It is assumed that 1Kg of soluble COD produces 0.5Kg biomass in aerobic degradation whereas in anaerobic degradation 1Kg of soluble COD produces only 0.1Kg of biomass.
To give a more specific answer you will have to tell us more about your aerobic system i.e. is this in an activated sludge reactor or in aerobic digestion of sewage sludge? in an activated sludge biological reactor, there are steady state models that are used to model the bioreactor processes and they help you calculate the mass of sludge (kg) you will get based on the biodegradable COD load to the bioreactor. all you need to calculate the mass of sludge in the system is the characteristics i.e. parameters COD, N,P etc. entering your system.
there are also models (I've attached) to help you model an aerobic digester and calculate the mass of sludge to be produced.
so the assumptions like kg soluble COD would produce this so and so biomass may be acceptable but they are merely assumptions which don't take into account very fundamental and important factors. so models kind of like come close to simulating what happens in real life of a bioreactor or digester as they are formulated based on the behaviour of the system and bugs (bacteria) doing the job.
Please see the attached resources, I believe you'll find them useful.
The stoichiometric value is 0.67 kg of COD (biomass) per 1 kg of COD removed. However, as Hopewell Molefe is pointing, this value depends on the specific characteristics of your process. For example, the sludge age and the wastewater biodegradability are crucial factors.
It is assumed that 1Kg of soluble COD produces 0.5Kg biomass in aerobic degradation whereas in anaerobic degradation 1Kg of soluble COD produces only 0.1Kg of biomass"