Experimental and Modeling Study of Catalytic Reaction of Glucose Isomerization: Kinetics and Packed-Bed Dynamic Modeling Asghar Molaei Dehkordi, Iman Safari, and Muhammad M. Karima Dept. of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran DOI 10.1002/aic.11460 Published online March 26, 2008 in Wiley InterScience (www.interscience.wiley.com). The kinetics and equilibrium of isomerization reaction of D-glucose to D-fructose have been investigated using a commercial immobilized glucose isomerase (IGI), Sweetzyme type IT1, in a batch stirred-tank reactor. The batch experimental data were used to model the reaction kinetics using the well-known Michaelis–Menten rate expression. The kinetic model was utilized in a dynamic-mathematical model for a packed-bed reactor to predict the concentration profiles of D-glucose and D-fructose within the reactor. The experimental results for the fractional conversion of D-glucose in the packed-bed reactor of IGI catalyst indicated that the model prediction of the transient and steady-state performance of the packed-bed reactor was satisfactory and as such could be used in the design of a fixed-bed IGI catalytic reactor. Moreover, the influences of axial mixing term, particle Re number, and axial peclet number (Pea) on the performance capability of the packed-bed reactor of IGI catalyst were investigated. Ó 2008 American Institute of Chemical Engineers AIChE J, 54: 1333–1343, 2008 Keywords: kinetics, packed bed, mathematical modeling, transient response, dynamic simulation, enzyme, glucose isomerase Introduction Solid–liquid enzyme reactions constitute important processes in biochemical industries. Among the latter, the isomerization of glucose to fructose is one of the most widely used processes in the food industry in producing dietetic ‘‘light’’ foods and drinks, because it improves the sweetening, color, and hygroscopic characteristics in addition to reducing viscosity. Also, fructose is about 75% sweeter than sucrose, is absorbed more slowly than glucose, and is metabolized without the intervention of insulin. For all these reasons, this process is widely studied both with cells and with enzymes, both free and immobilized.1–15 From the perspective of chemical kinetics, isomerization of glucose to fructose is a reversible reaction, with an equilibrium constant of Correspondence concerning this article should be addressed to A.M. Dehkordi at amolaeid@sharif.edu. Ó 2008 American Institute of Chemical Engineers AIChE Journal approximately unity at 558C.16 The heat of reaction is on the order of 5 kJ/mol16 and, consequently, the equilibrium product contains roughly a 1:1 ratio of glucose to fructose that does not change appreciably with temperature, such that at 558C the fructose content at equilibrium is 50%, and at higher temperatures such as 60, 70, 80, and 908C is 50.7, 52.5, 53.9, and 55.6%, respectively. However, increasing temperature decreases stability and the enzyme half-life and therefore productivity. Most industrial plants run at 58–608C, a temperature with low risk for microbial contamination. The process was originally carried out in batch reactors with soluble enzymes. It was later extended to one involving immobilized glucose isomerase (IGI), which is of interest to us in the present work. In addition to the aforementioned batch reactors, there are various types of enzyme reactors, including continuous stirred tank reactors, fixed-bed reactors, simulated moving beds,17 and fluidized-bed reactors. In the fixed- and fluidized-bed reactors, the immobilized enzymes are used with different shapes including cylindrical and May 2008 Vol. 54, No. 5 1333 spherical pellets. Because the microporous particles provide a large surface area and that packing such particles in a tubular reactor is rather straightforward, tubular packed-bed reactors consisting of IGI are extensively used. Isomerization of glucose to fructose is normally carried out in multiple tubular packed-bed reactors in parallel lines, with an isomerization time ranging from 0.5 to 4 h.16 The main objectives of the present work were (1) to investigate the kinetics of glucose to fructose isomerization by IGI (Sweetzyme type IT1); (2) to model and simulate dynamically packed-bed reactor using the kinetic parameters obtained by batch experimental runs; and (3) to validate the dynamic packed-bed model through experimental data. Theory Reaction kinetics Glucose–fructose enzymatic isomerization is a reversible reaction and is normally given by the following expression: k1 FþE GE k 1 (1) 2 where G, E, and F represent glucose, enzyme, and fructose, respectively, and GE is an intermediate complex formed during the reaction. According to the reversible modified Michaelis–Menten mechanism,2,8,18,19 the reaction rate is given by R¼ 1 d½GŠ Vm ½GŠ ¼ W dt Km þ ½GŠ (2) with ½GŠ ¼ ½GŠ ½GŠe ; Km ¼ ½GŠ0 ¼ ½GŠ þ ½FŠ ¼ ½GŠe þ ½FŠe ¼
