Discrete Chebyshev transform

2012-12-10T12:14:17Z

129.215.75.205:

'''CT Values''' are an important part of calculating [[disinfectant]] dosage for the [[Water chlorination|chlorination]] of [[drinking water]]. A CT value is the product of the concentration of a disinfectant (e.g. free chlorine) and the contact time with the water being disinfected. It is typically expressed in units of mg-min/L.

The goal of disinfection is the inactivation of microorganisms. This depends on: the microorganism, the disinfectant being used, the concentration of the disinfectant, the contact time, and the temperature and [[pH]] of the water.<ref>{{cite web|last=Pine|first=Rob|title=Everything You Ever Wanted to Know About CT (and then some)|url=http://www.nmenv.state.nm.us/dwb/whats_new/documents/CT.pdf|publisher=New Mexico Environment Department|accessdate=20 October 2013|coauthors=Joe Savage}}</ref>

==Kinetics==
The disinfection kinetics are conventionally calculated via the Chick-Watson model, named for the work of [[Harriette Chick]]<ref>{{cite journal|last=Chick|first=Harriette|title=An Investigation of the Laws of Disinfection|journal=The Journal of Hygiene|year=1908|month=January|volume=8|issue=1|pages=92-158|url=http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2167134/pdf/jhyg00376-0104.pdf|accessdate=20 October 2013}}</ref> and [[Harold Watson|H.E. Watson]].<ref>{{cite journal|last=Watson|first=Herbert Edmeston|title=A Note on the Variation of the Rate of Disinfection with Change in the Concentration of the Disinfectant|journal=The Journal of Hygiene|year=1908|volume=8|page=536|url=http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2167149/pdf/jhyg00379-0093.pdf|accessdate=20 October 2013}}</ref> This model is expressed by the following equation:<ref name=autogenerated2005>{{cite book|last=MWH|title=Water Treatment: Principles And Design|year=2005|publisher=John Wiley & Sons|location=Hoboken, NJ|isbn=0471110183|edition=2}}</ref>

: <math> \ln(\frac{N}{N_0})=\Lambda_{CW} C^n t \!</math>

Where:
* <math> (\frac{N}{N_0}) \!</math> is the survival ratio for the microorganisms being killed
* <math> \Lambda_{CW} \!</math> is the Chick-Watson coefficient of specific lethality
* <math> C \!</math> is the concentration of the disinfectant (typically in mg/L)
* <math> n \!</math> is the coefficient of dilution, frequently assumed to be 1<ref name="autogenerated2005"/>
* <math> t \!</math> is the contact time (typically in minutes or seconds)

The survival ratio is commonly expressed as a inactivation ratio (in %) or as the number of reductions in the order of magnitude of the microorganism concentration. For example, a situation where N0=107 [[Colony-forming unit|CFU]]/L and N=104 CFU/L would be reported as a 99.9% inactivation or "3-log10" removal.

In water treatment practice, tables of the product C×t are used to calculate disinfection dosages. These tables express the required CT values to achieve a desired removal of microorganisms of interest in drinking water (e.g. [[Giardia lamblia]] cysts) for a given disinfectant under constant temperature and pH conditions. A portion of such a table is reproduced below.

==Example CT Table==
CT Values for the Inactivation of Giardia Cysts by Free Chlorine at 5 °C and pH ≈ 7.0:<ref>{{cite book|last=Office of Drinking Water|title=Guidance Manual for Compliance with the Filtration and Disinfection Requirements for Public Water Systems Using Surface Water Sources|year=1991|publisher=United States Environmental Protection Agency|url=http://www.epa.gov/safewater/mdbp/guidsws.pdf|quote=Table E-2}}</ref>

{| class="wikitable"
|-
! ''Chlorine Concentration (mg/L)''
! 1 log inactivation
! 2 log inactivation
! 3 log inactivation
|-
| ''0.6''
| 48
| 95
| 143
|-
| ''1.2''
| 51
| 101
| 152
|-
| ''1.8''
| 54
| 108
| 162
|-
| ''2.4''
| 57
| 115
| 172
|}

Full tables are much larger than this example and should be obtained from the regulatory agency for a particular jurisdiction.

==See also==
* [[Water chlorination|Chlorination]]
* [[Disinfectant]]

==References==
{{reflist}}

==External links==
* {{cite book|last=Earth Tech, Inc.|title=Chlorine and Alternative Disinfectants Guidance Manual|year=2005|publisher=Manitoba Water Stewardship|location=Manitoba|url=http://www.gov.mb.ca/waterstewardship/odw/reg-info/approvals/odw_chlorine_and_alternative_disinfectants.pdf}}

[[Category:Water treatment]]
[[Category:Chlorine]]
[[Category:Public health]]

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Discrete Chebyshev transform