see if this reference is any help:

http://www.asce.org/templates/publications-book-detail.aspx?id=8161

An alternative might be the use of kalman-filter based models

Article Estimation of the Respiration Rate and Oxygen Transfer Funct...

Article Simultaneous On-Line Estimation of Oxygen Transfer Rate and ...

Article On-line Respirometry and Estimation of Aeration Efficiencies...

Hi Jeremy,

Thank you for the reply. My concern here is that as soon as I start the cell culture process once I put the inoculum inside the reactor, how can I calculate the kLa for different impeller agitation rate and air flow rate, while the cell culture process is going on. I am looking forward to hear from you.

Regards,

Sohail

I would suggest trying the Kalman filter methods. You need to estimate oxygen transfer, biomass growth, and respiration rate.

Hi Jeremy,

I actually need to calculate kLa (volumetric mass transfer coefficient) while the cells are growing inside the reactor.

Regards,

Sohail

You can measure the O2 in the outlet gas phase and assess the O2 transfer rate OTR from the O2 gas phase mass balance. Then you can measure the dissolved O2 in the liquid and estimate the kLa from OTR = kLa*(CG/m - CL) where CL is the O2 concentration in the liquid and CG is the O2 in the gas phase (if you can assume that your bioreactor is a perfectly mixed phase, this CG is the O2 concentration in the gas outlet). Finally you need a partition coefficient for O2 in the medium: m= CG/CL; you can determine CG/m measuring CL at the equilibrium with the gas (e.g. either at the beginning of the test or at the end). Of course this procedure holds only if CL is significantly lower than the equilibrium concentration.. so you have a driving force (CG/m - CL) that can be assessed with an acceptable uncertainty.

Dear Sohail, It is not clear to me if you mean calculating from measured data or estimating by correlations using measured biomass concentration. In the latter case it is not possible to exactly calculate kLa of course.

But also the gassing in - gassing out method has its limitations. (Should the method not be called gassing out - gassing in?). Nevertheless it does give biomass concentration dependent results, what is an advantage. Limitations are the same as for the gassing-in method: second order effects due to time constant of electrode, whether the electrode calibration values are constant during the experiment (check before and after), residence time of gas, gas and broth concentration inhomogeneity, used definition of concentration at high biomass concentration, anti-foam addition. Especially the latter will/may be a major problem. Next a proper estimation from the data is required. Be careful to neglect data close to the start of gassing-in or at the end. Do not estimate solubility from the 'final' value of the measurement but use the least square method to estimate both this value and the kLa. Also consider extremes: how are the dependencies using water, using medium, using broth at the end of fermentation while the organisms are still alive. Your results should be somewhere in between, helping to use less data during actual fermentation. Finally, consider the steady state method, if possible, being much more reliable. Do realise that your data will be highly geometry- and scale-dependent.

Remark: if your question was simply the idea behind the method: during gassing out the consumption rate is determined, during gassing in the kLa, using balance equations.

I hope this is answering your question and that I did not discourage you...

Hi Rob,

Thank you for the reply. I want to calculate it from the measured data (dissolved oxygen concentration). What my concern is I want to calculate the kLa (volumetric mass transfer coefficient) once I start the cell culture process inside the bioreactor. I am varying impeller agitation rate and air flow rate. How to do it exactly in this case using the gassing in-gassing out method. I carried out the kLa determination for simple air/water system, where I used to deaerate the system by sparging the N2 gas once the dissolved oxygen level reaches zero inside the reactor, I again start sparging the air and then record the dissolved oxygen w.r.t until it reaches saturation and I used this data for calculating the kLa. How can I use the same method, while I am carrying out the experiments with the cell culture instead of simple air/water system. I hope I am able to convey my question.

Regards,

Sohail

Hello Sohail

I plan to do the same procedure for my thesis. Although I haven´t been able to do it yet due to time reasons, I have an idea of how to do it. First, I solved the mass balance differential equations considering the electrode´s response time AND the microorganism´s OUR. I assumed that during the time interval of the measurement, the OUR is constant. I obtained the dissolved oxygen concentration as a function of time (by mathematical manipulation you can obtain the model in terms of pO2). The model´s parameters are the OUR, kLa and kp (electrode´s time constant).