 1 ð1 þ Ke Þ½GŠe ¼ 1 þ Ke ½FŠe    kmf kmg 1 Ke ½GŠe þ 1þ kmg kmf kmf kmg  Kr ¼ ½FŠ Xe vmg kmf ¼ Ke ¼ e ¼ ½GŠe 1 Xe vmf kmg (6) where vmg, vmf, kmg, and kmf are the maximum reaction rate for glucose to fructose, the maximum reaction rate for fructose to glucose, the Michaelis–Menten constant for glucose to fructose reaction, and the Michaelis–Menten constant for fructose to glucose reaction, respectively, and Xe is the equilibrium fractional conversion of glucose. Integrating Eq. 2 gives   1 ½GŠ0 ½GŠ Km ½GŠ0 (7) ln t¼ þ W Vm Vm ½GŠ Thus, by introducing the values of vmg, vmf, kmg, and kmf to Eqs. 4 and 5 together with Eq. 7, one can easily evaluate the fractional conversion of glucose at any given time for various initial concentrations of glucose. DOI 10.1002/aic (8)
 1 vmg 1 þ Ke kmg þ ½GŠ0 ½GŠ0 (9) and K¼ ½GŠ0 h
kmg kmf  kmg þ ½GŠ0 i 1 (10) where Ke, W, and X denote the equilibrium constant, catalyst loading, and the fractional conversion of glucose, respectively. Integrating Eq. 8 gives the following relation:   ½GŠ0 KXe þ 1 Xe ½GŠ0 K ln X (11) t¼ W W Kr Kr Xe X To evaluate K and Kr as a function of initial concentration of glucose, one can plot tW/(X[G]0) against 1/X ln[Xe/(Xe 2 X)] for various constant initial concentrations. Note that, the equilibrium fractional conversion of glucose (Xe) can be determined experimentally by conducting long enough experimental runs. On the other hand, the inversion of Eqs. 9 and 10 yields k 1 1 1
mg 
 ¼ þ Kr vmg 1 þ 1 ½GŠ0 vmg 1 þ K1e Ke (4) (5) 1 d½GŠ ðXe XÞ ¼ Kr W dt 1 þ KX with ð3Þ  kmf vmg Vm ¼ 1 þ Ke 1 kmf kmg  1334 R¼ k2 GþE k The conventional method reported in the literature for determining vmg, vmf, kmg, and kmf is that experiments with feed solution containing either glucose or fructose should be carried out. By estimating the initial rates of the glucose to fructose and vice versa, these parameters can be determined using the Lineweaver–Menten equation.20 However, one can evaluate these four key parameters (i.e., vmg, vmf, kmg, and kmf) by carrying out just experiments for glucose to fructose reaction. Rubio et al. have rewritten the rate of reaction as follows21: kmg 1 1 1 i ¼ h
 þ h
 kmg kmg K ½GŠ 0 1 kmf kmf 1 i (12) (13) Now, by plotting 1/K against 1/[G]0 one can easily evaluate kmg and kmf, and finally plotting 1/Kr against 1/[G]0, vmg could be determined. Having the value of Ke and using Eq. 6, vmf could be subsequently determined. Packed-bed modeling To model packed-bed reactor, the following essential assumptions were considered: (1) Superficial velocity is high enough so that the external mass-transfer resistance is not dependent on velocity. Lee et al. showed that the critical superficial velocity is 0.1 cm/s.22 Hence, at superficial velocities higher than this critical value, the external mass-transfer resistance may be considered the same for both the packed bed and the batch experimental runs carried out at a high-enough stirrer speed. (2) Effectiveness factor is only slightly dependent on bulk glucose concentration.9,23,24 Thus, the apparent kinetic parameters evaluated by batch experimental runs may be used Published on behalf of the AIChE May 2008 Vol. 54, No. 5 AIChE Journal in the packed-bed reactor, as the true effectiveness factor was taken into consideration. This assumption is valid when the concentration used for batch experimental runs is the same as those used for packed-bed reactors. Moreover, Pallazi and Converti showed that intraparticle mass-transfer resistance only becomes rather significant for dp 5 2 mm, and that the effectiveness factor approaches 1 for dp 5 0.4 mm.9 (3) Axial dispersion is considered, whereas radial dispersion is neglected. (4) The system is isothermal. (5) Fresh catalyst is used, and the time required for running the packed bed reactor is short enough, so that the deactivation is negligible. Mass balance applied to the concentration