By C.F. “Chubb” Michaud CWS-VI

In Part 1 of this two-part series, we discussed basic chemistry and ionization and the value of the Periodic Table of Elements to the water treatment professional. In Part 2, we examine the proper use of a water analysis and pitfalls to avoid in deciphering it.

To properly design a water treatment system, particularly with ion exchange and reverse osmosis (RO), it’s necessary to first get both a quantitative and qualitative listing of what the intended feedstream contains. This listing is known as the water analysis and a proper interpretation is a must to assure good results. Although the purpose of an ion exchange system is to remove only the offending ionic components of a feedstream, other factors such as temperature, total dissolved solids (TDS), pH and trace minerals also play a role and must therefore be considered.

Laboratories usually report a water analysis using certain approved test methods, which give the results in milligrams per liter (mg/L). This is convenient because one mg/L is equal to one ppm, or part per million. This number, however, is in units of weight. Ion exchangers, on the other hand, don’t deal with weight; they deal with ions, which are the real chemical components we are trying to remove. A milligram of magnesium or calcium does not contain the same number of ions or ionic equivalents as does sodium or hydrogen. The convention commonly used is to convert to ppm as CaCO3 (calcium carbonate). Confusion arises because both the mg/L value and the CaCO3 value can be and often are reported as ppm. A good practice would be to refer to elemental components (the analysis) as mg/L and the CaCO3 equivalents (the conversion) as ppm.

The convention: CaCO3 as ppm and ppm as CaCO3  
CaCO3 is an arbitrary name choice. It has a formula or molecular weight (MW) of 100 (compared to carbon with a MW of 12). Both the calcium (Ca+2) and carbonate (CO3-2) ions are divalent; i.e., they have a charge value of +2 and -2, respectively (compared to sodium at +1) and, thus, an equivalent weight of 50.

The equivalent weight of any substance is equal to its MW divided by its valence. In the case of CaCO3, this is 100 ÷ 2 = 50. It should be noted that neither Ca+2 nor CO3-2 have an equivalent weight of 50, but the combination does. The equivalent weight of Ca+2 is 20 (MW = 40 ÷ 2 = 20) and the equivalent weight of CO3-2 is 30 (MW = 60 ÷ 2 = 30). We must therefore equate even the Ca and CO3 content of water to the equivalent weight of CaCO3. We do this by multiplying by a conversion factor (which is derived by dividing the number 50 (the equivalent weight of CaCO3) by the equivalent weight of the substance). In the case of Ca, this is 50 ÷ 20 = 2.5. For CO3, it’s 50 ÷ 30 = 1.67. Note that for demineralizer calculations, the CO3-2 ion will not exist as a divalent carbonate ion but as a monovalent bicarbonate ion (HCO3-1) with a conversion factor = 0.82). We can readily see that most common components of water have a different molecular weight, so we will have a variety of conversion factors. Table 1 lists the common elements and their conversion factors. A simple water analysis converted from mg/L to ppm as CaCO3 is shown in Table 2.

While the total dissolved mineral content of this water (residual by evaporation) would measure 432 mg/L of raw water (cation = 113.4 + anion 300.4 plus silica 18 = 431.8), the TDS as CaCO3 is 273.5 ppm for deionization (or DI) purposes. One does not add the cation and anion values together to get total TDS as CaCO3.

For anion determinations, the silica is quoted as an afterthought: “I have 273.5 ppm water with 15 ppm of silica.” For mixed bed calculations, this is 288.5 ppm water. Since a grain (of mineral) is 17.1 ppm of TDS as CaCO3, we have 10 grain water (Ca + Mg = 170 ppm as CaCO3) and for dealkalization, it’s a 10.5 grain water (HCO3 + CO3 = 184 ppm as CaCO3). There are 16.0 grains of cations and 16.9 grains of anions for deionization.

Every ion has a partner
Every ion is assumed to have a counter ion (as a dancing partner, so to speak). It should be noted that with extreme pH conditions (i.e. <4 or >10), there will be an excess of cations or anions, respectively. Normally, every cation has an anion (with the exception of silica) so the total cations should equal the total anions (without silica). Silica, a weakly ionized acid, is presumed to exist (for DI purposes) as H2SiO3 (silicic acid) and has H+ as its partner. It therefore stands alone as an anion.

