Question 2 of 5: Ion Exchange Softening and the Significance of Five Water Quality Parameters

Question 2: Ion Exchange Softening and the Significance of Five Water Quality Parameters (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Part (a) — The ion exchange softening process (10 marks)

Given. A groundwater of total hardness 300 mg/L as CaCO₃ is to be softened to a delivered hardness of 100 mg/L as CaCO₃; the plant treats 2 000 m³/d; the sodium-form strong-acid cation resin has a working exchange capacity of 45 kg as CaCO₃ per m³ of resin and the vessel holds 3.0 m³ of resin.

Find. The chemistry of exchange and regeneration, and — as the quantitative demonstration — the split-treatment bypass fraction and the run length between regenerations.

Approach. Ion exchange is a reversible, stoichiometric, equivalent-for-equivalent swap on a solid; write the service reactions, then the regeneration reaction, then close the loop with an equivalents balance on the resin bed.

Ion exchange softening passes the raw water down through a packed bed of insoluble resin beads — a cross-linked polystyrene–divinylbenzene matrix bearing fixed sulfonate groups, $\mathrm{R\!-\!SO_3^-}$ — whose mobile counter-ions are sodium. The hardness ions Ca²⁺ and Mg²⁺ have a higher affinity for the sulfonate site than Na⁺ does (the selectivity sequence for a strong-acid resin is roughly $\mathrm{Ca^{2+} > Mg^{2+} \gg K^{+} > Na^{+}}$), so they displace sodium from the resin and are held. Writing the resin as NaR, the service reactions are:

$$\mathrm{Ca^{2+}} + 2\,\mathrm{NaR} \rightarrow \mathrm{CaR_2} + 2\,\mathrm{Na^{+}}$$

$$\mathrm{Mg^{2+}} + 2\,\mathrm{NaR} \rightarrow \mathrm{MgR_2} + 2\,\mathrm{Na^{+}}$$

Written on the parent salts, so that the anions are visible, the same reactions read

$$\mathrm{Ca(HCO_3)_2} + 2\,\mathrm{NaR} \rightarrow \mathrm{CaR_2} + 2\,\mathrm{NaHCO_3}$$

$$\mathrm{MgSO_4} + 2\,\mathrm{NaR} \rightarrow \mathrm{MgR_2} + \mathrm{Na_2SO_4}$$

Three features of these equations carry the marks. First, the exchange is equivalent for equivalent: two sodium ions leave for every divalent hardness ion retained, so the total cationic equivalents in solution — and hence the total dissolved solids in equivalents — are unchanged. Second, the anions are untouched: bicarbonate, sulfate and chloride pass through unaltered, which is why ion exchange, unlike lime softening, removes no alkalinity and produces no chemical sludge. Third, the process is sodium-substituting: every 1 mg/L of hardness removed as CaCO₃ adds $2 \times 23/100 = 0.46$ mg/L of sodium, which is the reason ion-exchange softening is restricted where sodium-restricted diets or sodium-sensitive irrigation are a concern.

When the exchange sites are exhausted the hardness front breaks through and the bed is regenerated with a strong brine, typically 8–12 per cent NaCl. Regeneration drives the reaction backwards by mass action: the sodium concentration in the brine is so high that it overwhelms the resin's intrinsic preference for calcium.

$$\mathrm{CaR_2} + 2\,\mathrm{NaCl} \rightarrow 2\,\mathrm{NaR} + \mathrm{CaCl_2}$$

$$\mathrm{MgR_2} + 2\,\mathrm{NaCl} \rightarrow 2\,\mathrm{NaR} + \mathrm{MgCl_2}$$

A hydrogen-form (strong-acid, H-cycle) resin can be used instead where dealkalisation is also wanted; it is regenerated with sulfuric or hydrochloric acid and its service reaction destroys alkalinity:

$$\mathrm{Ca(HCO_3)_2} + 2\,\mathrm{HR} \rightarrow \mathrm{CaR_2} + 2\,\mathrm{H_2CO_3} \rightarrow \mathrm{CaR_2} + 2\,\mathrm{H_2O} + 2\,\mathrm{CO_2}\!\uparrow$$

A complete service cycle is: service (downflow, until hardness breakthrough) → backwash (upflow, to lift out trapped turbidity and reclassify the bed) → brine injection (slow downflow contact) → slow rinse (displacement of brine) → fast rinse (to waste, until the effluent conductivity and hardness are on specification) → back to service.

