Cycles of Concentration (COC)¶

Cycles of concentration (COC, also written CoC or "cycles") is the single number that ties a cooling tower's water use to its scaling and corrosion risk. It is the ratio of the concentration of a conservative dissolved species in the recirculating water to its concentration in the makeup water:

COC = (concentration in recirculating water) / (concentration in makeup water)

Because an evaporative tower loses pure water vapour but leaves the dissolved solids behind, the recirculating water steadily concentrates. Conductivity, chloride, or silica — species that leave essentially only with blowdown and drift — are the usual tracers. A tower running at "5 cycles" holds five times the makeup's dissolved-solids concentration in the basin.

The water balance¶

Four streams close the balance on an evaporative tower:

Stream	Symbol	What it is
Evaporation	`E`	pure water lost to the air; concentrates the solids
Drift (windage)	`D`	liquid droplets carried out in the air stream
Blowdown (bleed)	`B`	water deliberately discharged to cap the solids
Makeup	`M`	fresh water added to replace every loss

Conservation of water and of dissolved solids gives the relationships the library implements in cooling_tower_chem.balance:

M = E + B + D                (makeup replaces all losses)
COC = M / (B + D)            (cycles from the water streams)
B   = E / (COC - 1) - D      (blowdown to hold a target COC)

The last line is the practical one: pick a target COC, and it tells you the blowdown needed to hold it. Raising COC shrinks the E / (COC - 1) term, so blowdown — and therefore makeup — falls. Evaporation itself follows a first-principles energy balance,

E = circulation_rate * cp * dT / latent_heat

where dT is the cooling range. This is the theoretical (100 % latent-heat) maximum; real towers reject some sensible heat, so field evaporation is roughly 75–90 % of it. These are the same formulas presented under Indices & the science → cooling-tower water balance; their derivation is a straightforward water/solids mass balance, not a fitted correlation.

Worked example¶

A 1000 m³/h tower with an 8 °C cooling range, good drift eliminators (0.02 %), run at a target of 5 cycles, on a soft makeup water:

from cooling_tower_chem import CoolingTower, WaterSample

tower = CoolingTower(circulation_rate=1000, delta_t_c=8, cycles=5)  # m3/h
print(tower.water_balance())
# {'evaporation': 13.6686, 'drift': 0.2, 'blowdown': 3.2171, 'makeup': 17.0857, 'cycles': 5}

The numbers check by hand: E = 1000 · 4.186 · 8 / 2450 = 13.67 m³/h, B = 13.67/(5−1) − 0.2 = 3.22 m³/h, M = 13.67 + 3.22 + 0.2 = 17.09 m³/h, and M/(B+D) = 17.09/3.42 = 5.0 cycles, as required.

Now project how that makeup concentrates in the basin, and read the Langelier index (LSI) of the water actually circulating:

makeup = WaterSample(
    ph=7.4, temperature_c=32, calcium_hardness=45,
    total_alkalinity=35, conductivity_us_cm=280,
)
basin = tower.concentrated(makeup)   # conservative species x cycles
print(round(makeup.lsi(), 2), "->", round(basin.lsi(), 2))
# -1.18 -> 0.15

The makeup is aggressive on its own (LSI −1.18); concentrating it five-fold brings the basin to a near-balanced LSI +0.15.

Typical COC ranges¶

There is no universal target — it depends on makeup quality, the treatment program, and discharge limits — but these bands are representative:

COC	Typical situation
2–3	poor makeup, minimal treatment, or tight scaling limits
3–5	common untreated / lightly treated baseline
5–8	well-run tower with scale/corrosion inhibitor and pH control
8–15+	high-purity (softened / RO) makeup with an engineered program

Below ~2 cycles a tower wastes water; above the point where the basin water turns strongly scale-forming, higher cycles trade a shrinking water saving for a rising fouling and cleaning cost.

Raising cycles: water saved vs. scaling risk¶

Every extra cycle saves less water than the one before, while the basin LSI keeps climbing. Sweeping the worked-example tower from 2 to 8 cycles makes the trade-off explicit:

from cooling_tower_chem import CoolingTower, WaterSample, interpret_lsi

makeup = WaterSample(ph=7.4, temperature_c=32, calcium_hardness=45,
                     total_alkalinity=35, conductivity_us_cm=280)
for c in range(2, 9):
    t = CoolingTower(circulation_rate=1000, delta_t_c=8, cycles=c)
    basin = t.concentrated(makeup)
    tendency, _ = interpret_lsi(basin.lsi())
    print(f"{c:>2} {t.makeup:>8.2f} {t.blowdown:>9.2f} {basin.lsi():>7.2f}  {tendency}")

cycles   makeup  blowdown  basin LSI  tendency
     2    27.34     13.47      -0.61  corrosive
     3    20.50      6.63      -0.28  balanced
     4    18.22      4.36      -0.04  balanced
     5    17.09      3.22       0.15  balanced
     6    16.40      2.53       0.30  balanced
     7    15.95      2.08       0.42  balanced
     8    15.62      1.75       0.53  scale_forming

Read the table as the operating window: at 2 cycles the water is both wasteful (27.3 m³/h makeup) and corrosive; the LSI enters the balanced band by 3 cycles and stays there to 7; at 8 cycles it tips scale-forming. The makeup saving also flattens — going 2 → 3 cycles saves 6.8 m³/h, but 7 → 8 saves only 0.3 m³/h. water_saved_by_increasing_cycles quantifies any such move directly:

from cooling_tower_chem import water_saved_by_increasing_cycles

tower = CoolingTower(circulation_rate=1000, delta_t_c=8, cycles=5)
saved = water_saved_by_increasing_cycles(tower.evaporation, 3, 6, drift=tower.drift)
print(round(saved, 2), "m3/h", "->", round(saved * 24, 1), "m3/day")
# 4.1 m3/h -> 98.4 m3/day

Raising this tower from 3 to 6 cycles saves about 98 m³/day of makeup — but note the basin LSI rises from −0.28 to +0.30 over the same move, so the water saving is bought with a real increase in scaling tendency that the treatment program has to absorb. The practical target is the highest COC that keeps the basin LSI inside the balanced band for your inhibitor.

To explore the same LSI/RSI/PSI/CCPP response interactively, try the water-stability calculator; enter your concentrated basin chemistry and watch the indices move. The full water-balance API — CoolingTower, cycles_from_flows, blowdown_loss, evaporation_loss, and water_saved_by_increasing_cycles — is documented in the API reference, and both worked scripts above are shipped as examples/optimize_cycles.py.

References¶

Langelier, W. F. (1936). The Analytical Control of Anti-Corrosion Water Treatment. J. AWWA 28(10). (LSI used for the basin-water read above.)
The evaporation / blowdown / makeup relationships are a first-principles water and dissolved-solids mass balance; see Indices & the science for the same equations in context.

Note

Cycles of concentration is a mass-balance quantity; the scaling and corrosion reads that go with it (LSI, RSI, PSI, CCPP) are screening estimates, not a substitute for site-specific engineering judgment or a jar test. The evaporation figure is the theoretical maximum — apply a heat-rejection factor (~0.75–0.9) for field estimates.