Sometimes the water analysis will be incomplete in that only the offending ions (calcium, magnesium, iron, alkalinity, sulfate and silica) are reported—sodium and chloride are missing. If the analysis appears incomplete, look for the obvious. You can estimate the ppm as CaCO3 by dividing conductivity (as micromhos, or mmhos) by 2.5. In Table 2, we show conductivity as 650 umhos. Dividing by 2.5 gives us a TDS of 260 ppm.

If the totals for cation and anion are not equal, we make them equal by adding to the sodium (Na+) or chloride (Cl) values. For instance, if the cation total were 15 less than the anion, we would add 15 ppm to Na+ as CaCO3 to the cation load. Include the ppm as CaCO3 values for all monovalent cations (K+, NH4+) as part of the Na+ total and monovalent anions (NO3– or F-) as Cl- totals. For DI purposes, iron (Fe+2) can be treated as Ca+2 after conversion.

We then add silica value to the anion total to get the total anion load. This is done after balancing the cation and anion totals. For the purposes of capacity calculations, it is generally safe to ignore any items with values below 0.1 ppm. Dividing these corrected totals by 17.1 converts the ppm as CaCO3 values to grains per gallon (gpg) values. Since the ion exchange capacity is usually determined in kilograins (Kgr) per cubic foot, (one Kgr = 1,000 grains), we can now determine the throughput capacity in gallons per cubic foot (gal/ft3) of resin. Simply divide the grains of loading into the capacity of the resin.

Values for any given water analysis are not done for the convenience of the poor engineer who is trying to treat the water. They are done by convention. Hardness (Ca and Mg) and alkalinity (HCO3 + CO3 + OH) are often given as ppm as +. Metals, including iron, are often given in micrograms/L or ppb (billion) and written as µg/L. The µ symbol is the Greek letter, mu and it stands for micro (millionth) and not milli (thousandth). Nitrates (and ammonium [NH4]) are often reported in ppm as N (nitrogen). This has to be converted to ppm as NO3 by multiplying by MW ratios. N = 14 and NO3 = 62. Therefore, 10 ppm NO3 as N becomes 10 x 62/14 = 44.3 ppm as ion and 44.3 x 50/62 = 35.7 ppm as +. SO4 and H2S may be reported as total sulfur and also must be converted to ion; then to ppm as CaCO3.

The capacity of DI resin is dependent upon the water analysis, particularly the ratio of sodium to total cation and alkalinity to total anion. First, simplify the water analysis by grouping the ions to show only Ca, Mg, Na as cations and HCO3, SO4, Cl and Silica as anions. Fe adds to Ca; K to Na; CO3 to HCO3 and NO3 to Cl. Conversion calculations can be rounded up to whole numbers and percentage calculations can be approximate (with the charts you will have to read, the width of your pencil lead is a percent or two). Always err in the direction of being conservative. Always understate your capacity. No one has ever been held liable for a DI system that still works and delivers after three years. If you design your system to just barely squeak by on Day One, it will not work on Day Two and all those following. Let’s give it a try!

Resin capacity determination
To use most engineering literature and charts, you first have to break down this analysis in percentages. Our cation content is 37.7 percent Na, 55 percent Ca and 7.3 percent Mg. Our anion is 63.8 percent alkalinity, 31.0 percent free mineral acid (total of Cl + SO4) and 5.2 percent silica. You can use 40 percent for sodium and 65 percent for alkalinity, etc. The literature shows that the cation capacity (at approximately 40 percent Na and 65 percent alkalinity) to be 27.5 Kgr/ft3. Using a 10 percent engineering downgrade, we have a net design capacity of 24.75 Kgr/ft3 (27.5 x .9 = 24.75) for the cation. The anion (use a Type II) will have a book capacity of 20.3 Kgr/ft3 (with five percent silica in the influent) and we will downgrade this by 15 percent for design purposes (multiply by 0.85), which leaves us with 17.25 Kgr/ft3. The engineering downgrade factor is a safety factor applied to DI calculations to allow for wear and tear, resin loss and some fouling, as well as variations in the feedstream over the life of the resin. It is usually 10 percent for cation resins and 15 percent for anion resins and is deemed to be a three-year projection. In other words, the system should still meet capacity specifications after three years of capacity losses.