of glucose in liquid phase is given by @½GŠ @ 2 ½GŠ ¼ DL @t @z2 U0 @½GŠ @z R (14) where R, DL and U0 denote the glucose reaction rate, axial dispersion coefficient, and the superficial feed velocity, respectively. Note that R is the observed rate of reaction defined by Km and Vm that are apparent parameters evaluated through the batch experimental runs. Combining Eqs. 2 and 14 and considering the bed porosity (e) results in the following equation @½GŠ @ 2 ½GŠ ¼ DL @t @z2 U0 Vm ½GŠ qp ð1 eÞ e Km þ ½GŠ @½GŠ @z (15) where qp is catalyst particle density. This governing equation is subject to the following initial and boundary conditions: ½GŠ ¼ 0 ; t ¼ 0; z DL @½GŠ þ U0 ½GŠ ¼ U0 ½GŠ0 @z @½GŠ @½GŠ ¼ ¼ 0; @z @z (16) t > 0; z ¼ 0 t > 0; z ¼ L (17) (18) where z and L are the z-direction along the packed bed reactor and the height of the reactor, respectively. By introducing the following dimensionless variables s¼ tU0 ; Le n¼ z L (19) Equations 15–18 can be rewritten as follows: @½GŠ DL @ 2 ½GŠ ¼ e @s LU0 @n2 @½GŠ @n Vm ½GŠ qp Lð1 eÞ U0 e Km þ ½GŠ ½GŠe ; DL @½GŠ þ ½GŠ ¼ ½GŠ0 U0 L @n @½GŠ ¼ 0; @n s ¼ 0; n ½GŠe ¼ ½GŠ0 ; s > 0; n ¼ 0 s > 0; n ¼ 1 (21) (22) (23) The similar analysis leads to the following equation for the fructose concentration. AIChE Journal May 2008 Vol. 54, No. 5 @½FŠ Vm ½GŠ qp Lð1 eÞ þ @n U0 e Km þ ½GŠ (24) subject to: ½FŠ ¼ 0 ; s ¼ 0; n DL @½FŠ þ ½FŠ ¼ ½FŠ0 ¼ 0; U0 L @n @½FŠ ¼ 0; @n s > 0; n ¼ 0 s > 0; n ¼ 1 (25) (26) (27) To obtain the concentration profile of glucose and fructose within the packed-bed reactor, Eqs. 20 and 24 along with their initial and boundary conditions should be solved. In the present investigation, the governing equations were solved numerically using the finite-difference method. Experimental Chemicals All chemicals used in the present study were of analytical grade; D-glucose in crystalline form was provided by Merck Co. (Germany). The immobilized enzyme, Sweetzyme IT, was provided as a gift by Novo Nordisk (Iran). The IGI enzyme particles were of cylindrical shape, with 0.2- to 0.4mm diameter, 1- to 1.5-mm length, and a particle density of 3300 kg/m3. The dry specific activity of the IGI enzyme was reported to be 450 IGIU/g by the manufacturer. The distilled water used was with conductivity 3 lS/cm. Method of analysis Fructose and glucose concentrations were determined by HPLC (Waters, refractive index detector 2410). The sugar packTM1 column was used with deionized water as the mobile phase at a flow rate of 0.34 mL/min. The HPLC detector was calibrated by introducing known samples of D-glucose and D-fructose solutions. The regression coefficient of the calibration curve of the detector was 0.996. Viscosity of feed solutions at 608C and at various concentrations was determined by a viscometer (Boorkfield LVSVE 230), and the density of these solutions was determined by a density meter (Anton Paar DMA 38). (20) subject to: ½GŠ ¼ @½FŠ DL @ 2 ½FŠ ¼ e @s LU0 @n2 Experimental apparatus Batch Stirred-Tank Reactor. The batch reactor was a 500-mL jacketed-stirred tank reactor. The reactor temperature was adjusted by means of hot water. The heating system was able to adjust the temperature of the reactor with the accuracy of 618C. Two connections located on the top of the reactor were provided (1) to introduce the desired amount of fresh catalyst to the reactor at the start of each experimental run; and (2) to withdraw samples from the reactor. The impeller was of flat-blade turbine type made of stainless steel (SS), and its rotation speed was adjusted from 100 to 1000 rpm by a variable-speed electric motor. Published on behalf of the AIChE DOI 10.1002/aic 1335 Table 2. Operating Conditions of Packed-Bed Experimental Runs Number of runs Operating temperature (8C) pH of glucose solutions Inlet concentration of glucose (kmol/m3) Flow rate (L/h) Bed porosity (e) Bed diameter, db (m) Working bed height, L (m) 16 60 6 1 7.5 0.10–1.10 2.50–16.50 0.36 0.02 0.60 mentioned analytical method for the glucose–fructose concentrations. For each data point, the experimental run was repeated at least two times, and thus each data point was determined based on the mean value of at least two measurements of glucose–fructose concentrations with a standard deviation of 1–2%. The operating conditions of all batch experimental runs are presented in Table 1. Figure 1. Experimental set up. (1) packed-bed reactor; (2) hot