2700
Znd. Eng. Chem. Res. 1995,34, 2700-2711
Ion Exchange of Phenylalanine in Fluidized/Expanded Beds Joon-HoKoh, N.-H. Linda Wang, and Phillip C. Wankat* School of Chemical Engineering, Purdue University, West Lafayette, Zndiana 47907
Experimental and theoretical studies were carried out to investigate the performance of a batch, fluidizedexpanded ion-exchange system. Exchange of phenylalanine on cation exchange resin was studied in the linear velocity range 5.5-39.8 c d m i n . The breakthrough curves were obtained a t various design and operating conditions with changes of column size, distributor, bed type, bed height, flow rate, and number of stages. The breakthrough data were analyzed by two theoretical models. A CSTR-type model which we called a lumped model fitted the data well when bed aspect ratio (bed heightbed diameter) was less than 1.5 and column diameter was less than 4 cm. We considered the fluidized bed as a bed that can be well simulated by the lumped model (uniform mixing), and the expanded bed as a bed where the lumped model fails because of reduced backmixing. Another model, which is adapted from a packed bed model (VERSE) with axial dispersion, film diffusion, and intraparticle diffusion, fitted the data for both fluidized beds and expanded beds successfully. Experimental and theoretical results showed the bed type changed from a fluidized bed to a n expanded bed as the bed aspect ratio increases. The breakthrough curves for the expanded bed and a packed bed were almost identical except a t very short times. When sieve plates were used as liquid distributors, the plate with more holes of a smaller size was most efficient. Mass transfer a t different flow rates and the effects of bed type and multiple stages are discussed.
Introduction Adsorption and separation in fluidized beds is not a new technology. Large scale fluidized ion-exchange processes have been used successfully in uranium recovery processes from leach solution (Streat, 1980). However, more interest has developed in recent years especially for biochemical separation processes. This technology has attracted attention because of its possibility of direct treatment of crude feed stocks from fermentation reactors, which will give several economic benefits. Several studies during the past several years were reviewed by van der Wiel and Wesselingh (1989). These studies were followed by a commercial system introduced by Pharmacia early in 1994. The products of Pharmacia sold under the STREAMLINE trademark included expanded bed columns (50-200 mm i.d.1 and two ion-exchange adsorbents (SP and DEAE). The recommended maximum velocity was 400 cm/h (6.67 c d min), and the mean size of the adsorbents was 200 pm. Though a commercial system has emerged, there still remain further experimental and theoretical questions. First, according to the recent report by Pharmacia, the company developed or modified the adsorbents for use in expanded bed columns though specific information was not given. It is interesting to see whether conventional adsorbents and ion-exchange resins used in packed beds can also be used in fluidizedexpanded beds without any chemical or mechanical modification. Second, the major difference between packed beds and fluidizedlexpanded beds is hydrodynamics. For packed bed chromatography, mathematical modeling is well established. The hydrodynamics is treated as plug flow with a constant velocity, and the bulk phase mass transfer is described in terms of axial dispersion in the model. The hydrodynamics in expanded beds can probably be simplified using the same models used in packed beds with a few modifications. The hydrodynamics in shallow fluidized beds can probably be approximated as a completely mixed system (or CSTR).
* To whom correspondence should be addressed.
One goal of this paper is to verify these hypotheses. Third, the hydrodynamics is influenced by several factors which are often not considered important in packed beds. Examples are column entrance or distributor effect, column size or geometry effect, density difference, etc. This paper analyzes the above issues and shows how to improve the performance of fluidizedexpanded beds. For this purpose, several design considerations such as the effects of distributor and column size are discussed on the basis of experimental data. It is also essential to find appropriate mathematical models for simulation and optimization of the processes. Two different models are used in this paper, and they are compared on the basis of fits to the data. The limitations of each model are also discussed. Our study focused on only the sorption step for a single compound. The terminology of fluidized beds applies to the beds when the fluid velocity exceeds the minimum fluidization velocity. We use the term fluidized bed to refer to well-mixed systems. In recent papers a new term, expanded bed, was frequently used with respect t o adsorption and ion-exchange processes for biochemicals. Although an expanded bed can be also called a fluidized bed, it usually refers to a bed which behaves more like a packed bed with increased bed voidage. We distinguished the two bed types by this difference.
Experimental Section Resin Material. Duolite C-20 (H+ form) was obtained from the Rohm and Haas Co. This is a strong acid cation exchange resin of a gel-type form, having sulfonated styrene-8% DVB (divinylbenzene)copolymer as a cross-linked structure. The particles are in the shape of almost perfect spheres with an average diameter 0.05 cm (500 pm) and wet density 1.2 g/mL. The capacity of the resin was measured from the breakthrough curve of H+/Na+ exchange experiments. The dynamic binding capacity was about 3.0 equivb of resin, based on the volume of resin particles. When this was
0888-5885/95/2634-2700$09.00/00 1995 American Chemical Society
m ,
Effluent
II U U U
spectrophotometer
Columns
I
i
I
6mM (washing) Phenylalanine at pH 2.4
Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2701
(elution)
atant d
I
(regeneration)
Figure 1. Experimental system. Table 1. Column Specifications (Figure 1) I I1 I11 column i.d. (cm) max bed length (cm) max no. of stages distributor a
Iv
V
1.0 10
1.42 16
2.64 22
4.0 35
4.0
1
1
1
1
5
loa
nylon glass glass Teflon Teflon mesh beads beads plate plate
For each stage.
