Improved Modeling of Bubble Column Reactors by Considering the

Article pubs.acs.org/IECR

Improved Modeling of Bubble Column Reactors by Considering the Bubble Size Distribution Mohammad Ramezani, Navid Mostoufi,* and Mohammad Reza Mehrnia Oil and Gas Processing Centre of Excellence, School of Chemical Engineering, College of Engineering, University of Tehran, Tehran, Islamic Republic of Iran ABSTRACT: Bioconversion of glucose to gluconic acid with glucose oxidase as enzyme was considered to occur in a bubble column reactor at 40 °C, atmospheric pressure, and pH 5.5 while oxygen gas velocity was varied in the homogeneous and transition regime in the range of 0.0014−0.0112 m s−1. It was found that the superficial gas velocity has a positive effect on gas holdup, mean bubble size, and volumetric mass transfer coefficient, while the glucose concentration has a negative influence on these hydrodynamic parameters. The modeling of bubble column by considering the complete bubble size distribution in the governing equations was carried out in this work. The model was also solved by considering the single and double sizes of bubbles instead of complete bubble size distribution. It was shown that the results of the model, considering the complete bubble size distribution, is in a good agreement with the experimental data, while the considered single and double bubble sizes cannot predict the experimental data of oxygen concentration in the reactor properly. It was also found that the superficial gas velocity has a positive influence on oxygen concentration while glucose concentration has negative influence at low superficial gas velocity and positive influence at high gas velocity. et al.16 investigated the performance of a slurry bubble column reactor of Fischer−Tropsch synthesis by assuming steady state conditions and considering hydrodynamic, kinetic, heat transfer, and mass transfer parameters for two classes of small and large bubbles. They determined the axial profile of CO conversion and hydrocarbon yield in the reactor. Since the bubble size has a strong influence on hydrodynamic parameters such as bubble rise velocity, gas residence time, gas−liquid interfacial area, and gas−liquid mass transfer coefficient, it can be claimed that considering bubble size distribution can assist the modeling of bubble columns more logically. In spite of previous studies on the modeling of bubble columns, comprehensive equations cannot be found that recognize bubble size distribution directly in the governing equations. The aim of the present study is to achieve a robust and accurate modeling of bubble column by taking the bubble size distribution into account. Since the key hydrodynamic parameters are influenced by the bubble size and its distribution, an attempt was made to present the governing equations of bubble column reactor by considering the size distribution of the bubbles. Accordingly, the modeling and scaleup of these reactors can be improved compared to considering single-size bubbles. The reaction considered in this work was bioconversion of glucose to gluconic acid with glucose oxidase, which acts as an enzyme. Gluconic acid plays the key role in various fields such as pharmaceutical, food, leather, photographic, and other biological industries.17−20 The difference between equations of single-size bubbles and distributed bubble size was also highlighted.

1. INTRODUCTION Bubble columns are gas−liquid contactors in which a gas consisting of one or more reactant is distributed into the column by a distributor and reacts with the liquid phase itself or with a component dissolved or suspended in it.1 These reactors are utilized in chemical, petrochemical and biological processes such as oxidation, hydro-desulfurization, chlorination, hydrogenation, fermentation, wastewater treatment, Fischer− Tropsch processes, and production of methanol or other environmental alternative fuels.2−7 The wide use of bubble column reactors has led to various modeling, design, and scaleup procedures for these gas−liquid contactors.8−12 It can be found in literature that only single size, or fairly less two sizes of bubbles, have been used for modeling the bubble column reactors. Shimizu et al.11 utilized the Sauter mean diameter as a single bubble size and took into account the bubble breakup and coalescence in the air−water system for predicting the gas−liquid volumetric mass transfer coefficient and gas holdup by simulation. Lehr at al.13 conducted separate balance equations for two classes of large and small bubbles and determined bubble size distribution and its flow fields by computational fluid dynamics (CFD). In their investigation, population balance equations were used for calculating the bubble breakup and coalescence. They utilized the Euler−Euler method for conducting CFD modeling while the gas phase was considered as a continuous phase. Guo and Al-Dahhan14 derived the governing equations of a bubble column reactorby assuming that the bubbles have the same size and determined the phenol conversion and catalyst activity dynamically. Maretto and Krishna15 carried out numerical modeling of a bubble column slurry reactor by taking into account two classes of small and large bubbles. In their study, hydrodynamic parameters and volumetric mass transfer coefficient were determined for large and small bubbles separately. Sehabiague © 2012 American Chemical Society