For the experimental procedure. First you would need to determine the electrode´s time constant. For this, fill 2 beakers with the same volume of your culture media and seal them with plastic (I use parafilm). Set both beakers at the temperature of your fermentations. Introduce air to one of the beakers and nitrogen to the other one. You have to wait several minutes to make sure that dO2 is 0 on one beaker and 100 on the other one (the dO2 probe should be calibrated at the same conditions of the experiment). Introduce the probe in the N2 media until a stable 0 measurement is achieved. Then quickly switch the probe to the O2 saturated media and record pO2 vs time data. Graph the data as you would for the kLa estimation, the slope should be the time constant of the probe.

To determine the OUR. Once you inoculate your bioreactor, try to saturate the media with oxygen. Once it reaches a stable value, turn of the air flow rate. Record pO2 vs time. Since we are assuming that OUR is constant you should see a straight line type decline in pO2. Reintroduce aeration before pO2 drops below 10%. At this point you should use the same agitation and aeration rate you intend to use in that particular fermentation. Once more, record the pO2 vs time data. If the inoculum density you are using is small enough and the agitation and aeration are high enough, you should be able to assume that the final pO2 you achieve is a saturation value and not a steady state value. Graph the data from the moment you reintroduce air to the time it stabilized. Adjust the data to the model I mentioned earlier using nonlinear regression. The only parameter you should be missing at this point is your kLa.

Take into consideration that the OUR you are determining at the start of your fermentation is the lag phase one. It won´t be the same in all the stages of growth of your organism. Dr. Van der Lans gave very important recommendations also. If you want, you can determine the oxygen saturation value using a chemical method (Winkler´s method for example, calculated without cells). I don´t know what type of organism you are using, bacteria should behave better than fungi for example. Feel free to get in touch if you need help solving the equations.

Good luck

Alejandro

You want to solve the problem

dC/dt = KLa (C* - C) - r() . f(C) - Q/V C

if you have a batch process, Q = 0

Choose operating conditions where f(C) is approximately 1 - so operate at high DO. Then you can track the problem where KLa and r() can be time-varying; C* needs to be specified.

Adding some comments on answers:

When I was a PhD student, back in the early eighties, papers from Irving J Dunn, and V. Linek published in the late seventies were the standard (and are still referred to). The common polarographic oxygen sensors from that time (Clark type) were rather slow. Which meant that some data on kLa published were in fact the electrode time constant (in case of fast transfer). Recently (2009) Linek published a paper on comparing presently used sensors. ( Liquid film effect on dynamics of optical oxygen probe. Comparison with polarographic oxygen probes. Diffusion coefficients measuring technique). Modern probes should be much faster.

Never rely on the factories calibration. Calibrate before and after measurement(s) or check beforehand the drift of the sensor. When there is drift do not wait for the final value of the method. It is not needed as stated above. When plotting data half-log you will notice deviations from the straight line at beginning (probe, dynamic gas concentration) and end (drift). Use the middle straight part. Using linear regression is risky because you need the saturation value and higher values weigh more. So use least mean square. To calibrate for zero oxygen concentration (also for measuring probe response time) one may use some sulphite instead of nitrogen bubbling (oxygen free nitrogen gas is more expensive).

A question on sensors was answered on Researchgate:

https://www.researchgate.net/post/How_exactly_does_a_Dissolved_Oxygen_probe_work

_Does_it_work_the_same_way_in_air_like_it_works_in_water

The size and aeration type of vessel are also important and what your purpose is. The mass balance equations assume ideal mixed phases! Jeremy's equation, lacking the electrode term, is for liquid. One should not neglect the gas phase balance, though probably at the first stage of fermentation (low consumption) the effect of gas depletion is not significant yet.

Personally I think it would be valuable to keep on exchanging experience with your 'colleague' PhD student Alejando.

Hi Alejandro,

Thank you for the detailed reply. I have come across the research papers where they have used the dynamic gassing out gassing in method for determining the kLa. I have also used the same method. I just wanted to know that can it be applied the same way as it is used for the air/water system. Can you please help me how to solve the equations.

For my system, the equation is dC/dt=kLa*(C*-CL)-qo2Cx or dC/dt=OTR-OUR.

I am using E.coli in my study.

