Difference between revisions of "Beer color to mash pH (v2.0)"

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Revision as of 03:32, 6 March 2012

Work in progress.jpg

This article outlines the derivation of two formulas that can be used to predict the grist pH (and with it the mash pH) based on the estimated color of the beer. It utilizes a correlation that exist between the color of a malt and its pH properties. While this correlation is rather loose in some cases it is sufficiently strong for specialty malts to allow the proposal of formulas that can predict the grist and mash pH from the beer's color.

When I talk about grist pH I mean the pH that is inherent to the grist and which can be measured when distilled (mineral free water) is used for mashing.

This article is rather heavy on math and formulas it is provided as a reference for brewers who want to know how mash pH and beer color can be connected on a mathematical level.

How mash pH and beer color use similar formulas

To estimate the grist (or distilled water mash) pH the following formula can be used:

SRM to mash pH formula 1.gif (1)

where

  • pHgrist: is the distilled water mash pH of the resulting grist
  • pHbi: is the distilled water mash pH of the base malt i
  • gbi: is the base malt i's portion of the grist (gbi = 0..1)
  • gsj: is the specialty malt j's portion of the grist
  • asj: is the specialty malt j's specific acidity in mEq/kg
  • B: is the buffer capacity of the malt. It is actually the weighted average of the buffer capacities of all the malts present in the grist, but that can be safely neglected here. It has a unit of mEq/(kg*pH)

This formula is a revised version of the formula given in "The effect of brewing water and grist composition on the pH of the mash" [1]. It simply does the following. The weighted average of the base malt pH and the titration end-point (5.7) of the specialty malts is calculated and used as a starting pH. Then the pH shift that stems from the specialty malts is subtracted. This pH shift is proportional to the total acidity of the specialty malts. The proportionality factor is the buffer capacity B.

Most home brewing software calculates SRM as follows

SRM to mash pH formula 2.gif (2)

where MCU means Malt Color Units. It is the MCU formula that shows striking similarity to the pH formula (1)

SRM to mash pH formula 3.gif (3)

where

  • MCU: are Malt Color Units
  • mbi: is the weight of base malt i in pound
  • cbi: is the color of the base malt i in Lovibond
  • msj: is the weight if the specialty malt j in pound
  • csj: is the color of the specialty malt j in Lovibond
  • Vw: is the produced volume of wort

The goal is to express the SUM(asj * gsj)/B term from (1) with the SUM(csj * msj) / Vw term from (3). This is simple for the crystal and lightly roasted specialty malts where the following relationship between color and acidity has been found [1]:

SRM to mash pH formula 4.gif (4)

In addition to that gsj needs to be expressed as msj

SRM to mash pH formula 5.gif (5)

Where mg is the weight of the grist in pound.

Using (4) and (5) to express asj and gsj in (1) gives:

SRM to mash pH formula 6.gif (6)

To continue working with (6) and (3) the assumption is made that the grist consists of light colored base malts and the majority of the color is coming from specialty malts. That base malt is assumed to have a pH of 5.7. This changes (6) to

SRM to mash pH formula 7.gif (7)

and with the assumption that a 5 gal batch uses 10 lb grain (mbi) with a color rating of about 2 Lovibond (cbi) (3) changes to

SRM to mash pH formula 8.gif (8)

Combination of (7) and (8) gives an equation that estimates the grist pH based on the beer's MCU.

SRM to mash pH formula 9.gif (9)

Through linear regression analysis a linear approximation can be found for the relationship between SRM and MCU

SRM to mash pH formula 10.gif (10)

Used in (9) we get

SRM to mash pH formula 11.gif (11)

This formula is useful when the grist weight and cast out volume are known, which strongly correlates to the original gravity of the beer. However it is not all that useful when the grist contains roasted malts since (4) made the assumption that there is a linear relationship between malt acidity and its color. This relationship only exists for crystal malts and lightly roasted malts [2].

grists with roasted malts

Let's assume that the color of the beer can be split into a color component from crystal, base and lighly roasted malts and a color component from strongly roasted malts. The percentage of color from roasted malts is called Pr and therefore

SRM to mash pH formula 12.gif (12)

To get the pH change from roasted malts into the pH formula we need to write (4) for roasted malts. To further simplify things we assume that there is only one type of roasted used, which has the color cr. The acidity for heavily roasted malts is independent of their color and was found to be around 40 mEq/kg

SRM to mash pH formula 13.gif (13)

The MCU contribution from that roasted malt is

SRM to mash pH formula 14.gif (14)

Using following steps outlined before the MCU based pH drop from that roasted malt can be estimated as

SRM to mash pH formula 15.gif (15)

Thus (9) can be enhanced to

SRM to mash pH formula 16.gif (16)

Some rearranging gives

SRM to mash pH formula 17.gif (17)


References

  1. 1.0 1.1 Kai Troester, The effect of brewing water and grist composition on the pH of the mash, 2009
  2. Kai Troester, Find the Zymurgy article