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Ind. Eng. Chem. Res. 1997, 36, 152-159
Simulated Moving-Bed Reactor: Application in Bioreaction and Separation C. B. Ching* and Z. P. Lu Department of Chemical Engineering, The National University of Singapore, Singapore 119260, Singapore
The performance of simulated moving-bed reactor for two semicontinuous chromatographic reaction-separation processes, namely, isomerization of glucose to fructose (Hashimoto et al., 1993) and inversion of sucrose to glucose and fructose (Ganetsos et al., 1993), has been studied by mathematical modeling and numerical simulations. Simulation results agreed well with the published experimental results. The process performance, which is stated in terms of the process performance parameters defined in this paper, was also studied for various operating conditions, for both the processes. Since the reaction was introduced in the process, reaction conversion becomes a process performance parameter of importance, which was considered along with product purity and recovery. The criteria of the operating parameter (Ruthven and Ching, 1989) for linear systems for a simulated moving-bed process is not applicable for a simulated movingbed reactor process in some cases. Introduction A chromatographic reactor-separator can be defined as a chromatographic system that is used to convert one or more components partially or totally and to simultaneously separate one or more of the products that are formed. The reaction can either be chemical or biochemical, taking place on the stationary phase, in the mobile phase, or both. In addition to financial and operational benefits achieved through process intensification, chromatographic reactor-separators are unique in applications where the removal of inhibitors, acceptor products, or poisons will improve the overall reaction yield. In reversible reactions, where higher conversion can be achieved by removing one or more of the products, thus shifting the equilibrium, chromatographic reactor-separators are very useful. The advantages of coupling chemical reaction and separation were recognized in the early 1960s; since then, largesize commercial applications have been developed mostly in the refining industries with the production of octane boosters like methyl tert-butyl ether and ethyl tert-butyl ether in reactive distillation processes. In the chromatographic reaction field the major part of the work was on theoretical studies and modeling (Roginskii et al., 1961; Magee, 1963; Schweich and Villermaux, 1982; Petroulas et al., 1985; Loureiro et al., 1993). The preparative applications of chemical chromatographic reactors are still in their early stages, and hence further development was the main objective of most works (Vaporciyan and Kadlec, 1987, 1989; Ray, 1992; Carr, 1993; Sardin et al., 1993; Chatsiriwech et al., 1993; Lu et al., 1993a; Lu and Rodrigues, 1994). The application of chromatographic reactors in the biochemical field was initiated in the 1980s by Barker and co-workers for biosynthesis of dextran, a polyglucose used in the pharmaceutical, chemical, and food industry, in batch chromatographic columns. The inherent advantages of continuous operation, such as product quality, no recycling, better utilization of the available mass-transfer area, and their success in separation applications, make them naturally the next step in the development of the chromatographic reaction-separa* To whom correspondence should be addressed. Telephone: 0065-7722883. Fax: 0065-7791936. e-mail: checcb@ leonis.nus.sg. S0888-5885(96)00317-X CCC: $14.00
tion principle. Based on published information, there appear to be only two applications of the continuous chromatographic reaction-separation principle in the biochemical field: simulated moving-bed bioreactors by Ganetsos et al. (1993) and Hashimoto et al. (1993). The simulated moving bed (Ruthven and Ching, 1989) normally consists of more than four columns and the dynamics of the process is very complicated. The simulated moving-bed reactor (SMBR) is derived from the simulated moving bed; hence, the principle of the process is almost the same. The design of a simulated moving bed mainly relies on the adequate choice of the different liquid flowrates and the bed switch period. Modeling and numerical simulation of a simulated moving bed have gained more and more attention because a significant savings in materials (particularly for an expensive material system) and time can be achieved by computer simulations even in the technology development stages (Hashimoto et al., 1993; Storti et al., 1993; Balannec and Hoiter, 1993; Nicould, 1992; Rodrigues et al., 1995; Lu and Ching, 1996). This work focuses on the process performance of the simulated moving-bed reactors applied in biochemical reactions with immobilized and mobilized enzymes (Hashimoto et al., 1993; Ganetsos et al., 1993). The process dynamics and the effect of operating parameters on the process performance will be addressed by modeling and simulations. Process Description Isomerization of Glucose to Fructose. In the food industry, syrup with a higher fructose content is desired for higher sweetness and solubility in water. An enzymatic isomerization of glucose to fructose gives an equimolar mixture due to the reversible reaction isomerize
fructose 798 glucose
(1)
In such cases, a process to separate fructose from the equilibrium mixture is indispensable. Hashimoto et al. (1993) proposed a process in which high-fructose syrup is produced by combining the adsorption and reaction on alternatively arranged adsorption and bioreaction columns (immobilized enzyme) as shown schematically in Figure 1. The inlet and outlet liquid lines divide the © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 153
Figure 1. Schematic diagram of the simulated moving-bed reactor for isomerization of glucose to fructose (Hashimoto et al., 1993).
