By C.F. “Chubb” Michaud
We all know how much wood a woodchuck could chuck if a woodchuck could chuck wood, but how fast can you run a one cubic foot softener? What does the “max flow” mean for an NSF/ANSI 44-listed softener, and what happens if that flow is exceeded? When I posed that question to a group of experts about 20 years ago, I got answers ranging from “nothing” to “total failure.” One of those answers is close to correct.
Kinetics is the branch of science that deals with the rate of change of a chemical reaction or system. But how fast is the water-softening reaction, and what factors control it? Water temperature could play a big role in how fast a softener can react. Since ion exchange is a diffusion process, particle size of the resin is important, and the ease with which ions can enter and exit the resin structure plays a key part, as well. That is controlled by the cross-linking level. Regeneration level and water composition impact capacity and leakage of a resin but not the rate at which ions exchange.
Impact of Temperature
Between water temperatures of 60℉ and 80oF, capacity improves by only about 5 percent. However, although cold water can be treated with a softener, cooler water (50oF) sees a steep drop in capacity, and temperatures below 40oF can cost you 50 percent in capacity due to the slower kinetics of the exchange reaction.
The real bottleneck in an ion-exchange reaction is the rate of diffusion through the static zone right next to the surface of the bead (called the Nernst layer). Diffusion of ions through the Nernst layer is as much as 10 times slower than diffusion through the bead itself. The faster the superficial flow through the resin bed, the thinner the Nernst layer becomes. Providing enough bed depth by using a narrower but deeper bed can improve the capacity of the bed and, therefore, has a positive kinetic effect. One cubic foot of resin in an 8-inch vessel will show a 16 percent increase in capacity over that of a 10-inch vessel at 10 gallons per minute (gpm).
The size range for standard softening resins is from 0.3 millimeter to 1.2 millimeters, a factor of 4x. Those larger beads are 16 times slower than the smaller ones. In addition, coarse resins will have thicker Nernst layers. The differences between a fine mesh resin (40-60 mesh) and a coarse resin (12-30 mesh) can be as much as 30 percent in capacity due to kinetics. The primary advantage is in the ability of the finer mesh beads to regenerate more thoroughly with a given salt level.
How Fast Is Max Flow?
|Since many kinetic reactions are driven by concentration, it is not difficult to understand that ion exchange is also driven by concentration. The kinetic equilibrium equation is as follows:
The larger the numbers in the numerator, the more favorable the reaction. The larger the numbers in the denominator, the slower the reaction.
We can see that as hard water travels through the bed, the amount of calcium (Ca) in the water decreases, as does the amount of sodium (Na) on the resin. Further, the amount of calcium on the resin increases, as does the amount of sodium in the water. With the numerator decreasing and the denominator increasing, we can see that the reaction is slowing down. The point at which two forces equal one another is called the equilibrium, and there the reaction stops.
The concept of half-lengths is often used in adsorption reactions to estimate retention time needed. It can also be applied to ion-exchange reactions. Simply stated, if it takes X amount of time to complete 50 percent of a reaction, it will take the same amount of time to complete 50 percent of what is left. In other words, if it takes 10 seconds to complete 50 percent of the softening process, it will take 10 seconds more to complete 25 percent additional softening, and 10 seconds to treat the next 12.5 percent, and 10 seconds to complete the next 6.25 percent, and so on, with each time interval completing half of the remaining process. Although this concept does not calculate to 100 percent complete, it can be shown that at 7 half-lengths, we are at 99.25 percent complete, and at 10 half-lengths, we arrive at 99.95 percent complete.
You never know your top speed until you try to exceed it. A well-run softener will reduce 20 grains of hardness to less than 0.2 grains. That’s 99 percent, or 7 half-lengths. To test our hypothesis on max flow, we tested a 10-inch softening cartridge on city water with 17 grains per gallon (gpg) hardness. Our effluent tested 0.20 gpg. This was a reduction of 98.8 percent, which we called 99 percent, and established what the equilibrium softening capability on that feed water would be.
