Batch sparging, making sense of the numbers

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Kaiser

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In order to better understand batch sparging and the efficiencies that I get with my system, I took some more measurements than usual on my last brew day. Tonight I ran the numbers and it took some time to match the brewday results. The most interesting discovery was, that the wort volume present in the mash tun after the mash is significantly larger (by about 22%) than the amount of water that was added. This has an affect on the calculation of the wort volume that is held back in the grain which affects efficiency. So far I was severely underestimating this volume by calculating it through (water used - wort volume collected). As a result my theoretical efficiency was always higher than the actual and I was wondering where I was loosing this efficiency. But now that I calculated that volume correctly, I found that I match the theory very well.

Here is the lengthy analysis:

* grist weight 5.6 kg
* total laboratory extract of that grist is 80% of 5.6 kg -> 4.5 kg
* water added to mash: 15.5 l (cold)
* extract of the first running in the kettle 22.5% (% extract is equal to Plato)
* volume of the first runnings in the kettle 9.75l at 65C -> 9.6l (cold)
* extract of the 2nd runnings: 11.75%
* volume in kettle after 2nd running: 20l at 75C -> 19.6l (cold)
* extract of the 3rd runnings: 7.4%
* volume in kettle after 3rd running (pre-boil volume): 26l at 90C -> 25l (cold)
* extract in kettle after 3rd running (pre-boil extract): 14.6%

The first analysis was for the extraction efficiency of the mash. The definition of extract percentages is:

(1) E = 100% * m_extract / ( m_water + m_extract)

If we want to know how much extract exist in a given wort of known extract content that has been created with a known amount of water we can do this by rearanging (1) to

(2) m_extract = (m_water * E / 100%) / (1 - E / 100%)

(3) m_extract = (15.5kg * 0.225) / (1 - 0.225) = 4.5 kg

This means that all of the extract available in the grain has been extracted in the mash (100% extraction efficiency). This was confirmed by a negative iodine test of the wort and the spent grain. I.e. no native starch was left.

Since batch sparging was used, a simple model can be used to calculate the lauter efficiency. lauter efficiency * extraction efficiency is the brewhouse efficiency. For that model we need the amount of wort that is held back in the lauter tun after each run-off. But this is not simply the amount of water used for the mash minus the amount of first wort collected because the volume of the wort increases when the extract is dissolved. To get that volume we can use this formula which is the weight of extract dissolved in a given volume of known gravity wort:

(4) m_extract = ( E / 100% ) * SG * V_wort

SG is the specific gravity and it will be estimated with 1+E*0.004.Rearranged to V_wort we get

(5) V_wort = m_extract / ((E/100%) * SG)

(6) V_wort = 4.5 kg / (0.225 * 1.090) = 18.3 l

This means the 15.5 l water and 4.5 kg extract from the 5.6 kg grain made 18.3 l of 22.5% wort. 9.6l of that wort were collected after the first run-off which indicates that 8.7 l are held back in the mash.

Batch sparing is a process of successive dilution of the wort remaining in the grain and running it off. This can be modeled mathematically and has bee analyzed here. But since not all run-offs were of equal size, lets just calculate the efficiency step by step:

The first run-off will extract this percentage of the extract from the mash:

(7) Eff_1st = v_1st_runoff / (v_1st_runoff + v_wort_in_grain)

(8) Eff_1st = 9.6l / (9.6l + 8.7l) = 0.52 = 52 %

If 52% were recovered by the 1st run-off, then 48% of the extract are still in the lauter tun. This extract is dilluted by the sparge water and run off. The volume of the 2nd run_off is 19.6l - 9.6l = 10l and the efficiency of that run-off is:

(9) Eff_2nd = v_2nd_run_off / (v_2nd_run_off + v_wort_in_grain)

(10) Eff_2nd = 10l / (10l + 8.7l) =0.53 = 53%

Using this and the fact that the 2nd run-off was only able to draw from 48% of the extract we can determine the combined efficiency from the 1st and 2nd run off as:

(11) Eff_1st_and_2nd = 52% + 48% * 53% = 78 %

78% of the extract are now in the boil kettle. This leaves 22% in the lauter tun. With a 3rd run off size of 5.4 l we find the efficiency of that run-off as

(12) Eff_3rd = 5.4 / (5.4 + 8.7) = 0.38 = 38%

and the combined efficiency of all 3 run-offs as:

(13) Eff_1st_2nd_3rd = 52% + 48% * 53% + 22% * 38% = 0.86 = 86%

This means that with the given run-off sizes, number of sparges and amount of wort left in the grain, an a lauter efficiency of 86% is to be expected.