Since we have an anion load of 16.9 gpg, we will have to remove 16.9 gr/gal x 20 gal/min x 60 min/hr x 12 hr/cycle = 243,360 grains/cycle. Dividing this by 17.25 Kgr anion capacity, we see we’ll need 14 cubic feet of anion resin.

Since the cation will have to produce the water required to regenerate the anion resin, we must now add that quantity of water to our cation load before determining the size of the cation exchanger. The total gallons are 20 gpm x 60 min/hr x 12 hr/cycle = 14,400 gal. Assuming 75 gallons of water is required to regenerate each cubic foot of anion resin, add 1,050 gallons (75 gal/cu.ft. x 14 cu.ft.). The cation must therefore treat 15,450 gallons (x 16.0 gpg) or 247,200 grains. Dividing this by our cation rating of 24.75 Kgr, we will need 10 cubic feet of cation resin.

The physical design guidelines
Standard and acceptable flow rates for DI design are one to three gpm/cu.ft. In our above design for a 20-gpm system, we are at 1.4 gpm/cu.ft. of anion and 2.0 gpm/cu.ft. of cation. Hydraulic considerations are 4 to10 gpm/sq.ft. of bed area. If we choose a 30-inch diameter tank for the anion, we have 4.0 gpm/sq.ft. and a 24-inch tank for the cation gives us 6.4 gpm/sq.ft. Most capacities are calculated on a minimum of a 30-inch bed depth (the capacity drops with shorter beds) and a 60-inch maximum. Our 10 cu.ft. of cation will have a bed depth of 38.2 inches and our 14 cu.ft. of anion will have a bed depth of 34.3 inches. It is suggested that under-bedding be used in DI systems to utilize the full capacity of the resin. If this service requirement of 12 hours is extended, it may be possible to add resin to either or both vessels to make up the extra capacity. If plastic tanks are used, they are usually only 72 inches high and the usable straight sidewalls are only 13.4 and 20.2 cu.ft. respectively. This means that the freeboard is only about 35 percent for the cation and 44 percent for the anion. These are minimal and neither system can tolerate more resin.  To increase the capacity, the user would have to install a duplicate system or a new, larger system. However, if you started with 84- or 96-inch sidewall tanks, the capacities could be increased by 50 to 60 percent simply by adding resin.

Resin capacities are dependent on the water analysis (among other things) and therefore not constant for every system. There is no one-size- fits-all solution. The ratios of various ions to one another will cause the resin capacity to vary as will the quality of effluent one is targeting. Flow rate per cubic foot will also affect capacity as will temperature of service and regenerant. In addition, the amount of regenerant is usually determined by the leakage values (quality) needed. Effluent water quality is what sets the whole thing in motion. Leakage, the background ions that appear to be incomplete removal of unwanted ions, is a result of incomplete regeneration. In this example, the literature tells us that we can expect a leakage of approximately 0.5 percent sodium as a percentage of total cations or (0.005 x 273.5= 1.4 ppm). This leakage will exist in the product water as sodium hydroxide (NaOH) because the anion resin will convert all anions to the hydroxide: H+ converts to HOH and Na+ converts to NaOH. So what does this mean in water quality?  Again, according to the literature, NaOH has a resistivity that is about one-fifth that of NaCl. To put it another way, NaOH is five times more conductive than an equivalent ppm of NaCl. 1.4 ppm of NaOH gives a resistivity of 120,000 ohms/cm at 25°C (77°F) or about 8.3 microsiemens (µS).

Sodium leakage is reduced with increased regeneration level. In the above example, increasing the HCl regeneration level to eight lbs/cu.ft. would improve the leakage to 0.9 ppm, reducing the conductivity to about five µS. Always start with the determination of how low your leakage has to be (using NaOH as effluent) which sets the regeneration level. The regenerant level sets the capacity and the capacity sets the volume of resin needed.

Softener loading
There is more to building a softener than simply measuring hardness of the water and setting the dial. Your customer not only wants his or her water softened today, they want it softened tomorrow, next month and 10 years from now. This means the regeneration procedure must also be a rejuvenation procedure to keep the unit operating satisfactorily for many years. The water analysis can help us determine how to do this.

Softener throughput is influenced not only by hardness, but also by TDS, iron, temperature, flow rate and regeneration level and technique. Since TDS and iron will generally be part of the water analysis, we’ll look at those.

