help with mash pH calculations

[Hommel]

I’m trying to build an easy to use tool to calc mash pH. i know there are a lot of tools out there but i’d like to build one so i understand how it works and make it work the way i want i've built a bunch already and have saved the most difficult for last! here is one example so you can see what i've been working on (http://www.hommelhomebrew.com/brewdesign/yeast.php)there is a lot of great documentation out there that i’ve gone through (thanks aj delange, martin brungard, braukaiser, john palmer etc…) and i think i have an ok grasp on the calculations required but i want to put it out there and get feedback / input. i searched through the forums and couldn't find a thread that addressed this already so my apologies if this is a repost. here it goes:

to calc mash pH do the following:

1> determine the base malt distilled water mash pH (pHdistilled)
+ only source i have found is in appendix of “the effect of brewing water….” by Kai Troester aka Braukaiser, any other sources greatly appreciated

2> adjust this pH based on residual alkalinity
each 10dH (3.55 mEq/L) of RA changes pH by 0.3 pH (from braukaiser)
RA = KH - ((CH - .5*MH)/3.5)
KH = carbonate hardness
CH = calcium hardness
MH = magnesium hardness

for conversion 1mEq/L = 50ppm as CaCO3 = 2.81 dH

or in ppm (from DeLange) this is:
pHmash2 = pHdistilled + 0.00168 ( alkalinityPpm - ((CaPpm / 3.5) + (MgPpm/7)))

3> adjust pH based on speciality malts

3a> roasted malts
acidity = 40mEq / kg

or pHmash3a = pHmash2 - (kg of roasted malts) * ( 40 mEq / kg ) * (50 ppm / mEq)

3b> caramel malts
acidity = 14 + 0.13*color in EBC

pHmash3b = pHmash3a - (14 +( 0.13) * (color in EBC))*(kg of caramel malt)*(50 ppm / mEq)

4> adjust for acid
acidulated malt = 335 mEq / kg
other liquid acids based on strength.

pH4 = pHmash3b - (mEq of acid) * (50 ppm / mEq)

I'm still getting head wrapped around things and rereading deLange's "understanding Alkalinity and Hardness" and braukaiser's "the effect of brewing water and grist composition on the pH of the mash" are a huge help but it's been a long time since high school biology and chemistry so i'm sure i'm totally mangling a lot of the terminology and basic equations.

Some open questions I can't seem to figure out:
1> it seems like for speciality malts that it is just taking into account weight of that grain but not how big your mash is. from the above calcs 1 lb of caramel 60 would have the same impact on a 1 gallon mash w/ 2 lbs of grain or a 10 gallon mash w/ 20 lbs of grain. this doesn't make sense so what am i missing?

2> same as 1 but for acid

 

[ajdelange]

The proper approach to estimating mash pH involves figuring out how many protons must be supplied to or absorbed from each mash component (water, grain, added acids and/or bases) to adjust its pH from its intrinsic pH (the pH at which it comes to you - examples include mash water pH and the DI mash pH of a grain) to a hpothesized mash pH. In a real mash the absorbed protons are exactly equal to the supplied protons so the sum is 0. Your task in computing mash pH is to find the pH at which the calculated proton deficits (positive number if protons must be supplied and negative if protons are supplied) sum to 0. As it is easy to compute proton deficits for the individual components it is pretty easy to do a spreadsheet which sums the individual deficits and fiddle with the hypothesized pH value until you zero out the deficit sum. Using Excels Solver does this automatically but people seem to run in terror from solver.

All the details are in Predicting and Controlling Mash pH Using Simple Models for Mash Component Acid/Base Characteristics, MBAA TQ Vol. 52, no. 1 • 2015 • pp. 3 - 12 and most of them are at http://wetnewf.org/pdfs/estimating-mash-ph.html. The website also has slides from a presentation to a local MBAA group and a sample spreadsheet.

The only dicey part is getting good malt data. It isn't enough to know the DI pH, you must also know how much the pH changes when protons are absorbed or added. The paper and website go into how to measure this and how to model it as a simple Taylor series about the DI mash pH.

Approaches based on RA, color etc. do work sort of but can't come close to the robust model we're talking about here. The problem with the robust model is that it can't come close to the truth either unless the malt model is good and it takes a lot of work to characterize a malt.

 

[ajdelange]

Some open questions I can't seem to figure out:
1> it seems like for speciality malts that it is just taking into account weight of that grain but not how big your mash is. from the above calcs 1 lb of caramel 60 would have the same impact on a 1 gallon mash w/ 2 lbs of grain or a 10 gallon mash w/ 20 lbs of grain. this doesn't make sense so what am i missing?

