Cooling towers and humidification

In short

Cooling towers cool circulating water by bringing it into direct contact with air so that a small part of the water evaporates, carrying away latent heat; humidification and dehumidification are the same gas-liquid contacting operation viewed from the air side. The theory is simultaneous heat and mass transfer, so the driving force is an enthalpy (or humidity) difference, not a simple temperature difference, and the limiting cold-water temperature is the ambient wet-bulb temperature. This topic is examined in Heat Transfer and Mass Transfer papers and in GATE (CH) through psychrometry, adiabatic saturation, wet-bulb theory, range/approach and the Merkel NTU integral. It matters on the job because almost every Indian refinery, fertiliser plant, power station, cement and textile unit rejects its waste heat through cooling towers, and water consumption, blowdown quality and plume/drift are regulated by CPCB and State Pollution Control Boards.

Explained

Psychrometry: the vocabulary of moist air

• Absolute (specific) humidity Y: kg water vapour per kg dry air = (18/29)·p_A/(P − p_A). Molal humidity uses kmol/kmol.
• Relative humidity (RH): p_A/p_As at the same temperature, as a percentage. Percentage (absolute) humidity: Y/Y_s × 100 — the two differ except at 0% and 100%.
• Dry-bulb temperature (DBT): temperature read by an ordinary thermometer. Dew point: temperature at which the air becomes saturated on cooling at constant pressure and total humidity.
• Humid heat c_s = 1.005 + 1.88 Y kJ/(kg dry air·K); humid volume v_H = (1/29 + Y/18)·22.414·(T/273) m³/kg dry air at 1 atm.
• Enthalpy of moist air (reference 0 °C liquid water) H = c_s·(T − 0) + λ₀·Y with λ₀ ≈ 2500 kJ/kg.
• Psychrometric chart: humidity on the y-axis against DBT, with saturation curve (100% RH), constant-RH lines, humid-volume lines and adiabatic-saturation/wet-bulb lines sloping down to the right. Indian design practice uses local summer DBT/WBT from the IS code on design weather data; 27–29 °C WBT is typical for coastal and north Indian plains in summer.

Adiabatic saturation and the wet-bulb temperature

• Adiabatic saturation temperature T_as: air contacted with recirculating water in an insulated chamber until saturated; sensible heat of the air supplies the latent heat, so the path is a straight line on the chart: c_s(T − T_as) = λ_as(Y_as − Y).
• Wet-bulb temperature T_w: steady-state temperature of a small wetted surface in a large moving air stream; it is a mass-transfer-controlled temperature, not a thermodynamic state: h(T − T_w) = k_Y·λ_w·(Y_w − Y).
• Lewis relation: for air-water, h/(k_Y·c_s) ≈ 1 (because Sc ≈ Pr ≈ 0.7). Hence the wet-bulb and adiabatic-saturation lines coincide for air-water only — a favourite exam point. For other vapours (e.g. toluene in air) h/k_Y c_s ≈ 1.5–2 and T_w > T_as.
• Order of temperatures for unsaturated air: DBT > WBT > dew point; all three are equal at saturation. The wet-bulb depression (DBT − WBT) measures dryness.
• Measurement: sling/whirling psychrometer or an aspirated psychrometer with air velocity above about 5 m/s so radiation and conduction down the stem are negligible.

Cooling towers: types and construction

• Classification by draft:
  1. Natural draft (hyperbolic): 100–170 m RCC chimney; air moves by density difference. No fan power, huge capital cost; used in large thermal and nuclear stations (NTPC units, Kakrapar).
  2. Mechanical draft — forced: fan at the air inlet, blows air in; fan handles cool dry air (longer life) but suffers recirculation of humid exit air.
  3. Mechanical draft — induced: fan on top, draws air through; most common industrial type (counterflow or crossflow), uniform air distribution, low recirculation, but fan sits in hot humid air.
  4. Atmospheric/spray towers: no fan, rely on natural wind and spray energy; small duties only.
• Classification by flow: counterflow (air up, water down — highest driving force, taller) and crossflow (air horizontal, water down — lower pumping head, larger plan area).
• Wet, dry and hybrid: wet towers evaporate water (approach to WBT); dry (air-cooled) towers are finned-tube heat exchangers approaching the DBT — used where water is scarce, bigger and costlier; wet-dry hybrid towers cut plume and water use.
• Key internals: distribution header and nozzles; fill/packing — splash bars (robust, tolerant of dirty water) or film fill (PVC honeycomb, much larger area per m³ but fouls); drift eliminators (zig-zag blades that return entrained droplets, limiting drift to about 0.005–0.02% of circulation in modern towers); louvres; cold-water basin; fan with gearbox/belt drive; FRP, RCC, timber or pultruded FRP structure. Fill, casing and louvres for Indian towers are commonly specified to the relevant IS/CTI standards; CTI ATC-105 is the usual field-test code and IS 14897 covers cooling-tower terminology and selection practice (confirm the current edition before quoting it in a specification).

