Dehkordi Et Al%2c2008

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termodinámica de la reacción
  Experimental and Modeling Study of CatalyticReaction of Glucose Isomerization: Kinetics andPacked-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 ( The kinetics and equilibrium of isomerization reaction of   D -glucose to  D -fructosehave been investigated using a commercial immobilized glucose isomerase (IGI),Sweetzyme type IT  1 , in a batch stirred-tank reactor. The batch experimental datawere used to model the reaction kinetics using the well-known Michaelis–Menten rateexpression. 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 -fructosewithin the reactor. The experimental results for the fractional conversion of   D -glucosein the packed-bed reactor of IGI catalyst indicated that the model prediction of thetransient 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, theinfluences of axial mixing term, particle  Re  number, and axial peclet number ( Pe a ) onthe performance capability of the packed-bed reactor of IGI catalyst were investigated.  2008 American Institute of Chemical Engineers  AIChE J,  54: 1333–1343, 2008  Keywords: kinetics, packed bed, mathematical modeling, transient response, dynamicsimulation, enzyme, glucose isomerase Introduction Solid–liquid enzyme reactions constitute important pro-cesses in biochemical industries. Among the latter, the isom-erization of glucose to fructose is one of the most widelyused processes in the food industry in producing dietetic‘‘light’’ foods and drinks, because it improves the sweeten-ing, color, and hygroscopic characteristics in addition toreducing viscosity. Also, fructose is about 75% sweeter thansucrose, is absorbed more slowly than glucose, and is metab-olized without the intervention of insulin. For all these rea-sons, this process is widely studied both with cells and withenzymes, both free and immobilized. 1–15 From the perspec-tive of chemical kinetics, isomerization of glucose to fructoseis a reversible reaction, with an equilibrium constant of approximately unity at 55 8 C. 16 The heat of reaction is on theorder of 5 kJ/mol 16 and, consequently, the equilibrium productcontains roughly a 1:1 ratio of glucose to fructose that doesnot change appreciably with temperature, such that at 55 8 Cthe fructose content at equilibrium is 50%, and at higher temperatures such as 60, 70, 80, and 90 8 C is 50.7, 52.5,53.9, and 55.6%, respectively. However, increasing tempera-ture decreases stability and the enzyme half-life and thereforeproductivity. Most industrial plants run at 58–60 8 C, a tem-perature with low risk for microbial contamination.The process was srcinally carried out in batch reactorswith soluble enzymes. It was later extended to one involvingimmobilized glucose isomerase (IGI), which is of interest tous in the present work. In addition to the aforementionedbatch 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 thefixed- and fluidized-bed reactors, the immobilized enzymesare used with different shapes including cylindrical and Correspondence concerning this article should be addressed to A.M. Dehkordi  2008 American Institute of Chemical Engineers AIChE Journal May 2008 Vol. 54, No. 5 1333  spherical pellets. Because the microporous particles providea large surface area and that packing such particles in a tubu-lar reactor is rather straightforward, tubular packed-bed reac-tors 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 isomerizationtime ranging from 0.5 to 4 h. 16 The main objectives of the present work were (1) to inves-tigate the kinetics of glucose to fructose isomerization by IGI(Sweetzyme type IT 1 ); (2) to model and simulate dynami-cally packed-bed reactor using the kinetic parametersobtained by batch experimental