Standing Wave Design of Carousel Ion-Exchange Processes for the

Nov 17, 2005 - The intrinsic parameters for the carousel design were estimated from a series .... Two carousel processes were designed based on the st...
0 downloads 0 Views 852KB Size
Download PDF
316

Ind. Eng. Chem. Res. 2006, 45, 316-329

SEPARATIONS Standing Wave Design of Carousel Ion-Exchange Processes for the Removal of Zinc Ions from a Protein Mixture Sungyong Mun* Department of Chemical Engineering, Hanyang UniVersity, Seoul, 133-791, Korea

Chim Chin, Yi Xie,† and Nien-Hwa Linda Wang School of Chemical Engineering, Purdue UniVersity, West Lafayette, Indiana 47907

Chelex 100 is a highly effective adsorbent for the separation of metal ions from proteins for three reasons: (i) it has a high affinity for metal ions; (ii) proteins with molecular weight of 1000 or higher are excluded from the particle pores; and (iii) it also allows high flow rates, because it can withstand a pressure drop up to 100 psi. In this study, a carousel process based on Chelex 100 has been developed for the removal of Zn ions from protein in a buffer solution. The intrinsic parameters for the carousel design were estimated from a series of single-column experiments, which showed that Chelex 100 has a high selectivity for Zn ions in 1 N acetic acid and it can be effectively regenerated using 0.1 N HCl. The exchange mechanisms between Zn2+ and H+ on Chelex 100 were studied and considered in rate model simulations. The effective zinc isotherm was determined to be unfavorable in 1 N acetic acid. A design method based on the standing wave analysis for unfavorable isotherm systems has been developed in this study to ensure high product purity and high yield in carousel ion-exchange processes. Computer simulations and several laboratory-scale carousel experiments showed that the design method and the proposed carousel process can achieve high product purity (100%) and high product yield (>99%). Compared to a batch size-exclusion chromatography process described previously [Xie et al., Biotechnol. Prog. 2002, 18, 1332], a three-zone carousel process that was based on Chelex 100 has more than 600 times the throughput per bed volume, requires only 63% of the mobile phase, and has a smaller residence time (by a factor of 50). 1. Introduction Chelex 100 has been widely used for metal ion removal or for the exchange of one metal ion for another from a protein mixture.1-4 Chelex 100 has a very strong attraction for metal ions, whereas proteins with a molecular weight of 1000 or higher are totally excluded from the resin particles. For these reasons, Chelex 100 is highly selective for the separation of metal ions from a protein mixture. Furthermore, Chelex 100 can withstand a pressure drop as high as 100 psi. These properties favor high productivity and a short residence time of the proteins. Chelex 100 is supplied in the sodium form, which has been used in all the previous studies for removing divalent ions from protein mixtures.4-15 The coelution of Na ions with proteins is not a major concern, because the objective was either to remove divalent ions or to recover a concentrated divalent metal ion solution. However, if the product of interest is a protein that should be free of both Na and divalent metal ions, Chelex 100 must be used in the hydrogen form instead of the sodium form. In this study, the feasibility of using Chelex 100 in the hydrogen form for the removal of Zn ions in a buffer solution was explored using a series of single-column experiments. A batch * To whom correspondence should be addressed. Tel.: +82-2-22200483. Fax: +82-2-2298-4101. E-mail: [email protected]. † Current address: Eli Lilly and Company, Lilly Corporate Center, Indianapolis, IN 46285.

Chelex process and a carousel Chelex process were then developed for the removal of metal ions from a protein solution. A single-column batch process can be easily understood, is easier to design, and requires only conventional chromatography equipment. For these reasons, a single-column process is preferred for small-scale production. Figure 1 shows the schematic diagram of a single-column batch process for zinc removal. The operation consists of four steps, feed loading, washing, regeneration, and re-equilibration. Each step occurs sequentially. During the loading and washing periods, most of zinc is adsorbed onto the resin, whereas protein molecules are excluded. To guarantee high product purity, the zinc adsorption wave should be confined within the column throughout the loading and washing periods. To guarantee high product yield, the end of the protein trailing wave should exit the column prior to the regeneration step. All the Zn ions adsorbed on the resin are removed from the column during the regeneration step. The column is then re-equilibrated with the eluent. After this reequilibration step, the column is ready for feed loading and the aforementioned four steps are repeated again. For large-scale production, a continuous process such as a carousel process is preferred.16-19 The term carousel refers to the operation of a set of columns where solution flows sequentially through the columns. The feed port moves periodically in the same direction as fluid flow, to simulate periodic column movement countercurrent to the fluid flow. Conceptual design of a four-zone carousel process with five columns, which

10.1021/ie050427k CCC: $33.50 © 2006 American Chemical Society Published on Web 11/17/2005

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 317

Figure 1. Diagram of a single column ion-exchange process for the removal of zinc from protein.

