##### Document Text Contents

Page 1

CE20186 CE20186 – – Mass Mass Transfer Transfer Charlie Charlie Lower Lower

Department Department of of Chemical Chemical Engineering Engineering 11

AbstractAbstract

This experiment monitors how mixing conditions affect the mass transfer of oxygen inThis experiment monitors how mixing conditions affect the mass transfer of oxygen in

a reaction vessel by observing the rate of change of dissolved oxygen concentrationa reaction vessel by observing the rate of change of dissolved oxygen concentration

in water and calculating the liquid-phase mass transfer coefficients for a curvedin water and calculating the liquid-phase mass transfer coefficients for a curved

pitched impeller and a pitched impeller under three different agitation speeds and twopitched impeller and a pitched impeller under three different agitation speeds and two

flow rates. Consequently, it is found that the greatest liquid-phase mass transfer flow rates. Consequently, it is found that the greatest liquid-phase mass transfer

coefficient is achieved is 0.0362 scoefficient is achieved is 0.0362 s

-1-1

using a curved pitched impeller with a speed of using a curved pitched impeller with a speed of

739 rpm and an air flow rate of 10 L min739 rpm and an air flow rate of 10 L min

-1-1

..

1 Introduction1 Introduction

Dissolved oxygen (DO) is a valuable component in biochemical engineering as itDissolved oxygen (DO) is a valuable component in biochemical engineering as it

allows the operation and efficiency of various biochemical processes to beallows the operation and efficiency of various biochemical processes to be

determined. One example of this is found in the aerobic fermentation process of determined. One example of this is found in the aerobic fermentation process of

particular microorganisms such as yeast. It is essential that the desired amount of particular microorganisms such as yeast. It is essential that the desired amount of

oxygen is transferred from one phase to another otherwise this could result inoxygen is transferred from one phase to another otherwise this could result in

denaturing of the cells present in the system and hence a waste of feedstock for adenaturing of the cells present in the system and hence a waste of feedstock for a

given process. It is therefore imperative to closely monitor and control the amount of given process. It is therefore imperative to closely monitor and control the amount of

DO is a system in DO is a system in order to achieve a desirable product yielorder to achieve a desirable product yield.d.

The primary factors governing the rate at which oxygen dissolves into a systemThe primary factors governing the rate at which oxygen dissolves into a system

include; the concentration of DO already present in the process fluid, the speed andinclude; the concentration of DO already present in the process fluid, the speed and

characteristics of the impeller for an agitated system and in some cases the processcharacteristics of the impeller for an agitated system and in some cases the process

fluid temperature. Careful control of these parameters is necessary for the successfulfluid temperature. Careful control of these parameters is necessary for the successful

operation of a system. In some processes, the process fluid can transform from low-operation of a system. In some processes, the process fluid can transform from low-

viscous Newtonian characteristics to a rheological complex viscous non-Newtonianviscous Newtonian characteristics to a rheological complex viscous non-Newtonian

fluid [1]. This means that correct choice of stirrer is essential. Impellers have differentfluid [1]. This means that correct choice of stirrer is essential. Impellers have different

designs mainly to accommodate different fluid viscosities. This experiment featuresdesigns mainly to accommodate different fluid viscosities. This experiment features

the gas-liquid mass transfer of oxygen in water for two stirrers (curved pitched andthe gas-liquid mass transfer of oxygen in water for two stirrers (curved pitched and

pitched impeller) under three different agitation velocities.pitched impeller) under three different agitation velocities.

The aim of this experiment is to investigate how mixing conditions affect the massThe aim of this experiment is to investigate how mixing conditions affect the mass

transfer of oxygen. In order to achieve this, the rate of change of dissolved oxygentransfer of oxygen. In order to achieve this, the rate of change of dissolved oxygen

concentration in water is investigated and the liquid-phase mass transfer coefficientsconcentration in water is investigated and the liquid-phase mass transfer coefficients

are calculated and compared.are calculated and compared.

2 Theory2 Theory

Mass transfer sees the transition of mass, in this case mass of oxygen, travellingMass transfer sees the transition of mass, in this case mass of oxygen, travelling

form a region of high concentration to low concentration. This is more commonlyform a region of high concentration to low concentration. This is more commonly

known as diffusion. Fick’s law expresses the relationship that relates diffusion toknown as diffusion. Fick’s law expresses the relationship that relates diffusion to

concentration of a substance;concentration of a substance;

== −−

!!

