Nonlinear Local Equilibrium Theory for Stepwise pH Elution with Flow Reversal. The degree of peak compression due to step pH change is affected by nonlinear isotherm effects such as peak tailing, peak fronting (the peak with a diffuse front and a sharp tail), and displacement effecta in nonlinear systems. Since the nonlinear isotherm effects are changed upon flow reversal, peak compression is also affected by flow reversal. In this section, we expand the linear local equilibrium analysis to nonlinear local equilibrium analysis to treat the systems with step pH change and flow reversal. The model developed in this section can be applied to multicomponent systems with interference effecta, while nonlinear local equilibrium analysis for a single-component system has been shown by Wankat (1990) for step changes with flow reversal. The nonlinear local equilibrium model considered in this study is an extension of the interference theory (Helfferich and Klein, 1970). Some of the major assumptions of this theory include negligible mass-transfer effects, constant separation factors, and coherence (where the concentration waves of different components are in phase with each other). The details of this theory for isocratic systems are explained elsewhere (Yu and Wang, 1986, Yu et al., 1987; Yu, 1988). The key variables in this theory are defined as follows: z
Z/L
(114
where z is the axial distance Z normalized by column length L and T i s a dimensionless time. Normally, integration in the interference theory is done in T, because it simplifies mathematical treatment.
At the time of flow reversal, flow in the entire column is reversed simultaneously. However, a constant T does not correspond to a constant real time, t as there is a spatial dependence on Z/Up Therefore, flow reversal cannot be considered in the T time frame. To avoid spatial dependence of T, the dimensionless time at the column inlet ( z = 0), To,is used for treatment of flow reversal. T
c,, uo
=-
0 -
GI, yt
(12)
At the instant of flow reversal, the concentration profiles in the mobile and stationary phases at a given time (To) remain the same and are used as the initial conditions for the remainder of the simulation. Following flow reversal, the displacement sequence is also reversed. Therefore, a sharp wave becomes diffuse and a diffuse wave gradually sharpens. A step pH change introduces a pH wave that affects the affinity of each component, and may change the affinity sequence. The concentrations in the mobile phase are thus changed to establish a new local equilibrium condition and are calculated from the new separation factors (eq 8) and the solid-phase concentrations. As mentioned previously, the solid-phase concentration is unchanged for U,= U,,. As a result of the affinity changes, sometimes the assumption of coherence no longer holds. In such a case, a wave can split into a set of new, coherent waves. In addition, a sharp wave can become diffuseand a diffuse wave can sharpen due to a change in the affinity sequence. For the local equilibrium simulations in this study, column profiles and effluent histories are shown in To.A corresponding dimensionless pulse size for a solute i is defined as follows: (13) where At is the duration of the pulse in time unit. 2.3. Rate Model (VERSE-LC) for Stepwise pH Elution with Flow Reversal. To consider band-broadening effects of mass transfer, a rate equation model must be used. A rigorous rate model which accounts for reaction, equilibrium, and maas-transfer effects, which include axial dispersion, film mass transfer, and intraparticle diffusion, have been developed and named the VErsatile ReactionSEparation Model for Liquid Chromatography (VERSELC) (Whitley et al., 1991; Van Cott et al., 1991; Beminger et al., 1991). In this study, VERSELC has been expanded to treat systems with stepwise elution and flow reversal. Since not all of the features available in VERSE-LC are considered in this work, only certain relevant concepts and some new features are presented here. Mobile Phase. For forward flow, mass balance leads to
-a c -b i ae (144
where 0 is a dimensionless time tUo/L, E b i , is axial dispersion coefficient, kfi is film mass-transfer coefficient, and cb i and cpj are respectively the concentrations in the mobile and pore phases normalized by the maximum inlet concentration, C, i. [ is the radial distance within a particle r normalized by particle radius R, and eb and tp are interparticle and intraparticle void fractions, respectively. is used with a negative For reversed flow, the term acb
Ind. Eng. Chem. Res., Vol. 31, No.7, 1992 1721 sign. The boundary and initial conditions are
LO,
Table 11. Parameters for Model Simulationsa paramete9 Na+ Glu LYS 1.77 73.8C kl 1.0 0.04 0.66 kZ 1.0 1.0 1.0 2.0 21 1.0 1.0 1.0 22 Ep (cmz/min) 1.2 X lo-" 1.95 X 1.95 X k, (cm/min) 7.27 X lo-' 6.43 X lo-' 6.43 X lo-'
reverse flow
where cf is the dimensionless feed concentration, which can be a function of time. (0,
forward flow
Hie
~
57.18' 1.69 2.0 1.0 1.95 x IOd 6.43 X 10-l
C I , = 2.3 equiv/L(bed);CN,+ = 0.2 M for presaturant, feed, and eluent; t b = 0.35; tp = 0.65;D = 1.0 cm; R = 2.5 X cm unlw specified otherwise. *The values of kl,kz, 21, and 2 2 were taken from Wang et al. (1989);Ebwaa estimated with the correlation by Chung and Wen (1968);Ep waa fitted from the data in Figure 6 (Lye peak of system C); kf waa estimated with the correlation by Wilson and Geankoplis (1966). 'Distribution coefficient of Na+ ion is calculated for system C and assumed to be constant (4.03). Table 111. Operating Parameters for Experimentsa A B C D E F system ~ _ _ _ _ _ Presaturant 2.0 3.42 3.5 3.5 3.5 PH 3.5
(154 where Ep is effective intraparticle diffusivity and is resin capacity based on per solid volume (excluding pore volumes).