Received: Revised: Accepted: Published: 5705

December 12, 2011 March 6, 2012 April 1, 2012 April 2, 2012 dx.doi.org/10.1021/ie202914s | Ind. Eng. Chem. Res. 2012, 51, 5705−5714

Industrial & Engineering Chemistry Research

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Figure 1. Schematics of experimental setup.

2. EXPERIMENTS AND METHODS 2.1. Bioreactor Setup. The rectangular bubble column was made of Plexiglas with the dimensions of 0.12 m width, 0.7 m height, and 0.05 m depth, as shown in Figure 1. Oxygen was introduced to the column from the side, below the distributor, and injected into the liquid through a perforated plate located at 0.03 m above the base of the reactor. The distributor was rectangular with the dimensions of 0.12 m length and 0.05 m width, containing 14 holes of 0.6 mm diameter and 1 cm square pitch. Design of the sparger was based on the recommendations of Buwa and Ranade,21 according to which even distribution of air into the reactor is ensured. 2.2. Materials. D-Glucose monohydrate (99% pure from Fluka) was used as the reactant at various concentrations of 0.0555, 0.222, 0.3885, and 0.5550 mol/L. Distilled water was used as the solvent in all experiments. Glucose oxidase produced by Aspergillus niger (Sigma-Aldrich Co.) fermentation contains 1 mg g−1 of flavine-adenine dinucleotide (FAD) and with the activity of 24 800 units g−1 (unit definition: required amount of enzyme to oxidize 1 μmol of glucose to gluconic acid and H2O2 per minute at 25 °C and pH 7). The catalase was produced by bovine liver with the activity of 3940 units mg−1. Acetate buffer with pH 5.5 was used to add glucose oxidase and catalase into glucose solution. The physical properties of glucose solution used in this work are listed in Table 1.

Table 1. Physical Properties of Glucose Solution Used at 40 °C glucose concentration (mol L−1) 0.0555 0.2220 0.3885 0.5550

ρ (kg m−3) 982.590 993.744 1000.522 1017.02

σ (N m−1)

μ (Pa s) 0.689 0.746 0.812 0.887

× × × ×

−3

10 10−3 10−3 10−3

69.794 69.638 69.473 69.298

× × × ×

10−3 10−3 10−3 10−3

2.3. Methods. All experiments were carried out at controlled temperature (±0.1 K) and pH value (±0.1) by a Mettler Toledo DL28 titrator using 1 M NaOH. The pH of the solution was maintained at 5.5 (maximum GOD activity) by NaOH, which was automatically added to the solution in order to neutralize gluconic acid. Catalase and glucose oxidase with the concentration of 0.0101 g/L were added to the aqueous glucose solution at various concentrations. Since oxygen was dissolved in the liquid, nitrogen gas was passed through the column to purge the oxygen. Then, oxygen gas was introduced into the column and its concentration in the liquid phase was measured by a Mettler Toledo oxygen sensor connecting to a PC and recorded online. Oxygen was introduced into the column at superficial velocities of 0.0014, 0.0028, 0.0056, and 0.0112 m/s. All experiments were carried out in the 5706

dx.doi.org/10.1021/ie202914s | Ind. Eng. Chem. Res. 2012, 51, 5705−5714


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3. REACTION SYSTEM The reaction considered in this work was bioconversion of glucose to gluconic acid with glucose oxidase, which acts as an enzyme. Gluconic acid plays the main role in various fields such as pharmaceutical, food, leather, photographic, and other biological industries.17−20 Previous investigations indicated that the reaction rate of oxidation glucose by glucose oxidase has been influenced by oxygen velocity entranced to the column.19,25,26 The rate of oxygen consumption reaction in this system can be expressed by the Michaelis−Menten equations:

homogeneous and transition regime, atmospheric pressure, and 40 °C. The overall gas holdup (εG) and liquid holdup (εL = 1 − εG) were determined by using the volume expansion method:1 HG − HL HG