converted in terms of bed volume, it was very close to the value given by the manufacturer (1.9 equivb bed volume). Reagents. A pure crystalline form of L-phenylalanine from Sigma, 37% aqueous solution of HC1 from Mallinckrodt, and 98.5%NaOH pellet from Mallinckrodt were used. A 0.006 M phenylalanine solution was prepared by weighing out 1.0 g of phenylalanine and diluting it to 1.0 L. Then 10 mL of 1 N HC1 solution was added to each 1 L of the solution to make the pH 2.4. Solutions of 1N HC1 and 1N NaOH were used for regeneration and elution, respectively. Resin was washed with more than 10 bed volumes of distilled water before each step. The concentration of phenylalanine was measured by a UV spectrophotometer (Perkin-Elmer, LAMBDA3). FluidizedlExpanded Bed System. The overall experimental diagram is depicted in Figure 1. A calibrated Masterflex peristaltic pump equipped with Tygon tubing was used to control the flow rate for the ion-exchange bed. Several columns of different sizes were used. The column specifications are listed in Table 1. Column I (Pharmacia, SR10) is one of the columns widely used for packed beds in laboratories. Columns I1 and I11 are cylindricalglass columns with round ends. Glass beads (4 mm diameter) filled the round bottom section and fimctioned as distributors. Columns IV and V are essentially the same except that column V was designed for experiments with multiple stages. Both columns have Teflon sieve plates as distributors which can be replaced easily. In column V, the stages were
connected vertically by metal clamps with O-ring joints. This column was originally designed to perform experiments for a continuous process similar to the CloeteStreat type, and the experimental and theoretical results were previously published (Agosto et al., 1993). In the experiments, the column was filled with resin and washed with water. A 1N NaOH solution was fed into the column to exchange for the preloaded ions. After washing again, 1N HC1 solution was used to regenerate the resin into the H+ form. The adsorption step began after the resin was well washed. The temperature was maintained at 25 f 1"C. During the adsorption period, liquid samples from each stage or from effluent were collected every 2 or 3 min. All liquid streams flowed from the bottom of the column to the top.
Mathematical Models Two different mathematical models were used to simulate the breakthrough curves in fluidized and expanded beds. The lumped parameter model is a linear driving force model based on the assumption of uniform mixing. This type of model was developed years ago and has been used extensively, but there are few applications to sorption systems in fluidized beds. Belter et al. (1973) used this model with a Freundlich isotherm for the isolation of novobiocin from broth. Agosto et al. (1993) also used the same model with linear isotherms for a continuous amino acid recovery system. We found the exact solution of this model for batch operation with linear isotherms and multiple stages. The other model by the name of VERSE was developed by Berninger et al. (1991), and many applications for chromatographic systems have been reported. VERSE is a computer simulation package for study of complex reaction-separation behavior in liquid chromatography. The model was developed for packed beds, but in this paper we show this model can be also used for fluidizedl expanded beds. The computer program for the VERSE model is available with several well-known correlations for axial dispersion and film mass transfer and many types of isotherms for both reversible and irreversible adsorption (Whitley, 1990). Lumped Mass Transfer Model. The equations for the lumped parameter model are the same as shown by Agosto et al. (1993) which were solved numerically for Cloete-Streat operation with resin movement. The model assumes that each stage consists of a uniformlymixed fluidized bed region and a uniformly-mixed supernatant liquid region with no resin. This is shown for the column on the right in Figure 1. The concentrations are represented by C and C', respectively. These two regions are observed experimentally. Solid particles are assumed to be a _homogeneous phase with an average concentration, Cs. The mass transfer through film and particles is represented by an overall mass transfer coefficient (k~).The governing equations for the n th stage are
(3) with a linear isotherm,
2702 Ind. Eng. Chem. Res., Vol. 34,No. 8, 1995
E',,, = m P n initial conditions:
input concentrations:
The exact solutions are shown in Appendix A. VERSE Model. The VERSE model contains liquid phase chemical reaction terms and adsorption kinetic terms, as well as mass transfer terms such as axial dispersion, film diffusion, intraparticle diffusion, and extracolumn dispersion. Bulk liquid phase is assumed t o be plug flow with axial dispersion. Resin particles consist of liquid pore phase and solid phase, and concentrations (C, and C,) depend on radial position inside particles. The diffusion rate inside particles is represented by an apparent intraparticle diffusivity (Dmp)based on driving force in the liquid pore phase. Diffusion on solid surface is also included in the model as explained in Appendix B. The equations for VERSE are given by Berninger et al. (1991). The reaction and kinetic terms in the original VERSE equations were not used in our fluidizedlexpanded bed system, because the system is nonreactive and local equilibrium is assumed. The governing equations for adsorbing species (phenylalanine) are
(8) with a constant separation factor isotherm,
a=
CS'C, C,HJC,H+
(9)
where C s - ~and + Cp-Ht are concentrations of hydrogen ions in solid and liquid phases inside particles. initial conditions: C(0,z) = C,(O,rq) = C,(O,r,z) = 0
(10)
boundary conditions: (11)
(12)
These equations are also solved for preloaded ionic species (hydrogen) with different initial and boundary conditions. The numerical methods to solve these equations were presented in detail by Whitley (1990) and Berninger et al. (1991).
