Softening (hardness correction).
Preliminary remarks.

Hard water also forms deposits that clog plumbing. These deposits, called "scale", are composed mainly of calcium carbonate (CaCO3), magnesium hydroxide (Mg(OH)2), and calcium sulfate (CaSO4). Calcium and magnesium carbonates tend to be deposited as off-white solids on the inside surfaces of pipes and heat exchangers. This precipitation (formation of an insoluble solid) is principally caused by thermal decomposition of bicarbonate ions but also happens in cases where the carbonate ion is at saturation concentration.The resulting build-up of scale restricts the flow of water in pipes. In boilers, the deposits impair the flow of heat into water, reducing the heating efficiency and allowing the metal boiler components to overheat. In a pressurized system, this overheating can lead to failure of the boiler. The damage caused by calcium carbonate deposits varies on the crystalline form, for example, calcite or aragonite.
It is often desirable to soften hard water. Most detergents contain ingredients that counteract the effects of hard water on the surfactants. For this reason, water softening is often unnecessary. Where softening is practised, it is often recommended to soften only the water sent to domestic hot water systems so as to prevent or delay inefficiencies and damage due to scale formation in water heaters.

Softening terms of reducing carbonate and non-carbonate hardness. Depending on the process, so we have:

Different softening methods include:

It will be discussed in these pages, only by precipitation processes (decarbonisation) and ion exchange, that are the most reliable and / or economic present and treated in Equilwin software.

Softening by carbonatation - Reducing carbonate hardness (calcium and Alkalinity ) :
Principle of lime softening.
(with caustic soda, shortcut> here)
The introduction of slaked lime Ca [OH]2 (in the form of limewater) causes the simultaneous reactions (precipitation as calcium carbonate CaCO3):

(therefore, to reduce the calcium of 4 mg (1 °F) requires 7.4 mg (74/10) of lime Ca [OH]2, and is formed 20 mg (200/10) of precipitated calcium carbonate CaCO3).
Note that the reduction of magnesium carbonate hardness (Mg) is feasible only that at pH> 9.5.
This reaction can continue until a residual degree of alkalinity of 15 mg/L as CaCO3 (1.5 °F).

(ie, 0.84 mg Ca [OH] 2 per mg of CO2 Aggressive).

The total quantity of reagent required is (100% pure product):

Ca[OH]2 (mg/l) = 7.4 [D hardness + D magnesium hardness + D(CO2/4.4)]

with, CO2 in mg /L, and hardness in mg/L as CaCO3 (or °F), and D as equal to the difference between the initial and final values.

Note the evolution of the alkalinity (TAC) during the reaction:

Final Alkalinity (TAV in ° F) = (initial Alkalinity - removed Calcium Hardness) + [10 °F/88] free CO2 removed

with, Alkalinity (TAC) and Ca in °F, free CO2 in mg/l.

When decarbonation and maximum softening are met, we have TAC = 2 TA.

The table below recalls the theoretical and practical quantities of reagents required, and the weight of carbonate (regardless of free CO2):
Carbonate hardness removed :
To decrease by 1 ° F:

Amount of precipitated CaCO3:

100% Ca(OH)2
Trade product

by °F
by mg Ca(OH)2

* ( % of purity/100)

 In practice, one may use the following formula:

Lime (in grams per cubic meter of water)= 10 x D Calcium Hardness (in °F)


Principle of caustic soda softening.
The introduction of caustic soda (in the form of solution) causes the simultaneous reactions:
(1) >precipitation of calcium carbonate CaCO3, and formation of sodium carbonate.

2NaOH (2x40=80 mg) + Ca[HCO3]2 (40 mg Ca ou 10°F) >>> CaCO3 (100 mg ou 10°F) + Na2CO3 (106 mg) + 2H2O

(2) >precipitation of calcium carbonate CaCO3, and formation of sodium bicarbonate (sodium hydrogencarbonate).

Na2CO3 (106 mg) + Ca[HCO3]2 >>> CaCO3 (100 mg or 10°F) + 2 NaHCO3 (84x2=168 mg or 10°F)

Note: sodium carbonate Na2CO3 formed can also react with the permanent hardness following the reactions below (although only at high pH):

CaSO4 + Na2CO3 >>> CaCO3 + Na2SO4
CaCl2 + Na2CO3 >>> CaCO3 + NaCl

And also, there is reaction with the dissolved free CO2:
Dissolved carbon dioxide is changed into sodium bicarbonate (NaHCO3-).

NaOH (40 mg) + CO2 (44 mg) >>> NaHCO3

(ie, 0.91 mg NaOH per mg of CO2)

Theoretical rate of caustic soda to soften. ( par rapport aux réactions (1) et (2) ).