system into three zones. The adsorption columns and reactors are alternately arranged in zone III. Zones I and II consist only of adsorption columns. The details can be found elsewhere (Hashimoto et al., 1993). Inversion of Sucrose to High-Purity Fructose and Glucose (Mobilized Enzyme). A process in which sucrose was continuously inverted into fructoseand glucose-rich product in the presence of mobilized enzyme invertase, by combining the reaction with the simulated moving-bed separation process, is shown in Figure 2. H2O + invertase
nsucrose 98 nfructose + nglucose (2) In this process, 95% pure products can be obtained. Details can be found elsewhere (Ganetsos et al., 1993). Mathematical Model Figures 1 and 2 show sketches of the simulated moving-bed reactors. Due to the fact that the immobilized enzyme is used for isomerization of glucose to fructose, reaction only occurs in the reactors in zone III and the catalyst is fixed in Figure 1. For inversion of sucrose to fructose and glucose, the reaction happens in fluid phase in zone III since the mobilized enzyme is used in Figure 2. In these configurations, liquid goes up and adsorbent goes down in each zone and then a countercurrent contact between solid and liquid occurs, leading to a high-mass-transfer driving force. Provided that the adsorption affinities of species A and B or B and C on the adsorbent are different, it is possible to choose the right flowrates of the solid and the liquid to force one species to move upward and the other species to move downward, thus leading to a spatial separation. Due to difficulty in handling the solid, its movement is
Figure 2. Schematic diagram of the simulated moving-bed reactor for inversion of sucrose to high-purity fructose and glucose (Ganetsos et al., 1993).
simulated by shifting inlet and outlet lines in between a number of fixed columns (normally 4-24 columns) which are looped together. A design guideline for the linear systems has been stated by Ruthven and Ching (1989), which mainly relies on the appropriate choice of different flowrates: recycle, feed, eluent, extract, raffinate, and solid (equivalent to the switching time). For the nonlinear systems, the estimation of the flowrates is extremely difficult. It is advised that simple mathematical models should be used for the complicated setup of the simulated moving-bed reactors to get useful insight on the process performance at an early stage. Process parameters to be studied for the abovementioned processes are listed in Tables 1 and 2, and mathematical models can be developed based on the following assumptions: (1) The desorbent and catalyst are homogeneous. Then the overall mass transfer between the fluid and solid can be described by the linear driving force (LDF) model (Glueckauf, 1955) on a parabolic intraparticle concentration profile assumption. The LDF model has been widely used in the modeling of many adsorption processes due to its remarkable simplicity and good agreement with the experimental results (Do and Rice, 1986). (2) The flow pattern inside adsorption columns and reactors can be described by axial dispersed plug flow which is acceptable if the ratio between the length and diameter of the column is larger than 5-8 (Ruthven, 1984). However, the variation of the fluid velocity and concentration in the radium shall be considered for the large radial columns or industrial columns. (3) The “dead” volumes at both ends of the columns and reactors are negligible. Dead volumes are hard to avoid in the packed columns, and they do affect the column behavior (Lu et al., 1993b; Ramkrishna and Amundson, 1974) which shall be
