Effect of the radical scavenger t-butanol on gas–liquid mass transfer

Chemical Engineering Science 64 (2009) 4375 -- 4382

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Effect of the radical scavenger t-butanol on gas–liquid mass transfer C. Tizaoui a, ∗ , N.M. Grima b , M.Z. Derdar b a b

Centre for Clean Water Technologies, Process and Environmental Research Division, Faculty of Engineering, University of Nottingham, Nottingham, NG7 2RD, UK School of Engineering, Design and Technology, University of Bradford, Bradford, BD7 1DP, UK

A R T I C L E

I N F O

Article history: Received 11 January 2009 Received in revised form 24 May 2009 Accepted 10 July 2009 Available online 18 July 2009 Keywords: Mass transfer Semi-batch reactor Gas holdup Bubble size Ozone t-butanol

A B S T R A C T

The alcohol t-butanol has been used as a radical scavenger in the studies of ozone reactions in water and has been found to affect the gas–liquid mass transfer rates. An understanding of the effects of t-butanol on mass transfer parameters, including bubble size, gas holdup, mass transfer coefficient and the mass transfer specific surface area, is of key importance to not only improve the knowledge of this particular system but also to gain fundamental understanding about the effects of gas/liquid surface modifiers on the contact between phases and the mass transfer rates. An experimental study has been carried out to investigate the effects of t-butanol concentrations on the physical properties of aqueous solutions, including surface tension and viscosity. It was found that t-butanol reduced both properties-by 4% for surface tension and by a surprising 30% for viscosity. These reductions in the solution physical properties were correlated to enhancement in the mass transfer coefficient, kL . The hydrodynamic behaviour of the system used in this work was characterised by a homogeneous bubbling regime. It was also found that the gas holdup was significantly enhanced by the addition of t-butanol. An equation to predict the gas holdup from the gas flow rate and t-butanol concentration was proposed to describe the experimental data. Moreover, the addition of t-butanol was found to significantly reduce the size of gas bubbles, leading to enhancement in the volumetric mass transfer coefficient, kL a. Bubble mean diameter was predicted using an equation developed by the Radial Basis Function Neural Network architecture obtained from the literature, and the mass transfer coefficient, kL , was predicted using an equation based on the surface coverage ratio model. The ratio was found not to depend either on t-butanol concentration or on gas flow rate. A significant increase in the volumetric mass transfer coefficient, kL a, due to an increase in both kL and a, was obtained following the addition of t-butanol, even at low concentrations. © 2009 Elsevier Ltd. All rights reserved.

1. Introduction Bubble columns are widely used as gas/liquid contactors for a range of applications. One of these applications is the transfer of ozone to water in order to disinfect the water and/or to oxidise certain pollutants present in the water. Because of the significant interest in the use of ozonation processes in the water industry, ozone studies have attracted the attention of both the scientific community and industry for many decades. Ozone is usually produced in diluted gas mixtures in either air or pure oxygen and transferred to water using gas/liquid reactors, such as bubble columns which are widely used in industry. Gas/liquid reactor studies are thus fundamental in understanding the design and operation of ozone/water processes. There is a wealth of information on ozone reactions with a large number of chemicals that may act as contaminants in

∗ Corresponding author. Tel.: +44 (0) 115 951 4078; fax: +44 (0) 115 951 4115. 0009-2509/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ces.2009.07.008

water or pose environmental concerns. Generally, ozone studies aim to determine, on the one hand, the chemical reaction kinetic parameters and mechanisms, and on the other hand, the gas/liquid mass transfer parameters using laboratory or pilot plant gas/liquid reactors. It is well established that ozone reactions may follow two pathways: direct reaction of molecular ozone (dipolar addition, electrophilic substitution), and indirect reaction involving free radicals (mainly hydroxyl radicals o OH) formed following ozone decomposition in water (Staehelin et al., 1984; Tomiyasu et al., 1985). Due to the complex nature of the chemical reactions that ozone may undergo in water, and in order to account for the contribution of each of the two pathways, additives such as radical scavengers have been used to gain fundamental mechanistic and kinetic information on the ozone reaction(s) with the studied compounds. One of these additives is t-butanol, which is frequently used in research studies to scavenge hydroxyl radicals (o OH) formed following ozone decomposition in water. By scavenging o OH, only the direct molecular ozone reaction pathway prevails in the system. However, a number of studies revealed, as should be expected, that t-butanol affects gas/liquid mass