cT
5 = 0:
(mL) AT0 Lyl
3.5 0.0 0.005 153 0.107
Feed 2.0 3.42 0.0 0.01 0.0005 0.01 510 10.8 0.039 0.053
PH time'(min)
5.0 153
6.4 510
0.193
0.014
PH Colu (M)
,C
flOwd
B
e=o
(M)
Vp
cpi
= c p i(0,O
(15d)
In the case of flow reversal, only the mobile phase (eq 14) is affected by the direction of convection. The application of a gradient system involves appropriate definition of cfi(e). In eq 15, T c i is the change in the solidphase concentration (due to adsorption) with respect to time. In the adsorption process is at local equilibrium, Tc is expressed by
whe!e E is the solid-phase concentration Cp normalized by Cp yhe dCpi/acpl term takes solute competition into consideration, and 1s calculated from an appropriate multicomponent adsorption isotherm expression. In this work, the isotherm used is the expression for multicomponent constant separation factor systems.
2
ajj,efCp j j=l
The separation factor (cqref) is a function of the pH (eq &), to allow for affiity dependence on pH, which is often observed with biochemical species. To simulate a pH wave, H+ is treated as an inert solute. This approach is valid when the buffering capacity of the solution is sufficient to suppress any pH change due to H+ ion exchange. The model equations are solved by orthogonal collocation of f i t e elements, which is a common numerical solution method (Villadaen and Michaelsen, 1978; Finlayaon, 1980, Baker, 1983). The details on the solutions of the VERSELC model are explained by Berninger et al. (1991).
+
+
3.5 0.01 0.01 40 0.056
3.5 0.01 0.01 40
3.5 0.01 0.01 40
0.056
0.056
+
3.5 65
-
5.0 65
5.0 65
1.0
1.0
0.193 0.193
Eluentb 3.42 65
+
-
"In all cases, C,,+ = 0.2 M,F = 1.0 mL/min, L = 7.3 cm, D = 1.0 cm, except system C, where F = 0.27 mL/min, L = 2.1 cm. bIsocraticelution with forward flow is wed between the end of the feed pulse and step pH change and/or flow reversal. 'Time when step pH change and/or flow reversal is applied. dFlow direction at the time of step change: + indicates forward flow; - indicates reversed flow.
In implementing the orthogonal collocation of finite elements in this study, 50 elements, 4 axial collocation points, and 2 particle collocation points are sufficient to produce converged solutions in a few hours of CPU time on a Sun workstation (SPARCstation 2). The adsorption and mass-transfer parameters used by VERSE-LC for simulations are shown in Table 11. Equilibrium isotherm parameters of amino acids are obtained from Wang et al. (1989). The separation factors of basic amino acids, Lys and His, depend on not only the pH but also the distribution coefficient of Na+ (Wang et al., 1989). In this study, the distribution coefficient of Na+ is calculated for system C and used as a constant for all casea. The retention times of Lys predicted by this method are in excellent agreement with experimental data. The void fractions, $, and cp,. are measured experimentally as described in the Experimental Section. The axial dispersion coefficient, Eb,is determined by a standard correlation developed by C h u g and Wen (19681, and the effective intraparticle diffusivity, Ep,is estimated by fitting one of the chromatograms obtained experimentally. The film mass-transfer coefficient, kf, is obtained by the correlation proposed by Wilson and Geankoplis (1966). 3. Experimental Section Six experimental systems were studied here (Table In). Systems A and B demonstrate compression of a lysine peak due to a step pH change. Systems C-F show the effects of flow reversal (system D), a step pH change (system E), or both (system F), on isocratic elution of a mixture of
1722 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
lysine and glutamic acid (system C), so that the contributions to peak compression from the pH change and flow reversal can be isolated. The amino acids, L-glutamic acid (Glu) and L-lysine (Lys), were purchased from Chemical Dynamics Corporation (South Plainfield, NJ) and were used as received. The buffer solutions were prepared from sodium citrate, purchased from Fisher Scientific (Fair Lawn, NJ), and were adjusted to the desired pH with hydrochloric acid. The pH was measured with an Orion pH meter, Model 901 (Cambridge, MA). The ion exchange resin used was AG50W-X8, a strongly acidic gel-type cation exchanger (2ocMoomesh), purchased from Bio-Rad Laboratories (Richmond, CA). It was received in H+ form and was converted to Na+ form with 1.0 N NaOH. A 1.0-cm (i.d.) glass column, purchased from Pharmacia (Uppsala, Sweden), was loaded with a slurry of the ion exchange min. Deionized water was then pumped through the packed column using a dual piston pump (Spectroflow 400,from Kratos Analytical, Ramsey, NJ), at a flow rate of 1.0 mL/min for 1h. To preequilibrate the column, a pH buffer was pumped through the column at a flow rate of 1.0 mL/min for at least 1 h. Since the feed pulses were large (in the range of 40-510 mL), a sample injector was not used. Instead, sample solutions were pumped directly from reservoirs into the column. Output from the column was collected in 5-mL samples with a fraction collector (Foxy, Model 220 from ISCO, Inc., Lincoln, NE). Each sample was analyzed using a ninhydrin derivatization method, which was adapted from Knott et al. (1981). In this procedure, ninhydrin reacta with an amino group to form Ruhmann’s purple, which strongly absorbs at 570 and 440 nm, and the concentration of amino acid is determined from the absorbance. The effluent history of system C was determined using a direct ninhydrin post-column derivatization technique. The effluent was mixed with ninhydrin solution in an FPLC mixer (Pharmacia), and the derivatization reaction was allowed to occur in a heated reactor (PCRS520, Kratos Analytical, Ramsey, NJ). A low flow rate, 0.27 mL/min, was used to ensure a complete reaction within the reactor. The solution was monitored at 440 nm with an HPLC detector (Spectroflow773 from Kratm, NJ). The interparticle void fraction, +, = 0.35, was estimated from the retention time of Blue Dextran (MW 2 X 10% purchased from Sigma (St. Louis, MO). A pulse of Blue Dextran (0.1 mL, 2% w/v, aqueous) was passed through the column a t a flow rate of 0.5 mL/min, and the absorbance of the effluent was monitored at 300 nm. The intraparticle void fraction, ep = 0.65, was determined from the retention time of a pulse of acetone (0.1 mL, 10% v/v, aqueous), which was eluted at 0.1 mL/min and monitored at 300 nm. 4. Results and Discussion 4.1. Peak Compression and Shape Change Due to
Stepwise pH Elution. Compression of two Lys pulses in stepwise elution is shown in Figure 2. In each of these systems (A and B), a column is preequilibrated at a low pH and a pulse injection is immediately followed by elution at a high pH. System B has a smaller 8, q f ,and AToLys than system A. As shown in Table IV, the Lys pulse was compressed and concentrated about 5 times (system A) and 35 times (system B) its feed concentration. Both the VERSE-LC and local equilibrium theories predict very well the retention time and peak shape for the large pulse (system A), but only VERSELC gives an accurate effluent history for the small pulse (system B). As expected from
0
LYS ( +++ FEED=SmM,l53mL) LYS (.....FEED=0.5mM,SlOmL)
- VERSE-LC
,;
