Sohar University

Study on Determination of

Volumetric Mass Transfer Coefficient

in Stirred Vessels

Done By

Laila Moosa Al-Blushi, Maryam Said Al-Oasimy Sahar Payam Allah Talebi, Shamsa Ahmed Al-Haddabi, and Sumaya Hamood Al- Maawali

A Final Year Report

Submitted to Sohar University

in partial fulfilment of the

requirements for the degree of

Bachelor of Engineering

in

Chemical Engineering

Sohar, Sultanate of Oman, June 2013

Supervised by: Dr. Ahmed Jawad Ali Al-Dallal

Declaration

We hereby declare that this report is based on our original work. We also declare that it

has not been previously and concurrently submitted for any other degree or award.

Signatures

We further permit Sohar University to reproduce this thesis by repetition or by other

means, in total or in part, at the request of other institutions or individuals for the purpose

of scholarly research.

Signatures

Acknowledgment

The project group would like to thank their supervisor Dr. Ahmed Al-Dallal for his

assistance, valuable advice, and support along the project. They also appreciate Mr.

Ibrahim Al-Ajmai and Mr. Rashid for their never end support, and their continuous help

during the design, manufacturing and experimenting the aeration device build.

Furthermore, the group members would also like to express their gratitude to their loving

parent and friends who had helped and encouraged them. Without the mentioned parties,

it was impossible to complete this final year project.

Executive Summary

In this thesis we will report the design and fabrication of an aeration experimental unit

used to calculate the oxygen gas-liquid volumetric mass transfer coefficient (kLa). The

total cost of manufacturing the unit was almost 500 O.R and was totally designed and

arranged by the students. The mixing tank designed to have a total volume of …… with

dimensions ……………. Distilled water at atmospheric pressure and room temperature

was used to determine the value of kLa.

Table of Contents

Declaration..........................................................................................................................2

Acknowledgment..................................................................................................................3

Executive Summary..............................................................................................................4

Nomenclature.......................................................................................................................6

Chapter 1 Introduction.........................................................................................................8

Chapter 2: Literature Survey............................................................................................10

2.1 Methods for measuring kLa:.....................................................................................11

2.2 Factors that affect kLa value:...................................................................................13

2.2.1 Effect of salt addition and viscosity:................................................................13

2.2.2 Effect of probe position:...................................................................................18

2.2.3 Effect of aeration rate:......................................................................................19

2.2.4 Effect of Temperature:......................................................................................22

2.2.5 Effect of medium depth:...................................................................................23

2.2.6 Effect of mixing:...............................................................................................24

2.2.6.1 Effect of impeller Type:.............................................................................24

2.2.6.2 The effect of impeller speed:.....................................................................28

2.2.6.3 Effect of impellers position:......................................................................28

Chapter 3: Theory.............................................................................................................30

3.1 Determination of kLa from experiments:.................................................................30

3.2 Determination of kLa from empirical correlations:..................................................31

REFERENCES..................................................................................................................35

Nomenclature

a Interfacial area (m2/m3)

C Dissolved concentration of gas in liquid phase (mol/m3)

C* Saturation concentration of the gas in liquid (mol/m3)

D Diameter of impeller (m)

g Standard gravity (9.81 m/s2)

H Depth of liquid in the tank (m)

kL Mass transfer coefficient (m/s)

kLa The volumetric mass transfer coefficient (1/s)

m Mass of liquid in STR (stirred tank reactor) (kg)

N Impeller speed (rev/s)

NP Power number of the impeller

P Power (W)

Qg Gas flow rate (m3/s)

T Diameter of the tank or vessel (m)

to Initial time

v Kinematic Viscosity (m2/s)

VG Superficial gas velocity (m/s)

VL Volume of liquid inside the reactor (m3)

w Weight

μ Viscosity of liquid phase (Pa. s)

ρl Density of the liquid phase (Kg/m3)

σ Interfacial tension (N/m)

Chapter 1 Introduction

In all aerobic chemical and biological process, effective oxygen supply and absorption is

one the most required and important principal. Some examples on operations that utilizes

between oxygen gas and a liquid phase are leaching of metal concentrates and

microbiological fermentation. Aeration is the process in which oxygen is added and

dissolved in water by utilizing the principles of mass transfer. It is one of the most

important processes used in public health engineering as it eliminates both smell and taste

from water. Transfer of oxygen into a mass of water can either occur naturally for

example, surface aeration of polluted surfaces, or under imposed conditions such as, the

activated sludge process. The reverse of aeration is also possible for example, losses of

oxygen to the atmosphere from supersaturated water due to photosynthesis.