εG =

(1)

Mean bubble size diameter (Sauter diameter) was evaluated through the photographic method. Bubble images were taken by a Canon Power Shot S5IS digital camera, which took photos along the length of the reactor. According to Deckwer and Field,1 the bubbles can be considered spherical up to a diameter of 1 mm, and the larger bubbles change to elliptical shape. Hence, all of the bubbles were assumed to have an ellipsoidal shape, and the volume-equivalent sphere diameter for each bubble was ascertained by measuring the major and minor axes of the projected ellipsoidal bubbles and utilizing the following correlation:22

di =

3

E L 2Es

rO2 = −

Table 2. Evaluation of kc and k1 for Different Oxygen Velocity27

(2)

∑i di 3 ∑i di 2

(3)

Gas−liquid interfacial area is one of the key parameters in the modeling and designing of gas−liquid contactors, since it affects the volumetric mass transfer coefficient. In the present study, the gas−liquid interfacial area represents the amount of interfacial area with respect to the continuous (liquid) phase according to the following equation:22 a=

6εG d32(1 − εG)

k1 (L mol−1 s−1)

kc (s−1)

gas velocity (m s−1)

1074.6 7583.1 7110.7 7766.8

33.158 59.121 62.314 88.167

0.0014 0.0028 0.0056 0.0112

4. MODELING In order to obtain a realistic model for describing the behavior of the reactor, all hydrodynamic as well as kinetic parameters must be taken into account. The bubble column considered in this work was assumed to operate in semibatch condition (continuous flow of gas through specific amount of liquid). Due to the fact that back mixing in the liquid phase for a narrow bubble column is negligible,28 both gas and liquid phases were assumed to be in plug flow. Moreover, it was assumed that the liquid phase moves upward concurrently with the gas bubbles and with the minimum speed of bubbles. Of course, it is wellknown that the liquid moves upward at the center of the column while near the wall the liquid phase flows downward. However, the bubbles can be found mainly at the center while the number of bubbles very close to the wall is negligible. Therefore, it is reasonable to consider that the liquid is rising cocurrently with the gas phase along the column when writing the mass balance for the components in the gas phase. A summary of these assumptions and other assumptions considered to simplify the analysis of the reactor is as follows: • Operation is isothermal. • Concurrent flow of liquid and gas phase was considered. • Operation is steady state. • Variation of concentration occurs only in the vertical direction along the reactor, and the changes in other directions were neglected. • Reaction occurs only in the liquid phase. • Constant physical properties were considered throughout the reactor. • Oxygen is transferred from gas into liquid and the mass transfer resistance in the bulk gas phase is negligible compared to that in the liquid film.

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In order to assess the overall mass transfer coefficient (kLa), a nonstationary or dynamic method was used. Under the assumptions of constant interfacial area and no significant change in oxygen concentration in the gas phase, the overall mass transfer coefficient can be determined from23 (e−kLat − kLaτpe−t / τp) c* − c L = c* − c 0 (1 − kLaτp)

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The kinetic parameters have been determined at various oxygen (gas) velocities and are summarized in Table 2. More details were reported in the previous study related to measuring these kinetic parameters.27

Accordingly, the mean bubble size diameter (Sauter diameter) was evaluated by1

d32 =

0 1 kcC ECG 2 kc/k1 + CG

(5)

in which τp represents the response time of the oxygen probe evaluated as the time needing to reach 63% of the final calculated value when exposed to a step change in concentration.23,24 In the present work, this constant can be assessed by transferring the oxygen probe remaining in a solution of sodium sulfite for 0.5 min (wherein the oxygen concentration is zero) to another solution saturated with oxygen (which in this work was glucose solution). The response time (τp) of the oxygen probe used in this work was evaluated to be 25 s at 40 °C. The overall mass transfer coefficient is the multiplication of the specific gas−liquid interfacial area (a) and the liquid-side mass transfer coefficient (kL). Once the overall mass transfer coefficient was determined, the liquid-side mass transfer coefficient can be evaluated, knowing the interfacial area based on the bubble diameter, by dividing the overall mass transfer coefficient by the interfacial area. 5707