__._ LOCAL . EQM.
0.02-
C[Ml
0.01
-
-0I
1
Table IV. E P Results system expt A 4.66 B 34.6 C 0.29 D 0.712 E 2.49 F 3.49*
I
local equilib 4.52 57.6 0.76 0.912 3.99 3.99
I
VERSE-LC 4.51 33.8 0.36 0.731 2.33 3.40
EF is calculated from peak concentration. bExtrapolatedfrom peak base width and mass balance.
eq 10, the smaller 8 and xu result in a higher EF for system B. However, system B has a small pulse size (AToLys= 0.019) and is more subject to band broadening due to mass-transfer resistances. Consequently, ita EF is not as high as predicted from eq 10. In order to demonstrate the contraction and concentration of the Lys band, the column profiles a t different times are shown in Figure 3a (local equilibrium simulation of system A) and Figure 3b (VERSE-LC simulation of system B). Each profile represents the solute distribution within the column at a given time. As the pH wave propagates through the Lys band, the concentration in the band starts to increase according to a new equilibrium relation. This concentration step results in two plateaus divided by the pH wave (see profile 4 in Figure 3a and profde 2 in Figure 3b). In system A, the band immediately after the passing of the pH wave is 94% of that before the pH wave (see Figure 3a, profile 3, Lf= 0.631 and profile 5,Le = 0.596). For this case, At, is very small and the pH wave velocity (Up)is much larger than the Lys band veand U,J. The contributions of band contraction locities (Uf to peak compression is relatively small (eq 5). The peak compression is mainly due to a large change in the Lys band velocity (Figure 3a). Figure 3b shows the speading due to mass-transfer resistances after the pH wave passes. The spreading causes dilution of the Lys band to ita final concentration, which is roughly half of its maximum concentration immediately following the pH wave. Peak compression due to nonlinear isotherm effects becomes significant as the solute concentration increases. Nonlinear isotherm effecta on peak compression are shown in the local equilibrium simulations in Figure 4. The
Ind. Eng. Chem. Res., Vol. 31,No. 7, 1992 1723
Bb
\\
z
x
Figure 3. (a, left) Local equilibrium simulation of column dynamics of stepwise pH elution of Lye (system A): -, column profiles at To= 0.78 (I), 1.56 (2), 2.37 (3), 2.40 (4), 2.43 (5), 2.64 (61, and 3.10 (7); -, To-z diagram; -(thick), effluent history of Lys at z = 1.0. All parameters are listed in Tables I1 and 111. (b, right) VERSE-LC simulation of column profiles of Lys at TO= 7.77 (l), 7.78 (2), 7.79 (3), 7.80 (4), 7.93 (5), 8.08 (6), and 8.53 (7) for stepwise pH elution of Lys, system B; -(thick), effluent history of Lys. All parameters are listed in Tables I1 and 111. Table V. Simulation Parameters' for Figures 4 and 5
B 1.0 0.089 0.089 0.089 0.023 0.015 0.015 0.015
PH, 2.0 3.5 3.5 3.5 4.5 6.4 6.4 6.4
a,
VP (mL)
44.7 4.0 4.0 4.0 1.0 0.66 0.66 0.66
300.0 300.0 2000.0 200.0 300.0 300.0 2000.0 200.0
CrLp = 5.0 mM AT0,L Figure 5a-2 0.227 4a, 5b-1 0.1512 0.227 0.227
5e-1 4b, 5b-2 4c, 5b-3
0.1512
5e-2
CfL, = 0.5 mM
0.0227 0.1512
Figure 5a-1 5~-1 5d-1
0.0227 0.0227 0.1512
5~-2 5c-3 5d-2
AT0 Lys
'See also Table I1 for equilibrium and mass-transfer coefficients. pHf = 2.0, at = 44.7; F = 1.0 mL/min, L = 7.3 cm.