There are different devices that are used to bring oxygen and liquid phase to contact such

as, packed bed, bubble column, tray tower, and plate columns. However, in this thesis a

mechanically agitated device will be used in which the liquid phase is the continuous

phase, compressed air is the dispersed phase and agitation is insured by a rotating

impeller [sulpite]. Mechanically agitated vessels are very widely used in reactions that

involve gas and liquid phase, because they can provide high heat and mass transfer

coefficient and mixing [O].

Oxygen is a non-polar gas and it is more soluble in water compared to nitrogen gas.

When water is in equilibrium with air, it will contain one molecule of dissolved oxygen

for every two molecules of nitrogen. The solubility of oxygen in water depends on the

temperature at which this process occurs. It is observed that at 25ᴼC and 1atm of air,

fresh water will contain approximately 6.04 ml of oxygen per litre. On the other hand,

seawater contains almost 4.95 ml per litre. This is due to presence of salt and other

impurities in seawater that will reduce the solubility of oxygen in water.

The volumetric mass transfer coefficient (kLa) is a lamped parameter as it depends only

on time not on space. It indicates the rate of oxygen that has transferred from the gas

phase to the liquid phase and has the unit of [1/time]. kLa is a very important parameter in

designing, scaling up from laboratory scale to pilot scale or production scale of

bioreactors especially. There are several factors that affect the transfer of oxygen to liquid

phase such as water and they are:

Depth of water used.

Water composition, if there are any salt or impurities present.

Design and arrangement of diffusers.

Flow rate of air supplied.

Speed of agitator used.

Water temperature.

Type of impeller.

Air pressure.

In this thesis, the affect of different impeller types and speed, gas flow rate, liquid

viscosity, and addition of salts on kLa will be studied and observed. At the end, an

empirical equation will be determined for possible causes of study.

Chapter 2: Literature Survey

Aeration is the process of making air and water in direct close contact for the purpose of

removing dissolved gases or to oxidize dissolved metals. This process can also be used to

remove volatile organic chemicals (VOC) in the water [*]. There are several industrial

applications that use’s the concept of aeration, such as: (1) oxidation of soluble metals

(iron and manganese); (2) removal of carbon dioxides during cold lime softening; (3)

reducing the concentration of VOC in water by air stripping process. There are two main

methods of pond aeration systems there are used, diffused aerators and surface aerators.

Diffusion aeration uses a tube that is connected to an air compressor to force the air in the

tube and forms bubbles which are then released in the water. The tubing system is usually

placed in the bottom of the pond. This method is also known as the lake-bed aeration or

bottom aeration. Diffused aerators has higher efficiency in deep ponds, depths more than

8 feet, because of the longer contact time and it's safer due to the ability of keeping the

electricity out of water by placing the compressor away and avoud direct contact with

water.

Surface aeration uses a pump which is placed just above the pond surface to circulate

water from the pond surface into the air or it can be just right at the surface. Surface

aerators are preferred in shallow ponds but it doesn't suits deep lakes.

Figure 2.1: An example on diffusion aeration and surface aeration [].

Advantages Disadvantages

The value of volumetric mass transfer

parameter can be very high.

A sparger and hence a compressor have to

be installed, leading to more investment

and to the process more complicated.

Large changes in the volumetric mass

transfer parameter could be achieved by

changing the gassing rate and power

input.

More power consumption due to the use of

a compressor.

Table 2.1: The advantages and disadvantages of diffusion aeration [].

2.1 Methods for measuring kLa:kLa is a common measure of mass transfer characteristic between a gas and a liquid phase

and a very important parameter in designing and scaling up bioreactors. It is calculated

using the film model of mass transfer between the two phases by assuming that the

resistance at the gas phase is negligible. There are several methods that are used for

measuring kLa and are described shortly below:

Dynamic method. This method applies changes in the dissolved oxygen

concentration either by a chemical reaction of by changing the pressure of the

system and consists of the following sub methods:

- Dynamic pressure method. Changes in concentration are achieved by

changing the pressure in the system and this will cause changes in the partial

pressure of oxygen. Pinelli et al. (2010) reported that if there is any sudden

change in the system pressure will cause a noticeable change on the partial

pressure of oxygen in all bubbles.

- Gassing in and gassing out method. The change in oxygen concentration of

the entering gas is done by either a step change from lower concentration to

higher and is known as the gassing in method or a step change from higher

concentration to lower and it is known as gassing out method. This is done

usually by using pure nitrogen gas. Although this method is expensive and

requires very pure nitrogen gas (99%), but it is fast, low time requirement and

the results obtained compromises the high cost.

The kLa value is calculated by fitting a model that had been chosen to represent

the system to the recorded transient curve of dissolve oxygen. There are several

factors that might affect the dynamic model such as, fluid dynamic model used for

the gas that is introduced to the system and the response time of oxygen probe.

