Introduction - research.manchester.ac.uk€¦  · Web viewIn addition to the mixing time within a gas-liquid stirred tank, the mass transfer is an important property when considering

Effect of Zoning on Mixing and Mass Transfer in Dual Agitated Gassed Vessels

Amna Jamshed, Michael Cooke, and Thomas L. Rodgers

School of Chemical Engineering and Analytical Science, University of Manchester, Oxford Road,

Manchester, M13 9PL, UK

Corresponding author:

Thomas Rodgers [email protected]

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Abstract

Gas-liquid multi-phase processes are widely used for processes that require reactions. To increase

productivity in these reactions one potential method is to increase the gas flow rate into the vessel.

This means that it is important to understand how these reactors perform at high gas flow rates,

which can create problems such as zones within the vessel. This paper investigates the mixing

performance and the mass transfer in dual agitated systems at high gas flow rates. Two

configurations have been compared a 6 blade disk turbine (Rushton turbine) below either a 6 Mixed

flow Up-pumping or down-pumping agitator. Zoning has been identified by Electrical Resistance

Tomography which affects the mixing time within the vessel, with increasing agitation rate

potentially increasing the mixing times at high gas flow rates. At these high gas flow rates the zoning

also affects the mass transfer meaning that it isn’t constant within the whole vessel. However,

dividing the vessel into the key zones allows the mass transfer rate to be predicted with a single

equation.

Keywords

Gas-liquid mixing; Mixing Time; Mass Transfer; Axial-radial dual system; Electrical Resistance

Tomography

Acknowledgements

The authors would like to thank the workshop staff of School of Chemical Engineering and

Analytical Science at The University of Manchester for their help with the modifications and

maintenance of the equipment.

Funding

This work was supported by The University of Manchester’s EPSRC DTA (Doctoral Training

Award), funded as part of first author’s PhD research project.

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Nomenclature

Latin symbolsC Clearance [m]D Agitator diameter [m]HL Height of liquid [m]H Henry’s law constant [Pa m3 mol–1]kG a Gas mass transfer coefficient [s-1]k L a Liquid mass transfer coefficient [s-1]n Number of measurementsN Agitator speed [rps]P Power [W]Qg Volumetric gas flow rate [m3 s-1]QH2 O 2

Volumetric rate of Hydrogen Peroxide [m3 s-1]T Tank diameter [m]V Volume [m3]V Voltage [V]V L Liquid Volume [m3]vs Superficial gas velocity [m s-1]Greek symbolsρ Density of fluid [kg m3]Dimensionless numbersPo Power numberθ90 90% Mixing time numberθ95 95% Mixing time numberAbbreviations6BDT 6 Blade Disc Turbine (Rushton Turbine)6MFD 6 Mixed Flow Downward pumping6MFU 6 Mixed Flow Upward pumpingDAS Data Acquisition SystemDOT Dissolved oxygen tensionERT Electrical Resistance TomographyH 2O2 Hydrogen PeroxideITS Industrial Tomography SystemNaCl Sodium ChlorideNaOH Sodium Hydroxide

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1. Introduction

Gas liquid mixing in mechanically agitated vessels is commonly used and a vital process in the

chemical and biochemical industries. Gas liquid processes such as fermentation, hydrogenation, and

oxygenation requires a large interfacial area which demands large gas handling capacity and

effective gas distribution (Vasconcelos et al., 1997).

Most gas liquid mixing systems are controlled by the mass transfer rate or by the mixing time

within the system (Nienow et al., 1997). As reported by Rodgers et al. (2011), various methods have

been tested in past to understand mixing time studies, for example dye addition (Mann et al., 1987),

pH shift (Singh et al., 1986), tracer monitored by conductivity probes (Cooke, 1988; Khang and

Levenspiel, 1976) and ERT (Cooke et al., 2001).

