I can tell you that Bru'n Water was not amended per AJ's results. That was with good reason.
There's your answer, Jewrican
AJ's results reflect the use of RO or distilled water which has very little alkaliity and I believe that his results are valid. But there is another factor that influences the result when water with more alkalinity is utilized in brewing.
That's true of my lagers but not true of my stouts (Lewis's Irish stout) which I usually brew with straight well water (alkalinity of about 80, calcium hardness about 60, Mg hardness about 50 - AFAIK those are pretty typical numbers). These are the beers that deviate most from the Bru'n water predictions (though the lagers do too). Normally I get 5.55 with this recipe. Last time I brewed it I reduced alkalinity and hardness to 2/3 of the usual values and the pH was 5.6.
The decarbonation of water due to heating affects the water alkalinity. As a more alkaline water is heated, the solubility of CO2 is reduced and that gas is driven out of the water. This results in the calcium carbonate (chalk) that is associated with that alkalinity to precipitate out of solution. This is the process that some brewers can use to reduce the temporary hardness of their water. This results in a two-fold change to the water, the calcium concentration is reduced and the bicarbonate concentration is reduced. This effect does not occur in distilled or RO water since there is very little temporary hardness.
When brewers decarbonate water with heat they bring it to boiling and sparge it with steam or bring it to near boiling and sparge with air in order to drive off the CO2. At mash tun temperature (protein rest) the solubility of CO2 is still half what it is at room temperature (and at saccharification rest temperature 40% or so) but that may be moot at least in my case because the water (being well water) is oversaturated WRT CO2. OTOH is is well undersaturated WRT calcium carbonate. If I drive the CO2 off by boiling/sparging then the pH rises and the solution becomes supersaturated WRT CaCO3 and I get precipitation. This also happens with long standing and I'm sure heat helps move it towards equilibrium quicker but without the sparging I don't believe much CaCO3 is being dropped. That's why brewers, from the day they figured out how to do it, heat to boiling or use lime or some other means to reduce alkalinity. If the hardness and alkalinity are large enough i.e. if the water is, going in supersaturated WRT both CO2 and CaCO3 (e.g.I synthesize Burton water and put it in the HLT) then things are different. CaCO3 does precipitate at mash temperature and, of course, the alkalinity drops. But a brewer will still boil to get as much as he can out.
Even at boiling (at SLP) the solubility of CO2 is about 1/4 which is, in part, why it is unlikely that alkalinity can be brought below 50 by this technique (though you can do better by adding additional calcium before boiling).
The net effect of this phenomena is that there is a mash pH shift due to that decarbonation.
At this point I am getting that decarbonated water produces mashes of lower pH than water that is not decarbonated. No problem with that concept. But I don't think much decarbonation takes place in the mash tun unless the water is close to saturation or supersaturated WRT CaCO3. I suppose if a brewer took alkaline water, mashed in with it cold and then heated it he would get CaCO3 precipitation in the mash tun but it would be a foolish brewer who did that. The object is to get rid of bicarbonate, not incorporate it in the mash as carbonate.
Dozens of mash results from brewers around the country were used to develop a relationship between the net acidity of the mash (grain acidity - water alkalinity) and mash pH. That effect is incorporated into the mash pH prediction in Bru'n Water and its apparently the reason that AJ concludes that the algorithm in Bru'n Water cannot be correct.
No, I say it can't be correct (and I don't really say that - I say it is subject to the limitations of empirical models) because I don't believe you can know the "net acidity" of the system due to the effects of variations in the acidity of the malts from maltster to maltster, from cultivar to cultivar and from batch to batch. For example I once measured the DI water mash pH of Maris Otter at 5.6 whereas the EZ spreadsheet lists it at 5.77. The last time i did stout I got a mash pH of 5.6 so it's clear the DI mash pH of the MO wasn't 5.6. Obviously there is appreciable difference between samples of Maris Otter. And even if you did I doubt that would be sufficient as I think you would have to know the acidity as a function of pH i.e. the titration curve to be able to solve for pH.
But as this is an empirical model it only need fit the data. As you state plainly that the model does not consider any data from me I assume that it doesn't include data from anyone else who brews with RO water or anyone from the Pacific Northwest (where the water is soft and low in alkalinity) and therefore doesn't fit all the data. Thus it is not a useful predictor for people like us. This is what I mean by a limitation in the model. I'm not saying that it can't be improved to fit a broader range of data nor am I even saying that it should be.
The shift in mash pH is about 0.15 units lower due to this decarbonation effect.
It almost looks as if you are saying that, putting the stouts aside for the moment, while Bru'n water underestimates pH for my Pils brewed with Pilsen like water were I to add some alkalinity it would produce a number closer to what I actually see and the reason for this is that the alkalinity would drop out in the mash tun. I have to admit I'm pretty confused here.
For most brewers, they deal with a brewing water with alkalinity. Bru'n Water works very well for them.
How much alkalinity is required? The reason for asking this is that while, as I admitted above, I'm pretty confused here, it seems as if this 0.15 is a bias that is valid when the water is alkaline but not when it isn't which suggests that an adjustable bias of 0.15*alk/alk_max might work.
For brewers working with distilled or RO water, they may see the pH result shifted about a tenth or so higher than predicted by Bru'n Water. I still consider that a pretty good result.
Given that most are using pH meters with accuracies of 0.05 to 0.1 I agree.
The interesting thing is that even though heating decarbonates the water and drives off the CO2, the chalk is left in the water. As AJ can attest, this leaves the chalk delivering only half the alkalinty that it would produce if it was fully dissolved via CO2 dissolution.
If you suspend 100 mg (1 mmol) of chalk in one liter of DI water and take it to a lab with a request for an alkalinity test the lab will add strong acid to it gradually while measuring the pH. After the lab has added 1 mEq of acid the pH will be 8.3 and all ( actually 98%) of the chalk will have dissolved and been converted to bicarbonate. The solution will contain (approximately) 1 mmol of bicarbonate and 1 mmol of chloride (assuming hydrochloric acid was used). Upon adding a second mEq the pH will reach 4.3 which is the usual endpoint and so no more acid will be added and 2 mEq/L will be recorded as the alkalinity (which will be multiplied by 50 to give 100 ppm as CaCO3 as the reported value). Now if you added the first mEq of acid before you took the sample to the lab it would only have to add the 1 more and thus report the alkalinity as 1 mEq/L (50 ppm as CaCO3) because that's all it would take to reach the endpoint.
If you suspend 100 mg (1 mmol) chalk in a liter of water and bubble CO2 through it until all the chalk is dissolved and the pH is brought to 8.3 it will contain approximately 2 mmol bicarbonate - one from the chalk and the other from the carbonic acid formed when CO2 reacts with water. If you give that to an analyst and he adds enough acid to convert all the bicarb to carbonic (reach pH 4.3) it will take 2 mEq of acid to do that - one for each of the 2 mmol of bicarbonate. The analyst will report 2 mEq/L or 100 ppm as CaCO3 as the alkalinity.
Thus chalk suspended in water has the same alkalinity as chalk dissolved in water with CO2 (at pH 8.3) - not half. Chalk dissolved in water using a strong acid (pH 8.3) has alkalinity half that of chalk suspended in water or dissolved with CO2. Pertinent to this discussion is that chalk precipitated from water does not produce a reduction in alkalinity unless the water is separated from the precipitated chalk.
It's late and I'm rambling.