How can we make a mathematical model for tracking micronutrients in an anaerobic system (Bioreactor) that has different chambers. The feeding ( Sargassum spp.) inters in the first chamber and should pass through the system 'til the last chamber. We know the concentration of micronutrients( Fe, Ni, Co, Mo, Zinc, Mg, Mn) in the feeding. And we have data (measure the concentration of micronutrient at the end of the system) on the effluent(out). We know normally how long takes(times) the feeding(HRT: hydraulic retention time) comes from the first chamber to the last chamber. How can we make a math model for this system if it is not stable(we never reach the steady state? Thank you for your help!

N.B: We din't reach the steady state because the agitation was not effective. Because the system set up for the agitation was not working as desired.

As per my knowledge, you can use numerical simulation of unsteady mass transfer. Or else you may try partial differential equation of transportation.

As per my knowledge, you can use numerical simulation of unsteady mass transfer. Or else you may try partial differential equation of transportation.

 

Yes agreed, both those approaches are valid although the system is complex so I expect you will need numerical methods to solve either the simulation or the analytic solution.

 

You should start by drawing a proper process diagram, including all the variables and fill in the known relationships.

This will help order your thoughts and enable suitable approximations to be made to develop and simplify the overall analysis.

 

Then you can separate your analysis into the part which tends to a steady state and the transients which introduce instability and compare their relative effects.

 

But much more information is needed to describe such a complicated system.