Lime treatment calculations

[petdocvmd]

Hi All,

New to the forum, and getting back into homebrewing after a 15 year hiatus

My question is about calculating calcium in brewing water after lime slaking.

Here is my info:

Tap water analysis:

pH: 7.7
Na: 16 ppm
K: 4 ppm
Ca: 51 ppm
Mg: 13 ppm
TH as CaCO3: 182 ppm
NO3-N: 2.7 ppm
SO4-S: 8 ppm
Cl: 35 ppm
CO3: < 1.0 ppm
HCO3: 150 ppm
TA as CaCO3: 123 ppm

Given my high pH and high temporary hardness, I have elected to treat my water by lime slaking. The tap water is carbon filtered, and I was also planning on pre-treating with Campden tablets as our water supply is treated with chloramine.

Using Kaiser_Water_Calculater to guide me, I am planning to add CaSO4 and CaCl2 to the water, then slake it with Ca(OH)2 overnight. I would then decant into holding buckets for mash and sparge water.

If I understand correctly, my starting calcium is a limiting factor in the total efficacy of reducing temporary hardness, hence the pre-addition of CaSO4 and CaCl2. According to Kaiser_Water's calculations, for 9 gallons of water I would add 3.4g of lime. However this would in theory use all but 2 ppm of calcium in my water, hence the need for CaSO4 and CaCl2. Since I want about 50 ppm calcium, I empirically plugged in 2g of CaSO4 and 5g of CaCl2. Kaiser_Water then shows a “Ca surplus” of 55 ppm. The final list of ions however is NOT updated to reflect this – instead it appears to calculate calcium from German Hardness inputs from the results of a standard aquarium test kit on the limed water.

My question is: how can I most accurately determine the calculated final calcium concentration in the treated water (ideally without submitting a treated sample to Ward)? Using the “Ca surplus” number, or the result calculated after determination of German Hardness? Ultimately I want to create a water profile in Beersmith for “Treated tap water” that represents my tap water after this treatment regimen.

Sorry if this was unclear – staring at this stuff too long makes my head start to spin ;-)

Thanks!

Scott

 

[ajdelange]

The first step is to calculate the amount of lime required to convert all the all the carbonic in the sample to bicarbonate. To do this you need to know the total amount of carbo in the sample. This is determined from the alkalinity and pH. Given a pH (and we'll be using three values here) calculate
r1 = 10^(pH - 6.38)
r2 = 10^(pH - 10.38
f0 = 1/(1 + r1 + r1*r2)
f1 = f0*r1
f2 = f1*r2
Q(pH) = -f1 -2*f2

This is the charge on a millimole of carbo at the given pH. Take the difference
&#8710; = Q(4.5) - Q(pHs)
where pHs is the pH of the sample and 4.5 is the (assumed) pH used for the alkalinity titration.

Calculate 50000*(10^(-4.5) - 10^(-pHs )) ~ 1.5 and subtract that from the alkalinity in ppm as CaCO3. Convert the remaining alkalinity to mEq/L by dividing by 50. Now divide this by &#8710; to get

Ct = alk/&#8710;

That's the total moles of carbo in a liter of your water.

Now compute
d = Q(pHs) - Q(8.3)
Then Ct*d is the amount of hydroxyl ion needed to convert the carbonic acid in a liter of water to bicarbonate. Divide by 2 to get the number of millimoles of Ca(OH)2 required to supply those hydroxyl ions.

So now we know that we have about Ct millimoles of bicarbonate ion per liter of water. The reaction with lime is

Ca++ + 2(OH)- + Ca++ + 2HCO3- --> 2CaCO3 + 2H2O

from which it is apparent that 1/2 mmol of lime is required for each mmol of bicarbonate to be removed. Calculate this, add it to the neutralization requirement and convert to mg/L by multiplying by the molecular weight of Ca(OH)2.

After all this DeClerck recommends preparing slurries with 90%, 100% and 110% of the calculate amounts and doing three test treatments to see which gives the best decarbonation (as measured by checking the alkalinity).