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Figure 2. Bubble column reactors with (a) monosize bubbles and (b) complete bubble size distribution.

corrected. Specific gas−liquid interfacial area is different for various bubble sizes. Therefore, the effective specific area is the sum of specific interfacial area for each bubble:

A bubble column consisting of monosize bubbles and the corresponding bubble size distribution are illustrated in Figure 2a. On the basis of the above assumptions, having considered single size bubbles in the reactor, the mass balance equations for oxygen in liquid and gas phases can be derived as follows: −VL

dcO2,L dy

+ kLa(1 − εG)(c*O2,L − cO2,L) + rO2(1 − εG) (7)

=0

−VG

area of bubble i (volume of gas + volume of liquid) volume of gas area of bubble i = × volume of gas total volume area of bubble i volume of bubble i = × volume of bubble i volume of gas volume of gas × total volume 6 = pv, i εG di

aG, i =

dcO2,G dy

− kLa(1 − εG)(c*O2,L − cO2,L) = 0

(8)

in which the interfacial area, a, for a uniform size of bubbles can be obtained from eq 4. It should be noticed that the negative sign before the convection term demonstrates the concurrent flow of the liquid and gas phases and the positive sign before the mass transfer term is for the sake of the enhanced oxygen transfer from gas phase to liquid phase. Equations 7 and 8 were developed for the case of monosize bubbles in the reactor. A bubble column consisting of various sized bubbles and the corresponding bubble size distribution are illustrated in Figure 2b. In order to take the effect of bubble size distribution into account, some parameters should be

(9)

and

ai =

aG, i (1 − εG)

(10)

Hence, the overall specific gas−liquid interfacial area based on liquid phase for all bubbles can be obtained from 5708


Industrial & Engineering Chemistry Research a=6

εG (1 − εG)

n

∑ i=1

Article

pv, i di

(11)

Accordingly, the overall mass transfer coefficient (kLa) should be evaluated from: n

kLa = kL ∑ pv, i i=1

6εG di(1 − εG)

(12)

By considering the above equations for distributed bubble size in the reactor, oxygen balance equations in liquid and gas phases become −VL

dcO2,L dy

n

+ kL ∑ pv, i i=1

6εG (c*O2,L, i − cO2,L) di

+ rO2(1 − εG)

−VGpv, i

Figure 3. Gas holdup for various glucose concentrations as a function of superficial gas velocity (error bars are standard deviations).

(13)

=0

dcO2,G, i dy

− kLpv, i

6εG (c*O2,L, i − cO2,L) = 0 di

viscosity of solution increases by increasing the glucose concentration, resulting in the formation of larger bubbles. Consequently, the number of bubbles decreases and their rise velocity increases, which makes the gas holdup decrease. 5.2. Bubble Size Distribution. A sample bubble size distribution along the reactor is demonstrated in Figure 4 at a

(14)

It should be noticed that eq 14 (oxygen balance oxygen in gas phase) should be considered for each bubble size i and the set of differential equations (13 and 14) should be solved together, simultaneously. In above correlations, the saturation oxygen concentration at the liquid interface was evaluated from1 cO2,G, i P c*O2,L, i = i = He He (15) RT

where He is the Henry’s constant for oxygen (equal to 756.7 L atm mol−1 at 40 °C) and R is the ideal gas constant (0.082 574 6 L atm K−1 mol−1). When there exist bubbles of different sizes in the reactor, the rate of mass transfer from each bubble is different from another one. As a result, bubbles of different sizes would have different concentrations of oxygen when passing through the column. In this case, the mean oxygen concentration should be evaluated, after solving a set of differential equations (13 and 14), on the basis of the concentration of oxygen in each bubble: n

cO2,G =

∑ pv,i cO ,G,i 2

i=1

Figure 4. The proportion of each bubble size to the total of bubbles in the whole of reactor for glucose concentration of 0.222 mol/L and at various superficial gas velocities.

