I've been checking the
lautering efficiency and got a couple questions, about it:
For a double batch sparge (2 sparge steps) the efficiency would be:
Eff_1st_runoff= 100% * V_1st_runoff / (V_1st_runoff + Vgrain_absorption + Vdead_space)
Eff_2nd_runoff= (100% - Eff_1st_runoff) * V_2nd_runoff / (V_1st_runoff + Vgrain_absorption + Vdead_space)
Eff_3th_runoff= (100% - Eff_1st_runoff - Eff_2nd_runoff) * V_3th_runoff / (V_1st_runoff + Vgrain_absorption + Vdead_space)
and the overall lauter effiency would be:
Lautering efficiency = Eff_1st_runoff + Eff_2nd_runoff + Eff_3th_runoff
do I'm right?? also squeezing the bag won't affect the Vgrain_absorption??
and about this formula
mextract_left_in_lauter = (Vwater_added + Vgrain_absorbed) * sg * extract
the
extract is no more than "mgrain * egrain", right, just gonna be sure to get it all right
I really admire Kai Troester's writings, and I have probably learned more from him about brewing than any other single author. But that said, I find some of his formulas and derivations somewhat obtuse and difficult to follow, and the lauter efficiency exposition I find very confusing myself. I mean no disrespect to Kai, and others may find his formulas more intuitive than I do. So, let's forget what Kai says about lauter efficiency, and start from scratch. This may or may not be better than Kai's approach, but I find it easier to follow.
Also, sorry for the delayed response, but I knew this post was going to require significant effort and time, so I put it off until it was more convenient for me.
All of the equations/formulas given below are valid in both imperial and metric units, which is not the case for those give by Troester. Any volumes involved should all be thermal expansion adjusted to a constant temperature, and for reasons I won't go into, 68°F (20°C) is recommended. The density of water at 68°F (20°C) is 8.33 lb/gal or 0.9982 kg/L.
Let's start by reviewing the general definition of efficiency, that applies to pretty much anything:
Efficiency = Amount_Actually_Obtained / Maximum_Amount_Available
[Eq. 1]
The equation above is for fractional efficiency, and to convert to percent efficiency you multiply fractional efficiency by 100%. When multiplying efficiencies it is necessary to work with fractional efficiencies, so percentage efficiencies need to be divided by 100% before multiplying.
When it comes to brewing efficiency, the "Amounts" we are interested in are Weights of Extract. Extract is mostly sugar (including dextrines), but also contains proteins, and many other minor components. In some cases we can use volumes in the efficiency formulas if the concentration of the liquid is the same for the numerator and denominator. Gravity points, which are just a proxy for weight, can also be used in many cases.
So let's look at some definitions for some of the efficiencies of interest in brewing. Unfortunately, the terms used by different authors and in different segments of brewing are not always the same, which can lead to confusion. But, if you truly understand the definitions and concepts, you can usually determine what a particular author is referring to. In the following definitions and formulas, Extract always refers to Extract_Weight. Modifiers will be used to describe which particular Extract_Weight is being referenced.
Conversion Efficiency is defined as:
Conversion_Efficiency = Extract_Created_in_Mash / Total_Potential_Extract
[Eq. 2]
Total_Potential_Extract is the sum of the extract potentials for each of the items in the grain bill, i.e.:
Total_Potential_Extract = Sum(Weight_1 * Yield_Potential_1 + Weight_2 * Yield_Potential_2 + ... + Weight_n * Yield_Potential_n)
[Eq 3]
Where Yield_Potential is the dry basis, fine grind fractional yield potential for each grain, usually about 0.8 or 80% for base grains. Since most grains have about 4% moisture, the as-is weights should be multiplied by 0.96 (or whatever the appropriate value is for actual moisture content) to obtain the most accurate extract potentials (although many calculators neglect to do this.)
Lauter Efficiency is defined as:
Lauter_Efficiency = Extract_in_BK / Extract_Created_in_Mash
[Eq. 4]
Or fraction of the extract created in the mash that makes it into the boil kettle.
Mash Efficiency is defined as:
Mash_Efficiency = Extract_in_BK / Total_Potential_Extract
[Eq. 5]
Mash_Efficiency = Conversion_Efficiency * Lauter_Efficiency
[Eq. 6]
Brewhouse Efficiency is defined as:
Brewhouse_Efficiency = Extract_in_Fermenter / Total_Potential_Extract
[Eq. 7]
In order to actually calculate any of the efficiencies above, we need to be able to measure the weight of the extract at various points in the process. But, measuring extract weight in a solution is difficult, so what can we do instead? Two items that are relatively easy to measure are volume and specific gravity (SG), and it turns out we can use these two values to calculate extract weight, as well as water weight in any volume of wort.