Performance terms and the water balance

• Range = T_hot water in − T_cold water out — set by the process heat load and water flow, not by the tower.
• Approach = T_cold water out − T_wet bulb — set by tower size and air flow; approach can never be zero. Typical design approach 3–5 °C in India; 2.8 °C (5 °F) towers are very large.
• Cooling tower effectiveness = Range/(Range + Approach) = (T₁ − T₂)/(T₁ − T_wb); typical 60–80%.
• L/G ratio: kg water per kg dry air, usually 0.8–1.5 for industrial towers; raising L/G lowers capital cost but worsens approach.
• Evaporation loss ≈ 0.00085 × circulation rate × range(°C) × 1.8 (the classic rule-of-thumb), roughly 1% of circulation per 5.5–6 °C of range.
• Drift: mechanically entrained droplets (carry dissolved solids). Blowdown: deliberate purge to control dissolved solids.
• Cycles of concentration COC = TDS in circulating water / TDS in make-up = (E + B + D)/(B + D) ≈ E/B + 1 when drift is small. Make-up = E + B + D. Indian plants run COC 3–6; higher COC saves water but risks CaCO₃, CaSO₄ and silica scaling.
• Fan and pump power: fan power ∝ (air flow)³ for a given tower, so fan laws govern part-load savings; typical specific fan power 2–3 kW per 100 m³/h of water circulated.
• Water treatment: biocide (chlorine/bromine) against *Legionella* and algae, scale inhibitors (phosphonates, polyacrylates), dispersants, pH control; side-stream filtration. Blowdown discharge must meet the SPCB consent limits under the Water (Prevention and Control of Pollution) Act, 1974, and CPCB prohibits the use of chromate-based inhibitors in cooling systems.

Design theory: Merkel equation and NTU

• Assumptions of the Merkel analysis: Lewis number = 1, evaporation loss neglected in the water balance, air leaving the fill is saturated, resistance in the liquid film neglected (interface at bulk water temperature).
• Energy balance over a differential height: L·c_w·dT_L = G·dH = K_Y·a·(H_i − H)·dV.
• Tower characteristic (NTU, or K_Y a V/L) = ∫ c_w dT/(H_i − H) between cold and hot water temperatures — evaluated graphically or by the four-point Tchebycheff rule.
• Demand curve: NTU required rises with range and falls with approach; the characteristic curve of a given fill is K_Y aV/L = c·(L/G)⁻ⁿ with n ≈ 0.4–0.8. The design point is where demand meets characteristic.
• Operating line (straight, slope L·c_w/G on an H–T plot) must lie below the saturation enthalpy curve; if it touches, the tower is at minimum air rate and NTU → ∞.
• For humidifiers and dehumidifiers the same equations are written with humidity driving force: N_tG = ∫dY/(Y_i − Y) and height = H_tG × N_tG, with H_tG = G/(k_Y a).
• Dehumidification routes: cool below the dew point (chilled-water or DX coil — the sensible-heat-factor line on the chart), compress and cool, or adsorb on silica gel / absorb in LiCl or triethylene glycol. Humidification routes: steam injection (isothermal-ish, humidity rises at nearly constant DBT), adiabatic water spray/pad (follows the WBT line, cools the air — the principle of the desert cooler), or air-washer with heated water.

Operating problems, testing and limitations

• Fouling and biofilm: cuts K_Y a and fouls condensers; a biofilm 1 mm thick can hurt more than scale.
• Scaling and corrosion: controlled by Langelier/Ryznar indices and COC limits.
• Plume and fogging: saturated exit air condenses in cold weather — a hazard near highways; plume-abated hybrid towers mitigate it.
• Recirculation and interference: exit humid air re-entering the inlet raises the effective WBT; spacing and orientation to the prevailing wind matter.
• Air and water maldistribution, broken fill, plugged nozzles, fan blade pitch errors are the usual causes of a tower that "cannot make temperature".
• Limitations of wet towers: cold water can never beat the WBT; consumptive water loss; drift carries chemicals; cold-weather icing; *Legionella* risk requiring a written cooling-water management plan in many Indian corporate standards.
• Performance test: measure circulating flow, hot and cold water temperatures, DBT/WBT at inlet, fan power; compute the achieved NTU and compare with the vendor's characteristic curve at the same L/G — the "% capability".