Steady state methods. In these methods a condition is created to keep the

concentration of dissolved oxygen constant at the same time that oxygen is

introduced into the system as an inlet gas and is continually consumed by an

oxygen sink such as, microbiological organisms. The kLa is calculated either from

the stoichiometric oxygen consumption and time required for total consumption

or from the mass balance on oxygen. The first method requires data generated for

dissolved oxygen and time and the second method requires the flow rate and the

oxygen concentration of the inlet and outlet gas. It is very important that the

reaction rate and the mass transfer rate are in right proportional to each other. If

the reaction rate is low compared to the mass transfer rate than the process is

controlled by the kinetics of the reaction, but if the reaction rate is very high than

the mass transfer will be higher and better [ اطروحه]. Sodium sulfite oxidation method. The sodium sulfite method is used in chemical

reactions to measure kLa, where it is used to calculate the oxygen uptake rate. The

sulfite is oxidized to sulfate which is consuming oxygen in the process [+]. by the

following reaction:

2Na2SO3 + O2 2Na2SO4

The amount of sodium should be around 10 to 15% of the total liquid volume and

has a concentration range from 0.04 to 1N [klz correlatin]. A catalyst of cobalt

should be introduced to the tank before the sodium sulphite. It is loaded only once

at the beginning of the process [_]. The reaction rate is faster than the oxygen

transfer rate, so the rate of the oxidation reaction will be controlled by the rate of

the mass transfer. If the overall rate is measured than the mass transfer rate could

be calculated. The concentration of the catalyst added affects the reaction rate

and bubble coalescence. The kLa value was estimated using steady state sulphite

method by Puskeiler and Weuster-Botz (2005). It was found that kLa value

increased as the power input increases in the steady state sulphite method on log-

log plot. Using dynamic sulphite method a maximum value of kLa can be reached

at certain power input after that as the power input value increases value the mass

transfer coefficient will decrease as it is shown in figure below.

2.2 Factors that affect kLa value:

2.2.1 Effect of salt addition and viscosity:One of factor that affects the transfer rate of oxygen and the value of kLa is the water

compositions and the presence of solid particles in water. This factor is very important in

soil treatment in slurry bioreactors. The efficiency of those types of reactors is described

as the amount of soil treated per unit volume of reactor, but there is a limit to the amount

of soil treated due to limitation in oxygen supplied. Researches and experiments have

shown that kLa values are significantly dependent on particle size of the soil and the clay

content, but are not affected noticeably with the concentration of soil organic matter. As

the soil content increases above 40% the kLa value decreases to about 60 to 70% of the

value of kLa in pure water. It was also noticed that the oxygen supply is limited, diameter

and the number of bubbles also decreases if the clay content is very high [ ].

Robinson et al. (1973) and Linek et al. (1987) have studied the effect of medium

properties on the value of kLa. They have found that adding small amounts of solute to

distilled water will cause reduction in bubble size even if other properties were kept

constant. They also reported in their research paper on kLa values in electrolytic mediums

that for electrolytic solutions the decrease in bubble size is due to the electrical effect of

the concentration gradient of the ionic species between the gas and liquid interface. This

makes the medium capable of preventing coalescence of bubbles so an increase in the

value of kLa is noticed [ two refrences ].

Juarez and Orejas (2001) reported the effect of medium properties on the value of kLa by

considering two different liquids which were distilled water and 0.5M Na2SO4 solution.

The distilled water is known to act as a coalescing system and the aqueous solution acts

as a non-coalescing system. The operating conditions used could be summarized in the

below table:

Operating variable Used Value

Liquid volume 0.0015 m3 if one impeller

0.002 m3 if two impellers

Temperature 20ᴼC

Rotation speed 5 to 15 r.p.s

Gas flow rate Varied between 2.5, 3.75 and 5×10-5 m3/s

Experiment time 200 to 700 s

Table 2.2: The operating condition used by Juarez and Orejas [ ].

The difference in the two mediums was absorbed from the results obtained and it was

noticed that sulphate solution has a higher kLa value due to its non-coalescing properties.

Although water is a coalescing system and showed low values of kLa when using only

one impeller, but increasing the number of impellers to two will help to break down the

bubble size and cause an increases in kLa. On the other hand, in sulphate solution the

value of kLa obtained is not affected if one or two impellers are used because the solution

prevents collection of bubbles.