Hard water leakage is caused by residual hardness that is left on the resin after regeneration and bleeds off during the service run. Increasing the salt dosage can minimize it. As hard water passes through a resin bed, the hardness is exchanged for sodium or potassium. The higher the sodium level (or TDS feed level), the higher the tendency for the softened water to leach hardness back off the resin. This reduces the run length (and thus the capacity) between the baseline leakage and the breakthrough leakage. Simply knowing the TDS ahead of time can allow you to avoid costly field calls to remedy low capacity or leakage complaints by adjusting the capacity setting and using a higher salt dose ahead of time. To achieve five ppm (or less) leakage during the run, use the salt settings from Table 3 for various TDS values.

Soluble iron is exchanged onto a cation exchanger as Fe+2. However, iron may oxidize on the resin to Fe+3 and is not readily removed by salt regeneration. In addition, NaCl usually produces an alkaline pH brine which will precipitate iron during regeneration. By assigning a higher value for iron, we will increase the softener load and reduce the throughput volume. This means you will regenerate more frequently (reducing the probability of iron oxidizing on and in the resin). To overcome the potential problems of alkaline brine, you can use a resin cleaner that automatically dumps phosphoric or citric acid into the brine during regeneration or use potassium chloride (KCl), which generally produces a slightly acidic pH.

A good practice is to treat each ppm of iron as one grain of hardness. As such, in our sample water analysis, we have 10 grains loading from hardness and we add 0.3 grains for the iron (total = 10.3). Soluble iron levels as high as 30 ppm has been successfully treated with a standard softener with 10 to 12 pounds of salt/ft3 regeneration level. Citric acid (available from most chemical suppliers) works well at a level of one pound per 50 pounds of salt and can be added directly to the brine tank.

Dirty waters can plug and foul ion exchange units, causing channeling and capacity loss. Use a pre-filter if the turbidity values are >5 NTU (nephelometric turbidity units).

Natural organics (such as tannins) or iron (colloidal, organic or precipitated) may cause color, reported as APHA units. Values for color below 25 APHA are usually not noticeable by eye. Again, try to determine what is causing the color and install proper prefiltration. Softeners do not remove color. Granular activated carbon (GAC) and/or salt regeneration anion resin can often do the job.

Ion exchange systems are usually intended to function with water feed temperatures of 10 to 37.77°C (50 to 100°F). Higher temperatures can be detrimental to anion resins in DI systems. A lab-supplied water analysis may list temperature, but it is meaningless. Rather, check with the intended installation site if anion exchange enters into the picture. Cation systems should have no trouble with temperatures above 121.11°C (250°F) .

Much of the ion exchange process depends upon ions’ ability to diffuse into and out of the resin bead matrix. This is temperature dependent and is seriously slowed by cold-water operations. Resin beds should be at least 50 percent larger in diameter and 100 percent larger in volume to effectively handle water streams below 4.44°C (40°F).

Obtaining and using a good water analysis is essential to the proper design of any water filtration system, particularly an ion exchanger. There is much valuable information on a lab analysis that can help you to avoid design errors. Make sure you understand the water analysis. Check the math to make sure the units add up. Make sure the cations are equal to the anions and then add in silica to determine total loading. Use a conservative design with a downgrade for engineering, even for softeners.


  1. Dictionary of Chemistry, McGraw-Hill, New York, 1994.
  2. Kunin, Robert, Ion Exchange Resins, Krieger Publishing, New York, 1972.
  3. Wachinski, A.M. and J.E. Etzel, Environmental Ion Exchange, Lewis Publishers, New York, 1997.

About the author
C.F. ‘Chubb’ Michaud is the CEO and Technical Director of Systematix Company, Buena Park, Calif., which he founded in 1982. An active member of the Water Quality Association, Michaud has been a member of its Board and of the Board of Governors and past Chair of the Commercial/Industrial Section. He is a Certified Water Specialist Level VI. He serves on the Board of Directors of the Pacific WQA (since 2001) and chairs its Technical Committee. A founding member of WC&P’s Technical Review Committee, Michaud has authored or presented over 100 technical publications and papers. He can be reached at Systematix Inc., 6902 Aragon Circle, Buena Park CA 90620; telephone (714) 522-5453 or via email at [email protected]



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