The goal is proper mash pH. RA was conceived as a means of comparing water sources. It was never intended to be used as means of mash pH prediction. Going further gets complicated pretty quickly.
I thought about this a bit more. It isn't actually that complicated at all so I thought I'd show how one estimates/controls mash pH. RA is sort of buried in there as we shall see. Estimation or control of pH is effected by calculation of the sum of a list of proton deficits, one for each item added to the mash. This sum is
m1*a1*(pHz - pHDI1) + m2*a2*(pHz - pHDI2) + ... + Ab*Nb - Aa*Na + Vw*Qw(pHz,pHs,alk) - r*Vw*([Ca] + [Mg]/2)/3.5
The hardest part about computing this sum is keeping track of what all the symbols mean so you can come up with a number to put in the formula. Let's define the symbols first and then go on to discuss where we get numbers for them
m1 is the mass, in kg, of the first malt
a1 is the linear term in this malt's buffering capacity
pHz is the pH you are either trying to estimate or the pH you want to hit.
pHDI1 is the distilled water mash pH for the first malt
m2,a2 and pHDI2 are the parameters for a second malt, m3,a3 and pHDI3 etc
Ab is the 'amount' of any base added to the mash (or its liquor). Nb is the strength of the base (mEq protons absorbed by a unit amount).
Aa is the 'amount' of any base added to the mash (or its liquor). Na is the strength of the base (mEq protons emitted by a unit amount).
Vw is the volume of the mash liquor (litres)
Qw is the number of protons required to lower the pH of the water from pHs to pHz
pHs is the pH of the untreated water (i.e. no acids or bases added to it)
r is factor that represents the portion of the calcium/phosphate reaction that takes place in the mash tun
[Ca] is the calcium hardness, mEq/L
[Mg] is the magnesium hardness, mEq/L
The obvious way to compute the sum is to assign adjacent cells in a spreadsheet to m , a and pHDI for each of the malts, and to have additional cells where the water parameters (Vw, pHs, alk,r) and the acid and base parameters (Aa, Na, Ab, Nb) can be entered. Then put each of the terms in the sum into a cell in a column at the bottom of which have a cell with =Sum(Ax:Ay) in it which cell will contain the sum. In this way you will have a clear display of what each malt is contributing to the sum, what the acid and base additions are contributing and what the water is doing.
Right below the sum put a cell for pHz. This is the 'master variable'.
Now enter everything you know about the malts, the acids or bases and the water (we'll get to how to compute Qw, Na and Nb shortly) into the assigned cells. Then:
To estimate mash pHz put values into the pHz cell until you find one which causes the sum to equal 0.
To hit a particular desired pHz (z stands for Ziel - the German word for goal) enter that pHz and fiddle with amounts of malts, acids, bases etc until you find value which zeroes the sum.
Excel has a powerful tool called the Solver which does the trials for you and finds the zeroing value(s) automatically.
Now let's look at Qw(pHz,pHs,alk) - r*([Ca] + [Mg]/2)/3.5. This looks pretty close to RA = alk - ([Ca] + [Mg]/2)/3.5 which is Kolbach's definition of RA. Were Qw(pHz,pHs,alk) = alk and r = 1 it would be the RA. Qw(pHz,pHs,alk) obviously depends on pHz and pHs but only weakly. It is almost always right arounf 0.9*alk. r = 1 represents the full proton release at knockout. As we know protons are released in the kettle when calcium is present we must assume that not all the protons are released in the mash but really don't have much insight as to what typical fractions are in the mash. So we use r = 0.5. This is clearly a parameter you can play with. Typically the proton release from the calcium reaction is small so what value you choose for r won't make much difference. So if we define a new RA' = 0.9*alk - ([Ca] + [Mg]/2)/7 we could say that mash pH prediction does indeed depend on residual alkalinity.
To be continued...