Figure 2. Schematic of a conceptual four-zone carousel ion-exchange process for the removal of zinc from protein.

corresponds directly to the single-column batch process, is illustrated in Figure 2. This carousel is operated in the following manner. Zone IV is the loading zone. In step N, the feed is loaded in zone IV through the lead column (D), while the fourth column (E) acts as a guard column. When the leading adsorption wave of zinc reaches the end of column D, step N+1 begins; the feed inlet is switched to column E, which becomes the new lead column in zone IV. Column A, which has been in the reequilibration zone in step N, moves into zone IV and becomes the new guard column. Meanwhile, column D, which has been loaded with zinc during step N, moves into the washing zone (zone III). The column C, which has been washed and is free of the feed during step N, moves into the regeneration zone, zone II. Column B, which has been regenerated during step N,

moves into the re-equilibration zone (zone I). The system is operated continuously in this cyclic manner. For protein purification using Chelex 100, the nonadsorbing solute in the feed (protein) is the product of interest. For this case, the loading zone and the washing zone (zones III and IV, respectively) can be combined into a single zone so that all the protein is collected at the outlet of the loading and washing zone. The four-zone carousel process is therefore simplified to a three-zone carousel, as explained later in the Theory section. The primary advantage of a carousel process is the continuous loading of feed solution and high column utilization. In a batch operation, the loading of feed must stop when the leading edge of the adsorption wave of Zn ions (or saturation front) reaches the column outlet. Column utilization is poor if the saturation wave is broad, as a result of large mass-transfer resistances or thermodynamic spreading (for a diffuse wave). If the saturation wave is a diffuse wave in nature, it spreads continuously with increasing column length. For such a system, the diffuse wave in a carousel process is periodically interrupted and its concentration is increased by the addition of feed. The increased loading improves column utilization and throughput per bed volume. It also reduces product dilution if the washing step is performed in a separate zone (see Figure 2). Because of the high product concentration, less mobile phase is required for elution (per unit of product). A continuous carousel process is also more efficient in equipment utilization. All the columns share the same set of pumps and control. For these reasons, a carousel process is highly efficient for large-scale production. However, the design of a continuous carousel process is more complex. There have been several previous studies on the design and simulation of a carousel process. Svedberg20 and Liapis and Rippin21 showed that column utilization is significantly better for carousel systems, as opposed to single-column systems. Ernest et al.16 developed a carousel ion-exchange process that was based on a resorcinol-formaldehyde resin for cesium removal. Hritzko et al.18 studied the optimal design and ratemodel simulation of a carousel process based on crystalline silicotitanate cation-exchange resin for cesium removal. Until now, only carousel design for systems with favorable isotherms has been reported. No previous studies addressed the design of a carousel process for systems with unfavorable isotherms. The first goal of this study is to prove the feasibility of using Chelex 100 in the hydrogen form for the removal of zinc from a protein solution. The second goal is to develop the design method of a carousel process for systems with unfavorable isotherms. On the basis of the developed design method, a threezone carousel process based on Chelex 100 is proposed for protein purification. Finally, the third goal is to verify the design method and the proposed carousel process using a series of laboratory-scale experiments. A systematic model-based approach (Figure 3) is applied to design the Chelex process. In this approach, one of the important tools is the VERSE (VErsatile Reaction and SEparation) simulator.22-32 VERSE is a simulation package that can be used to predict the dynamic phenomena of both batch and multicolumn carousel systems. A series of pulse and frontal tests are first applied to obtain the intrinsic engineering parameters, which are then used in a new design based on the concept of standing waves to determine the carousel operating parameters. The experimental data of batch and carousel experiments are needed to verify the parameters used in the VERSE simulation. The verified VERSE model then can be used for further process optimization.

318

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006

where Ci (in units of equiv/L) is the concentration of component i in the solution phase and C h i (in units of equiv/L of packed bed) is the concentration of component i on the resin phase. KZn,H is the mass-action equilibrium constant, which should be determined from experiments. Ka is the dissociation equilibrium constant of acetic acid, which has been reported in the literature.33 Because the ion exchange and dissociation reactions are coupled, the aforementioned relations and constraints (eqs 3-6) are solved simultaneously in VERSE. 2.2. Equilibrium Isotherms. Equation 3 is typically normalized by defining the dimensionless groups34,35

xi ≡

Figure 3. Diagram of systematic model-based design approach.

In a previous study, Zn ions were removed from a crude mixture of protein using a size-exclusion chromatography (SEC) process.22 This system was chosen as an example in this study. Two carousel processes were designed based on the standing wave method and tested experimentally. Experimental results show that the three-zone carousel process with four columns can achieve high purity (100%) and high yield (>99%). Close agreement between the experimental data and the model prediction is achieved. The results indicate that the model-based design approach is efficient and robust. Compared to the batch SEC process,22 the Chelex carousel process has more than 600 times the throughput per bed volume and requires only 63% of the mobile phase. The protein residence time was also reduced by an order of magnitude. 2. Theory 2.1. Ion-Exchange Equilibrium between Zn2+ and H+ on Chelex 100. In this study, equilibrium occurs between zinc chloride that has been dissolved in 1 N acetic acid and Chelex 100 in the hydrogen form. The species involved include Zn2+, Cl-, CH3COOH, CH3COO-, and H+. There are two reactions in this system. First, the mass action ion-exchange that is occurring between Zn2+ and H+ on Chelex 100 is given by the following stoichiometric expression:

Zn2+ + 2R-H+ T 2H+ + R2-Zn2+

(1)

where R- represent the fixed negatively charged ionic sites on the resin. The positively charged ions, Zn2+ and H+, are the counterions. Second, acetic acid undergoes the following partial dissociation reaction:

CH3COOH T CH3COO- + H+

(2)

To simulate the dynamic phenomena that results from the aforementioned two reactions, the following equilibrium relations and constraints are used in VERSE:

C h ZnCH2 CZnC h H2

) KZn,H

CHCCH3COO CCH3COOH

(ion-exchange equilibrium)

(3)

(dissociation equilibrium)

(4)

) Ka

CZn + CH ) CCH3COO + CCl (electroneutrality in solution) (5) C h Zn + C hH ) C hT

(electroneutrality in ion exchanger) (6)

yi ≡

Ci CT

(7a)

C hi

(7b)

C hT

where CT and C h T are the total solution phase concentration and the total exchange capacity, respectively. The new equilibrium constant is thus defined as

KZn,H ≡ KZn,H

( ) ( )( ) ( )(

)

C hT yZn xH 2 yZn 1 - xZn ) ) CT xZn yH xZn 1 - yZn

2

(8)

The shape and type of equilibrium isotherm curve (yi vs xi) are dependent on the value of KZn,H from eq 835 and have important implications on fixed-bed dynamics.36 When KZn,H < 1, the isotherm curves are concave and fall below the y ) x line. Isotherm curves of this type are considered “unfavorable”. Conversely, when KZn,H > 1, the isotherm curves are convex and above the y ) x line. Isotherm curves of this type are considered “favorable”. The type of isotherm, favorable or unfavorable, has a significant impact on the nature of a shock wave or a diffuse wave and the optimal design of a carousel process, as explained in the following section. 2.3. Design Method for a Carousel Process for Systems with Favorable and Unfavorable Isotherms. The length of the mass-transfer zone (MTZ) is an important factor affecting column utilization and throughput in a carousel process. The MTZ is the region of changing concentration within a column or a series of columns. The MTZ length is not always constant. At the start of feeding, the dispersive forces have a tendency to spread the concentration wave. However, the spread is opposed by thermodynamic self-sharpening forces for favorable isotherms. If the column is sufficiently long, the net result is the development of a constant pattern wave where the MTZ length is constant for sufficiently long columns.18,36 To achieve maximum column utilization and throughput, the MTZ should be contained within the second column of the loading zone (see Figure 2) while the first column is kept saturated.16,18 In other words, the length of each column in a carousel process should be equal to or longer than the MTZ length, to ensure high column utilization. As will be reported in the Results section, the isotherm curve in this study is unfavorable. Because the constant-pattern MTZ is not developed for unfavorable isotherms, the method of Hritzko et al.18 cannot be applied to design a carousel process for zinc removal using Chelex 100. In this section, two shortcut design methods for a carousel process with unfavorable isotherm are developed for the three-zone process shown in Figure 2. 2.3.1. Design of a Single-Column Batch Process. The selection of cycle time, loading time, and washing time for a single-column process is straightforward. First, the cycle time

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 319

Figure 4. Wave-propagation behavior for the three-zone carousel process based on design method I: (a) 0.05th step, (b) 0.83th step, and (c) 0.99999th step.

is determined from the zinc breakthrough time in a singlecolumn frontal test, which can be done by experiments or VERSE simulations. Next, the washing time is obtained from a single-column protein saturation and elution test using experiments or simulations. Finally, the loading time is calculated by subtracting the washing time from the cycle time. No trial and error is needed in the design. 2.3.2. Design of a Three-Zone Carousel: Method I. A straightforward method in designing a three-zone carousel is to follow the same principle of designing a single-column batch operation, except the four steps in the batch operation (see Figure 1) are performed simultaneously using multiple columns. The loading and washing schedules are kept the same as those of the batch process (method I). Figure 4 shows the wave migration behavior for the three-zone carousel based on design method I. In this design, the second column in zone III (the loading zone) is used as a guard column. After feed loading, the columns in zone III are washed until the protein exits the first column of

Figure 5. Wave-propagation behavior at steady state for the three-zone carousel process based on design method II: (a) 10.05th step, (b) 10.83th step, and (c) 10.99999th step.

zone III before column switching (see Figure 4). The end of the zinc adsorption wave is allowed to reach the end of the first column at the end of washing. The column that contains only zinc enters zone II after switching. This design can guarantee high protein yield but results in low column utilization. 2.3.3. Design of a Three-Zone Carousel: Method II (Standing-Wave Design). To improve column utilization and throughput per bed volume, both columns in zone III can be utilized for separation. As shown in Figure 5, the zinc adsorption wave is allowed to enter the second column in zone III. In this case, the switching time cannot be directly determined from a batch test as in design method I. The reason is that, after the first switching, the first column of zone III is no longer free of zinc, whereas in a batch operation, a column is always free of zinc before loading. The switching time can be obtained from a series of carousel experiments or simulations by a trial-and-error approach. To avoid trial and error, the concept of standing wave in a continuous process37 is adopted here. In this second design

