Page 119 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

^ m ¼ 0.2 h 1 tipped in favor of advection; convection seemed to
K m ¼ 6mg=L be more associated with heat.]
Y ¼ 0.31 kg cells synthesized=kg substrate degraded CSTR: (1) A common acronym for ‘‘completely stirred tank
3
2
¼ 31.4 m media surface area=m bulk volume reactor.’’ (2) A ‘‘complete-mix’’ reactor is also a

2
X ¼ 1.0 kg cells=m media surface area CSTR.
porosity, P ¼ 0.40. Detention time: The residence time of a fluid in a volume of
Let design variables be: some kind in which the hypothetical ‘‘plug’’ flow
depth of the filter, D ¼ 2.0 m occurs.
2 3 Diffusion: Molecular transport by random motion of mol-
HLR ¼ Q=A ¼ 5.0 gpm=ft ¼ 3.395 10 m=s and
recall, v ¼ HLR=P ecules. Fick’s first law describes the transport rate.
Dispersion: The ‘‘spread’’ of a substance in flow. In porous
Operating conditions are:
media flow and in turbulent flow, the mechanism is a
S 0 ¼ 200 mg BOD=L, and
statistical variation of velocity about the mean
S(2.0 m) ¼ 30 mg BOD=L
advective velocity. In flow through basins, ‘‘short
[Note that S(2.0) is a nomenclature adopted here that circuiting’’ causes a portion of the flow to reach the
means the effluent concentration is at 2.0 m depth in the end of the basin sooner than the ‘‘plug-flow’’ vel-
filter.] ocity. At the same time, a portion of the flow will
(a) Assume steady state conditions and determine a exchange mass with dead zones of the basin which
‘‘calibration’’ coefficient, K for the model. The will cause a long tail on a dispersion curve. A dye
value for K is determined by trial and error and is test or a salt test is used commonly as a means to
the value selected when the calculated S(2.0) equals evaluate dispersion. Intuitively, if 100 molecules are
30 mg=L (the assumed actual effluent concentration). transported to a point in front of or behind the mean
(b) Assume a flow variation over a 24 h period (use flow due to a statistical mechanism the same statis-
sinusoidal variation if you wish), and determine the tics are applicable to those 100 molecules in the new
S(2.0 m) versus t. position. In the next ‘‘step’’ some of the 100 will be
4.9 Global Atmosphere as a Reactor behind the average and some will be ahead.
Suppose that a gas (any gas) is emitted by various surface Fick’s first law: The mathematical relation in which flux
sources. Let the gas be nonreactive in the atmosphere, but density of a given substance is proportional to the
will dissolve in water (in accordance with Henry’s law). concentration gradient.
If the atmosphere has a uniform concentration of the gas Finite difference equation: The expression of a differential
3
at x kg=m , estimate the number of years for the atmos- equation in terms of infinitesimal differences, that is,
phere to purge itself to a concentration 0.05 fraction of DC, Dt, DZ,
the original concentration. [Hint: The rate of contact with Fit: The relationship between a ‘‘form’’ and its ‘‘context.’’
water surfaces is probably rate limiting.] As a second Flow net: Analysis method for ‘‘irrotational flow’’ and is
aspect of the problem, consider the complexity of the applicable to turbulent flow where viscosity is not a
movement of air masses and the assumption of homo- major influence and to ground water flow for cases in
geneity (i.e., complete mix is only a first approximation). which R 1 (which is usual). The flow net is
4.10 Global Atmosphere as a Reactor with Carbon comprised of streamlines and potential lines (or sur-
Dioxide faces) and is unique for a particular set of ‘‘boundary
Suppose that the gas in the previous problem is carbon conditions.’’
dioxide. Develop a rough global model of a carbon Flux: Rate of transport of mass (or heat) across a boundary
balance. (kg=s)
Flux density: Rate of transport of mass (or heat) across a
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boundary per unit area (kg=s=m )
GLOSSARY
Form: The kind of design synthesized that may or may not
Advection: The transport of molecules or mass by a fluid flow ‘‘fit’’ the ‘‘context’’ at hand.
with such flow responding to a pressure gradient. Gaussian: The probability curve that is ‘‘normal’’ in shape,
Appropriate fit: A ‘‘form’’ that relates to a given ‘‘context’’ that is, bell-shaped; it may be the outcome of meas-
in an appropriate manner. urements of a given random variable.
Biofilm: Bacteria film that adheres to a surface. Homogeneous reactor volume: The part of a reactor in
Contactor: A reactor in which reaction occurs. which the contaminant of interest, for example, A
Context: The situation or setting that comprises the basis for has a constant concentration from point to point
a design. within the volume. It is important to designate
Convection: The movement of a fluid under a pressure gra- because the materials balance relation is valid
dient (see advection). [In this text, convection was only for a homogeneous volume. A ‘‘complete-
used initially and then was replaced with ‘‘advec- mix’’ activated sludge reactor could approach this
tion’’; in splitting hairs to decide, the scales were homogeneity. A plug-flow reactor does not, by