How to use the CSI/Langlier Index tables??

[dvcavall]

I have read several papers/discussions on calculating the saturation index. All of them used examples, and all of them chose example test numbers that matched exactly with a number on the table. As you know, the table listings have wide gaps between the number ranges listed. For temperature it starts as 32, the next in the sequence is 37, followed by 46. I have not been able to find anything that describes how to handle the most likely case of when your reading falls between a range? Do you estimate what the corresponding factor might be? Do you choose the closest reading w/o going over? Do you choose the closest reading, even if it is higher? For instance, calcium hardness goes from 100 with a 1.6 index, to 150 with a 1.8 index factor. If your reading is 126, what factor do you use? 1.6, 1.8, or estimate it to be 1.7???

I'd like to see the answer in a formal paper or somethng, but short of that, just knowing the right answer will be helpful.

 

[duraleigh]

I have moved this post to The Deep End forum as it is not a subject of particular interest to the average pool owner. Calculating CSI, while perhaps interesting to some, is not necessary for the successful management of pool water chemistry.

 

[JasonLion]

This is whey we use the Pool Calculator, instead of the tables. It does all of the math for you (and is more precise than a finite table ever could be). If you are using the tables you simply use the closest number in the table.

 

[CaOCl2]

Alkalinity Factor (AF) = log (carbonate alkalinity as caco3)
Hardness Factor (CF) = log ([ca]) (or substract 0.4 from AF, there's always a 0.4 difference between AF and CF)
Temperature Factor (TF) = If I recall Wotowicz says -0.276 + (0.00825 * °F)
TDS = It's a constant, some sources use -12.1, then some says increase that by 0.1 for every increase of 1000 ppm TDS, and then Wotowicz says TDS= -11,30 - (0.333 * log (tds))

Look at http://www.poolhelp.com, under JSPSI, you may find articles by Wotowicz describing in detail the Langelier index, and this:

http://www.aquaticsintl.com/2009/apr/0904_techtalk.html

If you contact the author, Matthew Griffith, he'll probably forward you his calculations/corrections of the temperature factor based on the original Langelier paper.

 

[chem geek]

You can see a technical derivation of the Calcite Saturation Index (CSI) near the bottom of my Pool Equations spreadsheet where you can see that the formula comes from the actual solubility product of calcium carbonate relative to the equilibrium solubility product (it's the logarithm of the ratio of the two). You can see a simplified version of the formula that is essentially what is used in The Pool Calculator in this post. The original Langelier Saturation Index used temperature dependence and ionic strength formulas that were over-simplified and don't match the most recent tables/calculations anymore.

Note that while the tables you typically find will match this formula for CH and adjusted TA (CarbAlk), the tables for temperature and TDS (ionic strength) factors vary somewhat though not a lot. APSP-11 and now CDC MAHC use tables that result in a saturation index roughly 0.10-0.15 higher than the calculation I have though in my spreadsheet if you set "Use Davies instead of Debye-Hückel" on line 228 and "Use Alt. Carbonate and CaCO₃ K's" on line 229 then you will get very close to these newer standard tables. I originally did the formulas to try and match the Taylor watergram I had at the time years ago. The precise equilibrium constants and their temperature dependence has changed slightly over time which is at least partly why you see different tables.