The actual efficiency into the boiler is the following:

(14) Eff_kettle = V_kettle * E * SG / (m_grain * 0.8)

the 0.8 represents the 80% laboratory extract of the grain.

(15) Eff_kettle = 25l * 0.146 * 1.058 l/kg / (5.6 kg * 0.8) = 86%

Since the Efficiency is the product of extraction efficiency and lauter efficiency and the extraction efficiency was determined to be 100%, the actual lauter efficiency must have been 86%, which matches the theoretical result very well. As a result no efficiency was lost due to process inefficiencies and to increase that efficiency the following process parameters could be changed:

* more sparge water: this would lead to a larger pre boil volume and longer or stonger boils and may not be desired
* less wort kept in the grain: This mash was done with conditioned malt which makes for a"fluffier" mash. Such a mash may hold more wort and I wonder if an unconditioned mash may result in less wort being held back and thus increasing the efficiency
* equalize the run-offs: the boost expected from that is very low. Se here.
* fly sparging: this method follows a different principle and should yield better efficiencies when done properly. But in addition to more time, it also needs a better lautertun which I don't have.

So, 86% for that beer is fine with me.
 
Wow, just wow. I hope when I grow up, I can understand half of your post's.:eek:
 
Based on similar tests I've done (albeit with a lot less formula) is based on a 1.3qt/lb thickness and a simple runoff (no heat, no infusions), first runnings represent 50% extraction of the available sugar (very similar to your numbers). Now, the following sparge runoffs have depended on whether I do one bulk infusion or two (both 185F each).

With one large infusion runoff is 35% more. (total efficiency of 85%)
With two equal, the combined runoff is 40% more. (total efficiency of 90%)

The lazy man in me uses the PPG given to me in Beertools based on the variety and malster I'm using. It's inexact but I doubt the total efficiency is in error by more than 1/2 a percent.
 
Based on similar tests I've done (albeit with a lot less formula) is based on a 1.3qt/lb thickness and a simple runoff (no heat, no infusions), first runnings represent 50% extraction of the available sugar (very similar to your numbers). Now, the following sparge runoffs have depended on whether I do one bulk infusion or two (both 185F each).

With one large infusion runoff is 35% more. (total efficiency of 85%)
With two equal, the combined runoff is 40% more. (total efficiency of 90%)

The lazy man in me uses the PPG given to me in Beertools based on the variety and malster I'm using. It's inexact but I doubt the total efficiency is in error by more than 1/2 a percent.

Bobby...couple of quick questions:

When you say two equal...are you saying you rinse twice or just that once you drain your initial mash water you only sparge once?

Also...if you were to do multiple rinses...would there be a higher tendancy to extract tannins and how do most people cool there rinsed samples to make sure they are still above 1.010? I guess I could just put a sample in a fridge but I'm looking for a more immediate way to measure
 
how do most people cool there rinsed samples to make sure they are still above 1.010? I guess I could just put a sample in a fridge but I'm looking for a more immediate way to measure

I use a large stainless steel bowl to cool the 100 ml sample. Once it is at 40C I can use the hydrometer and correct for temperature with a table.

It’s easier with a refractometer, but I generally only take post-boil readings b/c I feel that my efficiency is predictable enough that I don’t have to worry about checking where I am during the sparge or before the boil.

The thing with batch sparging is, that you settle on a pre boil volume and number of run-offs before you start. Batch sparging lauter efficiency is predictable and robust (against procedure details) enough to actually do that. If you decide that you want to make another, unplanned, sparge to get more of the sugar, you may have been better off making the previous runnings larger as that will also gain you efficiency but won’t drop the extract and increase the pH of the last sparge so much.