Results and Discussion Isotherm of Phenylalanine. Experiments for phenylalanine equilibrium on the cation exchange resin were
Langmuir fit: Cs= 642.1C/(l'+198.4C) Linear fit: Cs = 3 5 6 . X
'1
1'0
20 30 40 50 C (liquid. conc., M) x 1000
60
Figure 2. Isotherm of phenylalanine on Duolite C-20 at external pH 2.4.
carried out in a liquid-circulating shallow packed bed system (Saunders et al., 1989) at different liquid concentrations. The pH was measured in the bulk liquid phase. The experimental data are plotted in Figure 2 and were fitted by the Langmuir equation:
aC c, = 1+ bC In the low liquid concentration range (belowthe 6 mM used for the feed solution in the fluidizedlexpanded bed experiments), the data fit a linear isotherm which validates the assumption in the lumped parameter model. The internal pH should be different from the external pH. However, both the isotherm and breakthrough experiments were done at the same conditions in terms of external pH. Therefore, these isotherm data are appropriate for use in the models. Fluidized Bed Characteristics. The minimum fluidization velocity was calculated with the Ergun equation (McCabe and Smith, 1967) and the Rowe and Henwood correlation (Rowe and Henwood, 1961). Theoretical calculation showed that the minimum fluidization velocity is 2.08 and 2.51 cdmin, respectively, from each correlation. Since most of our experiments were done at a linear velocity of 20 c d m i n and the lowest velocity was 5.53 cdmin, the bed was expected to be fluidized under our operating conditions. The degree of bed expansion depends on the resin size, resin density, volume of resin, liquid velocity, and solution properties such as density and viscosity. Experiments were carried out with resin of known properties and water in a single-stage column. Expanded heights of the fluidized bed (hf) were measured as a function of flow rate and height of the settled bed (h,,). These were used to calculate fluidized porosity (cf) by the following equation derived from a mass balance: Ef =
1 - (1- Ee)(hJhf)
(14)
where represents bed void fraction or external porosity of the packed bed. The results are given in Figure 3. The porosity increased with increasing liquid velocity. The changes in porosity with changing bed height at the same liquid velocity, however, were small except when a very small amount of resin was used. This implies the effect of
Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2703 1
I
I
I
1-7-7
1
Table 2. Specifications for the Distributors (Figure 5) A B C D E ~
Solid lines: quadratic bivariate polynomial fit e, = 0.2663
0.8 h
.-cx 2
+ 0.0265
- 0.00211
ho + 0.0115 uo
holediameter(") no. of holes open area (cm2) ./, opening
h t . 1.196 x 1 0.4u:
v)
0.6
1
3 3
2
0.4
8
1; 0
Y
W-
0.2
Column I.D.= 4 cm Fluid: water
3.6 cm 6.2 cm 6.7 cm 1f.5 cm
I
I
I
0
Type-A
W
Type-C Type-D
0.8
1.5 33 0.58 4.6
2.5 13 0.64 5.1 I
I
1.5 33 0.58 4.6
I
Uo- 20 cmlmin Column ID.- 4 cm Senled bed hi.-4 cm Fluidized bed porosity
.
0.56
0.6
(Settled bed heights)
0
3.5 26 2.50 19.9
3.5 7 0.67 5.3
U.
Y
0
1
1
I
I
I
I
I
5
10
15
20
25
30
35
0.4
uo (superficial velocity, cm/min)
Figure 3. Bed porosity during fluidization.
0.2
1
0.8
E Expandedted Feed rate -15.27 cmlmin A Pxkdbed Feed rate -15.72 cmlmin 1 Column I D = 1 cm m Packed bed ht.. 6 cm Expanded bed ht.=10 cm A=
= 0.36 (packed) = 0.62(expanded)
0
0
8
,$
200
15
20
25
size (see Table 2).
p~ (external)
I
100
10
Figure 5. Effect of distributor on breakthrough at the same bed
0.41
0
5
t (minute)
A
--o-
0
300
-1 0 400
Effluent volume/bed volume (settled)
Figure 4. Comparison of a packed bed and an expanded bed.
bed height on bed expansion is negligible a t the same flow rate as long as the bed is not too short. The low porosity a t the low bed height seems to be due to channeling. The fluidized porosity of our system was in the range 0.45-0.7. All the data were fitted by a quadratic bivariate polynomial as a function of liquid superficial velocity (uo,c d m i n ) and settled bed height (ho,cm) as shown in the figure. Comparison of Breakthrough in Packed Bed and Expanded Bed. A packed bed experiment was carried out to compare breakthrough for the expanded bed. Both experiments were done in column I with the same amount of resin. All experimental conditions were set up equally, but the length of the expanded bed was adjusted to bed expansion while the length of the packed bed was kept close to the settled height. The breakthrough curves are compared in Figure 4. The breakthrough curves look alike except during the initial period. The early breakthrough in the expanded bed during the initial period is due t o high axial dispersion, but the difference gradually disappears as the bed becomes more saturated. The different mass transfer at the early stage of adsorption may also be related to interstitial velocity. The interstitial velocities were 31.4 c d m i n for the expanded bed and 55.6 c d min for the packed bed in Figure 4. The higher interstitial velocity in the packed bed will increase lzf
and give slower breakthrough than the lower interstitial velocity in the fluidized bed. Chase and Draeger (1992) also reported that the expanded bed behaved similarly to a packed bed when the same amount of adsorbent was used a t the same linear flow velocity in a packed configuration. Our experiments are similar to theirs except for the particle size. They used particles of a smaller size with a low density difference between particles and liquid, which resulted in a low value for the terminal velocity. Consequently, the void fraction was large even at low flow rates, whereas we needed higher flow rates to obtain bed expansion. Since the major difference in breakthrough curves of the packed bed and fluidizedexpanded bed occurs during the early period, in the following sections we focused more on the early breakthrough behavior, and the data were collected and analyzed for less than 50 min after start-up. Effect of Distributor. In fluidized or expanded beds, the particle motion and the flow pattern in the entrance region are strongly affected by liquid distributors (Asif et aE., 1991, 1992). In order t o see the effect of distributors, we used five different Teflon sieve plates for distributors in column IV. Each distributor had different size and number of holes as specified in Table 2. The distributors D and E had the same numbers and sizes of holes, but the latter had an additional distributor layer of about 2 cm height filled with spherical glass beads of 4 mm average diameter. The same amount of resin and a constant flow rate were maintained in all tests. The breakthrough curves are compared in Figure 5. The result shows there is a certain trend of the effect of distributor. When the open area is about the same (A, C, and D), the smaller holes proved to be better than the larger holes. The large open area (B) was slightly more effective compared to the small open area at the same size of holes (A), and significantly worse than those a t the smaller sizes of holes (C and D). One can conclude that these results were caused by the change
2704 Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995
'1
I
I
I
I
Column 1.D.- 2.64 cm
0.8 .