Puthli et al. (2004) experimented the effect of liquid viscosity on kLa values using three

different concentrations of carboxymethyl cellulose (CMC) which were 0.25, 0.5 and

0.75% w/v. The actual volume used was 1.81m3. The effect of changing the viscosity was

estimated at an impeller speed of 600 rpm and gas flow rate range from (0.9-3.4)*10-5

m3/s. The following table and graph shows the results obtained [&]:

Concentration of CMC Viscosity of solution Air flow rate range Value of kLa

%w/v mPa 10 -5(m3/s)

(s-1)

0.25 4.33 0.9 0.0082

3.4 0.0161

0.5 5.99 0.9 0.0058

3.4 0.0095

0.75 11 0.9 0.0021

3.4 0.0037

Table 2.3: The effect of medium velocity on the kLa value obtained by Puthli et al [].

Figure 2.2: Effect of viscosity at 600 rpm at varying gas flow rate (triple impeller (♦) water, (□) 0.25% CMC (w/v), (∆) 0.375% CMC (w/v), (○) 0.5%CMC (w/v)) obtained by Puthli et al [].

From the results obtained the writes concluded that increasing the viscosity of the

medium will reduce the kLa values regardless the speed of impeller or the gas flow rate

used. This behaviour is probably because of the decreases in the surface area of the

bubbles due to the viscous forces generated in the fluid.

Ozbek and Gayik (2000) have studied the effect of adding glycerol to distilled water with

the following composition 10,20,30,40 and 50% glycerol solution w/w. A volume of 0.6

L at a temperature of 37ᴼC and a pH of 7 was used .The operation condition used in the

experiments and the values obtained is described and summarized as following:

Agitation

speed

(rpm)

Air flow

rate

(L/min)

Range of composition of

glycerol solution

(% w/w)

Viscosity

(cpoise)

kLa value

(min-1)

300 0.3 10 0.935 2.65

50 6.948 1.4

Table 2.4: The effect of changing the viscosity of water by Ozbek and Gayik [].

Figure 2.3: The kLa values versus the viscosity of the medium by Ozbek and Gayik [].

The graph proves the truth that any increase in the medium viscosity will decrease the

value of kLa. The authors than investigated what happens if medium viscosity is changed

under the same operating condition, but also the agitation speed and the flow rate of air is

varied. The following graphs were obtained when changing both impeller speed and

aeration rate:

Figure 2.4: The effect of stirrer speed on kLa in glycerol solution by Ozbek and Gayik [O].

Figure 2.5: The kLa value verses air flow rates in glycerol solution by Ozbek and Gayik [O].

It is noticed that although increasing the viscosity will decreases the value of kLa, but

increasing the agitation rate or the gas flow rate could reduce this effect as it is noticed

from the graphs. It is also noticed from the figure that after 300 rpm the value of kLa

increased linearly with increasing the agitation rate.

2.2.2 Effect of probe position: Hashsham, S.A. in his research article under the title of “Design of an Experimental Unit

for Determination of Oxygen Gas-Liquid Volumetric Mass Transfer Coefficient using

Dynamic Re-Oxygenation Method” has experimented and determined the volumetric

mass transfer coefficient in a bubble column reactor.

The writer’s goal was to design and build a bubble column reactor for measuring kLa. He

installed several polarographic dissolved oxygen sensors in various axial positions along

the column to measure the dissolved oxygen. The author assumed that the bubble column

follows the model of a CSTR and the liquid used was distilled water at room temperature.

The equipments used could be described as following:

1- Bubble column. A hexagonally shaped tower with a height of 1.27m and a diameter of 0.318m was used. Three holes were drilled carefully at three different positions along the length of the column to hold the sensor seal. Water was filled from the top using a plastic tube and removed through the bottom hole made for the sensor. The conditions of the reactor under which the experiments were performed are summarized in the below table:

Parameter conditionsTemperature Room temperaturePressure Atmospheric pressureSuperficial gas velocity 0.3 m/sGas hold up 0.009Bubble diameter 7.5 mm

Table 2.5: Operating conditions used by Hashsham, S.A.

2- Air diffuser. The air diffuser used was bought from a pet store and had a diameter of 7.6 cm. However the writes suggested using special designed air diffusers for further experiments.

3- Dissolved oxygen sensors. Three sensors were used in the experiments, but they were not calibrated. The author recommended that for better and accurate results the sensors should be calibrated. A Vernier dissolved sensor was used that contains a platinum cathode and Ag/AgCl reference anode dipped in KCl electrolyte and are separated from the surrounding sample solution by an oxygen permeable membrane.

A fixed voltage is applied to the platinum electrode and the following reactions take place:

0.5 O₂ + H₂O + 2e⁻ 2OH⁻ reduction reaction

Ag + Cl⁻ AgCl + e oxidation reaction

As a result of the reactions, an electrical current flow is generated and measures the

concentration. The current is converted to voltage, amplified, and recorded.

4- Other equipments such as, sensor seal, air compressor, nitrogen cylinders, and personal computer were all used.