Kai
 
Ok thanks...that makes sense. I think i read somewhere...maybe in an Orfy post...that after the 1st runoffs are done the grain has absorbed all that it can so at that point you could accurately figure out how much you should add for your next sparge to be able to acheive your pre-boil volume....did I understand that properly?

Pre-boil volume seemed to be my one misstep in my 1st AG that I noticed thus far.... batch is currently fermenting away
 
My numbers are much the same. Typically, 50% of the sugars are in the first runnings, 33% in the second and 16% in final sparge. Overall efficiency, high 80's to low 90's.

Teabagging, for small beers and partial mashes, runs 75-80%. This result is in line with single sparges.

I suspect assertions of batch sparging inefficiency are based on single sparges. Since this requires much larger mash tuns, I doubt most people would use the method.

Diablotastic - correct. The grain does not absorb any more water during the sparge. Sparge water in == wort out.
 
Bobby...couple of quick questions:

When you say two equal...are you saying you rinse twice or just that once you drain your initial mash water you only sparge once?

Also...if you were to do multiple rinses...would there be a higher tendancy to extract tannins and how do most people cool there rinsed samples to make sure they are still above 1.010? I guess I could just put a sample in a fridge but I'm looking for a more immediate way to measure

It's two equal batch sparge infusions but I vorlauf and drain each one:
vorlauf and drain mash, infuse, vorlauf, drain, infuse, vorlauf, drain.

I've cooled my 3rd runnings to check the gravity a few times but they ALWAYS come out above 1.010. The only time I'd recommend a single batch sparge is when the intended OG is under 1.040.
 
Thanks to all the vets for answering what must seem like a constant barrage of reduntant questions...I've learned a ton here and this is truely a great resource
 
The 1.010 criteria doesn't apply to batch sparging. My second sparges tend to be around 1/3 the target gravity, so for a TG of 1.050 the final sparge will be around 1.016-18. As an experiment, I've added a third sparge of a gallon or so. Both times, it came out under 1.008 and they were for 1.060+ beers.
 
One interesting observation I made when modeling batch sparging in Excel was that the gravity of the last run-off does not depend on the number of sparges if the pre-boil volume is kept the same and the run-offs are of equal size. I.e. if you run a batch sparge with 1 sparge and collect 2 runoffs of 3 gal each, the gravity of the 2nd run-off will be the same as the gravity of the 3rd run-off in a 2 sparge scenario where you collect 2 gal from each of the run-offs.

At first this surprised me and seemed counterintuitive, but it does make sense.

Kai
 
Seems intuitive to me in that once you infuse and stir, ALL the wort in the tun at that moment has the same gravity (even the stuff that doesn't leave the tun upon draining). I guess the biggest reason for misunderstandings of batch sparging lies in 100 years of fly sparging history. I still contend this is one reason people want to try infusing to mash out in batch sparging. Stop that ;-)
 
I guess I don't really have anything against it if you understand exactly why you do it. It's when someone just does it because they think it's required in the batch sparge process.

If you're willing to use two discrete batch sparge infusions following a direct drain of the mash, you'll probably find that efficiency does not suffer. At least that is my experience. However, you make the sparge temp up in the 185F area and that does the same job to loosen sugars. Skipping the mashout leaves more water for discrete sparging which is important if you like to break it into two small portions.
 
I spent some time this weekend to create a spreadsheet in which you enter grain bill information, total water used and pre-boil volume/gravity. It will then calculate the actual brewhouse efficiency and theoretical batch sparge lauter efficiency.

I run it on a few of my past batches and it seems to estimate the lauter efficiency correct, but one important caveat is accuracy of the measurements. In particular the total amount of water used and the amount of wort collected. It doesn’t work if you didn’t run all the wort into the boil kettle.

I do plan to add some error estimation to the spreadsheet, i.e. you can add confidence intervals (e.g. +/- 0.25 qt) to the measurements and it will also calculate a confidence interval for the efficiency. This way you can see how inaccuracies in the measurements can skew the result.

Give it a try.

Kai
 
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