Bio301 Overview of TopicsIntro

Bioprocessing – Biotechnology: Make money from bioprocesses

Inputs are of lower value than outputs (products)

Computer based learning activities (CBLA) are onhttp://sphinx.murdoch.edu.au/units/extern/BIO301/teach/index.htm

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Lecture overview L1-3

Lecture 1: Intro, study guide, what is a bioreactor,Learning by interacting

Lecture 2: 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, kLa

Lecture 3: oxygen transfer rate, kLa value. Graphical method of determining the kLa. Mathematical (2 point) determination of kLACalculation and prediction of oxygen transfer as function of DO. Oxygen transfer efficiency. Bacterial OUR, DO. steady state

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

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Oxygen Transfer Rate (OTR)Overview

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

Diffusion is random …. and yet predictable.A simple model simulation can show that although the diffusion movement is random, it can be precisely predicted for large number of molecules (e.g. Fick’s law of diffusion)

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Oxygen Transfer Rate (OTR)(diffusion, convection)

LowOTR High

OTR

Transfer by diffusion is extremely slowand depends on surface area

Wind

Oxygen transfer by convection(turbulences) is more efficient

Air In

••

•

••• • ••

• • Bioreactors combine maximum convectionwith maximum diffusion

• Course bubbles cause more convection,fine bubbles more diffusion

How soluble is oxygen?11

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).

•The saturation concentration is also the oxygen solubility

•How soluble is oxygen?

Oxygen solubility (cS)

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Oxygen is not very polar poorly soluble in water.

Oxygen Solubility is described by Henry’s Law which applies to all gases

p = k*cSp = partial pressure of oxygenk = constant depending on gas type, solution

and temperaturecS = concentration of oxygen dissolved in water

• 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 gasincreases with O2 concentration in gas

increases with total gas pressure

How to calculate partial pressure? (refer to CBLA)

Oxygen solubility (cS)

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Examples of using the proportionality between partial pressure of oxygen in the atmosphere and the saturation concentration cS:

p = k*cSp = partial pressure of oxygenk = constant depending on gas type, solution

and temperaturecS = concentration of oxygen dissolved in water

• If the reactor is operated under 2 times atmospheric pressure (200kPa instead of 100 kPa air pressure), the new saturation concentration will be abou 16 mg/L instead of 8 mg/L.

• If air (partial pressure = 0.21* 100 kPa) is replaced by pure oxygen atmosphere (partial pressure 100kPa) the oxygen saturation concentration is about 40 mg/L (more precise 8*100/21) instead of 8 mg/L.

How to calculate partial pressure? (refer to CBLA)

Oxygen solubility (cS)

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Effect of temperature

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).

0

5

10

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0 20 40 60

cs =468

(31.6 + T)

Oxy

gen

Sat

ura

tio

n

Co

nce

ntr

atio

n c

s (

mg

/L)

Temperature (°C)

Oxygen solubility (cS)

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Oxygen Transfer Rate (OTR)(gradient, driving force)

Question: What is the driving force for oxygen dissolution?

OTR At oxygen saturation concentration (cs): dynamic equilibrium exists between oxygen transferred from the air to water and vice versa. No driving force

Answer: The difference between cS and the actual dissolved oxygen concentration (cL) is the driving force. OTR is proportional to the that difference. Thus:

OTR ~ (cS – cL)

Need to determine the proportionality factor

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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)

Significance of OTR: critical to know and to control forall aerobic bioreactors

0 5 10

8 Air On

cL (

pp

m)

Time (min)

OTR – depends on DO (cL)

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OTR = kLa (cs - cL)

Mg/L/h h-1 mg/L

4. Observation: OTR decreases over time (and with incr. cL)

5. OTR is not a good measure of aeration capacity of a bioreactor

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

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

8. OTR is negatively correlated to cL

9. 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 – depends on DO (cL)

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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

OTR –Significance of gradient

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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:

12. kLa = the key parameter oxygen transfer capacity. How to determine it?