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transfer parameters (Gurol, 1985). Notwithstanding, this effect is not considered in many studies dealing with the determination of reaction rate constants, and there has been no detailed research carried out to investigate the effect of t-butanol on ozone mass transfer parameters. Some of the limited literature explained that t-butanol increased ozone volumetric mass transfer coefficients, kL a, owing to possible changes in the surface tension of the solution. However, it was found in this work that the addition of t-butanol at concentrations similar to those used in ozone studies would only cause a small decrease in surface tension, as also demonstrated by Hey and Kippax (2005) and Lopez-Lopez et al. (2007). The effect of t-butanol on ozone mass transfer is still poorly understood. Therefore, there is a need to carry out fundamental studies to understand the real effect of t-butanol on mass transfer parameters, including bubble size, gas holdup, mass transfer coefficient and the mass transfer specific surface area. This was precisely the aim of this paper.

(Eq. (1)), knowing that the length of the cell was 1 cm. This value of the emissivity was obtained from a preliminary study aimed to calibrate the spectrophotometer, by correlating the ozone concentration measured by the indigo method (Bader and Hoigné, 1982) with the absorbance at 260 nm. It agrees well with the literature (Gottschalk et al., 2000). With the aid of a peristaltic pump, the aqueous solution was pumped in a closed loop through a 1 cm quartz flow-through cell placed in the UV/VIS spectrophotometer. t-Butanol of reagent grade was purchased from Sigma Aldrich Co. and was added to the reactor at different concentrations. All experiments were carried out at a constant temperature of 20 ± 1 ◦ C. CAL =

Abs260 L

(1)

where CAL is the aqueous ozone concentration, Abs260 is the measured absorbance at 260 nm,  is the ozone emissivity, and L is the path length of the quartz cell.

2. Materials and methods 2.2. Model development 2.1. Experimental set-up The experimental set-up is shown in Fig. 1. A semi-batch stirred reactor, made of borosilicate glass with a capacity of 0.5 L and having a cross sectional area of 33 · 16 cm2 , was used in this work. The reactor was stirred with a magnetic stirrer placed at its bottom to ensure good mixing of the liquid phase. A Grade 1 (pore index 90-150 m) Pyrex䉸 sintered glass gas distribution sparger was used to disperse the gas into bubbles. Aqueous solutions of Millipore Q deionised water were used at different pH values ranging from 2 to 9, adjusted using phosphoric acid and sodium hydroxide solutions. The pH was measured with an Inolab (Terminal level 3) (WTW) pH-meter, calibrated with two buffer solutions at pH 4 and 7. Ozone was generated from pure oxygen using an ozone generator Model (Triogen, LAB2B). The flow rate of oxygen varied between 200 and 800 mL/min. The gas ozone concentration was measured using an ozone analyser (BMT 963 VNT g/m3 NTP 0 ◦ C, 1 atm). At a given oxygen flow rate, ozone gas concentration was fixed by changing the ozone generator input power with the aid of a manual potentiometer. Ozone concentration in the liquid phase (CAL ) was determined using a UV/VIS spectrophotometer (Agilent HP8453) by measuring the ozone solution absorbance at the maximum absorbance wavelength max = 260 nm (Abs260 ). The ozone concentration was then calculated from the Beer–Lambert law by dividing the measured value of absorbance at 260 nm by the ozone emissivity;  = 3000 M−1 cm−1

A model to describe the ozone mass transfer from the gas phase to the aqueous phase in a semi-batch reactor was developed. The model was particularly important in the determination of the volumetric mass transfer coefficient, kL a. The determination of kL a is essential in cases when ozone reaction is controlled by the rate of mass transfer rather than by the chemical reaction rate. Due to the reactive nature of ozone, its absorption in water, even impurity-free water, is generally accompanied by a complex decomposition reaction that converts ozone to radical species and molecular oxygen. Hence it is essential to take into account of the ozone decomposition reaction when developing the mass transfer model. For this reason, a preliminary study was carried out in a homogeneous system aiming to determine the effect of pH and t-butanol on ozone decomposition. Ozone decomposition rate can generally be described by an n-th order kinetics given by Eq. (2). The mathematical solution of Eq. (2) in a homogeneous system, assuming initially saturated ozone solution at a concentration CAL0 , is given by Eq. (3). rA = −

dCAL n = kd CAL dt

(2)

