Revision as of 22:12, 9 January 2008

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 ...

As you can see with each sparge a new term is added to the efficiency, but it's contribution to the total efficiency will be smaller and smaller as the number of run-offs is increased. The following sections will vary various parameters in these formulas to give the brewer an idea how they will effect the efficiency.

Effect of the relative run-off sizes

The first parameter that should be examined is the effect of the relative run-off sizes. Obviously this only applies to batch sparging with 1 or more sparges as there is only one run-off in no-batch sparging. To make this experiment, batch sparging with 2 run-offs is used and the parameter that is varied is the ratio between the first run-off volume (V_r-1) and the pre-boil volume (V_b). In the E_one-sparge formula this will affect V_LT-1 and V_LT-2. The experiment is repeated for 2 grist weights (10 lb, 15 lb and 20 lb).

An efficiency optimum exists when the 1st and 2nd run-off are of equal sizes, but it is also apparent that even slightly uneven run-offs are very close to the optimum. Towards the edges, where one of the run-offs comes close to or is the total boil volume, the efficiency drops by almost 10%. This is the efficiency for a no-sparge lauter.

The efficiency curve is shifted towards lower efficiency as the amount of grain increases (note that the pre boil volume is held constant and that all the curves are for single batch sparging). This comes from the increased amount of wort that is left behind in the greater amount of grain.

Conclusions:

• in batch sparging the run-offs should be of equal size to achieve maximum lauter efficiency
• But, eyeballing the volumes is just fine since slight or moderate inequalities will not lead to a significant drop in efficiency

Though it was only shown for the one-sparge case that the run-offs should be of equal size, further experiments will assume that all run-offs are of equal size even for the 2 and 3 sparge cases.

Effect of the grist size (weight)

The size of the grist and/or its absorption ratio have a significant effect on the max batch sparging efficiency. The more wort is held back by the grain and the lauter tun's dead space, the more extract will remain in the grains. Subsequent sparging batches can not deliver all the extract into the boil kettle, they can only capture a part of the extract that was left behind. But as the number of sparges is increased the increase in efficiency is diminishing. Keep in mind that in all these cases the pre-boil volume is kept the same. As a result, the run-off amount for each sparge gets smaller as the number of sparges is increased.

The following graph illustrates the effect of the grain weight and number of run-offs (1, 2, 3 and 4) on the lauter efficiency.

lauter efficiency based on the grain weight and number of run-offs (V_b=6.5 gal, A = 0.13 gal/lb, V_D=0 gal)

The range interesting for most brewers is between 8 and 20lb of grain (assuming 5gal batches).

Conclusions

• the more grain is used, the more the efficiency will suffer. This can be counteracted by more sparging batches, but there is a limit to the efficiency that can be achieved with a given grist size, absorption ratio and pre-boil volume