Q10095 - HOWTO: Calculate CT in Hach WIMS Client

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,

1. calc the CT Achieved for the hour that the Peak Hourly Flow rate (for the segment) occurred.

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 * 28.29 * 7.48 / 1000000

Where: 28.29 is Cross-Sectional Area of a 3 foot radius (πr2)

7.48 is number of gallons in 1 cubic foot

1000000 is used to convert gallons to MG

1. 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 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

1. 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

1. 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,"") * 28.29 * 7.48 / 1000000

Where: DDWHEN(V100,V1,”MAX”,V1,"",V1,"") returns V100 for the hour when the Max Flow (V1) occurred.

28.29 is Cross-Sectional Area of a 3 foot radius (πr2)

7.48 is number of gallons in 1 cubic foot

1000000 is used to convert gallons to MG

1. 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

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

*For a clearwell with no baffling the Baffling Factor is 0.1

1. 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

1. 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.  Depending on type of disinfectant used and what you are trying to remove (Giardi or Viruses) different equations or lookup tables are used.  In this example we will calculate the 3 log (AKA CT99.9) inactivation of Giardi and the 4 log (CT99.99) inactivation of Viruses.

There are three methods for calculating the CT Required but they all derive from the CT Tables provided in the EPA Guidance Manual Disinfection Profiling and Benchmarking.  All three methods use the Water Temperature, pH, and CL2 Residual:

V121:             Water Temp in Deg C (Deg C = (Deg F – 32) * 5/9)

V131:            pH

V141:            Cl2 Residual at the end of the segment

#### Method 1: Use WIMS Lookup Tables

Go to Lookup Table Setup and load the following tables:

0.5 C, 5C, 10C, 15C, 20C, and 25C

CT_Giardia_FC_pt5C_3LOG

CT_Giardia_FC_5C_3LOG

CT_Giardia_FC_10C_3LOG

CT_Giardia_FC_15C_3LOG

CT_Giardia_FC_20C_3LOG

CT_Giardia_FC_25C_3LOG.

Then enter the equation:

V151:            CT Required - 3 Log IA of Giardi

IF(V121<5,TABLE("CT_Giardia_FC_pt5C_3LOG",V131,V141,3,0),

IF(V121<10,TABLE("CT_Giardia_FC_5C_3LOG",V131,V141,3,0),  IF(V121<15,TABLE("CT_Giardia_FC_10C_3LOG",V131,V141,3,0), IF(V121<20,TABLE("CT_Giardia_FC_15C_3LOG",V131,V141,3,0), IF(V121<25,TABLE("CT_Giardia_FC_20C_3LOG",V131,V141,3,0),  TABLE("CT_Giardia_FC_25C_3LOG",V131,V141,3,0))))))

#### Method 2: 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)))

#### Method 3: Use CTR3LGC Math Toolbox and/or Spread 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

Use the CT_InactivationofViruses_FC lookup table (table C-7 EPA Guidance - Disinfection Profiling and Benchmarking).

V121:             Water Temp in Deg C (Deg C = (Deg F – 32) * 5/9)

#### Method 1: Use WIMS Lookup Tables

Go to Lookup Table Setup and load:

CT_InactivationofViruses_FC.

V155: CT Required for 4 Log IA of Viruses

TABLE("CT_InactivationofViruses_FC ",V121,4,3,0)

##### 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

V171 =  3 * V161

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 + …

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Article Attachments
 EPA L11ESWTR Disinfection Profiling and Benchmarking.pdf EPA Guidance - Disinfection Profiling and Benchmarking.pdf