Key points

• Cooling tower - direct-contact device that cools water mainly by evaporation of 1–2% of the circulating flow.
• Wet-bulb temperature - theoretical limit for the cold water from a wet tower; dry towers are limited by DBT.
• Range - hot minus cold water temperature; fixed by the process load and water flow, not by tower size.
• Approach - cold water minus WBT; fixed by tower size, fill and air flow; never zero.
• Effectiveness - Range/(Range + Approach); 60–80% typical.
• L/G ratio - 0.8–1.5 kg water/kg dry air for industrial towers; higher L/G means a warmer cold-water temperature.
• Merkel equation - K_Y aV/L = ∫c_w dT/(H_i − H); driving force is enthalpy difference, not temperature.
• Lewis relation - h/(k_Y c_s) ≈ 1 for air-water, which is why WBT = adiabatic saturation temperature for this pair only.
• Adiabatic saturation - insulated air-water contact; sensible heat supplies latent heat along a constant-enthalpy-like line.
• Humid heat - c_s = 1.005 + 1.88Y kJ/(kg dry air·K); enthalpy H = c_s T + 2500Y.
• Relative vs percentage humidity - partial-pressure ratio vs humidity ratio; equal only at 0% and 100%.
• Evaporation loss - about 1% of circulation for every 5.5–6 °C of range.
• Blowdown and COC - COC ≈ (make-up)/(blowdown + drift); Indian plants run 3–6 with chemical treatment.
• Drift eliminators - cut mechanical droplet carry-over to 0.005–0.02% of circulation.
• Induced draft counterflow - the commonest industrial configuration; natural draft hyperbolic towers suit very large power plants.
• Fill types - film fill gives high area but fouls; splash fill tolerates dirty water.
• Recirculation - exit plume re-entering the inlet raises effective WBT and spoils approach.
• Regulation - blowdown quality under the Water Act, 1974 and SPCB consent; chromate inhibitors banned by CPCB.

Formulas and examples

Example 1 — Psychrometric properties. Air at 40 °C DBT, 1 atm, RH 30%. Vapour pressure of water at 40 °C ≈ 7.38 kPa.

• p_A = 0.30 × 7.38 = 2.214 kPa → Y = (18/29) × 2.214/(101.3 − 2.214) = 0.6207 × 0.02235 = 0.01387 kg/kg dry air.
• Saturation humidity Y_s = 0.6207 × 7.38/(101.3 − 7.38) = 0.6207 × 0.07858 = 0.04878 → percentage humidity = 100 × 0.01387/0.04878 = 28.4% (not 30% — note the difference).
• c_s = 1.005 + 1.88 × 0.01387 = 1.031 kJ/(kg·K); H = 1.031 × 40 + 2500 × 0.01387 = 41.25 + 34.7 = 75.9 kJ/kg dry air.
• v_H = (1/29 + 0.01387/18) × 22.414 × 313/273 = (0.03448 + 0.000771) × 22.414 × 1.1465 = 0.03525 × 25.70 = 0.906 m³/kg dry air.
• Dew point = saturation temperature at 2.214 kPa ≈ 19 °C (from steam tables).

Example 2 — Range, approach, effectiveness, evaporation and make-up. An induced-draft tower circulates 3,000 m³/h, cooling water from 42 °C to 33 °C; ambient WBT 28 °C; make-up TDS 250 ppm, circulating water held at 1,000 ppm.

• Range = 42 − 33 = 9 °C; Approach = 33 − 28 = 5 °C; Effectiveness = 9/(9 + 5) = 64.3%.
• Heat load: L = 3,000 m³/h ≈ 3,000,000 kg/h = 833.3 kg/s → Q = 833.3 × 4.187 × 9 = 31,400 kW (≈31.4 MW).
• Evaporation ≈ 0.00085 × 1.8 × 3,000 × 9 = 41.3 m³/h (1.38% of circulation).
• COC = 1,000/250 = 4 → blowdown + drift = E/(COC − 1) = 41.3/3 = 13.8 m³/h; make-up = 41.3 + 13.8 = 55.1 m³/h.
• If COC is raised to 6: B + D = 41.3/5 = 8.3 m³/h, make-up = 49.6 m³/h — a saving of 5.5 m³/h, about 48,000 m³/year, at roughly ₹25/m³ for treated industrial water ≈ ₹12 lakh/year (water tariffs vary widely by state, so use the local rate).