simulation parameters are listed in Table V. In these examples, a pulse containing component 1(Lys) is injected into a column which is presaturated with component 2 (Na+),where alga= 44.7. Immediately following the pulse injection, the eluent solution is changed to the new pH. When ( Y ~ ,>~ 1 , ~ (0 = 0.089),the affinity of Lys is larger than that of Na+ during elution. A trailing diffuse wave is generated, resulting in significant tailing of the Lys peak (Figure 4a). When alg,e= 1(B = 0.023),Lys and Na+ have the same affinity. Both waves of the eluted peak are sharp, resulting in a symmetric peak (Figure 4b). When < 1 (B = 0.015),the effluent peak Bows peak fronting instead of peak tailing (Figure 4c). As can be seen in eq 10, EF is limited by l//3and l/xlf. The effects of j3 and xlf on EF are shown in Figure 5, and the parameters for these simulations are listed in Table V. The systems of Figure 5 are similar to those of Figure 4 except that several different loading factors are used to show thermodynamic effects on a large concentrated pulse (ATo~ys = 0.23 and 0.15) and mass-transfer effects on a dilute pulse (AToLy,= 0.023). Figure 5a shows isocratic elution (j3 = 1.0) for two different feed concentrations. The more dilute pulse (peak 2)elutes later and has more spreading due to mass-transfer resistances. Mass-transfer effects are clearly shown by comparing the local equilibrium predictions with the VERSELC predictions. In Figure 5b, the effects of a step pH change for the more concentrated pulse (peak 1 of Figure 5a) are shown. As expected from eq 10,a smaller /3 gives a higher EF and a shorter cycle time. As /3 approaches zero, EF approaches l/xla, and the peak emerges immediately following the pH wave (not shown). In each
6
n
f f 4 2
I
0
1
0.6 0
n
i
/ I
I
i
i o
6
7
T O
Figure 4. Effect of eluent affinity (al,z,e)on peak shape. Local equilibrium simulations of stepwise pH elution of Lye: -, effluent histories; -(thick), To-zdiagrams. The arrows indicate the end of feed pulse as well as the time of step p H change. All parameters are listed in Table V.
case, the local equilibrium predictions of EF are acceptable
because of the high loading. Because of nonlinearity of the adsorption isotherm at this concentration, peak 1 shows tailing, whereas peak 3 shows fronting as explained in Figure 4.
I
1724 Ind. Eng. Chem. Res., Vol. 31, No. 7,1992 0.04 -0 1000
-0 30-1
EF
20
-
4doo
3doo
2000
I
I
400
-04u 7.000 (d)
'
I
I
I
2100
2200
2300
2400
Feed = 0.5mM. 3MhnL AT,
n
*-..
C[Ml 0.02
7w
--
1 A m 300
600
500
I
I
-0
__---
-0 7
360
= 0.023
1
I
I
400
500
600
i
J 1
1. j3 -7069 2. p = 0.023 3. I3 = 0.015
I
I
-0
I
700
I
I
I
200
400
600
t
.-
.O
200
-
LYS, ISOCRATIC ELUTION without FLOW REVERSAL VERSE-LC LOCAL EQM.
+
0.03
1. =0.089 2. = 0.023 3. =0.015
10 -
GLU LYS, ISOCRATIC ELUTION with FLOW REVERSAL
A
*
Fffid = S m M , 3oomL, ATTs. = 0.23
(b)
4
[min]
1
I
I
300
400
I
I
500
600
EF
thnl 0.
Figure 6. Effects of affinity change (8) on peak height and peak shape: (a) isocratic; (b) concentrated input; (c) large, dilute input; (d) small dilute input; (e) small,concentrated input -, VERSELC; - - -,local equilibrium. The arrows indicate the breakthrough time of the pH wave. Each peak representa the simulated effluent history of stepwise pH elution of Lye with different simulation parameters. Simulation parameters are listed in Table V.
As expected from eq 10, a large dilute pulse shows greater peak compreseion than a small concentrated pulse. For a relatively large pulse (ATOL > OJ), a lower feed concentration results in a higher I&for the same values of fl (see Figure 5b,c). However, reducing AToLysto 0.023 by reducing the volume of the pulse at a constant concentration introduces significant band broadening due to mass-transfer effects (Figure 5d). Thus,for a low loading system (AToi= 0.023),decreasing fl from 0,089 (peak 1) to 0.023 (peak 2) and to 0.015 (peak 3)did not significantly increase EF. In general, a higher feed concentration results in more pronounced nonlinear effects; the peaks in Figure 5e are more asymmetric than those in F i 6c with a lower feed concentration but with the same column loading (AToLys = 0.15). These figures clearly show that peak compression is more effective for a more dilute feed, for which nonlinear isotherm effects are less important; peak compression is also more effective for a larger pulse, for which masstransfer effects are less significant. 4.2. Flow Reversal. In this and the following sections, the elution of a mixture of Glu and Lys is considered. The mixture was eluted isocratically (pH = 3.42)without flow reversal (system C,Figure 6a). At this pH, Glu has a very low affinity, and is eluted quickly. In Figures 6a and 7b, on the right upper comer of the Glu peak, a notch is observed because the total concentration of the eluent (0.2 M)is different from that of the feed solution (0.22 M); a concentration wave is generated as soon as elution start$ and it propagates through the column at the interstitial velocity. Since the concentration wave propagates faster than the trailing wave of Glu band, a latter part of the Glu band experiences the new total concentration, while the dimensionless composition of the Glu band remains unchanged. This decrease in total concentration results in
I
.
.
--nm
.
.
.
.
.
mend
3.0
1.o
0.5
0.
Z 7
1.0
1.o
To 2.0
3 .Q
\ \
,
0.5
0.
