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Intro

Bioprocessing – Biotechnology:

Make money from bioprocesses

Inputs are of lower value than outputs (products)

Lecture 1: Intro, study guide, what is a bioreactor,

Lecture 2: Intro to CBLA use, oxygen solubility, show bioprosim, download material, use floppy disks, Henry’s law, temperature effect on oxygen solubility. Use of spreadsheets for data processing

Lecture 3: What is diffusion, how can we predict the behaviour of a randomly moving molecule? moving dots, entropy, driving force, equilibrium, rate of diffusion, first order kinetics

Lecture 4: oxygen transfer rate, kLa value. Graphical method of determining the kLa. Mathematical (2 point) determination of kLA

Calculation and prediction of oxygen transfer as function of DO. Oxygen transfer efficiency. Bacterial OUR, DO. steady state

Lecture 5: In situ method of determining kLa

sulfite method of determining kLa

Lecture 6: Online OUR monitoring as a key bioprocess monitoring tool. Saturation behaviour of OUR. Critical DO. Respirometric testing of substrates and inhibitors. Numeric integration of rate data

Molecular diffusion relies on random movement resulting in uniform distribution of molecules

Overview

Diffusion, how does it work, how can we predict it?

Diffusion is random …. and yet predictable.

•

•

•

•

•

•

•

•

•

Oxygen Transfer Rate (OTR)

(diffusion, convection)

Low

OTR

High

OTR

Transfer by diffusion is extremely slow

and depends on surface area

Wind

Oxygen transfer by convection

(turbulences) is more efficient

Air In

• Bioreactors combine maximum convection

with maximum diffusion

• Course bubbles cause more convection,

fine bubbles more diffusion

How soluble is oxygen?

- The net transfer of oxygen from
- gas phase to solution reaches a dynamic equilibrium
- O2 input = O2 output
- equilibrium results in defined saturation concentration (cs).

Oxygen is not very polar poorly soluble.

Oxygen Solubility is described by Henry’s Law

p = partial pressure of gas

k = constant depending on gas type, solution

and temperature

c = concentration of gas dissolved in water

p = k*C

- Meaning: The amount of oxygen which dissolves in water is proportional to the amount of oxygen molecules present per volume of the gas phase.
- Partial pressure ~ number of O2 molecules per volume of gas
- increases with O2 concentration in gas
- increases with total gas pressure
- How to calculate partial pressure? (refer to CBLA)

cs =

(31.6 + T)

Oxygen solubility (cS)

Effect of temperature

Oxygen Saturation

Concentration cs (mg/L)

Temperature (°C)

Oxygen solubility decreases with increasing temperature.

Overall: oxygen is poorly soluble (8mg/: at room temp.)

More important than solubility is oxygen supply rate (oxygen transfer rate OTR).

(gradient, driving force)

Question: What is the driving force for oxygen dissolution?

At oxygen saturation concentration (cs): dynamic equilibrium exists between oxygen transferred from the air to water and vice versa.

OTR

Answer: The difference between oxygen partial pressure and oxygen in solution) is the driving force. OTR is proportional to the that difference. Thus:

1. OTR depends on dissolved oxygen concentration (cL).

2. No oxygen transfer at saturation concentration.

3. Maximum oxygen transfer when dissolved oxygen is zero.

How does an aeration curve look like?

First: steep step in oxygen (top layer saturated, next layer oxygen free)

Then: buildup of a gradient of many layers.

Each layer is only slightly different from the next

Transfer from layer to layer has little driving force.

Gradient build-up inhibits fast diffusion

Air On

cL (ppm)

0

5

10

Time (min)

OTR – depends on DO (cL)

Significance of OTR: critical to know and to control for

all aerobic bioreactors

1. Deoxygenation (N2, sulfite + Co catalyst)

2. Aeration and monitoring dissolved oxygen concentration

(D.O. or cL) as function of time

3. OTR = slope of the aeration curve (mg/L.h or ppm/h)

4. Observation: Slope is not constant but depends on cL

What is the real OTR?