runs; and (3) to validate thedynamic packed-bed model through experimental data. Theory   Reaction kinetics Glucose–fructose enzymatic isomerization is a reversiblereaction and is normally given by the following expression:G  þ  E k  1 k   1 GE k  2 k   2 F  þ  E (1)where G, E, and F represent glucose, enzyme, and fructose,respectively, and GE is an intermediate complex formed dur-ing the reaction. According to the reversible modifiedMichaelis–Menten mechanism, 2,8,18,19 the reaction rate isgiven by  R  ¼   1 W d  ½ G  dt   ¼  V  m ½ G   K  m  þ ½ G  (2)with ½ G  ¼ ½ G   ½ G  e ;  ½ G  0  ¼ ½ G  þ ½ F  ¼ ½ G  e  þ ½ F  e  ¼ 1  þ  K  e ð Þ½ G  e  ¼  1  þ  K   1 e   ½ F  e  ð 3 Þ  K  m  ¼  k  mf  k  mg k  mf     k  mg 1  þ  1 k  mg þ  K  e k  mf    ½ G  e    (4) V  m  ¼  1  þ  K   1e    k  mf  v mg k  mf     k  mg (5)  K  e  ¼ ½ F  e ½ G  e ¼  X  e 1    X  e ¼  v mg k  mf  v mf  k  mg (6)where  v mg ,  v mf  ,  k  mg , and  k  mf   are the maximum reaction ratefor glucose to fructose, the maximum reaction rate for fruc-tose to glucose, the Michaelis–Menten constant for glucoseto fructose reaction, and the Michaelis–Menten constant for fructose to glucose reaction, respectively, and  X  e  is the equi-librium fractional conversion of glucose. Integrating Eq. 2gives t   ¼  1 W  ½ G  0   ½ G  V  m þ  K  m V  m ln ½ G  0 ½ G     (7)Thus, by introducing the values of   v mg ,  v mf  ,  k  mg , and  k  mf  to Eqs. 4 and 5 together with Eq. 7, one can easily evaluatethe fractional conversion of glucose at any given time for various initial concentrations of glucose.The conventional method reported in the literature for deter-mining  v mg ,  v mf  ,  k  mg , and  k  mf   is that experiments with feed so-lution containing either glucose or fructose should be carriedout. By estimating the initial rates of the glucose to fructoseand vice versa, these parameters can be determined using theLineweaver–Menten equation. 20 However, one can evaluatethese four key parameters (i.e.,  v mg ,  v mf  ,  k  mg , and  k  mf  ) by car-rying out just experiments for glucose to fructose reaction.Rubio et al. have rewritten the rate of reaction as follows 21 :  R  ¼   1 W d  ½ G  dt   ¼  K  r  ð  X  e    X  Þ 1  þ  KX   (8)with  K  r   ¼ v mg  1  þ  K   1 e   k  mg  þ ½ G  0 ½ G  0  (9)and  K   ¼½ G  0 k  mg k  mf      1 h i k  mg  þ ½ G  0 (10)where  K  e ,  W  , and  X   denote the equilibrium constant, catalystloading, and the fractional conversion of glucose, respec-tively. Integrating Eq. 8 gives the following relation: t   ¼ ½ G  0 W  KX  e  þ  1  K  r  ln  X  e  X  e    X     ½ G  0 W  K  K  r   X   (11)To evaluate  K   and  K  r   as a function of initial concentrationof glucose, one can plot  tW   /(  X  [G] 0 ) against 1/   X   ln[  X  e  /(  X  e  2  X  )] for various constant initial concentrations. Note that, theequilibrium fractional conversion of glucose (  X  e ) can be deter-mined experimentally by conducting long enough experimentalruns. On the other hand, the inversion of Eqs. 9 and 10 yields1  K  r  ¼  k  mg v mg  1  þ  1  K  e   1 ½ G  0 þ  1 v mg  1  þ  1  K  e    (12)1  K   ¼  k  mg k  mg k  mf      1 h i 1 ½ G  0 þ  1 k  mg k  mf      1 h i  (13)Now, by plotting 1/   K   against 1/[G] 0  one can easily evalu-ate  k  mg  and  k  mf  , and finally plotting 1/   K  r   against 1/[G] 0 ,  v mg could be determined. Having the value of   K  e  and using Eq.6,  v mf   could be subsequently determined.  Packed-bed modeling To model packed-bed reactor, the following essentialassumptions were considered:(1) Superficial velocity is high enough so that the externalmass-transfer resistance is not dependent on velocity. Leeet 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 thesame for both the packed bed and the batch experimentalruns carried out at a high-enough stirrer speed.