For one mole of NaOH, is removed:

and in milliequivalents, there is a decrease of 2 °F of Calcium Hardness and 1°F TAC (Alkalinity).

To precipitate 1°F of Calcium, requires 0.1 mmol as NaOH, or 4 mg /L of pure sodium hydroxide.

The total quantity of reagent required is (100% pure product, in g/m3 or mg/L) :

NaOH (mg/L) = (4 x DCalcium) + (0.91 x D CO2)

with, Calcium in °F et CO2 in mg/L, and D as equal to the difference between the initial and final values.

Note the evolution of the alkalinity (TAC, °F) during the reaction:

final TAC = [initial TAC - 1/2 removed Ca] + [5 °F / 44] removed free CO2

with, Alkalinity (TAC) and Ca in °F, free CO2 in mg/l.

The table below recalls the theoretical and practical quantities of reagents required, and the weight of calcium carbonate (regardless of free CO2):
Carbonate hardness removed :
To decrease by 1 ° F:

Amount of precipitated CaCO3:

pure 100% NaOH
Trade product

by °F
by mg NaOH

* ( % of purity/100)

In practice, one may use the following formula:

NaOH (in gramme by cubic meter of water) = 5 x D THCa

(D as equal to the difference between the initial and final values).

A visit possibly the Hydro-land French site :
1 - Mise en oeuvre des traitements
2 - Calculation method > Free program offered by the author: see Programmes informatiques >>> Decarbo (in French) > calculation spreadsheet (Excel sheet type).

Ion exchange softening.
See possibly by this link on Hydro-Land, the general principles of ion exchange (in French) > principes généraux de l'échange d'ions

Ion exchange resins are organic polymers containing anionic functional groups to which the dications (Ca2+) bind more strongly than monocations (Na+). Inorganic materials called zeolites also exhibit ion-exchange properties. These minerals are widely used in laundry detergents. Resins are also available to remove carbonate, bi-carbonate and sulphate ions which are absorbed and hydroxide ions released from the resin.

Principle of softening with ion exchange resins..
The ion exchange devices reduce the hardness by replacing calcium and magnesium (Ca2+ and Mg2+) with sodium or potassium ions (Na+ and K+):

[C+, A-] ......+...... R-Na+ >>>>>>>>>>>>>>>>>>> R-C+.....+.......... [Na+, A-]
..................Water inlet.......resin, form Na....................................fixed ions.............removed ions (water outlet)

(with, C+ = cations, A- = anions, R = indicates the organic portion of the resin )

Specifically, we have:


Regeneration of ion exchange resins:
After exhaustion, the resin can be convened to the sodium form with a sodium chloride solution. The waste waters eluted from the ion exchange column containing the unwanted calcium and magnesium salts are typically discharged to the sewage system.

R-(Ca²+/ Mg²+) ....+..Na+,C+ >>>>>>>>>>>>>>>> R - Na+ ...+ .....Ca²+,Cl- / Mg²+,Cl-
saturated resin......sodium chloride.............. .................fixed ions..... removed ions (waste water)
(with, C+ = cations, A- = anions, R = indicates the organic portion of the resin )

Resin capacity is usually expressed in terms of equivalents per liter (eq/L) of resin (10 000°F/l).
The degree to which the exchange takes place is limited by the preference the resin exhibits for the ion in solution. Consequently, the use of the resins exchange capacity will be limited unless the selectivity for the ion in solution is far greater than for the exchangeable ion attached to the resin.
Useful exchange capacity is according to regenation rate and depending to cocurrent and countercurrent flow.
The ionic leakage is also a function of the elements of water to be treated and the quantities of regenerant.
Note that the regeneration against the current (countercurrent regeneration) makes a substantial gain in capacity and leakage of hardness.

Examples of useful capacities that are based on:

Example (in French): Resin HP 111E (Imac™ HP of Rohm & HAAS manufacturer), substituted by HP1110 Na ).


(equivalents per liter of resin)

Correction factor C
(based on the total hardness)
Hardness (meq/liter)
Correction factor D
(based on the height of the resin layer)
Height (mm)


Examples of ionic leakage based on flow regeneration sense, the total salinity and the sodium :

Correction factor A & B:
Correction factor A
(based on the total salinity)
Salinité (en meq/litre)
Correction factor B
(based on the amount in sodium)
Sodium (% Na)

Example of calculation:
Reminder: 1 eq / liter = 5000 ° F / liter (meq 1 = 5 ° F or 1 ° F = 0.2 meq), mineralization in meq L = mineralization in mg L / 75.86 (approximate formula).