water jacket; (3) sampling valve; (4) rotameter; (5) stainless steel feed pump; (6) stainless steel feed vessel; (7) hot water jacket. Packed Bed Reactor. The flow diagram of the experimental setup, shown in Figure 1, consisted of the following parts: packed-bed reactor (1) equipped with a hot water jacket (2), where the dimensions of the packed-bed reactor were of 2 cm diameter (db) and 60 cm working height (L); sampling valve (3); rotameter (4); feed pump made of SS (5); feed vessel (6) equipped with jacket (7) made of SS. Experimental procedures The D-Glucose solution was prepared by dissolving the required amount of D-glucose in a solution containing 2.465 g MgSO4
7H2O per liter of deionized water to stabilize the enzyme; the pH of the solution was adjusted at 7.5 by Na2CO3. Because oxygen in the syrup inactivates the enzyme and is responsible for increased formation of secondary products during isomerization, a low oxygen tension thus has to be achieved by adding Na2SO3. Batch Experimental Runs. In each experimental run, the feed solution with desired volume, concentration, temperature, and pH was fed to the reactor. Afterward, the impeller speed was adjusted at 700 rpm and the temperature of the reactor was kept at 608C, and then the desired amount of IGI catalyst was suddenly added to the reactor. This time was considered as the starting time of the reaction. During the course of the reaction, samples were taken through the sampling connection by means of a syringe equipped with a filter to separate the catalyst. The progress of the reaction within the sampling bottle was ceased by adding sulfuric acid solution. Analysis of the samples was performed by the aforeTable 1. Operating Conditions of Batch Experimental Runs Number of runs Operating temperature (8C) pH of glucose solutions Initial concentration of glucose (kmol/m3) Catalyst loading (g/L) Duration of each experimental run (min) 1336 DOI 10.1002/aic 16 60 6 1 7.5 0.10–1.25 5–20 120 Figure 2. Variations of fractional conversion of glucose with time. Published on behalf of the AIChE May 2008 Vol. 54, No. 5 AIChE Journal Figure 3. Variations of tW/(X[G]0) with ln[Xe/(Xe 2 X)]/X. AIChE Journal May 2008 Vol. 54, No. 5 Published on behalf of the AIChE DOI 10.1002/aic 1337 Table 3. Kinetic Constants of Eq. 8 3 6 [G]0 (mol/m ) K Kr [10 mol/(g cat s)] 100 500 1000 1250 20.070 20.206 20.244 20.335 2.991 9.390 11.460 12.530 Packed-Bed Reactor Experimental Runs. In each experimental run, the feed solution at the desired temperature (608C), with the desired inlet glucose concentration and pH was fed to the packed-bed reactor at given volumetric flow rate, while hot water was introduced into the jacket to maintain the temperature of the reactor at 608C. The samples were taken through the sampling connection of the effluent stream of the reactor for the measurement. Experimental runs were conducted at four different flow rates (Re number) and four different initial concentrations of glucose. The range of operating conditions is presented in Table 2. The procedure for analysis of samples was the same as that for batch experimental runs. Results and Discussion Evaluation of kinetic parameters Figures 2a–c demonstrate typical experimental data regarding the kinetic behavior of glucose to fructose reaction. As may be noticed, slight deviations from Michaelis–Menten kinetic model at low fractional conversions are observed which are shown by the rectangles. In fact a sinusoidal shape at fractional conversions \15% particularly for small values of Figure 4. Variations of 1/Kr and 1/K with 1/[G]0. 1338 DOI 10.1002/aic Table 4. Kinetic Parameters of Eq. 2 kmg (mol/m3) 474.3 kmf (mol/m3) vmg [106 mol/(g cat s)] vmf [106 mol/(g cat s)] 793.9 8.869 14.910 W/[G]0 is clearly visible. As fractional conversion increases, however, this sinusoidal shape is vanished and the fractional conversion curve perfectly matches with the Michaelis– Menten kinetic model. This kind of deviation has been reported formerly in the literature.25 This behavior may be caused by a transitory behavior of the particles reflecting the time needed for the establishment of steady concentration profiles within the particles. These disturbances prevented us from relying on the initial rate of reaction to use Lineweaver– Menten method for calculating the kinetic parameters. Using the method mentioned earlier, one can easily