To determine the volumetric mass transfer coefficient first of all, any amounts of

dissolved oxygen in the water was removed by supplying nitrogen gas until the

concentration of oxygen felled below 1%. This step usually took 30 min. After that,

oxygen was introduced to the column as compressed air through the diffuser, and the

dissolved oxygen was measured every second until water became saturated. This process

usually took less than 20 min. The experiments were performed three times and the re-

oxygenation profile for each experiment was analyzed individually.

The author noticed that the re-oxygenation plots were almost linear and the estimated

mass transfer coefficient for the three sensors was almost 0.31 ± 0.01 min⁻1. This

observation proves that kLa is a lumped parameter as it didn’t depend on the position of

the sensors.

2.2.3 Effect of aeration rate:Another important factor that affects the kLa values is the gas flow rate which is also

referred to as the aeration rate. Any changes in the flow rate of air entering the system

will cause changes in fractional gas hold up and the interfacial area between gas and

liquid phases, so changes in kLa values are expected to take place.

Puthli et al. (2004) have experimented the effect of changing the air flow rate in a

bioreactor. They have observed that any increase in the gas flow rate will cause increase

in the interfacial area between the two phase due to increase in the surface area of the

bubbles, thus causing an increases in kLa value especially when very high air flow rate

were applied to the system. The total capacity of the bioreactor used was 2.01m3 and the

actual volume was 1.81m3. The following table and graph summarizes the results

obtained [&]:

Type of impeller Speed of the impeller

(rpm)

Air flow rate range

applied (cc/s)

kLa value

(s-1)

Triple impellers

(disc turbine-

pitched blade

downflow turbine-

pitched blade

down-flow turbine

300 8.92 0.0026

33.81 0.0035

400 8.92 0.0045

33.81 0.0081

500 8.92 0.0062

33.81 0.0098

600 8.92 0.0082

33.81 0.0161

Table 2.6: The experimental values of kLa obtained by Puthli et al. using different speeds of impeller and air flow rate [].

Figure 2.6: Effect of aeration rates on kLa values at different impeller speeds (triple impeller (♦) kLa (300 rpm), (□) kLa (400 rpm), (○) kLa (500 rpm), (∆) kLa (600 rpm)) by Puthli et al [].

Eric Jackson studied the effect of aeration rate of kLa values and he also noticed that any

increase in the gas flow rate will increase the kLa of the system. The operating condition

used and the results obtained are all summarized in the coming tables [ ]:

Volume

(L)

Type of

impeller

Speed of

impeller

(rpm)

Air flow rate

Range

(L/min)

kLa value

(s-1)

5 Six blades 500 0.5 0.02

6 0.12

Table 2.7: The operating conditions and the effect of air flow rate of kLa used by Jacjson.

Figure 2.7: kLa versus Aeration Rate in distilled water by Eric Jackson [O].

Ozbek and Gayik (2000) have also studied the effect of aeration rate on kLa values in a

system containing distilled water. They have also proved that increasing the aeration rate

will cause an increase in the value of kLa. The operation conditions used in the

experiments performed and the results obtained are as follows:

Volume

(L)

Temperature

(ᴼC)

pH Agitation rate

(rpm)

Range of

flow rate of

air

(L/min)

kLa value

(min-1)

0.6 37 7 300 0.15 1.728

0.9 5.35

Table 2.8: The experimental values of kLa obtained using different air flow rates for a distilled water system by Ozbek and Gayik [O].

Figure 2.8: The kLa values versus air flow rate in distilled water system obtained by Jackson [O].

In conclusion it is noticed that the kLa value is a strong function of the aeration rate with

a direct proportional relationship between them. Any increase in the gas flow rate will

cause on increases in the number of bubbles and the interfacial area, so kLa value

increases.

2.2.4 Effect of Temperature: Another important factor that affects the kLa value is the temperature at which the

operation takes place. Zhen et al. (2003) have studied this factor and its effects, by

measuring the temperature using a thermometer or by the dissolved oxygen meter. They

assured that the difference in temperature had an accuracy of ± 0.50C at the beginning and

the end of each test. Figure 2.7 shows the standard oxygen transfer coefficient in the

range of tested water temperatures between 27.60 oC to 29.0 oC.

The tests were done in 0.30 m depth of water [].

Figure 2.9: The effect of water temperature on kLa [].

2.2.5 Effect of medium depth:Zhen et al. (2003) have studied the effect of different water depths on the standard

oxygen transfer efficiency (SOTE). Figure 3 shows that SOTE increases as water depth

increases. This is because of the increase on oxygen partial pressure and because of the

increase in time contact between the bubble and water [].

