CT is a measure of the strength of the disinfectant for the time that the water and disinfectant are in contact. CT is determined by multiplying the residual disinfectant concentration (C) by contact time (T). In order to calculate log inactivation for compliance with the surface water treatment rule the CT Achieved and CT Required must be calculated for each disinfection segment in your system.

Calculating CT Achieved For A Segment
EPA rules state - "Measurements must be taken on the same day of the week, every week, for one year (52 measurements), during peak hourly flow for that day.  Data can be measured manually or with on-line instrumentation." 

To meet EPA compliance you must calculate the CT Achieved for a day.  There are 2 methods you can choose:

1. Calc the CT Achieved for each hour and report the minimum.
2. Calc the CT Achieved for the hour that the Peak Hourly Flow rate (for the segment) occurred.
   

In the examples below the following variables are used:

• V1: Hourly Flow Rate in MGD
• V100: Clearwell Water Depth (Ft.) Hourly Minimum
• V101: Clearwell Volume in MG

Method 1: Calculate CT Achieved for each hour:

1. Calculate segment volume in MG.

Based on current conditions (i.e. level in tank, number of filters on, etc…)

V101 = V100 * 28.27 * 7.48 / 1000000

• 28.27 is Cross-Sectional Area of a 3 foot radius (Pi r2 = 3.14159 * 3^2)
• 7.48 is number of gallons in 1 cubic foot
• 1000000 is used to convert gallons to MG

2. Determine Baffling Factor (T10/T)

Baffling Condition	T10/T	Baffling Description
Unbaffled (mixed flow)	0.1	None, agitated basin, very low length to width ratio, high inlet and outlet flow velocities. Can be approximately achieved in flash mix tank. For a clearwell with no baffling you would use 0.1.
Poor	0.3	Single or multiple unbaffled inlets and outlets, no intra-basin Baffles
Average	0.5	Baffled inlet or outlet with some intra-basin baffles
Superior	0.7	Perforated inlet baffle, serpentine or perforated intra-basin baffles, outlet weir or perforated launders
Perfect (Plug Flow)	1.0	Very high length to width ratio (pipeline flow), perforated inlet, outlet, and intra-basin baffles

3. Calculate T10 time in minutes

T10 = Detention Time (Mins) of Segment * Baffling Factor

= ((Segment Vol {MG} / Flow {MGD}) * 24 * 60) * Baffling Factor

V111 = (V101 / V1 * 24 * 60) * 0.3

4. Calculate CT Achieved

CT Achieved {mg/L-mins} = CL2 Residual {mg/L} * T10 {mins}

V115 = V141 * V111

Method 2: Calculate CT Achieved for Peak Hourly Flow Rate hour:

1. Calculate segment volume in MG.

Based on current conditions (i.e. level in tank, number of filters on, etc…)

V101 = DDWHEN(V100,V1,”MAX",V1,"",V1,"") * 28.27 * 7.48 / 1000000

• DDWHEN(V100,V1,”MAX”,V1,"",V1,"") returns V100 for the hour when the Max Flow (V1) occurred.
• 28.27 is Cross-Sectional Area of a 3 foot radius (Pir2)
• 7.48 is number of gallons in 1 cubic foot
• 1000000 is used to convert gallons to MG

2. Determine Baffling Factor (T10/T)

Baffling Condition	T10/T	Baffling Description
Unbaffled (mixed flow)	0.1	None, agitated basin, very low length to width ratio, high inlet and outlet flow velocities. Can be approximately achieved in flash mix tank. For a clearwell with no baffling you would use 0.1.
Poor	0.3	Single or multiple unbaffled inlets and outlets, no intra-basin Baffles
Average	0.5	Baffled inlet or outlet with some intra-basin baffles
Superior	0.7	Perforated inlet baffle, serpentine or perforated intra-basin baffles, outlet weir or perforated launders
Perfect (Plug Flow)	1.0	Very high length to width ratio (pipeline flow), perforated inlet, outlet, and intra-basin baffles

3. Calculate T10 time in minutes

T10 = Detention Time {Mins} of Segment * Baffling Factor

      = ((Segment Vol {MG} / Flow {MGD} ) *24 * 60)  * Baffling Factor

V111 = (V101 / DDMAX(V1,0,23) * 24 * 60) * 0.1

4. Calculate CT Achieved

CT Achieved {mg/L-mins} = CL2 Residual {mg/L} * T10 {Mins}

V115 = V141 * V111

Calculating CT Required for Segment
Determine which CT Required you need to calculate from the CT Tables provided in the EPA Guidance Manual Disinfection Profiling and Benchmarking

1. Determine if you need table for Giardi or Viruses removal
   
2. Determine the type of Disinfectant
   
3. Determine the Log Inactivation Required.  Example, 3 log inactivation is required but the system may get "credits" for certain treatment techniques so they only need 1.5 log inactivation by disinfection. 
   
