11.6 CT Calculations: Baffling Factors, T10, Temperature and pH Corrections & Multi-Segment Compliance

The calculation that keeps pathogens out of the water

Disinfection concepts are covered in the disinfection chapter. This section is about doing the arithmetic under exam conditions, because CT is the most calculation-dense topic on a water treatment exam and the one candidates most often get partially right.

The definition

CT is the product of disinfectant residual concentration and contact time:

CT = C x T

• C is the residual disinfectant concentration in mg/L measured at the end of the contact segment, not the applied dose. Chlorine demand has already been exerted, so C is always less than the dose.
• T is the contact time in minutes, and it is T10, not theoretical detention time.

The product has units of mg/L·min.

T10 and the baffling factor

Water does not move through a basin as a uniform plug. Some of it short-circuits to the outlet quickly, and the fast-moving fraction receives the least contact. Regulators therefore credit T10, the time for 10 percent of the water to pass through — that is, the detention time achieved by 90 percent of the water.

T10 is determined by tracer study, or estimated as:

T10 = theoretical detention time x baffling factor

where theoretical detention time is volume divided by flow.

The pipeline case is worth remembering: transmission piping between the point of chlorine application and the first customer counts at a baffling factor of 1.0, and for many small systems that pipeline supplies most of the available CT.

Required CT and what changes it

The CT required for a given log inactivation is read from tables in the Surface Water Treatment Rules, indexed by disinfectant type, water temperature, and pH. The direction of each effect must be known cold:

• Colder water requires MORE CT. Reaction rates fall as temperature drops, and Colorado's cold source water is the single biggest driver of CT requirements in this state. A plant that comfortably meets CT in August can fail in February at the same dose.
• Higher pH requires MORE CT for free chlorine. Above about pH 7.5, the equilibrium shifts from hypochlorous acid (HOCl), the strong disinfectant, toward the hypochlorite ion (OCl−), which is far weaker. Lime softening plants and plants feeding caustic must account for this.
• Higher log inactivation requires proportionally more CT.
• Different disinfectants have different tables: ozone and chlorine dioxide require far less CT than free chlorine, and chloramines require far more.

The CT ratio and the compliance test

Compliance is expressed as the CT ratio:

CT ratio = CT achieved ÷ CT required

A ratio of 1.0 or greater demonstrates the required inactivation. Where multiple disinfection segments exist in series, the ratios from each segment are summed, and the total must be at least 1.0.

Worked example 1: basic CT

A clearwell has a volume of 250,000 gallons. Peak hourly flow is 3.6 MGD. The baffling factor is 0.5. Free chlorine residual at the clearwell outlet is 1.3 mg/L. Water temperature is 5 degrees Celsius and pH is 7.4, for which the table requires CT of 78 mg/L·min for 3-log Giardia inactivation.

1. Convert flow to gallons per minute: 3,600,000 gpd ÷ 1,440 min/day = 2,500 gpm
2. Theoretical detention time = 250,000 gal ÷ 2,500 gpm = 100 minutes
3. T10 = 100 min x 0.5 = 50 minutes
4. CT achieved = 1.3 mg/L x 50 min = 65 mg/L·min
5. CT ratio = 65 ÷ 78 = 0.83

The plant fails. It has achieved only 83 percent of the required inactivation. Options: raise the residual, reduce peak flow through the clearwell, or improve baffling. To pass at this flow the operator needs C of at least 78 ÷ 50 = 1.56 mg/L.

Worked example 2: adding a pipeline segment

The same plant has 4,200 feet of 16-inch transmission main between the clearwell and the first customer, and the residual at the first customer is 1.1 mg/L. Pipeline baffling factor is 1.0.

1. Pipe volume per foot = 0.785 x (16/12)² x 7.48 gal/cu ft = 0.785 x 1.778 x 7.48 = 10.44 gal/ft
2. Total pipe volume = 4,200 ft x 10.44 = 43,848 gallons
3. Detention time = 43,848 ÷ 2,500 gpm = 17.5 minutes, and T10 = 17.5 x 1.0 = 17.5 minutes
4. CT achieved in the pipeline = 1.1 mg/L x 17.5 min = 19.3 mg/L·min
5. Segment ratio = 19.3 ÷ 78 = 0.25

Summing: 0.83 + 0.25 = 1.08, which is greater than 1.0. The plant now complies, and this is exactly why the transmission main is included in the CT calculation.

Common errors to avoid

1. Using the applied dose instead of the measured residual for C. The dose is always higher, and using it overstates CT.
2. Using theoretical detention time instead of T10. Forgetting the baffling factor overstates CT by a factor of 2 to 10.
3. Using average flow instead of peak hourly flow. CT compliance is evaluated at the peak, when detention time is shortest.
4. Using the wrong table row. Temperature and pH must match the conditions at the time, and using summer values in winter is the classic failure.
5. Forgetting to sum segment ratios rather than summing CT values across segments with different required CTs.