Figure 2.10: The effect of Water Depth on SOTE

2.2.6 Effect of mixing: Mixing is one of the most important parameters that must be studied is biochemical

reaction. Several types of impellers are used in gas- liquid system some examples are: (1)

disc turbines impellers with radial flow are capable of eliminating uniformity of the flow

caused by open turbines. Moreover, they can collect the gas moistures and force it to stay

at high shear zone near the blades where the bubbles are form; (2) the classical Rushton

Disk turbine which is one of the most commonly used mixers for gas-liquid mass transfer

especially in the cases of low and intermediate gassing rate, because it creates high local

shear that is good for dispersion processes (Myers et al., 1994).

2.2.6.1 Effect of impeller Type:Vasconcelos et al. (2000) studied the performance of six blade turbine in an agitated tank

to find the effect of using blade turbine on many factors such as power consumption,

mixing, gas hold up and mass transfer characteristics. These factors were studied under

turbulent agitation. Six blade turbines are the most important impellers used in industries.

However, there are some limitations of six blade turbine an example is that when the gas

is introduced to the system it causes a sudden decrease by about 50% of total power

demand. This limitation will lead to a reduction in both potential of mass and heat

transfer. The liquid used in the experiments was tap water at 37 0C. A compressor used to

supply air to the vessel through 0.66 mm tube. In addition, the diameter of the standard

Rushton turbine D =T/3 [].

Table 2.9: Geometries and operating condition used by Vasconcelos.

Vessel diameter (m) 0.392

Depth to diameter

ratio H/T

2

Superficial gas

velocity (m/s)

0.013

Gas flow rate (vvm) 0.125

The six blade turbine used in this study had several shapes. Figure 2.8 shows the

dependence of kLa value on the shape of the impeller and it is noticed that does not

depend on the type of impeller.

Figure 2.11: kLa results for the extreme values of constant air flow rate QG, by Vasconcelos et al. Full lines represent the overall correlation. Dashed lines stand for 95% confidence interval [].

Nelson et al. (1998) reported that Rushton turbine is used in most industries but

according to the limitations discussed previously which leads to power drop due to the

gas cavitations near the blades. In this experiment, hollow blade impellers which are

concave in shape, a tank of 0.4m diameter made of clear Perspex to notice the gas

dispersion, and baffles were used. It was noticed that hollow blade impellers can

eliminate the reduction in the power demand, provide more handling capacity and gas

hold up capacity which makes them better than Rushton turbine.

The effect of using single, double and triple impellers was studied by Puthli et al. (2005).

The impellers used in this study were single impeller contisting of a disc turbine (DT),

double impeller consisting of disc turbine-pitched blade downflow turbine (PTD), triple

impeller consisting of disc turbine-pitched blade downflow turbine- pitched blade

downflow turbine. The reactor used in this study was concentrated of glass with baffles

and it has the following dimensions:

Height to diameter ratio = 1.692

Internal diameter = 13 cm

Number of baffles = 4

Baffle height = 19 cm

Baffle width = 0.7 cm

Volume of the tank = 1.81 m3

Moreover, the impeller was located 4.5 cm from the bottom of the reactor. The ratio of

the diameter of the impeller into the diameter of the tank was 0.333 in the three cases.

Impeller

configuration

blades Impeller

diameter

(cm)

Impeller

blade

length (cm)

Impeller blade

width (cm)

Power

number

(Np)

Single

impeller

Six blade DT 4.33 1.4 1.2 4.8

Double

impellers

Six blade DT 4.33 1.4 1.2 6.3

450 PTD (4

blades)

4.33 1.8 1.4

Triple

impellers

Six blade DT 4.33 1.4 1.2 7.8

450 PTD (4

blades)

4.33 1.8 1.4

450 PTD (4

blades)

4.33 1.8 1.4

Table 2.10: Impellers configuration used by Puthli et al [].

During the study it was noticed that using single, double and triple impellers had an effect

on the kLa vakues at different impeller speed and gas flow rates. Distilled water was used

in this experiment at a temperature of 35 C0. With an impeller speed range of 300 to 600

rpm and the rang of the gas flow rate was 8.92-33.8 cc/s the results of kLa value at

600rpm and 33.8 cc/s are shown in the following table:

Type of impeller Impeller speed

(rpm)

Gas flow rate

(cc/s)

kLa value

(s-1)

Single impeller

600 33.18

0.0073

Double impeller 0.0098

Triple impeller 0.0161

Table 2.11: kLa value of single, double, and triple impeller obtained by Puthli et al. [].

Figure 2.12: Effect of impeller speed on kLa with respect to impeller configuration (triple impeller (♦) kLa (8.92 cc/s), (□) kLa (19.5 cc/s), (○) kLa (29.4 cc/s), (∆) kLa (33.81 cc/s) by Puthli et al. [].