154 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 Table 1. Parameters Used in the Simulations for SMBR I section III section II section I each column diameter: length: porosity: distribution coefficients for glucose and fructose in the solid phase: KA ) 0.686 KB ) 0.586
8 adsorption columns, 7 reaction columns 3 adsorption columns 3 adsorption columns D ) 1.38 cm L ) 10.2 cm ) 0.4
overall mass-transfer coefficients between fluid and solid: reaction rate coefficient: feed composition: operation parameters switch time: feed: desorbent: recycle:
ktA ) ktB ) 0.41 min-1 kr ) 0.0617 min-1 cAf ) cBf ) 1.0 mol/L t ) 3.0 min Vfe ) 0.145 mL/min Vde ) 0.43 mL/min Vrc ) 4.0 mL/min
Table 2. Process Parameters Used in the Simulations for SMBR II section I section II section III reaction occurs in sections I and II each column diameter: length: porosity: distribution coefficients for sucrose, glucose, and fructose in the solid phase KA ) 0 KB ) 0.45 KC ) 0.65
1 adsorption column 5 adsorption columns 6 adsorption columns D ) 5.4cm L ) 75cm ) 0.4
studied separately. (4) Isothermal operation for the system is assumed due to temperature control (Hashimoto et al., 1993; Ganetsos et al., 1993). The heat effect for liquid-solid systems is normally quite small (Ching and Ruthven, 1986); however, it must be considered for the gas-solid systems (Lu et al., 1993b). Simulated Moving-Bed Reactors I (Isomerization of Glucose to Fructose, Figure 1). After introducing the dimensionless variable:
x ) z/Lj where Lj is the length of the column j, the following model equations can be obtained: (1) Mass balances inside the sections and columns for species i (i ) A and B, A for glucose and B for fructose) 2 1 d cij dcij 1 - dqij ξ )0 Pej dx2 dx j dx (referring to the adsorption columns)
(for sections I and II where j ) 1, 2, ..., 6) (for section III where j ) 7, 9, 11, ..., 21)
(3a)
2 1 d cij dcij 1 - r )0 Pej dx2 dx ij (referring to the reaction columns)
overall mass-transfer coefficients between fluid and solid: reaction rate coefficient: feed composition: operation parameters switch time: feed: eluent: desorbent:
ktA ) ktB ) 0.2 min-1 kr ) 0.02 min-1 cAf ) 1.0 mmol/mL t ) 30 min Vfe ) 9.0 mL/min Vel ) 31.5 mL/min Vde ) 76 mL/min
(3) Reaction rates (Hashimoto et al., 1993):
-rAj ) rBj ) Daj(cA - cB) (referring to the reaction columns) (5) (4) Linear adsorption isotherms (Hashimoto et al., 1993):
fi(cij) ) Kicij (referring to the adsorption columns) (6) (5) Boundary conditions for the adsorption and reaction columns
1 dcij ) cij-1|x)1 (except for j ) 1 Pej dx and 7 where desorbent and feed are introduced)
x ) 0,
cij -
dqij ) 0 (except for j ) 8, 10, ..., 20 for dx reaction columns) (7a) For j ) 1 and 7 where the desorbent and feed are introduced:
x ) 0,
(for section III where j ) 8, 10, 12, ..., 20) (3b)
ci1 -
1 dci1 V3 ) ci21|x)1 Pe1 dx V1 (there are no A and B in the eluent)
ci7 -
1 dci7 V2ci6|x)1 + Vfecif ) Pe7 dx V3
(7b)
For a reaction column, the mass-transfer resistance between mobile and stationary phases is assumed to be negligible compared with the reaction rate. (2) Mass-transfer rates between the fluid and the solid (LDF model):
x ) 1,
dqij 1 ) (fi(cij) - qij) dx Rij (referring to the adsorption columns) (4)
dcij ) 0; qij ) qij+2|x)0 dx (for section III where j ) 7, 9, ..., 21, and if j + 2 > 21, then j + 2 ) 1) (7c)
dcij ) 0; qij ) qij+1|x)0 dx (for sections I and II where j is below 7)
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 155
(6) Overall mass balances at the nodes of the sections
V3 ) Vrc
V2 ) Vrc - Vje
