Page 107 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

Rifai et al. (1956) presented a method of obtaining D that flocculation basins, anaerobic digesters, disinfection basins,
was done by measuring the whole breakthrough curve. This ozone contactors, etc. The fixed bed reactors include trickling
equation is filters, slow sand filters, rapid rate filters, granular activated
carbon beds, etc.

1 L Turbulence characterizes the transport mechanism of a
v (4:7)
D ¼ 2 2
4p V S fluidized reactor in which the reactants contact each other by
0 0
the random motion of turbulence. In the fixed bed reactor, the
in which media is ‘‘passive’’ and the reaction depends upon the other
3
V 0 is the throughput volume at C=C 0 ¼ 0.50 (m ) reactant being advected to a site with the final transport step
being diffusion (sedimentation may have a role if larger
S 0 is the slope of the breakthrough curve at C=C 0 ¼
3
0.50 (m ) particles are involved).
The foregoing list may be disaggregated further. For
For Equation 4.7, the breakthrough curve is plotted with example, within the activated sludge category of fluidized-
throughput volume instead of time as the abscissa. This bed reactors, there are complete mix reactors and plug flow
method is in lieu of using Equation 4.6 to solve for D. The reactors. There are also ‘‘film’’ reactors, which are films on a
throughput volume is given as V ¼ Q t. media (this is the fixed bed reactor category). The media may
Rifai et al. have also shown experimentally that D= v is a be rocks (trickling filters), granular media (slow sand), and
constant. This is also evident from the analogy with Brownian rotating plates (rotating biological contactors). And if there is
motion in which it is the number of steps that determines no flow across the boundaries, then the volume is a batch
position probability in the diffusion process. Velocity merely reactor. If there is flow across the boundaries the volume is a
determines the number of steps taken per unit of time. continuous flow reactor.
This term D= v is a property of the porous media and is the From this discussion, a reactor description has several char-
term calculated from the experimental data indicated in Equa- acteristics. We must describe it in terms of whether the contacts
tion 4.7. Thus D is obtained for any value of v once D= v is within the reactor are caused by the bed being fluidized by
evaluated. turbulence, or whether the bed is fixed, as in granular media. If
the reactor is fluidized it may be complete mix and the whole
reactor is thereby homogeneous; on the other hand, if there is
4.2.3 SUMMARY
no mixing, the reactor is plug flow and nonhomogeneous.
The ‘‘sink’’ is the place where the contaminant is removed from Fixed-bed reactors are nonhomogeneous. If the reactor is
the water stream or is transformed into another species. The homogeneous, concentrations do not vary spatially; for a
manner of reaching the sink depends on the transport mechan- nonhomogeneous reactor, concentrations vary spatially.
ism, for example, advection, turbulence, diffusion, or gravity. In terms of its flow, the reactor may be either batch or
continuous flow. The mathematical description of a reactor,
4.3 REACTORS that is, mathematical modeling, may have special conditions
imposed, depending upon the type of reactor.
A reactor is the place where something ‘‘happens,’’ that is,
removal of a selected contaminant. Usually, the ‘‘place’’ is
within an engineered volume where the transport is controlled 4.3.3 MATHEMATICS OF REACTORS
along with the character of the sinks.
Reactor mathematics is based upon two principles: (1) mater-
In the ambient environment, the reactor concept is applicable
ials balance and (2) reaction kinetics. A mathematical depic-
to any arbitrary volume. A volume element of a lake behaves
tion of a reactor, so formulated, constitutes a model. Such a
mathematically as a reactor, as does a volume element of a
model is applicable to most of the engineered unit processes
stream, or a volume element within a ground water stream tube.
(and, as noted, to processes that occur in the ambient envir-
onment). A proper kinetic depiction is usually the most diffi-
4.3.1 EXAMPLES OF REACTORS cult part of the model. The materials balance=kinetic model
Under the definition of a reactor stated, the reactor concept is provide a basis for analysis and for rational process design.
applicable to any kind of unit process. Examples of reactors The critical aspect of a reactor model is that the materials
include: an activated sludge basin, a bed of granular activated balance is applicable to a specified volume element. A key
carbon, a granular media filter, a rapid mix basin, a floccula- point is that the contents of the volume element must be
tion basin, a disinfection basin, etc. Even a sedimentation homogeneous, that is, concentration is constant from point to
basin may be considered a reactor under the more liberal point throughout the volume, regardless of the kind of reactor.
definition, that is, as place where something ‘‘happens.’’
4.3.3.1 Materials Balance: Concept
The basic idea of a reactor model is quite simple and is
4.3.2 TYPES OF REACTORS
embodied in Equation 4.8, a word statement of the materials
Two basic reactor types are fluidized volume and fixed bed. balance principle. Figure 4.4 shows a volume element (two
Within the former are activated sludge, rapid mix basins, dimensional) which illustrates the terms of Equation 4.8. In this