BIAB mathematical relationship between mash efficiency and L:G ratio

[ballantynedewolf]

Having recently discovered maxiBIAB, it occurs to me that the potential yield of a BIAB system can be expressed in terms of:

• Pot size in L
• Grain yield potential in points per kilo per litre
• Mash efficiency
• Liquor-to-grist ratio
• OG required

This would yield a number of litres that can be produced at the required OG. We could, ahem, boil this down further because mash efficiency is a function of liquor-to-grist ratio, assuming all other mash parameters are maximised.
It seems with an L-to-G ratio of 0, ie no water, efficiency would be zero. It would then rise rapidly with increasing L-to-G, but never reach 1. At L-to-G of 4, efficiency would be about 0.9, at 3 it would be about 0.84, at 5 it would be about 0.93. This is thus logarithmic, and the best fit I have so far is:

Efficiency=(log10(L+1))^0.3 where L is the liquor-to-grist ratio
​

This seems to look good over a liquor-to-grist ratio range of 2 to 6.

Has anyone any better idea of this function?

 

[Lyrebird_Cycles]

I get a mash efficiency of over 100% at a liquor to grist ratio of 3, so I am suspicious of your algorithm. Whence came it?

 

[ballantynedewolf]

It came out of my mind - it's sort of by eye. I wasn't aware you could go over 1 in efficiency - wouldn't that mean you are extracting more gravity from the grain than it is possible to extract? Wouldn't it in fact mean that the quoted potential of your grain is wrong - too low?
Anything that rises towards but never reaches a value is logarithmic, so I just messed around in Excel with a logarithmic function til I got something taht looked about right over a typical range.

 

[MHB]

There is a handy little formula for predicting the OG of first runnings

oP (first runnings) = Yield Potential (in percent) / L:G + Yield Potential (in percent)

To keep it simple say we were doing a single malt mash with malt having a Coarse Grind as is Potential of 76% (Yield Potential)
We choose to mash in at 5:1

oP=0.76/5+0.76= 0.76/5.76= 0.1319 or 13.2oP giving 1.0528 if you want the density in SG terms.

Clearly you need to manipulate the numbers a bit more if you want to express the outcome as efficiency, but for an in-sparged mash (like maxi BIAB).
Say we mashed 5kg of malt in 25L of Liquor (5:1)
We have to figure that the malt will retain around 0.8L/kg (depending on fineness of grind, drain time, how hard you squeeze...)
There would be (5*0.8) 4L of liquor left in the malt, so at the start of the boil there would be 21L with an of OG of 1.0528, or 21*1.0528=22.11kg of wort at 13.2oP, from that we know we have obtained 22.11*13.2%= 2.92kg of extract.
the 5 kg of malt at 76% means 3.8kg was available.
Efficiency is 2.92/3.8*100 = 76.84%

If your half handy with excel, you could whip up a spreadsheet that lets you goal seek most any of the variables you want.
Mark

PS from Handbook of Basic Brewing Calculations Page 19, if you are going to screw around with brewmaths - its a very handy book

 

[MHB]

The results is what we get from the "Congress Mash", an agreed standard lab method, it is conducted in distilled water, so no minerals...
You can get a bit more out of malt, its hard to do but possible.
Congress Mash.PDF

 

[ballantynedewolf]

Thank you MHB. This relationship between LG ratio and mash efficiency is indeed part of a larger set of formulae, but I'm concentrating on that for the moment because I've got all the rest pretty much worked out.

 

[MHB]

From personal experience I can assure you that working in % Yield, Plato... is a hell of a lot easier than Points/L/kg or even worse the silly American system (or non-system if you prefer).
Remember that oP is %W.W and all the numbers line up.
You can use a weighted average table, or a variation on Aa+Bb=Cc to work out the potential of a mixed grain bill
You can also tie in colour and most any other variables you want to work with.
Mark

 

[Lyrebird_Cycles]

It came out of my mind - it's sort of by eye. I wasn't aware you could go over 1 in efficiency - wouldn't that mean you are extracting more gravity from the grain than it is possible to extract? Wouldn't it in fact mean that the quoted potential of your grain is wrong - too low?

No, for the reasons MHB gives above.

Anything that rises towards but never reaches a value is logarithmic.

Or an inverse exponential eg 1-1/(e^0.6*n) gives a reasonable approach to your curve (n is the liquor to grist ratio)

 

[RdeVjun]

in-sparged mash (like maxi BIAB).

Mark, not sure of this terminology but it seems that you are infering MaxiBIAB is full volume? If so, no, that isn't the case, there is a separate sparge step, after mashing in the 19L pot full to the brim, then sparge in a bucket or another pot. Of course, scaling as anyone sees fit is always possible.
I tried to work it out from context, don't think I'm wrong but will always stand corrected, particularly if I've misunderstood.

Oh BTW pistol patch will be having kittens, see if he blows up telling us how wrong and backward we are for even contemplating this, seeing as he invented BIAB an' all... /s

 

[MHB]

My bad, much as I like Pat, I stoped following the details of the many daughters spawned from the original BIAB, so anything is possible.

Thinking about it, the little approximation I posted above could perhaps be used in a two stage mash/sparge process.
Do the calculation as above based on the L:G you do use, calculate the mass of extract in the wort, subtract that from the starting potential of the malt, then recalculate using the remaining un-extracted material as the new potential and the sparge water as the new L:G.
Just have to be careful to keep track of where all the liquor goes, the partly extracted malt will have somewhere around 1L/kg of water...
Mark

 

[ballantynedewolf]

From personal experience I can assure you that working in % Yield, Plato... is a hell of a lot easier than Points/L/kg or even worse the silly American system (or non-system if you prefer).
Remember that oP is %W.W and all the numbers line up.
You can use a weighted average table, or a variation on Aa+Bb=Cc to work out the potential of a mixed grain bill
You can also tie in colour and most any other variables you want to work with.
Mark

Thank you for that tip MHB - like you say, it's so much simpler in that system. My refracto has Plato, and the formulas are so much neater without that 46*0.78*90%*2.2*3.78 factor in there. Beautiful. I suppose there is also a neat adjustment factor for hop utilisation. did I read somewhere it's 10% for each 10 points above 1.050, so that would be 10% for every 2.5°P above 12.5?
I'm still pretty unsure of my efficiency-in-terms-of-LG-ratio function - examples worked seem not quite right, with yield only falling off significantly at 2L/kg, which seems low.
Because one factor is the volume of the pot, reducing L:G ratio massively increases your grain bill. Where that intersects with your falling mash efficiency is your sweet spot.

 

[Lyrebird_Cycles]

There are two conflicting sets of data on hop utilisation vs gravity, one from Tinseth (1.65 x 0.000125^(SG-1).) and one from Kappler which shows a bounded linear relationship from 90% at 10oP to 52% at 18oP.

The strange form of the Tinseth curve appears to be because it combines with another function for boil time and together they appear to include an initial utilisation factor of ~70%.

The Kappler curve does not account for initial utilisation. It also implies >100% utilisation for anything below 8 oP and <0 for anything above 26 oP, which seem unlikely.

To get around these problems I use AvP = Av0 * 1.038^-P. This is a decent fit to the linear part of the Kappler curve and to the central section of the Tinseth curve once initial utilisation is taken out. It avoids the strange results at extremes, is neater and is more computationally tractable.

You will need to add a factor for initial utilisation which is highly brewhouse dependent: at a brewery for whom I used to work we had two different plants which differed by about 40% in utilisation on the same beer: with a wort of 12.5 oP and expected IBU of 30, all Saaz boiled 90 minutes at 102 oC we got net 30% utilisation in one and 42% in the other.