bimr's answer above is correct for the question you have asked but if you won't, can't or don't do it that way, there is another option, that may give you the result you require.
If you are able to test for the nutrient being added, start testing the effluent from the reactor for this nutrient. I assume that it is currently zero or very low. Start adding about 5mg/l(i don't know what you are proposing to add so we start off with a modest amount) to the influent continuously and test the effluent everyday and keep doing this until you see that the level of the nutrient in the effluent stabilise or returns to zero . This assumes that the cell mass is using the nutrient. It it may take weeks before it gets to zero but it may also be very quick. If it does not get to zero but stabilises you can than work out what your dose needs to be. If it stabilises at zero increase the dose and repeat the procedure. This will take some time and there is a risk of wasting some nutrient but it will get ultimately give you the operational result you require.
Regards
Ashtree
"Any water can be made potable if you filter it through enough money"