0.6 -
I
Settled bed height = 4 cm Linear velocity = 19-21 cmlmin Fluidized bed porosity = 0.56-0.57
I
I
1
I
I
5
10
15
20
25
30
t (minute)
Figure 6. Effect of column diameter on breakthrough at the same residence time.
of hydrodynamic flow pattern through the holes. The difficulty is t o predict the flow patterns for distributors of different sizes and numbers of holes. The inert layer of glass beads (E) resulted in a slightly earlier breakthrough compared to the case of the same distributor but without the glass bead layer (D)as shown in Figure 5 . Overall, however, the inert distributor layer was as good as the type D sieve plate which showed the most effective breakthrough curve in this comparison. The effect of the glass beads as a distributor layer will depend on the size and shape of the beads. We speculate the efficiency would increase if glass beads of a smaller size were used. The type D distributor was used in columns IV and V for the other data in this paper unless specified otherwise. Effect of Column Diameter at the Same Residence Time. Columns of three different diameters (11, 111, and IV in Figure 1)were used for this study. The resin volume varied in each column to make the settled bed heights of all three columns equal. The linear superficial velocity was maintained at about the same value so that the residence time is the same regardless of the column diameter. The glass beads (distributor type E) were used as the distributors of all the columns. The breakthrough curves are compared in Figure 6 a t a settled bed height of 4 cm. First of all, the bed expansion was time-dependent until the bed was stabilized. The expanded bed height was largest just after the start-up, and slowly decreased as the resin particles are redistributed in the order of their sizes. Large particles tended t o settle near the bottom of the bed, and small particles moved upward. The time to reach stabilization was a few minutes for the largest column (IV)which had the bed aspect ratio of 1.0, and was a little longer for the smallest column which had the largest bed aspect ratio. The stabilized bed heights were almost the same in all three columns and close to the data in Figure 3. In principle, the breakthrough should be unchanged if the flow patterns are the same. But this did not occur for the experimental results shown in Figure 6. When the column diameter was reduced, breakthrough became slower. We interpreted this in terms of the bed aspect ratio which is the value of the expanded bed height to the bed diameter. The bed type appears to
change from a fluidized bed t o an expanded bed as the bed aspect ratio increases. This is because of reduced backmixing when bed height is much longer than column diameter. The mass transfer in the particle phase should be the same in both fluidized and expanded beds if the same resin is used, but the mass transfer in the bulk liquid phase depends on the bed type. Effect of Bed Height. We showed that the bed type seems to be determined by the bed aspect ratio, based on the data from columns of different diameters. If the column diameter is fixed and the bed height is increased, we would expect more adsorption since the bed aspect ratio is increasing. The experiments were done in column IV a t four different bed heights. Most other experimental conditions were the same as those in Figure 6. The breakthrough data during up to 30 min are plotted in Figure 7 and quantitatively analyzed with the two different mathematical models. The best fits for each set of data are also shown in Figure 7 and will be discussed in the next section. Mathematical Models for FluidizedIExpanded Beds. Both the lumped parameter model and VERSE were used to fit the data in Figure 7. In the lumped model, the overall mass transfer coefficient (KL) was determined by the Marquardt method for nonlinear regression with the linear isotherm constant from Figure 2. In the VERSE model, the axial dispersion coefficient ( E b ) was adjusted t o fit the data. The film mass transfer coefficient (Kf) was estimated from a packed bed correlation by Wilson and Geankoplis (1966), and adjusted if fitting was not good. Other parameters such as intraparticle diffusivity were obtained by fitting data from packed beds with VERSE. The important parameters are listed in Table 3. The run time of the VERSE simulation was usually several hours, and the best fit was approximately decided by trial and error. When the bed aspect ratio was 1.0, the lumped model fitted the data well as shown in Figure 7a. For aspect ratios greater than 2.0, the lumped model failed to fit the data. This result reflects the assumption of uniform mixing in the lumped model. The bulk liquid phase is not uniform throughout the bed when the bed is long. Therefore the lumped model works only when bed height or aspect ratio is small. The fitting with the VERSE model was reasonably good for all the data shown in Figure 7, and especially good for the largest aspect ratio (Figure 7d). The change of bed type from the fluidized bed to the expanded bed is well represented by the change of axial dispersion coefficient. As shown in Figure 7, the axial dispersion coefficient decreases as the bed height increases. This quantitative result clearly supports that the bed becomes closer to an expanded bed as the bed aspect ratio increases. The axial dispersion coefficient is the most important parameter in simulation of fluidizedlexpanded beds with the VERSE model. A very large value of E b is needed for fluidized beds. The results in Figure 7a also indicate the film mass transfer coefficient is a little lower in fluidized beds than in packed beds. Some correlations for fluidized beds (Rowe, 1975;Rahman and Streat, 1981) also estimated lower values of film mass transfer coefficient, compared to Wilson's correlation under the same conditions. When the aspect ratio is greater than 2.0, however, the film mass transfer coefficients from the packed bed correlation are satisfactory.