$
'
I
1 .o
2
Figure 6. (a, top) Comparison of simulated effluent histories of Lys and Glu with experimental data for isocratic elution (syeteme C and D).All parameters are listed in Tables I1 and III. (b, middle) Local equilibrium simulation of column dynamics of elution with reversed flow for a mixture of Lys and Glu (system D): -, column profiles of Lye at different 2';s; -.,To-zdiagram; -(thick), effluent histories of Lye at z = 0.0 and Glu at z 1.0. All parameters are listed in Tables I1 and 111. (c, bottom) VERSE-LC simulation of column dynamics of reversed flow elution of a mixture of Lys and Glu (system D): -, column profilee of Lye at different 2';s; -(thick), effluent btoriea of Lys at z = 0.0 and Glu at z = 1.0. All parameters are listed in Tables I1 and 111.
-
Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 1725 0.04
n
n
I,
I,
A
j j Ij
-
0.03
GLU LYS,pH STEPWISEELUTION with m w REVERSAL LYS.pH STEPWISEELUTION without m w REVERSAL VERSE-LC
. . _ - -LOCAL _ EQM.
C[M] 0.02
0.01
-0 7
-0
1
I
t
EF
2.0 "O
P.
I
400
200
Mx)
[min]
i \ " " \ " " 9.
\a
9-
z
!E P.
Figure 7. (a, top) Comparison of simulated effluent histories of Lys and Glu and experimental data for stepwise pH elution (systems E and F). All parameters are listed in Tables I1 and 111. (b, middle) Local equilibrium model simulation of the column dynamics of stepwise pH elution with reversed flow for a mixture of Lye and Glu (system F): -, column profilea of Lya at To= 0.34 (l), 0.69 (2), 1.07 (3),1.15 (4), and 1.30 (5);-, To- diagram; -(thick), effluent historim of Lye at z = 0.0 and Glu at z = 1.0. All parameters are listed in Tables I1 and 111. (c, bottom) VERSE-LC simulation of the column dynamics of stepwise pH elution with reversed flow for a mixture of Lys and Glu (system F): -, column profiles of Lys at TO= 0.34 (l),0.69 (2), 1.07 (3),1.13 (49, 1.15 (4),1.22 (4% and 1.38 (6); To-z diagram; -(thick), effluent histories of Lys at z = 0.0 and Glu at z = 1.0. All parameters are listed in Tables I1 and 111. e-,
the notch in the glutamic acid peak. Because of the low retention time of Glu, band spreading is minimal and the local equilibrium theory works very well. Lys, however, has a much higher affinity and is considerably slower to elute. Comparing the data with the predictions from the local equilibrium model and VERSE-LC, we can see that the spreading of the Lys band is a result of both thermodynamic effects and mass-transfer effects. As shown in Figure 5a, the experimental data show more tailing than is predicted by VERSE-LC. This additional tailing is likely due to extra-column mixing in the reaction vessel during the derivatization process. The effects of flow reversal on the mixture are shown in Figure 6a (system D). After Glu is completely eluted, the direction of flow is reversed. In this system, Lys remains near the column inlet after Glu is eluted, so the use of flow reversal significantly shortens the total distance that Lys travels. As a result, band broadening is reduced and the effluent concentration is higher than that in unidirectional elution (system C). The dynamics of this flow reversal system are shown in Figure 6b,c. Initially, a high-affmity solute (Lys) displaces a low-affimity presaturant (Na+),and a sharp wave resulta. Following the pulse input, Na' displaces Lye, resulting in a diffuse wave. When the direction of flow is reversed, the displacement sequence is also reversed, and the sharp wave gradually becomes diffuse while the diffuse wave gradually sharpens,as shown in the To-zdiagram of Figure 6b. The flat top portion of the peak remains because of a shorter migration distance, resulting in less band broadening due to nonlinear isotherm effecta. Also, since the affinity of the solute does not change, there is neither a velocity change nor a peak compression, therefore EF < 1. The corresponding VERSE-LC simulation also shows a more concentrated peak than isocratic elution because of a shorter migration distance, and thus less spreading due to mass-transfer effects. The profile shapes are similar to those shown by the local equilibrium model, but are not as sharp because of mass-transfer effects. In general, flow reversal gives a shorter cycle time and a higher effluent concentration if the desired solute is highly retained. This approach is particularly useful when a small feed size is used to separate a mixture of widely different affinities, for which the desired solute is retained near the inlet of the column after being separated from other solutes. Flow reversal is also useful for the regeneration of a sorbent to remove highly retained impurities. 4.3. Stepwise pH Elution. For the mixture of Glu and Lys, a single step pH change was used to compress the Lys peak, and the resulting effluent histories are shown in Figure 7a (system E). After Glu was eluted from the column, the eluent pH was changed to pH 5.0. At this high pH, Lys is far leas preferred than Na+ (a= 0.7, eq &), and thus the diffuse tailing wave of Lys is sharpened. In addition, the mobile-phase concentration and migration velocity of Lys significantly increase. By this method, the cycle time is reduced and the effluent Lys is significantly concentrated. 4.4. Stepwise pH Elution with Flow Reversal. Finally, stepwise pH elution is applied with flow reversal for the mixture of Glu and Lys. The result of the combined effects on effluent history are shown in Figure 7a (system F). After it is separated from Glu, the Lys peak is concentrated and accelerated by the pH change and quickly eluted by the reversed flow. As shown in Figure 7b, the diffuee wave of the flow reversal system (Figure 6b) is compressed to a sharp wave by the pH change. As the pH wave passes the Lys band, the band concentration
1726 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992 Table VI. Simulation Parametersa for Figures 9-12 Figure pH, V, (mL) timeb (min) flo+ 700 3300 + 9a 3.85 700 2000 + 3.85 9b 700 700 + 9c 3.85 700 26W + 1Oa 3.85d 700 130e + 10b 3.85d 1oc 3.85d 700 650' + lla 3.5 700 700 + llb 5.5 700 700 + llc' 5.5 1500 1500 + 700 3300 12a 3.85 12b 5.5 700 3300 12c 5.5 1400 3300 12d 5.5 1400 2300 2100 2100 + 12# 3.6 5.5 2275 See also Table 11. In all cases, pHold = 2.0; F = 1.0 mL/min; L = 30.0 cm; D = 1.0 cm. *Time when step change or/and flow reversal is applied. 'Flow direction at the time of step change; + indicates forward flow; - indicates reversed flow. Final pH value for linear gradient. e Duration time of linear gradient after the end and 5.0 X cm. S T w o step of the feed pulse. f R = 2.5 X changes.
