Recarbonation and pH Correction with CO2 After Lime Softening or Lime Dosing

Carbonate equilibrium after lime treatment

Lime softening raises pH to precipitate CaCO₃ (from about pH 9.5) and Mg(OH)₂ (from about pH 10.8), so the clarified water contains carbonate alkalinity, a few tens of mg/L of excess hydroxide alkalinity if magnesium removal was the target, and a residual supersaturation of CaCO₃ that the clarifier did not have time to settle. Carbon dioxide dissolved into this water reacts in stages that follow the two dissociation constants of carbonic acid:

Two consequences follow. First, in a two-stage design the first dose is stopped near pH 10.3, where hydroxide has gone, carbonate is at its maximum and the extra CaCO₃ formed can be settled in an intermediate basin; the second dose then takes the clarified water to 8.3 to 8.8 with minimal calcium carried into supply. Single-stage recarbonation, the commoner UK arrangement after lime dosing for pH correction rather than full softening, goes straight to 8.5 to 9 and accepts that any precipitate still in suspension at that point redissolves, raising finished hardness. Second, the buffering changes with pH: between 11 and 10 the water is poorly buffered and pH drops quickly for little CO₂; between 9.5 and 8.3 the carbonate to bicarbonate conversion absorbs most of the dose, and below 8.3 the curve flattens because further CO₂ simply accumulates as dissolved gas. Overshoot below pH 7.5 is therefore slow and self-limiting, the main process-safety advantage over mineral acid.

Calculating the CO2 demand

Stoichiometry sets the base demand. Expressing alkalinity fractions in mg/L as CaCO₃ (50 mg per milliequivalent) and CO₂ at 44 g/mol:

Worked example. A single-stage softening plant delivers 10,000 m³/d at pH 11.0 with hydroxide alkalinity 30 mg/L and carbonate alkalinity 40 mg/L as CaCO₃ and 5 mg/L of unsettled CaCO₃. Target pH 8.6. Demand = 0.88 × 30 + 0.44 × 40 + 0.88 × 5 = 26.4 + 17.6 + 4.4 = 48 mg/L. At 85 percent transfer efficiency (fine-bubble diffusers at 3 m submergence) the applied dose is 57 mg/L, or 570 kg/d, roughly one 20 t bulk delivery every five weeks. A published full-scale case at Bloomington, Illinois, treating 14 MGD (53,000 m³/d) from pH 10.5 to 11.5 down to 8.8 to 9.2, reports an average CO₂ usage of 330 lb per million gallons, which is 40 mg/L, close to the theoretical dissolved requirement, with diffusers at 18 ft (5.5 m) depth and 30 minutes contact. Sizing on stoichiometry plus 10 to 20 percent is therefore sound where submergence is generous; shallow basins or coarse bubbles can double the figure.

Real waters contain other buffers (phosphate, silicate, ammonia, organic acids), so the final figure should come from a bench titration of the actual clarified water with CO₂-saturated water or a gas sparge, not from alkalinity arithmetic alone. Magnesium hydroxide in suspension consumes CO₂ slowly and raises finished magnesium if it is not removed before the second stage.

Reaction kinetics: why pH sets the rate-limiting step

Dissolved CO₂ reacts by two parallel routes. Hydration with water, CO₂ + H₂O → H₂CO₃, is slow: the first-order constant is 0.037 s⁻¹ at 25 °C and 0.008 s⁻¹ at 10 °C, half-lives of 19 and 88 seconds. Direct reaction with hydroxide, CO₂ + OH⁻ → HCO₃⁻, has a second-order constant from the Pinsent correlation log₁₀k = 13.635 − 2895/T, giving 8,400 L/mol/s at 25 °C and 2,600 at 10 °C. At pH 11 ([OH⁻] = 10⁻³ mol/L) the pseudo-first-order rate is 8.4 s⁻¹ at 25 °C, a half-life of 80 milliseconds; at pH 9 it falls to 0.08 s⁻¹, which is then slower than the sum with hydration. Above pH 10 the chemistry is effectively instantaneous and the process is limited by how fast gas can be dissolved; near the endpoint it becomes reaction-limited and a few minutes of plug-flow contact after the last dosing point are needed for the pH to settle before it is measured and acted on.

Chemical enhancement of the mass transfer itself is modest in lime water. With the Hatta number Ha = (k_OH[OH⁻] D)^0.5/k_L, D = 2 × 10⁻⁹ m²/s and a bubble-side k_L of 2 × 10⁻⁴ m/s, Ha is about 0.65 at pH 11 and the enhancement factor Ha/tanh(Ha) is 1.13; at pH 12 Ha reaches 2 and enhancement about 2. Diffuser systems should therefore be sized on physical absorption, with the enhancement treated as margin.

