Batch sparging, spread sheet experiments

[Kaiser]

This is an article that I wanted to write for a wile now. It deals with the mathematical modeling and analysis of Batch sparging. Though done before, I haven't seen one yet that focusses more on graphs than on formulas.

It' was pretty interesting to see how the efficiency in batch sparging is limited and that, with my last batch, I reached 96% of the theoretical max efficiency for my receipe.

Kai

 

[DeathBrewer]

looked through it a little bit. pretty awesome as always, kaiser. i'll have to read it more thoroughly after my session is done.

 

[Got Trub?]

Excellent article Kaiser. I'll need to go back and compare my efficiencies to theoretical. I just did a 1.070 Helles and ended up with 73% brewhouse eff but needed a 120min vigorous boil to do so as my volume was 8.5g. For my session beers I'm at 80% with a 60min boil of 7g.

GT

 

[Sixbillionethans]

Nice work on the article. Definitely bookmarked for further reading.

Although you didn't list references, I'm guessing you took some of the theory from Ken Schwarz's work available online.

I recently switched from partial-mashing (limited by 5 gal brewpot) to all-grain and subsequently totally overhauled by brew spreadsheet to accomodate the increase. Part of my new spreadsheet was to include the theoretical mash efficiency based on many of the same (or quite similar) variables that you have considered here.

Just going thru the math helped me a great deal to understand where losses in mash efficiency probably come from. I think a lot of the "why is my efficiency low" questions could be answered if people took time to understand the science.

My next few brews will be interesting as I validate the models I included in the spreadsheet.

Very cool to see other math-inclined brewers considering some of these theories and putting them into use. What a great hobby. Thanks!

 

[Kaiser]

Although you didn't list references, I'm guessing you took some of the theory from Ken Schwarz's work available online.

I only glanced over his article and actually did a lot of the experiments before I came across his article. But he is only one of many since most scientific inclined brewers may have been thinking the same as batch sparging is so easy to model.

Very cool to see other math-inclined brewers considering some of these theories and putting them into use. What a great hobby. Thanks!

Maybe you can help me finding the limit of this infinite sum

SUM (n = 0 -> inf) (A/B)^n

with A < B

This is an equation at the core of the batch sparging efficiency and it will determine the absolute max batch sparging efficiency. I haven't bothered much with spending time on this as it's knowledge doesn't add much value. It would only be nice to know.

I wonder if there is an on-line list of all sorts of SUMs and their limits

Kai

 

[ohiobrewtus]

that makes my brain hurt

 

[salzar]

Its a geometric sum. If i remember correct the answer should be 1/(1-(A/B)).

 

[Kaiser]

Its a geometric sum. If i remember correct the answer should be 1/(1-(A/B)).

That's the pointer I needed "Geometric Sum".

Thanks,
Kai