ai.NI*
I
1
I
I
I
I
3
4
5
6
PH Figure 8. Separation factors (ui,~.,+)of Lys and His as a function of pH (Wang et al., 1989). The distribution coefficient of Na+ is assumed constant (=8.03) in the calculation.
:I
gradually increases as shown in Figure 7c (see profiles 3, 4-, and 4). Because of spreading due to mass-transfer resistances, profile 4- does not have the two distinct plateaus as in profile 4, Figure 3a.
Since mass-transfer effects are not considered, the local equilibrium prediction of EF for system F is the same as that for system E (Figure 7a). The VERSE-LC predictions show that the combined effects of flow reversal and stepwise pH elution gave a higher EF than a pH change alone. This conclusion is not obvious from the data because of experimental errors resulting from fraction collection. The concentration of the Lys peak was nearly quadrupled, while the cycle time was reduced by nearly 80% compared to the isocratic elution case (system C). 4.5. Strategies in Stepwise pH Elution with Flow Reversal. Several key questions need to be addressed for the impact of peak compression on resolution of two adjacent peaks: (1) When should the step pH change be applied? (2) How much should the step change be? (3) How does stepwise pH elution compare to linear gradient elution? An example of Lys and His separation (Table VI) is studied here to address these questions. The separation factors of these two amino acids against Na+ are shown as a function of pH in Figure 8 (Wang et al., 1989). These two amino acids have similar affinities and therefore are more difficult to separate than the Glu-Lys system. This system is also more complex than the Glu-Lys case because selectivity reversal between Lys and His occurs at pH 3.85. In addressing the first question, we choose a low pH (pH 2) for sample loading and separation, followed by a high pH (pH 3.85) for peak compression. Lys affinity is higher than that of His at pH 2; the large affinity difference during loading and elution helps separation of the bands before peak compression. To avoid any possibility of remixing, we choose pH 3.85 for peak compression. The step change to pH 3.85 is applied at three different times in Figure 9a-c. In Figure 9a, the step pH change is applied immediately after the two bands are separated in the column (t = 3300 min) according to local equilibrium simulations (not shown). The two peaks are separated first and then Compressed using the pH change. The separation of the two peaks takes most of the cycle time. Displacement of His by Lys leads to a sharp boundary between the two peaks and enhances His peak concentration. Both peaks show tailing because Na+ has a lower affinity than
1
2
H
l6
EF
h"
(c)mmin
I 0
j
I I
I
1
lK0
my)
Moo
1 [rmnl
4Mo
-
Figure 9. Comparison of stepwise pH elution systems with three different times of step change (pH 2 3.85): -, VERSE-LCsimulation of effluent history of a mixture of Lys and His; - - -,breakthrough of pH wave. L and H represent Lye and His, respectively. All simulation parameters are listed in Tables I1 and VI.
both in this pH range. In Figure 9b, the step pH change is applied before the two bands are separated (t = 2000 min). The two peaks are not as well separated as in Figure 9a. The His peak, however, is more compressed because His is concentrated by displacement during loading and the trailing diffuse wave did not spread before peak compression. In Figure 9c, the step change is applied immediately after the sample injection (t = 700 min). The His band is compressed more than in the two previous cases,
Ind. Eng. Chem. Res., Vol. 31, No. 7,1992 1727
ma
0
4am
I \I \ 0
loo0
I MbO
ma
o ( 0
4ml
2s
.
. I
I zay)
loo0
,
2s
m L Irn,"]
-
- -
4am
-,
loo0 1Irnl"i
i
I
Moo
m
-
Figure 10. Comparison of pH linear gradient elution systems with three different gradient slopes (pH 2 3.85): -, VERSE-LC simulation of the effluent history of a mixture of Lys and His; - - -, effluent pH history; .-,in (c), VERSE-LC simulation of effluent history of His in the absence of Lys. All simulation parameters are listed in Tables I1 and VI.