Ind. Eng. Chem. Res., Vol. 34,No. 8, 1995 2705
a --
11
I
I
-
I
I
I
I
I
h
11
I
Feed rate 260 mllmln Column dia.- 4 cm Settled bed ht.d.8 cm
0.8
I
I
I
I
I
Expanded bed ht.- 8cm VERSE model fit VERSE with Gunn's correlation
-____
I
1
25
30
I
kf = 0.17 cmlmin (Wilson correlation)
Feed rate = 260 mllmin
0.6 - Column 1.D.- 4 cm
Expanded bed porosity-0.58
A
Expanded bed ht.= 4.cm [i]Lumped model fit
......... [2] VERSE fit (best fit) [3] VERSE with packed bed kf
. . . . . [4] VERSE with packed bed Eb 5
0
10
15
20
25
30
"0
5
t (minute)
kf
0.6 U.
P 0
-
10
15
20
t (minute)
0.17 cmlmin (Wilson correlation)
0.6 -
Feed rate = 260 mllmin Column 1.D.- 4 cm Expanded bed porosity=0.58
U
0.4 -
k, = 0.17 cmlmin (Wilson correlation) Feed rate = 260 mllmin Column 1.D.- 4 cm Expanded bed porosity=0.58
0.4 -
t (minute)
t (minute)
Figure 7. Breakthrough data at different bed heights compared to theoretical analysis. The expanded bed heights were (a) 4,(b) 8, (c) 12, and (d) 16 cm.
Table 3. VERSE Parameters for Simulation of Expanded Beds (for Phenylalanine at the Feed Condition) parameter
value
source
film diffusion coefficient solution diffusivity intraparticle diffusivity on solid phase (see Appendix B) separation factor bed void fraction effective particle porosity capacity no. of axial elements for numerical computation no. of collocation points in each axial element no. of collocation points in radial direction inside particles maximum integration time step absolute tolerance relative tolerance
0.170 c d m i n cm2/min 3.12 x 2.0 x 10-5 cmVmin 3.0 0.58 0.7 1.9 equivL bed (in settled beds) 50
Wilson and Geankoplis correlation (1966) Wilke and Chang equation (1955) fitting packed bed data fitting packed bed data Figure 3 pulse experiments Fbhm and Haas
4 4 0.01 bed volume 0.00001 0.001
From these results, the bed aspect ratio is an important design parameter, and a value between 1.0 and 2.0 appears to be a turning point for a significant change of bed type. We recommend the lumped model for short (fluidized) beds or when the aspect ratio is near or less than 1.0, and the VERSE model for longer (expanded) beds or when the aspect ratio is larger than 2.0. The VERSE simulation results in Figure 7 show a small peak in the breakthrough curves at the early period. The peak becomes smaller as the axial dispersion coefficient decreases. This behavior was also seen in other VERSE simulations with large axial dispersion coefficients (Figure l l b ) , but was not observed in
simulation results for packed beds where small axial dispersion coefficients were used. A high axial dispersion rate causes fast breakthrough for the initial effluent because of increased input concentration, but then the concentration is reduced by increased mass transfer to the particles. VERSE simulation results shown in Figure 8 indicate the main reasons for the early peak. In Figure 8a where a large axial dispersion coefficient was used, the early peak is amplified as film diffusion becomes fast. Curves E and F in Figure 8a show no peaks, but these breakthrough curves are not realistic because the film diffusion coefficients are too small. Figure 8b shows the peaks are significantly reduced by
2706 Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995
I&
0.4
Id
-F- 0- . 0.0.1
I
C
.-
e
5
10
.-
'11
15
20
25
30
/
-
0
/
0
U.ll
10
100
1000
uo (superficial velocity, cm/min)
Bed h t . 4 cm Bed porosity-0.58 Column dia.- 4 cm Flow rate = 260 mllmin
.
(Gunn's correlation)
0
10
,
-
/
Figure 9. Comparison of axial dispersion coefficients.
9
5
/:
cm2/min
(cmlmin) f
/
/
/
lor
.-
F
I
...'
u)
-m
t (minute)
b
........
.... ...'....'.
1oor
n
Bed ht.-4 cm Bed porosity-0.58 Column dia.= 4 cm Flow rate 3 260 mllmin
+=loo uO
;:or
15
20
25
30
t (minute)
Figure 8. VERSE simulation: effect of axial dispersion and film diffusion on early column breakthrough.