2> same as 1 but for acid

Missed this bit. Mass is indeed important. One pound of 80L Briess caramel will, if mashed to pH 5.5, give up 23.9 mEq of acid. One gallon of water at pH 7 which has alkalinity of 100 ppm as CaCO3 will require 6.4 mEq of acid to get it to pH 5.5. If you mix, therefore, 23.9/6.4 = 3.73 gal of this water with 1 pound of this malt you should hit pH 5.5. Thus with malts it is their weights that matter (proton deficit is in units of mEq/kg) whereas with water it is the volume because the alkalinity is expressed in mg/L as CaCO3. Proton deficits are computed for the entire grain mass and the entire water volume as it is the proton deficit for the whole mash system which must be 0.

The proton surfeit (negative deficit) of a strong acid is added to the total sum for all the other mash components. Noting that strong hydrochloric acid is 12.4 N that means that we add 12.4 mEq protons for each mL of the acid.

Suppose we have 5 lbs of Crisp Maris Otter in 3 gallons of the 100 ppm water and want pH 5.5. The malt will need 20.6 mEq, and the water 19.2 mEq for a total of 39.8 mEq - this is for the 3 gallons and 5 lbs mixed. We would then need 39.8/12.4 = 3.92 mL of 12.4 N HCl to get this mash to pH 5.5.

 

[dmr]

There are a couple of papers on the following site that describe the details of models used in several of the calculators out there:

homebrewingphysics.blogspot.com.

You can at least see what some others have done in this regard.

 

[ajdelange]

I had a quick look at the second dmr paper and while I can hardly say that I gave it a careful review a couple of things popped out. The first is that a formula for alkalinity is given as

A = {HCO3-} + {CO3--} + {OH-} - {H-}

This is incorrect as it does not take into account the initial pH of the water nor the end point to which it is titrated. The Correct formula is

A = Ct*(Qc,e - Qc,i) + Qw,e - Qw,i

Where Ct is the total moles of carbo (carbonic, bicarbonate, carbonate) in the water initially, Qc,e is the charge on a mole of carbo at the end point pH (a small negative number), Qc,i is the charge on a mole of carbon at the initial pH (a more negative number) , Qw,e = 10^-pHe - 10^(pKw - pHe) and Qw,i = 10^-pHi - 10^(pKw - pHi). IOW it is the number of protons which are required to
1)Increase the water's (just the water) H+ ion concentration from what it is at the initial pH to what it is at the titration end point plus...
2)Neutralize the difference in OH- ions between the initial pH and the titration end point (where there are fewer)
3)Convert most, not all, of the bicarbonate to carbonic
4)Convert most, not all of the carbonate to carbonic.

Details are found in the water book and at the website I mentioned in an earlier post.

The alkalinity is, thus, the proton deficit of the water. This must be accounted for in predicting mash pH as must every other proton deficit (or surfeit) including the pseudo surfeit that comes from the reactions of calcium and magnesium with malt phosphates. IMO, these should not be combined with the alkalinity measure. With modern understanding there is no reason to do that and it only leads to confusion. One of the main reasons to separate out the metal surfeits is so that one can see how small they typically are. For example in a typical pilsner malt mash using water with calcium hardness of 4 mEq/K and alkalinty of 2 which we set to pH 5.5 with lactic acid the lactic acid is responsible for a pH reduction of 0.18. The (appreciable) calcium hardness only shifts pH 0.05.

Given the RA formula:

RA = alk - ([Ca] + [Mg]/2)/3.5

it is quite clear that 3.5 moles of calcium produces 1 mole of H+ and that 7 moles of Mg are required to do the same. Note that these empirical findings are based on knockout pH, not mash pH and were no doubt derived from the kind of brewing that Kohlbach was familiar with. Reason says that as further proton release occurs in the kettle larger denominator numbers should be used for mash estimates which will, as a result, be a bit higher but as the shifts are small anyway, this shouldn't be a significant part of the error budget. This is the shakiest part of the modern pH estimation algorithm.

I discourage people from following the old approaches without giving solid consideration to the new which is certainly more robust, easier to understand and much easier to put into a spreadsheet. Empiricism does sneak in because we don't have malt data. I appeal to the maltsters in the TQ paper to make the necessary lab measurements for each batch of malt. If they would do that I think we could have very good mash pH predictions.


The second thing that I noticed is that buffering capacities of worts are listed in several places as L/mEq. The correct units are L•pH/mEq (the slope of a pH vs mEq/L curve).