(2) Effectiveness factor is only slightly dependent on bulkglucose concentration. 9,23,24 Thus, the apparent kinetic pa-rameters evaluated by batch experimental runs may be used 1334 DOI 10.1002/aic 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 whenthe concentration used for batch experimental runs is thesame as those used for packed-bed reactors. Moreover, Pal-lazi and Converti showed that intraparticle mass-transfer re-sistance only becomes rather significant for   d  p  5  2 mm, andthat the effectiveness factor approaches 1 for   d  p 5 0.4 mm. 9 (3) Axial dispersion is considered, whereas radial disper-sion is neglected.(4) The system is isothermal.(5) Fresh catalyst is used, and the time required for run-ning the packed bed reactor is short enough, so that the deac-tivation is negligible.Mass balance applied to the concentration of glucose inliquid phase is given by @  ½ G  @  t   ¼  D L @  2 ½ G  @  z 2    U  0 @  ½ G  @  z    R  (14)where  R ,  D L  and  U  0  denote the glucose reaction rate, axial dis-persion coefficient, and the superficial feed velocity, respec-tively. Note that  R  is the observed rate of reaction defined by  K  m  and  V  m  that are apparent parameters evaluated through thebatch experimental runs. Combining Eqs. 2 and 14 and consid-ering the bed porosity ( e ) results in the following equation @  ½ G  @  t   ¼  D L @  2 ½ G  @  z 2    U  0 @  ½ G  @  z    V  m ½ G   K  m  þ ½ G  q p  1    e ð Þ e  (15)where  q p  is catalyst particle density. This governing equationis subject to the following initial and boundary conditions: ½ G  ¼  0 ;  t   ¼  0 ; z  (16)   D L @  ½ G  @  z  þ  U  0 ½ G  ¼  U  0 ½ G  0  t   >  0 ;  z  ¼  0 (17) @  ½ G  @  z  ¼  @  ½ G  @  z  ¼  0 ;  t   >  0 ;  z  ¼  L  (18)where  z  and  L  are the  z -direction along the packed bed reac-tor and the height of the reactor, respectively. By introducingthe following dimensionless variables s  ¼  tU  0  L e  ;  n  ¼  z L  (19)Equations 15–18 can be rewritten as follows: @  ½ G  e @  s  ¼  D L  LU  0 @  2 ½ G  @  n 2    @  ½ G  @  n    V  m ½ G   K  m  þ ½ G  q p  L  1    e ð Þ U  0 e  (20)subject to: ½ G  ¼ ½ G  e  ;  s  ¼  0 ;  n  (21)   D L U  0  L @  ½ G  @  n  þ½ G ¼½ G  0  ½ G  e  ¼½ G  0 ;  s > 0 ;  n ¼ 0 (22) @  ½ G  @  n  ¼  0 ;  s  >  0 ;  n  ¼  1 (23)The similar analysis leads to the following equation for the fructose concentration. @  ½ F  e @  s  ¼  D L  LU  0 @  2 ½ F  @  n 2    @  ½ F  @  n  þ  V  m ½ G   K  m  þ ½ G  q p  L  1    e ð Þ U  0 e  (24)subject to: ½ F  ¼  0 ;  s  ¼  0 ;  n  (25)   D L U  0  L @  ½ F  @  n  þ ½ F  ¼ ½ F  0  ¼  0 ;  s  >  0 ;  n  ¼  0 (26) @  ½ F  @  n  ¼  0 ;  s  >  0 ;  n  ¼  1 (27)To obtain the concentration profile of glucose and fructosewithin the packed-bed reactor, Eqs. 20 and 24 along withtheir initial and boundary conditions should be solved. In thepresent investigation, the governing equations were solvednumerically using the finite-difference method. Experimental Chemicals All chemicals used in the present study were of analyticalgrade;  D -glucose in crystalline form was provided by MerckCo. (Germany). The immobilized enzyme, Sweetzyme IT,was provided as a gift by Novo Nordisk (Iran). The IGIenzyme particles were of cylindrical shape, with 0.2- to 0.4-mm diameter, 1- to 1.5-mm length, and a particle density of 3300 kg/m 3 . The dry specific activity of the IGI enzyme wasreported to be 450 IGIU/g by the manufacturer. The distilledwater used was with conductivity   3  l S/cm.  