Ion Exchange calculator (2)

This calculator is under construction.

This calculator is based on theoretical calculations and explains how to use selectivity coefficients, separation factors and how to determine the maximum volume of water that can be treated with a resin before breakthrough happens. The calculator also shows some calculations that are needed for the sizing of an ion exchange installation. But again be careful, the calculations are based on theoretical formulas and are not corrected with results from real ion exchange water treatment plants.

There is an example under the calculation tables to show how the calculations are made by the calculator.

Table 1: Input table for anion concentrations

Anions	MW g/mol	Concentration	unit	converted concentration	unit
NO3-	62.00		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
NO2-	46.01		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
Cl-	35.45		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
SO42-	96.06		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
HCO3-	61.02		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
F-	19.00		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
TOTAL			eq/L

Table 2: Input table for cation concentrations

Cations	MW g/mol	Concentration	unit	converted concentration	unit
Na+	22.99		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
K+	39.10		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
Ca2+	40.08		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
Mg2+	24.31		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
NH4+	18.04		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
Mn2+	54.94		eq/L meq/L g/L mg/L mol/L mmol/L		eq/L meq/L g/L mg/L mol/L mmol/L
TOTAL			eq/L

Table 3: Table for some sizing parameters for an ion exchange installation

	Anion removal	Cation removal
Exchange capacity			eq/L meq/L
Density Resin			kg/L kg/m3
service flow			m3/h l/h m3/day l/day
time between 2 regenerations (1 cycle)			hour(s) day(s)
Ions in water (1 cycle)			eq/cycle
required-resin volume theoretical			L/cycle
calculated mass of resin			kg/cycle
Total required surface area			m2
Diameter Column			m

Table 4: Output table for equilibrium composition and percentile distributions for occupied sites on the resin

Anions (eq/L) Lwater/Lresin NO3- NO2- Cl- SO42- HCO3- F- total

Cations (eq/L) Lwater/Lresin Na+ K+ Ca2+ Mg2+ NH4+ Mn2+ total

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Example calculation to illustrate the equations used by the calculator:

The following points are treated in the example:

• Determine the separation factor for an ion with respect to the other ions in the water.
• Determine the equilibrium composition of the resin, thus calculating how much of the Exchange capacity is used by the different ions.
• Determine the maximum amount of water that can be treated per liter of resin before breakthrough occurs.
• Determine the percentile distribution of the occupied sites in the resin by the different ions.

Lets take water with the following composition:

Table 5: Composition of the water used in this example

We want to eliminate anions from the water so we have to use an anionic resin. The resin has a standard exchange capacity of 1,4 eq/L and a density of 0,7 kg/L.

In the Literature¹ you can find the following values for selectivity coefficients and separation factors (Table 6).

Table 6: Selectivity coefficient and separation factor for a strong base anionic resin

Anion	Selectivity Factor	Separation Factor
Cl-	1.0	1
NO3-	4	3.2
SO42-	0.15	9.1

Explanation of the selectivity coefficient and separation factor notation:

	selectivity coefficient for anion i exchanging with Cl- onto resin
	separation factor for anion i exchanging with Cl- onto resin

The resin has different preferences for the ions in the water. So at equilibrium the ions do not occupy the same amount of resin. The resin prefers much more ions with a high valence. Relation (1) can be written regarding the selectivity of the resin for the different ions in our water sample:

(1)

The different separation factors for an ion with respect to the other are calculated with formula (2):

(2)

	separation factor for counterion i with respect to ion k
	separation factor for counterion i with respect to ion j
	separation factor for ion j with respect to ion k

Calculation separation factor for Nitrate NO₃^- with respect to the 2 other ions using formula (2):

example formula used to calculate

So by putting the write parameters in formula (2) the following separation factors can be calculated for nitrate with respect to the 2 other ions:

The calculated separation factors for SO₄^2- with respect to the 2 other ions are:

With these separation factors calculated above you can determine the equilibrium capacity of the resin for the different ions.

eq/L

eq/L

eq/L

To control if the result is coherent you can add the equilibrium capacities used by the different ions to see if it is equal to the total exchange capacity of the resin which is 1,4 eq/L.

eq/L

So you can see that the sum of the equilibrium capacities occupied by the different ions is equal to the total exchange capacity of the resin.

Calculation of the maximum volume of water that can be treated per liter of resin before breakthrough occurs:

Lwater/Lresin

Lwater/Lresin

Lwater/Lresin

As you can see from the calculations of V_max the breakthrough occurs first for Chloride when 60 L of water has been treated. So if you don't want to have chloride in your water you have to stop the ion exchange system or if you have a duplex system you can switch to the other column available and regenerate the column that is saturated with the absorbed ions. If the presence of chloride ions in water in not an issue you can than treat 178 L of water per liter of resin before the breakthrough for Nitrates occurs.

Calculation of the percentile repartition of the occupied sites in the resin:

Lets calculate the percentile distribution for the different concentrations of ions in our water sample (table 5)

As you can see the percentile distribution for concentrations is not the same as the percentile distribution for the occupied sites in the resin at equilibrium. This is due to the fact that the resin is more selective for certain ions. The results for the calculation above are placed in the comparative table 7.

Anion
	20,8 %	4,3 %
	41,7 %	72,9 %
	37,5 %	22,8 %

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Warning: Lenntech BV cannot be held responsible for errors in the calculation, the program itself or the explanation. For questions or remarks please contact us.