320

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006

method, the switching time is chosen so that the zinc adsorption wave is confined in zone III. For this purpose, the port movement velocity (ν) is kept the same as the velocity of the leading zinc wave (uZn,avg|xZnf0) as follows:

( )

ν ≡

Lc ) uZn,avg|xZnf0 ts

(9)

where Lc is the length of the single column and ts is the switching time. Note that the zinc wave velocity in eq 9 is the average of wave velocities during loading and washing. The zinc wave velocity for each step is estimated from the ion movement theory27 as follows:

uZn|xZnf0 )

u0

( ) ( )( )

(10)

|

1 - b h T dyZn 1 C 1+ p + b b C dxZn T

xZnf0

where u0 is the interstitial linear velocity, b the interstitial bed voidage, and p the porosity of the particle. Differentiation of eq 8, with respect to xZn, gives

( )[

C h T 1 + xZn dyZn (1 - yZn)2 ) K dxZn 1 + yZn ZnH CT (1 - x )2 Zn When xZn approaches zero,

]

(11)

()

C hT dyZn |xZnf0 ) KZnH dxZn CT

(12)

In our previous studies of standing wave designs, masstransfer correction terms are incorporated in the equations for finding the zone flow rates and step time.37-42 Both the design methods I and II do not include mass-transfer correction terms. Rate model simulations and experimental results (discussed later) show that, for the system of interest, mass-transfer effects are relatively unimportant, compared to thermodynamic effects, and can be ignored in the carousel design. For other applications, where mass-transfer effects are important, the port velocity in eq 9 can be increased by a certain amount (the mass-transfer correction term), so that the port velocity is slightly higher than the zinc wave velocity in zone III. The difference in the port velocity and the zinc wave velocity (the correction term for mass-transfer effects) is used to focus the zinc wave, so that the leading edge of the zinc wave is confined in zone III. The mass-transfer correction terms developed previously by Ma and Wang37 can be easily incorporated into eq 9. 2.4. Rate Model Simulations. The VERSE simulator is based on a detailed rate model including axial dispersion, film diffusion, intraparticle pore diffusion, intraparticle surface diffusion, and mass action ion exchange. Its capabilities and features have been documented in several papers.22-32 The mathematical equations describing carousel ion-exchange operations are essentially the same as those for single-column fixedbed ion exchange.16,18 The reaction features of VERSE have been reported previously.26 In this study, the dissociation of acetic acid (eq 2) is considered in the simulations. To account for axial dispersion and delay in the extra-column dead volume, the extra-column dead volume was considered as a continuously stirred tank (CST) between two connected columns. The general equation for the CST is given by

Substitution of eq 12 into eq 10 gives eq 13.

uZn|xZnf0 ) 1+

( )

DV

u0

()

1 - b C hT 1 p + (KZnH) b b CT

2

(13)

To account for any delay in the extra-column dead volume, the wave velocity equation is modified as follows:

uZn|xZnf0 ) 1+

( )

u0

()

1 - b C hT 1 p + (KZnH) b b CT

2

(14) +

DV LcSb

The only difference in eq 14 between the loading and washing steps lies in the total solution phase concentration, CT. An average velocity of the zinc wave is calculated from eq 15.

uZn,avg|xZnf0 )

uZn,load|xZnf0tl + uZn,wash|xZnf0tw tl + t w ts ) tl + tw

(15) (16)

where tl and tw are the loading time and washing time, respectively. Because the washing time can be determined directly from experiments or simulations, the washing time is a known value in eqs 15 and 16. For a given column length Lc, eqs 9, 15, and 16 are used to solve for the three unknowns ν, ts, and tl. Design method II (the standing wave method) needs no trial and error and allows a quick determination of the operating conditions for a carousel process. This method will be compared with design method I in the Results section.

dCout ) F(Cin - Cout) dt

(17)

where DV is the extra-column dead volume, F the volumetric flow rate, Cin the concentration at the CST inlet, and Cout the concentration at the CST outlet. 3. Experimental Section 3.1. Materials. The crude insulin powder provided gratis by Eli Lilly and Co. (Indianapolis, IN) was used in the singlecolumn and carousel experiments. Distilled deionized water (DDW) was obtained from a Milli-Q system (Millipore, Bedford, MA). Glacial acetic acid from Mallinckrodt Baker, Inc. (Paris, KY) was mixed with DDW to prepare 1 N acetic acid, which was used as the mobile phase and the solvent to dissolve the protein powder. A solution of 37 wt % HCl from Mallinckrodt Baker, Inc. was diluted with DDW. The diluted HCl solution was used as the regenerant. Acetone for column characterization was purchased from Mallinckrodt Baker, Inc. Zinc chloride was also purchased from Mallinckrodt Baker, Inc. and used in the single-column and carousel experiments. Highperformance liquid chromatography (HPLC)-grade acetonitrile and L-arginine, which were used to prepare the mobile phase for HPLC assay, were purchased from Fisher Scientific (Fairlawn, NJ) and Sigma Chemical Co. (St. Louis, MO), respectively. The Chelex 100 (analytical grade in the sodium form) purchased from Bio-Rad Laboratories (Hercules, CA) was used as the stationary phase, which has an average diameter of 112.5 µm. Table 1 lists the properties of the Chelex 100, which were taken from the manufacturer’s technical information. Columns with two different sizes were tested. Column A (1.1 cm in