!"!"

!"!"

[2][2]

The dissolution rate of oxygen in water, which is driven by a concentrationThe dissolution rate of oxygen in water, which is driven by a concentration

gradient between maximum DO saturation (at constant temperature, pressure andgradient between maximum DO saturation (at constant temperature, pressure and

salinity of water) and bulk DO salinity of water) and bulk DO concentratconcentration is defined as;ion is defined as;

!"!"

!"!"

== ((!!))((!! −− )) [3][3]

LetLet ∗∗ denote the dimensionless DO concentration i.e. DO percentage anddenote the dimensionless DO concentration i.e. DO percentage and !! is theis the

initial DO concentration. Integrating equation (2.2) with these parameters gives;initial DO concentration. Integrating equation (2.2) with these parameters gives;

lnln 100100 −−

∗∗

== ((−−!!))

∴∴ lnln 100100 −− %% == ((−−!!))

Hence by plottingHence by plotting lnln 100100 −− %% as a function of time, the gradient of the slope isas a function of time, the gradient of the slope is

equal toequal to −−!!..

(2.1)(2.1)

(2.2)(2.2)

2.32.3

2.42.4

Page 4

CE20186 CE20186 – – Mass Mass Transfer Transfer Charlie Charlie Lower Lower

Department Department of of Chemical Chemical Engineering Engineering 44

Pitched Pitched 5 5 538 538 0.01130.0113

5 5 661 661 0.01710.0171

5 5 749 749 0.02270.0227

10 10 538 538 0.01570.0157

10 10 661 661 0.02460.0246

10 10 749 749 0.03240.0324

5 Calculations5 Calculations

In order to calculate ln(100-DO%), the observed experimental value for the dissolvedIn order to calculate ln(100-DO%), the observed experimental value for the dissolved

oxygen saturation is subtracted and the natural logarithm of the answer is taken. For oxygen saturation is subtracted and the natural logarithm of the answer is taken. For

example, a DO value of 30%;example, a DO value of 30%;

100100 −− 3030 == ((7070)) == 44..24852485

This value is then plotted against the corresponding time value. In this case, t=0 asThis value is then plotted against the corresponding time value. In this case, t=0 as

DO=30% is the initial value. From DO=30% is the initial value. From the ln(100-DO%) versus time plots, the gradient isthe ln(100-DO%) versus time plots, the gradient is

found by plotting a linear trend line. The equation of the linear trend line is in the formfound by plotting a linear trend line. The equation of the linear trend line is in the form

of y=mx+c where m is the gradient, x is time, c is the ln(100-DO%) intercept and y isof y=mx+c where m is the gradient, x is time, c is the ln(100-DO%) intercept and y is

ln(100-DO%).ln(100-DO%).

The gradient is the relevant part of the equation as this is equal toThe gradient is the relevant part of the equation as this is equal to ((−−!!). The). The

gradient of the linear trend line for 528 rpm from figure 4.1 is y= -0.0086x + 4.2625.gradient of the linear trend line for 528 rpm from figure 4.1 is y= -0.0086x + 4.2625.

Hence;Hence;

−−!! == −−00..00860086

!!!!

∴∴ !! == 00..00860086

!!!!

6 Discussion6 Discussion

Figures 4.1-4.4 show the same trends in the sense that all four plots express a linear Figures 4.1-4.4 show the same trends in the sense that all four plots express a linear

increase in dissolved oxygen intake as time progresses. All four of these plots alsoincrease in dissolved oxygen intake as time progresses. All four of these plots also

show that as the agitation speed of each impeller is increased, the liquid-phase massshow that as the agitation speed of each impeller is increased, the liquid-phase mass

transfer coefficient increases. This is noticeable as the gradients of each impeller transfer coefficient increases. This is noticeable as the gradients of each impeller

speed slope increase with impeller speed. This relationship is expected as thespeed slope increase with impeller speed. This relationship is expected as the

increased impeller speed allows greater agitation within the vessel. This is supportedincreased impeller speed allows greater agitation within the vessel. This is supported

by Doran (2011) who states, “Under typical operating conditions, increasing theby Doran (2011) who states, “Under typical operating conditions, increasing the

stirrer speed improves the value of stirrer speed improves the value of !!”. [2]”. [2]

