Ion Exchange Resin: Breakthrough Curve & Regeneration

Feed & Column Controls

Flow rate 15 BV/hr

Feed hardness (as CaCO₃) 250 mg/L

Resin bead diameter 0.6 mm

Column State

Effluent hardness

Bed volumes treated

0.0

Resin capacity used

0 BVBreakthrough curve C/C₀

Na⁺-loaded resin (fresh)

Ca²⁺/Mg²⁺-loaded resin (exhausted)

How it works

Softening resin is a sulfonated polystyrene bead pre-loaded with sodium. Hardness ions displace the weaker-held Na⁺ because the resin binds divalent cations more strongly:

2 R–SO₃⁻Na⁺ + Ca²⁺ ⇌ (R–SO₃⁻)₂Ca²⁺ + 2 Na⁺

As feed water flows down through the packed bed, exchange doesn't happen uniformly — a narrow mass-transfer zone (MTZ) forms and travels downward. Resin above the MTZ is fully Ca²⁺-loaded (exhausted); resin below it is still fresh Na⁺-form. Effluent stays essentially hardness-free until the MTZ reaches the bottom of the bed, then hardness "breaks through" and rises quickly. This simulation uses the standard Thomas model for a fixed-bed breakthrough curve:

C(t)/C₀ = 1 / (1 + exp[k_Th·(q₀ − C₀·BV(t))])
BV(t) = bed volumes of water treated so far
q₀    = resin capacity ÷ feed hardness → BV at 50% breakthrough
k_Th  = rate constant — larger for smaller beads (shorter
        intraparticle diffusion path → sharper front)

Flow rate — higher throughput means the bed volumes counter climbs faster, but the MTZ shape stays the same; the whole curve just plays out sooner.
Feed hardness — a higher Ca²⁺/Mg²⁺ concentration burns through the same fixed resin capacity in fewer bed volumes, so breakthrough (BV₅₀ = q₀/C₀) arrives earlier.
Bead diameter — smaller beads shorten the diffusion path inside each particle, sharpening (steepening) the breakthrough front; larger beads spread it into a broader, earlier-leaking MTZ.
Regenerate — flushing with concentrated NaCl brine reverses the exchange by mass action (a large excess of Na⁺ drives the equilibrium back), restoring the bed to Na⁺-form for another service cycle. Real softeners repeat this automatically once resin capacity is exhausted.

Water flow (top → bottom) Mass-transfer zone front

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