V1 ) Vrc + Vde (8)
(7) Process performance parameters can be defined as:
(a) Dilution ratio Rd )
Vfe + Vde Vfe
fi(ciJ) ) KiciJ (5) Boundary conditions for the sections
dqiJ 1 dciJ ) 0; )0 PeJ dx dx (no liquid recycle is considered in this work, J ) 1, 2)
x ) 0, ciJ -
(9) ci3 -
(b) Enhanced reaction conversion cBp/cAp E) cBf/cAf
(10)
x ) 1,
1 dci3 V2c2|x)1 + Vfecfe ) ; Pe3 dx V3 dciJ ) 0; dx
qiJ ) qiJ+1|x)0
V1 ) Vde (11a)
V2 ) Vel
yi ) (11b)
Lj vj
RB ) (11c)
(11d)
x ) z/LJ where LJ is the length of the section J, the following model equations can be obtained: (1) Mass balances inside the sections for species i [i ) A, B, and C; A ) sucrose (nonadsorbable), B ) glucose, and C ) fructose] 2 1 d ciJ dciJ (1 - ) dqiJ ξJ + riJ ) 0 PeJ dx2 dx dx (reaction occurs in the fluid phase and J ) 1, 2, 3) (12)
(2) Mass-transfer rates between the fluid and the solid (LDF model):
(13)
(3) Reaction rates:
-rAJ ) rBJ ) rCJ ) DaJcAJ
∑ci
(i ) B, C)
(18)
(Vfe + Vel)cB3|x)1 VfecAf
(19a)
VdecC1|x)1 VfecAf
(19b)
RC )
Simulated Moving-Bed Reactors II (Inversion of Sucrose to Glucose and Fructose). After introducing the dimensionless variable:
dqiJ 1 ) (fi(ciJ) - qiJ) dx Ri
ci
(b) Products recovery
(d) Reaction Damkohler number Daj ) kr
(17)
(a) Products purity in their enriched streams
(c) Reciprocal of mass-transfer unit 1 us Rij ) kti Lj
V3 ) Vel + Vfe
(7) Process performance parameters
(b) Ratio of the flowrate between solid and liquid us ξj ) vj
(16a)
(6) Overall mass balances at the nodes of the sections
(a) Axial Peclet number vjLj DLj
dqiJ )0 dx
(if J + 1 > 3, then J + 1 ) 1) (16b)
(8) The model parameters are:
Pej )
(15)
(14)
(4) Linear adsorption isotherms (Ching et al., 1987):
(8) The model parameters are the same as those stated in eq 11 except the LJ referring to the length of the section J. Simulation Results and Discussion In this work, only linear adsorption isotherms have been considered. The range of the operation conditions (fluid and solid flowrates in each zone) for a three-zone simulated moving bed can been determined by the equation (Ruthven and Ching, 1989)
βiJ )
(1 - )ξJKi
(20)
where i ) A, B for the two species with different linear adsorption coefficient KA and KB and J ) I, II, III for the three zones. From the concept of simulated moving bed, for a good separation, the above operating parameter must satisfy the values listed in Table 3, for each zone. However, this is not always valid for the simulated moving-bed reactor process, since a new process performance parameter, namely, reaction conversion, must be considered in this case. The model equations were solved by the numerical method of orthogonal collocation in finite elements, and the details can be found elsewhere (Lu and Ching, 1996). (I) Isomerization of Glucose to Fructose. Three operation modes, (a) a conventional chromatographic process to separate glucose and fructose, (b) a glucosefructose separation process using a simulated moving bed separator (in a and b modes a raffinate solution
156 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 Table 3. Ranges of the Values of the Operating Parameter for a Good Performance no. of zones
I
II
III
βfJ βgJ
>1 >1
1
1
Table 4. Values of the Operating Parameter for the On-Column Concentration Profiles in Figure 3 no. of zones
I
II
III
βfJ βgJ
1.14 1.34
0.87 1.02
0.94 1.10
Figure 3. On-column concentration profiles of the simulated moving-bed reactor arrangement for isomerization of glucose to fructose where the process parameters are listed in Table 1, where Vrc ) 34.0 mL/min, Vde ) 0.43 mL/min, Vfe ) 0.145 mL/min, and t ) 3 min.
