| |
Stoichiometry-Based
Alcohol Estimation
|
©
|
James M. Gossett (July 31, 2012)
|
|
|
| |
(from initial Brix and final Brix
measured before bottling sugar added)
|
|
|
|
| |
|
|
|
|
|
| |
|
Inputs
|
|
|
| |
Measured Initial Brix (20˚C)
|
|
|
| |
Measured Final Brix (20˚C)
|
|
before bottling sugar added
|
|
| |
Bottling Sugar Added (oz per 5 gal)
|
|
|
|
| |
|
|
|
|
| |
|
Outputs
|
|
| |
Pi (initial real extract, %)
|
|
*
|
Pi = measured initial Brix/1.04
|
|
| |
Pf (final real extract, %)
|
|
**
|
Pf =100*(Pi - C) / Wf
|
|
| |
Real Attenuation (%)
|
|
|
100*(Pi - Pf) / Pi
|
|
| |
Est. final Brix (after boiling-off EtOH
|
|
|
Some use
this as a measure of residual, Real Extract.
I think it over-estimates because it includes non-carbohydrate
contributors to refraction.
|
|
| |
&
reconstituting volume)
|
|
|
|
| |
%ABW before bottle-conditioning
|
|
|
| |
%ABV before bottle-conditioning
|
|
at 15˚C.
|
ABV (15˚C) = ABW*(final SG) / 0.794
where 0.794 = density of EtOH at 15˚C.
|
|
| |
%ABV after bottle-conditioning
|
|
at 15˚C.
|
|
| |
|
|
|
| |
g sugar consumed per 100 g original wort
|
|
|
C = g sugar consumed per 100 g original wort
|
|
|
| |
g EtOH produced per 100 g original wort
|
|
Eq [1]
|
g EtOH = 0.484*C
|
|
|
| |
g wort remaining per 100 g original wort
|
|
Eq [2]
|
Wf = g wort = 100 – C*(0.494 + 0.088)
|
|
|
| |
|
|
|
|
| |
Initial SG (15˚C) from initial Brix***
|
|
|
=1.000019 + 0.003865613*Pi +
0.00001296425*Pi^2 + 0.00000005701128*Pi^3
|
|
| |
|
|
|
+ 0.001 (to correct from 20˚C to 15˚C)
|
|
|
| |
Final SG (15˚C) from
initlal and final Brix****
|
|
|
=1.001843 – 0.002318474*Pi –
0.000007775*Pi^2 – 0.000000034*Pi^3
|
|
| |
+ 0.00574*Bf
+ 0.00003344*Bf^2 + 0.0000000*Bf^3
|
|
| |
|
|
|
| |
Assumptions:
|
|
|
|
| |
"extract" = maltose
|
342
|
g/mol
|
|
| |
Mass EtOH produced
|
EtOH g = 0.484 per gram maltose consumed
|
|
| |
Mass CO2 produced
|
CO2 g = 0.494 per gram maltose consumed
|
|
| |
Mass TSS produced
|
TSS g = 0.088 per gram maltose consumed
|
|
| |
k
|
0.445
|
= contrib of
EtOH to Brix at 20˚C [ Brix units per
1%(w/w) EtOH]
|
|
|
|
|
|
|
|
| |
Final Brix= [Initial Brix – C + (g EtOH/100 g orig
wort)*(k)]*(100/Wf)
|
|
|
|
|
|
|
|
|
|
|
| |
Eqs [1] and [2] can be subst into
this one, and C can be explicitly solved-for as function
|
|
|
| |
of initial and final Brix values:
|
|
|
|
|
|
|
|
|
|
| |
C = 100*(Bi – Bf) / [100 – 0.484*k*100 – {0.494 + 0.088}*Bf]
|
|
| |
| |
Notes:
|
|
|
|
|
*
|
Pi (initial
real extract). 1.04 is often-assumed
attenuation factor (reflecting relation between wort sugars and Brix). It accounts both for refraction-producing
agents in wort that are not carbohydrates, and also for wort carbohydrates
not being sucrose (on which the Brix scale is defined).
|
|
| |
|
|
**
|
Pf (final real extract) relates to the sense of
"body" and residual sweetness in a beer.
|
|
|
***
|
From
Siebert, K.J., "Routine Use of a Programmable Calculator for Computing
Alcohol, Real Extract, Original Gravity, and Calories in Beer," J. Amer. Soc. Brewing Chemists., Vol
38 (1), 27-33 (1980).
|
|
| |
|
|
|
|
****
|
From Bonham, L. K., "The Use of
Handheld Refractometers by Homebrewers," Zymurgy, 43-45, January/February (2001)
|
|
| |
|
| |