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 321 Table 1. Typical Properties for the Chelex 100 Resin (from Bio-Rad Laboratory) property grade structure cross-linking density bulk density maximum capacity maximum allowable pressure drop a

value analytical styrene divinylbenzene copolymers containing paired iminodiacetate ions 1% 0.65 g/mL 0.4 mequiv/mLa 100 psi

Milliliters of packed bed in the sodium form.

diameter and 30 cm in length) from Ace Glass, Inc. (Louisville, KY) were used in the carousel experiments. Column B (1.0 cm in diameter and 12 cm in length), from Alltech (Deerfield, IL), was used to estimate the mass-action equilibrium constant and mass-transfer parameters. 3.2. Equipment. The HPLC system consists of two pumps (Waters model 515), a photodiode array detector (Waters model 996), and a Rheodyne model 7725i injector. The Waters Millennium software, which operates in the Windows environment, was used for data collection and analysis. The concentration of ZnCl2 in the samples was measured using an atomic absorption spectrometer (Perkin-Elmer, model AAnalyst-300) that was equipped with a zinc hollow-cathode lamp. The zinc hollow-cathode lamp was purchased from VWR Scientific Co. (West Chester, PA). A Pharmacia (Piscataway, NJ) fast protein liquid chromatography (FPLC) system was used in the single-column experiments. This system consists of two pumps (Pharmacia P-500), a liquid chromatography controller (Pharmacia LCC-500), and an injection valve (Pharmacia MV-7). Effluent from the column was monitored using a photodiode array detector (Waters, model 990) or a conductivity detector (Waters, model 431), which was connected to a chart recorder (Pharmacia REC-482). The Purdue Versatile SMB was used in the carousel experiments. The details of this unit have been described elsewhere,43 and its schematic diagram is shown in Figure 6. For the Versatile SMB to function as a three-zone carousel in this study, four rotary valves and four columns were used. The four ST rotary valves were purchased from Valco Instruments, Inc. (Houston, TX). The number of columns in each zone can be varied by changing the connection paths between the columns and the rotary valves. A computer with LabView software controlled the valve switching. Four Ismatec pumps (Glattbrugg, Switzerland) were used to control the flow rates. A 5-psi back-pressure regulator purchased from Upchurch Scientific (Oak Harbor, WA) was applied to each column outlet. Effluent from the product port was monitored using the conductivity detector. Because the flow cell of the conductivity detector has a relatively high flow resistance, a single-piston pump (model RHV) that was purchased from Fluid Metering, Inc. (Syosset, NY) was used to deliver a portion of the product stream to the detector. 3.3. Column Preparation. The Chelex resin was supplied in the sodium form. The resin was weighed and poured into a vessel that contained DDW. The resin in DDW was pretreated with 10 bed volumes of 1 N HCl, followed by washing with 10 bed volumes of 1 N acetic acid. After this treatment, the resin was converted to the hydrogen form and the resin volume was reduced to ∼40% of that in the sodium form in DDW. Two different sets of columns, A and B, were packed for the experiments using a slurry-packing technique. After packing, several bed volumes of 1 N acetic acid were allowed to pass through the column to ensure a well-packed bed. Table 2 lists the parameters of the two sets of columns.