Regards,

Sohail

I thought I gave an answer, but it wasn't published. So here goes again:

dC/dt=kLa*(C*-CL)-qo2Cx or dC/dt=OTR-OUR

equation is only good if we dont try to compare with the air/water system Kla. This is because the two systems have different oxygen gas depletion rate; my proposal is that the difference in the gas depletion rate is the microbial respiration in your cell culture. This changes the above equation to:

dC/dt=kLa*(C*-CL)-2 (qo2Cx) or dC/dt=OTR-(OUR)

At steady state, OTR must equal OUR and dC/dt=0, therefore,

kLa*(C*-CL)-OUR = OUR

kLa = 2(OUR)/(C*-CL)

kLa can be determined by the gassing-out method, or by the reaeration test of clean water or tap water, the resulting kLa modified by a contamination factor alpha.

By doing so, the two gas depletion rates are more or less equal, and you can calculate kLa in your culture if u know OUR, and vice versa. I hope this helps. Pl read my attached file.

Hello Lee,

I have one question. How do we get this term 2 in the final equation for kLa calculation. The other doubt I have OUR will keep on changing once I start the cell culture. Which one I can use for kLa calculation?

Regards,

Sohail

yes, the OTR is affected by the OUR. Based on my study, OTR=kLa(C*-C)-OUR. Since dC/dt =OTR -OUR, therefore, dC/dt=[kLa(C*-CL) -OUR]-OUR. This is how I got 2R.

PL read my uploaded paper?

I would question the factor of 2 in Johnny Lee's derivation. The OTR should not have been modified by the OUR term.

Rob van der Lans proposes adding in the DO probe dynamics. I have done this with a first order model when using a chemical sensor. This was with the easier clean water tests. With respiring systems I think the added complexity and uncertainty introduced by the respiration rate reduces the benefits of modelling the DO probe unless you have transfer rates or slow probes. I was using wastewater level transfer rates where it did not make such a difference.

Hello Lee,

As far as I have read from the literature, OTR=kLa*(C*-CL) only. However, dC/dt=OTR-OUR. If we assume steady state and no accumulation of oxygen inside the bioreactor, under such conditions OTR=OUR. So, kLa*(C*-CL)=OUR. So, kLa=OUR/(C*-CL) and OUR is generally calculated as OUR=qO2*Cx. Therefore, kLa=qO2*Cx/(C*-CL), where qO2 is the specific oxygen uptake rate of oxygen and Cx is the biomass concentration. I would request everyone to please correct me if I am wrong.

Regards,

Sohail

Well, this is straightforward reasoning. At steady state that is. And at ideal mixing. You still need C* and CL. C* is in equilibrium with the actual oxygen concentration in the gas. Depends on gas flow rate, mass transfer rate and medium characteristics. Actual CL can be measured provided the probe is in a proper position and properly calibrated. Oxygen consumption by the probe may lower the reading by depletion of the liquid layer at the membrane (if you use polarographic). So put the probe in the outflow of the stirrer (if you use one) to refresh that layer as much as possible. Use the lower part of the outflow to prevent bubbles to touch the membrane.

The literature is wrong for bubble gassing oxygen transfer, which is why I'm publishing this paper. Pl read. "

In submerged bubble aeration, gas transfer is by means of gas depletion. The difference between the oxygen content of the feed and exit gas is termed "exit gas depletion" or simply "gas depletion". This gas depletion is the gas transferred to the liquid. Without gas depletion, there is no gas transfer, and the input feed gas mass flow rate would be the same as the exit gas mass flow rate. According to the two-film theory advanced by Lewis and Whitman, gas depletion rate is governed by the films' resistance between bubble and liquid, so that when the resistance is high, gas depletion becomes small and the exit gas content becomes large. There is evidence that the gas depletion rate is also affected by any biochemical reactions such as the respiration rate of any microorganisms occurring within the liquid. The hypothesis presented in this manuscript is that the effect of such reactions is a negative impact on gas depletion, so that the higher the reaction rate, the smaller the gas depletion rate, and therefore less gas will be transported or transferred into the liquid under aeration. This paper cites the experiments of three of several investigators on this subject, (Mahendraker et al., Jing Hu, and Garcia-Ochoa), and their results were used to verify and to prove that the above hypothesis is correct. The objective of this paper is to present mass-balance equations that would include the gas depletion effect. The revised equations for the ASCE (American Society of Civil Engineers) testing methods, based on this hypothesis, result in a consistent estimation of the mass transfer coefficient (KLaf) where previously the estimation among the methods using the present equations has a discrepancy of around 40 to 50% between the steady-state and the non-steady state methods. A corollary of this hypothesis is that the difference between the gas depletion rates due to any such reactions is the reaction rate itself. In mathematical terms, F1-F2 = R, where F1 is the gas depletion rate unaffected by any biochemical reactions; F2 is the gas depletion rate in the presence of biochemical reactions in the liquid; and R is the reaction rate or the microbial respiration rate." Bottom line, the clean water test Kla is different from the Kla measured in a respiring cell broth, because of the different gas depletion rates, which is fundamental in oxygen transfer in a bioreactors when the gas can escape in a gas stream exiting the reactor. Hence, dC/dt=(Kla(C*-CL) -R)-R where (Kla(C*-CL) -R) is the OTR.