Figure 4.5 displays very significant results. One being that higher values of Figure 4.5 displays very significant results. One being that higher values of !! are inare in

fact achieved at the higher air flow rate. Furthermore, higher fact achieved at the higher air flow rate. Furthermore, higher !! values are achievedvalues are achieved

in this experiment using the curved pitch impeller. This may not seem feasible at firstin this experiment using the curved pitch impeller. This may not seem feasible at first

analysis, however it is not necessarily correct to use an impeller with more blades toanalysis, however it is not necessarily correct to use an impeller with more blades to

achieve greater gas dispersion. This finding is supported by Doran (2011) whoachieve greater gas dispersion. This finding is supported by Doran (2011) who

states, “increasing the number of impellers on the stirrer shaft does not necessarilystates, “increasing the number of impellers on the stirrer shaft does not necessarily

improveimprove !! even though the power consumption is increased”. [2]even though the power consumption is increased”. [2]

There are various mechanisms that are related to the bubble flow rate and sizeThere are various mechanisms that are related to the bubble flow rate and size

influencing the uptake of dissolved oxygen. Examples such as temperature, sparger influencing the uptake of dissolved oxygen. Examples such as temperature, sparger

flow rate and design, however most importantly bubble size. It is very difficult toflow rate and design, however most importantly bubble size. It is very difficult to

engineer a sparger that allows for accurate manipulation of bubble size so it isengineer a sparger that allows for accurate manipulation of bubble size so it is

therefore necessary to agitate the reaction vessel with stirred impellers to alter thetherefore necessary to agitate the reaction vessel with stirred impellers to alter the

size off bubbles. This is supported by Doran (2011) who states, “The efficiency of size off bubbles. This is supported by Doran (2011) who states, “The efficiency of

gas-liquid mass transfer depends to a large extent on the characteristics of bubblesgas-liquid mass transfer depends to a large extent on the characteristics of bubbles

in the liquid medium. Bubble behaviour strongly affects the value of in the liquid medium. Bubble behaviour strongly affects the value of !!” [2] and “The” [2] and “The

most important property of air bubbles is their size. For a given volume of gas, moremost important property of air bubbles is their size. For a given volume of gas, more

interfacial area is provided if the gas is dispersed into many small bubbles rather interfacial area is provided if the gas is dispersed into many small bubbles rather

CE20186 CE20186 – – Mass Mass Transfer Transfer Charlie Charlie Lower Lower

Department Department of of Chemical Chemical Engineering Engineering 11

AbstractAbstract

This experiment monitors how mixing conditions affect the mass transfer of oxygen inThis experiment monitors how mixing conditions affect the mass transfer of oxygen in

a reaction vessel by observing the rate of change of dissolved oxygen concentrationa reaction vessel by observing the rate of change of dissolved oxygen concentration

in water and calculating the liquid-phase mass transfer coefficients for a curvedin water and calculating the liquid-phase mass transfer coefficients for a curved

pitched impeller and a pitched impeller under three different agitation speeds and twopitched impeller and a pitched impeller under three different agitation speeds and two

flow rates. Consequently, it is found that the greatest liquid-phase mass transfer flow rates. Consequently, it is found that the greatest liquid-phase mass transfer

coefficient is achieved is 0.0362 scoefficient is achieved is 0.0362 s

-1-1

using a curved pitched impeller with a speed of using a curved pitched impeller with a speed of

739 rpm and an air flow rate of 10 L min739 rpm and an air flow rate of 10 L min

-1-1

..

1 Introduction1 Introduction

Dissolved oxygen (DO) is a valuable component in biochemical engineering as itDissolved oxygen (DO) is a valuable component in biochemical engineering as it

allows the operation and efficiency of various biochemical processes to beallows the operation and efficiency of various biochemical processes to be

determined. One example of this is found in the aerobic fermentation process of determined. One example of this is found in the aerobic fermentation process of

particular microorganisms such as yeast. It is essential that the desired amount of particular microorganisms such as yeast. It is essential that the desired amount of

oxygen is transferred from one phase to another otherwise this could result inoxygen is transferred from one phase to another otherwise this could result in

denaturing of the cells present in the system and hence a waste of feedstock for adenaturing of the cells present in the system and hence a waste of feedstock for a

given process. It is therefore imperative to closely monitor and control the amount of given process. It is therefore imperative to closely monitor and control the amount of

DO is a system in DO is a system in order to achieve a desirable product yielorder to achieve a desirable product yield.d.