As a conclusion to this study, kLa values in triple impeller was higher compared to single

and double impeller this results from the sudden brakeage in gas bubbles as the impeller

speed increased in triple impeller therefore the size of bubbles will be smaller which will

lead to higher interfacial area so the value of the mass transfer coefficient will increase.

2.2.6.2 The effect of impeller speed:The effect of the impeller speed on the kLa value was studied by Ozbek and Gayik (2001)

using speed range of 100 to 500 rpm and at gas flow rate of 0.31 L/min. The temperature

was 37 C0 and the fluid used was distilled water. It was reported that the value of kLa

increased as the impeller speed increased from 100 to 500 rpm and the values were 0.31

and 5.274 min-1 respectively. However, it was noticed that the relation between kLa value

and the impeller speed, as it is shown in figure 2.10, consists of two regions first one,

when the impeller speed was lower than 300 rpm the slope was very small compared with

second region at impeller speed above 300 rpm where the kLa value increased noticeably.

Figure 2.13: the effect of impeller speed on the kLa value obtained by Ozbek and Gayik [].

2.2.6.3 Effect of impellers position:Gas-liquid mass transfer in reactors with two Rushton Disk turbines has been studied by

Arcella et al. (1997). This paper shows the suitable placement of two disk turbines for gas

liquid mass transfer. A flat- Plexiglas bottomed cylindrical was used in the experiment.

The reactor was equipped with two six-blade Disk turbine, four baffles, and a ring

sparger with eight orifices.

Temperature 250C

Diameter of the reactor 0.202m

The orifice of 1mm

Liquid used Distilled water

Dispersed gas phase used air

Table 2.12: The operating conditions used by Arcella et al. [].

In this work the correct position of the two disk turbine (the upper and lower) has been

obtained experimentally. After all the investigation in the experiment, it was found that

the upper disk turbine should be moved upward to apposition near the static liquid

surface. This is to increase the contribution of gas entrainment from free surface to gas-

liquid mass transfer. On the other hand, the lower disk turbine should be moved near the

sparger to re-disperse the aerated gas immediately. So the basic role obtained for the

upper disk turbine is for both re-dispersing the aerated gas and sucking in the gas from

the top space of the reactor, while the lower disk turbine is for re-dispersing the aerated

gas.

It should be mentioned that the increase in gas entrainment from free space as a result

from the upward movement of the upper disk turbine, increases the volumetric mass

transfer parameter. Sometimes, gas entrainment from free space is unwanted, especially

when back-mixing of gas phase is unwanted. In such cases, increasing the immersion

depth of the upper Disk turbine is a must. (A study of gas-liquid mass transfer in reactors

with two Disk turbines).

Chapter 3: Theory

3.1 Determination of kLa from experiments: The Dynamic method that depends on the response of an oxygen probe to changes in the

concentration of dissolved oxygen in the liquid medium during the absorption or

desorption of oxygen was used in this thesis. In absorption dynamic technique, the

concentration of dissolved oxygen is eliminated and reached to zero at the beginning

either by bubbling nitrogen gas or using sodium sulfite. Then air is supplied to the liquid

and the increase in the concentration of oxygen is measured with time until saturation

point is reached. In desorption dynamic method, air is supplied at the beginning of the

process until the saturation level of oxygen is reached. After that, nitrogen gas is supplied

and the decrease in the oxygen concentration is recorded as a function of time.

The mass transfer resistance in the gas phase is usually neglected, because it is much

smaller compared to the resistance in the liquid phase [=]. For a perfectly mixed liquid,

the mass balance on the dissolved oxygen could be established as following:

dCdt = OTR – OUR

(3.1)

Where OTR is the oxygen transfer rate (mol O2/m3.s) and is:

OTR = kLa (C* - C) (3.2)

OUR is the oxygen uptake rate (mol O2/m3.s).

Because the system used in this thesis does not use any microorganisms than OUR is

equal to zero and the equation becomes as:

dCdt = kLa (C* - C) (3.3)

Separating the variables and integrating from C0 to C and t0 to t:

ln ( C∗−CC∗−Co ) = - kLa (t – t0)

(3.4)

The plot between ln ( C∗−CC∗−Co ) and t will result in a line with a slope of - kLa as in the

following example graph:

Figure 3.1: An example on how to use equation (3.4) [=].

3.2 Determination of kLa from empirical correlations:

Over the past decades different equations have been developed for estimating kLa as a

function of different variables. However, very large deviations are found in values of kLa

between the experimental and estimated values, especially when kLa for systems

containing microorganisms are estimated for equations developed for aqueous solutions.

Empirical correlations for estimating kLa values depend on many geometrical parameters,

but there is no specific rules followed in literatures. For example, Van’t Riet (1979)

proposed a correlation showed in table (3.2) that depends only on (P/V) and (VG). He has

not considered the effect of stirrer geometry and number of impellers.

