Example Scenario:
1) 6 gallons of cooled wort collected post boil
2) Cooled Pre boil wort pH = 5.5
3) Cooled post boil wort pH = 5.3
4) Target cooled post boil wort pH = 5.0 prior to pitching yeast
6 gallons x 3.7854 ~= 22.7 Liters
Moles of hydronium ions present (per Liter) for the initial post boil pH 5.3 wort = 10^-5.3 = 0.000005012
Moles of hydronium ions desired (per Liter) when at the target of pH 5.0 = 10^-5.0 = 0.00001
Moles of current Hydronium ion deficiency post boil (per Liter) = 0.00001 - 0.000005012 = 0.000004988
22.7 Liters x 0.000004988 moles/Liter deficiency = 0.000113228 moles of overall H+ deficiency
It seems to me that the goal is to supply sufficient acid to cover this overall amount of moles of H+ deficiency in order to move the wort from 5.3 pH to 5.0 pH before pitching the yeast. This should be a function of the molar concentration (or normality) of the acid.
I have a more empirical idea.
About 3 years ago, I developed a spreadsheet based Sauergut calculator for my longtime collaborator The Beerery. He had been using Sauergut for a while and we wanted to incorporate that capability into our shared spreadsheet.
We went to Kunze, whose sections on biological acid are great and very current, yet based firmly in observations and values from Kolbach’s time.
The basic dosing information is as follows:
A biological acid solution with Lactic acid % of 0.8% will drop the pH of the mash by 0.1 when dosed at 60 ml/kg of malt used and 0.1 pH of the boil when dosed at 30 ml/kg of malt.
Just a quick note before equations and math and theorizing: you can’t treat Sauergut like Lactic acid in the normal sense, i.e. you can’t plug low acid percentages into a Lactic acid calculator and expect sensible values for Sauergut amounts. However, you can use the biological acid’s Lactic acid percentage and the above equations to reliably predict Sauergut amounts. Remember this as it may come in handy.
I can’t access the original equation right now but I will post it here when I can.
Move forward 3 years and The Beerery and myself were talking about how to help him with his automation and auto Sauergut dosing and we wanted to be able to enter 2 pH values, find the Δ and then give us the ml amount of Sauergut required. The original equation gave a Δ pH output.
So I did some algebra and reorganized the equation:
Sauergut (ml) =(((Δ pH/0.1)*(60*Total kg))/Sauergut Acid %)*0.008
The 0.008 factor corrects for values higher than the 0.8% in the above dosing rates.
Now full disclosure: I have never proposed or tried what I am about to theorize.
Let’s say that we would like to take a Grist pH of 5.75 down to 5.40 and we are using Sauergut with a Lactic Acid % of 1.8%. Our Grist consists of 5.67 kg of malt:
Sauergut (ml) = (((0.35/0.1)*(60*5.67))/0.018)*0.008 = 529.2 ml
Now remember when we said before that modeling Sauergut with Lactic Acid equations using normality and such don’t work well? Well we shouldn’t have that problem here because these dosing rates and this equation doesn’t factor that stuff in.
Here we enter the purely hypothetical as I’ve not tested or discussed this before.
Let’s say that for the same mash as above, we measure 5.40 pH in the mash and near flameout in the boil we measure 5.30 pH. We would like to use 88% Lactic Acid to drop the pH to 5.00 at flameout. We are going to change the equation slightly to reflect the 30 ml/kg above.
Lactic Acid (ml) =(((0.3/0.1)*(30*5.67))/0.88)*0.008 = 4.64 ml
Viola?!?!
Seems logical to me.
EDIT: Keep in mind this only works for Lactic acid and I did not notice AJ’s more robust treatment above. Take my post as an interesting tidbit. Ive been curious for some time if the Sauergut calcs could be used in the opposite direction so not an altogether worthless exercise after all if it works.