Page 91 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

3.2.2.1 Plots
BOX 3.1 PHILOSOPHY OF MODELING
The kind of experimental program outlined above might
Modeling has two themes of logic: inductive and be called ‘‘parametric exploration.’’ Figure 3.2 illustrates the
deductive, formalized by Sir Francis Bacon (1561– output of f as a function of x and y,with z constant, i.e., fv x
1626) and René Descartes (1596–1650), respectively. for y ¼ y 1 , y 2 , ... , y n and z ¼ z 1 , where z represents a set of
Bacon extolled observation and practical outcomes, conditions that are maintained constant during the testing. To
while Descartes believed that pure reasoning was the be more specific, the system being modeled is a rotating drum
basis for problem solving (Durant, 1926). microscreen. The flow of water through the screen divided by
The essence of empiricism is observation. Engineer- its submerged area is the velocity of water through the screen,
ing forms include bench scale testing, pilot plants, dem- v, which is the ‘‘dependent’’ variable, i.e., f. Then v is
onstration plants, evaluations of existing plants, etc. affected by the independent variables, headloss, h, across the
Also included in this category are judgment, lore, and screen, as seen by the curve and the rotational velocity, v,of
‘‘black box’’ approaches. Rational models include equa- the drum, in which h and v correspond to x and y, respect-
tions based on a premise leading to an understanding of ively. The set of curves of Figure 3.2 is for all other conditions
process mechanisms. Mathematical modeling, scen- being maintained constant. If, for example, the suspension
arios, animations, etc., are modern outcomes. Most changes (such as one species of algae instead of another) or
problem solving is a blend of empiricism and rationality the screen size changes, then another set of conditions exists
rather than being exclusively one or the other. and another set of curves must be generated. Thus, a set of one
The organization and displays of solutions are or more plots, such as seen in Figure 3.2, is the end result of a
important also, as the amount of data generated by black box experimental program.
physical models or computer models may be over-
whelming. Spreadsheets and plots provide a means to
3.2.3 PHYSICAL MODELS
organize and present results such that a wide range of
conditions can be communicated easily and clearly. A physical model is a smaller-scale setup of equipment
Computer animations provide a means to display suc- intended to replicate the process being considered. One appeal
cinctly and to grasp more easily complex results that of a physical model is that variables not anticipated are included
could be otherwise difficult to assimilate. passively. The outputs, i.e., dependent variables, thus reflect all
All of these various kinds of models have roles in independent variables, not just the ones identified.
engineering problem solving. Even when we know little With the smaller scale, the model is cheaper and easier to
about a problem, some form of model provides a means operate than a full-scale system. Further, the independent
to identify variables, organize data, test assumptions, variables can be controlled so that the influence of each on
generate plausible solutions, and communicate results. the dependent variables can be investigated. Physical models
include bench scale testing, pilot plants, and demonstration
scale plants.

box, illustrating the idea of how the values of dependent 3.2.3.1 Bench Scale Testing
variables are generated by maintaining y and z constant Bench scale testing may include jar tests to determine chemical
while varying x; f and c are measured for each level of x at dosages, kinetic coefficients, isotherm constants, and generat-
fixed values of y and z. Then y is changed to a new value, and ing relationships between various other kinds of intensive
the process is repeated. After all the values of y are explored, z variables. The testing is ‘‘one dimensional’’ in nature, i.e., the
may be changed to a new level, and the foregoing is repeated intent is to examine the influences of only one or two inde-
for each value of z that is to be explored. Suppose that there pendent variables (such as screen size) in selected dependent
are 5 levels of x,8of y, and 10 of z. Then the number of variables (such as effluent concentration).
experiments would be 5 8 10 ¼ 400. In exploring a hypo-
thetical ‘‘surface,’’ a substantial amount of effort is required. 3.2.3.2 Pilot Plants
An example of the foregoing in more concrete terms is the One purpose of a pilot plant is to generate functional relation-
traditional jar test. Thousands of experiments may be done ships between dependent and independent variables. The
where a treatment process is being explored, i.e., to determine extent to which this is done, i.e., the scope of the experimental
coagulant dosage, x, and polymer dosage, y, for several sea- program, depends upon the nature of the problem and the
sonal water quality conditions, z. budget available.
The ‘‘black box’’ is a device to generate outputs (depen- Another purpose of a pilot plant study may be to determine
dent variables—f and c) from selected inputs (independent coefficients of a mathematical model. A mathematical model
variables—x, y, z), which may define a useful portion of a has greater utility than a set of plots.
functional relationship. Virtually any means to generate out- Pilot plant experiments will yield, almost without exception,
puts from inputs can be considered a ‘‘black box.’’ Such unexpected results that lead to new insights and serendipitous
means could include judgment, physical models, and math- findings. Thus, any plan devised in anticipation of a set of
ematical models. results should have flexibility to incorporate new findings.