Easy way to do this?

[jerni21]

Just got my water report back from ward labs, and i've been reading and playing around with the calculators, am i missing something? i've just been throwing numbers at different additions to get the ranges correct, is there something that does this automatically, or a formula to get things exact? heres my water, thanks for the help!

pH 7.1 Total Dissolved Solids (TDS) Est, ppm 62 Electrical Conductivity, mmho/cm 0.10 Cations / Anions, me/L / 0.7 0.7
ppm Sodium, Na 10
Potassium, K < 1
Calcium, Ca 4
Magnesium, Mg 1
Total Hardness, CaCO3 14
Nitrate, NO3-N < 0.1 (SAFE)
Sulfate, SO4-S 3
Chloride, Cl 8
Carbonate, CO3 < 1.0
Bicarbonate, HCO3 14
Total Alkalinity, CaCO3 11
"<" - Not Detected / Below Detection Limi

 

[AZCoolerBrewer]

Are you bragging about your super soft water that you don’t have to filter and is basically RO water without have to put it through an RO filter? All I can say is we in Phoenix AZ salute you.

 

[thehaze]

That's some very good water. You are lucky. With the right mineral additions, you can brew pretty much everything, and especially " lighter " beer styles. You pretty much need some Gypsum, some chloride and epsom slats to possibly elevate the Mg levels and you are set.

I recommend using the Bru'nWater spreadsheet. It works wonders.

Cheers!

 

[Silver_Is_Money]

If it's actually possible, this gets it nigh on exact. Best I've found:

http://www.jimsbeerkit.co.uk/water.html

Put in your water analysis, then your target mineralization, and this online calculator will spit out all that you need to add to hit your target. Perhaps its Achilles heel is that it does not include baking soda among its mineral options. And ditto that it does include Calcium Carbonate and Magnesium Carbonate among its mineral options.

All other software which I'm aware of (mine included) makes you endlessly hunt and peck (use trial and error) until you either get lucky or you exhaust yourself in the frustration of hitting your defined mineralization target.

 

[ajdelange]

I'd stay away from that one. While it is probable that it will work under some conditions (DI water with no alkalinity, no chalk additions, no CRS additions) I don't want to spend the whole day trying to figure out what all the caveats are. It is a simple matter to figure out how much calcium sulfate and calcium chloride to add to DI water to get as close to a desired profile as possible using Excel's Solver and, of course, the author of this calculator could have implemented a similar algorithm for finding the best solution in his calculator but his notes suggest that he has implemented a simple solution of a set of linear equations which can lead to impossible answers which he deals with by ignoring or having the user change the inputs until the errors go away.

In a few minutes fiddling I found that if I tell this calculator that I have water with alkalinity 50 ppm as CaCO3 it tells me I have 1 mEq/L cation charge and 29.98 mg/L CO3 anion. I would indeed have -1 mEq/L charge if the pH were 5.9 but were it 8 the anion charge would be - 0.97 and for pH 9 it would be -0.96. I certainly do not have 39.98 mg/L CO3--. At pH 8 I would have 0.32 mg/L with 58.34 mg/L bicarbonate ion which isn't even mentioned. I've tried to figure out what this guy is doing in order to come up with 30 mg/L CO3-- from alkalinity of 1 mEq/L. The maximum carbonate possible with 50 ppm alkalinity is 17.9 mg/L. So when this guy says 'carbonate' it doesn't mean carbonate any more than Bru'n water means bicarbonate when it says 'bicarbonate'. Why to these guys want to make things so difficult for us poor slobs just trying to understand this stuff.

Be suspicious of any calculator that purports to analyze your water chemistry but does not ask for the pH of the source water nor the pH of the water you want to synthesize. This one is an example. It is clear that this author does not understand the chemistry involved here and even though this calculator may give the right answers under some conditions there are going to be others where it doesn't. And it doesn't handle bicarbonate additions at all which is probably a good thing given the authors apparent level of understanding of the carbonic/bicarbonate/carbonate system.

Should the content of this post ever make it to the author of this calculator I include in it my offer to try to explain this chemistry to him though it is explained in plenty of places including the sticky at the top of this forum.

 

[cire]

Should the content of this post ever make it to the author of this calculator I include in it my offer to try to explain this chemistry to him though it is explained in plenty of places including the sticky at the top of this forum.

You can rest assured it won't reach him.
As the original software was written before the internet, the author wouldn't have read your sticky.
Graham was a greater critic of it than perhaps you ever might be.