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5. RESULTS AND DISCUSSION 5.1. Gas Holdup. The overall gas holdup in the glucose solution with the various concentrations as a function of superficial gas velocity is illustrated in Figure 3. The error bars demonstrated in this figure represent a sample of standard deviations of the measured values. As anticipated, the overall gas holdup for all the glucose concentrations increases by increasing the superficial gas velocity. On one hand, increasing the gas velocity increases the amount of gas injected into the bed. On the other hand, dispersion of small bubbles, as well as their proportion, is raised by increasing the superficial gas velocity. Small bubbles have less rise velocity compared to large bubbles, resulting in the increase of the gas holdup. Both of these phenomena result in increasing the holdup by increasing the gas velocity. Influence of glucose concentration on gas holdup can also be seen in Figure 3. The overall gas holdup decreases by increasing the glucose concentration. In fact, the

glucose concentration of 0.222 mol/L at various gas velocities. The bubble size distribution for other glucose concentrations follows the same trend. It can be seen in this figure that the mean size, width of the distribution, and the number of bubbles increase by increasing the superficial gas velocity. The range of bubble size distribution as well as their fraction is in good agreement with the previous studies.29−32 The reason for these trends upon increasing the gas velocity can be attributed to the growth of collision frequency by increasing the gas velocity due to the increase of coalescence and breakup. It is worth mentioning that, according to Buwa and Ranade,21 at the gas velocity of 0.0112 m s−1 there was a transition regime in the bubble column reactor. Effect of the glucose concentration on the mean bubble size is shown in Figure 5. This figure demonstrates that the glucose concentration has a negative effect on the mean bubble size. 5709



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Figure 5. The mean bubble size diameter (d32) as a function of glucose concentration at various superficial gas velocities (error bars are standard deviations).

Figure 6. Effect of superficial gas velocity (VG) on volumetric mass transfer coefficient (kLa) for various glucose concentrations (error bars are standard deviations).

This trend can be explained by the coalescence phenomenon. In general, the coalescence occurs during three steps: collision, liquid film drainage, and rupture.30 When two bubbles collide, the liquid film created from the liquid trapped between them begins to drain until the film becomes thin enough to rupture and the larger bubble is produced. In low viscosity solutions, the viscosity has an inverse effect on the coalescence compared to highly viscous solutions. However, increasing the viscosity, in low viscosity solution, prohibits film drainage during the thinning process and consequently hinders the coalescence between bubbles.33 On the other hand, increasing the viscosity reduces the turbulent intensity in the continuous phase, resulting in decreasing the breakage frequency. As a result, the number of bubbles reduces and the mean bubble size decreases by increasing the glucose concentration. Figure 5 also demonstrates the effect of the superficial gas velocity on the mean bubble size. It can be seen in this figure that the mean bubble size increases by increasing the superficial gas velocity. This behavior can be attributed to the turbulence increase through which large bubbles are formed due to coalescence. Moreover, by increasing the gas velocity, more bubbles are built; thus, the number of bubbles also increases. The exception to this trend is the case of glucose concentration of 0.555 mol/L in which, when the gas velocity increases from 0.0014 to 0.0028 m/s, the mean bubble size remains almost unchanged. The reason for this trend may be due to the changes of viscosity and surface tension of the liquid phase. Increasing the glucose concentration results in the viscosity increase (producing larger bubbles) and the surface tension decrease (producing smaller bubbles) of the liquid. At glucose concentration of 0.555 mol/L, these two effects cancel out each other. Therefore, increasing the gas velocity from 0.0014 to 0.0028 m/s does not considerably change the bubble size. 5.3. Mass Transfer Coefficient. Volumetric mass transfer coefficient of oxygen is shown in Figure 6 as a function of superficial gas velocity at various glucose concentrations. It can be seen in this figure that the mass transfer coefficient increases by increasing the superficial gas velocity. The reason for this trend is that by increasing the gas velocity, the number and size of bubbles increase due to the increase in coalescence and breakup in the reactor. Accordingly, the gas holdup increases and volumetric oxygen transfer coefficient increases as a result