a smaller axial dispersion coefficient, and in fact disappear with fast mass transfer to particles which is the case of most packed bed operations. Interestingly, some of the experimental data in Figure 7 also appear to show a small initial peak in the breakthrough data. Axial Dispersion Coefficient in Expanded Beds. The VERSE fits for fluidizecVexpanded beds required appropriate axial dispersion coefficients. Gunn's correlation (1987) has been well-known to determine the axial dispersion coefficient in packed beds. For comparison, the VERSE simulation results using Gunn's correlation are also shown in Figure 7. The axial dispersion coefficient in the expanded bed becomes closer to that in the packed bed as the bed aspect ratio increases. There have been many correlations for the axial dispersion coefficient in fluidized beds. In Figure 9, we compare three correlations within their valid ranges (see Table 4) and the axial dispersion coefficients determined by fitting in Figures 7b and l l b at the same bed height and different flow rates. The figure indicates that our data do not match any of the three correlations, and the correlations do not match each other, probably because the axial dispersion coefficient in fluidized beds strongly depends upon operating conditions and physical properties of the resin. Effect of Column Diameter at the Same Aspect Ratio. From the results in Figure 7, a bed aspect ratio
between 1.0 and 2.0 is the transition point in our system for the change of the bed type from a fluidized bed t o an expanded bed. To confirm this, columns of three different diameters (11, 111, and IV) were used to compare breakthrough at a bed aspect ratio of 1.5. The distributors were type E (glass beads). At the same aspect ratio, the residence time is proportional to the column diameter. Therefore, breakthrough is slower as the column diameter increases as shown in Figure 10. The important point is that the three sets of data were well fitted by the lumped model at this bed aspect ratio regardless of the column size. We can conclude that the transition point with respect to the bed aspect ratio should be between 1.5 and 2.0 for the diameter range we studied. Another interesting thing in Figure 10 is the difference in the overall mass transfer coefficient (KL). While the K L values at the bed diameters 2.64 and 4.0 cm are very close, the K L at the bed diameter 1.42 cm is half the other two K L values. This indicates that there is another effect of column size on mass transfer rate even at the same bed aspect ratio. In the previous section concerning the data in Figure 3, we discussed channeling for the bed height of 1 cm. In Figure 10, we see a low efficiency in mass transfer rate for the bed height of 1.42 cm. From these two results, very shallow fluidized beds seem to have channeling which decreases the effective overall mass transfer rate. Effect of Liquid Flow Rate. Process throughput is directly proportional to flow rate. The liquid flow rate also affects the ion-exchange rate in two different ways: mass transfer rate and residence time. As the flow rate increases, the liquid residence time decreases and a longer column may be required in order to achieve a given level of separation. The thickness of the hydrodynamic boundary layer surrounding the resin particles becomes smaller as the flow rate increases, and thus mass transfer resistance through the film is reduced a t high flow rates. Experiments were done in the 4 cm column at two different bed heights, with change of liquid flow rate. The results are shown in Figure 11. The ion-exchange conversion (1 - C/CF) is higher at the lower flow rates. Thus, increasing residence time appears to have more influence than decreasing film mass transfer rate. The data in Figure 11 were fitted by the lumped parameter model for the short bed (a) and by the
Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2707 Table 4. Correlations for Axial Dispersion Coefficient in Liquid Fluidized Beds valid range
Chung and Wen (1966)
Re or uo( c d s )
Krishnaswamy et al. (1978)
5 1- 1286
particle diameter (mm) particle density (g/cm3) bed porosity bed aspect ratio ( c d c m )
Tang and Fan (1990)
fitted values for our data
0.5-4.0 1-2.5 1.05-1.3 0.5-0.92 17.1 (130/7.62)
1.0-3.3 0.2-0.66 0.5 1.2 0.5-0.7 2.0 (8/4)
1-1000
2.03-6.35
0.5-14.3 1.28-1 1.3
7-8 0.4-0.8 16 (81.2W5.08)
-
Bed aspect ratio 1.5, Expanded bed porosity = 0.6 Linear velocity = 19-21 cmlmin H
0.8 H
0.E
0.6
-
A A
L
U
A kL=0.053cm/mi
9 0
9 0
o,21 0;
Column I.D=4 cm Settled bed h b 2 . 6 cm Expanded h t d . 8 - 4 . 0 cm Bed porosity = 0.45-0.61
0.4
0.4 Column 1.D.- 4 s m Column 1.D.- 2.64 cm Column 1.D.- 1.42 cm
H
A
Fining with lumped model I
I
5
10
1
I
15 20 t (minute)
I
25
I
0.2
W
A
-
Flow rate = 406 mllmin Flow rate 117 mllmin
Fitting with lumped model
I 30
Od
5
10
15 20 t (minute)
25
~
Figure 10. Effect of column size a t the same aspect ratio.
VERSE model for the longer bed (b). In Figure l l a , the fitted value of k L increased from 0.053 to 0.085 c d m i n as the flow rate increased from 117 to 406 mumin. The Rahman and Streat correlation estimated kf at 0.112 c d m i n (at 117 mumin) and 0.209 c d m i n (at 406 mL/ min) for this fluidized bed. The increase in kf caused the increase in k ~ . Much longer breakthrough curves and higher capturing efficiency were obtained using an expanded bed with a higher bed aspect ratio (7.2-10 cm height/l cm diameter) a t different flow rates. The results are shown in Figure 12. The lower velocity in Figure 12 was just above the minimum fluidization velocity, and therefore the increase of bed voidage was small. The breakthrough at the lower flow rate is slow. The VERSE simulation results are shown in Figure 12. The simulation parameters were the same as those in Table 3. The simulation is very accurate at the low flow rate, and predicts reasonably well the data a t the high flow rate. We speculated many possible explanations for the deviation at the high flow rate. Since the parameters in Table 3 were obtained from fitting of the data in Figure 7 where the column size was larger (4 cm), some mass transfer parameters may not be appropriate for a smaller column if there is a column size effect on mass transfer. The deviation may also be related to distributor effects, or it may be related to the diffusion and isotherm models used. The correlations that we used may also be inaccurate for different columns or different flow rates. Further investigation is needed. Mass Transfer to Particles. Mass transfer to particles was lumped into k~ in the lumped model, and was distributed as kfand D,, in the VERSE model. By comparing the overall mass transfer coefficient ( k ~from ) fitting with kf from correlations, we may be able to evaluate a rate-controlling mechanism in this ionexchange system. kL combines mass transfer contributions of both kf and Dmp.If k~ is much less than kf,there is a significant mass transfer resistance other than film diffusion. In Figure 7a, the fitted k L was 0.076 c d m i n
b 1 0.8 -
0.6 -
Column i.D.= 4 cm Settled bed ht.=5.6 cm Expanded ht.- 6.7-9.5 cm Bed porosity 0.50-0.65
-
Simulation by VERSE model
LL
%=500 cm2/m I n
9 0
0.4
"0
5
10
15
20
25
t (minute)
Figure 11. Effect of flow rate on breakthrough in a large column (4 cm id.) at different bed heights.
