6.1 Engineering Bernoulli EquationMost engineering problems in fluid mechanics can be solved using the ing Bernoulli equation, also called the mechanical energy balance.. Under these con
Trang 1∆G = RT ln ƒ ƒ2
Here, ƒ1 is the fugacity at pressure P1 The fugacity may be considered as anadjusted pressure It is defined so as to coincide with the pressure at low densities:lim
Consider a solution consisting of n species A, B, The Gibbs free energy of
the solution is given by
5.5 Fugacity and Activity
The chemical potential is generally a function of temperature, pressure, andcomposition It is common practice to write
where µ˚A(T) is the standard chemical potential and aA is the activity of species
A The activity is defined as the ratio of the fugacity ƒA to a standard-state
fugacity ƒ˚A:
aA = ƒ˚ ƒA
A
(84)Activities and standard states are discussed in greater detail in many texts onchemical thermodynamics (11,12)
Trang 26 ENGINEERING FLUID MECHANICS
Fluid mechanics deals with the flow of liquids and gases For most engineeringapplications, a macroscopic approach is usually taken
Trang 36.1 Engineering Bernoulli Equation
Most engineering problems in fluid mechanics can be solved using the ing Bernoulli equation, also called the mechanical energy balance It can be
engineer-derived from the macroscopic energy balance (see Ref 13), subject to thefollowing restrictions: (a) the system is at steady state; (b) the system has a singlefluid intake and a single outlet; (c) gravity is the sole body force, with constant
|g|; (d) the flow is incompressible; (e) the system may include one or more pumps
or turbines Under these conditions, the macroscopic energy balance becomes
where
P = the fluid pressure
〈ν〉 = the velocity averaged over the cross section of the pipe or conduit
α = average velocity correction factor (2.0 for laminar flow and 1.07 forturbulent flow)
W⋅2 = rate of work done by pumps or turbines (positive for pumps,negative for turbines)
F⋅ = frictional loss rate
Dividing by the acceleration of gravity |g| yields the so-called head form of the
Bernoulli equation:
∆
P ρ|g| + z + α2|g|〈ν〉2
=
W⋅ s
Each of the terms in this equation has the dimensions of length
6.2 Fluid Friction in Pipes and Conduits
The frictional loss rate F⋅ equals the rate at which useful mechanical energy is
converted to thermal energy by friction It is usually computed from an equation
where ƒ is the Fanning friction factor.* In general, the friction factor is a function
*This is not the only friction factor in widespread use Some authors prefer the Darcy-Wiessbach friction factor, ƒ DW = 4ƒ.
Trang 4of the pipe diameter D, the surface roughness ε, and the Reynolds number Re,the latter being defined as
where µ is the fluid viscosity
In the laminar-flow regime, ƒ = 16/Re For turbulent flows, a number ofcharts, graphs, and equations are available to compute the friction factor TheColebrook equation has traditionally been used, although it requires a trial-and-error solution to find ƒ:
pipe diameter D is replaced in Eqs (94–100) by the hydraulic diameter DH:
DH = 4 area wetted by fluidvolume of fluid (101)
6.3 Minor Losses
The relations developed in the previous section apply only to straight pipes orconduits Most pipelines, however, include bends, valves, and other fittings whichcreate additional frictional losses These additional losses are often called “minorlosses,” although they may actually exceed the friction caused by the pipe itself.There are two common ways to account for minor losses One is to define
an equivalent length Leq which equals the length of straight pipe that would givethe same frictional loss as the valve or fitting in question The total equivalent
Trang 5length Ltotal is the sum of the true length of the pipe and the individual equivalentlengths of the valves and fitting:
Ltotal = Lpipe + ∑
fitting i
The total equivalent length Ltotal is used in Eq (94) in place of L to compute the
total frictional losses
The second common approach to computing minor losses relies on the
concept of a loss coefficient K L, defined for each type of valve or fitting according
6.4 Fluid Friction in Porous Media
A porous medium is a solid material containing voids through which fluids mayflow The most important single parameter used to described porous media is the
porosity or void fractionε:
ε = void volumebulk volume = Vvoids
2 M M Denn, Process Fluid Mechanics Englewood Cliffs, NJ: Prentice-Hall, 1980.
3 R W Fahien, Fundamentals of Transport Phenomena New York: McGraw-Hill,
1983.
