Dear Muhammad: the necessity to add nutrient solution for enhancement of anaerobic digestion depends on substrate used as a raw material for anaerobic digestion and its composition. For example when you apply sewage sludge as a raw materiál, no nutrient amendments are need. Nutrient addition is governed by raw materiál composition.
As said above, if you use sewage sludge or cow manure you do not need any supplements. Supplements help to stabilize the biogas process, if you operate with very high load rates (> 10 kg oTM m-3 d-1) or with a mono substrate like maize, which does not include enough micro nutrients.
This refrence is in German language, but you will be able to understand the tables: www.duesse.de/znr/pdfs/2011/2011-11-10-biogas-03.pdf
Check this one: http://www.biogas.org/edcom/webfvb.nsf/res/Biogas_1_2015_80-84_Wiss_Spurenelemente.pdf/$file/Biogas_1_2015_80-84_Wiss_Spurenelemente.pdf , you can contact the authors Mr. Feher and Mr. Fritz (with my best wishes). They can give you insight to their analysis in this special field.
Hi. As mentioned above, the need of nutrients (nitrogen, posphorous), vitamins, trace metals, will depend on the nature of the substrate (s) being digested. Please give some details of what you want to achieve so we may assist you better.
Dear Muhammad: Different authors pose different relationshions for COD:N:P, because if Nitrogen concentrantion is too high it can cause ammonia inhibition to your process. You can find it as C:O:N or COD:N:P; this is for macronutrients, for trace metals; you can prepare a solution, lookup for the book "Biomethanization of the organic fraction of municipal solid waste" by J. Mata-alvarez.
I agree with Jean-Claude Frigon as mentioned above, the need of nutrients (nitrogen, posphorous), vitamins, trace metals, will depend on the nature of the substrate (s) being digested.
We are still lacking details to help you better. Do you have a characterization of your substrate (C, N, P) ? Any specific conditions for your process ? I am unfamiliar with that specific substrate although we have worked with other ligno-cellulosic substrate. There was some deficiency, notably in phosphorous and trace metals, that would prevent an efficient digestion on the long term. Simply co-digesting with manure was helping the process and provided sufficient nutrient (and constant re-inoculation with active microorganisms).