For single phase mixing in the turbulent regime the dimensionless mixing time is independent

of the Reynolds number and has been correlated by Grenville and Nienow (2004) to give:

θ95 N=5.2 Po−1 /3 ( D /T )−2(H L

T )1/2

(1)

The exponent on the HL/T term can be modified in accordance to Rodgers et al. (2011) when

the value of HL/T exceeds 1. For a 6MFD/6MFU this is 1.67 and for Rushton Turbine this is 2;

multiple impellers can actually increase this exponent further due to zoning forming within the

vessel; for example Otomo et al. (1995) reports a lower mixing time in a dual axial system with

much less zoning than the system reported by Cooke et al. (1988). To improve the mixing time, it

was reported to reduce the spacing distance between the impellers, to prevent stagnant zones (Hari-

Prajitno et al., 1998).

Aerated conditions tend to reduce the power number of agitators, provided the conditions are

not flooded, thus increasing the mixing time. However under flooded conditions the mixing time will

reduce with increased gas flow rates but can increase when increasing the agitator speed (Nienow,

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1998; Xie et al., 2014). However, an extensive study on different types of agitator used under very

high gas flow rates is needed for process industry development.

In addition to the mixing time within a gas-liquid stirred tank, the mass transfer is an important

property when considering the mixing performance as often the mass transfer rates determine the

equipment size. In gas-liquid mixing, the mass transfer rate depends largely on the liquid phase

diffusion and the size of the gas bubbles. This means that the mass transfer is dependent on various

factors such as physical properties of gas and liquid, type of gas distributor, orifice diameter and

position, dimensions of tank, number of baffles, and of course the size, type and speed of agitators.

Even if these parameters are constant for a given system, the mass transfer rate is still dependent on

the bubble size, gas hold up, bubble rise velocity and input power (Sideman et al., 1966). Therefore

all of these factors have to be taken into account to determine the optimum mixing conditions.

Mass transfer rates are usually represented by the mass transfer coefficient, k L a, which is often

correlated as a function of energy dissipation rates and superficial gas velocity. For example Gezork

et al. (2001) suggested a correlation that could fit a wide range of specific power inputs and gassing

rates as,

k L a=0.0059( PV )

0.61

v s0.36 (2)

Where P/V is the shaft paper per unit liquid volume in W m–3 and vs is the specific gas velocity in

m s–1, which means to increase mass transfer rate, an increase in specific power input or gas rate is

required. Many authors have used a similar style of equation such as,

k L a=constant ( PV )

a

vsb (3)

Cooke et al. (1988) found no differences on using different agitators, Bujalski et al. (1990)

reported no effect between up pumping impeller and Rushton Turbine, Martin et al. (1994) found

very little difference between the Prochem Maxflo and Rushton Turbine, John et al. (1997) showed

no effect of agitator type used and Whitton and Nienow (1993) reported that the relationship was

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independent of scale. Some of the main values found have been summarized in Table 1, using

different agitator systems.

Table 1. Summary of parameters for equation (3) from previous studies.

References Fluid Constant a b vs / m s–1 T / m

(Cooke et al., 1991)Air-water 0.0019 0.70

00.30

0 Not given 0.29

Air-0.1M KCl 0.0109 0.60

00.42

0 Not given 0.29

(Vasconcelos et al., 1997) Air-water 0.0053 0.66 0.34

0 0.0025 to 0.02 0.61

(Gezork et al., 2001)Air-water 0.0059 0.60

70.36

0 0.0015 to 0.01 0.29

Air-0.2M Na2SO4

0.0028 0.790

0.349 0.0015 to 0.01 0.29

(Moucha et al., 2003)Oxygen-

0.5M Na2SO4

0.00081 1.190

0.549 0.0021 to 0.0085 0.29

(Puthli et al., 2005) Air-water 0.000138

0.580

0.430

0.00017 to 0.00064 0.13

(Shewale and Pandit, 2006)