3.4. Assay. The protein was assayed using the Waters HPLC system with a Waters size-exclusion HPLC column (Milford, MA). The mobile phase consisted of 65% 1.0 g/L L-arginine solution, 20% acetonitrile, and 15% glacial acetic acid. The flow rate was 0.5 mL/min, and the sample injection volume was 20 µL. The column temperature was kept at room temperature. The column effluent was monitored at a wavelength of 276 nm, using the photodiode array detector (Waters, model 996). The amount of zinc in the samples was determined using atomic absorption spectrometry (AAS). The sample was aspirated into the flame, where the Zn atoms become activated. The amount of 214-nm monochromatic light absorbed by the activated Zn atoms in the flame was measured. From this measurement, the amount of zinc present was determined. Standard samples were run at the beginning of every analysis, and after every 10 samples. These checks ensured that the instrument remained in calibration. 3.5. Single-Column Experiments. All experiments were performed at atmospheric pressure and 4 °C. The feed solution was equilibrated at 4 °C before experiments and used within 12 h after the feed preparation. For single-column experiments (pulse and frontal tests), the FPLC system was used. Effluent from the column was monitored with the conductivity detector or the photodiode array detector (Waters, model 990). Before the experiments, the columns were equilibrated with 1 N acetic acid. Extra-column dead volume was determined by measuring void volumes of the column adaptor and tubing separately. In the pulse tests, the injection volume was 0.1 mL for the protein and acetone. The mobile phase (1 N acetic acid) flow rate was 1 mL/min. The column effluents were monitored at the wavelengths of 287 nm for the protein and 293 nm for acetone. In the frontal and elution tests, two FPLC pumps were used to deliver 1 N acetic acid and a feed solution (0.3 g/L ZnCl2, 0.6 g/L ZnCl2, or 80 g/L insulin in 1 N acetic acid). The mobile phase flow rate ranged from 0.5 mL/min to 6.0 mL/ min. After a concentration plateau fully developed at the column outlet, 1 N acetic acid was used to wash the column. 3.6. Carousel Experiments. Two carousel experiments were performed at 4 °C. The four columns (Chelex-A) were used in each experiment, and the column configuration (allocation of the four columns in the three zones) was 1-1-2, as shown in Figure 6. The extra-column dead volume was estimated from the valve and tubing inner diameters (see section 4 for details). The columns were equilibrated with 1 N acetic acid prior to each experiment. The carousel experiment was started by triggering the timer of the valve controller (LabView). To prevent channeling that may result from the drainage of the fluid in the column, 5-psi back-pressure regulators were installed in each column outlet, as shown in Figure 6a. The feed for the first experiment (run 1) was 0.6 g/L in 1 N acetic acid. The feed for the second experiment (run 2) was prepared by dissolving the protein powder (containing ZnCl2) into 1 N acetic acid. The regenerant and re-equilibrant were 0.1 N HCl and 1 N acetic acid, respectively. Samples were collected from the outlet of each zone over an entire switching period (between two switchings). Therefore, the concentration of each sample represents the average concentration over a switching period. The run 1 experiment was stopped at the end of the 15th step, and the run 2 experiment was stopped at the end of the 12th step. 4. Results and Discussion 4.1. Ion Exchange between Zn2+ and H+ on Chelex 100. Zinc frontal tests were performed to determine whether Zn2+

322

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006

Figure 6. Laboratory-scale carousel equipment with four packed columns. Panel a shows a schematic diagram (legend: B, back-pressure regulator (5 psi); C, conductivity detector, and P, pump), whereas panel b shows a schematic of the detailed tubing and valve connections. Table 2. Column Properties columna

length (cm)

inside diameter, ID (cm)

b

p

resin diameter (µm)

C hT (equiv/L of BVb)

Chelex-A Chelex-B

30 12

1.1 1.0

0.406 0.380

0.598 0.598

75-150 75-150

1.07 1.06

a The large column (Chelex-A) was used in the three-zone carousel experiments, and the small column (Chelex-B) was used to validate the mass action equilibrium constant and mass-transfer parameters. b Equivalents per liter of packed bed in the hydrogen form.

cations can exchange for H+ cations on the resin in 1 N acetic acid. Figure 7 shows the effluent histories from the zinc frontal tests where the conductivity of the column effluent was monitored. Before the injection of the feed, the conductivity of the effluent was maintained at that of 1 N acetic acid (1510 µS), because the column was pre-equilibrated with 1 N acetic acid. After the column was saturated, the conductivity of the effluent was kept constant at that of the feed solution (see region IV in Figure 7). If there is no ion exchange, the conductivity of the effluent should increase monotonically. However, the experimental data in Figure 7 show that the conductivity increases sharply (region I) and then decreases gradually (region

III). In addition, the maximum conductivity value (region II) is much higher than the conductivity of the feed (region IV). The observed phenomena can be explained by the ion-exchange mechanism as follows. If Zn2+ cations in the solution phase are replaced by H+ cations on the resin phase, the amount of H+ in the column effluent increases with time. Because the conductivity of the H+ cation is much higher than that of the Zn2+ cation (Table 3), the conductivity of the effluent increases sharply beyond that of the feed and reaches its maximum (region II). The displacement of H+ by Zn2+ then occurs gradually, because the wave is diffuse, as explained in the Theory section. For this

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 323

Figure 8. Experimental data of the pulse tests with the Chelex-A column: (a) protein and (b) acetone. Table 4. Summary of the Experimental Conditions and Results of the Zinc Frontal Tests

Figure 7. Experimental data and simulation results of the zinc frontal tests: (a) Chelex-A column at a flow rate of 4 mL/min, and (b) Chelex-B column at a flow rate of 2 mL/min.

column

ZnCl2 (Zn) concentration in feed (g/L)

flow rate (mL/min)

temperature (°C)

KZn,H

Chelex-A Chelex-B

0.6 (0.288) 0.3 (0.144)

4 2

4 4

3.465 × 10-4 3.384 × 10-4

The bed voidage (b) is calculated from the void volume as follows:

Table 3. Equivalent Ionic Conductivitya (λ0) of Species Involved in This Study species

λ0 (× 10-4 m2 S/mol)

H+ 2+ 2Zn CH3COOCl-

349.65 52.8 40.9 76.31

1/

a

From ref 33; data collected at 25 °C.

reason, the conductivity of the effluent decreases gradually (see region III). Finally, if ion-exchange equilibrium is attained, the column becomes saturated with Zn ions and the conductivity of the effluent becomes equal to that of the feed (see region IV). The results in Figure 7 confirmed the exchange between Zn2+ and H+ and indicated that Chelex 100 in the hydrogen form can be used for zinc removal from a protein solution in 1 N acetic acid. 4.2. Pulse Tests for Estimation of Interparticle and Intraparticle Void Fraction. The column properties at cold room temperature (4 °C) were determined from pulse tests using the Chelex-A column. The chromatograms of the pulse tests are shown in Figure 8. The elution volume of each pulse is estimated from the mass center of the chromatogram and is used to determine the column properties. Note that the extra-column dead volume is subtracted to obtain the net elution volume through the column. The elution volume of a protein pulse is the interparticle void volume (V0), because the proteins or polymers with a molecular weight of >1000 are totally excluded from the resin particle.

b )

V0 BV

(18)

where BV is the bed volume (expressed in milliliters). The component mass balance shows no protein adsorption on Chelex 100. Acetone is much smaller than protein and is chosen as the tracer to estimate the total void volume (Vt), which includes both the interparticle and intraparticle volumes. Because the interparticle void volume (V0) is determined from the insulin pulse test, the total void volume (Vt) can be used to calculate the particle porosity, p.

p )

V t - V0 BV - V0

(19)

The properties of the columns are summarized in Table 2. 4.3. Frontal Tests (Saturation Tests). The mass-action equilibrium constants for Zn2+ with respect to H+ (KZn,H) were obtained from two zinc frontal tests with different feed concentrations, flow rates, and column dimensions (see Table 4). In both tests, the temperature was maintained at 4 °C. The frontal chromatography data are shown in Figure 7. From the wave-center time (tcenter) of the frontal chromatogram, the concentration of zinc on the resin phase at equilibrium (C h Zn) is calculated from the Zn2+ balance as follows:

C h Zn (equiv/L of packed bed) )

(tcenter - tvoid)FCZn,feed BV

(20)

324

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006

where tvoid is the holdup time (or the retention time of a nonretained component), F the flow rate, and CZn.,feed the concentration of zinc in the feed (in units of equiv/L). The concentration of hydrogen on the resin phase at equilibrium (C h H) is obtained from the difference between C h Zn and C h T. The total exchange capacity (C h T) listed in Table 2 was estimated from the amount of packed resin and the resin capacity given from the Bio-Rad Laboratory. The resulting C h Zn and C h H values are used to determine the mass-action equilibrium constant as follows:

( )( )

C h Zn CH,feed KZn,H ) CZn,feed C hH

2

(21)

where CH,feed is the concentration of H ions in the feed (in units of equiv/L). The results and experimental conditions of the two frontal tests are compared in Table 4. One can see that the value of the mass-action constant is consistent over a wide range of concentrations and flow rates in the carousel experiments (see Tables 6 and 7, presented later in this work). The mass-action constant is small; therefore, the product of KZn,H(C h T/CT) is always less than unity in the systems of interest, indicating that the system has an unfavorable isotherm. Because MTZ does not reach a state of constant pattern for unfavorable isotherms, the design methods proposed in the Theory section was used to determine the operating parameters of the Chelex carousel process for zinc removal. 4.4. Regeneration Tests (Elution Tests). After the column is saturated with zinc, a solution with a sufficient amount of H ions should be used to remove all the Zn ions on the resin in a regeneration step. Three regenerants were tested in this study: 1 N acetic acid, 0.1 N HCl, and 0.008 N HCl. First, we tested 1 N acetic acid as a regenerant. Figure 9a shows the chromatogram of elution test where 1 N acetic acid was eluted through the Chelex-B column that was preequilibrated with a zinc solution (0.3 g/L ZnCl2 in 1 N acetic acid). The elution profiles in both conductivity and zinc concentration have three plateau regions (Figure 9a). In the first plateau region (region I), the pre-equilibrating solution (0.3 g/L ZnCl2 in 1 N acetic acid) that remains in the void space exits the column. Therefore, the conductivity and zinc concentration of the effluent are the same as those of the pre-equilibrating solution. The second plateau (region II) covers a wide region where the regeneration occurs. The conductivity of the effluent in this region is maintained at 1360 µS, which is lower than that of 1 N acetic acid (1510 µS). As the H+ ions in the solution phase exchange for the Zn2+ ions on the resin, this exchange leads to a decrease in the conductivity of the effluent, because Zn2+ ions have a much lower conductivity than H+ ions (see Table 3). All the retained Zn ions are eliminated from the column before the start of the third plateau (region III). In the third plateau region (region III), no zinc exits the column and the conductivity of the effluent is that of 1 N acetic acid. Overall, more than 60 bed volumes of 1 N acetic acid are needed for complete regeneration. Next, we tested 0.008 N HCl as a regenerant. Figure 9b shows the chromatogram of elution test where 0.008 N HCl was eluted through the Chelex-B column that was pre-equilibrated with a zinc solution (0.3 g/L ZnCl2 in 1 N acetic acid). Approximately 28 bed volumes of 0.008 N HCl are needed for complete regeneration. The regeneration time for 0.008 N HCl is less than that for 1 N acetic acid.