1−n − (1 − n)kd t)1/1−n CAL = (CAL0

CAL = CAL0 . exp(−kd t)

n
1

n=1

(3)

Off-gas ozone destructor Variablearea flow meter

Gas O3 analyser

Two-way valve

Valve (A) Ozone generator

Pressure regulator

Oxygen cylinder

Valve (B) UV/Vis Spectro. Peristaltic pump Magnetic stirrer Fig. 1. Scheme of the experimental set-up.

C. Tizaoui et al. / Chemical Engineering Science 64 (2009) 4375 -- 4382

QG

QG CAG

QG

CAG0

4377

CAG

Gas

Liquid

o ° ° °o oo NA

oo o ° o o o o oooo o oo o o o

QG CAG0

NA = kL (CAL*- CAL)

Fig. 2. Semi-batch gas/liquid reactor.

Table 1 Rate constant and order of the ozone decay reaction. pH

2.2 5.0 7.3 9.0

[t-butanol] = 0 (mol/L) 1−n −1

n

kd (M

2 2 2 1

1.02 10.44 18.51 0.030

s )

is the ozone partial pressure in the gas phase in atm; H is Henry's law constant given by Eq. (6) as a function of temperature and pH (Roth and Sullivan, 1981). It was also assumed that t-butanol, which was used at relatively low concentrations, does not affect the equilibrium concentration at a given ozone partial pressure and pH (Ku and Wang, 2002).   2428 (6) H (atm/mol/mol) = 3.84 × 107 (10pH−14 )0.035 exp − T

[t-butanol] = 0.2 (mol/L) n

kd (M1−n s−1 )

1.5 1.5 1.5 1

0.182 0.222 0.359 0.023

where CAL and CAL0 are the ozone liquid concentrations at times t and t = 0 respectively; kd is the ozone decomposition rate constant; n is the order of reaction. Values of kd and n were determined by fitting experimental results to the model given by Eq. (3) as discussed in the results section. Once the parameters governing ozone decomposition are determined, the ozone mass transfer model was applied. A physical representation of the model depicting the semi-batch reactor used in this work is shown in Fig. 2. In this model, it was assumed that both the liquid and gas phases are well mixed, and the double film theory is valid to describe the gas/liquid mass transfer. Furthermore, it was assumed that the only chemical reaction that may occur in water is that of ozone decomposition. Generally, ozone decomposition in impurity-free water proceeds at slow rates, which do not significantly enhance mass transfer. For this reason, the enhancement factor for mass transfer with chemical reaction, which is defined as the ratio between the rate of ozone absorption with chemical reaction in the liquid phase to the rate of only physical absorption without reaction (Levenspiel, 1999), was assumed equal to one and the mass ∗ −C ), where transfer rate NA can simply be expressed as: NA =kL (CAL AL ∗ kL is the mass transfer coefficient and CAL is the ozone concentration in the liquid at equilibrium with the gas phase. Taking into account the ozone decomposition equation and that of mass transfer, Eq. (4) was derived from a mass balance carried out over the liquid phase in the semi-batch reactor (Fig. 2). dCAL ∗ n = kL a(CAL − CAL ) − kd CAL dt

(4)

An analytical solution of Eq. (4) is possible when n = 1, which is given by Eq. (5), whilst a numerical solution was used when n
1. The values of kd and n were determined as discussed above (Table 1), and the initial ozone concentration was taken equal to zero. CAL =

kL a C ∗ [1 − exp(−(kL a + kd )t)] kL a + kd AL

(5)

∗ was calwhere kL a is the volumetric mass transfer coefficient. CAL ∗ culated applying Henry's law: CAL (mol/L) = 55.56(PA /H), where PA