Wort_Weight = Wort_Volume * Wort_Density,
[Eq. 8]
Wort_Density = Water_Density * SG, so
[Eq. 9]
Wort_Weight = Wort_Volume * Water_Density * SG, and
[Eq. 10]
Wort_Volume = Wort_Weight / (Water_Density * SG)
[Eq. 11]
Once we know the wort weight, we can determine the extract weight if we know the weight percent of extract in the wort. It turns out that weight percent (Wt%) of extract is just the °Plato (°P):
°P = 100° * Extract / (Extract + Water_Weight)
[Eq. 12]
°P = 100° * Extract / Wort_Weight
[Eq. 13]
And there is an equation that we can use to convert SG to °P, which is:
°P = 1111.14 * SG - 630.272 * SG^2 + 135.9975 * SG^3 - 616.868
[Eq. 14]
To calculate the Extract in a volume of wort, we need to know the SG and wort volume. From there we calculate the °P of the wort (using Eq 14), and the wort_weight (using Eq. 10). Now calculate Extract and water weight, using:
°P = 100° * Extract / Wort_Weight, so
Extract = Wort_Weight * °P / 100°, and
[Eq. 15]
Water_Weight = Wort_Weight - Extract
[Eq. 16]
Calculating Conversion Efficiency
The first efficiency we are interested in is the Conversion Efficiency, so we need to determine Extract Created in Mash and Total Potential Extract. We calculate Total Potential Extract from Eq. 3. To get Extract Created in Mash we will need to solve Eq. 12 for Extract:
°P = 100° * Extract / (Extract + Water_Weight)
Extract = (°P/100°) * (Extract + Water_Weight)
Extract = (°P/100°) * Extract + (°P/100°) * Water_Weight
Extract - (°P/100°) * Extract = (°P/100°) * Water_Weight
(1 - °P/100°) * Extract = (°P/100°) * Water_Weight
Extract = (°P/100°) * Water_Weight / (1 - °P/100°)
[Eq. 17]
We measure the SG of the wort at the end of mash (after aggressive stirring or recirculation to insure that the SG is uniform throughout) and use Eq. 14 to determine the °Plato of the wort in the mash.
°P_of_Mash_Wort = 1111.14 * SG - 630.272 * SG^2 + 135.9975 * SG^3 - 616.868
Eq. 8 to Eq. 11 are equally valid for water if we change "Wort" to "Water" and SG = 1, So, we use Eq. 8 and the strike water volume to calculate the Water Weight in mash
Water_Weight_in_Mash = Strike_Volume * Water_Density
And then use Eq. 17 to calculate the Extract Created in Mash:
Extract_Created_in_Mash = (°P_of_Mash_Wort/100°) * Water_Weight_in_Mash / (1 - °P_of_Mash_Wort/100°)
Once we have both the Total Potential Extract and Extract Created in Mash, we calculate the Conversion Efficiency using Eq. 2:
Conversion_Efficiency = Extract_Created_in_Mash / Total_Potential_Extract
Calculating Lauter Efficiency
Calculating lauter efficiency is where my thinking parts ways with Troester's. Troester goes thru calculating a "lauter step efficiency" for each run-off (initial plus sparge(s).) I believe the step efficiency concept to be useless in practice, and not worth calculating. My reasons are that what you really want to be able to do is compare results across no-sparge, single batch sparge, multiple batch sparge, and fly sparge processes. But, a no-sparge lauter efficiency will always be better than the initial run-off step lauter efficiency from a batch sparge, but the eventual lauter efficiency of a batch sparge will always be better than a no-sparge (assuming equal pre-boil volumes.) So, comparing step efficiencies provides no useful information, nor does it help with recipe calculations. To get useful information, you have to compare efficiencies at the end of the full lauter process. Plus it's simpler to just calculate the efficiency for the full lauter process than calculating individual steps.
For lauter efficiency we need to know Extract in BK and Extract Created in Mash. We calculated Extract Created in Mash above when determining conversion efficiency. To calculate Extract in BK we will make use of Eq. 10, 14 & 15. First we calculate Wort Weight in BK with Eq. 10:
Wort_Weight_in_BK = Wort_Volume_in_BK * Water_Density * SG_in_BK
Next determine the wort's °P with Eq. 14:
Wort_°P_in_BK = 1111.14 * SG - 630.272 * SG^2 + 135.9975 * SG^3 - 616.868
Next calculate the Extract_in_BK using Eq. 15:
Extract_in_BK= Wort_Weight_in_BK * Wort_°P_in_BK / 100°
And finally we calculate Lauter Efficiency using Eq. 4:
Lauter_Efficiency = Extract_in_BK / Extract_Created_in_Mash
Calculating Mash Efficiency
Mash Efficiency can be calculated using either Eq. 5 or Eq. 6, since we calculated the required factors while calculating Conversion Efficiency and Lauter Efficiency. An approximate way to calculate mash efficiency is to divide gravity points in BK by total potential points. In this case gravity points in BK is a proxy for Extract in BK, and total potential points is a proxy for Total_Potential_Points, where there are approximately 46 gravity points per pound of extract.
Calculating Brewhouse Efficiency
To calculate Brewhouse Efficiency, we start by calculating Extract in Fermenter the same way we did for Extract in BK in the Lauter Efficiency section. We then calculate Brewhouse Efficiency using Eq. 7:
Brewhouse_Efficiency = Extract_in_Fermenter / Total_Potential_Extract
You can also calculate brewhouse efficiency approximately by dividing gravity points in fermenter by total potential points.
Squeezing
Squeezing does affect the grain absorption, since if you get more wort out of the mash, there is less wort left behind. If you get more wort out you also get more extract out, so lauter efficiency, mash efficiency, and brewhouse efficiency are all increased.
Brew on