containing mainly glucose is recycled to a main reactor to isomerize to fructose), and (c) the process described in Figure 1, had been studied and compared by Hashimoto et al. (1993). They found that the conventional chromatographic process has the lowest performance of the three processes and that process b can achieve the highest fructose content at a relatively high dilution ratio, Rd. When producing a fructose content of 55% syrup (an assumed desired level), process c shows the highest performance of the three modes. The on-column concentration profiles from the numerical simulation (eqs 3-7) are shown in Figure 3 for the process parameters stated in Table 1 (equivalent to run 6 of Hashimoto et al., 1993). These are similar to the experimental results obtained by Hashimoto et al. (1993), and the values of the operating parameters (eq 20) in each zone are listed in Table 4 which satisfied the requirement shown in Table 3. In Figure 3, one can see that the concentrations of glucose and fructose at the inlet and outlet of the reactors are almost the same, which means that efficiency of the reactors is very low in the process. In reactor 1 (column 7) an undesirable reaction occurs since a higher fructose concentration than that of glucose can be seen at the inlet. There is no raffinate stream in this arrangement, and it is different from a three-zone simulated moving bed. Therefore, the range of operating parameters shown in Table 3 is not valid for the simulated moving-bed reactor arrangement. Based on the above conclusion, influence of the operating fluid and solid flowrates on the process performance was extensively studied. Effects of the desorbent flowrate for a given dilution ratio and for a given desorbent flowrate are shown in parts a and b of Figure 4, respectively. Higher desorbent flowrate for a
Figure 4. Effect of the operating parameters on the process performance for the simulated moving-bed reactor arrangement shown in Figure 1. (a) Effect of the desorbent flowrate on the enriched reaction conversion for a given dilution ratio R ) 3 where the process parameters are listed in Table 1 except Vrc ) 3.9 mL/ min. (b) Effect of the dilution ratio on the enriched reaction conversion for a given desorbent flowrate where the process parameters are listed in Table 1 except Vrc ) 3.9 mL/min and Vde ) 1.48 mL/min.
fixed dilution ratio means higher process productivity. In Figure 4a, the enriched reaction conversion increases with the desorbent flowrate for a given dilution ratio Rd initially, and it reaches the maximum value E ) 1.23 at desorbent flowrate Vde around 1.5 mL/min and then decreases drastically. Higher dilution ratio means more diluted products. In Figure 4b, the enriched reaction conversion increases with dilution ratio Rd for a given desorbent flowrate Vde, and it reaches a plateau value when Rd is greater than 3. The switch time (solid flowrate) and recycle fluid flowrate in zone III were also investigated. Their effects on the process performance are quite smooth, and the process gives the best enriched reaction conversion at dilution ratio Rd ) 3, desorbent flowrate Vde ) 1.48 mL/min, switch time t ) 3 min, and recycle flowrate Vrc ) 3.9 mL/min. The on-column concentration profiles for the simulated moving-bed reactor arrangement operated at Rd ) 3, Vde ) 1.48 mL/min, Vrc ) 3.9 mL/min, and t ) 3 min are shown in Figure 5, and the values of the operating parameters are listed in Table 5. The concentration gradient is much larger and the highest concentration level is almost double than that in the previous operation. The concentration of glucose is always lower than the fructose concentration in zones I and II, which reverses in zone III. Also the reaction does not reach equilibrium at the outlet of the reaction columns since the difference between the glucose and
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 157
Figure 5. On-column concentration profiles of the simulated moving-bed reactor arrangement for isomerization of glucose to fructose where the process parameters are listed in Table 1 except Vrc ) 3.9 mL/min, Vde ) 1.48 mL/min, Vfe ) 0.5 mL/min, and t ) 3 min. Table 5. Values of the Operating Parameter for the On-Column Concentration Profiles in Figure 5 no. of zones
I
II
III
βfJ βgJ
1.60 1.87
0.70 0.82
0.89 1.044