Regards,

JL

Hello Lee,

Thank you for the reply. How can I agree with you when it has not been published in any peer reviewed journal. As I can see from the literature, nobody has reported what you are saying above. Can you cite any research paper which has published such work.

Regards,

Sohail

Dear Jenny Lee,

Youth starting hypothesis appears to be that the intrinsic mass transfer is enhanced because of biological reaction.

This hypothesis was considered in terms late 1980s in the USA and discarded because the experimental evidence did not support it. The only paper I saw on this was an unpublished manuscript circulated to members of the ASCE committee on oxygen transfer. I had sight of it through my then manager.

Unless I can find that paper I have the weak response that an invited authority has tested and rejected your hypothesis. That is a poor response. But that it has been considered 30 years ago and not gone mainstream is a slightly better argument.

When I have access to a PC rather than a phone I will read your paper and comment further.

Dear Johnny Lee,

Well, your hypothesis is rather revolutionary, as also Jeremy pointed out. And with all revolutionary ideas it will meet some scepticism, as by me.

The oxygen transport path consists of transfer, mixing and consumption. Gas depletion is the result of mass transfer. Mass transfer may be or not be influenced by the broth, including microorganisms. The broth is a very complex fluid with all kind of stuff that may influence mass transfer. Transfer is almost completely determined by the liquid side resistance. Of course, there is no film, that is just a model. The most crucial compound influencing transfer is antifoam. Although used frequently, it is not possible to determine kLa accurately using antifoam. Reports on kLa are NOT reproducible without the very precise description of the antifoam used and how it was added. Most literature state something like 'antifoam was added as needed'. In our own laboratory a linear dependency on yeast concentration was measured once by a student. This ended even up in an European simulation program on yeast growth. But it could be attributed to antifoam addition.

Oxygen gas depletion rate (GDR ) equals OTR and OUR during (quasi)steady state (provided that the same volume is used to 'scale' the absolute values). GDR results in lower oxygen gas concentrations, reducing transfer. Not taking this in account, in fact not using also the gas phase balance, will result in an apparent kLa that is lower than the actual. In fact with a factor 1/(1+(kLa*H)/vGsc*m): kLa (actual value), H (unaerated liquid height), vGsc (height average superficial gas velocity), m (distribution coefficient, about 30). Low height, low mass transfer and high gas flow rate reduce the effect (lab scale). (See 'Gas Transfer' by me on this site)

An increasing biomass concentration means also an increasing amount of compounds influencing mass transfer as stated above.

Literature should be checked on very careful measurements and interpretation. Results can easily be misinterpreted as happened to ourself.

As to Sohail, only parts of this discussion are relevant to you. When reporting your results, present data graphically as relative to a chosen condition. Absolute values are disputable. Refer to Johnny if you like, when he has published his hypothesis. Science should always be open for discussion.

Hi Rob,

Thank you for the reply. It looks like this discussion has become interesting. But I am still not able to get a clear answer to my question. What I have been doing in my case is that I inoculated a reactor with the cell culture, and then started taking the dissolved oxygen reading once it aerated again and then continued with that dissolved oxygen unless it starts decreasing and once it started decreasing, I changed the agitation rate keeping the air flow rate same as before and then again started taking the dissolved oxygen reading at this particular agitation rate and used this dissolved oxygen data for calculating the kLa for my study. I want to know am I doing right approach. I am waiting for your reply.

