work in progress

--Kaiser 22:28, 7 January 2008 (CST)

Because of its simplicity and dependency on only a few factors, batch sparging lends itself to being easily modeled mathematically. Though lots of the work has already been done before and publicized (for example Ken Schwartz's evaluation), this article tries to focus on the conclusions that can be drawn from the mathematical analysis of batch sparging rather than the derivation of the formulas themselves. For the interested reader, the final section provides information on how the formulas were derived.

Assumptions

In order to model batch sparging, two fundamental assumptions must be made:

• All extract that is going to be available after mashing has completely been dissolved in the mash water
• after the mash has been drained, all the extract that remains in the mash tun is contained in water that is held by the grain or the dead space of the mash tun
• adding another batch of sparge water will only dilute the wort left in in mash tun and not extract additional extract from the grains

Model and Formulas Used

The mathematical model for batch sparging assumes that all the extract is dissolved in the water volume in the lauter tun (V_LT) and that this liquid is drained until only the dead space and volume absorbed by the grain remains in the lauter tun (V_DG). More water is then added to the lauter tun which will evenly dillute the amount of wort that remained there after the first run-off. The lauter is then drained again and added to the run-offs already in the boil kettle.

With these parameters

• V_LT-n - wort volume in the mash tun before run-off step n (in gal)
• V_D - dead volume of the lauter tun. This is the volume of water that cannot be drained from the lautertun even if it doesn't contain any grain (in gal)
• m_G - the weight of the grist (in lb)
• A - the grain absorption ratio for wort (in gal/lb)
• V_DG - the amount of wort left in the lauter tun after draining it equals the dead space plus the wort absorbed by the grain: V_DG = V_D + A * m_G
• V_r-n - run-off volume for each run-off. It is the difference between the volume in the lauter tun and the volume kept in the lauter tun: V_r-n = V_LT-n - V_DG
• V_b - the preboil volume of wort collected. It is the sum of the run-off volumes: V_b = V_r-1 + V_r-2 ...