Because a sodium-cycle bed produces water of essentially zero hardness — which is corrosive, unstable and unpalatable — the plant is always operated in split treatment: only enough flow is softened to hit the delivered target, and the balance bypasses. The bypass fraction follows from a hardness mass balance on the blend point, taking the softened stream as zero hardness:

1. Set the blend fraction from a hardness balance. With $x$ the bypass fraction, $x\,C_{\text{raw}} + (1-x)(0) = C_{\text{target}}$, so $$x = \frac{C_{\text{target}}}{C_{\text{raw}}} = \frac{100}{300} = 0.333$$ One third of the flow, 667 m³/d, bypasses and the remaining 1 333 m³/d is softened.
2. Convert the softened flow into a hardness load on the resin. Recalling that 1 mg/L equals 1 g/m³, $$L = Q_{\text{soft}} C_{\text{raw}} = 1\,333 \times 300 = 4.00\times10^{5}\ \text{g/d} = 400\ \text{kg/d as CaCO}_3$$
3. Divide the bed capacity by the load to get the run length. The bed holds $45 \times 3.0 = 135$ kg as CaCO₃, so $$t_{\text{run}} = \frac{135}{400} = 0.3375\ \text{d} = \boxed{8.1\ \text{hours between regenerations}}$$
4. Size the regenerant. Taking 50 g CaCO₃ per equivalent, the bed carries $135\,000/50 = 2\,700$ equivalents. At 58.44 g NaCl per equivalent and the 80 per cent excess normal for a strong-acid resin, $$m_{\text{NaCl}} = 2\,700 \times 58.44 \times 1.8 / 1\,000 = 284\ \text{kg salt per regeneration}$$ which is about three regenerations per day and roughly 850 kg/d of salt — the operating cost that dominates ion-exchange softening and the reason larger utilities prefer lime softening.

Part (b) — Significance of five water quality parameters (15 marks)

The five parameters below are grouped by why they are measured: two are health-based (fluoride, nitrate), one is aesthetic and operational (sulfate), and two are process-control parameters that shape every other treatment decision (alkalinity, hardness). Numerical limits are those of the Guidelines for Canadian Drinking Water Quality (Health Canada), which distinguish a maximum acceptable concentration (MAC, health-based and enforceable when adopted provincially), an aesthetic objective (AO), and an operational guidance value (OG).

Fluorides. Fluoride is the classic dose–response parameter, beneficial and harmful within a factor of two. At about 0.7 mg/L it is incorporated into tooth enamel as fluorapatite and measurably reduces dental caries, which is why Health Canada sets 0.7 mg/L as the optimal concentration for community water fluoridation. Above roughly 1.5 mg/L — the Canadian MAC — chronic exposure produces dental fluorosis (mottling and pitting of enamel), and prolonged exposure at several mg/L causes skeletal fluorosis. High natural fluoride is a groundwater problem, associated with fluorite and apatite-bearing formations. Because both the deficiency and the excess matter, fluoride is one of the few parameters a utility may deliberately add, and the associated risk is a feed-system failure: an overfeed incident is an acute public-health event, so fluoride saturators are interlocked and continuously monitored. Removal, where natural levels are high, is by activated alumina adsorption, bone char, or reverse osmosis — conventional coagulation and filtration are ineffective.