Air-water 0.0191 0.57 0.7 0.005 to 0.02 0.3

Air-water 0.0057 0.701 0.59 0.005 to 0.02 0.3

Sideman et al., (1966) reviewed the available studies on mass transfer in gas liquid contacting

systems and reported that the developed correlations are limited to their particular systems and range

of operating conditions. In the same study it was reported that at low gas flow rates (less than 0.005

m s-1), the bubble diameter is a strong function of orifice diameter and a weak function of gas

velocity in the orifice. At moderate gas flow rates (0.005-0.09 m s-1), this functionality is reversed

and bubble diameter becomes stronger function of gas velocity and above 0.09 m s-1, at high gas flow

rates both orifice diameter and velocity in the orifice have weak influences on bubble diameter. It

was deduced that the ultimate bubble size in the gas liquid systems depends primarily on the

turbulence in the continuous phase. So the average bubble size increases with the gas hold up from

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the result of the coalescence of the smaller bubbles. It was also reported that the bubble size

decreases in the presence of electrolytes or increased agitation.

2. Material and Method

2.1. Experimental Set up

The same vessel as used for Jamshed et al. (2018) was used in this study, the key dimensions are

listed in Table 2 for Figure 1(a); the vessel also has 4 baffles. The vessel was fitted with two

impellers, a 6 Blade Disc Turbine (6BDT) at the bottom and a 6 blade Mixed Flow

Upwards/Downwards Pumping (6MFU/6MFD) at top, Figure 1(b) and (c). Rotating shaft clockwise

and anticlockwise provided different combination of agitators i.e. 6BDT plus 6MFD and 6BDT plus

6MFU respectively. The gas was provided from a sparge ring which was placed under the bottom

agitator.

(b)

(a) (c)Figure 1. Equipment used for the experiments (a) schematic diagram of the rig, (b) 0.3048m diameter 6BDT, and (c) 0.3048m diameter 6MFD/6MFU.

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Table 2. Key measurements for the system used.

Dimension 6BDT 6MF

Tank diameter (T) / m 0.610

Cross sectional area / m2 0.290

Height of liquid (HL) / m 0.763

Dispersion Volume / m3 0.208

Baffle width / m 0.061

Sparge pipe diameter / m 0.020

Sparger clearance from base / m 0.080

Diameter (D) / m 0.305 0.305

Blade length / m 0.076 0.120

Blade width / m 0.060 0.085

Clearance (C1/C2) / m 0.230 0.530

Pitch / o 90 45

The vessel contains an electrical resistance tomography baffle cage which consists of 8 rings of 16

equally spaced stainless steel electrodes (3 cm high and 2 cm wide), though only 7 are used due to

the eight being above the liquid height. The electrodes were connected to an Industrial Tomography

System P2000 Data Acquisition System (DAS) which was connected to computer allowing the

measurements to be taken.

2.2. Mixing Time Measurements

The mixing in the vessel was monitored by both colour change and ERT with conductivity

change. This allowed accurate measurement of the mixing time (ERT), but also visualisation of any

zones within the vessel (colour change). The vessel was prepared for measuring the mixing times by

adding 50 ml of 1 M of sodium hydroxide (NaOH) and 50 ml of 50 g/l NaCl solution with 12 ml of

phenolphthalein indicator to tap water (0.2 m3), making the solution pink. The addition of a tracer of

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55 ml (5 ml to give 10% excess) of 1 M glacial acetic acid and 45 ml of NaCl solution (50g/l) was

then monitored to measure the mixing time. Before the experiment, it was checked by titration that

the salt did not affect the acid-base reaction end point. The addition was monitored simultaneously

by a video camera set up on a tripod, and the ERT system. For every condition, 6 repeats for mixing

time were undertaken.

The DAS set-up for the ERT mixing time was set as in Table 3. The values of the voltages

collected from the ERT can be combined together using the log root mean squared voltage,

ln [V RMS ]= 12

ln [ 1n∑i=1

N

( V t ,i−V 0 ,i

V ∞,i−V 0 ,i−1)

2] (4)

where VRMS is the root mean squared voltage, n is the number of elements, Vt,i is the voltage of

measurement i at the given time step, V0,i is the initial mean voltage for measurement i and V∞,i is

the final mean voltage for measurement i. This approach gives a good calculation of the turbulent

mixing time as it weights the answer towards the areas that take the longest to mix, and provides a

global result. When the value drops below -2.3 the system can be considered 90% mixed, and below

-3.0 for 95% mixed. A new reference was taken for every run with agitator and gas supply on, at the

same setting for the mixing, to ensure the reference is made on fair basis. The tracer was added after

a few seconds of data acquisition running to allow an average for V0,i.Table 3. ERT DAS Settings used for Mixing Time measurement.