5. The statement of OTR only makes sense when cL is specified

6. OTR is highest at cL = zero (Standard OTR)

7. OTR is zero at oxygen saturation concentrations (cs)

8. OTR is correlated to the saturation deficit (cs - cL),

which is the driving force for oxygen transfer

9. The factor of correlation is the volumetric mass transfer

coefficient kLa

OTR = kLa (cs - cL)

ppm/h h-1 ppm

10. OTR is not a useful parameter for the assessment of the

aeration capacity of a bioreactor. This is because it is

dependent on the oxygen concentration (cL)

11. The kLa value is a suitable parameter as it divides

OTR by saturation deficit:

OTR

(cs - cL)

kLa =

12. kLa = the key parameter oxygen transfer capacity.

How to determine it?

OTR – from aeration curve to kLa summary

(first order kinetics)

(cs)

Air on

Dissolved Oxygen

Aeration Curve

Time

max OTR

Slope = kLa

Rate is proportional to concentration First order kinetics

OTR (mg/L.h)

Dissolved oxygen [mg/L]

OTR = kLa (O2 saturation (cS) – O2 concentration (cL))

OTR – Aeration curve from CBLA

During aeration of oxygen free water, the dissolved oxygen increases in a characteristic way

OTR – aeration curve from CBLA

- Highest Rate at lowest dissolved oxygen concentration
- Rate of zero when DO reaches saturation concentration

Can the relationship between rate and DO be expressed mathematically?

Air On

6

cL (mg/L)

5 ppm

4.5 min

0

5

10

Time (min)

OTR – How to determine kLA

Example: determine OTR at 6 ppm

OTR is the slope of the tangent for each oxygen concentration

OTR = ∆ cL/ ∆ t

= 5 mg/L/ 4.5 min

= 1.1 mg/L/min

= 66 mg/L/h

kLa = OTR

(cs-cL)

= 66 ppm / h

(8 ppm – 6 ppm)

= 3.3 h-1

Q: Problem with this method?

A: based on one single OTR slope measurement and unreliable to obtain from real data.

DO

Time

6

4

2

0

5

10

OTR – Graphical determination of kLa

1. Monitor aeration curve

2. Determine graphically the OTR at various oxygen

concentrations (cL)

At 6 ppm: OTR = 25 mg/L/h

At 4 ppm: OTR = 50 mg/L/h

cL (ppm)

At 3 ppm: OTR = 60 mg/L/h

At 0.5 ppm: OTR = 30 ppm/h

Time (min)

3. Tabulate OTR and corresponding cL values

cL (mg/L)

Cs - cL (mg/L)

OTR (mg/L/h)

0.5

3.0

4.0

6.0

8.0

7.5

5.0

4.0

2.0

0.0

30

60

50

25

0

kLa = = 12 h-1

6 mg/L

OTR – Graphical determination of kLa

4. Plot OTR values as a function of cs - cL.

Standard OTR

100

OTR (mg/L/h)

cs

50

0

0

2

4

6

8

cs- cL (mg/L)

5. A linear correlation exists between kLa and the saturation

deficit (cs - cL) which is the driving force of the reaction.

6. The slope of the plot OTR versus cs - cL is the kLa value.

7. The standard OTR (max OTR) can be read from the intercept with

the cs line. (Standard OTR = 100 ppm/h)

(cs- cL)

cs - co

(

)

cs

3. kLa = ln

cs - ci

•

ci = 6

ti - to

Dissolved Oxygen

Concentration (mg/L)

•

co = 3

to

ti

Time (min)

= ln 2.5

8- 3 ppm

(

)

kLa = ln

4.4 min

8 - 6 ppm

10.5 - 6.1 min

Mathematical Determination of kLa

1. OTR is a change of cL over time, thus = dcL/dt

Integration gives

= 12.5 h-1

= 0.21 min-1

4. This method should be carried out for

3 to 4 different intervals

5. Once the kLa is known it allows to calculate the OTR

at any given oxygen concentration:

OTR = kLa (cs - cL)

Factors Affecting the Oxygen Transfer Coefficient kLa

kLa consists of:

• kL = resistance or thickness

of boundary film

• a = surface area

Bulk

Liquid

Bubble

[Oxygen]

Cell

Distance

Main boundary layer = steepest gradient

→ rate controlling, driving force

Effect of Fluid Composition on OTR

The transfer across this boundary layer increases with:

1) ↓ thickness of the film, thus ↑ degree of shearing (turbulence)

2) ↑ surface area

3) ↓ surface tension

4) ↓ viscosity (best in pure water)

5) ↓ salinity

6) ↓ concentration of chemicals or particles

7) detergents?

