Capacity: Operating Capacity
One definition of capacity is the ability to do something. This is a quantitative value. In the ion-exchange softening process, we define not only the quantitative capacity of the resin (total capacity) but the qualitative capacity (operating capacity or column capacity), as well. In other words, the operating capacity tells us how much work the resin can do in removing a certain element (hardness) to a given break point.

The operating capacity for a softener is defined as the hardness a certain quantity of resin can remove from a feed stream at a specific flow rate and temperature to a given break point using a defined level of salt as a regenerant. It is all specific to the job at hand—if you change one variable, you change the results. Operating capacity will always be a percentage of the total capacity, typically 60 percent to 70 percent.

Capacity: Total Capacity
The total capacity for a resin that is given on the specification sheet is a quality control measure to determine how the functionalization reaction went during production. It is determined by chemical analysis on a dry-weight basis.

To start, the resin is carefully weighed. Then a portion of the sample is brined to convert it to the sodium form and then dried to determine the percent moisture, which is also an assessment of the level of cross-linking. The test sample is weighed and fully converted to the hydrogen form with a huge excess of acid so that every reactive site is now in the hydrogen ion (H+) form. During the conversion step, the resin swells considerably, and the wet weight increases, but the backbone dry weight does not. Then it is exhausted by running an excess of dilute caustic (sodium) through the resin; this is called a titration step. The solution that exits the resin is then carefully analyzed to determine how much of the caustic was taken up by the resin.

Reaction 1. Titration to Determine
Total Capacity
NaOH + OH+ → ONa+ + H2O + NaOH (excess)

Now, knowing the amount of dry resin in grams and the amount of sodium from caustic (sodium hydroxide) in milliequivalents (mEq), we can calculate the milliequivalents per dry gram of resin. This value is reported as the total capacity and is converted to a wet basis using the value for the predetermined moisture content, reported as total capacity on a volumetric basis as milliequivalents per milliliter (mEq/ml or equivalents per liter).

This value can be expressed as either the sodium or hydrogen form of the resin. The total capacity per gram of resin will be higher for H+ form resin than for sodium ion (Na+) form resin because each reactive site picks up one ion, and H+ has a molecular weight of one, whereas Na+ has a molecular weight of 23. Thus, one reactive site weighs more in the Na+ form, so that total capacity value is slightly lower, typically in the range of 4.5 milliequivalents per gram (mEq/g) and 4.9 mEq/g for Na+ and H+ forms, respectively.

The effort is to determine how many reactive sites reside on a given volume of resin. The conversion of the total capacity value to the more familiar kilograins per cubic foot (one kilograin equals 1,000 grains) is calculated by multiplying the volume (wet) capacity by 21.87. A softening resin will have a volumetric capacity of 1.9-2.0 mEq/ml. The corresponding grain capacity will be 41.5-43.7 kilograins per cubic foot (Kg/cu ft). Unless you are operating two or more softeners in series, you will not achieve such high values. Operating capacity will always be a fraction of the total capacity. This can be visualized in Figure 1.

Figure 1. Total capacity versus operating capacity.

In Figure 1, the total capacity is represented by the total area above the red curve and below the feed water value line. The operating capacity is the area described by the rectangle EDCF. The difference between the two is that, even though the run would normally terminate at the break point C, the softener continues to run and remove hardness (above the red curve from C to G). In a series operation, the polishing softener will pick up the breakthrough hardness below the red curve CG and thus allow the primary to run to near-complete exhaustion.

Why Can’t We Achieve 100 Percent
of the Total Capacity?
There are two forces governing the ion-exchange process: selectivity and equilibrium. Table 1 is a listing of select cations arranged by valence (+1 and +2). Note: The selectivity for any specific ions tends to increase as the DVB (cross-linking) increases. Higher cross-linking means lower moisture. Lower moisture means more “plastic.” The reactive sites are closer together, and the ion-exchange resin, therefore, has a higher charge density and stronger attraction for ions in solution.

For softening, our focus is on sodium (Na), calcium (Ca), and magnesium (Mg). These are highlighted in the table. The selectivity for the hardness ions is considerably stronger than for sodium. In other words, the resin will prefer the hardness ions. In dilute solutions such as city or well water, the hardness will replace the sodium on the resin, and sodium will enter the solution. You will never achieve 100 percent of total capacity because it requires 100 percent effective regeneration and 100 percent exhaustion.

Reaction 2. The Softening Reaction
Ca(HCO3)2 + MgSO4 + ONa → OMgCa + NaHCO3 + Na2SO4

The calcium and magnesium salts are soluble in the feed water. “O” represents the cation resin in Na+ form. The softening process removes the hardness, replacing it with sodium salts, which do not react with soap or form scale.

Table 1. Cation selectivity.

Will My Softener Be 100 Percent Efficient in Hardness Removal?
The average softener with moderate salt settings of six pounds to 10 pounds per cubic foot will not remove 100 percent of the hardness. The product water will show a decrease of around 98 percent to 99 percent, depending on the regeneration level and the overall challenge of the feed water. This means that if your feed water has a hardness level of 300 parts per million (ppm), your product will still have 3 ppm to 5 ppm of hardness. This is considered soft water by the Water Quality Association (WQA). WQA defines soft water as having less than 17.1 ppm (one grain per gallon) of hardness expressed as CaCO3.