ERT DAS Settings

Sampling time interval 40 ms

Number of sensing planes 7

Injection current 15 mA

Frequency of current 9600 Hz

Samples per frame 1

Delay cycles 3

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Do to the large flow rate of gas there is noise in the results, this means that it is often difficult to

measure a 95% mixing time, in this case the θ95 can be scaled from θ90 using (Rodgers et al., 2011),

θ95=θ90ln [1−0.95]ln [1−0.9]

(5)

2.3. Mass Transfer Measurements

The 6BDT and 6MFD/U were examined in air water system to investigate the mass transfer in gas

liquid mixing using the same methodology and approach described by Cooke et al. (2008). A

hydrogen peroxide steady state method was used for measuring the mass transfer coefficient; the

method was originally proposed by Hickman (1988). 30% hydrogen peroxide was continuously fed

to the liquid phase at a molar feed rate, QH2 o 2, and is broken down by manganese (IV) oxide catalyst

in the vessel (about 2.4 g l−1). The hydrogen peroxide rate was measured by weighing the hydrogen

peroxide on an electronic balance and timing the addition of a measured weight with a stop watch.

The oxygen produced in the liquid phased by the reaction is stripped by the continuous flow of gas

coming from the bottom of the vessel. The addition of hydrogen peroxide eventually reaches steady

state with the production rate of oxygen which allows the oxygen transfer rate to be calculated.

Two polar-graphic dissolved oxygen tension (DOT) probes were used to measure the liquid phase

oxygen concentration. The probes were in contact with in the liquid, inserted through the analysis

block of the vessel. One probe was positioned at the upper impeller level and the other was

positioned at bottom impeller level. The data was recorded as a voltage (mV) using Picolog software.

The probes were pre-calibrated to achieve the DOT zero, by stripping all of the oxygen from the

vessel using sodium sulphite with copper VI oxide as a catalyst. Once the probes were zeroed, the

fluid was changed and the gas flow rate and agitation speed was set at desired condition, and time

was taken to reach air equilibrium in the vessel. The temperature was recorded throughout the

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experiment, and any change in temperature was taken into account when doing the calculations,

though it did not vary throughout each experiment.

The mass transfer rate, r MT, can be expressed in terms of a liquid mass transfer factor, k L a, or a

gas mass transfer factor, kG a,

r MT=k L a (CL−Ci ) (6)

r MT=kG a ( pi−pG ) (7)

where Ci is the interfacial oxygen concentration, CL is the bulk liquid oxygen concentration, pG is

the bulk gas oxygen partial pressure and pi is the interface oxygen partial pressure. Using Henry’s

Law an overall equation can be formed where H is the Henry’s Law constant,

r MT=( 1kG aH

+ 1k La )

−1(CL−pG

H ) (8)

The value of kGa > kLa therefore 1/(kGaH) << 1/kLa. This means that equation (8) can be

simplified by neglecting the kGa term,

r MT=k L a(CL−pG

H ) (9)

The decomposition of hydrogen peroxide with manganese (IV) oxide catalyst can be represented

by the following reaction

H 2O2 MnO2→

H2 O+12

O2

(10)

Now at steady state the hydrogen peroxide decomposition rate, r PD, is equal the oxygen mass

transfer rate in the stoichiometric ratio shown by the above reaction. Also at steady state the

hydrogen peroxide decomposition rate must be equal to the rate of addition of the hydrogen

peroxide, this means that the following equation must hold true,

r PD=12

QH 2 O2

V L(11)

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where QH2 O 2is the volumetric rate of hydrogen peroxide addition. To eliminate the rates, equation

9 and 11, can be combined to give an equation for k L a,

k La=QH 2 O2

2V L(C L−pG

H ) (12)

Hence the k L a mass transfer coefficient was calculated using the above equation. The

equilibrium concentrations were obtained from the final average steady state readings. The driving

force (CL−pG /H ) then depends on the flow assumptions in the vessel, the two extremes are plug

flow and well mixed, Cooke et al. (2008). The physically more realistic model of the gas phase,

especially for larger vessels with higher superficial gas velocities, is ideal plug flow, therefore this

model will be used in this paper.

