Cooling tower short of duty: heat balance, cycles of concentration and a pitting problem
At a textile processing unit, a cooling tower rejects heat from a process exchanger. Circulating water flows at 5 m³/h (density 1,000 kg/m³, specific heat 4.18 kJ/kg·K) and leaves the exchanger 8 °C warmer than it enters. The tower was sized at 40 kW. Make-up water comes from a borewell with total dissolved solids of 350 mg/L, and the tower is limited to a maximum circulating TDS of 2,000 mg/L before scaling becomes unacceptable. The operator reports three things: the tower pH has drifted down to 6.2, the make-up carries 180 mg/L chloride, and mild-steel cold-water pipes in the circuit are pitting within 14 months while the condenser tubes show almost no scale. The maintenance head proposes installing a water softener and leaving everything else unchanged. Take the latent heat of vaporisation as 2,260 kJ/kg.
1. Calculate the heat the circuit must reject and decide whether the 40 kW tower is adequate. State the practical consequence of the answer.
Read the worked answer
Q = ṁ × c × ΔT = (5 m³/h × 1,000 kg/m³) × 4.18 kJ/kg·K × 8 K = 5,000 × 4.18 × 8 = 167,200 kJ/h = 167,200 / 3,600 = 46.4 kW.
The tower is rated 40 kW, so it is short by 6.4 kW, about 16%. The 8 K rise is only achievable if 46.4 kW is actually rejected; the tower cannot deliver it, so the return water temperature climbs until the exchanger's mean temperature difference falls far enough to shed 46.4 kW at 40 kW of tower duty. The process side therefore runs hotter than design, which in a textile plant usually shows up first as poor dye-bath temperature control rather than as an obvious tower fault.
The judgement to record is that the tower - not the pump, not the piping - is the binding constraint, and any attempt to force 8 K by raising flow would simply push the shortfall elsewhere.
2. Compute the evaporation rate, the cycles of concentration permitted by the TDS limit, the resulting blowdown and make-up, and the chloride concentration actually seen by the steel.
Read the worked answer
Evaporation is what carries the heat away: m_evap = 167,200 / 2,260 = 74.0 kg/h.
Cycles of concentration = allowed circulating TDS / make-up TDS = 2,000 / 350 = 5.71.
At steady state the solids leaving in blowdown equal those entering in make-up, which gives blowdown = evaporation / (COC − 1) = 74.0 / 4.71 = 15.7 kg/h.
Make-up = 74.0 + 15.7 = 89.7 kg/h, about 2.15 m³/day.
The number that matters metallurgically is not TDS but chloride. At 5.71 cycles, 180 mg/L in the make-up becomes 180 × 5.71 ≈ 1,030 mg/L in the circulating water. That single figure explains the pitting better than any other number in the case, and it also shows why the COC limit is a corrosion limit as much as a scaling limit.
3. Diagnose why the mild steel is pitting while the condenser tubes stay clean, and assess the maintenance head's proposal to install a softener and change nothing else.
Read the worked answer
Scale-free tubes and pitted mild steel are the same fact seen twice: this water is aggressive, not scaling. At pH 6.2 the Langelier saturation index is strongly negative, so the water dissolves the thin protective oxide/carbonate film instead of laying one down. Nothing deposits on the condenser, and bare steel is left exposed.
Chloride at roughly 1,030 mg/L in the circuit is far above the few hundred mg/L that carbon steel tolerates. Low pH plus high chloride is the textbook pitting couple, and 14-month penetration on cold-water pipe is exactly the expected signature.
The softener treats the wrong problem and partly worsens it. Hardness is already too low to protect anything; removing it lowers the scaling potential further while leaving sodium and chloride in solution, so the water becomes more corrosive, not less.
What should actually be done: raise pH to 7.5-8.0 with caustic or soda ash; dose a corrosion inhibitor suited to the metals present; increase blowdown so that circulating chloride stays within the steel's limit; and if a softener is fitted at all, run it on a partial stream to trim hardness rather than stripping it completely. Also inspect where mild steel meets brass or stainless, since that is where the pitting will be worst.