Population balance model

Question

I have some experimental data and I need to make a population balance model to compare the experimental results with. The experimental results are from the bubble size distribution in a bioreactor. I have compared $5$ different population balance models and made a comparison between these and I found the Luo and Svendsen model is most suitable for my problem. But even this model has unknown parameters which need to be determined and I have not much experience in this matter.

I have the experiment result, which they said I need to use to compare the population balance model with and use some of the data to find the population balance equation. And I have the setup of the experiment: the experiment result is the bubble size distribution in a bioreactor, with an aeration of $0.25 \mathrm{vvm}$, an agitation speed of $250 \mathrm{rpm}$ and an oil fraction (in water) of $30\%$ (density= $1230$).

Is it possible to solve and calculate the population balance equations for this case?

Answer 1

I noticed this question after very long time since posted but maybe you are still looking for the answer. Yes, it is possible to use population balance equations your case cause as I understood you want to simulate bubble size evolution dynamics in your bioreactor. Depending upon the kernels you have chosen in your case, you will have to first calibrate your model using your the experimental data and then use it for prediction of bubble size evolution dynamics. In order to calibrate your model,

1. Collect bubble size distribution data (PSD1 and PSD2) at two different time point/space (t1, t2) in the bioreactor.
2. Use your PBE to simulate bubble size evolution over the period of (t2-t1) using PSD1 as the initial condition.
3. Set an objective function to minimising the difference between your PBE prediction and experimental data PSD2, by any suitable optimisation method.

Having this, you will get calibrated parameters to be used in your PBM, and using which you can simulate bubble size evolution in your bioreactor.