Water tools

Lime and soda ash softening: doses, recarbonation, sludge and finished hardness

Lime removes carbonate hardness as calcium carbonate; magnesium needs excess lime and a higher pH; noncarbonate hardness needs soda ash. The stoichiometry is a bookkeeping exercise in milligrams per litre as calcium carbonate.

Flowm³/d

Calciummg/L as CaCO₃

Magnesiummg/L as CaCO₃

Alkalinitymg/L as CaCO₃

Temperature°C

Process

Residual calcium hardnessmg/L as CaCO₃

Chemicals

Quicklime (CaO, 100%)

168.6mg/L

Quicklime

8,430kg/d

Hydrated lime equivalent

222.8mg/L

Soda ash (Na₂CO₃)

0.0mg/L

Recarbonation CO₂

16.5mg/L

Sludge

Calcium carbonate sludge

459mg/L

Calcium carbonate sludge

22,929kg/d

Magnesium hydroxide sludge

0.0mg/L

Water

Finished total hardness

55.0mg/L as CaCO₃

Raw total hardness

212.5mg/L as CaCO₃

Carbonate / noncarbonate

195 / 18

Carbonic acid in the raw water

113.6mg/L as CaCO₃

How it works

Lime reacts first with carbonic acid, then with calcium bicarbonate, and magnesium takes a second equivalent:

{CO}_{2} + {Ca(OH)}_{2} \to {CaCO}_{3} + H_{2} O {Ca}^{2 +} + 2 {HCO}_{3}^{-} + {Ca(OH)}_{2} \to 2 {CaCO}_{3} + 2 H_{2} O

(1)

{Mg}^{2 +} + 2 {HCO}_{3}^{-} + 2 {Ca(OH)}_{2} \to 2 {CaCO}_{3} + {Mg(OH)}_{2} + 2 H_{2} O

(2)

With everything in mg/L as calcium carbonate, selective calcium removal takes lime equal to carbonic acid plus calcium carbonate hardness; excess lime takes carbonic acid plus alkalinity plus magnesium plus the excess. Quicklime is 0.56 times the figure, carbon dioxide 0.44, soda ash 1.06 per unit of noncarbonate hardness. Carbonic acid from pH and alkalinity:

[H_{2} {CO}_{3}^{\cdot}] = \frac{[{HCO}_{3}^{-}] [H^{+}]}{K_{1}} \log K_{1} = 14.8435 - \frac{3404.71}{T} - 0.032786 T

(3)

where

$[H_{2} {CO}_{3}^{\cdot}]$: carbonic acid, mol/L
$[{HCO}_{3}^{-}]$: bicarbonate, mol/L, from the alkalinity
$[H^{+}]$: hydrogen ion, 10⁻ᵖᴴ mol/L
$K_{1}$: first dissociation constant of carbonic acid
$T$: absolute temperature, K

Complete-reaction stoichiometry corrected only by the practical solubility residuals, for predesign; jar tests and equilibrium models refine it. Residual calcium about 30 and magnesium about 10 mg/L as calcium carbonate are the practical floors.

Lime and soda ash softening: doses, recarbonation, sludge and finished hardness

How it works

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