 

[jerni21]

Thanks for the help everyone, didnt realize my water was pretty good, been brewing for years and havent really made a bad beer, just want to give it that something extra, will play around with the calculators, pretty much thought you just had to play around until you got the correct combination of minerals, will try that on my next brew!

 

[ajdelange]

You can rest assured it won't reach him.
As the original software was written before the internet, the author wouldn't have read your sticky.

I didn't invent or discover this chemistry. It's been around for a long time.

Based on your familiarity with the author would you have any idea what the contents of the CO3 column mean?

 

[ajdelange]

... pretty much thought you just had to play around until you got the correct combination of minerals,

That may be the most practical means for most people. I'll point out again that Excel has tool called the "Solver" that automates the playing around and takes you to the best solution (sometimes you can't get what you want in such cases Solver will get you as close as possible). For some reason people are terrified of the Solver but it is well worth the effort to try to learn to use it.

This is an member of the class of so called optimization problems and there is a rich literature on methods of solution for the mathematically inclined.

 

[cire]

Based on your familiarity with the author would you have any idea what the contents of the CO3 column mean?

Yes.

 

[ajdelange]

Yes.

And would you pass that along? Best I can figure is that it is just under 60% of the alkalinity number in ppm and that doesn't suggest anything to me.

 

[Silver_Is_Money]

And would you pass that along? Best I can figure is that it is just under 60% of the alkalinity number in ppm and that doesn't suggest anything to me.

A guess:
------------
Molecular weight CO3 = 60
Molecular weight CaCO3 = 100
Ratio = 60%

 

[cire]

https://www.waterboards.ca.gov/drin...s/drinkingwaterlabs/AlkalinityConversions.pdf

When all else fails, read the instructions. Alternatively examine the first user input box.

 

[ajdelange]

A guess:
------------
Molecular weight CO3 = 60
Molecular weight CaCO3 = 100
Ratio = 60%

That's probably a pretty good guess (and I feel pretty stupid not thinking of it) because if you take 1 mmol (100 mg) of CaCO3 and dissolve it in 1 L of water with CO2 to pH 8.3 you would have

CaCO3 + CO2 + H2O --> 2HCO3- + 2Ca++

The concentration of the HCO3- would be 2 mEq/L, it would take 2 mEq of acid to convert it to CO2 and so the alkalinity would be 2*50 and the amount of carbonate taken from the limestone would be 60 mg. In this case the number in the CO3 column relates to the alkalinity and our practice of reporting alkalinity as 50 times the alkalinity in mEq/L stems from this chemistry which is, of course, what happens when ground water dissolves limestone.

But if a brewer dissolved 100 mg of CaCO3 in a liter of water using CRS instead of CO2 for the acid then he would have

CaCO3 + 0.5HCl + 0.25*H2SO4 --> HCO3- +0.5Cl- + 0.25SO4-- + Ca++

it would take 1 mEq to neutralize the bicarbonate and the alkalinity would be 50 which, if entered into this calculator, would tell us that CO3 is 30 mg/L when, in fact, the CO3 derived from the original 100 mg of CaCO3 is still 60. So I guess I'm still pretty confused as to how this number should be interpreted.

 

[ajdelange]

https://www.waterboards.ca.gov/drin...s/drinkingwaterlabs/AlkalinityConversions.pdf

I'm afraid that doesn't help me much. I can convert alkalinity to 'as Vanadate' if you like.

When all else fails, read the instructions. Alternatively examine the first user input box.

I'm afraid that doesn't help me much either. The notes for that box say

If you have an alkalinity figure, enter it in the alkalinity box and select the way it is expressed. This will put an accurate figure for carbonate in the carbonate box in row 2.

As I showed in No. 14 it puts a correct number for the lime derived carbonate in the carbonate box (labeled CO3 under anions with no charge shown) when we assume the CaCO3 was dissolved by CO2 if I interpret the number to mean the millimoles of C extracted from CaCO3 and when CO2 addition proceeds to pH 8.3. As I showed in No. 5 it does not represent the amount of any ion. I also showed in No. 14 that it does not represent the amount of C extracted from the limestone when any acid other than CO2 was used to dissolve it. So my question remains. What does it mean?

I think it means 30 times the alkalinity expressed in mEq/L e.g. 100 ppm as CaCO2 ==> 2 mEq/L; 2*30 = 60. It is technically OK to express alkalinity in this way if you want to - as I noted we could do it in terms of vanadate ion as long as everyone understands how we are doing it. Bru'n water expresses it as bicarbonate (well not as bicarbonate - it just calls alkalinity bicarbonate). As long as the internals of the program can reduce whatever the units are to mEq/L and uses those in actual calculations things are going to work out.