Figure 9. Experimental data of the regeneration tests (zinc elution tests) with the Chelex-B column: (a) eluted with 1 N acetic acid; (b) eluted with 0.008 N HCl; and (c) eluted with 0.1 N HCl. Symbols denote zinc concentrations, and lines represent conductivity data.

Finally, 0.1 N HCl was tested as a regenerant. The resulting chromatogram is shown in Figure 9c. The regeneration time is much shorter than those for 1 N acetic acid and 0.008 N HCl, because 0.1 N HCl contains a much higher concentration of H ions. A quantity of only eight bed volumes of 0.1 N HCl is sufficient for complete regeneration. For this reason, 0.1 N HCl was chosen as the regenerant in the design of a Chelex carousel process (see Figure 6a). 4.5. Parameter Verification with Batch Chromatography Data. Simulations with the parameters estimated previously were conducted as a check against the batch chromatography data for zinc and insulin. The mass-transfer parameters, reaction parameters for acetic acid dissociation, and numerical parameters used in the simulations are listed in Table 5. Figure 10 shows that the simulations are in close agreement with the experimental zinc saturation and elution data. Similar results were also obtained in simulations without the dissociation reaction of acetic acid, indicating that the reactions are unimportant in this system. This is because the concentration of Zn ions in the feed is relatively small (2.2 mM). In the absence of the dissociation reaction, a net increase in H+ concentration of 4.4 mM is expected. However, the H+ ions displaced by Zn2+ from Chelex 100 participate in the reaction to form acetic acid, causing a net increase in H+ concentration of 2.8 mM in the mobile phase. The increase in H+ concentration based on the assumption of reaction equilibrium agrees with the conductivity data. The selectivity of Zn2+ over H+ is >10; therefore, the small difference in H+ concentrations between the cases with the

Ind. Eng. Chem. Res., Vol. 45, No. 1, 2006 325 Table 5. Mass-Transfer, Reaction, and Numerical Parameters Used in the Simulations of This Study Mass-Transfer Parameters protein 5.49 ×

(cm2/min)a

D∞ Dp (cm2/min)b Kf (cm/min) Eb (cm2/min)

H+

CH3COOH

10-5

10-4

CH3COO-

10-3

10-4

3.85 × 2.96 × 3.47 × 1.17 × 10-4 9.01 × 10-4 1.06 × 10-4 Wilson and Geankoplis correlation (1966) Chung and Wen correlation (1968)

Zn2+ 3.96 × 10-4 2.65 × 10-5

Reaction Parameters for Acetic Acid Dissociation k+ (s-1)c k- (M-1 s-1)c

1.8 × 10-5 1.0 Numerical Parameters Collocation Points

axial elements per column

axial

50

4

particle 2

absolute tolerance

relative tolerance

1.0 × 10-5

1.0 × 10-4

a D values of protein and Zn2+ are obtained from the Wilke and Chang correlation (1955). D values of CH COOH, H+, and CH COO- are obtained ∞ ∞ 3 3 from Cussler (1984) and adjusted for temperature and viscosity, using the Wilke and Chang correlation (1955). b Dp values of CH3COOH, H+, and CH3COOare estimated from the Mackie and Meares correlation (1955). The Dp value of Zn2+ is obtained by fitting the data with VERSE simulations. c k+ and k- are obtained from the equilibrium constant for acetic acid dissociation (from ref 33) and the data-fitting with VERSE simulations.

Figure 10. Comparison of the experimental data and simulation results for the zinc saturation and elution tests with the Chelex-B column at a flow rate of 2 mL/min: (a) eluted with 1 N acetic acid, (b) eluted with 0.008 N HCl, and (c) eluted with 0.1 N HCl. Symbols denote experimental data, and lines represent simulation results.

reaction and without the reaction does not affect the partition of Zn2+ in the stationary phase significantly. The spread of the Zn2+ saturation wave is dominated by the thermodynamic effects. The dissociation reaction of acetic acid or intraparticle diffusion has no discernible effect on the zinc wave. The experimental data of the insulin saturation and elution tests are compared with the simulation results at different flow rates in Figure 11. They show a close agreement if the interstitial

Figure 11. Comparison of the experimental data and simulation results for the protein saturation and elution tests with the Chelex-B column: (a) 1 mL/min, (b) 2 mL/min, (c) 4 mL/min, and (d) 6 mL/min. Symbols denote experimental data, and lines represent simulation results.

linear velocity (uo) was