Once the necessary parameters were determined for given experimental conditions, kL a was determined using the least squares method to fit the experimental data with either the numerical solution of Eq. (4) or with the analytical solution (Eq. (5)). It was found that the discrepancy of kL a values calculated by the analytical method (i.e. n = 1) with that calculated by the numerical method was always less than 5%, which gives confidence in the results obtained by the analytical method when n
1. 3. Results and discussion 3.1. Ozone decay Ozone decay in water has been extensively studied, and several models have been proposed in the literature to describe the rates by which ozone decomposes (Anselmi et al., 1984; Chelkowska et al., 1992; Gurol and Singer, 1982; Kuosa et al., 2005; Minchew et al., 1987; Mizuno et al., 2007a, 2007b; Sotelo et al., 1987; Staehelin et al., 1984; Tomiyasu et al., 1985). Due to the complexity of ozone decay mechanisms and the variability in experimental conditions used to carry out ozone decomposition studies, no single general model can be applied and be valid for all types of water. Indeed inconsistent results have been reported with respect to the reaction order and the rate constant, and equally a wide range of mechanisms have been reported (Roth and Sullivan, 1983). These inconsistencies are expected due to the reactive nature of the ozone molecule, in addition to variability in experimental conditions and methods such as the purity of the water, buffer systems used, and the techniques used to measure the aqueous ozone concentration. For these reasons, caution should be taken when using numerical values for the ozone decay reaction rate constant and order available in the literature. Therefore, ozone decomposition was studied in this work to determine the rate constants and reaction orders as a function of the pH and t-butanol concentrations applicable to this work. The ozone decomposition was studied at pH values of 2, 5, 7, and 9 in a 500 mL reactor initially saturated with ozone. At each pH value, the experiment was either carried out in the absence or presence of t-butanol at 0.2 mol/L. With the aid of a peristaltic pump, the aqueous solution

C. Tizaoui et al. / Chemical Engineering Science 64 (2009) 4375 -- 4382

was pumped in a closed loop through a 1 cm quartz UV/VIS spectrophotometer flow-through cell, in the same fashion as for the other experiments. Values of the parameters kd and n were determined using the Solver tool available in Microsoft Excel to minimise the objective function (Eq. (7)) given by the sum of the absolute values of the difference between experimental and model (Eq. (3)) ozone concentration values at a given time, divided by the experimental value. objective function =

 |CAL exp − CAL model | CAL exp

(7)

The values of the order and rate constant of ozone decay reaction are shown in Table 1. In the absence of t-butanol, ozone decomposition was found to follow a second order reaction at pH values less than 7, whilst it was first order at pH 9. When the scavenger t-butanol was added, the decomposition of ozone progressed at a lower reaction order of 1.5 for pH values less than 7, and at the same order of one when without t-butanol at pH 9. In the absence of t-butanol, the kinetic data presented in Table 1 (i.e. kd and n) show that ozone decomposition rate, which is a function of both the rate constant and the reaction order, increases significantly with pH, due to the increase of hydroxide ion concentration, which promotes ozone decomposition. Although at pH 9 the value of the reaction rate constant decreased as compared to the other pHs, the rate of the decomposition reaction has in fact increased significantly due to reduction of the reaction order. On the other hand, the results also show that although t-butanol was used as a radical scavenger, ozone decomposition was not fully inhibited. 3.2. Effect of t-butanol on solution properties Mouza et al. (2005) showed that liquid properties have important effects on bubble size distribution and gas holdup for the liquid–air systems they studied. It was demonstrated by Kazakis et al. (2008) that an increase in liquid viscosity reduced the size of the formed gas bubbles, due to an increase of the drag force that opposes the growth of a bubble during its formation at the sparger pores. Moreover, Mouza et al. (2005) and Zahradnik et al. (1997) have shown that viscosity decreases bubble sizes by inhibiting bubble coalescence as they rise towards the liquid surface. The liquid surface tension also has a very important effect on the size of the gas bubbles (Camarasa et al., 1999; Chaumat et al., 2007; Mouza et al., 2005). It was demonstrated that a decrease in the surface tension would result in the formation of small gas bubbles, which increases specific surface area, a. Overall, it is evident that both viscosity and surface tension, which are affected by the addition of t-butanol, have a great effect on bubble sizes and their distribution. Moreover, the addition of t-butanol, which is an alcohol, would reduce the probability of gas bubbles to coalesce and increase the gas holdup. The inhibition of bubble coalescence following the addition of alcohols is the result of the accumulation of the alcohol molecules at the gas–liquid interface forming a rigid layer. This rigid layer serves to immobilise the gas–liquid interface, thus inhibiting the coalescence of bubbles when they approach each other. Clearly, all these bubble characteristics that would result following the addition of t-butanol will affect ozone mass transfer. The effect of t-butanol concentration on the solution viscosity, , and surface tension, , was studied in two independent studies. The viscosity of aqueous solutions at different concentrations of t-butanol was measured using a Physica MCR series 501 Modular Compact Rheometer (Anton Paar, USA) operated at 20 ◦ C and a shear rate of 300 s−1 , and the surface tension was measured with an FTA 188 video tensiometer manufactured by First Ten Angstroms, Inc. (http://firsttenangstroms.com/) using the pendant drop method (Campbell, 1970; Harkins and Brown, 1919). Each experiment was