Thank you!

Regards,

Sohail

Sohail

I see you are trying to maintain a steady-state so that the OTR is always equal to the OUR? When u changed the agitation rate, I presume u INCREASED it? However, increasing the agitation rate is similar to increasing gas flow rate, u still ended up changing one of the system variables and so your kLa is not the true kLa for your design system, since the gas depletion rate has changed when you changed the agitation rate.

To Jeremy

This has nothing to do with the enhancement effect (which has long been discarded as unfounded). This is about mass balance, and the current equation has missed out one important element which is the off-gas which is different in every scenario. (Off-gas is the other side of gas depletion in the same coin).

To Rob:

The air/water system test that Sohail described is the only method on earth available to define kLa in a bulk liquid. It is reproducible if all operating conditions are kept constant. (Standard methods). The difficulty is in the use of this parameter to predict kLa in broth (or wastewater for that matter). Your mentioning of foam is interesting as no doubt it interferes with the measurement of kLa. In the UK (United Kingdom), they used surfactant-added water to mimic the water in bioreactors (or wastewater), so that the kLa determined more closely resembled the water characteristics in the bioreactor.

I would suggest Sohail to filter out the solids in his broth, (so that the respiring cells are eliminated), and then do his re-aeration test, (or his steady-state test), but using my revised equations to calculate his kLa. If his OUR is always changing, he would need to conduct a series of steady-state tests to determine a range of his uptake values.) I bet he would find that a consistent kLa value can be obtained, no matter that the test is steady-state or non-steady test, if he can determine the OUR values at each of his tests. My paper has been submitted to JEE and is under peer review, but you can read it from this website.

Regards,

JL

Hi Lee,

Thank you for the reply. But I have no option other than increasing the agitation rate, otherwise the dissolved oxygen will keep on decreasing as the cells keep on growing inside the reactor with time. So, have to change one of the variables in order to maintain dissolved oxygen. I don't think we can leave the system as such without changing any one of the variables which can help to maintain the dissolved oxygen.

Thank you!

Regards,

Sohail

Sohail

If u cannot help but change one of the variables in order to maintain a constant dissolved oxygen, May I suggest the following:

1/ Use a high gas flow rate to start with (bear in mind that Qa should be height averaged---see Rob's answer) and don't make it too high;

2/ Since the gas flow rate is higher than necessary to start with, u will not have a steady-state in the beginning; but as your cells grow, eventually a steady-state can be reached;

3/ Separately, determine your kLa in an air/water system, with the same gas flowrate, and adjust it if for a contamination factor, usually around 0.8 for wastewater but maybe different for your broth but u can estimate it by another bench scale experiment---one using your broth without the cells and one with ur water only system;

4/ Use the equation dC/dt=kLa(C*-CL)-2(OUR) for the unsteady state, and the equation kLa(C*-CL)=2(OUR) at steady-state. However, OUR needs to be separately measured at each test, perhaps using a respirometer. For ur unsteady test, make sure the OUR remains constant during the test. To obtain kLa, u can either plot the DO vs. time and use Excel solver to calculate kLa, or measure the step changes in the DO to calculate dC/dt at specified time intervals.

Finally, if u can plot the kLa values against Qa (if u can try it for different gas flow rates), there should be a relationship in the form:

kLa = k' Qa^n. If u can determine n, u can estimate kLa for any gas flowrate that u like to establish for ur system.

Hopefully, this will give u a consistent value of kLa for your system for all your tests.

JL

Hi Lee,

Thank you for the reply. Even if I may agree you, but I can't use it practically as I have to determine the effect of agitation rate, air flow rate and different impeller configurations on the volumetric mass transfer coefficient in the presence of cell culture inside the reactor. So, I need to determine kLa for each individual agitation rate, air flow rate and different impeller configurations. That is what my concern is. So, I have use each agitation rate and air flow rate to get the kLa. I hope you understand what I am trying to convey.

Thank you!

Regards,

Sohail

Try to keep the agitation constant and jus vary the flow rate. U do need to repeat with a few flow rates in order to establish the relationship between kLa and Qa.

Hi Lee,

It is not possible to keep the agitation rate constant as the air flow rate doesn't have much influence on kLa when compared to agitation rate.