The primary factors governing the rate at which oxygen dissolves into a systemThe primary factors governing the rate at which oxygen dissolves into a system

include; the concentration of DO already present in the process fluid, the speed andinclude; the concentration of DO already present in the process fluid, the speed and

characteristics of the impeller for an agitated system and in some cases the processcharacteristics of the impeller for an agitated system and in some cases the process

fluid temperature. Careful control of these parameters is necessary for the successfulfluid temperature. Careful control of these parameters is necessary for the successful

operation of a system. In some processes, the process fluid can transform from low-operation of a system. In some processes, the process fluid can transform from low-

viscous Newtonian characteristics to a rheological complex viscous non-Newtonianviscous Newtonian characteristics to a rheological complex viscous non-Newtonian

fluid [1]. This means that correct choice of stirrer is essential. Impellers have differentfluid [1]. This means that correct choice of stirrer is essential. Impellers have different

designs mainly to accommodate different fluid viscosities. This experiment featuresdesigns mainly to accommodate different fluid viscosities. This experiment features

the gas-liquid mass transfer of oxygen in water for two stirrers (curved pitched andthe gas-liquid mass transfer of oxygen in water for two stirrers (curved pitched and

pitched impeller) under three different agitation velocities.pitched impeller) under three different agitation velocities.

The aim of this experiment is to investigate how mixing conditions affect the massThe aim of this experiment is to investigate how mixing conditions affect the mass

transfer of oxygen. In order to achieve this, the rate of change of dissolved oxygentransfer of oxygen. In order to achieve this, the rate of change of dissolved oxygen

concentration in water is investigated and the liquid-phase mass transfer coefficientsconcentration in water is investigated and the liquid-phase mass transfer coefficients

are calculated and compared.are calculated and compared.

2 Theory2 Theory

Mass transfer sees the transition of mass, in this case mass of oxygen, travellingMass transfer sees the transition of mass, in this case mass of oxygen, travelling

form a region of high concentration to low concentration. This is more commonlyform a region of high concentration to low concentration. This is more commonly

known as diffusion. Fick’s law expresses the relationship that relates diffusion toknown as diffusion. Fick’s law expresses the relationship that relates diffusion to

concentration of a substance;concentration of a substance;

== −−

!!

!"!"

!"!"

[2][2]

The dissolution rate of oxygen in water, which is driven by a concentrationThe dissolution rate of oxygen in water, which is driven by a concentration

gradient between maximum DO saturation (at constant temperature, pressure andgradient between maximum DO saturation (at constant temperature, pressure and

salinity of water) and bulk DO salinity of water) and bulk DO concentratconcentration is defined as;ion is defined as;

!"!"

!"!"

== ((!!))((!! −− )) [3][3]

LetLet ∗∗ denote the dimensionless DO concentration i.e. DO percentage anddenote the dimensionless DO concentration i.e. DO percentage and !! is theis the

initial DO concentration. Integrating equation (2.2) with these parameters gives;initial DO concentration. Integrating equation (2.2) with these parameters gives;

lnln 100100 −−

∗∗

== ((−−!!))

∴∴ lnln 100100 −− %% == ((−−!!))

Hence by plottingHence by plotting lnln 100100 −− %% as a function of time, the gradient of the slope isas a function of time, the gradient of the slope is

equal toequal to −−!!..

(2.1)(2.1)

(2.2)(2.2)

2.32.3

2.42.4

Page 4

CE20186 CE20186 – – Mass Mass Transfer Transfer Charlie Charlie Lower Lower

Department Department of of Chemical Chemical Engineering Engineering 44

Pitched Pitched 5 5 538 538 0.01130.0113

5 5 661 661 0.01710.0171

5 5 749 749 0.02270.0227

10 10 538 538 0.01570.0157

10 10 661 661 0.02460.0246

10 10 749 749 0.03240.0324

5 Calculations5 Calculations

In order to calculate ln(100-DO%), the observed experimental value for the dissolvedIn order to calculate ln(100-DO%), the observed experimental value for the dissolved

oxygen saturation is subtracted and the natural logarithm of the answer is taken. For oxygen saturation is subtracted and the natural logarithm of the answer is taken. For

example, a DO value of 30%;example, a DO value of 30%;

100100 −− 3030 == ((7070)) == 44..24852485

This value is then plotted against the corresponding time value. In this case, t=0 asThis value is then plotted against the corresponding time value. In this case, t=0 as

DO=30% is the initial value. From DO=30% is the initial value. From the ln(100-DO%) versus time plots, the gradient isthe ln(100-DO%) versus time plots, the gradient is

found by plotting a linear trend line. The equation of the linear trend line is in the formfound by plotting a linear trend line. The equation of the linear trend line is in the form

of y=mx+c where m is the gradient, x is time, c is the ln(100-DO%) intercept and y isof y=mx+c where m is the gradient, x is time, c is the ln(100-DO%) intercept and y is

ln(100-DO%).ln(100-DO%).

