Your understanding of the chart seems to be substantially correct, but the number of days between regeneration appears to be slightly off.
For a 1X/week regen frequency to deliver 15,000 grains capacity over 7 days (2143 grains/day), the softener would need to regenerate at least 17,143 grains capacity. If the softener was programmed to regenerate only 15,000 grains, then the regeneration frequency will be approx 6-days as 'Reserve Capacity' will be subtracted from the total amount regenerated.
An appropriate reserve allocation will normally be 1-day usage capacity. This anticipates the worst-case scenario where remaining regular capacity (ie: last of 15000 grains) is consumed early on the last day, to provide the additional capacity consumed during the remainder of that day until the following regeneration cycle. The depletion of regular capacity at any time throughout the day, will trigger a regen cycle, but a single tank softener will delay regeneration until the programmed regeneration time which is usually 2-am the following morning. The capacity consumed during the delay will be 'Reserve', will not always be fully consumed prior to regeneration.
Regarding hardness leakage, as the resin is prepared for maximum softening capacity initially (32K grains/ft3), the amount of hardness leakage specified will not occur immediately, but will slowly increase to that amount only after repeated regeneration using the low salt quantity specified.
There has been plenty of threads on this forum that discuss upflow vs downflow in which to search and review. The usual advice continues to utilize downflow for residential applications.
The appropriate tank diameter is generally standardized for the quantity of media the tank is to contain. A softener with 1 ft3 resin will commonly utilize a 9" X 48" tank, 10" X 54" for 1.5 ft3, 12" X 52" for 2 ft3 etc. Those are standard tank sizes used in the industry. Some clients have special needs such as a height limitation, so their system may be configured with a shorter 10" tank for 1 ft3 of media, or a short 12"tank for 1.5 ft3, but those are exceptions.
If you wanted to utilize a 9" diameter tank with 1.5 ft3 of media, the taller tank would likely need to be custom made, and I anticipate there would be a significant flow reduction through the media due to the increased column height of media to the bottom distributor basket.
Your comments in post #3 mention doubling and tripling the amount of salt which results in declining efficiency, but that view is based on the extreme low salt dose being the starting point whereas in water treatment, the opposite is usually true.
For example, to regenerate 1 ft3 of resin to restore all 32,000 grains total capacity, will require 20 lbs salt resulting in maximum efficiency of 1,600 gr/lb. Reducing the usable capacity setting by only 25% of the total, will result in a significant 60% reduction of salt needed, further improving salt efficiency as well as other benefits. Many people with no softener experience that buy a softener advertised with 32K grains capacity, often think all 32K will need to be used before regeneration will occur.
Water softeners for residential use have in the past been time clock operated, so not equipped with any water measurement capability. Softeners were also usually smaller so all of the resin capacity was often regenerated multiple times each week, using the maximum salt amount, regardless of the amount of capacity that was actually needed or consumed.
Water treatment methods have been developed, improved and refined over several decades. Significant improvements now include the use of metering so regeneration will occur when the programmed capacity has been consumed. Also, a better understanding of capacity vs salt setting allows for improved efficiencies, especially when paired with a programmable controller and a larger quantity of media to provide a longer duration between regeneration cycles. Further improvements continue to evolve, particularly with digital controllers.
