# sizing a derived filtration

Cooling air will entrain suspended solids into the water circuit. These solids are most often organic, but not solely.

For example: a cooling tower at a cement works will generate incoming suspended solids, which are mostly of mineral origin, linked to cement dust.

It is for this reason that it is important to build the cooling tower according to dominant winds.

Nevertheless, it remains necessary to control incoming suspended solids, otherwise the circuit will quickly become clogged.

For example: hypotheses:

• Circuit circulation flow: 1,000m3/h;
• Suspended solids in the atmosphere: 0.5mg/Nm3 (guide value: 0.1 to 1 mg/Nm3);
• Cooling air flow: 700,000Nm3/h (guide value: 500 to 1,000Nm3/m3 of water);
• Suspended solids in make-up water: 2mg/l;
• Circuit concentration factor (K): 3;
• Make-up water flow (A): 50m3/h.

The material balance calculation allows the suspended solid concentration in the circuit to be deduced:

• Incoming suspended solids via make-up water = 50m3/h x 2g/m3 = 100g/h;
• Incoming suspended solids via cooling tower = 700,000 Nm3 x 0.5mg/Nm3 = 350g/h;
• Blowdown flow: A / K = 50 / 3 = 16.7m3/h;
• Suspended solids in the circuit at the balance point = (100 + 350) / 16.7 = 27 mg/l.

To limit fouling in the circuit and counter the risks of legionella bacteria proliferation, the suspended solids in the circuit should be maintained at a level of less than 10mg/l.

In our example, it is therefore necessary to remove the 17mg/l in excess.

Quantity of suspended solids to be eliminated (excluding blowdown) = 16.7 m3/h x 17g/m3 = 284g/h or 6.8kg/day.

Sand filtration with air washing is the best adapted technology. Filtration rate: 15 to 20m/h depending on the type of solids to be retained.

For our example, the choice of a sand filter (NES 0.75 (nominal effective size) of a 1,600mm diameter (2m2 of section), will capture approximately 4.5kg of suspended solids per filtration cycle (2 to 2.5 kg of suspended solids/m2).

Given the filtration rate (15 to 20m/h), the relatively high temperature of water, and the nature of the solids to be filtered (significant presence of Organic Matter), we can consider that the suspended solids leak into filtered water will be in the order of 20%, and so a capture of 80% of suspended solids by the sand filter.

Thus, the filtration flow will be 284g/h / (10g/m3 x 80%) = 35.5m3/h, or using a Ф1,600 = 17.2m/h.

The volume of the filtration cycle will be 4,500g / (10 x 80%) = 560m3, or in hours 560 / 35.5 = 16h.

Note: water losses during washing are around 5 to 6m3/m² of filter surface, which in our example represents 11m3 for a 16 hours cycle or an hourly average of 0.7m/h. This flow of 0.7m3/h contributes to the dilution in the circuit if washing is performed with water from the circuit.