of the increase in the specific interfacial area. The exception to this trend is the glucose concentration of 0.555 mol/L for which the volumetric oxygen transfer coefficient decreases in the range of gas velocity of 0.0028−0.0056 m/s. This trend occurs due to the fact that at gas velocity of 0.0056 m/s the proportion of small bubbles to the large ones decreases because of the higher frequency of coalescence producing more large bubbles, as compared to that at 0.0028 m/s. Figure 6 also reveals that the volumetric mass transfer coefficient decreases by increasing the glucose concentration. This negative effect of glucose concentration on mass transfer coefficient can be attributed to the viscosity of solution. Increasing the glucose concentration increases the viscosity of solution; thus, the turbulent intensity and gas holdup decreases. Hence, the specific gas−liquid interfacial area decreases as well as the oxygen transfer coefficient. Moreover, by increasing the viscosity, the diffusion of oxygen reduces, which results in the reduction of the volumetric oxygen transfer coefficient.34 Effect of the superficial gas velocity on liquid-side mass transfer coefficient is illustrated in Figure 7. This figure reveals that the liquid-side mass transfer coefficient has a contradictory

Figure 7. Effect of superficial gas velocity (VG) on liquid side mass transfer coefficient (kL) for various glucose concentrations (error bars are standard deviations). 5710



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trend by increasing the superficial gas velocity. In some cases the liquid-side mass transfer coefficient increases while for others it decreases. Former investigations also reported a contradictory effect of superficial gas velocity on liquid-side mass transfer coefficient. Diaz et al.35 highlighted liquid-side mass transfer coefficient increases upon increasing the superficial gas velocity, while Deng et al.36 emphasized the negative effect of superficial gas velocity on the liquid-side mass transfer coefficient. The liquid-side mass transfer coefficient (kL) is the quotient of dividing the overall mass transfer coefficient (kLa), which has a positive effect on liquid-side mass transfer coefficient, by the specific gas−liquid interfacial area (a), which has a negative effect on liquid-side mass transfer coefficient. In some cases, since the latter parameter (a) increases upon increasing the gas velocity, the liquid-side mass transfer coefficient decreases as a result. Of course, the volumetric mass transfer coefficient increases by increasing the gas velocity, which has a positive effect on liquid-side mass transfer coefficient, but its positive effect is negated by the negative effect of the specific gas−liquid interfacial area, and eventually, the volumetric mass transfer coefficient decreases by increasing the superficial gas velocity. Figure 8 illustrates the influence of superficial gas velocity on kLa/εG. It can be seen in this figure that by increasing the gas

Figure 9 demonstrates the parity plot of experimental vs calculated mass transfer coefficient. As can be seen in this

Figure 9. Comparing the experimental results with the correlation postulated by Akita and Yoshida.39

figure, the correlation of Akita and Yoshida39 provides the mass transfer coefficients of the same order of magnitude but underpredicts these values by about 30%. 5.4. Modeling Results. The model equations were solved for the same operating conditions of the experiments of this work. Samples of calculated profile of oxygen concentration along the height of the reactor at the glucose concentration of 0.3885 mol/L and the superficial gas velocity of 0.0056 m/s is illustrated in Figure 10 for single bubble size, double bubble

Figure 8. Effect of superficial gas velocity (VG) on kLa/εG for various glucose concentrations.

