Decoctions

Sizing a decoction is a heat balance: pull enough of the mash that boiling it and stirring it back carries the rest up to the next rest temperature. The decoction guide is the walk through the planner; this page is the arithmetic.

The textbook’s three assumptions

The classic formula makes three assumptions, and all three bias it the same way, toward too small a pull and a mash that undershoots.

The tun cools while the pot is off it. A thick pull is away for the best part of forty minutes once you count its own conversion rest, the ramp to a boil, the boil and a slow stir-in, and an insulated cooler drops a degree or three in that time. The pull does not come back at 100 °C either; it comes back at 96 to 99, cooled by the pot and the transfer. And the boil costs water, a liter or two across three decoctions, which never reaches the kettle and thickens the mash as you go.

We model all three. Set the standing loss to zero, the return temperature to 100 °C and the boil-off to zero, and it collapses exactly to the classic formula, which is the contract: a recipe carrying no decoction detail keeps the numbers it had.

Thickness

What the formula produces is a heat capacity, not something you can pour, and turning it into a pot reading needs to know how much grain is in the pull. A thick pull is the bigger bucket, which surprises people. Grain is dense but carries less heat per kilogram than water, so a thick pull has to be about a fifth larger to do the same job.

The beer these numbers come from

Reference pale ale — 20 L into the fermenter, a 60 minute boil.

Grist	Amount	Color
Crisp Maris Otter Pale Ale Malt	4.5 kg	2.8 °L
Thomas Fawcett Caramalt	0.35 kg	9.9 °L

Hops	Amount	Alpha	Addition
Magnum	15 g	13.5 %	60 min boil
Cascade	30 g	6.8 %	10 min boil
Citra	40 g	13 %	20 min stand at 80 °C

It comes out at
Original gravity	1.0507
Final gravity	1.0094
Alcohol	5.52 %
Bitterness	35.66 IBU
Color	5.14 SRM (10.12 EBC)
Into the fermenter	20 L

The numbers

Decoction pull

6.88 L, from decoction-heat-balance.

C_pull = (C·(T₂ − T_r) + e·(T_ret − T₂)) / (T_ret − T_r)
⇒ Decoction pull = 6.88 L

Input	Value	Unit
Mash water	16	L
Mash grain	5	kg
Mash capacity	18	L water-equivalent
Current temp	52	°C
Target temp	65	°C
Rest temp at return	50.766666666666666	°C
Return temp	98	°C
Evaporation	0.5	L
Pull capacity	5.77346506704305	L water-equivalent
Ratio	1	L/kg
Grain specific heat ratio	0.4	—

What it assumes:

• Pulled at 1.00 L of liquid per kg of grain.
• The tun is left for 37 min and drifts 1.2 °C, which the pull is sized to make up.
• Color, efficiency and pH effects of the boil are not modeled.

Sources:

• How to Brew — John J. Palmer, Brewers Publications, 2017