Nitrates. Nitrate is the fully oxidised, most mobile form of nitrogen and the endpoint of nitrification of ammonia from fertiliser, manure, and septic-field or sewage discharges. It is significant on two fronts. In drinking water it is an acute infant hazard: in the low-acid stomach of an infant under six months, nitrate is reduced to nitrite, which oxidises haemoglobin to methaemoglobin and destroys its oxygen-carrying capacity — methaemoglobinaemia, or blue-baby syndrome. The Canadian MAC is 45 mg/L as nitrate, equivalent to 10 mg/L as nitrate-nitrogen. Because nitrate is fully soluble, anionic and non-volatile, it passes straight through conventional treatment; removal requires anion exchange, reverse osmosis, or biological denitrification, and boiling concentrates it, so a boil-water advisory is exactly the wrong advice. In the receiving environment nitrate is the second significant issue: with phosphorus it drives eutrophication, particularly in estuarine and marine waters where nitrogen rather than phosphorus is the limiting nutrient. Nitrate is also a reliable tracer of agricultural or septic contamination of an aquifer, so a rising trend is an early warning about well-field vulnerability well before any pathogen appears.

Sulfates. Sulfate enters water from gypsum and other evaporite minerals, from the oxidation of sulfide ores (acid rock drainage), and from industrial discharge. Its significance is chiefly aesthetic and operational rather than toxicological: Health Canada sets an aesthetic objective of 500 mg/L, above which the water tastes bitter and has a transient laxative effect on unaccustomed consumers, especially infants and travellers. Operationally, sulfate is more consequential than that limit suggests. Calcium sulfate scales membranes and heat-exchange surfaces; sulfate is not removed by lime softening and so passes through as non-carbonate hardness requiring soda ash; and in the anaerobic zones of a sewer or a sludge digester, sulfate-reducing bacteria convert it to hydrogen sulfide, which causes odour complaints, is acutely toxic in confined spaces, and is oxidised biologically on crown surfaces to sulfuric acid — the crown corrosion that destroys concrete sewers. Sulfate is also a marker parameter for acid rock drainage from mining and for coal-fired plant emissions.

Alkalinity. Alkalinity is not itself a health or aesthetic parameter; its significance is that it is the master variable of process chemistry. It buffers pH, so it determines how far the pH will move when a plant doses a chemical: alum and ferric coagulants are acids and consume roughly 0.50 and 0.55 mg/L of alkalinity as CaCO₃ per mg/L of coagulant respectively, and if the raw alkalinity is too low the pH will fall out of the coagulation window and the floc will not form — a soft, coloured surface water may need lime or soda ash added simply to make coagulation work. In wastewater treatment the constraint is sharper still: nitrification destroys 7.14 mg/L of alkalinity as CaCO₃ per mg/L of ammonia nitrogen oxidised, so a nitrifying plant treating a strong sewage can run its aeration basin down to pH 6 and stall the nitrifiers unless alkalinity is supplemented (or recovered, at 3.57 mg/L per mg N, by anoxic denitrification). Alkalinity, with calcium and pH, also fixes the Langelier saturation index and therefore whether the distribution system deposits protective calcium carbonate or dissolves lead and copper from service lines and solder. Finally, it is the buffer that keeps a receiving stream from being acidified by an effluent.

Hardness. Hardness is the sum of the polyvalent metallic cations, in practice Ca²⁺ and Mg²⁺, reported as mg/L as CaCO₃. It has no health-based guideline in Canada — the epidemiological evidence is, if anything, mildly protective — but it governs the economics of a supply. Hard water precipitates soap as an insoluble curd, so consumers use more detergent; it deposits calcium carbonate scale in kettles, water heaters, boilers and heat exchangers, which insulates the surface and wastes energy; and the scale progressively reduces the bore of distribution and service piping. Against that, very soft water is corrosive and aggressive to metal, which is a direct public-health issue where lead service lines remain. The practical target for a treated supply is therefore an intermediate 80–100 mg/L as CaCO₃, which is exactly the target used in part (a). Hardness is further split into carbonate hardness — that portion associated with bicarbonate and carbonate alkalinity, which precipitates on boiling and is removable by lime alone — and non-carbonate hardness, associated with sulfate and chloride, which requires soda ash in lime softening or full ion exchange. The split, not the total, is what determines the chemical bill.