Figure 11. Comparison of stepwise pH elution systems with two different pH steps: (a) pH 2 3.5, 700-mL feed; (b) pH 2 5.5, 700-mL feed; (c) pH 2 5.5, 1500-mL feed, R = 2.5 X 10" cm; (d) pH 2 5.5, 1500-mL feed, R = 5.0 X cm. -, VERSE-LC simulation of effluent history of a mixture of Lys and His; --,local equilibrium model simulation; - - -, effluent pH history.
but the two bands do not have sufficient time to separate before the compression. In Figure loa, a linear gradient is applied immediately after the sample injection, and the two peaks are completely separated. Compared to Figure 9a, the cycle time is shorter, but the two peaks are not as compressed because they elute before the pH reaches 3.85. In Figure 10b,c steeper linear gradients are applied after the sample injection. The cycle times are further reduced and the two peaks are more compressed as the gradient slope increases. The peak compression in Figure 1Oc is slightly higher, but the cycle time is only about 50% of that of Figure 9 a This example clearly shows the advantage of linear gradient elution over that in Figure 9a, in which the separation of the two bands is slow because of the slow migration and spreading of the diffuse waves. Gradient elution, Figure lOc, allows separation in a shorter time because the two bands accelerate and the two diffuse waves are sharpened by the gradient, resulting in easier separation. Furthermore, the displacement of His by Lys also enhances His peak Compression (compare His peak in the absence of Lys with His peak in a mixture in Figure 104. In addressing the second question on the size of the pH step, we examine two different step pH changes for the case in Figure 9c. Local equilibrium simulations are compared to VERSE-LC simulations in Figure 11. In Figure lla, immediately after the sample injection a smaller step pH change (from pH 2 to pH 3.5) is applied in order to compress the Lys and His bands. Because Lys still has a higher affinity than His at pH 3.5, the two peaks are
better separated than in Figure 9c. As expected from eq 10, a smaller pH change results in a smaller peak compression than in Figure 9c. In Figure l l a , the two bands are compressed first and then separated. In contrast, in Figure 9a, the two bands are separated and then compressed; in Figure lob, the two bands are simultaneously compressed and separated in a linear pH gradient. Comparison of these three cases show that compression before separation (Figure l l a ) can give a shorter cycle time and higher product purity than the latter two cases. For Figure l l b , a larger step pH change (from pH 2 to pH 5.5) is applied, resulting in a larger peak compression. Once compressed, the two bands separate quickly. However, because the Lys/His selectivity is reversed at pH 5.5, the Lys peak elutes before the His peak. In this case, the column length is sufficiently long to allow the Lye peak to overtake the His peak and to be totally separated. Because the two bands are compressed first and then separated, this case gives a larger peak compression and a shorter cycle time than in Figure 9a. As long as there is some difference in their affinities after the pH change, the increase in migrational speeds and sharpening of the diffuse waves allow the separation to be completed in a short time. As expected from the large step pH change, peak compression is larger than in Figure 9. The gap between the two peaks suggests that the throughput can be further improved if a larger sample is applied. In Figure llc, a feed of 1500 mL, instead of 700 mL, is used. This case gives the best resolution, peak concentration, and throughput.
-
1728 Ind. Eng. Chem. Res., Vol. 31, No. 7, 1992
The local equilibrium predictions in Figure 11 agree closely with those of VERSE-LC, indicating minimal mass-transfer effeda despite of the large particle sizes. As shown in Figure llc, the two peaks are very well resolved using large sorbent particles (R = 25 and 50 pm), which give resolutions similar to those of the local equilibrium cases. This result suggests that peak compression can help achieve high resolutions using relatively large sorbent particles and thus decrease sorbent costa. A combination of step pH change with flow reversal can further improve peak resolution for the case in Figure 9a. In Figure 12a, the two bands are separated first and then compressed and eluted with reversed flow. The Lys peak in this case elutes before the His peak and is slightly more concentrated than in Figure 9a. Both waves of each peak are diffuse because during loading and separation, elution by Na+ muses tailing,while during reversed flow, the sharp waves also gradually become diffuse, resulting in spreading of the leading waves. For the case of Figure 12a, if a larger step pH change (to pH 5.5) is applied, the two peaks can be further compressed as shown in Figure 12b. In addition, because of the selectivity reversal,lhe two peaks are more separated, indicating that a higher loading can be used to improve throughput. For Figure 12c, the feed size is doubled and the two peaks are more compreased because during loading and one-way elution, His is displaced by Lys, resulting in peak concentration of His. During the reversed flow, His now displaces Lys, resulting in peak concentration of Lys. The separation between the two peaks in Figure 12c suggests the step change and flow reversal can be applied earlier. In Figure 12d, the step change is applied at t = 2300 min. This approach shortens the cycle time by about 30% and further improves peak compression. In Figure 12e, a large feed pulse, 2100 mL, is injected. Two step pH changes are applied. Immediately after feed injection, the pH is changed to 3.6 in order to compress and accelerate the two bands. An isocratic hold period follows the pH change, allowing partial separation of the two bands. A second step pH change to 5.5 is then applied in conjunction with flow reversal. The peaks are separated and compressed further. Because the selectivity between Lys and His is reversed, remixing of the two bands during the reversed flow is avoided. As a result of the larger feed size, the displacement effects in Figure 12e are more than in Figure 12d and help concentrate the two peaks to yield the largest peak compression of all the cases shown. The throughput and product concentrations for this case are respectively about 10 times and 100 times higher than in isocratic elution. 5. Summary and Conclusions Quantitative models have been developed to understand peak compression in ion exchange systems with stepwise pH elution and flow reversal. The model predictions were compared with the data for amino acids in cation exchange systems. The results show that the nonlinear local equilibrium model can provide good predictions of retention times and peak shapes for large, compressed peaks and for low retention solutes, for which mass-transfer effects are insignificant. The detailed rate model (VERSELC) gives accurate predictions of both peak shape and retention time for all the six experimental systems tested. The analysis shows that as a pH wave propagates across an adsorbed band, solute reequilibration occurs and results in an increase in band migration speed. The acceleration facilitates separation and reduces peak spreading due to both diffuse concentration waves and mass-transfer resistances. The trailing wave of a band migrates faster than
l O i
I
1
O
Moo
I003
L
H
I m
(c)Fsed: 14wmL
20
EF
1
IS
01
0
I
I
I
I000
m
Moo
0 25
EF
Moo
,
m
4000 I
151
o / 0
I
I
1000
moa
IA
i Moo
40%
I [rnt"]
Figure 12. Simulations of effluent history of atepwiee pH elution with flow reversal for a mixture of Lye and Hie: -, VERSELC; .-,
local equilibrium model; ---,breakthrough of pH wave. Arrows indicate the times of flow reversal. All simulation parameters are listed in Tables I1 and VI.
