SIr,

1. In ur study, agitation was not working means ur system was in anaerobic but generally agitation provides slowly aerobic cond. while u prefer to operate agitation.

2. for considering mathematical modeling is for to get optimization of process variables required for ur working system.

3. if u fix the conc. of micronutrients and u know the conc. of micronutrients before and after process, which one is essential and how much can be utilized, so that u can select ur different variables with respect to various parameters to run the process at optimized condition.

4. Use the statistical software tools to optimize the variables and choose the best model that fit to ur work. i.e design experimental models.

Dear Jodany,

I understand that your AD reactor consists of several mixed compartments. If each compartment would be completely mixed (which seems not be in your case), then the appropriate basic model would be Continuously Stirred Tank Reactors (CSTR's) in series. Please also note that Residence Time Distribution (RTD) shall be considered which is not the same as the theoretical HRT for plug flow. In a single CSTR most of the liquid will reside far less in the CSTR  than the theoretical HRT.

As to proceed in practice, I would recommend to first upgrade your mixing system as to ensure that complete mixing is achieved in each compartment.

I think, for your case, you can use numerical simulation of unsteady mass transfer . Otherwise, you may apply partial differential equation of transportation to your case.

Dear Jodany,

I aggree with Bruno. A tank in series model should be reasonable.

However, I guess it is quite difficult to find one distinct solution to the problem. I believe that the nutrients are consumed during the passage throughout your reactor compartments and without knowing the kinetics of the consumption reactions it will prove quite difficult to find the correct kinetic reaction model. Also to properly model the system you need to have some information on the kinetics of the biomass so some concentration of cells in the reactor compartments.

Of course you could lump all the compartments into one CSTR and use some pseudo-kinetics to model the overall consumption of your micronutrients. But since they are consumed by biomass you at least need some measure of biomass concentration as well.

There is a book on chemical engineering by Ingham that deals with this kind of modeling also for biological reaction systems. Maybe you can get your hands on it.

Chemical Engineering Dynamics: An Introduction to Modelling and Computer Simulation, Includes CD-ROM, 3rd, Completely Revised Edition

John Ingham, Irving J. Dunn, Elmar Heinzle, Jiri E. Prenosil, Jonathan B. Snape

Finally Bruno is quite correct when it comes to appropriate values of the fluid residence time. Even though the mean residence time that you get when you divide the reaction volume by the average flow rate is a good measure of magnitude, the residence time of individual fluid parcels may differ significantly. An easy way to check that is a trancer experiment during an abiotic run. Just run the reactor without  biomass and add some salt to it at the inlet. Then record the conductivity of the solution at the exist. You should see after some amount of time a peak of conductivity that is due to the tracer applied at the inlet. The peak value is an estimate of the "true" average residence time. Also the peak form gives some inside into how strong the variation of residence time ist.

Best regards and good luck with your research,

André

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