Example 3 — Air rate from an energy balance. For the tower above, air enters at 28 °C WBT/36 °C DBT with Y₁ = 0.0205 kg/kg and leaves saturated at 38 °C with Y₂ = 0.0436 kg/kg.

• H₁ = (1.005 + 1.88 × 0.0205) × 36 + 2500 × 0.0205 = 1.0435 × 36 + 51.25 = 37.57 + 51.25 = 88.8 kJ/kg.
• H₂ = (1.005 + 1.88 × 0.0436) × 38 + 2500 × 0.0436 = 1.0870 × 38 + 109.0 = 41.31 + 109.0 = 150.3 kJ/kg.
• G = Q/(H₂ − H₁) = 31,400/(150.3 − 88.8) = 31,400/61.5 = 510.6 kg dry air/s (≈1.84 × 10⁶ kg/h).
• L/G = 833.3/510.6 = 1.63; water evaporated = G(Y₂ − Y₁) = 510.6 × 0.0231 = 11.8 kg/s = 42.5 m³/h, which cross-checks the rule-of-thumb value of 41.3 m³/h.

Example 4 — NTU by the Tchebycheff four-point rule. Water 42 → 33 °C, air enthalpy at inlet 88.8 kJ/kg, L/G = 1.63 so the operating line slope = c_w·L/G = 4.187 × 1.63 = 6.83 kJ/kg per °C.

• Mean of 1/(H_i − H) = (0.0407 + 0.0415 + 0.0395 + 0.0352)/4 = 0.03923.
• NTU = c_w·ΔT·mean = 4.187 × 9 × 0.03923 = 1.48. Compare with the vendor characteristic K_Y aV/L = 1.85(L/G)^−0.6: at L/G = 1.63 this gives 1.85 × 1.63^−0.6 = 1.85 × 0.745 = 1.38 — slightly short of the demand, so the tower would run a little warm and needs more air (lower L/G) or more fill.

Example 5 — Adiabatic (evaporative) air cooling, as in a desert cooler. Air at 40 °C DBT, Y = 0.01387 kg/kg (Example 1) passes through a wetted pad of 85% saturation effectiveness. WBT of this air ≈ 25.5 °C, with Y_s at 25.5 °C ≈ 0.0207 kg/kg.

• Saturation effectiveness ε = (T₁ − T₂)/(T₁ − T_wb) → T₂ = 40 − 0.85 × (40 − 25.5) = 40 − 12.3 = 27.7 °C DBT.
• Humidity gained: Y₂ ≈ Y₁ + 0.85(0.0207 − 0.01387) = 0.01387 + 0.0058 = 0.0197 kg/kg; RH at 27.7 °C rises to roughly 85%.
• Enthalpy check: H₁ = 75.9 kJ/kg; H₂ = (1.005 + 1.88 × 0.0197) × 27.7 + 2500 × 0.0197 = 1.0420 × 27.7 + 49.25 = 28.86 + 49.25 = 78.1 kJ/kg — nearly constant, as expected for an adiabatic process (the small rise is the enthalpy of the make-up water).
• Water used per kg dry air = 0.0058 kg; for 5,000 m³/h of air at v_H ≈ 0.91 m³/kg → 5,495 kg dry air/h × 0.0058 = 31.9 kg/h ≈ 32 litres/h.

Where it is used

• Refineries and petrochemicals (IOCL, BPCL, RIL Jamnagar, HPCL): large induced-draft cell banks serving crude-unit condensers and compressor inter-coolers; cooling-water supply/return temperature is a standard process-design datum.
• Thermal and nuclear power (NTPC, Adani Power, NPCIL): natural-draft hyperbolic towers for closed-cycle condenser cooling, mandatory where once-through sea/river cooling is restricted; tower performance directly sets turbine back-pressure and heat rate.
• Fertiliser, chlor-alkali, cement and steel plants (IFFCO, Tata Steel, UltraTech): process cooling, compressor and quench-water duties, where high-COC operation and zero-liquid-discharge schemes decide the water balance.
• HVAC and district cooling: chiller condenser water in malls, airports and metro stations; evaporative air-washer humidification is used in textile spinning and weaving mills (Coimbatore, Tiruppur, Surat) where 55–70% RH is needed to stop yarn breakage.
• Agro and food processing: grain and spice drying (dehumidified or heated air), cold-store humidity control, pharmaceutical AHUs where RH is a GMP-controlled parameter.
• Job roles: process/utilities engineer sizing towers and water balances; energy-audit roles computing tower capability and fan savings (BEE certified energy auditor syllabus covers cooling towers explicitly); vendor design engineers at Paharpur, Bell, Advance Cooling Towers, SPX and Thermax.