1.1

Surface tension

Viscosity

1

ratio relative to DI water

4378

0.9 0.8 0.7 0.6 0.5 0.000

0.003

0.006 0.009 [t-butanol] (mol/L)

0.012

Fig. 3. Effect of t-butanol concentration on viscosity and surface tension.

conducted three times and average values were calculated. The maximum relative error calculated was 4%. The effect of t-butanol concentration on  and  is shown in Fig. 3. This figure shows that the addition of t-butanol decreased the viscosity of the solution by almost 30% and further increases in t-butanol concentration did not cause a significant effect on viscosity. Although there is no data in the literature to endorse this finding, the large decrease in viscosity following the addition of t-butanol may be attributed to the formation of lubricating thin film(s) that reduced shear forces and thus the measured viscosity. On the other hand, t-butanol caused only a small decrease in surface tension of less than 4%, which is in agreement, within the range of concentrations used in this work, with results obtained by Hey and Kippax (2005). These results show that the changes in both viscosity and surface tension following the addition of t-butanol should be taken into account to explain t-butanol effects on mass transfer parameters. 3.3. Effect of liquid properties on kL As shown earlier, t-butanol affects the solution properties and its presence in the solution would cause changes in the mass transfer coefficient. In fact, the double film theory established the relationship between the mass transfer coefficient kL and the diffusivity of the gas in water, DA , as given by Eq. (8), where  is the film thickness which depends on the hydrodynamic properties of the system and is a function of the reactor geometry, liquid agitation, and physical properties. Accurate measurement of the film thickness is very difficult and generally experimental studies are required for the determination of kL . In general, if the degree of turbulence of the fluid is increased, the effective film thickness will be reduced causing the mass transfer coefficient to increase since they are inversely proportional, as shown by kL =

DA



(8)

The diffusivity DA is generally correlated to the liquid viscosity, , and temperature, T, by an equation of the form DA = kT/  (Wilke and Chang, 1955), where k is a constant. Therefore, if T is assumed constant, the mass transfer coefficient can be inversely correlated to the viscosity and film thickness by kL =

kT



(9)

Since accurate measurement of the film thickness, , is difficult, the effect of t-butanol on kL , was studied under a constant specific surface area (a) condition throughout all experiments. This was achieved by

C. Tizaoui et al. / Chemical Engineering Science 64 (2009) 4375 -- 4382

4379

1.20

105×kL (m/s)

1.00 0.80 0.60 0.40

[t-butanol] = 0 mol/L, pH 7

0.00

kL

[t-butanol] = 0.01 mol/L, pH 7 k L

0.20 0

200

with tb

= 1.5 ± 0.2

without tb

400 600 Gas flow rate (mL/min)

800

100mL/min no tb

400mL/min no tb

800mL/min no tb

100mL/min, 10-6M tb

400mL/min, 10-6M tb

800mL/min, 10-6M tb

100mL/min, 0.2M tb

400mL/min, 0.2M tb

800mL/min, 0.2M tb

1000

Fig. 4. Effect of t-butanol on the mass transfer coefficient, kL (the gas was flowing above the solution surface). Marker: experimental data and straight line: average values.