4. Identify the variables for:
1. Water Temperature (Deg C)
2. pH
3. Disinfectant Residual
   
5. Use the CT Spread or CT Math Toolbox function to determine the CT Required. (NOTE: If you are calculating the 3 log removal of giardia by Free Chlorine you may want to use the CTR3LGC spread function or CTR3LGC Math Toolbox function)

Example: Get CT Required for 2 log removal of Giardia by Free Chlorine

Using the Spread Function : CT(InactivationOf, Disinfectant, LogInactivation, Temp, pH, Cl2)

InactivationOf = "Giardia" or 1
Disinfectant = 1 for Free Chlorine
LogInactivation = 2
Temperature = V121 or in cell T10 in Spread Report
pH = V131 or in cell P10
Cl2 = V141 in cell C10

Spread Formula to Return CT is: CT(1,1,2,T10,P10,C10)
Math Toolbox formula is: V151 = CT(1,1,2,V121,V131,V141)

Calculate Segment Inactivation

1. Calculate the CT Ratio for 3 Log of Giardia and 4 log of Viruses.

CT Ratio = CT Achieved / CT Required

V161 = V115/V151

V165 = V115/V155

2. Calculate the CT Log Inactivation

Giardia Log Inactivation = 3 * CT Ratio

V171 =  3 * V161

Viruses Log Inactivation = 4 * CT Ratio

V175 = 4 * V165

Calculate the total Inactivation
We now must calculate the Segment Inactivation for all disinfection segments (steps).   Then total the Inactivation for all segments to get the total Inactivation:

V901 = C171 + C271 +…

V905 = C175 + C275 + …

Other Methods to Calculate the CT Required which may match user's current method. 

Use EPA Regression Equation

This method is calculated using regression equations developed by Smith et al. (1995). The equations can be found in Appendix E of USEPA Disinfection Profiling and Benchmarking Guidance Manual (EPA 815-R-99-013), August 1999.

V151: CT Required - 3 Log IA of Giardi

CT = (0.353*I)(12.006+e (2.46-0.073*temp+0.125*C+0.389*pH)) (for temperature < 12.5 °C)

CT = (0.361*I)(-2.261+e (2.69-0.065*temp+0.111*C+0.361*pH)) (for temperature >= 12.5 °C)

Where:

• I = 3, the number of logs inactivation required
• Temp= temperature in degrees Celsius
• C = residual chlorine concentration in mg/L
• pH = the negative log concentration of hydrogen ion
• e = 2.7183, the base for the natural logarithm

Therefore the Math Toolbox equation would be:

IF(V121<12.5,0.353*3*(12.006+EXP(2.46 -.073*V121+0.125*V141+0.389*V131)), 0.361*3*(-2.261+EXP(2.69-0.065*V121+0.111*V141+0.361*V131)))

 

Use CTR3LGC spread function or CTR3LGC Math Toolbox function

This is a method for approximating the CT Tables for 3 Log Inactivation of Giardia Cysts.  The CT99.9 calculations for free chlorine use a complex interpolating polynomial which correctly reproduces virtually all of the CT table values for chlorine achieving a coefficient of correlation of .99999.  Calculated values vary less than the instruments used to gather the data used in the calculations.  The interpolating polynomial for calculating CT99.9 were developed by Russell J. Topham with the Utah Division of Drinking Water as part of his work with water treatment processes under the Surface Water Treatment Rule.

 V151: CT Required for 3 Log IA of Giardi

            =CTR3LGC (Disinfectant ID, Water Temperature, pH, Cl2 Residual)

            =CTR3LGC(1, V121, V131, V141)

            Disinfectant ID has one of the following settings:

1. Free Chlorine
2. Chlorine Dioxide
3. Chloramines
4. Ozone