omit these initial points and estimate kinetic parameters using the higher conversion experimental data. Moreover, using the method explained in the theoretical section, it is not necessary to conduct experimental runs with feed solutions containing only fructose to estimate vmf and kmf. To obtain the kinetic parameters K and Kr, the experimental data concerning tW/(X[G]0) were plotted against 1/X ln[Xe/(Xe 2 X)] as shown in Figures 3a–g. From these figures, the kinetic parameters K and Kr could be evaluated by linear regression analysis. Results are summarized in Table 3. In addition, the equilibrium fractional conversion of glucose was experimentally obtained to be 49.9% and the equilibrium constant of the reaction was calculated by Eq. 6 to be 0.996. With these values of K and Kr, one can easily evaluate the four key kinetic parameters, i.e. kmg, kmf, vmg, and vmf. To achieve this goal, the obtained values of 1/Kr and 1/K could be plotted against 1/[G]0 as shown in Figures 4a,b. Using the linear regression analysis, the four key kinetic parameters were found and were summarized in Table 4. To show the goodness of the kinetic model parameters obtained by this procedure, the predicted fractional conversion of glucose using the obtained kinetic parameters is compared with the batch experimental data in Figures 5a–d and 6. As may be observed from these figures, there is a fair agreement between the experimental and predicted fractional conversions of glucose. In addition, to quantify the deviation between the predicted and experimental results, the root mean square (RMS) of the normalized residuals was calculated according to the following expression: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N   u1 X Xi ðcalÞ 2 1 (28) RMS ¼ 100t N i¼1 Xi ðexpÞ The RMS of the predicted values of fractional conversion of glucose was calculated to be 14.94%. This value of RMS clearly shows the goodness of the kinetic model. It should also be noted that in Figures 5b–d the results of experiments for 5 g/L of catalyst were not used to adjust the parameters of the proposed model, because these experiments resulted in the low conversions after 2 h and, hence, most of the data points were in the range of fluctuations. As explained earlier, the deviations from the Michaelis–Menten rate expression is observed for this fluctuation range; therefore, these results Published on behalf of the AIChE May 2008 Vol. 54, No. 5 AIChE Journal Figure 5. Variations of fractional conversion of glucose with time for batch experiments and comparison with the kinetic model predictions. were not reliable enough to be used for the adjustment of the model parameters. Considering the earlier facts, the results of experiments with 5 g/L of IGI catalyst in Figures 5b–d could not be used for the estimation of RMS and therefore the exclusion of these data points would result in much lower values of RMS (6%). Packed-bed runs Packed-bed reactor experiments were carried out using the experimental set up shown in Figure 1. The feed solution with a known concentration of glucose and at 608C was continuously fed to the top of the column at a given volumetric flow rate. The feed flow rate was regulated by means of a rotameter. The temperature of the reactor was kept constant at 608C by hot water introduced into the jacket. For all the column tests, the samples from the reactor effluent were intermittently taken and analyzed by HPLC. The packed bed runs were carried out at four different inlet glucose concentrations [(100, 470, 880, and 1100) mol/m3], and four different Re numbers for each inlet concentration of glucose. To simulate the experimental conditions of packed-bed reactor, the axial dispersion coefficient, DL, molecular diffusivity, Dm, and physical properties of the feed solution at 608C should be known. The density and viscosity of feed solution were measured and the molecular diffusivity of glucose at 608C was found elsewhere.26 The axial dispersion coefficient may be estimated by using reported correlations. The following correlation was proposed by Fried27 to model dispersion effects: Table 5. Physical Properties at 608C Figure 6. Comparison of calculated fractional conversions of glucose with experimental ones. AIChE Journal May 2008 Vol. 54, No. 5 Inlet Glucose Concentration (mol/m3) q (kg/m3) l (104 kg/(m s)] Dm (109 m2/s) 100 470 880 1100 987.2 1008.5 1039.2 