3. Results and Discussion

3.1. Mixing Time

The dimensionless mixing time, θ95 is plotted against the superficial gas velocity for both

configurations as shown by Figure 2. The graphs show a linear trend at lower superficial gas

velocities and higher agitation speeds where the mixing time increases with the superficial gas

velocity. However, at higher superficial gas velocities and lower agitation speeds the mixing time

decreases. This change in behaviour is at the point where the regime changes from loaded (linear

trend) to flooded (reducing mixing time) (Jamshed et al., 2018).

In the loaded regime the increasing gas flow rate is detrimental to the mixing, this in part is due to

reduction of the agitator power with increasing gas flow rate. In the flooded regime the increasing

gas flow rate helps the mixing, this is due to the large power input into the system from the gas.

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Figure 2. Dimensionless mixing time, Nθ95 against superficial gas velocity for configuration 6BDT with 6MFU (left) and 6MFD (right). Error bars show 1 standard deviation for the results. Lines are equation (13).

For ungassed conditions, 6MFD configuration gives shorter mixing time than 6MFU

configuration as an average mixing time. The 6MFD configuration has a dimensionless mixing time

of 14.8 with a standard error of 0.97 while the 6MFU configuration has a dimensionless mixing time

of 23.3 with a standard error of 0.45. This can be compared to a predicted value of about 12 if using

equation (1) (Grenville and Nienow, 2004). These values are larger than expected due to zoning

within the vessel, especially the 6MFU. Figure 3 and Figure 4 show the zoning within the vessel

when mixing with no gas; the 6MFD system has less zoning, in fact potentially no zoning (the vessel

clears at both the top and bottom simultaneously), and thus has a dimensionless mixing time close to

the predicted value. The 6MFU has clear zoning images 2.5 – 3 seconds in Figure 4 has a clear top of

the vessel and a purple bottom of the vessel.

0 s 0.5 s 1 s 1.5 s 2 sFigure 3. Colour experiments images for 6MFD and 6BDT configuration at 240 rpm with no gas

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0 s 0.5 s 1 s 1.5 s 2 s

2.5 s 3 s 3.5 s 4 sFigure 4. Colour experiments images for 6MFU and 6BDT configuration at 240 rpm with no gas

As the gas flow rate is increased the dimensionless mixing time increases linearly with the

superficial gas velocity for the loaded regime, and for the two configurations the variation can be

written as equation (13) with the values from Table 4. As the condition moves into the flooded

regime the mixing time ratio reduces from the linear fit (at lower superficial gas velocities for the

lower agitator rates)..

N θ95( gas)

N θ95(no gas)=av s+1 (13)

Table 4. Key mixing time values for equation (13).

Value 6MFU 6MFD

N θ95(no gas) 23.3 14.8

Standard error 0.45 0.97

a 15.0 30.2

Standard error 0.90 0.88

In terms of agitator configuration, with no gassed conditions, the 6MFD configuration gives a

shorter mixing time than 6MFU; however, when gas in introduced 6MFU gives shorter mixing time

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than 6MFD, due to the a value in equation (13) being half the value for the 6MFU system. The

images in Figure 5 and Figure 6 help to explain this effect.

When the gas is introduced, a zoning effect is visible with the 6MFD configuration, 4 seconds in

Figure 5 with a clear purple area only at the bottom of the vessel, while there is very little zoning for

the 6MFU configuration, 2.5 seconds in Figure 6 with purple all over the vessel. The zoning effect in

the vessels is due to the balance between the flow loops from the top and bottom impellers. The

addition of the gas affects these flow loops, it could be expected that the gas will enforce the flow

loop for the 6MFU as the gas passes through the agitator in the same direction as the liquid and

dampen the flow loop for the 6MFD as the gas passes through the agitator in the opposite direction

as the liquid. These affects are coupled with the reduction in power from the agitators when they are

gassed. The enforcing of the 6MFU flow by the gas in this case is enough to reduce the effect of the

zoning in the system and produce a dimensionless mixing time faster than the 6MFD system. It is

likely that the spacing between the two impellers will affect this behaviour and future studies should

investigate this.