Regards,

Sohail

In that case, u have to plot kLa against the impeller's rotation speed, and find the relationship that is reputedly an exponential one.

JL

What measurements are you taking?

May I assume

Gas mass flow, in and out

Exit oxygen content

Use of air

Dissolved oxygen. What sensor type?

Temperature

Turbidity?

Rpm

Power draw

Anything else?

From this you can do mass balances. You can decide to do preliminary clean water tests to include sensor dynamics.

Having the mass balance you can get your kla estimates. With repeat tests you can better assess associated error.

Hi Jeremy,

I am taking the measurement of the dissolved oxygen with respect to time. I am using Optical Dissolved oxygen probe and I am using the dissolved oxygen data for calculating the kLa at a particular RPM and air flow rate. I am carrying out all my experiments at 37 degrees.

Regards,

Sohail

If you can add the off gas measurements it may make life easier.

Turbidity could be used as a surrogate to estimate biomass concentrations.

That may help with estimating your growth rates.

Hi Jeremy,

Yes optical density measurements can be used as a measure of the biomass concentration. The more the OD, the more the biomass concentration. But here I am concerned about kLa more as compared to OD.

Regards,

Sohail

what kind of biomass constitution do u have? In the experiment by Mahendraker et al. (2005), they used yeast extract as the synthetic culture, and managed to maintain the DO concentration between 2.5+/-0.5 mg/L in the aerobic reactor at all times, simply by adjusting the airflow rate. This will ensure a common oxygen gradient. Why can't u do the same?

Hi Lee,

I am using E.coli for my study. It oxygen consumption is very high. So, just adjusting the air flow rate won't serve the purpose of maintaining the dissolved oxygen inside the reactor. So, we have to change the agitation rate in order to maintain the dissolved oxygen.

Regards,

Sohail

E. coli in what concentration? what else is in the water?

This paper is useful: https://www.cawq.ca/journal/temp/article/190.pdf

Again, I believe their equation (1) is missing an R term. So their results are off by 50% between the steady-state tests (off-gas and OUR) compared to the non-steady-state tests. If the E.coli grows so fast, why can't u dilute the bacterial concentration to determine kLa first, and then scale up with higher concentrations?

Hi Lee,

It is simple LB broth, which I am inoculating with E.coli to start the culture inside the bioreactor. I use 5 % (v/v) inoculum. The link that you send above is not working. What I have to do is that I have to inoculate the reactor with E.coli and then determine the kLa at different agitation rates and air flow rates. I am adding around 250 ml of inoculum to the 4.75 L LB broth in order to make it 5 L broth. So, I think it is well diluted in the start itself. Hope you get my point.

Regards,

Sohail

So you start with medium only, aerate it until saturation and determine kLa first (nitrogen or gassing in). kLa will be much different from water, but depending on the medium it will be larger or lower. After adding the low amount of biomass you cannot expect a significant change, unless the inoculum contains a different medium. Small amounts of some additives may change kLa considerably. Such as anti-foam. By the way, I think it will be difficult to measure kLa accurately at such low OUR.

Hi Rob,

Thank you for the reply. I think it won't be much different from that of water initially since both the liquids almost behave as Newtonian. Recently, I ran an experiment on a 5 L reactor for the cell culture. I used LB broth as the medium. I inoculated the reactor with 250 ml fresh inoculum and the LB medium inside the reactor was 4.75 L to make it to 5 L. I ran it at 100 rpm and 1 Lit. air/minute. Once I inoculated the reactor, I observed that the DO levels went down abruptly going even in negative values, which I don't understand why it happens to go to negative. They remained almost in negative mode for almost 8 hours and after that it started increasing towards positive values. After around 10 hours, it continuously started increasing which I believe indicates that there is no cell growth going on inside the reactor once the stationary phase has reached. I couldn't understand the negative value of dissolved oxygen. Is it some error with the dissolved oxygen sensor or may be the agitation rate and the air flow rate is too small to maintain the dissolved oxygen inside the reactor. Moreover, I also kept on checking the viscosity of the fermentation broth on hourly basis as the culture was going on, I found that the fermentation broth inside the reactor almost behaves as Newtonian with viscosity almost near to water. Can you please respond.

Thank you!

