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Batch Sparging Theory

This post is intended to serve primarily as documentation for the Batch Sparging Calculator. If you’re looking to skip to the end of the page, head over that way instead.

One great thing about batch- or no-sparge brewing is that it’s fairly easy to predict lauter efficiency, and with good results. This is due to the fact that in batch sparging, the actual mechanics of the lauter tun – the way that wort flows through the grain bed – are neglected. Some of the wort is drained, and a set fraction is left behind in the tun. We begin with a few assumptions:

  • Conversion efficiency is 100%.
  • Conversion is complete before lautering begins.
  • No additional grain is added during lautering.
  • Each infusion is fully drained, less any deadspace.

The lauter efficiency is then a simple ratio of the two wort fractions:

E = V1/V0

Where E is the lauter efficiency, V1 is the volume run off to the kettle, and V0 is the total strike volume in the lauter tun. As a practical matter, efficiency is maximized when the tun is drained as completely as possible, and so the volume run off is equal to the infusion volume minus the volume absorbed by the grain and any deadspace that can’t be drained:

V1 = V0 – Va – Vd

There is one additional factor that must be considered, and that is the expansion of the wort due to dissolved sugars. When measuring the volume and gravity of the wort, the apparent extract will be less than the estimated efficiency. We can compensate by defining an expansion coefficient, C, which is the inverse of the wort specific gravity:

C = 1/SG

When it comes to analytically determining the expansion coefficient, however, we encounter a Catch-22: the efficiency determines how much extract is in solution, but the amount of sugar extracted also depends on efficiency. In practice, the calculator just takes a brute-force numerical approach of iterating the efficiency calculation three times, approximating the expansion coefficients. The full expression for lauter efficiency is therefore:

E = CV1/(V1 + Va + Vd)

For a no-sparge beer, this is all that is needed. When considering one or more sparges, however, we have to add the extract contributions from the additional infusions. The extract available for sparging is, by definition, whatever remains after draining the previous infusion(s). This is the complement of the lauter efficiency:

(Va + Vd)/(V1 + Va + Vd)

And so the overall efficiency contribution of the n-th sparge is:

En = Cn(Vn/(Vn + Va + Vd))*((Va + Vd)/(Vn-1 + Va + Vd))

Summing the individual extract efficiencies gives the overall lauter efficiency. Expanded to four terms (three sparges), which is about the most that would ever be reasonable, the expression becomes:

E = C1((V0 – Va – Vd)/V0) + C2((Va + Vd)/V0)(V2/(V2 + Va + Vd)) + C3((Va + Vd)/V0)((Va + Vd)/V2)(V3/(V3 + Va + Vd)) + C4((Va + Vd)/V0)((Va + Vd)/V2)((Va + Vd)/V3)(V4/(V4 + Va + Vd))

Which I realize looks ridiculous written out like that but is computationally really straightforward.

With that done, all that remains is to multiply the efficiency by the (apparent) total extract, and divide by volume to get gravity. If you look at the source code for the calculator you’ll see that everything else is just parsing input and prettying up the results for output.

By the way, this is nothing new; batch sparging analysis has previously been taken up by Ken Schwartz and Kai Troester, among others.

Batch Sparging Calculator

Like many brewers, I use recipe software (BeerTools Pro in my case) to design recipes, log notes, track inventory, etc. And I really like it; the only thing it won’t do is estimate my efficiency based on the actual mash parameters. Hence this little tool, which does exactly that (and pretty much only that). For documentation, please see Batch Sparging Theory.
 

Mash Parameters Infusions
Grist Mass: lb
kg
First Infusion: gal or L
Post-Boil Volume: gal
L
Second Infusion:
(First Sparge)
gal or L
Potential Extract:
(AICG; Default 77%)
%
point-gal/lb
Third Infusion:
(Second Sparge)
gal or L
Lauter Deadspace:
(Default 0)
gal or L Fourth Infusion:
(Third Sparge)
gal or L

If you have any feedback on the calculator, feel free to contact me.

Batch 100 (and 101)

Last week, without any real pomp, I brewed a couple beers for that thing in the desert. Turns out they were my 100th and 101st batches of homebrew. Yay! They’re both finished – or at least they’d better be, since I’m kegging them today. I had to use Wyeast 1056 (courtesy of DBC) for the [...]

10K, Bitches!

Obviously I haven’t updated in a long time. For the most part, that’s because my brewing equipment is packed up in expectation of moving somewhere or other. Pretty much all I’m doing these days is running in the mornings and trying to avoid heat in the afternoons.

Anyway, I ran 10 km this morning. Probably [...]

Success Sits on a Sliding Scale

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Name: Track 096 Date: Jun 5, 2013 9:41 am Map: View on Map Distance: 1.51 miles Elapsed Time: [...]

A Tale of Two Yeasties

Brewing test batches isn’t necessarily a whole lot of fun, but it does lend itself to some potentially useful experimentation. Throughout my (home) brewing career, I’ve bounced more or less randomly from one Belgian strain to another, in the process collecting most of the common strains, but without really settling on a “house” yeast. For [...]

The $30 Electric HLT

It is exactly as dangerous as it looks.

Heat sticks are becoming popular among home brewers, and for good reason. Having two heated vessels really streamlines a brew day, and makes double brew days significantly less painful. And the economics of electric heat are compelling (in fact, that’s the way I’ve decided to go [...]

Stuffed Shrooms

Shaved Parmesan doesn’t work quite as well as shredded.

A recipe that doesn’t involve beer?! I know, I’m in danger of becoming a well-rounded person. These are delicious, though, and very easy to make, and quickly becoming my go-to appetizer for guests. If you have access to Trader Joe’s, they sell a can of all-claw [...]

Draft System Balancing, Revisited

Just a quick note. While I was doing some calculations for Two Mile, I decided to expand on a year-old post on draft system balancing, primarily just to include the relevant results for longer draft systems. Enjoy.

Or not. It doesn’t really affect me either way.

[...]

Burning Beers 2: Electric Boogaloo

I haven’t posted in… let’s see… six months. Yikes. Here’s a quartet of beer recipes, though, so that’s basically the same as posting almost once per month.

10.2 Mk2: I’m still struggling to get the attenuation I need out of my Belgian-style “Blond” (I use quotation marks because BJCP-wise, it would be a Belgian Specialty [...]