Cooling Tower Sizing

1. Evaporative Heat Rejection Principles

Cooling towers are massive, specialized heat exchangers that reject process heat to the atmosphere by utilizing the latent heat of vaporization of water. They are the ultimate heat sink for refineries, power plants, and chemical complexes.

Unlike sensible heat exchangers (which rely purely on temperature differences), cooling towers operate on evaporative cooling. As hot return water falls through the tower fill, a small percentage evaporates into the upward-flowing air. This phase change absorbs massive amounts of thermal energy (approx. $2260\,\text{kJ/kg}$ of water evaporated), drastically chilling the remaining water.

2. The Wet-Bulb Temperature Limit

The absolute theoretical limit to which water can be cooled in an evaporative tower is the ambient Wet-Bulb Temperature ($T_{wb}$). The wet-bulb temperature is a psychrometric property representing the lowest temperature attainable by evaporating water into the air at constant pressure.

The efficiency of a cooling tower is evaluated using two primary metrics:

• Range: The temperature difference between the hot return water and the cold supply water ($T_{hot} - T_{cold}$).
• Approach: The temperature difference between the cold supply water and the ambient wet-bulb temperature ($T_{cold} - T_{wb}$).

A smaller approach (e.g., $3\text{--}5^\circ\text{C}$) requires a significantly larger and more expensive cooling tower, as the driving force for evaporation approaches zero.

3. Water Balances: Drift, Blowdown, and Makeup

Cooling towers require massive volumes of continuous makeup water to maintain operation. The mass balance incorporates:

• Evaporation Loss ($E$): Pure water lost to the atmosphere as vapor.
• Drift Loss ($D$): Liquid water droplets entrained in the exhaust plume (prevented by drift eliminators).
• Blowdown ($B$): Intentional draining of basin water to prevent the accumulation of dissolved solids and scale formation (Cycles of Concentration).

$$Makeup = E + D + B$$

Proper sizing of these parameters is critical for environmental compliance and chemical treatment programs.

4. Step-by-Step Worked Example: Cooling Tower Water Balance

Scenario: A cooling tower circulates $5000\,\text{m}^3\text{/h}$ of water. The hot return water is $42^\circ\text{C}$ and is cooled to $30^\circ\text{C}$ (Range = $12^\circ\text{C}$). The tower operates at 5 Cycles of Concentration (CoC). Calculate the required makeup water rate.

1. Calculate Evaporation Loss ($E$):

A standard empirical rule is that evaporation loss is $0.15\%$ of the circulation rate for every $1^\circ\text{C}$ of cooling range (due to the latent heat of vaporization of water).

$$E = 0.0015 \times \text{Circulation} \times \text{Range} = 0.0015 \times 5000 \times 12 = 90\,\text{m}^3\text{/h}$$

2. Calculate Blowdown ($B$):

To maintain the dissolved solids at 5 times the concentration of the fresh makeup water, the blowdown is calculated as:

$$B = \frac{E}{\text{CoC} - 1} = \frac{90}{5 - 1} = 22.5\,\text{m}^3\text{/h}$$

3. Calculate Drift Loss ($D$):

For modern towers with efficient drift eliminators, drift is typically $0.005\%$ of the circulation rate.

$$D = 0.00005 \times 5000 = 0.25\,\text{m}^3\text{/h}$$

4. Total Makeup Water Required:

$$Makeup = E + B + D = 90 + 22.5 + 0.25 = 112.75\,\text{m}^3\text{/h}$$

The facility must supply $112.75\,\text{m}^3\text{/h}$ of fresh water to sustain continuous operation.