simply passing the gas flow just above the solution surface, instead of bubbling the gas into the aqueous solution (i.e. the gas diffuser was not immersed in the liquid). The level of mixing was carefully chosen in order to not only ensure a homogeneous liquid phase, but also to ensure a constant surface area of the interface gas/liquid. These experiments were carried out in the presence and absence of t-butanol at pH 7, and variable gas flow rates (200, 400, 600, 800 mL/min). The volume of the solution was reduced to 150 mL instead of 500 mL, giving a specific surface area of 22.11 m2 /m3 . Fig. 4 shows the changes in kL in the presence of t-butanol compared to those without it as a function of the gas flow rate. According to this figure and under the experimental conditions explored in this section, the gas flow rate had little effect on kL , which remained almost constant for each solution. On the other hand, it is remarkably clear that t-butanol has caused a significant increase of the average kL , by almost 50%. This clearly indicates that the presence of t-butanol has affected the mass transfer, as a result of changes in the liquid physical properties (i.e. viscosity), as demonstrated in the previous section, and possibly as a result of thinning of the mass transfer liquid film. In fact, from Eq. (9), the ratio of kL with and without t-butanol should be equal to the ratio of  without and with tbutanol, respectively. According to Fig. 3, the ratio of viscosities was calculated to have a value of 1.41. On the other hand, the ratio of the average kL values for solutions with and without t-butanol, respectively, calculated from Fig. 4 gave a value of 1.50, which is slightly higher than the viscosities ratio, possibly owing to a decrease in the mass transfer liquid film thickness around the liquid/gas interface. This result may thus prove that t-butanol has increased the value of kL by 50%, attributed to a decrease of the solution viscosity by almost 30% and a reduction of the liquid film thickness by 5%. 3.4. Effect of t-butanol on bubble regime and gas holdup Simple visual observations showed that t-butanol increased the number of bubbles available in the reactor, and significantly decreased their sizes (Fig. 5). This behaviour is commonly observed by several authors following the addition of t-butanol (Ku and Wang, 2002). Ultimately, a decrease in the mean bubble diameter dB would increase the specific surface area, a, expressed by Eq. (10). On the other hand, the addition of t-butanol would also cause a substantial increase in the gas holdup g , and thus a, as demonstrated by Veera et al. (2001) in their work with the alcohol n-butanol. a=

6g dB

(10)

where dB is the mean bubble diameter and g is the gas holdup.

Fig. 5. Effect of gas flow rate and t-butanol concentration on gas bubbles.

In this work, the effect of t-butanol on gas holdup, g , was studied. The gas holdup was measured using the bed expansion method. This method relies on the fact that the height of the reactor content expands after passing the gas and this expansion is due to the volume of gas that occupied the reactor. The method involves measurement of the difference between the reactor heights after and before letting the gas to flow through the reactor. The difference in the reactor heights was measured using a mm-graduated scale placed at the proximity of the gas/liquid interface and a digital camera well focused and zooming (×3 optical) the area of interest. The photos obtained were then processed and the difference in heights (h) was determined. Eq. (11) was used to calculate the gas holdup.

g =

h.S VL + h.S

(11)

where S is the cross sectional area of the reactor, VL is the liquid volume and h is the height difference. The effect of t-butanol on gas holdup is shown in Fig. 6. This figure shows, for solutions with t-butanol, a linear relationship between the gas holdup and gas flow rate in the range of gas flow rates used in this work, which demonstrates homogeneous bubbling regime behaviour (Zahradnik et al., 1997). This regime entails the formation of discrete bubbles having uniform size and which rise undisturbed to the water surface, with negligible coalescence and breakup behaviour. Fig. 6 clearly shows that t-butanol caused a significant increase in the gas holdup, which is in agreement with results obtained by Camarasa et

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C. Tizaoui et al. / Chemical Engineering Science 64 (2009) 4375 -- 4382

Gas holdup, εg (%)

3.0

kL a to then reach slowly changing values that have almost doubled from those without t-butanol. According to the results obtained in the previous sections, the increase of kL a following the addition of t-butanol would result from the increase in both kL and a. Several correlations have been proposed in the literature to calculate the liquid-side mass transfer coefficient, kL , in bubble columns. Generally, the experimental values of kL vary between an upper limit predicted by Higbie's model (Bird et al., 1960) for bubbles with a totally mobile surface (Eq. (13)) and a lower value predicted by, for example, the Calderbank and Moo-Young (1961) equation for bubbles with a totally rigid surface (Eq. (14)).