Method of analysis Fructose and glucose concentrations were determined byHPLC (Waters, refractive index detector 2410). The sugar pack TM 1 column was used with deionized water as the mo-bile phase at a flow rate of 0.34 mL/min. The HPLC detector was calibrated by introducing known samples of   D -glucoseand  D -fructose solutions. The regression coefficient of thecalibration curve of the detector was 0.996.Viscosity of feed solutions at 60 8 C and at various concen-trations was determined by a viscometer (Boorkfield LVSVE230), and the density of these solutions was determined by adensity meter (Anton Paar DMA 38).  Experimental apparatus  Batch Stirred-Tank Reactor.  The batch reactor was a500-mL jacketed-stirred tank reactor. The reactor temperaturewas adjusted by means of hot water. The heating system wasable to adjust the temperature of the reactor with the accu-racy of   6 1 8 C. Two connections located on the top of the re-actor were provided (1) to introduce the desired amount of fresh catalyst to the reactor at the start of each experimentalrun; and (2) to withdraw samples from the reactor.The impeller was of flat-blade turbine type made of stainlesssteel (SS), and its rotation speed was adjusted from 100 to1000 rpm by a variable-speed electric motor. AIChE Journal May 2008 Vol. 54, No. 5 Published on behalf of the AIChE DOI 10.1002/aic 1335   Packed Bed Reactor.  The flow diagram of the experi-mental setup, shown in Figure 1, consisted of the followingparts: packed-bed reactor (1) equipped with a hot water  jacket (2), where the dimensions of the packed-bed reactor were of 2 cm diameter ( d  b ) 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 dissolvingthe required amount of   D -glucose in a solution containing2.465 g MgSO 4   7H 2 O per liter of deionized water to stabi-lize the enzyme; the pH of the solution was adjusted at 7.5by Na 2 CO 3 . Because oxygen in the syrup inactivates theenzyme and is responsible for increased formation of second-ary products during isomerization, a low oxygen tension thushas to be achieved by adding Na 2 SO 3 .  Batch Experimental Runs.  In each experimental run, thefeed solution with desired volume, concentration, tempera-ture, and pH was fed to the reactor. Afterward, the impeller speed was adjusted at 700 rpm and the temperature of the re-actor was kept at 60 8 C, and then the desired amount of IGIcatalyst was suddenly added to the reactor. This time wasconsidered as the starting time of the reaction. During thecourse of the reaction, samples were taken through the sam-pling connection by means of a syringe equipped with a filter to separate the catalyst. The progress of the reaction withinthe sampling bottle was ceased by adding sulfuric acid solu-tion. Analysis of the samples was performed by the afore-mentioned analytical method for the glucose–fructose con-centrations.For each data point, the experimental run was repeated atleast two times, and thus each data point was determinedbased 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 experimentalruns are presented in Table 1. Figure 1. Experimental set up. (1) packed-bed reactor; (2) hot water jacket; (3) samplingvalve; (4) rotameter; (5) stainless steel feed pump; (6) stain-less steel feed vessel; (7) hot water jacket. Table 1. Operating Conditions of Batch Experimental Runs Number of runs 16Operating temperature ( 8 C) 60 6 1pH of glucose solutions 7.5Initial concentration of glucose (kmol/m 3 ) 0.10–1.25Catalyst loading (g/L) 5–20Duration of each experimental run (min) 120 Table 2. Operating Conditions of Packed-BedExperimental Runs Number of runs 16Operating temperature ( 8 C) 60 6 1pH of glucose solutions 7.5Inlet concentration of glucose (kmol/m 3 ) 0.10–1.10Flow rate (L/h) 2.50–16.50Bed porosity ( e ) 0.36Bed diameter,  d  b  (m) 0.02Working bed height,  L  (m) 0.60 Figure 2. Variations of fractional conversion of glucosewith time. 1336 DOI 10.1002/aic Published on behalf of the AIChE May 2008 Vol. 54, No. 5 AIChE Journal
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