kla

Experimental Techniques for kLa determination http://www.youtube.com/watch?v=8441Bz07qQ0 Theory: Narasimha

dC AL dt

(

= k L a C *AL − C AL

)

integrating…. C AL 2

∫

C AL1

(C

1 * AL

− C AL

)

t

dC AL = k L a ∫ dt 0

 C * − C AL1   = k at ln AL L  C* − C  AL2   AL

Therefore a plot of

 C * − C AL1   ln AL C* − C  vs AL 2   AL

t should result in a straight line of

slope kLa. Static Gassing Out Method (Unsteady State)

•

In the absence of respiring organism (no O2 consumption)

•

Sparge vessel contents with N2, displacing O2

• Monitor variation in dissolved oxygen concentration (DO) using a (polarographic) DO probe

•

Allow DO to fall to 0% saturation, then turn off N2 flow

• Sparge vessel contents with air at a known flowrate • Monitor and record variation of DO concentration with respect to time.

•

plot of

 C * − C AL1   ln AL C* − C  vs AL 2   AL

t should result in a straight line of slope

kLa Dynamic Gassing Out Method • In the presence of respiring organsims

•

At time t0, turn off air supply to vessel

•

Monitor and record reduction in DO between t0 and t1

•

At t1, turn the air supply on again

•

Monitor and record rise in DO

Theory: For respiring systems dC AL dt

(

)

= k L a C *AL − C AL − q o 2 X

Where X is the biomass concentration and qo2 is the specific oxygen consumption rate (mmols O2 / g biomass s)

We assume that when we conduct dynamic kla determinations, that the timescale of the experiment is several orders of magnitude lower than that of the fermentation. In this case, we can assume that a quasi-steady state exists at the time of the experiment between oxygen transfer and oxygen consumption. i.e.

)

(

− k L a C *AL − C AL = qo 2 X − C AL

is the quasi steady state oxygen concentration at the time of the experiment Substituting for dC AL dt

qo2 X

in the original equation

(

)

(

− = k L a C *AL − C AL − k L a C *AL − C AL

)

Rearranging results in the following equation dC AL dt

(

= k L a C −AL − C AL

)

Integrating, results in….  C − − C AL1   = k a(t 2 − t1) ln AL L C− − C  AL2   AL

Notes of the Dynamic Gassing Out Method • Non-invasive method, suitable for use with respiring systems • Assumes rapid disengagement of air bubbles when air supply is turned off -inappropriate for highly viscous broths • If headspace aeration is significant, use N2 blanket

• Requires DO probe with fast response • CL(1) determined by critical DO concentration for organisms for bacteria and yeast mould cultures plant cultures

Ccritical ~ 5-10% saturation Ccritical ~ 10-50% saturation Ccritical ~ 10-30% saturation

Important: On the degassing stage of the experiment, dC AL dt

= −q o 2 X

Therefore from the slope of the line in this region (if both axes of the graph are in the correct units), the specific oxygen consumption rate can be calculated once the biomass concentration is known (easy to evaluate). For the mathematically challenged, the slope of the line in a plot of CAL vs. time is

dC AL dt

!

Doran 9.5 – Dynamic kLa measurement An experiment was performed on an exponential phase microbial culture, where the oxygen supply was disconnected and the DO concentration was allowed to fall to 43.5% saturation. At this point, aeration was resumed and the increase in DO concentration was monitored with respect to time. From the following data of the reoxygenation stage, calculate the gas-liquid mass transfer coefficient for the reactor. Time (s)

% Saturation 10 43.5 20 53.5 30 60 40 67.5 50 70.5 60 72 70 73 100 73.5 130 73.5

80 70

% Saturation

60 50 40 30 20 10 0 0

50

100

150

Time (s)

Figure 1. Plot of % saturation vs. time Solution: Whats the quasi-steady state O2 concentration? 73.5% sat. Let 10s = t1 Plot  C − − C AL1  vs(t 2 − t1) ln AL C− − C  AL2   AL

4.5 4 3.5

ln...

3 2.5 2

y = 0.0611x

1.5

2

R = 0.9502

1 0.5 0 0

20

40

60

80

(t2-t1) (s)

Slope is equal to kLa – 0.0611 s-1 Note: due to the form of the equation the line has to intercept at the origin.