Aren't you glad you asked?

Once put into a spreadsheet of course there is little labor involved in doing the calculations beyond plugging in the numbers.

A more empirical approach (no calculation!) is to take about 2/3 the volume of water you want and adding lime slurry, with stirring, until the pH is around 10. Precipitation should occur and the pH will fall back. Now add more of the untreated water until pH 8.3 is reached.

Your basic question is as to how to calculate the calcium content. You can't really as precipitation reactions are wierd. That's why deClerck recommends the experimental approach even for a brewery that does this every day. You will have to measure calcium hardness after the treatment if you want a good number.

If you don't want to do a measurement then you can assume, given starting calcium was greater than starting alkalinity, that alkalinity will be reduced to about 1 mEq/L and that calcium content will be reduced by the same amount that alkalinity was. For example, with your alkalinity if 123/50 = 2.46 mEq/L, that reduced to 1 mEq/L implies the loss of 1.46 mEq/L alkaliity and, thus, the loss of 1.46 mEq/L calcium. Deduct this from the sum of the water's starting calcium plus any you added before lime treatment. Not that all the calcium added by the lime precipitates so you don't count that.

 

[petdocvmd]

Calculate 50000*(10^(4.5 - 6.38) - 10^(pHs - 6.38)) ~ 2.5 and subtract that from the alkalinity in ppm as CaCO3.

Wow! Okay, digging deep into my memories of college chemistry I was able to follow along - except for the above quoted line. By "~ 2.5" do you mean "the answer is approximately 2.5" or is "~" some sort of mathematical operator?

My sample pH was 7.7, so plugging in would give:

50000 * (10^(-1.88) - 10^(1.32)) = 50000 * (0.0132 - 20.893) = 50000 * (-20.88) = -1.044 x 10^6. This doesn't seem to make sense if it's to be subtracted from the alkalinity in ppm as CaCO3 (which for me is 123 ppm). Can you clarify for me?

Impetuous as usual, I actually went ahead with my additions prior to your response .

I added ~ 2g of CaSO4, 5g of CaCl2, and 4g of lime to 10 gallons of filtered tap water. An immediate check of pH showed ~ 10 (crude pH strips with colors that show 2, 4, 6, 8 or 10). After a while it dropped to about 7. I checked hardness and alkalinity with an aquarium test kit and got 358 ppm general hardness ("GH") and 71.6 ppm for alkalinity ("KH"). So it appears that I was successful at reducing alkalinity somewhat (though less than theoretical max reduction to 50 ppm), but was perhaps overzealous with CaSO4 and CaCl2 as I compute my calcium to be about 121 ppm based on the measured hardness and known [Mg], and this agrees with Kaiser_Water's calculation.

I'm beginning to think maybe I should just buy R.O. water (or install a filtration system) and add ions as needed for a particular beer ;-)

Thanks!

Scott

 

[ajdelange]

The correct formula is 50000*(10^(-4.5) - 10^(-pHs)) = 1.58 which represents another mistake as the 2.5 approximate answer pertains when the titration end point is 4.3 which used to be the accepted one in brewing but people seem to be moving towards 4.5 these days as it is the ISO standard.

The real point being that you can skip this step without introducing appreciable error.

 

[D-Train]

As you found out the lime treatment section of Kaiser's spreadsheet requires the post-treatment GH&KH to give you the resulting profile. However, the water treatment with boiling section does not require these values, and those results are more or less the same from a practical standpoint. Try setting the dropdown in the boiling section to "yes", and enter 9 gallons in that section too. Then check the resulting water profile for your estimates.

I tried the above in the spreadsheet using some of your values, and get 75 Ca, 50 CaCO3 (2.86 dH), and -11 RA. I'd say this is about right. I personally get 3 dH tested with the aquarium kit after lime treatment. Before lime treatment I get 14 dH. I modeled my process on Kaiser's writings and spreadsheet. It works. Get the test kit, it's cheap and nice insurance to make sure you're successful.