Partial Boil Kettle Sour

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catman

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I have a wort in my kettle currently souring. When it’s reached desired pH, the plan is to bring it to a boil, add more DME, cool, and top off with water. I’ve been able to find online calculators to determine what the pH of a solution is after diluting with water. But because I’ll also be adding DME after the souring is done, I’m not sure how to determine my target pH.

Put another way: suppose I have a wort of pH x and volume v. I add p pounds of DME and volume y of water. How do I calculate the final pH?
 
I’ve been able to find online calculators to determine what the pH of a solution is after diluting with water.

Those calculators (at least the ones I know) are only valid for an ideal solution that contains only "strong" acids. Or, they cover simple "weak" acid solutions. Wort is mostly not a solution of strong acids. And it's not a simple solution of weak acids. Perhaps counterintuitively, it's much harder to change (and predict the change of) the pH of beer wort by dilution than it is to change the pH of a strong acid solution by dilution.

But because I’ll also be adding DME after the souring is done, I’m not sure how to determine my target pH.

Which makes it even harder.

Put another way: suppose I have a wort of pH x and volume v. I add p pounds of DME and volume y of water. How do I calculate the final pH?

You really can't. It's not really the pH of that wort that matters. It's the buffering capacity that matters most in this scenario. But, you can measure the result with a pH meter.
 
You really can't. It's not really the pH of that wort that matters. It's the buffering capacity that matters most in this scenario. But, you can measure the result with a pH meter.
I came across this. Are the methods here not applicable? The idea would be to treat the addition of DME and water as the addition of a wort of pH ~5.6
 
I came across this. Are the methods here not applicable? The idea would be to treat the addition of DME and water as the addition of a wort of pH ~5.6

No, none of those examples consider the buffering capacity of wort, let alone a soured wort. But if it helps what you're doing at all, I once measured a sample of soured wort at a pH of 3.49. I then doubled the volume by dilution with distilled water, and the pH did not move. When I tripled the original volume by dilution with distilled water, the pH increased to 3.50, which is an insignificant change and possibly nothing more than noise in the measurement. The point is that it's very hard to move the pH of a soured wort by dilution.
 
A ballpark method to determine the pH shift might be conceived as follows:

Question: What would be the new pH if we tripled the volume of a presently 3.5 pH beer with a measured and confirmed Wort buffering capacity of 40 mEq/Kg_pH via adding DI water?

1st, what would the pH of the diluted beer be expected to be if there was no buffering capacity at all?

Molar H+ concentration (initial) = 10^-3.5 = 0.000316228

New molar concentration of H+ after tripling the volume = 0.000316228 / 3 = 0.000105409

New pH for the case of no buffering capacity = -Log(0.000105409) = 3.977

pH shift for no buffering = 3.977 - 3.5 = 0.477 pH points

2nd, what is the pH shift with buffering capacity applied?

Buffer is diluted by a factor of ~3 due to the 'Kg' factor in its units denominator, so is now:
40/3 = 13.333 mEq/Kg_pH

Buffered pH shift estimate = 0.477/13.333 = 0.036

Final pH estimate after 3-fold dilution with DI water = 3.50 + 0.036 = ~3.536

Disclaimer: I'm not quite sure that it actually works quite this way for buffering and pH shift, thus consider this as purely a ballpark method until someone with knowledge in this arena of expertise comes along.
 
@VikeMan is correct in mentioning "none of those examples consider the buffering capacity of wort, let alone a soured wort". Since lactic acid increases wort buffering capacity, the buffering capacity of a lactic acid soured beer would be measurably somewhat higher than the buffering capacity of a standard beer, so if 40 is typical of a standard beers buffering capacity, a soured beers buffering capacity would be greater than 40 to some degree, and the final pH shift for three fold dilution for that case would be somewhat less than for my example above.
 
The regression analyses suggested that the buffering capacity of wort linearly increased with an increase in the level of organic acids,including acetic acid, lactic acid, citric acid, succinic acid, furmaric acid and pyruvic acid in wort.
Organic acids contributed substantially to the buffering capacity of wort.
Phosphate, which has been said to be responsible for some of the buffering capacity of wort, was found to be an ineffective buffer at the pH of wort.
https://www.onlinelibrary.wiley.com/doi/epdf/10.1002/jib.286
Thus lactic acid additions to wort substantially contribute to increasing the initial buffering capacity, and phosphoric acid additions to the wort do not. Beer is "soured" via adding lactic acid. So soured beer has an even higher buffering capacity than regular beer.
 
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No, none of those examples consider the buffering capacity of wort, let alone a soured wort. But if it helps what you're doing at all, I once measured a sample of soured wort at a pH of 3.49. I then doubled the volume by dilution with distilled water, and the pH did not move. When I tripled the original volume by dilution with distilled water, the pH increased to 3.50, which is an insignificant change and possibly nothing more than noise in the measurement. The point is that it's very hard to move the pH of a soured wort by dilution.
Is it safe to assume that the effect on pH of adding wort to soured wort would be less than the effect of adding water, since the former is acidic?
 
Is it safe to assume that the effect on pH of adding wort to soured wort would be less than the effect of adding water, since the former is acidic?

All wort is buffered. Due to its buffering capacity, you may actually find dilution via wort to be more effective in moving the pH of a sour upward than for simple dilution with unbuffered water. This would require experimentation whereby an acidic sour is split into two portions, with one diluted by water and the other diluted to the same volume extent by the addition of a less acidic wort, and the pH results are compared.
 
Is it safe to assume that the effect on pH of adding wort to soured wort would be less than the effect of adding water, since the former is acidic?

Wort has some considerable buffering capacity. Distilled water has none. So a wort addition would have more impact on the soured wort's pH than a distilled water addition. Don't be distracted by distilled water's nominal pH of 7.0 (or a little lower when CO2 from the air is dissolved), It's very different than a solution of acids and bases that has settled at, say, 7.0 (or wherever).

But what you really want to know is how much the added wort is going to change your soured wort's pH. While I don't know of a wort pH model that I would necessarily trust down in that range, my guess is that for an "average" soured wort at 3.5, with and equal volume addition of "average" non-soured wort you're probably looking at an increase in pH of something less than 1.0.

But the way to find it is to actually try it and measure it. The result should be fairly repeatable, given the same recipe and process.
 
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