What Is the Relationship Between Softener Performance and Regeneration Level?
The higher the regeneration salt dose level, the cleaner the resin becomes, and it achieves a higher operating capacity with lower leakage. This is shown in Figure 2.
Salt dose is an important consideration if your application cannot tolerate 3-5 ppm of hardness (leakage). Leakage is a result of not getting all the hardness off the resin in the previous regeneration. It is not hardness bypassing the resin.

Figure 2. Operating capacity and leakage versus regenerant dose.

The blue curve in Figure 2 represents the operating capacity expected with the corresponding level of salt used for the regeneration. To get an idea of what to expect, first select the level of leakage desired from the vertical axis on the right. In this illustration, 3 ppm of leakage is our set point. The dotted line from the right axis is traced to the orange leakage curve. At the point where they intersect, a line projects straight down to the regeneration level axis. This example shows 10 pounds per cubic foot (lbs/cu ft). To determine capacity, this intersection point is then projected straight up to the blue capacity curve and then to the capacity axis on the left (showing a capacity of about 28 Kg/cu ft). The green line represents the theoretical 100 percent salt efficiency line of 6,000 grains of capacity per pound of salt. In this example, we calculate a “perfect” operating capacity of 10 x 6,000, or 60,000 grains/cu ft. We will see that 28,000/60,000 = 47 percent salt efficiency.

By moving our salt dose to the left on the axis, we achieve higher salt efficiency, but capacity drops and leakage increases. If we calculate the capacity recovery for the 10 lbs/cu ft setting, we see 28,000 grains of usable capacity is 42.65 Kg/cu ft (our 1.95 mEq/ml data sheet capacity x 21.87 Kg/cu ft/mEq/ml). Our recovery is 65 percent (28.0/42.7).

My Competitor Is Quoting a One-Cubic-Foot Unit with a Capacity of 32,000 Grains
You, too, can quote 32,000 grains per cubic foot. According to Figure 2, you would get 32 Kg/cu ft with a 15-pound salt dose. It would have a salt efficiency of 2,133 grains per pound (32,000/15 lbs). You might have a hard time selling that in the United States, since many states have minimum salt-efficiency numbers well over 3,000 grains per pound. To achieve those values, the salt dose is reduced to the range of 6-8 lbs/cu ft.

The second of our controlling forces in softening is equilibrium. The equilibrium equation for softening is expressed as follows:
Figure 3. The equilibrium relationship.
Equilibrium states that the progress of the softening reaction toward completion is increased by the level of hardness in the water, expressed here as [Ca++]W, and the level of sodium [Na+]R on the resin, and it is decreased by the level of hardness on the resin and sodium in the water. Both the amount of sodium on the resin and level of calcium on the resin are the result of a good regeneration. We want [Na]R to be large and [Ca]R to be small. We also want [Ca]W to be large and [Na]W to be small. This relationship applies to dilute solutions such as those typically encountered in municipal feed streams (less than 3,000 ppm).
How Does Equilibrium Affect Regeneration?
There is a reversal of selectivity in concentrated solutions. Salt brine at 10 percent concentration is 100,000 ppm. The [Na]W value is so large that it reverses the relationship and forces sodium back onto the resin, replacing the hardness.

The Complexity of Figure 2
Figure 2 represents operating capacity. Recall that operating capacity is influenced by water composition, flow rate, desired quality, salt regeneration level, and temperature. Technically, we need a separate representative set of curves for every possible set of conditions. In addition, the selectivity for calcium is much higher than that of magnesium, so even the ratio of calcium to magnesium enters into the process.

From the equilibrium relationship, if the sodium levels in the feed water are high, the reaction is sluggish. Capacity goes down and leakage goes up. Throwing a lot of salt at the system during regeneration reduces the effect of the high total dissolved solids from sodium but doesn’t eliminate it. The high sodium level continuously polishes hardness off the bottom of the bed, and the leakage goes up and the capacity comes down.

Conclusion
The total capacity of ion-exchange resin is a representation of the total number of reactive sites on the bead. Operating capacity is that portion of the total capacity that is utilized with considerations of quality and economics. Increasing the salt level improves both capacity and quality but may be limited by locality. The theoretical salt efficiency of resin is 6,000 grains recovery per pound of salt. High efficiency is considered 4,000 grains per pound. To achieve that, the salt dose is typically 6 lbs/cu ft or less. Using 8 lbs/cu ft will get you to about 24,000 grains, or 24 Kg/cu ft, which is 3,000 grains per pound. The dose level of six to eight pounds will handle more than 99 percent of city-supplied water. To claim a capacity of 32,000 grains per cubic foot, the salt dose must be more than 12-15 lbs/cu ft.

About the author C.F. “Chubb” Michaud, MWS, is the technical director and CEO of Systematix Company of Buena Park, California, which he founded in 1982. He has served as chair of several sections, committees, and task forces within 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.

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