0 s 1 s 2 s 3 s 4 s

5 s 6 s

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Figure 5. Colour experiment images for 6MFD and 6BDT configuration at 240 rpm with a superficial gas velocity of 0.04 m s–1.

0 s 0.5 s 1 s 1.5 s 2 s

2.5 s 3 s 3.5 s 4 s

Figure 6. Colour experiment images for 6MFU and 6BDT configuration at 240 RPM with a superficial gas velocity of 0.04 m s–1.

3.2. Mass Transfer

The mass transfer coefficients for the air-water systems, for 6BDT with 6MFD and 6MFU

configuration are shown in Figure 7. Both configurations show very similar results, with the mass

transfer coefficient being higher for the 6BDT that the 6MFD/U. A general trend is observed in the

results, that increasing the superficial gas velocity produces an increase in mass transfer coefficient,

and that increasing the impeller speed produces a larger increase in the mass transfer coefficient.

Cooke et al. (2006) found similar results for the same configurations he investigated for air water

systems. As there is a measurable difference in mass transfer between the impellers as depicted by

Figure 7, this shows that the liquid is not well mixed between the two impellers. This agrees with the

mixing results, and also confirms that out of the 2 mass transfer mixing models the plug flow model

is more appropriate.

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Figure 7. Variation of the mass transfer coefficient with the superficial gas velocity. Value measured by the 6BDT (left) and by the 6MFU/D (right).

As Gezork et al. (2001) did, we can fit a correlation based on the total shaft power per unit liquid

volume and the superficial gas velocity to the results, as Figure 8(a). There is an average of 22.2%

error between the measured and predicated kLa values, also it can been seen that the 6BDT values all

lie above the line of equality and the 6MFU/D values all line below the line of equality. This is not

surprising as Figure 7 shows the lower values for the 6MFU/D impeller.

(a) (b)

Figure 8. Variation of the measured kLa with the predicated value for (a) total vessel model and (b) individual impeller model. Dashed lines are 20% error.

Due to the two zones within the vessel, it could be better to create a correlation for the kLa based

on each impeller rather than the vessel as a whole. The tank was divided into two halves taking the

upper and lower impellers as individual systems, with their own power in half the tank volume. This

17

double fit gave better results as all data can be correlated in one line with an average of 15.2% error

as shown by Figure 8(b).

The best fit for the data is given by equation (14),

k L a=0.0058( Pagi

V L/2 )0.68

v s0.31 (14)

For equation (14) the standard errors for the fitted values are 0.00038, 0.04, and 0.03 respectively

(0.0058, 0.68, 0.31). If equation (14) is compared to that from Gezork et al. (2001) it can be seen that

the values are very similar, 0.0059, 0.61, and 0.36 respectively.

4. Conclusions

The introduction of gas to the system increases the mixing time within the vessel, the effect of this

is lower for the 6MFU system, which would suggest that this system is the better for the gas flow

rates in the loaded regime. If the gas flow increases further, pushing the system into the flooded

regime, the gas has the dominant effect on the mixing time, with the lower mixing times at the higher

superficial gas velocities and the lower agitation speeds.

Very little difference is observed for the mass transfer coefficients between the two configurations

studied. However, at these high gas flow rates it is clear that the vessels cannot be thought of as well

mixed with differences in the mass transfer constant in the regions of the different agitators. The

mass transfer coefficient can be correlated under these conditions if each agitator is thought of as

operating only in its own zone such as, equation (14).

This means under high gas flow rates with multiple impellers it is important to think about zoning

within the vessel from both a mixing and mass transfer point of view, and if this is performed an

equation very similar to that of Gezork et al. (2001) would correlate both zones.

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