Regards,

Sohail

Negative DO suggests that your probes are not accurately calculated. It may mean that the DO was low and the intrinsic measuring error of your probest high, even if accurately calibrated. But if consistently negative for 8 hours I would check calibration.

Checking calibration other than two point (0 and 100%) will be a challenge. You are going to need to consult the standards for chemical titration methods unless one of the others looking on knows of something better. You could look around made up mixtures of depleted oxygen. They were used for calibrating gas spectrometers and were relatively ex pensive.

Hi Jeremy,

The probe was added with the electrolyte solution and kept for polarization for some time. there after it was calibrated between (0 and 100%). Then, it was used in the cell culture. May be the probe is the old one.

Regards,

Sohail

Hi Sohail

My hunch is that your air flow rate is too low. Why not try 2~3 lit/min?

Also use Winkler's titration method to determine DO to avoid sensor problems. With a high flowrate and a low microbes concentration (therefore low consumption rate R), u should be able to do a re-aeration test after reducing the DO to say 10% saturation. The re-aeration test would only take a few minutes, ur bacteria should not grow so fast during this period to significantly alter your experimental estimation of kLa. Garcia has done similar experiments as follows:

In Garcia’s experiment, the bioreactor was allowed to reach a steady state before stopping the aeration when the dissolved oxygen (DO) concentration was around 55% saturation. The oxygen uptake rate in the bioreactor was measured by linear regression of the subsequent DO measurements as the DO was continually monitored. The DO would approach zero due to microbial respiration in a linear fashion. The slope of the curve is the oxygen uptake rate (R). This gives an R value of 0.125%.

After the test period (around 5 minutes), the remaining DO concentration was observed to be around 15%. At that point, the aeration was turned on again, and the DO concentration increased until it reached a steady-state concentration, and this concentration was observed to be quite close to the original steady-state concentration prior to the test Cr (i.e 55%). The re-aeration curve was plotted, and the slope of the response curve at any given point was measured to get the dissolution rate, dC/dt, and KLaf was calculated from the mass balance equation using the current ASCE equations.

Note that this becomes a steady state method when C is constant and dC/dt is zero. Alternatively, the data can be analyzed by the integrated form of the basic transfer equation giving the re-aeration plot.

kLa can be determined by interpreting data using Microsoft Excel Solver or similar.

In Garcia’s paper, the KLaf value was reported calculated to be around 0.0057 s-1. Since at steady state, the consumption rate as determined by the respiration rate must equal to the transfer rate, therefore R is calculated by the ASCE equation to give:

kLa = 0.256% s-1

However, this is almost exactly twice the respiration rate as measured by the oxygen uptake rate method using the slope of the oxygen consumption during the air shut-off period.

Since the uptake rate was measured in-situ, believed to be correct, the non-steady state method’s equation must be wrong in terms of predicting the respiration rate R. It would be correct if R is replaced by 2R.

If KLaf in non-steady test is considered a constant, changing only by the effect of wastewater characteristics (α’), α’ is defined herewith as the ratio of the KLa’s (i.e. α’=KLaf/KLa) without the respiring cells, then to have comparable KLaf in wastewater/broth for the steady state, the mass transfer coefficient must be halved in order to match the equivalent KLaf in a steady state method.

This value is then compatible with the previous calculation using the DO depletion plot giving an R value of 0.125% s-1. In the above example, the correct value of R is 0.125% if measured based on the air-off test, or 0.128% if measured from the air-on (re-aeration) test. The correct value of KLaf is 0.0057/s as from the re-aeration test.

To double check, we note that at SS, the OTRf must equal the respiration rate R. Therefore, OTRf = 0.125%V where V is the volume of the bioreactor. OTRf is also given by KLaf (C* - Cr)V – RV as proposed. Using this equation yields OTRf = 0.0057 (100-55)%V – 0.125%V = 0.131%V which is close to 0.128%V and close to the RV value as measured.

The same finding can be obtained using Mahendraker's data. I attach Mavinic/Mahendraker's experiment for your ref. Hope this works.

JL

Hi Sohail

Here is the file by Garcia-Ochoa et al. U can see that their results are off by 50% between their gassing-out and gassing-in tests, see Fig. 6 of their paper.

JL

Those interested at this discussion may possibly want to check also this related RG discussion: https://www.researchgate.net/post/Theoretical_calulation_of_kla_in_bioreactors