[t-butanol] = 0.2 mol/L

2.5

[t-butanol] = 8e-6 mol/L

2.0

[t-butanol] = 0 mol/L

1.5 1.0 0.5 0.0

1. Higbie's model (Bird et al., 1960)  0.2

0

0.4

0.6

0.8

1

kmobile L

=

Gas flow rate (L/min)

4DA ut h

(13)

2. Calderbank and Moo-Young (1961) Fig. 6. Gas holdup as a function of gas flow rate and t-butanol concentration.

 rigid

kL

= 0.31

ut =

g d2B 18L

pH = 7

0.012 0.010

kLa (s-1)

0.008 0.006 0.004 0.002 0.000

200mL/min 600mL/min 0

0.002

0.004 0.006 [t-butanol] (mol/L)

400mL/min 800mL/min 0.008

0.01

al. (1999), Mouza et al. (2005) and Veera et al. (2001) who effectively showed that gas holdup increased following the addition of alcohols to aqueous solutions. Since t-butanol has the character to suppress coalescence of gas bubbles, the size of the gas bubbles in the reactor should be close to the initial size of the gas bubbles formed at the orifice of the sparger. Moreover, a narrow bubble size distribution can also be obtained, as shown by the work carried out by Camarasa et al. (1999), using non-coalescing alcohol solutions, which validates the assumption of constant average bubble diameter, dB . Based on the experimental results obtained in this work, Eq. (12) was proposed to describe the change of the gas holdup as function of t-butanol concentration and the gas flow rate, QG , where s, s and S0 are three constants and Ctb is the t-butanol concentration in mol/L. The three constants S0 , s and s were determined as having values of 1.1 (min/L), 2.8×105 (min/mol) and 8.7×104 (L/mol) respectively.

g (%) =

S0 + sCtb Qg 1 + s Ctb

(12)

3.5. Effect of t-butanol on kL a Fig. 7 shows the effect of t-butanol concentration on the volumetric mass transfer coefficient, kL a, determined from the experimental results at different gas flow rates. As can be observed, small increase in concentrations of t-butanol have significantly increased

1/3 Sc−2/3

(14)

(15)

where h is the bubble height, which is assumed equal to its diameter dB , ut is the bubble rising velocity obtained by Stokes' equation (Eq. (15)), DA is the liquid diffusivity,  is the difference between liquid and gas densities, Sc is the Schmidt number. Due to the presence of t-butanol, the average kL value is expected rigid and kmobile (Painmanakul et to lie between the extreme values kL L al., 2005; Sardeing et al., 2006; Vasconcelos et al., 2003). In this work, kL may be predicted using Eq. (16), which is based on the surface coverage ratio model presented by Painmanakul et al. (2005). rigid

Fig. 7. Effect of t-butanol concentration on the volumetric mass transfer coefficient, kL a, at different gas flow rates.

 L g 2L

k L = kL

+ (1 − )kmobile L

(16)

where is the surface coverage ratio that varies between 0 and 1. In order to apply the above correlations, bubble diameters were estimated assuming that coalescence and break-up are negligible. The bubble sizes were estimated using Eq. (17), which was developed using the “Radial Basis Function Neural Network” architecture, taking into account the operating conditions and the physical properties of liquid solutions used in a large number of available experimental data in the literature (Jamialahmadi et al., 2001). Eq. (17) was found to predict gas bubble sizes, with an absolute mean average error of 3.2%.  1/3 5 9.261Fr0.36 db 0.51 = + + 2.147Fr d0 Ga0.39 Bd1.08 0

(17)

where Bd0 = L gd20 /  is the Bond number in terms of orifice diameter d0 ; Fr=u2s0 /d0 g the Froude number; Ga=g 2L d30 / 2 the Galileo number. Once db was determined from Eq. (17), Eqs. 13, 14 and 10 were rigid , kL and a, respectively, takused to calculate the values of kmobile L ing into account the effect of t-butanol concentrations on the values of surface tension, viscosity and gas holdup (Sections 3.2 and 3.4). The values of required in Eq. (16) were determined using the least squares regression method to fit the experimental data to those calculated by the surface coverage ratio model. Fig. 8 shows good agreement between the experimental results and the surface coverage ratio model. It was found that was independent of both t-butanol concentration and gas flow rate (Figs. 8 and 9), and an average value of equal to 0.930 ± 0.012 was determined.

