Page 673 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

19.3.7.3.6 Radiant Power Efficiency a certain fraction will receive a dose that equals or exceeds
The radiant power efficiency of a lamp is defined (Bolton, the critical inactivating dose. Another fraction will receive
2001, p. 9) as a damaging, but repairable dose, and another fraction
will have a dose that is less than what may cause damage.
The distribution of doses among 100 microorganisms is due
P(lamp)
(19:39) solely to the reactor hydraulics, given that other factors are
P(wire)
E(lamp) ¼
the same.
Suppose, for a given reactor, that log R(inactivation) ¼ 1.0
where (i.e., 0.90 fraction inactivation for a sample collected over a
E(lamp) is the radiant power efficiency of lamp (dimen- period of time). This means that 90 cells were inactivated and
sionless) 10 cells remained viable (and could reproduce). To achieve
P(wire) is the power input to lamp from electric energy 4-log inactivation, that is, log R(inactivation) ¼ 4, then four
source (W) modules, of the type used for the test, must be placed in series
(in the pipeline or in the channel).
In other words, if the efficiency, E(lamp), is known, for
example, as a published value, one can calculate the power 19.3.7.4.2 Mathematical Modeling of a UV Reactor
that must be supplied to a given lamp. As another point, if Equation 19.40 gives the materials balance=kinetics modeling
the wire power, P(wire), is increased, P(lamp) increases relation for a plug flow reactor, which for microorganisms
correspondingly. becomes

19.3.7.3.7 Aggregate Effect of Multiple Tubes UV qN qN q N qN
2
Radiation Intensity at Any Given Point ¼ v þ D 2 (19:40)
qt
o qZ qZ qt r
The intensity of radiation at any given coordinate point within
a bank of UV tubes is the aggregate effect of the radiation
where
‘‘field’’ resulting from a collection of tubes. A computation 3
N is the concentration of the microorganisms (#=m )
such as Equation 19.38, done for each tube, would yield the
t is the elapsed time (min)
UV field strength, I(r, u) at any point in the cross section, as
Z is the distance from the entrance to the reactor (m)
done by Snicer et al. (2000, p. 15).
v is the mean velocity in reactor, that is, Q=A (m=s)
[qN=qt] o is the rate of change of microorganism concen-
19.3.7.3.8 Factors Affecting UV tration as ‘‘observed’’ in an infinitesimal reactor ‘‘slice,’’
3
The target microorganism must be exposed to the required DZ, that is normal to the velocity vector, v (#=m =s)
[qN=qt] r is the rate of change of microorganism concen-
flux density of the UV for such time duration that I o t
(dose-for-required-log R). Thus, if the lamps are fouled, or if tration due to the reaction of microorganisms with the
radiation blocking particles are in the water, or if absorbing disinfectant, and as described by a kinetic equation
3
solutes are in the water, the UV emitted by a given lamp, that (#=m =s)
is, I o , will be attenuated (Snicer et al., 2000, p. 2). A dose
criterion may be met by adding sufficient banks of UV lamps For a ‘‘steady-state’’ condition, the left side of Equation
in series, that is, by a longer reactor (preferable to parallel). 19.40 is zero, that is, [qN=qt] o ¼ 0, which makes the equation
Alternatively, the needed exposure, that is, It, may be more amenable to solution (see Chapter 4).
achieved by a higher density of lamps (giving a higher prob-
ability that the needed It will be obtained), or by a higher 19.3.7.4.3 Kinetic Constant Determination
emission strength of the lamps, that is, increasing I by How to determine the kinetic constant exactly in Equation
increasing ‘‘P(wire).’’ 19.5 is not apparent. Following the pattern of Example 19.1,
however, one may calculate k for UV by a similar protocol:
19.3.7.4 Reactor Design
1. For a given organism Table 19.7 gives the ‘‘dose,’’
Reactor design for UV is the same in principle as any other,
It, for N=N o ¼ 0.1, that is, log R ¼ 1.
but with a ‘‘target microorganism’’ as the basis for the mass
For example, It(adenovirus strain 40) ¼ 30
balance reaction and kinetics. 2
mJ=cm for log R ¼ 1.
2. From Equation 19.32, ln N=N o ¼ k (It), solve for k.
19.3.7.4.1 Dose and Exposure For example, ln(0.1)¼ 2.325851¼ k (30
2
2
Bolton (2001) defines the UV inactivation ‘‘dose’’ as the UV mJ=cm ); solving for k, k¼ 0.078 cm =mJ-s
radiation that is assimilated by the microorganism and that
could cause damage to the cell. The UV dose received by a The kinetic constant, k, may then be used in the kinetic
given microorganism depends on its specific path of exposure equation for a quantitative solution to Equation 19.40, for
within the reactor. Of 100 microorganisms entering a reactor, example, by finite difference.