There are two rather different ways that chlorine gets depleted and these have very different rates.
1) Chlorine gets used up via the oxidation (breakpoint) of ammonia, the oxidation of organics, and the disinfection of bacteria and viruses. This sort of usage is wholly dependent on the amount of ammonia, organics and pathogens in the water and is therefore independent of the amount of chlorine you have (assuming you have enough to not get to zero). So this rate is often quoted as ppm chlorine per day.
2) Chlorine also gets used up through the breakdown from sunlight (UV) and some through breakdown from temperature and a very small amount outgassing as chlorine gas (except in salt pools without CYA where the amount is more significant). This sort of usage has a rate that is directly proportional to the amount of chlorine in the pool, so the rate is often quoted as a half-life or the time it takes to use up half of the chlorine.
You say that your pool normally consumes around 2 ppm of chlorine per day but unfortunately this does not tell us how much of this is due to (1) vs. (2) above. My guess is that without an opaque pool cover, an outdoor pool will generally have most of its chlorine loss due to (2) so let's just say for sake of argument that you lose 1.5 ppm per day due to the breakdown from sunlight and 0.5 ppm due to bather load and other organics and bugs. The other assumption to make is that the total chlorine level when you lose 2 ppm per day is 6 ppm.
Chlorine Loss per Day = 0.5 + (1.5/6.0) * 6.0 = 2.0
Now, with a chlorine level of 20, your loss would be greater as follows:
Chlorine Loss per Day = 0.5 + (1.5/6.0) * 20 = 5.5
Now I made some pretty bold assumptions, but the basic principle still holds that as long as some of the chlorine loss is due to processes that are proportional to the amount of chlorine in your pool (e.g. breakdown from sunlight), then higher levels of chlorine in your pool mean a greater absolute loss. [EDIT] Also note that the "5.5" number is an instantaneous rate and that this rate will decrease as the chlorine level drops. I also didn't take that into account in the original "2.0" calculation, but the point is still true that higher chlorine levels will have a greater absolute chlorine loss. [END-EDIT]
I wasn't sure if I should just give you the answer or give you the details on this. I chose the latter and I hope it wasn't too much info.
Richard
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