Gas transfer: diffusers against pressurised contactors

Henry’s constant for CO₂ is 0.034 mol/L/atm at 25 °C and 0.054 at 10 °C, so water in contact with pure CO₂ at atmospheric pressure holds 1.5 to 2.4 g/L, thirty to fifty times the process dose. Solubility is never the constraint; interfacial area and contact time are. Three arrangements are used:

• Fine-bubble diffusers in a basin. Ten States Standards (GLUMRB 2018, section 4.9.3) call for a total detention of 20 minutes in two compartments, a mixing compartment of at least 3 minutes, and diffuser submergence of at least 7.5 ft (2.3 m). Transfer efficiency rises with submergence, roughly 5 to 7 percent per metre for fine bubbles, and the Bloomington plant at 5.5 m achieved near-stoichiometric use. Porous diffusers foul with CaCO₃ and Mg(OH)₂ in exactly the water they serve; allow for acid cleaning or specify non-porous membrane diffusers.
• Pressurised side-stream saturators. A side stream of 1 to 3 percent of flow is saturated with CO₂ in a pressure vessel with gas headspace at 2 to 4 bar and injected ahead of the basin. Pure CO₂ at 3 bar absolute dissolves to 4.5 to 7 g/L, so a 2 percent side stream carries 90 to 140 mg/L into the main flow. A 120 MGD lime plant at Minneapolis reported 21 to 57 percent (average 40 percent) less CO₂ than round-plate diffusers for a 15 mg/L dose, jar tests showing 85 percent of the pH change within five minutes, and stable pH readings in place of a 9 to 10.5 scatter across the chamber. Injection before the basin inlet rather than at the old diffuser location was what fixed the mixing.
• In-line injection and jet-loop reactors. Venturi or two-fluid nozzle contactors for smaller flows and site water; a laboratory jet-loop study with 15 percent CO₂ gas reached 85 to 98 percent gas utilisation at liquid to gas ratios above 1.1.

For a new municipal plant the pressurised side stream is usually the better whole-life choice because gas efficiency, pH stability and controllability all improve at once; diffusers remain sensible where a deep basin already exists and gas cost is low. Either way, the pH probe used for control must sit after a few minutes of plug flow, not at the dosing point, or the controller chases a reading that has not finished reacting; see the pH neutralisation systems article for loop design.

Finished water stability: Langelier and CCPP

Recarbonation is finished not at a pH but at a stability target. Langelier’s saturation index compares the actual pH with the pH at which the water would be in equilibrium with CaCO₃:

LSI tells the sign but not the magnitude of scaling, so the calcium carbonate precipitation potential (CCPP) is preferred: the mass of CaCO₃ in mg/L that would precipitate (positive) or dissolve (negative) for the water to reach equilibrium, found by solving the carbonate system iteratively or in PHREEQC. Softened waters are commonly finished at LSI 0 to +0.3 or CCPP 0 to +4 mg/L, enough to maintain a thin protective layer on iron mains without fouling meters and heaters, and with alkalinity held at or above 20 mg/L as CaCO₃, the Ten States minimum for a stable pH. Worked check on the example water: finished calcium 50 mg/L (pCa = 2.90), alkalinity 70 mg/L as CaCO₃ (pAlk = 2.85), at 10 °C with activity corrections giving pK₂ − pK_s = 2.0, pH_s = 2.0 + 2.90 + 2.85 = 7.75. At the target pH of 8.6 the LSI is +0.85 and the CCPP about 6 mg/L: too scale-forming. Dosing on to pH 8.1 brings the LSI to +0.35 and CCPP near 2 mg/L. Lime plants that stop at 8.6 because that is where the pH curve flattens often ship water that scales; the endpoint must be set from CCPP, and it moves with temperature.

Safety and control points

• CO₂ is denser than air and toxic in its own right: GB workplace exposure limits are 5,000 ppm over 8 hours and 15,000 ppm over 15 minutes, and effects become life-threatening well before oxygen displacement matters. Ten States require recarbonation tanks to be outdoors or sealed and vented, with CO₂ alarms in low areas; sumps and galleries beside the basin are confined spaces.
• Bulk storage at about 20 bar and −20 to −30 °C with electric or ambient vaporisers; size the vaporiser for peak dose, not average, and keep the gas line above 8 bar during transfer to avoid dry-ice blockage.
• Control is feedforward on flow and alkalinity, trimmed by downstream pH; a pure feedback loop on a probe at the injection point oscillates because of the reaction lag described above.
• Expect diffuser fouling, carbonate scale on the probe and crystalline deposits in the pipe between clarifier and basin; the Bloomington plant found that pipe incrustation, not the basin, became its bottleneck, which argues for dosing as close to the clarifier outlet as mixing allows.