velocity, the value of kLa/εG decreases significantly. This trend is in agreement with those previously reported in the literature.37,38 Vandu et al.38 concluded that, in the air−water system, kLa/εG decreases with increasing the gas velocity until VG = 0.08 m/s and reaches a plateau afterward in the churnturbulent regime. This trend was reemphasized by Asgharpour et al.37 for distilled water and water−hydrocarbon systems. Decreasing of kLa/εG can be attributed to the fact that with increasing the gas velocity, the gas holdup increases more than the volumetric oxygen transfer coefficient kLa. Existing experimental correlations were examined in order to find the best prediction for the experimental results of the liquid-side mass transfer coefficient obtained in this work. Among them, the correlation proposed by Akita and Yoshida39 is in better agreement with the experimental data: kL = 0.5g 5/8DL1/2ρL 3/8 σ −3/8d321/2

Figure 10. Comparing different modeling results with experimental O2 concentration along the height of reactor at a glucose concentration of 0.3885 mol/L and superficial gas velocity of 0.0056 m/s for gas and liquid phases.

sizes, and complete distribution of bubble sizes, respectively. Corresponding experimental data are also shown in this figure. In the simulation with single bubble size, the Sauter mean diameter (d32 = 4.75 mm) was used. In the case of two bubble sizes, bubbles smaller than 4.25 mm were considered as small bubbles and those larger than 4.25 mm were considered as large ones. Oxygen reacts with glucose from its entrance to the reactor until it reaches the surface of the bed. Therefore, oxygen concentration decreases along the column as it reacts with glucose along the column. Although all modeling profiles show

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that the oxygen concentration decreases along the column height, Figure 10 demonstrates that only taking into account the complete distribution of bubbles can provide a reasonable prediction of the performance of the bubble column reactor. The reason for this disagreement between modeling results and experimental data is related to the hydrodynamics of the bed, specifically the value of ∑[pv,i(6εG/di)] in the governing equations. This parameter is larger than the actual value for single and two sizes of bubbles compared to the complete bubble size distribution. Therefore, the volumetric mass transfer coefficient in eqs 13 and 14 becomes considerably larger than its actual value, and the modeling results report a greater amount of oxygen transferred into the liquid phase. Effect of the superficial gas velocity on oxygen concentration is shown in Figure 11 at the glucose concentration of 0.222

Figure 11. Influence of superficial gas velocity on O2 concentration as a function of height of reactor at a glucose concentration of 0.222 mol/ L.

Figure 12. (a, top) Influence of glucose concentration on O2 concentration as a function of height of reactor at a superficial gas velocity of 0.0014 m/s. (b, bottom) Influence of glucose concentration on O2 concentration as a function of height of reactor at a superficial gas velocity of 0.0112 m/s.

mol/L as a sample. It can be seen in this figure that by increasing the gas velocity, oxygen concentration increases in the liquid phase. Increasing the gas velocity increases the mass transfer coefficient and more oxygen from bubbles enters the liquid phase; thus, the oxygen concentration increases in the liquid phase. The effect of glucose concentration on oxygen concentration in the liquid phase for the superficial gas velocities of 0.0014 and 0.0112 m/s, respectively, is illustrated in Figure 12a,b. As can be seen in this figure, the glucose concentration has two opposite effects on oxygen concentration. While for the lower velocity, it has negative influence and for the higher velocity has the positive one. At the gas velocity of 0.0014 m/s, the oxygen concentration decreases whereas at gas velocity of 0.0112 m/s, oxygen concentration increases by increasing the glucose concentration. The disparity for this behavior is attributed to the challenging effect between turbulent intensity and viscosity. At a gas velocity of 0.0014 m/s, the turbulence is considerably less compared to that at a gas velocity of 0.0112 m/s. Hence, the viscosity becomes crucial at a gas velocity of 0.0014 m/s. According to what was emphasized before, by increasing the glucose concentration, the viscosity increase resulted in reduction of turbulent intensity, gas holdup, specific gas−liquid interfacial area, and volumetric mass transfer coefficient. Therefore, less oxygen is transferred from gas phase to liquid and its concentration decreases upon increasing the glucose

concentration. On the other hand, at a gas velocity of 0.0112 m/s, the influence of turbulent intensity surpasses the effect of viscosity, as the gas velocity is significantly more than the former. By increasing the glucose concentration as the reactant material, the initial reaction rate is increased and more oxygen from gas phase is reacted with glucose, so the value of oxygen concentration increases in the liquid phase. It should be noticed although that at this velocity the volumetric mass transfer coefficient is also decreased by increasing the glucose concentration; the negative effect of this phenomenon is negligible compared to the positive effect of improving reaction rate by increasing the glucose concentration.

