The Effect of Grain Bed Depth and Cross-Sectional Area on Filtration Flow Rate

Figure: The Darcy equation and grain bed depth and cross-sectional area

Figure: The Darcy equation and grain bed depth and cross-sectional area

Darcy’s Law proves that decreasing grain bed depth will increase filtration flow rate, and vice versa. For a given malt charge, the only way to spread out the grain bed and make it shallower, is to increase its bed cross-sectional area. If we reduce grain bed depth, this automatically increases the grain bed cross-sectional area. This gives us a double benefit of reducing a Darcy bottom line variable and increasing a Darcy top line variable.

Reduced bed depth results in faster filtration. How thin can we go?

With the mash tun and lauter tun, we rely on a bed depth sufficient enough to achieve wort clarity. The lauter tun must have a minimum bed depth of around 500 mm to achieve acceptable clarity. The mash tun, with a coarser grind, requires 1,000 mm. Thus for the same grist charge, to achieve a thinner bed depth, the lauter tun will have a larger diameter, and a greater cross-sectional area compared to the mash tun.   

The mash filter uses a bed depth of 50 mm. This requires a very high surface area, which is accommodated in multiple chambers. 

If we factor in the grain bed depth L and the bed cross-sectional area A, for each mash separation device, Darcy’s Law provides us with relative filtration flow rates.

Table: Lower grain bed loadings increase flow rate

 

Lauter Tun

Mash Tun

Meura 2001

Mash Filter

Grain bed loading (11 t) (kg/m2)

200

500

30

Grain bed depth  L (m)

0.5

1.0

0.05

Grain bed cross-sectional area A (m2)

50

20

330

Tun diameter (m)   

8

5

20  (58 filter chambers)

  A / L

100

20

6600

Relative flow rate

5

1

330

 

 

 

 

Darcy’s Law predicts that the low bed loading of the mash filter should allow it to run 330 times faster than a mash tun. In reality, it is only four times faster.

Why do we not get the same mash filter flow rates as predicted by Darcy’s Law?

To understand, we must consider grain bed permeability.

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