4 W M Deen, Analysis of Transport Phenomena New York: Oxford University Press,
1998.
5 E L Cussler, Diffusion Mass Transfer in Fluid Systems, 2nd ed Cambridge, U.K.:
Cambridge University Press, 1997.
Trang 66 O Levenspiel, Chemical Reaction Engineering, 2nd ed New York: Wiley, 1972.
7 H S Fogler, Elements of Chemical Reaction Engineering Englewood Cliffs, NJ:
PTR Prentice-Hall, 1992.
8 L D Schmidt, The Engineering of Chemical Reactions New York: Oxford
Univer-sity Press, 1998.
9 F P Incropera and D P DeWitt, Fundamentals of Heat and Mass Transfer, 3rd ed.
New York: Wiley, 1990.
10 D R Lide (ed.), CRC Handbook of Chemistry and Physics, 80th ed Cleveland, OH:
CRC Press, 1999.
11 I M Klotz and R M Rosenberg Chemical Thermodynamics: Basic Theory and
Methods, 3rd ed Menlo Park, CA: W A Benjamin, 1972.
12 K Denbigh, The Principles of Chemical Equilibrium, 3rd ed Cambridge, U.K.:
Cambridge University Press, 1971.
13 N De Nevers, Fluid Mechanics for Chemical Engineers, 2nd ed New York:
McGraw-Hill, 1991.
14 Flow of Fluids Through Valves, Fittings, and Pipe, Crane Technical Paper 410.
Chicago: The Crane Company, 1988.
Trang 7on, and applicability to, an engineer’s ability to achieve waste minimization goals.
It has had demonstrated success with recycling programs via the generation ofbiogas as an alternative fuel Bioremediation approaches have also been used for:point source reduction via biopolishing (3) and individual stream treatment (4);by-product utilization (5); material substitution (6); facilitation of new enzy-matic/metabolic pathways to produce “cleaner” organic substances (7); andend-of-pipe treatments (8–10) This chapter will highlight a few of the biotech-nology approaches to waste minimization
When utilizing any biotechnology, it is important to remember that theprimary function of a microorganism is not to destroy man’s unwanted contami-nants Instead, a microbe must reproduce itself and maintain its cellular functions
To that end, as shown in Figure 1, every microorganism must: (a) protect itselffrom the environment, (b) secure nutrients (catabolism), (c) produce energy in ausable form (catabolism), (d) convert nutrients/food into cellular material (anab-olism); (e) discard unnecessary waste products, and (f) replication genetic infor-
Trang 8F IGURE 1 Overview of general cellular functions applicable to all living cells.
Trang 9mation It is an added benefit to mankind that the result from the microbialmetabolism of substrates (i.e., step d), that the unwanted contaminants aredegraded Once it was realized that microorganisms could degrade unwantedcontaminants, engineers started to manipulate the surrounding environment toensure that the microbes would thrive and utilize the contaminant as the substrate.Engineers currently use microorganisms to treat drinking water, municipalwastewater, and various industrial effluents Usually the chemical and petrochem-ical industry is considered the only “real” contributor to industrial effluent (11).However, as shown in Table 1, more than just the chemical industry utilizesmicroorganisms for the treatment of waste on-site.
Regardless of whether the microorganisms are being used for cleaningdrinking water, or municipal or industrial wastewaters; for end-of-pipe treatment
at contaminated sites; or for waste minimization applications, certain key aspectsapply (75) The following sections will outline the key aspects applicable toany biological treatment, provide a brief description and design criteria forthe common waste minimization technologies, as well as highlight a few of the
T ABLE 1 Some of the Industries that Utilize
Biological Treatment for the Reduction of
Heavy metals processing 13,39–45
Oil processing and refineries 46–49
Trang 10innovative of bioprocesses that enable the selective removal of unwanted icals in product streams.