The average leakage is obtained by multiplying the basic leakage (see graph above) by the correction factors A and B (Tables), ie, average leakage = ionic leakage x A x B

The regeneration mode and regeneration level selected to determine the average figures, a useful basic capacity to be multiplied:

So: Usable capacity = cap. useful x C x D

Example (continued):
Analysis of water to be treated (softening):

Data :

Results :
- Available capacity (for the rate and direction of regeneration selected): : 1,2 x 0,95 (C) x 1,0 (D) = 1,140 eq/L de resin R , or 1140 meq/l R (5 700 °F/liter R)

- Average ionic leakage (water outlet) : 0,010 x 1,9 (A) x 1(B) = 0,019 meq/L (or 0,095 °F)

- Calculating a bypass of the incoming water (the untreated part flow):

Calculation of treated water flow (water outlet in m3 per hour): admixture

Total flow (m3/h) x (inlet hardness - desired hardness)
(inlet hardness - hardness leakage)

thus, for example:
Treated water flow :

50 x (40 - 12)
—————— = 35.083, rounded to 35.1 m3/h (ie, 70 % of the total inlet flow)
..(40 - 0.095)

Total flow bypass (inlet water derived, therefore untreated input) :
(total production rate - treated water flow)

(50 - 35.1) = 14.9 m3/h (ie, 30 % of the total inlet flow ).


Volume of resin (RV) :
base: 1 regeneration for 1 production cycle (20 hours time), we obtain a volume of 702 m3 of treated water per cycle (35.1 m3/h x 20), or 702,000 liters.

RV = [treated water (m3/h) x duration of cycle (h) x 1000 x D Hardness (°F) ] / available capacity (°F/L R)

with D Hardness = (inlet hardness - output hardness ), RV in liters


RV = [35.1 x 20 x 1000 x (40-0.095)] / 5,700 = 4914,62 liters
> 4,915 liters (rounded), ou 4.915 m3

NB - exchanged ions (water inlet> resin) = (40 -0.095) = 39.905 ° F or meq (8-0.019) = 7.981 meq / L,
and total fixed ions (one cycle) = (7.981 x 702) = 5602.662 equivalents.

Note that the load volume (treated water production) will be 7.14 V / V (35.1 / 4.915).
[Water Volume (m3/h) / Resin volume]

Composition of water in the exchanger outlet:

Note: we can see that this treatment added 128.8 mg / L of sodium (approximately) to the existing content in the inlet water (10 mg /L).

Design of the facility (Tank of ion exchange).
- If the chosen resin to a height of 1.50 m (RV = 4.915 m3), is obtained a circular inner section of an exchanger of about 3.277 m² (4.915 / 1.50), and therefore an inner diameter of 2.043 m. (Root² [4 x 3.277 / p]).

Choose (for example), two identical tanks, with a resin volume (unit) of 2.458 m3, with:

The total amount of salt (sodium chloride solution 100 gNaCl / liter of water).
Rate (regeneration level) = 100 g/liter of resin ou 100 kg/m3 resin, thus :

(100 x 4,915 ) = 491,500 g NaCL ou 491.5 kg NaCl (for the complete regeneration of the two tanks).

Total volume of solution (concentration 100 gNaCl / l) = 4915 liters of solution (4.915 m3), or 2457.5 liters (2.4575 m3) of solution by tank.
Minimum contact time of 30 mm> flow regeneration / exchanger (2.4575 / 30 x 60) = 4.915 m3 / h.

The column is backwashed to remove suspended solids collected by the bed during the service cycle and to eliminate channels that may have formed during this cycle. The back- wash flow fluidizes the bed. releases trapped particles. and reorients the resin particles according to size.
Volume of water (countercurrent):

Backwash rate flow by tank :

Backwash duration :

Final Note:
The softened water may be aggressive and / or corrosive; Indeed, replacement of calcium ions with sodium ions, not possible to envisage a protective deposit of calcium carbonate (Tillmans layer); and also the presence of sulphates and / or chlorides, accelerates corrosive tendencies of the water towards the metals.
For this reason, it is advisable to water distribution (and heating), not down the hardness below 5 °F (50 mg/L as CaCO3).

Process control:
The measurement of hardness is the method which allows monitoring of a softening system : measuring water output hardness (the leakage), and the hardness of water outlet of the facility (after mixing water).

Attached is a sample tracking curve (TH=Total Hardness):

Calculation method.
Free program offered by the author (in French): see Programmes informatiques >>> AdouEI (Adoucissement par Echanged'Ions)
> calculations spreadsheet (Excel sheet type).

Note: Calculations are valid whatever the amount of water to be softened, so domestic or industrial installation (knowledge dimensional, physical and chemical parameters of the water and the resin are essential ).

(use your browser)