1054.2 7.8 8.1 8.5 8.8 1.046 1.225 1.439 1.604 Published on behalf of the AIChE DOI 10.1002/aic 1339 Figure 7. Variations of transient outlet concentration of fructose with dimensionless time for packed-bed reactor. h i DL ¼ Dm 0:67 þ 0:5ðRe ScÞ1:2 (29) The parameters used in the simulation studies are summarized in Table 5. The effects of particle Re number, and inlet glucose concentration on the concentration profile of fructose were investigated. The simulation and experimental results in terms of fructose concentration, [F], and as a function of particle Re number are presented in Figures 7a–d. As shown in Figures 7a–d, there are fair agreements between the experimental results and those predicted by the model. ween the rate of transport by convection and that by axial diffusion: Pea ¼ U0 L DL (30) The high values of the axial peclet number show that convection predominates on diffusion and dispersion phenomena, whereas low values of Pea indicate that axial mixing occurs in the axial direction. Other authors have stipulated conditions that are required to be satisfied in order to exclude the axial mixing term in the material and energy balance equa- Effect of particle Re number Figure 8 shows the variations of steady state fractional conversion of glucose both experimental data and model predictions with the particle Re number as a function of the inlet glucose concentration. As may be noticed form Figure 8, with an increase in the particle Re number the steady state fractional conversion of glucose decreases. This behavior is expected and can be explained by a decrease in the mean residence time of the liquid in the bed. Effect of axial mixing The importance of dispersion term in reactor modeling is usually considered by determining the axial peclet number (Pea), which is a representation of the ratio bet1340 DOI 10.1002/aic Figure 8. Variations of steady-state fractional conversion of glucose with particle Re number for packed-bed reactor. Published on behalf of the AIChE May 2008 Vol. 54, No. 5 AIChE Journal Table 6. Variations of Steady State Dimensionless Time (sss) with Re Number and [G]0. Figure 9. Effect of axial mixing term on the performance of the fixed-bed reactor. tions for a packed-bad catalytic tubular reactor. For example, Hill,28 Carberry and Wendel29 suggested that if the ratio of catalyst bed length to the catalyst particle diameter (L/dp) is larger than 100, the axial mixing term will be negligible. Also, Froment and Bischoff30 and Rase31 suggested that the effect of the axial mixing term is negligible when L/dp [ 50 and db/dp [ 10. To evaluate the applicability of these criteria in the glucose to fructose reaction, we have solved the governing equations together with the initial and boundary conditions with and without the axial dispersion term. The model predictions are plotted in Figure 9 as a function of the particle Re number for a given inlet glucose concentration (1100 mol/m3), where the solid lines represent the model predictions with the axial mixing term (dispersed plug flow reactor), whereas the dashed lines indicate those without the axial mixing term (plug flow reactor). As may be observed from this figure, there are slight differences in the outlet fructose concentration predicted by the model with and without the axial mixing term, which goes on to support the mentioned criteria. Effect of Pea number Figure 10 shows the variations of steady state fractional conversion of glucose both experimental data and model predictions with the Pea number as a function of inlet glucose concentration. As may be noticed form Figure 10, with an [G]0 (mol/m3) Re sss 100 100 100 100 470 470 470 470 880 880 880 880 1100 1100 1100 1100 1.7 3.6 5.4 7.3 1.6 3.4 5.1 6.8 1.1 2.8 4.5 6.1 1.1 2.7 4.1 5.7 3.09 3.02 3.01 3.00 3.05 3.00 2.99 2.99 3.06 3.00 2.99 2.98 3.04 3.00 2.99 2.98 increase in the Pea number the steady state fractional conversion of glucose increases. This behavior can be attributed to a decrease in the particle Re number, which in turn increases the Pea number because of the strong dependence of DL on the Re number. This behavior of axial peclet number of liquid phases is expected over the low range of particle Re number, i.e. 1–10.32,33 Steady state dimensionless time (sss) Table 6 lists the predicted values of steady state dimensionless time (sss) for various Re numbers and inlet glucose