Many developed correlations apply dimensionless quantities such as, Reynolds (Re). The

impeller Reynolds number represents the ratio of the inertial forces created by the

rotating impeller and the viscous forces of the liquid:

ReN = ρl . N . D2

μ (3.5)

When the impeller Reynolds number is less than 104 then the liquid is in the laminar

region; while in the turbulent region, the impeller Reynolds number is more than 104.

Usually the mechanical stirred vessels operate in turbulent region, where the velocity

fluctuates in both time and three dimensions in space. The table below shows other

dimensionless groups used in kLa correlations:

Dimensionless quantities Equation

Froude Number (Fr) Fr = N 2 Dg

gas flow rate (FlG) FlG =Qg

N . D3

Sherwood (Sh) Sh = k L a D ²T

Stanton (St) St = k L aV LQ g

Schmidt (Sc) Sc = μρT

Weber (We) We = ρ N ² D ³σ

Aeration (A) A = N DVG

Table 3.1: Dimensionless groups used in kLa correlations [].

Another important parameter used in calculating kLa is the power consumption of an

impeller which depends on the power number that is strongly dependent on the impellers

geometry, vessel geometry if baffles are used and how many, the impellers clearance

from the bottom of the vessel, and the spacing between impellers if multi impellers are

used. The power could be calculated by, where NP is found from graph 3.2:

P = NP. ρl. N3. D5 (3.3)

Figure 3.1: Power number estimation for different impellers

Another method for determining the power consumed by the impeller is using a

laboratory dynamometer. Before performing experiments, the torque of the impeller

could be measured at different impeller speeds and in air. This value represents the

system friction. During the experiments, the torque value is measured again in water.

Subtracting the two values than substituting in the below equation will result the amount

of power consumed by the impeller in the liquid:

P = K × N × S (3.4)

Where K is the dynamometer constant

S is the net value of torque (N.m)

In the table below different correlations from literatures are reported. Some depends on

the gassing rate and the mixing power of the impellers, others are based on dimensionless

groups:

Researchers Correlation ProposedCalderbank (1958) van 't Riet (1979) kla =0.026(P/VL)0.4(VG)0.5

Hickman (1988) For T = 0.60 mkLa = 0.043 (P/VL)0.4(VG)0.57

For T = 2 mkLa = 0.027(P/VL)0.54(VG)0.68

Linek et al. (1987) kLa = 4.95 × 10-3 (P/VL)0.593(VG)0.4

Linek et al. (1991) kLa =3.84 × 10-3 (P/ VL)0.654(VG)0.4

Moucha et al. (1995) kLa =14.6 × 10-3 (P/ VL)0.611(VG)0.554

Robinson and Wilke (1973) kLa = (P/ VL)0.4(VG)0.35

Smith (1991) kLa =1.25 ×10-4 (D/T)2.8(Fr)0.6(ReN)0.7

(FlG)0.45(D/g)-0.5

Smith et al. (1977) kla = 0.01(P/VL)0.475(VG)0.4

Smith et al.(1977) kLa =10.4 × 10-3 (P/ VL)0.475(VG)0.4

Stenberg and Andersson (1987) kLa = 5.3 × 10-3 (P/ VL)0.55(VG)0.32

Van’t Riet (1979) kLa =26 × 10-3 (P/ VL)0.4(VG)0.5

Whitton and Nienow (1993) kLa =0.57 (P/m)0.4(VG)0.55

Zhu et al. (2001) kLa =0.031 (P/ VL)0.4(VG)0.5

Juarez and Orejas (2001) kLa =1.11 × 10-3 (P/ VL)0.9504(VG)0.6282

Wu (1995) kLa =10.36 × 10-3 (P/ VL)0.67(VG)0.56

Perez and Sandall (1974) kLa=21.2 (Re)1.11(Sc)0.5 (Vg.T/σ)0.45(µG/µa) (DL/T2)Yagi and Yoshida (1975) kLa=0.06 (Sc)0.5(Re)1.5 (Vg.µa/σ)0.6 (Fr)0.19 (A) (DL/T2)Nishikawa et al. (1981) kLa=0.368 (Re)1.38 (Sc)0.5 (Vg.µa/σ) (Fr)0.367 (A)0.167(T/D)0.25

((P/V)/ρN3T5)0.75 (DL/D2)Albal et al. (1983) kLa=1.41× 10-3 (Re)0.67 (Sc)0.5 (We)1.29 (DL/T2)Schluter and Deckwer (1992) kLa= C. [(P/VL)/ρ (v.g4)1/3] [(Q/VL). (v/g2)1/3]0.23 (g2/ v)

Table 3.2: Correlations proposed by different researchers to estimate the value of kLa in stirred tank reactor [three ref].

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