Page 659 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

614 Fundamentals of Water Treatment Unit Processes: Physical, Chemical, and Biological

Ct(coxsackievirus) ¼ 10, for example, if C ¼ 5 mg chlorine=L, trends with temperature for log R ¼ 1, 2, 3, respectively. The
then t ¼ 2 min. top scale shows the temperature for each point in 8C and the
For a given log R, K is a function of the organism, the lower scale is the inverse of absolute temperature. The plot
disinfectant, pH, and temperature. Thus, K is different for shows (1) the log Ct versus 1=T (K) plots are linear and fit the
different microorganisms, for example, E. coli, coxsackievirus, Arrhenius relation; (2) the log R plots are displaced by a linear
Cryptosporidium parvum oocysts, etc. K varies also with the factor from each other (for example, log R ¼ 2 values are
disinfectant, for example, chlorine, ozone, chloramines, chlor- twice the log R ¼ 1 values; log R ¼ 3 values are 3 times the
ine dioxide, ultraviolet radiation, etc. Also, K may vary with log R ¼ 1 values); (3) the Ct values for Giardia using ozone as
pH if the dissociation species is affected. Temperature influ- a disinfectant are markedly lower than for chlorine.
ences kinetics in accordance with the Arrhenius equation.
19.3.2 APPLICATION OF CHICK–WATSON RELATION
19.3.1.3 Ct’s Compiled
Table 19.3 is a compilation of empirical Ct data for various Example 19.1 illustrates how Chick’s law can be applied to
organisms, for example, bacteria, viruses, and cysts, under utilize Ct data, per Equation 19.12, to estimate the percent
conditions stated, for example, pH, temperature, and disin- inactivation for any time of contact. Example 19.2 illustrates
fectant. As seen, the Ct’s have a wide range depending on the how to convert Ct(99% kill) to Ct(99.9% kill) applying Equa-
organism and conditions. The Ct values are useful for design. tion 19.6. This is done by first calculating t for 99% inactiva-
The disinfectant concentration is limited, as a rule, based on tion, per Equation 19.12, for a given Ct and a given
practice or regulations. As an example, from Table 19.3, if Ct disinfectant concentration, and then determining the kinetic
(G. lamblia, chlorine, pH ¼ 7.0, T ¼ 18C) ¼ 289, and if, coefficient, k, per Equation 19.6, and finally, with k deter-
C(chlorine) ¼ 2mg=L, then, t 150 min (2.5 h). mined, the N can be determined for any t specified.

19.3.1.4 Ct(chlorine) for Giardia lamblia Cysts Example 19.1 Application of Chick’s Law
Equation 19.13 calculates Ct(Giardia) for chlorine as a func- to a Practical Problem
tion of conditions, that is, C(chlorine), pH, and T, and for log
R ¼ 4. The equation was obtained from regression analysis by Given
Clark et al. (1989) of 167 data points from Hibler et al. (1987) A city has a clear well with 60 min detention time and uses
for use in the EPA draft ‘‘Surface Water Treatment Rule.’’ chloramines to disinfect. The chloramine concentration is
The Hibler et al. data were based on gerbil infectivity for a maintained at 2.5 mg=L and is mostly in the form of
monochloramine. Assume the concentration of hetero-
dose of 50,000 cysts per gerbil; experimental conditions were
trophic plate count (HPC) bacteria for the flow entering
the clear well is 10,000 organisms=mL (which is very high
0.4 C(chlorine) 4.2 mg=L; 7.0 pH 9.0; 0.58C T
58C; the regression coefficient for the fit of Equation 19.13 to but is used for illustrative purposes).
2
the data was, r ¼ 0.80. The Ct’s for other log R values may be
calculated, for example, Ct(1 log) ¼ Ct(4 log)=4. Similar Required
regression analyses were done for Cryptosporidium and Estimate the average concentration of HPC bacteria leav-
ing the clear well.
ozone (Clark et al., 2002) and Cryptosporidium and chlorine
dioxide (Clark et al., 2003). Table CD19.4 (excerpt in text) Solution
calculates Giardia Ct values from Equation 19.13 for various The approach is to define terms, then determine the time
log R values. for 99% kill by the Watson relation, then obtain the kinetic
coefficient for the disinfectant concentration specified by
Chick’s law. Knowing the kinetic coefficient, we can cal-
0:176 2:752 0:147 2
Ct(4-log ) ¼ 0:985C pH T r ¼ 0:80 (19:13)
culate the kill for any different contact time (without chan-
ging the disinfectant concentration).
where Step 1:Define terms as given,
Ct(4-log) is the Value of Ct for a 4-log inactivation of
C(monochloramine) ¼ 2.5 mg=L
Giardia lamblia cysts by chlorine (dimensionless)
C is the concentration of chlorine (mg=L) t ¼ 60 min
t is the time of contact (min) N 0 ¼ 10,000 org=mL
pH is the pH of solution N ¼ (to be determined)
T is the temperature of reacting vessel (8C) Step 2: Apply Equation 19.12 to determine t(99% kill).
2
r is the regression coefficient for fit of equation to Hibler
From Table 19.3, K(monochloramine, HPC) ¼ 102
et al. (1987) data
K ¼ Ct(0.99 kill)
19.3.1.5 Inactivation by Ozone
Applying Equation 19.12,
Some of the salient points regarding disinfection are encap-
sulated in a plot of Ct versus temperature data for ozone 102 ¼ 2.5 mg=L t(99% kill)
inactivation of Giardia lamblia cysts. Figure 19.2 shows Ct t(99% kill) ¼ 40.8 min