Interview questions

• Q: Why can a wet cooling tower not cool water below the wet-bulb temperature? A: Because the wet-bulb temperature is the equilibrium temperature of a water surface evaporating into that air; at that point the enthalpy driving force vanishes and no further heat can be transferred.
• Q: Difference between range and approach, and which one does the tower designer control? A: Range is the hot-to-cold water temperature drop set by the process load and water flow; approach is the cold water temperature above WBT and is what the tower size, fill and air flow determine.
• Q: Why is the driving force in the Merkel equation an enthalpy difference? A: Heat and mass transfer occur together; assuming the Lewis relation holds, the sensible and latent contributions combine into a single enthalpy potential between the saturated interface and the bulk air.
• Q: For air-water, why is the wet-bulb temperature equal to the adiabatic saturation temperature? A: Because h/(k_Y c_s) ≈ 1 for air-water (Sc ≈ Pr), so the wet-bulb line coincides with the adiabatic saturation line; for other vapour-gas pairs the ratio exceeds 1 and the two differ.
• Q: Roughly how much water does a tower evaporate? A: About 1% of the circulation for every 5.5–6 °C of range, so a 10 °C range tower loses nearly 1.5–1.8% of its flow.
• Q: What is cycles of concentration and why not run it very high? A: It is the ratio of circulating-water to make-up TDS; raising it saves water but concentrates calcium, sulphate and silica until scale forms and heat transfer drops.
• Q: Difference between drift and evaporation loss? A: Evaporation is pure water vapour and concentrates the dissolved solids; drift is liquid droplets carried out mechanically, which removes both water and dissolved solids and so counts with blowdown in the COC balance.
• Q: Forced draft versus induced draft — which would you pick for a 30 MW industrial duty and why? A: Induced draft counterflow, because it distributes air uniformly through the fill, has far less recirculation of humid exit air, and is the standard, well-supported design at that size; the penalty is the fan working in a hot, wet, corrosive stream.
• Q: A tower that met guarantee last year now gives 3 °C higher cold water. What do you check? A: First the inlet WBT and the actual water flow and heat load (the usual false alarms), then fan pitch and power, air recirculation, and finally blocked nozzles, collapsed or fouled fill and drift-eliminator plugging.
• Q: How do you humidify air without raising its temperature much, and how do you do it without cooling it? A: Adiabatic water spray or a wetted pad follows the wet-bulb line and cools the air as it humidifies; direct steam injection adds humidity at almost constant dry-bulb temperature.
• Q: How is air dehumidified below the dew point in practice? A: Cool it on a coil below its dew point so moisture condenses and then reheat it to the required dry-bulb; alternatively use a desiccant such as silica gel or a lithium chloride wheel when very low humidity is needed.
• Q: Why does a cooling tower perform worse in the monsoon than on a dry summer day at the same dry-bulb temperature? A: High relative humidity raises the wet-bulb temperature, so the approach starts from a higher base and the achievable cold-water temperature rises even though the air is cooler.

Common mistakes

• Treating relative humidity and percentage humidity as identical, or quoting Y per kg of moist air instead of per kg of dry air (all psychrometric relations are on a dry-air basis).
• Assuming the cold water can approach the dry-bulb temperature, or that a dry air-cooled tower can reach the wet-bulb temperature.
• Using a log-mean temperature difference and a U·A calculation for a cooling tower instead of the enthalpy-based Merkel NTU.
• Taking WBT = adiabatic saturation temperature for every gas-vapour system; the equality is an air-water special case from the Lewis relation.
• Forgetting that evaporation removes only water, so dissolved solids concentrate — then computing make-up as blowdown alone, or omitting drift from the COC balance.
• Mixing up range and approach, or expecting a bigger tower to increase the range (it lowers the approach; range is set by the process).
• Arithmetic slips in enthalpy: leaving out the 2500·Y latent term, or using c_p = 1.005 instead of the humid heat c_s.

Related topics

Boiling, condensation and evaporators · Heat exchangers · Mass transfer: absorption and stripping · Drying of solids · Psychrometry and HVAC refrigeration · Industrial water treatment and zero liquid discharge