My gripe is that, while these strange ways of representing alkalinity are technically OK, they lead the users of these programs, especially the neophytes, away from understanding the chemistry.

 

[cire]

My gripe is that, while these strange ways of representing alkalinity are technically OK, they lead the users of these programs, especially the neophytes, away from understanding the chemistry.

Very true. I think, sorry, know Graham intended that to be used by brewers wanting to brew, not chemists wanting to understand chemistry.

 

[ajdelange]

Many brewers want to understand the chemistry because they know that the better they understand the process the more likely it is they will make good beer. And getting rid of these archaic units makes not only understanding the chemistry easier but it makes brewhouse calculations easier. But these old schemes die hard. Plantagenet Palliser never was able to get his 5 farthing penny adopted.

 

[mabrungard]

Very true. I think, sorry, know Graham intended that to be used by brewers wanting to brew, not chemists wanting to understand chemistry.

Indeed. My experience with the tens of thousands of Bru'n Water users isn't that they are upset that it uses a bicarbonate ion definition for the proton surfeit/deficit within the program, its that they want a simpler and effective way to brew better beer. I would say that 99% of the users could care less about the chemistry behind a piece of software. They just want assurance that it works to make better beer.

 

[ajdelange]

Alas, you are probably right. Let's all toast the increasing American, and, apparently, British, acceptance of mediocrity. But this is the Brewing Science forum and we assume, therefore, that the readers here are interested in the science.

 

[ajdelange]

The question in the original post was "Is there a formula to get this exact" and the answer is "yes" under certain conditions. It just never dawned on me how simple it is so there's two Homer Simpson moments for me from this thread. There are some caveats which we will get to but here are the formulas. The first one gives the number of millimoles of CaCl2 to add to the water to increase the calcium content by Ca mmol, the chloride content by Cl mmoi, the magnesium content by Mg mmol, the sodium content by Na mmol and the sulfate content by SO4 mmol. The second line gives the number of mmol of CaSO4 to be added for the same desired increases in the individual ions, the third the mmol of table salt and the fourth the mmol of MgSO4. Note that waters of hydration are not specified. When the formula give you the number of mmol of CaCl2 to add it means that you must provide that many mmol of CaCl2 and calculate the weight of CaCl2 corresponding to that by including the water of hydration if any. The same applies to gypsum (2 H20) and Epsom salts (7 H2O).

CaCl2 = 0.142857*Ca + 0.428571*Cl + 0.142857*Mg -0.428571*Na -0.142857*S04
CaSO4 = 0.571429*Ca -0.285714*Cl -0.428571*Mg + 0.285714*Na +0.428571*S04
NaCl = -0.142857*Ca + 0.0714286*Cl -0.142857*Mg + 0.928571*Na + 0.142857*S04
MgSO4 = -0.285714*Ca + 0.142857*Cl +0.714286 *Mg -0.142857*Na + 0.285714*S04

Now the caveats:

First, obviously, I'm only giving you the ability to add CaCl2, CaSO4, NaCl and MgSO4. No acids, sodium bicarbonate, calcium hydroxide or any other salt can be used. The simple formula works for any salt that does not change the pH of the mix. Any addition that does renders the problem non-linear and takes away this simple solution. Clearly we could extend to salts like KCl, NaSO4, MgCl2...

Second, you can't always get what you want because the ions are paired in the salts in fixed proportion. For example 1 mmol of CaCl2 contains 1 mmol Ca++ and 2 mmol of Cl-. Thus, if, for example, you want to increase calcium by 2 mmol, chloride by 3, magnesium by 1, sodium by 1 and sulfate by 2 and put those numbers into the formulas they will tell you to add 1 mmol of each of the 4 salts and it ought to be clear that doing so will add the amounts of the ions we just specified. In the following formulas Ca, for example, represents the increase in mmol of calcium from an addition of CaCl2 mmol of calcium chloride, CaSO4 mmol of calcium sulfate, NaCl mmol of sodium chloride and MgSO4 mmol of magnesium sulfate.

