In the context of how we use the term, intensity refers to the intensive property of the disinfectant. Intensive properties, in turn, are those properties that are independent of the total mass or volume of the disinfectant. For example, concentrations are expressed as mass per unit volume; the phrase "per unit volume" makes concentration independent of the total volume. Hence, concentration is an intensive property and it expresses the intensity of the disinfectant. Another intensive property is radiation from an ultraviolet light. This radiation is measured as power impinging upon a square unit of area. The "per unit area" here is analogous to the "per unit volume." Thus, radiation is independent of total area and is, therefore, an intensive property that expresses the intensity of the radiation, which, in this case, is the intensity of radiation of the ultraviolet light.

It is a universal fact that the time needed to kill a given percentage of microorganisms decreases as the intensity of the disinfectant increases, and the time needed to kill the same percentage of microorganisms increases as the intensity of the disinfectant decreases, therefore, the time to kill and the intensity are in inverse ratio to each other. Let the time be t and the intensity be I. Thus, mathematically, t œ -

Note: I has been raised to the power m, which is a constant. This is to make the relationship more general.

Letting k be the proportionality constant, the equation becomes t = k (17.2)

In this equation, if Im is multiplied by t, and if I is expressed as the concentration of the disinfectant C in mg/L, the equation is the famous Ct concept with m equal to 1 and t in minutes. Ct values at given temperatures and pH are tabulated in Ct tables used by regulating authorities and by the U.S. Environmental Protection Agency. The time to kill t is synonymous with the time of inactivation of the microorganisms.

The constants may be obtained from experimental data by converting the above equation first into an equation of a straight line. Taking the logarithms of both sides, lnt = lnk - mlnI (17.3)

This equation is the equation of the straight line with y-intercept ln k and slope m. The constants may then be solved using experimental data.

Assume n experimental data points, and divide them into two groups. Let there be l data points in the first group; the second group would have m - l data points. From analytic geometry,

Substituting Equation (17.4) into Equation (17.2) and solving for k produces k = exp

X1 lnt, I Xi lnIi

Having obtained m and k, the time t can be solved using Equation (17.2) from a knowledge of the value of I. This time is called the contact time for disinfection, and the intensity I is called the lethal dose. From Equation (17.2) any reasonable amount of dose is lethal when administered in a sufficient amount of contact time as calculated from the equation. We call Equation (17.2) the Universal Law of Disinfection.

Example 17.1 It is desired to design a bromide chloride contact tank to be used to disinfect a secondary-treated sewage discharge. To determine the contact time, an experiment was conducted producing the following results:

Contact Time (min/residual fecal coliforms) (No./100 mL)

BrCl Dosage (mg/L) 15 30 60

3.6 10,000 4,000 600

15.0 800 410 200

Determine the contact time to be used in design, if it is desired to have a log 2 removal efficiency for fecal coliforms. Calculate the Ct value. The original concentration of fecal coliforms is 40,000 per/100 mL.

Solution: The percentage corresponding to a log removal can be obtained by first assuming any original value of the concentration of the microorganisms x1, computing the next value x2 based on the given log removal, and computing the corresponding percentage. Thus, let x1 = 8888888. Then, log 8888888 - log x2 = 2 and x2 = 88888.88

Note: Any number could have been assumed for x1 and the answer would still be 99. Thus, log 2 removal is equal to 99% removal or 99% inactivation.

BrCl Dosage (mg/L)

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