Page 90 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

3 Models

In education, especially at the undergraduate level, we empha- 3.2 MODELS
size problems in which the parameters are well defined. In
A model is a means to represent a portion of a reality. The
practice, however, this is not the reality. Knowledge may be
model is ‘‘valid’’ if the points of the model predict accurately
incomplete: data on inputs may be lacking, methods of solu-
the corresponding points of the system being modeled. As a
tion may not be well delineated, and even the objectives may
rule, the system being modeled, i.e., the ‘‘prototype,’’ is a full-
be nebulous. All of this is contrary to the common perception
scale process. Examples include an activated sludge reactor, a
of engineering, i.e., that it is deterministic and largely a matter
biofilm reactor, a plate settler, a slow sand filter, a rapid rate
of computation.
filtration system, a granular activated carbon reactor, an ozone
This chapter examines some of the approaches for attack-
reactor, etc. Natural systems may be modeled also, e.g., water
ing problems. The concept of modeling is a theme common to
quality of streams and lakes, groundwater, etc., with math-
all. Modeling is an engineering method (Box 3.1).
ematical models being a primary method of determining the
effects of pollutant discharges on such systems.
Table 3.2 lists various forms of models and describes their
3.1 UNIT PROCESSES
respective characteristics and positive and negative attributes.
About 10–15 unit processes comprise the field of water treat- The notion of what may comprise a model, Table 3.2, illus-
ment, depending on how they are categorized. Perhaps there trates that a wide range of forms may be encompassed. Thus, a
are 80–100 technologies developed from them. Table 3.1 lists model may include lore, judgment, description, bench testing,
13 unit processes and associated technologies. Fundamental pilot plants, demonstration plants, and mathematical models.
principles operative include
3.2.1 CATEGORIES OF MODELS
. Sieving of particles by screens (ranging from bac-
teria by membranes to large objects by bar screens) A model is a means to ‘‘represent.’’ Thus, a photograph is a
. Creating conditions for application of a ‘‘passive’’ model, along with language, a drawing, a painting, a map, a
force on particles (e.g., gravity), or an ‘‘active’’ force plot, an equation, an array of 0 and 1 digits stored in a
(e.g., centrifugal) to cause transport computer, or any kind of representation. To be an engineering
. Turbulence and diffusion for the transport of par- model, this is necessary but not sufficient. An engineering
ticles to cause contacts between reactants model, we might assert, must also have utility in projecting
. Charge neutralization from the unknown to the known.
. van der Waals attraction between molecules and a More commonly in engineering, we think of a model in
surface (such as activated carbon), or charge attraction terms of a pilot plant or as a set of coordinated equations in a
(such as between ions and an ion-exchanger material) computer algorithm or in a spreadsheet or even a single equa-
. Various chemical reactions such as tion. Table 3.2 lists some of the more common things that we
. Redox, acid–base do in engineering that are really ‘‘forms’’ of models. They
. Precipitation qualify as meeting the requirements of a ‘‘model,’’ as defined
. Complexation here. Indeed, the various model forms comprise engineering
. Biochemical practice, e.g., lore, judgment, extrapolation, bench scale test-
. Cell synthesis ing, pilot plants, demonstration plants, and mathematical mod-
. Membrane processes involving retention of ions and eling. As an additional note, each model form in Table 3.2 may
molecules, i.e., reverse osmosis=nanofiltration be thought of as a ‘‘black box.’’ In other words, a model as a
‘‘black box’’ accepts a set of ‘‘inputs,’’ without regard to how it
Generally, the unit processes listed in Table 3.1 are the results works, and generates outputs.
from a heritage of only since about 1900, albeit the earliest
technology was slow sand, with the first installation in 1829
3.2.2 THE BLACK BOX
for London. Proprietary innovations have expanded the array
of technologies, but most are variations of the unit processes The proverbial ‘‘black box’’ has its place as a primary engin-
listed in Table 3.1. eering method. Figure 3.1 depicts the concept of the black

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