The gradient is the relevant part of the equation as this is equal toThe gradient is the relevant part of the equation as this is equal to ((−−!!). The). The

gradient of the linear trend line for 528 rpm from figure 4.1 is y= -0.0086x + 4.2625.gradient of the linear trend line for 528 rpm from figure 4.1 is y= -0.0086x + 4.2625.

Hence;Hence;

−−!! == −−00..00860086

!!!!

∴∴ !! == 00..00860086

!!!!

6 Discussion6 Discussion

Figures 4.1-4.4 show the same trends in the sense that all four plots express a linear Figures 4.1-4.4 show the same trends in the sense that all four plots express a linear

increase in dissolved oxygen intake as time progresses. All four of these plots alsoincrease in dissolved oxygen intake as time progresses. All four of these plots also

show that as the agitation speed of each impeller is increased, the liquid-phase massshow that as the agitation speed of each impeller is increased, the liquid-phase mass

transfer coefficient increases. This is noticeable as the gradients of each impeller transfer coefficient increases. This is noticeable as the gradients of each impeller

speed slope increase with impeller speed. This relationship is expected as thespeed slope increase with impeller speed. This relationship is expected as the

increased impeller speed allows greater agitation within the vessel. This is supportedincreased impeller speed allows greater agitation within the vessel. This is supported

by Doran (2011) who states, “Under typical operating conditions, increasing theby Doran (2011) who states, “Under typical operating conditions, increasing the

stirrer speed improves the value of stirrer speed improves the value of !!”. [2]”. [2]

Figure 4.5 displays very significant results. One being that higher values of Figure 4.5 displays very significant results. One being that higher values of !! are inare in

fact achieved at the higher air flow rate. Furthermore, higher fact achieved at the higher air flow rate. Furthermore, higher !! values are achievedvalues are achieved

in this experiment using the curved pitch impeller. This may not seem feasible at firstin this experiment using the curved pitch impeller. This may not seem feasible at first

analysis, however it is not necessarily correct to use an impeller with more blades toanalysis, however it is not necessarily correct to use an impeller with more blades to

achieve greater gas dispersion. This finding is supported by Doran (2011) whoachieve greater gas dispersion. This finding is supported by Doran (2011) who

states, “increasing the number of impellers on the stirrer shaft does not necessarilystates, “increasing the number of impellers on the stirrer shaft does not necessarily

improveimprove !! even though the power consumption is increased”. [2]even though the power consumption is increased”. [2]

There are various mechanisms that are related to the bubble flow rate and sizeThere are various mechanisms that are related to the bubble flow rate and size

influencing the uptake of dissolved oxygen. Examples such as temperature, sparger influencing the uptake of dissolved oxygen. Examples such as temperature, sparger

flow rate and design, however most importantly bubble size. It is very difficult toflow rate and design, however most importantly bubble size. It is very difficult to

engineer a sparger that allows for accurate manipulation of bubble size so it isengineer a sparger that allows for accurate manipulation of bubble size so it is

therefore necessary to agitate the reaction vessel with stirred impellers to alter thetherefore necessary to agitate the reaction vessel with stirred impellers to alter the

size off bubbles. This is supported by Doran (2011) who states, “The efficiency of size off bubbles. This is supported by Doran (2011) who states, “The efficiency of

gas-liquid mass transfer depends to a large extent on the characteristics of bubblesgas-liquid mass transfer depends to a large extent on the characteristics of bubbles

in the liquid medium. Bubble behaviour strongly affects the value of in the liquid medium. Bubble behaviour strongly affects the value of !!” [2] and “The” [2] and “The

most important property of air bubbles is their size. For a given volume of gas, moremost important property of air bubbles is their size. For a given volume of gas, more

interfacial area is provided if the gas is dispersed into many small bubbles rather interfacial area is provided if the gas is dispersed into many small bubbles rather