8) ↑ emulsifiers, oils, “oxygen vectors”

Engineering Parameters Influencing OTR

Increase depth vessel

Deeper vessel bubbles rise a long way ↑ OTR, OTE

but more pressure required ↑ $$

Decrease bubble size

- Larger surface area ↑ OTR, OTE

smaller bubbles rise slower more gas hold up

↑ OTR, OTE

Increase air flow rate

↑ Number of bubbles ↑ OTR but ↓ OTE

Increase stirring rate

- ↑ turbulence ↓ thickness of boundary layer ↑ OTR, OTE

↓ Bubble size ↑ OTR, OTE

OTE =

oxygen supplied

oxygen transferred (mol/L.h)

X 100

% OTE =

oxygen supplied (mol/L.h)

Oxygen Transfer Efficiency (OTE)

Significance of OTE: economical, evaporation

Calculation of OTE (%):

Why do students find this type calculation difficult?

Units are disregarded. Molecular weights are misused.

X 100

% OTE =

34.3 (mol/L.h)

Oxygen Transfer Efficiency (OTE)

A bioreactor ( 3 m3) is aerated with 200 L/min airflow. If the OTR is constant (100 mg/L/h) determine the %OTE.

1. Convert the airflow into an oxygen flow in mmol/L/h

200 L air /min = 12000 L air/h

(x 60)

= 2520 L O2/h

(x 21%)

= 102.9 mol O2/h

(÷ 24.5 L/mol)

(÷ 3000 L)

= 34.3 mmol O2/L.h

2. OTR

100 mg/L.h = 3.1 mmol O2/L.h

(÷ 32 g/mol)

= 9%

% OTE

5

Airflow

Oxygen Transfer Efficiency (OTE)

OTE is dependent upon the cL in the same way than OTR

OTE decreases with increasing airflow

(more oxygen is wasted)

Microbial oxygen Uptake Rate (OUR)

Depends on:

1. Specific activity of cells (QO2)

2. The number of cells (X)

OUR = QO2 . X

QO2 depends on:

1. Strain

2. Substrate

3. [Substrate]

4. Temperature

5. Growth conditions

6. [Oxygen] (cL)

OUR

[Substrate]

Time

OUR – Variation during batch culture

In batch culture OUR changes strongly over time due to

increase in biomass (X)

depletion of substrate (S).

However OUR can be considered constant:

• over short time intervals (min)

• in continuous culture

- Critical indicator of culture status (respiration rate).
- Inidicator or growth (relationship X / OUR).
- Indicator of health, inhibition etc ( if X= constant).
- Essential for culture optimisation.
- Should be ideally monitored online.

1. Aerate to maximum

2. Stop aeration

3. Monitor cL

cL

Time (sec)

Conclusion:

1. OUR is linear over most cL values

2. A critical D.O. exists

1. Aerate to maximum

2. Stop aeration

3. Monitor cL

OUR not dependent on DO

cL

O2 dependent

OUR

Time (sec)

Conclusion:

1. OUR is linear over most cL values

2. A critical D.O. exists

The OUR is mostly independent of D.O.

At very low D.O. the OUR is strongly dependent on D.O.

OUR

(mg/L/h)

D.O. (mg/L)

Key words:

D.O. saturation

D.O. limitation

first order reaction

zero order reaction

Michaelis Menten kinetics

OUR

(mg/L/h)

D.O. (mg/L)

Critical DO

0.5

1

2

DO (ppm)

Dependence of OUR on DO (cL)

Conclusions:

1. Typical Michaelis Menten relationship

2. ks at about 0.1 ppm (critical D.O.: 0.2 ppm)

Air On

DO (ppm)

A

B

C

Time (sec)

OUR – Indirect online monitoring

Steady state:

1. OUR constant

3. DO constant

2. OTR constant

4. OUR = OTR

A

dcL/dt = 0

dcL/dt = OUR

B

= - QO2.X

dcL/dt = OTR - OUR

C

= kLa (cs - cL) - QO2.X

When dcL/dt = 0

→ OUR = OTR

→ OUR = kLa(cs – cL)

Conclusion: When kLa is known, steady state OUR can be

calculated from the dissolved [oxygen] (D.O.) (cL)

On

Feed

On

DO (ppm)

Feed

Off

Feed

Off

Feed

Off

Time (min)

OUR – Dependency on DO

The addition of feed to a starving culture of microbes

results in an instantaneous increase of OUR, which

Causes a drop in the D.O.

