The 5600 series, can only support 7 GPM drain flow, which will also equal the maximum Backwash flow rate. For this reason, Fleck recommends the 5600 for Softeners equipped with 12" or smaller media tanks, or Filters equipped with 10" or smaller tanks. Since there is a wide range of filter medias, each requiring a unique backwash rate, it's always best to verify the backwash requirements necessary for the intended media, before choosing the control valve.
Reason I ask is my home's GPM coming in is 13 GPM. PSI is 113.
Assuming your water source is municipal, then you need a pressure regulator installed at point of entry. Residential plumbing should not be regularly exposed to pressures exceeding 80 psi. Most municipal water supply systems are designed to provide 60 psi.
Although your home's plumbing system maybe capable of delivering 13 GPM, most actual water use is typically 6 GPM or less.
Isn't the GPM dependent on the tank's capability?
Yes, but not in the manner you think.
Water treatment is rarely an immediate process, but requires sufficient contact time with sufficient media for optimal treatment performance to take place. To increase the media contact time will require either a larger volume of media, or a lower flow rate through the media, or both.
Media manufacturer's typically publish the effective Service Flow Rate for each media, stated as GPM per square foot of cross section (ft2). Also usually stated will be the media bed depth to achieve optimal performance to achieve the SFR specified.
For example, a softener equipped with 1 ft3 resin within a 9" diameter tank, will have ~32" bed depth to support 6 GPM Service Flow Rate across 0.4415625 ft2 of tank cross section.
Depending on the control valve utilized, the valve may support a Peak Flow rate of 12 GPM, but when the media SFR is exceeded, then hardness will be more likely to leak through the resin, so softened water supplied to fixtures will be less soft and lower in quality than when the flow rate is 6 GPM or less.
Increasing the tank diameter will increase the cross sectional area of media which will allow an increased service flow rate to fixtures, but a larger quantity of media will then be necessary to provide the required bed depth. Of course, a larger quantity of resin will also increase the total Capacity of hardness that maybe removed before regeneration will be necessary.
I am about to buy a water softener, and calculated that the 32000 grain 9"x48" is sufficient based on the calculations of hardness, etc of water report.
I suspect you are basing usage on all 32K grains of resin capacity. If so, this will result in extremely inefficient and wasteful performance.
To regenerate 32K grains capacity in 1 ft3 resin, will require 20 lbs salt each regen cycle. Efficiency will then equal 32,000 gr/ 20 lbs = 1,600 gr per lb.
To achieve significantly higher efficiency and performance, always recommended to obtain a larger capacity softener, but program less capacity to be consumed before regeneration takes place using a lower salt quantity.
For example, a 10" softener containing 1.5 ft3 resin, will have a total hardness reduction capacity of 48K grains, but will require only 12 lbs salt to provide 36K grains of usable capacity each cycle. (36,000 / 12 lbs = 3,000 gr/lb)
A 12" softener equipped with 2 ft3 resin (64K gr total capacity), will require 16 lbs salt to regenerate 48K grains of usable capacity to provide the same 3,000 gr/lb efficiency.