Batch Sparge Gravities

I've been looking over Kaiser posts but can't figure out the answer to this.

It there a way to figure out the gravity of each running in a batch sparge?
The decline in gravity must follow some sort of curve.

Say my first runnings and two batch sparges are all equal volume and I knew that my total pre-boil wort gravity was 1.042. Using a half-life assumption I'd get:

First Runnings = 1.072
First Batch Sparge = 1.036
Second Batch Sparge = 1.018

That's guessing that each running has half the gravity as the one before, but that is just a guess. Anyone know what that number actually is?

it greatly depends on your system - the amount of dead space in your tun, for example. In my system, for an 'average' gravity recipe, I get approximately 85-90% of my sugars in the first runnings, at a mash thickness of about ~2.5qt/lb - i.e. when I 'no-sparge' by adding in the sparge water before beginning the runoff, my overall efficiency goes down by 10 or 15%

What I'm looking for is a constant in the decline of gravity over a series of lauters that would be proportional to your efficiency (and system), but not dependent on it. I would think it would be contingent on the grains ability to hold sugar from one lauter to the next.



Edit:
It's probably effected by the type of grain and the crush, but I was hoping that some generalizations could be made.

that, in turn, would be dependent on your system, though, would it not? How fine you crushed, how long you let it rest between run-offs, possibly the temperature, whether or not you used a mash-out, whether or not you stir your mash, the geometry of your mash tun (the weight of the column of grains could wring out more sugars).

Such a constant would therefore only be applicable to the system it was measured on, assuming that consistent processes were followed brew after nrew

There are some generalizations made for each sparge round, at least in information I've come across for partyguilling purposes. I remember coming across it when I did that pumpkin partigyle a couple years back.

IIRC the numbers are mentioned in some of the links in my old thread https://www.homebrewtalk.com/f36/lets-partyyyy-gyle-pumpkin-porter-ale-one-mash-74927/ I tihk it's in Randy Mosher's article;

http://www.brewingtechniques.com/library/backissues/issue2.2/mosher.html

There's some tables there it may give you a rough guestimet, or at least help you figure out how to get that guestimate.

This table may help. It give the breakdown of each round based on the OG of the total, but it does it for a 1/3 + 2/3 split or a 50/50 split in partyguile batches.

http://www.brewingtechniques.com/library/backissues/issue2.2/moshertable.html

Great stuff Revvy! It looks like the half-life estimate holds close to true. It's right there on the 1/2 -1/2 split chart and close on the numbers that Mosher comes up with when doing three equal runnings. Thanks.

My simplified math for three runnings went like this:

AG = Average gravity of entire batch
BC = Batch constant

BC = 3 * AG / 7

Gravity of 1st sparge = 4 * BC
Gravity of 2nd sparge = 2 * BC
Gravity of 3rd sparge = BC
(w/ three equal sparge volumes)

Quote Mosher:
Thus, a 16 °P entire batch will yield 5 gal of beer at 24 °P, 5 gal at 16 °P, and 5 gal at 8 °P. Actual gravities will vary from batch to batch, depending on many factors; these estimates provide a starting point only.

Click to expand...

I charted a few of my brews, and they dropped ~50% from mash runnings, 1st sparge, 2nd sparge...

That's been my experience too. ~ 50% each step.

The last batch I checked was 46%, 30% and 24%

All the same volumes?

Tom said:

All the same volumes?

Click to expand...

This wasn't directed to me, but I'll follow up on the OP.

Brewed my first 10 gallon batch Sunday night. Did a double batch sparge with the first running and the two batches sparges being pretty equal in volume. The pre-boil gravities came out close to what was predicted: 1.081, 1.044, and 1.023.

Don't know if what I did was a true partigyle. I did some fuzzy math and mixed the different gravities to get two five gallon batches. One was the normal version of my American Wheat, the other an "Imperial" version. OG's going into the fermenters came withing a few points of predicted, so I'm really happy with two bubbling carboys in the basement.

I think the trouble with trying to model this is that it has to account for so many variables.

Mash thickness and conversion efficiency will dictate first runnings gravity. However, the net sugar that comes out of each running is based on relative volumes.

Let's say 12 pounds of 35PPG grain in 18qts of strike. 12x35= 420. Assuming 95% conversion efficiency you'd get 400GP diluted by 4.5 gallons or 1.089.

Odds are, first runnings would yield 3 gallons leaving 1.5 gals of 1.089 wort, or 134 gravity points.

When you figure out the resulting gravity from the first sparge infusion, the dilution also includes the volume of liquid still in the grain. So, if you sparge 3 gallons, you have 134 gravity points diluted with 4.5 gallons (1.5g absorbed into the grain and 3g added) now even though 3 gallons will come out.

134 / 4.5 = 1.030 so that's the gravity of the 2nd runnings. However, the net sugar out is 1.030 x 3 = 90 gravity units.

Perhaps only variable based on crush. Coarse bits would require a bit more time/stirring to create a completely homogeneous wort.

Sugar in the mash is fully dissolved as Maltose/Glucose etc at the molecular level so it's not a particle that can be filtered out by something as coarse as a wet grist.

Once you stir sparge water in, all remaining sugar in there becomes homogeneous assuming the crush isn't horribly coarse. The sugar you can't drain out as runnings is isolated to the liquid left in the grain and any lauter tun dead space.

Bobby_M said:

Sugar in the mash is fully dissolved as Maltose/Glucose etc at the molecular level so it's not a particle that can be filtered out by something as coarse as a wet grist.

Click to expand...

Thought that this was the case, but was reaching for straws because my first runnings come out lower and later ones higher than the math would indicate.