fructose concentrations can still be observed. If the reaction column is longer or the reaction rate is fast, a better process performance is expected. A test simulation with 5 times higher reaction rate was done, and the enhanced reaction conversion E ) 1.6 was obtained. From the above analysis, we can see that the process development can also be done through mathematical modeling and numerical simulations. Of course, experimental results are necessary to verify the simulation results. (II) Inversion of Sucrose to Glucose and Fructose. The bioreaction of the inversion of sucrose to glucose and fructose takes place at 55 °C and at pH about 5.5. The invertase enzyme is added to the eluent, and the reaction occurs in the mobile phase (eq 12). Complete reaction conversions were obtained in the experiments with feed concentrations of up to 55% w/v sucrose for the process configuration shown in Figure 2 (Ganetsos et al., 1993). The reference parameters used in this work are listed in Table 2. Since the adsorption isotherms for sucrose, glucose, and fructose for the system were not given by Ganetsos et al. (1993), they were taken from elsewhere (Ching et al., 1987). The reaction stated in eq 2 is irreversible, and the process shown in Figure 2 is very similar to the three-zone simulated moving-bed process without liquid recycle. Although the values of operating condition parameters (eq 20) in zone II are not within the range listed in Table 3 for the system shown in Table 2, a reasonably good process performance has still been obtained. Effects of the feed flowrate, eluent flowrate, and switch time on the purity and recovery of the products are shown in Figure 6. Higher feed flowrate leads to higher process productivity and more concentrated products. Higher eluent flowrate and longer switch time lead to a more diluted product and lower productivity. With an increase of the feed flowrate, eluent flowrate, and switch time, the ratio of the liquid and the solid flowrates increases in one zone (zone III), two zones (zones II and III), or all zones, which will lead to the concentration peaks moving upward in the sketch as shown in Figure 2. For a better understanding of
Figure 6. Effect of the operating parameters on the process performance for the simulated moving-bed reactor arrangement shown in Figure 2 where the process parameters are listed in Table 2 except noted. (a) Effect of the feed flowrate on product purity and recovery: Vde ) 76 mL/min, Vel ) 31.5 mL/min, and t ) 30 min. (b) Effect of the eluent on product purity and recovery: Vde ) 76 mL/min, Vfe ) 9 mL/min, and t ) 30 min. (c) Effect of switch time on product purity and recovery: Vde ) 76 mL/min, Vel ) 31.5 mL/min, and Vfe ) 9 mL/min.
the process dynamics, on-column concentration profiles are shown in Figure 7 and the values of the operating parameters are listed in Table 6. The sucrose concentration gradually decreases to zero in zone III, which means that the reaction is almost complete. The concentration peaks of glucose and fructose are only found in zone III and the concentration plateaus occur mostly in zone II, which means that this zone is not fully used. With an increase of the feed flowrate, eluent flowrate, or switch time, the peaks in zone III move forward and the plateaus are lowered down, which leads to results as shown in Figure 7. Since the values of the operating condition parameters (eq 20) in zone II do not satisfy those listed in
158 Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997
Figure 7. On-column concentration profiles of the simulated moving-bed reactor arrangement for inversion of sucrose to glucose to fructose where the process parameters are listed in Table 2 where Vde ) 76 mL/min, Vel ) 31.5 mL/min, Vfe ) 9.0 mL/min, and t ) 30 min. Table 6. Values of the Operating Parameter for the On-Column Concentration Profiles in Figure 7 no. of zones
I
II
III
βfJ βgJ
1.43 2.06
0.54 0.78
0.95 1.37