concentrations. This parameter is defined as a ratio of the steady state time to the mean residence time of liquid stream in the fixed-bed reactor. The steady state time was considered as the time it takes the concentration of fructose [F] reach almost the final steady state value with D[F]  1%. As may be noticed, the values of sss do not appreciably vary with the Re number and inlet glucose concentration. This behavior shows that an increase in the Re number, i.e. decrease in the mean residence time of liquid stream, results in a decrease in the steady state time (tss) in such way that the value of tss 3 Re remains almost constant. In addition, the system behaves in such way that the variations of inlet glucose concentration do not significantly affect of sss for the range of operating conditions investigated in the present work. Conclusions Figure 10. Effect of axial Pea number on the steadystate fractional conversion of glucose. AIChE Journal May 2008 Vol. 54, No. 5 An experimental and theoretical investigation was conducted on the kinetics, dynamic modeling, and simulation of isomerization reaction of D-glucose to D-fructose using commercial IGI catalyst, Sweetzyme type IT. The kinetic parameters of the reaction were determined by analysis of experimental data through the Michaelis–Menten kinetics. From batch experimental runs, it was founds that: (1) The equilibrium fractional conversion of D-glucose to D-fructose at 608C is 49.9%. (2) It was observed that there are some slight deviations from the Michaelis–Menten kinetic model at low fractional conversions as reported previously by Benaiges et al.25 But, Published on behalf of the AIChE DOI 10.1002/aic 1341 as the fractional conversion is increased the experimental results perfectly match the Michaelis–Menten kinetic model. (3) The parameters of the kinetic model of glucose to fructose reaction could be evaluated by the procedure described in the present work. The packed-bed reactor was dynamically modeled by the dispersed-phase model, and it was observed that there are fair agreements between the experimental data and those predicted by the model at various inlet glucose concentrations and particle Re number. Moreover, it was found that the effect of axial mixing on the performance capability of the packed-bed reactor over the range of operating conditions investigated in the present work is negligible. Notation dp 5 particle diameter, m db 5 bed diameter, m DL 5 dispersion coefficient, m2/s Dm 5 molecular diffusion coefficient, m2/s E 5 enzyme concentration, mol/m3 [F] 5 concentration of fructose, mol/m3 [F]0 5 initial or inlet concentration of fructose, mol/m3 [F]e 5 equilibrium concentration of fructose, mol/m3 [G] 5 concentration of glucose, mol/m3 [G]e 5 equilibrium concentration of glucose, mol/m3 [G]0 5 initial or inlet concentration of glucose, mol/m3 ½GŠ 5 concentration of glucose, Eq. 3 ½GŠ0 5 concentration of glucose ([G]0 2 [G]e) GE 5 intermediate complex, Eq. 1 K 5 kinetic constant, Eq. 10 Ke 5 equilibrium constant, Eq. 6 Km 5 apparent Michaelis–Menten constant, Eq. 4, mol/m3 Kr 5 kinetic constant, Eq. 9, mol/(g cat s) kmf 5 Michaelis–Menten constant for fructose, mol/m3 kmg 5 Michaelis–Menten constant for glucose, mol/m3 L 5 height of reactor, m Pea 5 axial peclect number (5U0L/DL) R 5 reaction rate, mol/(g cat s) Re 5 particle Reynolds number (5qU0dp/l) Sc 5 Schmidt number (5l/(qDm) t 5 time, s tss 5 steady state time, s U0 5 superficial velocity, m/s Vm 5 maximum apparent reaction rate, Eq. 5, mol/(g cat s) vmf 5 maximum apparent reaction rate for fructose, mol/(g cat s) vmg 5 maximum apparent reaction rate for glucose, mol/(g cat s) W 5 immobilized catalyst loading, g/L X 5 fractional conversion of glucose Xe 5 equilibrium fractional conversion of glucose z 5 axial distance, m Greek letters e 5 void fraction of bed s 5 dimensionless time, Eq. 19 sss 5 steady state dimensionless time n 5 dimensionless axial distance, Eq. 19 q 5 fluid density, kg/m3 qp 5 catalyst particle density, kg/m3 l 5 fluid viscosity, kg/(m s) D 5 difference Abbreviations cal 5 calculated cat 5 catalyst exp 5 experimental mod 5 model 1342 DOI 10.1002/aic Acknowledgments The authors gratefully acknowledge Novo Nordisk (Iran) for providing IGI catalyst, Sharif University of Technology for providing financial support, and Professor F. 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