(cs – cL)

OUR – calculation from in situ DO monitoring

1. Calculation of OUR from kLa and cL

e.g. kLa = 20 h-1, cL = 2 ppm, cS= 8 ppm OUR = ?

OUR = 20 h-1 x 6 ppm

= 120 ppm/h

2. Determination of kLa in situ (dynamic method)

Since under steady state: OTR = OUR

OUR – applications of online DO monitoring

3. Calculation of new OUR from old OUR and cL

Original OUR = 120 mg/L/h at cL of 4 mg/L

After further growth DO lowered to 2 mg/L

What is the new OUR?

OUR 120 mg/L/h

(cS – cL) 4 mg/L

kLa = = = 30 h-1

OUR = kLa * (cS – cL) =

30 h-1 * (8 mg/L – 2 mg/L) = 180 mg/L

OUR – applications of online DO monitoring

1. Calculation of new kLa from old kLa and cL

Original kLa = 30 h-1 at cL of 2 mg/L

After increasing airflow the new cL was 5 mg/L

What is the new kLa?

OUR = kLa * (cS – cL) = 30 h-1 * (8 mg/L – 2 mg/L) = 180 mg/L

OUR 180 mg/L/h

(cS – cL) 3 mg/L

new kLa = = = 60 h-1

OUR- Comparison of Methods for kLa determination

- Static Gassing Out Method (N2)
- De-oxygenate solution, monitor DO increase over time. Determine kLa (a) graphically or (b) mathematically

- 2. Sulfite Method
- Titration of sulfite consumption during oxygenation trial
- - indirect measurement
- + no oxygen probe required
- + allows direct monitoring of standard OTR
- standard OTR = kLa . cs

- 3. Dynamic Method (in situ kLa)
- + measured real in situ value considering changes of
- medium such as viscosity, particles, surface tension ...
- depends upon known OUR
- + only slight process interuption necessary
- + only works when DO >> critical DO

OUR- Comparison of Methods for kLa determination

4. Oxygen Balance Method = Direct Monitoring

OTR = specific air flow . ([O2]in - [O2]out )

mg/L.h

L(g)/L(l).h

mg/L(g)

+ integrates over the whole reactor volume

+ not affected by fine air bubbles

+ excludes lag of oxygen probe

+ no lag of large reactors

- dependent on precise flow of air

- longer response time to step changes

OUR – indirect respiration activity monitoring

There is very useful information in the OUR response of microbial cultures to the addition of substrates or inhibitors

Add feed

D.O.

(mg/L)

Time

Effect of minute feed addition on D.O. profile of

aerated starving microbial culture

OUR

cS

D.O

cS

D.O

Add feed

D.O.

(mg/L)

Time

Effect of minute feed addition on D.O. profile of

aerated starving microbial culture

OUR – indirect respiration activity monitoring

OUR

(mg/L/h)

Add feed

D.O.

(mg/L)

Time

Effect of minute feed addition on D.O. profile of

aerated starving microbial culture

OUR – indirect respiration activity monitoring

40

OUR

(mg/L/h)

20

20 mg/L/h

* 0.1h =

2 mg/L

6

12

Time (min)

24

OUR response to feed spike by starving microbial culture.

Numerical integration (counting squares) allows to determine

the amount of oxygen used due to the feed spike addition.

Beyond this point some spare slides

Time (min)

Time (min)

Feed

Applications of Relationship OUR – D.O.

3. Degradabilitymonitoring

OUR (ppm/h)

DO(cL) (ppm)

4. Optimising aeration or growth conditions

5. Estimation of yield coefficient (Y)

468

cs =

(31.6 + T)

Oxygen Solubility

Oxygen Solubility is described by Henry’s Law

p = partial pressure of gas

k = constant depending on gas and solution

c = concentration of gas dissolved in water

1. Meaning: The amount of oxygen which dissolves in water is proportional to the amount of oxygen molecules present per volume of the gas phase. What is partial pressure? (refer to CBLA)

Effect of temperature on oxygen solubility

Oxygen solubility

decreases with

increasing temperature.

3. Overall: oxygen is poorly

soluble (8mg/: at room temp.)

Oxygen Saturation

Concentration cs (mg/L)

Temperature (°C)

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