Saturation Index (Langelier, etc.)

[chem geek]

This thread discusses the Saturation Indices, especially Langelier and some corrections I made to that index.

I've read the following three threads that Evan (waterbear) referred me to:

http://www.poolforum.com/pf2/showpos...91&postcount=7
http://www.poolforum.com/pf2/showpos...3&postcount=13
http://www.poolforum.com/pf2/showpos...1&postcount=17

I'm going to start off in a controversial way so please, no one take offense. If I'm wrong about this, I'd like to know. Though I start out sounding defensive, my conclusions are not different then yours in a limited use of the index, but I still think it is of some rough use.

One argument against using the LSI for pools is that pools are an open system while the LSI was designed for boilers which are a closed system. This is a bogus argument (see, I told you I'd be controversial). It is true that the pool is an open system and is in fact a system that is out of equilibrium, but that does not mean that parts of the system, namely the pool water and its chemical contents, do not follow equilibrium chemistry. The only part of the pool water chemistry system that is significantly out of equilibrium is the amount of dissolved CO2 in the water vs. the amount of CO2 gas in the air. It is true that if this out of equilibrium situation was dynamically changing at a rapid pace on par with the rate of the equilibrium reactions, then you couldn't apply equilibrium equations to the rest of the pool system. However, this is simply not the case -- except for low pH, high alkalinity situations possibly with aeration where a regular rise of pH is being observed and is rapid, it is simply not true that the rest of the pool is not in equilibrium. The chemical reactions for the rest of the cabonate buffer system and calcium carbonate balance (and ion pairs and almost everything else) are absolutely occurring at extremely rapid rates with the exception of the scaling or corrosion of calcium carbonate solid (plaster and grout) itself. In other words, the pool water chemistry behaves as if it were a closed system with the air having a much higher quantity of CO2 gas (i.e. an equilibrium quantity so that no outgassing would occur). The bottom line reason that the pool is more like a closed system than an open system is that the chemical reactions in water are equilibrating extremely rapidly while the out-of-equilibrium state of CO2 is changing very slowly. Obviously, the pool isn't "closed" when you add chemicals to it, but after such chemicals get close to equilibrium (which is typically within a few hours, with decent circulation) then the system behaves as if it were "closed" and close to equilibrium [EDIT] in the short run. Obviously over time the outgassing of CO2 occurs and must be taken into account, but the huge difference in the fast equilibrium inside the pool water compared with the slow outgassing of CO2 means you can look at these two processes separately. [END-EDIT]

I have seen the reaction rate constants for various parts of the chemical system and the slowest ones are with the chlorinated cyanurates, but are still occurring with half-lifes of 1/4 and 4 seconds. The hypochlorous acid and carbonic acid and cyanuric acid equilibriums are incredibly fast (as expected for simple protonation reactions). Reactions of chlorine with organics can be slow and breakpoint of chlorine (when it occurs) is usually slow (on the order of a 15-minute half-life), but this doesn't enter into the LSI since it is not related to the concentration of either calcium nor carbonate ion.

The Langelier Saturation Index, or a better version of it (that I developed -- more on that later), is simply based on the solubility of Calcium Carbonate in water. It really has nothing specific in it related solely to boilers except possibly the interpretation of the values of the index itself (more on that later) and maybe the simplifications in the temperature and TDS parts of the index (which I have fixed). The LSI index does take into account the effect of ionic strength (mostly via TDS but done as an approximation), temperature (again, does an approximation), pH and alkalinity (both done correctly). The LSI index does not take into account ion pairs, but my spreadsheet calculations do though this doesn't have much of an effect unless you have a lot of sulfates in the water. I agree with you that the Ryznar Stability Index (RSI) does not apply at all to pools because it is not simply based on the solubility of calcium carbonate, but is an attempt to compare scale vs. corrosion of metal (not plaster) and is really quite simplistic for both. After all, the index is 2(pHs)-pH so that even when the pH is equal to the pHs (which means that there is chemical equilibrium for calcium carbonate), the RSI is equal to pHs which is ridculous as a general solution. It works only for certain pHs ranges as found in the database of water systems he used.

As for whether to use the Hamilton index (even more simplistic) or to look at the total alkalinity instead of carbonate alkalinity, the answer is no, not in pools. All that matters is 1) what could possibly percipitate out of the pool water and 2) what could the pool water possibly dissolve. The answer to (2) is calcium carbonate found in plaster and grout. The answer to (1) is also calcium carbonate if you have this at equilibrium levels to prevent (2). The other items that could percipitate do not do so because they are not at saturation levels though it is theoretically possible to precipitate calcium sulfate but you'd need extremely high levels of both such as 1000 ppm calcium with 10,000 ppm sulfate (there is a neutral ion pair CaSO4º that prevents precipitation earlier). Magnesium Carbonate could percipitate if there is more than about 170 ppm of Magnesium (I calculated ppm is as Magnesium, not MgCO3) in the water. Of course, there are various sorts of reactions to precipitate metals, but these concentrations are minor (as far as the carbonate and calcium equilibriums are concerned).

As for the variability of each of the components, it is true that pH is the biggest factor since it is a direct component while the other factors are logarithmic so that larger changes are required (and that alkalinity is more important than calcium hardness). That means that measuring those other factors doesn't have to be particularly precise while pH should be the most precise (how precise is debatable -- more on that later). However, it is not true that you'd see a big difference with salt pools since the difference in TDS is roughly from the 550-1000 range in a non-salt pool to the 3000-3500 range in a salt pool (remember that some of the initial 550-1000 is already salt so the total TDS number is pretty close to the salt number). The difference in the LSI is only about 0.1 while in my improved index it's about 0.2 which is still pretty small.

Now the only thing I've tried to demonstrate so far is that the chemistry of equilibrium for calcium carbonate is valid. This does not tell us the meaning of the index in terms of its scale (meaning "size"). Sure, a "0" means theoretical equilibrium, but how far does the scale need to stray before either scaling or corrosion of the plaster/grout occurs? This is where I agree with you guys that the recommendation of staying with "+/- 0.3" and that you run into trouble outside of "+/- 0.5" is something that is probably not correct and that these are not the right numbers for pools. All reaction rates will be slower at the lower temperature of pool water compared to boiler water so at a minimum, any straying from equilibrium will either scale or corrode very, very slowly. Of course, pool surfaces are exposed to the water all year long for many years, but if Ben says he's never seen a problem, then I most certainly believe him. I can't find the link anymore, but somewhere I saw a post or something from Ben giving two extreme examples where he never saw any scaling or corrosion, but those examples produced an LSI (or my improved index) from around -0.15 to +0.55 which only proves that this range for the index doesn't say that problems will occur. Perhaps problems only start to occur when the range gets to +/- 1.0 or +/- 2.0 or perhaps a lopsided range. It is unfortunate that no one seems to have done any research on this.

Now as to whether it matters to have calcium in your pool at all, I think you all agree that it is needed for plaster/grout pools. When I added sodium carbonate to the pool I noticed it being cloudy until it dissipated and I also found that if I dumped it rapidly in one place I could precipitate calcium carbonate. So on another day I took a sample of pool water and added sodium carbonate to it and saw it first get cloudy and then precipitate (what I believe was) calcium carbonate. Then I added acid (diluted muriatic acid) to this sample and saw the precipitate dissolve and the water become clear. What I didn't do was to see where the "boundaries" were when these processes occurred (i.e. at what LSI levels). Even if I did that, it wouldn't be the same as having a safety range for the long-term exposure of plaster/grout to water.

(a little more to be continued in next post)