Using fresh cartridges made with 8 percent and 10 percent softening resin, we then ran flat out with hopes of exceeding the “just barely” softened flow rate. We were successful, with flow rates approaching 250 gallons per minute (gpm) per cubic foot (cu ft). The data is presented in Figure 2.
Discussion of Results With our 8 percent resin cartridge containing 48 cubic inches (cu in) of resin, we filled a 5-gallon bucket in 42.23 seconds. That gave us an equivalent flow rate of 255.6 gpm/cu ft and an empty bed contact time (EBCT) of 1.76 seconds. The feed water was tested at 12 gpg and softened to 1.33 gpg. That calculates to 88.9 percent softening, or 3.224 half-lengths. One half-length is calculated to be 0.546 seconds (1.76 seconds/3.224). Seven half-lengths is 3.822 seconds. This is the equivalent of 15.7 bed volumes (BVs) per minute (60/3.822) or 117.4 gpm/cu ft.
We repeated the testing with a 10 percent resin cartridge and calculated the max flow at 118.2 gpm. We noted that over the course of the testing, the feed water had warmed slightly from 70oF to 74oF, which may account for the slightly faster kinetics of the 10 percent resin.
Some dealers may upsell a residential user based on what’s parked in the driveway. However, that 12,000-square foot manse on the five-acre lot sporting a 28 gpm fixture count for a two-kitchen, eight-bathroom bungalow could probably get by with a 1 cu ft softener. The only reason to upsize would be that the total water usage per day exceeds the capacity of the 1 cu ft unit.
The kinetics of a water softener are surprisingly fast. A variable flow end-user needing 5 gpm with spikes of 25 gpm need not require a large system to cover the spikes. Pay attention to pressure drop, however. A 1 cu ft softener running at 10 gpm may experience a pressure loss of 10 pounds per square inch (psi). Trying to push that same system to 25 gpm will incur a pressure loss over 50 psi. Because the softening reaction is completed farther down in the vessel, higher flows mean lower capacity. If running 1 cu ft at 3 gpm produces a capacity of 24,000 grains, running at 10 gpm will see a drop to 22,000 grains, and 50 gpm will provide only 12,000 grains.
This all pertains to residential uses only. Commercial and industrial systems are designed more for total capacity and tend to be larger due to the demand for continuous flow and total water volume per day. A residence with a peak flow of 10 gpm may still use only 400-500 gallons per day. An industrial user with a continuous 10 gpm demand will use 14,000 gallons per day, and at 15 gpg needs to remove 216,000 grains of hardness every 24 hours while exhausting 9 cu ft of resin. The ideal design for this use is a twin alternating 5 cu ft softener.
Max flow is not a physical flow limitation, but, instead, it is the flow at which the pressure drop equals 15 psi. If you exceed the flow, the pressure drop increases.
The ion-exchange process is a complex mass-transfer sequence that is diffusion-rate limited. Better kinetics favors the use of smaller beads, lower cross-linked resin, warmer water, deeper beds, and dilute solutions. You are not likely to ever overrun a softener with high flow alone
About the author
C.F. “Chubb” Michaud, MWS, is the technical director and CEO of Systematix Company of Buena Park, CA, which he founded in 1982. He has served as chair of several sections, committees, and task forces within the Water Quality Association (WQA), as well as served as a past director and governor. He served on the Pacific Water Quality Association (PWQA) board, chairing the Technical and Education Committees for 12 years. Michaud is a proud member of both the WQA and PWQA Halls of Fame, has been honored with the WQA Award of Merit, and is a two-time recipient of the PWQA Robert Gans Award. A frequent and well-published author and speaker, Michaud has contributed over 100 original papers on water treatment techniques and holds four U.S. patents on ion exchange technologies. He holds a BS and an MS degree from the University of Maine.
About the Company
Systematix Company, founded in 1982, is an innovative media supply company with a focus on ion exchange media, processes, and systems design. Expert advice is offered for the asking. The company can be reached at (714) 522-5453, or email [email protected].