Ca = 1*CaCl2 + 1*CaSO4 + 0*NaCl + 0*MgSO4
Cl = 2*CaCl2 + 0*CaSO4 + 1*NaCl + 0*MgSO4
Mg= 0*CaCl2 + 0*CaSO4 + 0*NaCl + 1*MgSO4
Na= 0*CaCl2 + 0*CaSO4 + 1*NaCl + 0*MgSO4
SO4= 0*CaCl2 + 1*CaSO4 + 0*NaCl + 1*MgSO4


If, OTOH, you want to increase calcium by 2.2 mmol, chloride by 3, magnesium by 1, sodium by 1 and sulfate by 2 and put those numbers into the formulas you will get answers telling you to add, respectively for the four salts 1.02857, 1.11429, 0.971429, and 0.942857 mmol. If you put those numbers into the second set of equations you will find that they give you
Ca = 2.14286, Cl = 3.02857, Mg = 0.942857, Na = 0.971429 and SO4 = 2.05714. This is not quite what you wanted but pretty close. You have asked the impossible and the formulas cannot, therefore, give you exactly what you want but they do give you the best answer they can (in the rms sense) under the circumstances. You should always put the answers you get back into the second set of formulas in order to see how close you can get to what you want.

Third, if you make really foolish demands such as for 2 mmol of sulfate with only 0.1 mmol of Calcium and 1 mmol of everything else the formulas will blithely compute a calcium chloride addition of -0.12 mmol. This is, of course, impossible to do chemically (but not mathematically).

Some of you will have figured out how this works. The column vector

Ca
Cl
Mg
Na
SO4

in which the chemical symbols represents the mmol increase in the named ion, is the product of the matrix

1 1 0 0
2 0 1 0
0 0 0 1
0 0 1 0
0 1 0 1

with the column vector

CaCl2
CaSO4
NaCl
MgSO4

where the chemical symbols represent the mmol of added salt. The numbers in the first set of formulas clearly represent another matrix which is the Moore - Penrose pseudo-inverse of this matrix. We have to use the pseudo-inverse because we have 5 equations in 4 unknowns and these equations may not be consistent (and indeed often aren't in most cases). But the beauty of this is that when they are not consistent, we get the best solution possible even though our demands were unreasonable. I have often though about looking into this but never did. The huge insight is, of course, that the matrix is always the same for a given set of salts so that the pseudo-inverse only has to be computed once. The dumb and proud of it crowd don't even have to know where the numbers came from. They can just plug into the formulas.

 

[mongoose33]

The question that comes to my mind is what college chemistry class I should take that would get me to the point where I can intuitively, rather than by rote, understand this. I have a couple chemistry professor friends; maybe I'll ask them.

 

[ajdelange]

Actually the chemistry is trivial. The chemical formula for the salt CaCl2 says that it contains 1 calcium atom and 2 chlorine atoms. When such a salt is put into water it comes apart
CaCl2 + H2O ---> Ca++ + 2Cl- + H2O. Everywhere I said mmol in the previous post you could put the words atom or molecule (as appropriate) instead. But atoms and molecules are inconveniently small quantities to deal with so we use moles and millimoles instead. A mole is a fixed number of atoms or molecule sufficiently large that the mass of one mole of an atom is close to the atomic weight in grams and one millimole of a molecule close to the molecular weight of the molecule in grams (mole is short for gram-molecule). Thus one mole of sodium weighs 23 grams and one mole of calcium 40. For millimoles use milligrams instead of grams. In this problem we are usually calculating the salts to be added to a liter of water and ion concentrations are usually at most a couple of hundred milligrams per liter and thus a few mmol e.g. 230 mg/L sodium would be 10 mmol.

It's very easy to build a spreadsheet into which you put an amount of a salt from which it calculates the weight of calcium it contains, the amount of sodium it contains etc. If you set one up this way for each of several salts and then sum the sodium contributions from each, the chloride contributions from each etc you have a spreadsheet into which you can enter amounts of salts and compute amounts of ions. To hit a particular ion profile you fiddle with the salt amounts until the ion amounts look about right. What we are doing here is automating the fiddling part (though Excel has a tool that does this for us) for the simple situation where salts, other than bicarbonate, are being added to water.

The intuitive feel you seek will have to come from the math department where they will get into solving the system of linear equations A*x = b (A is the matrix with the proportions of the elements in the salts, x is a vector of amounts of salts to add and b is a vector with the amounts of the ions desired) which don't have a solution if they are inconsistent in which case the best that can be done is find x which minimizes |A*x - b| with || representing the vector norm. If you have enough matrix algebra to be able to implement what I put in No. 20 playing around with it and looking at the numbers will give the insight you are looking for. If these terms are unfamiliar the course you need to take is linear algebra (or a broader math course that covers it as most freshman math courses do).

Were you to show No. 20 to a chemistry professor he might or might not see what I am up to. A math professor would know right away.

Note that mathematically this problem is identical to one in which you wanted to know how much of 5-10-5, 16-4-8 and 10-10-10 fertilizers you should mix to get 100 lbs of 12-14-8.