Table 3, the major part of the zone is unused and hence the process performance (stated by product purity and recovery) is limited. For the process shown in Figure 2, one can either reduce the feed flowrate, which, in turn, leads to lower productivity and more diluted product, or alternatively use an adsorbent with better separation performance for glucose and fructose, i.e., different adsorption isotherms. Of course, introduction of liquid recycle and extension of three-zone arrangement to four-zone arrangement may be the third solution. For the first two options, the on-column concentration profiles are presented in Figure 8a,b, and the values of the operating condition parameter are listed in parts a and b of Table 7, respectively. The large concentration gradient of glucose over zone II can been seen in the figures. The purity and recovery of the glucose and fructose products are all over 95%. Test simulations showed that, even if sucrose is adsorbable on the adsorbent and the adsorption coefficient is lower than that of glucose, the simulated moving-bed reactor arrangement mentioned above is still applicable. Conclusions Two simulated moving-bed reactor arrangements which consist of three zones each have been studied by mathematical modeling and numerical simulations. In the application of isomerization of glucose to fructose, the satisfactory operating condition parameters (eq 20) in each zone for a good process performance of a simulated moving-bed arrangement are not applicable to the new process. This is because another process performance parameter, namely, reaction conversion, has been introduced. It is also found that the process performance for the SMBR arrangement is very insensitive to the operating conditions. In the application of inversion of sucrose to fructose and glucose, the SMBR arrangement shows similar process characteristics as in a simulated moving-bed arrangement. Although the process performance, stated by product purity and recovery, is good for the operating conditions used, the products are much diluted due to the absence of liquid recycle. It is possible to get some useful clues for us to modify and improve the processes by analyzing the
Figure 8. (a) On-column concentration profiles of the simulated moving-bed reactor arrangement for inversion of sucrose to glucose to fructose where the process parameters are listed in Table 2 except: Vde ) 60 mL/min, Vel ) 33 mL/min, Vfe ) 4.5 mL/min, and t ) 35 min. (b) On-column concentration profiles of the simulated moving-bed reactor arrangement for inversion of sucrose to glucose to fructose where the process parameters are listed in Table 2 where Vde ) 76 mL/min, Vel ) 31.5 mL/min, Vfe ) 9.0 mL/min, and t ) 30 min except KB ) 0.24 and KC ) 0.55. Table 7. Values of the Operating Parameter for the On-Column Concentration Profiles in Figure 8a,b no. of zones
I
II
III
βfJ βgJ
a. Profiles in Figure 8a 1.90 0.72 2.75 1.05
0.98 1.42
βfJ βgJ
b. Profiles in Figure 8b 2.81 0.46 6.44 1.04
0.93 2.14
process performance and studying the process dynamics for various operating conditions with modeling and simulations. Notation ci ) species i concentration in the fluid phase, mol/L D ) column diameter, m DL ) axial mass dispersion coefficient, m2/s Da ) reaction Damkohler number (eq 11d) E ) enhanced reaction conversion Ki ) linear adsorption isotherm coefficient of species i kr ) reaction rate coefficient, 1/min kti ) overall mass-transfer coefficient of the LDF model between fluid and solid of species i, 1/min L ) length of the section or column, m Pe ) Peclet number (eq 11a) qi ) species concentration in solid phase of species i, mol/L Rd ) dilution ration stated in eq 10 R ) product recovery ri ) reference reaction rate, mol/L‚min t ) switch time, min us ) interstitial solid flowrate inside column ()L/t), m/min v ) interstitial fluid flowrate inside column, m/min V1 ) fluid flowrate in section I, mL/min
Ind. Eng. Chem. Res., Vol. 36, No. 1, 1997 159 V2 ) fluid flowrate in section II, mL/min V3 ) fluid flowrate in section III, mL/min Vde ) desorbent flowrate, mL/min Vel ) eluent flowrate, mL/min Vfe ) feed flowrate, mL/min Vrc ) recycle flowrate, mL/min x ) dimensionless axial coordinate in the column or section y ) product purity z ) axial coordinate in the column or section, m Greek Letters R ) reciprocal of the mass-transfer unit (eq 11c) β ) operating condition parameter (eq 20) ) overall column porosity ξ ) ratio of solid and fluid flowrates (eq 11b) Subscripts f ) feed i ) species j ) column J ) section p ) product
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Received for review June 7, 1996 Revised manuscript received October 3, 1996 Accepted October 22, 1996X IE9603171 X Abstract published in Advance ACS Abstracts, December 15, 1996.