6. CONCLUSIONS Bubble size and its distribution have a considerable effect on the hydrodynamic parameters of a bubble column reactor, including bubble rise velocity, gas residence time, and overall gas−liquid mass transfer coefficient. In the present work, bubble size distribution was directly implemented in the equations of the bubble column reactor model. Experiments were carried out for acquiring hydrodynamic, kinetic, and mass transfer parameters. Experimental results revealed that increasing the superficial gas velocity increases the gas holdup, 5712



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kL k La pv,i R rO 2

mean bubble size, specific gas−liquid interfacial area, and volumetric mass transfer coefficient. The effect of the glucose concentration was also investigated and found to have a negative effect on the above-mentioned parameters. This negative effect was attributed to the viscosity of the liquid, which increases by increasing the glucose concentration. It was found that, at low gas velocity, oxygen concentration decreases upon increasing glucose concentration, while at high gas velocity, the inverse effect was observed. The modeling results revealed that implementing the complete bubble size distribution resulted in considerably better agreement of the model with the experimental data compared to single or double sizes of bubbles. Since the mass transfer term in the governing equations for single and double sizes of bubbles is significantly greater than its actual value, results of the model predict greater value of oxygen concentration in the liquid phase. It was shown that the superficial gas velocity has a positive influence on oxygen concentration because by increasing the gas velocity more oxygen transfers from gas phase to liquid phase. On the other hand, the glucose concentration has two opposite effects on oxygen concentration such that at the low gas velocities it has a negative effect while at the high gas velocities this effect is positive.

■

t T VG VL νx νy νz

liquid side mass transfer (m s−1) volumetric oxygen transfer coefficient (s−1) volumetric fraction of bubble i ideal gas onstant (L atm K−1 mol−1) Initial oxygen consumption rate of reaction (mol m−3 s−1) time (s) temperature (K) superficial gas velocity (m s−1) superficial liquid velocity (m s−1) velocity at x-direction (m s−1) velocity at y-direction (m s−1) velocity at z-direction (m s−1)

Greek Letters

τp εG εL μ ρ σ

response time of the oxygen probe (s) gas holdup liquid holdup dynamic viscosity (Pa s) density (kg m−3) surface tension (N m−1)

Subscripts

G gas L liquid

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: (+98-21)6696-7797. Fax: (+98-21)6646-1024. E-mail: mostoufi@ut.ac.ir.

REFERENCES

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Notes

The authors declare no competing financial interest.

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NOMENCLATURE specific gas−liquid interfacial area based on the liquid volume (m−1) aG,i specific gas−liquid interfacial area based on the gas volume for bubble i (m−1) ai specific gas−liquid interfacial area based on the liquid volume for bubble i (m−1) c* equilibrium concentration of oxygen between water and gas phase (mol L−1) CG glucose concentration (mol L−1) cL liquid dissolved-oxygen concentration (mol L−1) CO2,G,i gas oxygen concentration in bubble i CO2,L liquid dissolved-oxygen concentration (mol L−1) C*O2,L saturation concentration of oxygen in liquid phase (mol L−1) C*O2,L,i saturation concentration of oxygen in liquid phase for bubble i (mol L−1) c0 liquid oxygen concentration at start of measurement (mol L−1) di sphere equivalent diameter (m) d32 Sauter mean diameter (m) EL major axes of the ellipsoid (m) Es minor axes of ellipsoid (m) g gravitation acceleration (m s−2) HG liquid height after presence of gas bubbles (m) HL liquid height without presence of gas bubbles (m) He Henry’s constant (L atm mol−1) kc kinetic parameter of Michaelis−Menten equation (mol g−1 h−1) k1 kinetic parameter of Michaelis−Menten equation (L g−1 h−1) a

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