C. Tizaoui et al. / Chemical Engineering Science 64 (2009) 4375 -- 4382

QG = 200mL/min

QG = 400mL/min

QG = 600mL/min

QG = 800mL/min

Notation

0.012 0.01

kLa (s-1)

0.008 0.006 0.004 0.002

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

0 1.E-01

[t-butanol] (mol/L) -log scale Fig. 8. Effect of t-butanol on kL a determined using the surface coverage ratio model.

a Bd0 CAG CAL Ctb dB d0 DA

specific surface area, m2 /m3 Bond number Bd0 = L gd20 /  gas concentration, mol/m3 liquid concentration, mol/L concentration of t-butanol, mol/L bubble diameter, m sparger orifice diameter, m gas diffusivity in the liquid phase, m2 /s

Fr Ga h H k kd kL kmobile L

Froude number Fr = d s0g 0 Galileo number Ga = g 2L d30 / 2 bubble height, m Henry's constant, atm/mol/mol constant in Wilke and Chang equation (D = kT/ ), kg/s2 K decay rate constant, M1−n s−1 liquid-side mass transfer coefficient, m/s liquid-side mass transfer calculated by Higbie's model, m/s

kL

liquid-side mass transfer calculated by Calderbank and Moo-Young equation, m/s volumetric mass transfer coefficient, s−1 reaction order, dimensionless mass transfer rate, mol/m2 s partial pressure, atm gas flow rate, m3 /s reaction rate, mol/L s three constants in the equation of gas holdup Eq. (10) (g (%) = (S0 + sCtb )/(1 + s Ctb )Qg ) Schmidt number (Sc = / DA ) time, s temperature, K bubble rising velocity, m/s

rigid

Surface coverage ratio, α (-)

1.2

kL a n NA PA QG rA s, s , S0

1.0 0.8 0.6

Sc t T ut

0.4 0.2 0.0

0

200

400

600

800

4381

1000

u2

Greek letters

Gas flow rate (mL/min) Fig. 9. Effect of gas flow rate on the surface coverage ratio .

4. Conclusions Precise knowledge of the hydrodynamics and mass transfer parameters in gas/liquid reactors is very important in order to determine the correct reaction kinetics. Alcohols added to aqueous solutions reduce gas bubble sizes by inhibiting coalescence of the small gas bubbles formed by the gas sparger (Camarasa et al., 1999). Small bubble sizes imply enhancement of the specific surface area, thus increasing the volumetric mass transfer coefficient. The effect of the alcohol t-butanol on mass transfer parameters in an ozone/water system was studied in this work. The study revealed that t-butanol added to the aqueous solution reduced the surface tension of the solution by about 4% and the viscosity by 30%. The effect of the reduction in viscosity was an enhancement of the mass transfer coefficient, kL , as evidenced by the experiments carried out in this work. Further, it was visually observed that small gas bubbles formed following the addition of t-butanol, and their sizes did not change significantly throughout the length of the reactor. As well as reducing the bubble sizes, t-butanol caused a significant increase in gas holdup, thus causing considerable increase in the volumetric mass transfer coefficient kL a. The effect of the addition of t-butanol on the mass transfer coefficient was successfully modelled using the surface coverage ratio model (Painmanakul et al., 2005), and it was found that neither t-butanol concentration nor the gas flow rate affected the value of the surface coverage ratio.

  P  g  L

surface coverage ratio surface tension, Pa m mass transfer liquid-film thickness, m interphase pressure difference, Pa difference between liquid and gas densities, kg/m3 gas holdup, dimensionless viscosity, Pa s liquid density, kg/m3

Subscripts 0 G L *

initial or relative to the sparger orifice gas liquid equilibrium

Acknowledgements The authors would like to acknowledge Professor Hadj Benkreira, Dr Raj Patel and Mr David Steele at the University of Bradford for their support with surface tension and viscosity measurements. References Anselmi, G., Lignola, P.G., Raitano, C., Volpicelli, G., 1984. Ozone mass-transfer in stirred vessel. Ozone-Science & Engineering 6 (1), 17–28. Bader, H., Hoigné, J., 1982. Determination of ozone in water by the indigo method; a submitted standard method. Ozone-Science & Engineering 4, 169–176.

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