the leading wave, resulting in adsorption band contraction, which enhances peak compression. In addition, displacement of low-affmity solutes by high-affmity solutes enhances peak compression of the low-affinity solutes. Peak compreasion is significant if a large change in solute affmity can be induced for a large, dilute pulse. A dilute pulse can show greater peak compression and little spreading due to peak fronting and peak tailing, and a large pulse has little spreading due to mass-transfer resistancea. We have shown experimentally that a dilute Lys
Ind. Eng. Chem. Res., Vol. 31, No. 7,1992 1729 pulse can be compressed to 35 times its feed concentration. Stepwise elution can be very useful for multicomponent separations. Choosing an initial pH value which gives high solute affinities allows high sample loading. Under high loading conditions, displacement effects help concentrate low-affinity solutes. Applying a step pH change immediately after sample loading suppresses the generation of diffuse waves and reduces spreading due to mass-transfer resistances. Choosing a final pH value which gives a large change in solute affinities enhances peak compression. A final pH value where solute affinities are different allows separation of the peaks after compression. Since the migration speeds are increaeed and spreading due to diffusewaves and mass-transfer resistances is reduced, peaks can quickly separate, resulting in concentrated products in a short cycle time. Thus, compression prior to separation often works better than linear gradient elution. More importantly, peak compression allows the use of relatively large sorbent particles to acieve high resolution. In linear gradient elution, gradual peak compression occurs simultaneously with peak separation. For a mixture of many solutes, linear gradient elution gives better resolution but less peak compression and longer cycle time than stepwise pH elution. Flow reversal can be quite useful when a desired product or an impurity has a very slow migration speed, because the net distance traveled by the desired product or impurity is shortened upon flow reversal. For this reason, cycle time and peak spreading due to diffuse waves and mass-transfer resistances can be significantly reduced. Flow reversal combined with stepwise pH elution can improve the separation of two similar solutes. Flow reversal allows larger volumes to be processed, and thus increases column utilization. During forward flow, a sample is loaded and bands are partially separated, and lowaffinity solutes are concentrated by displacement effects. During reversed flow with a step pH change, bands are compressed and further separated. Selectivity reversal between two solutes can prevent remixing upon flow reversal, and displacement effects also enhance peak compression of low-affinity solutes. A novel process with flow reversal combined with stepwise pH elution for a mixture of Lys and His is shown to have higher throughput and higher product concentration than linear gradient elution. The simulations presented here help explain the peak compression phenomena and can be useful for the design of novel process scale chromatography with significantly improved resolution, throughput, and product concentration. Acknowledgment This work was supported by the National Science Foundation under Grant BCS 8912150. A David Ross fellowship for S.U.K. provided by Purdue University is also acknowledged. We thank Prof. E. Franses, Prof. P. C. Wankat, and Mr.X.Jin for their helpful comments and input during the preparation of the manuscript. Some computing reaourcea were provided by the National Center for Supercomputing Applications through Grant CBT 900015N. Nomenclat ure C = mobile-phase concentration, M or N Cmi= maximum inlet concentration of solute i, M or N C‘ = mobile-phase concentration, equiv/L(bed) Cl,= total mobile phase concentration, equiv/L(bed) Cl,= resin capacity, equiv/L(bed) C = solid-phase concentration, equiv/L(solid)
CT = resin capacity, equiv/L(solid) c = dimensionless mobile-phase concentration E = dimensionless solid-phase concentration
D = column diameter, cm EF = enrichment factor, defined in eq 1 E,, = axial dispersion coefficient, cm2/min Ep = effective intraparticle diffusivity, cm2/min F = volumetric flow rate, mL/min Glu = glutamic acid His = histidine kl, k2 = values of a at very low and high pH, respectively, defined in eq 8c kf = film mass-transfer coefficient, cm/min L = column length, cm Le = adsorption bandwidth following pH change, cm Lf = adsorption bandwidth prior to pH change, cm Lys = lysine N, = number of components r = particle radial position, cm R = radius of sorbent particle, cm t = time, min Ate = duration of peak elution, min Atf = duration of pulse injection, min At = time for a step change to pass through an adsorption band, min T = dimensionless time, defined by eq 11 To = dimensionless time, defined by eq 12 AToi = dimensionless pulse size of solute i, defined by eq 13 Ue = solute migration speed following a pH change, cm/min Uf = solute migration speed prior to a pH change, cm/min U = velocity of a pH wave, cm/min v”, = interstitial velocity, cm/min Vp = pulse volume, mL x = mole fraction of a solute in mobile phase y = mole fraction of a solute in stationary phase z = dimensionless axial distance z, = average valence number of amino acid, defied in eq 8d zl, z2 = valence numbem at very low and high pH, respectively, defined in eq 8d 2 = axial distance, cm Greek Letters a = separation factor = ffnew/%ld
+, = interparticle void fraction = intraparticle void fraction = dimensionless radial distance within sorbent particle B = dimensionless time, tUo/L Tc = dimensionless adsorption rate, defined in eq 16 ep
Subscripts b = bulk phase e = effluent or outlet f = feed or inlet i = component counter p = pore phase
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