OTR(cs - cL)

kLa =

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Lec 2 summary:

Oxygen is poorly soluble depending mainly on •partial pressure in headspace•Temperature

OTR is driven and proportional to driving force (cS-cL)

kLa is the proportionality factor (first order kinetics)

kLa describes the performance of a bioreactor to provideOxygen to microbes

Next lecture: quantify kLA

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Lec 3 outlook:

•Aeration curve•Quantify OTR at a given point of an aeration curve•Quick estimate of kLa•Graphical determination of kLa•Mathematical determination of kLa•Run computer simulation to obtain data•Oxygen transfer efficiency (OTE)•OTR proportional to cs-cL•OTR inverse proportional to cL

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OTR – Quick estimate of kLAExample: determine OTR at 6 mg/L

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

0 5 10

8 Air OncL

(m

g/L

)

Time (min)

6

4.5 min

5 mg/L

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kLa = OTR

= 66 ppm / h

(cs-cL)

= 3.3 h-1

(8 ppm – 6 ppm)

Q: Problem with this method?

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

OTR – quick estimate of kLA

Time

DO

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1. Monitor aeration curve

2. Determine graphically the OTR at various oxygen concentrations (cL)

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2

4

6

0 5 10

3. Tabulate OTR and corresponding cL values

cL (

pp

m)

0.53.04.06.08.0

Time (min)

7.55.04.02.00.0

306050250

cL (mg/L) Cs - cL (mg/L) OTR (mg/L/h)

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

At 4 ppm: OTR = 50 mg/L/hAt 3 ppm: OTR = 60 mg/L/h

At 0.5 ppm: OTR = 30 ppm/h

OTR – Graphical determination of kLa

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0

50

100

0 2 4 6 8

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

TR

(m

g/L

/h) Standard OTR

cs

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)

kLa = = 12 h-170 mg/L/h

6 mg/L

OTR – Graphical determination of kLa

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Mathematical Determination of kLa1. OTR is a change of cL over time, thus = dcL/dt

Integration gives2. kLa = dcL/dt

(cs- cL)

( )cs - co3. kLa = ln cs - ci

ti - to

( )8 - 3 ppm kLa = ln 8 - 6 ppm

10.5 - 6.1 min

= 0.21 min-1 = 12.5 h-1= ln 2.5

4.4 min

•

•D

isso

lved

Oxy

gen

Con

cent

ratio

n (m

g/L)

ci = 6

co = 3

to ti Time (min)

cs

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4. This method should be carried out for 3 to 4 different intervals. By aver

5. Once the kLa is known it allows to calculate the OTR at any given oxygen concentration:

OTR = kLa (cs - cL)

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Factors Affecting the Oxygen Transfer Coefficient kLa

kLa consists of:

• kL = resistance or thickness of boundary film• a = surface area

Bubble BulkLiquid

Cell

[Oxy

gen

]

Distance

Main boundary layer = steepest gradient→ rate controlling, driving force 29

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”

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Oxygen Transfer Efficiency (OTE)

OTE =oxygen transferred

oxygen supplied

Significance of OTE: economical, evaporation

Calculation of OTE (%):

% OTE =oxygen transferred (mol/L.h)

oxygen supplied (mol/L.h)X 100

Why do students find this type calculation difficult?Units are disregarded. Molecular weights are misused.

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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

= 2520 L O2/h

= 102.9 mol O2/h

= 34.3 mmol O2/L.h

(x 21%)

(÷ 24.5 L/mol)

(÷ 3000 L)

2. OTR

(x 60)

100 mg/L.h = 3.1 mmol O2/L.h (÷ 32 g/mol)

% OTE =3.1 (mmol/L.h)

34.3 (mol/L.h)X 100

= 9% 32

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)

% O

TE

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10

Airflow

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Engineering Parameters Influencing OTR

Increase depth vessel

Decrease bubble size

Increase air flow rate

Increase stirring rate

Deeper vessel bubbles rise a long way ↑ OTR, OTE but more pressure required ↑ $$

Larger surface area ↑ OTR, OTEsmaller bubbles rise slower more gas hold up ↑ OTR, OTE

↑ Number of bubbles ↑ OTR but ↓ OTE

↑ turbulence ↓ thickness of boundary layer ↑ OTR, OTE

↓ Bubble size ↑ OTR, OTE 34

Rate is proportional to concentration First order kinetics

Slope = kLa

max OTR

OT

R (

mg

/L.h

)

Dissolved oxygen [mg/L]

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

(first order kinetics)

Aeration Curve

Time

Dis

solv

ed O

xyg

enAir on(cs)

OTR – from aeration curve to kLa summary

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

OTR – Aeration curve from CBLA

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Can the relationship between rate and DO be expressed mathematically?

•Highest Rate at lowest dissolved oxygen concentration

•Rate of zero when DO reaches saturation concentration

OTR – aeration curve from CBLA

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