while kf estimated was 0.17 c d m i n . This is the same for Figure l l a , where two K L values from fitting (0.053 and 0.085 c d m i n ) were much less than 0.17 or the kf from the Rahman and Streat correlation. Both results in Figures 7a and l l a were obtained at a bed aspect ratio of 1.0. In Figure 10, on the other hand, the fitted k~ values at 2.64 and 4.0 cm columns were very close to 0.17 cdmin, but the increase of k~ in Figure 10 compared t o Figures 7a and l l a seems to be due to reduced backmixing, because the bed aspect ratio is higher (1.5). It should be remembered that the lumped model with K L is less useful when mixing is reduced. From these results, we believe both film mass transfer and intraparticle diffusion are important in this system. Multiple Stages. Compared to single-stage columns, multistage columns are difficult to operate. The data shown in Figure 13 are much more scattered than the previous results. The experiments were done in column V with three stages. The bed height in each stage was 2.6 cm when settled by gravity. The effluent concentra-
2708 Ind. Eng. Chem. Res., Vol. 34,No. 8, 1995 1
I
1
I
I
I
1
r
r
Single stage (expanded ht =12cm)
0.8
0.8
0.6 -
0.6 VERSE with parameters in Table 3
U
9
0
U
-
W
0
100
400
Figure 12. Effect of flow rate on breakthrough in a small column (lcm i.d.1 at a settled bed height 6.4cm.
,
I ,
I
1
I
Flow rate = 406 milmin
0.8
__-.a'- - .I-it& 3
0.6 !A
Y
0
0.4 kL-0.063cmlmin (fit for stage 1 ) Solid line: fitting the data Dotted lines' prediction, Setlied bed ht.- 2.6 cm in each Expanded bed porosity = 0.61 Column I.D.= 4 cm
0
10
20
30
40
50
t (minute)
b
' 0.E
1
I
,
I
?ow rate = 117 mllmin kL=0.049cm/min (fit lor stage 1 ) Solid line: fitting the data Dotted lines: prediction
0.E U
9
0
0.4
0.;
0
__--
-
Sealed bed ht.= 2.6 cm in each stag Expanded bed porosity 0.45 Column I.D.= 4 cm 1
t
"0
5
10
15
20
25
30
t (minute)
t (min)
a
-
4.34 ml/min 15.27 mllmin
300
200
Feed 6mM Phenylalanine (pH 2 4) Flow rate = 260 mllmin Column I D 4 cm Distributor type-0 Bed porosity = 0 58
0.4
Feed conc.=0.006M Senled bed h t d . 4 cm
A
2
3 stages (expanded ht -4cm each)
I
I
t (minute)
Figure 13. Breakthrough in multiple stages and theoretical predictions by the lumped model at flow rates (a)406 and (b) 117 mumin.
tions were measured as a function of time throughout the column. The data of the first stage were fitted by the lumped model to determine k~ at each flow rate. The lumped model was chosen because of the small bed aspect ratio (around 1.0). The overall mass transfer coefficients from the first stage were used to predict the
Figure 14. Comparison of ef€luent concentration from a singlestage expanded bed and a three-stage fluidized bed.
concentration profiles in the second and third stages. The data and the theoretical results are shown in Figure 13. Overall, the model predicts the column behavior reasonably well. At the higher flow rate, the model prediction fits the data satisfactorily. At the lower flow rate, some deviation is seen in the upper stages. A possible reason for the deviation at the lower flow rate is nonuniform mixing. Comparison of Expanded Bed and Fluidized Bed. It is interesting to compare breakthrough for the expanded bed and for the fluidized bed when the same amount of resin is used. The experiments were done with columns N and V. The expanded bed result was shown in Figure 7c. The same total amount of resin was divided into three equal amounts and filled column V with three stages. The bed aspect ratio was about 3.0 for the single-stage expanded bed and about 1.0 for each stage of the three-stage fluidized bed. As shown in Figure 14, the three-stage bed showed poorer adsorption performance compared to the single-stage bed. This result is surprising because a multistage system usually gives better adsorption efficiency than a single-stage column. This result was repeated in three runs. The explanation is directly related to the results in Figure 7. Backmixing is significantly reduced as bed height increases. Each stage of the multistage system has large backmixing which results in loss of capturing efficiency. A long single stage has less backmixing, and comparison of Figure 7 shows that Eb is orders of magnitude lower. This result implies that a single stage can be more efficient than a multistage system because of reduced backmixing. Perspective of Scale-up. It should be mentioned that all the data and theoretical analysis shown in this paper are limited to column diameters up to 4 cm. We think column diameter will have a major effect when much larger columns are considered. For example, a 100 cm diameter bed with an aspect ratio of 1.0 may look more like an expanded bed than a fluidized bed. The critical bed aspect ratio at which bed type changes is about 1.5 from our result when column diameter is no larger than 4 cm, but is possibly a function of column diameter when column diameter is much larger than 4 cm (see Figure 15). For this reason, our conclusion cannot be global since we do not have data at very large column diameters.
Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995 2709
Acknowledgment
10
This research has been partially supported by National Science Foundation Grants BCS-8912150 and GER-9024174 and by the Purdue Research Foundation. The donation of resin by Rohm and Haas is gratefully acknowledged.
a
5-
6
5E
.-9)
2
Nomenclature 4
3 2
0
a = Langmuir isotherm parameter, eq 13 b = Langmuir isotherm parameter, eq 13
(The scope of this study)
/
Fluidized F Iuidi zed bed
2
C = concentration in bulk liquid phase, mom
j ~ I
4
6
a
10
Column diameter (dc, cm)
Figure 15. Significant range of bed size for our results.
Conclusions Increasing the bed aspect ratio decreased the axial dispersion or backmixing. The experiments were done by changing the column diameter (up to 4 cm) a t a fixed bed height and by changing bed height at a fixed column diameter. We defined the fluidized bed as a uniformly mixed bed and the expanded bed as a bed with lower backmixing than a fluidized bed. We applied the lumped parameter model successfully for the fluidized bed and the VERSE model successfully for both fluidized and expanded beds. The comparison of experimental results and theoretical analysis proved that the fluidized bed behavior was maintained when the bed aspect ratio was below 1.5, and the bed type gradually changed into the expanded bed as the bed aspect ratio increased. The axial dispersion Coefficient became closer to the value for packed beds as the bed aspect ratio increased. While the bed type was dependent on bed aspect ratio, the bed expansion ratio (hdh,)was not affected by change of bed height at a constant bed diameter except for very shallow beds which showed channeling. Each mathematical model has advantages. Though application of the lumped model is limited to fluidized beds only, it is a convenient model because exact analytic solutions exist for linear isotherm systems. The VERSE model can be used for both fluidized and expanded beds. A n axial dispersion coefficient is a key parameter for simulation with VERSE. The film mass transfer coefficient for an expanded bed can be estimated from packed bed correlations, but it needs adjustment for some extreme conditions. The effects of several operating variables on column breakthrough were investigated. The breakthrough curve in the expanded bed was almost the same as that in the packed bed except for an earlier breakthrough during the initial adsorption period. The distributor with more holes of the smaller size was more efficient compared to distributors with fewer holes of larger sizes. High flow rates resulted in poorer adsorption efficiency than low flow rates in spite of increased mass transfer coefficients, because of reduced residence time. When the same amount of resin was loaded in the columns, the single-stage expanded bed was better in capturing ability than the multistage fluidized bed because of reduced backmixing.
C' = concentration in supernatant region, mom C, = liquid pore phase concentration inside particles, mom C,= solid phase concentration inside particles, m o m solid = average solid phase concentration inside particles, mom solid C* = equilibrium concentration, mom d, = column diameter, cm Do= diffusivity of a single solute in solution, cm2/min D,, = apparent intraparticle diffusivity, cm2/min D, = pore diffusivity, cm2/min D, = surface diffusivity, cm2/min Eb = axial dispersion coefficient, cm2/min hf = height of fluidized bed, cm h, = height of packed bed, cm h, = bed height when settled by gravity, cm h,, = height of supernatant region, cm kf = film mass transfer coefficient, cdmin k L = overall mass transfer coefficient, cdmin m = linear isotherm parameter QL = liquid volumetric flow rate, mumin r = radial position inside particles, cm R , = average particle radius, cm or mm s = Laplace domain variable t = time, min ui = interstitial velocity, cdmin uo = superficial velocity, cdmin x = dimensionless concentration in liquid phase, C/CF x' = dimensionless concentration in supernatant region, C'/
e,
CF y = dimensionless
concentration in solid phase, C $ ( ~ C F ) or CAmCF) z = axial position in column, cm Subscripts F = feed liquid solution in = input stream to each stage n = stage number Greek Letters a = separation factor, eq 9 al= parameter used in eq (A-10) a2 = parameter used in eq (A-10) = external porosity of packed bed Ef = porosity of fluidizedexpanded bed E , = intraparticle porosity ZL = hf lui (residence time in fluidized region), min tsp= hs&, (residence time in supernatant region), min w = Laplace domain solution term, eq (A-9) Dimensionless Groups = ( 3 k ~ t ~ ) /(dimensionless R, mass transfer coefficient) 1 = tL/tsp(residence time ratio)
2710 Ind. Eng. Chem. Res., Vol. 34, No. 8, 1995
4 = (1 - ~ f ) / q(volumetric ratio of solid to liquid) e = t / q (dimensionlesstime variable)
Appendix A. Exact Solutions of the Lumped Parameter Model for Linear Isotherms and Multiple Stages The governing equations for the lumped model in dimensionless forms are
where X1,in = 1.0 and xn,in = X'n-1 when n = 2, 3, 4, ...
&',Id% = A(x, - x ' ~ )
(A-3)
with the equilibrium expression in dimensionless form
Other transforms are done in the same way, but care must be taken to adjust the order of each term on the denominators of functions related with wn. These solutions are easily programmed on a computer for any n.
Appendix B. Intraparticle Diffusivity in the VERSE Model The apparent intraparticle diffusivity in the VERSE model is the sum of a pore diffusivity and a solid diffusivity by the following equation:
The initial conditions are
(A-12)
The equations to be solved are a set of linear ordinary differential equations with constant initial conditions. These were solved by the Laplace transformation. Analytical time domain solutions were obtained by partial fractions with repeated factors (Churchill, 1958) of the Laplace domain solutions. The solutions for batch operations are
where the (aC$aC,) term is simply a constant (m)in the linear isotherm region. Gel-type resins have small pores which are formed by polymer chains, but the pore size is so small that the diffusion through the pores is restricted. For this reason, the main diffusion mechanism in gel-type resins is considered t o be solid phase diffusion or surface diffusion. Therefore , the diffusivity for a linear system becomes
+Ip