chem-2 KEY ELEMENTS ESSENTIAL TO ALL BIOLOGICAL
TREATMENT METHODS
Several basic biological requirements are essential for any biological treatmentprocess to be successful They are based on the principles required to support allecosystems and include the presence of: appropriate microbes for degrading thecontaminant(s), substrate for carbon and energy source, required terminal electronacceptor (TEA), inducer to facilitate enzyme synthesis, nutrients for supportingmicrobial growth, microbes to degrade metabolic byproducts, environmentalconditions to minimize growth of competitive organisms (76–78) These factorswill be discussed below
2.1 Adequate Microbial Population
The primary requirement for any successful biological treatment or waste mization strategy is the presence of an adequate microbial population Luckily forenvironmental engineers, Mother Nature has supplied a wide variety of microbes
mini-to select from and mini-to cultivate The organisms are subdivided inmini-to differentcategories based on their metabolic capabilities and/or requirements Table 2
contains the classifications based on the microbial carbon source, energy source,and respiration mode If a contaminant can only be degraded in the presence ofanother organic material that serves as the primary electron source, then co-metabolism is occurring If the interaction of the two organisms is nonobligatory,then it is a synergistic relationship Mutalism occurs if the interaction is beneficialyet obligatory Since microbes are very versatile, it is important to remember thatthey may belong to more than category
The microbe’s versatility may also enable it to treat more than one ticular type of contaminant As shown in Table 3, different species of Pseudo- monas have demonstrated success at reducing agricultural, heavy metal, food,
par-and solvent wastes In each instance, the primary requirement for successfultreatment is the presence of an adequate population Researchers have deter-mined that a microbial count of 103–108 cfu/liter, 104–107 cfu/g would beadequate for groundwater and soil applications, respectively (77,79–81) There-fore, to ensure a successful biological treatment for waste minimization, aminimum of 108 cfu/liter would be recommended If the contaminant concen-tration or toxicity increases, the microbial population will have to increase aswell If the increase in biomass concentration does not result in the desiredtreatment efficiency, the microbes being utilized may have to be changed toanother source
Trang 11The species indigenous to a natural environment contain several differentmicrobes living together (i.e., mixed population) Therefore, it is reasonable topresume that it is highly unlikely that one bacterial strain will be successful for acomplete waste minimization scheme Table 3 includes bacteria that have beensuccessful at degrading the parent compound of the specified waste Most of thereferences did not report the achievement of complete mineralization (conversion
of contaminant into CO2, biomass, H2O, and salts) Complete mineralizationwould require the use of a microbial consortium A consortium is more than asimple group of bacteria that can grow together The overall net effect of theconsortium is greater than what the individual microbes can accomplish on itsown Consortiums facilitate the degradation sequence where one microbe de-
T ABLE 2 Microbial Classification Based on Growth Requirements: Carbon and Energy Source, Respiration Mode
Prototrophs Most self-sufficient Can synthesize all
required growth compounds given
CO2 or a single organic compound.
required for growth.
chemicals.
Lithotrophs Energy from oxidation of inorganic
chemicals.
TEA:
Anaerobe (oligate) Cannot grow in the presence of oxygen.
Obtain TEA from different source Facultative anaerobe Can utilize O2 if present; however prefer-
able growth in absence of O2 via ent TEA.
Trang 12T ABLE 3 Select Microbial Genus with Demonstrated Success for Treating Industrial Contaminants Based on Waste Classification
Acinetobacter Mycobacterium Arthrobacter Pseuodmonas Bacillus Vibrio
Flavobacterium
Agricultural (pesticides, Achromobacter Flavobacterium
Arthrobacter Penicillium* Athiorocaceae Pseudomonas Corneybacterium* Zylerion*
Dyes Aeromonas Phaneorchaete*
Micrococcus Shigella Klebsiella Trametes* Pseudomonas
Food, dairy, slaughter Acinetobacter Nitrosomonas
Arthrobacter Pseudomonas Bacillus Rhodococcus Brevibacterium Vibrio
Alteromonas Saccharomyces† Bacillus
Enterobacter
Eisenia Trichoderma* Chromobacter Xanthomonas Sporotrichum*
Citrobacter Nocardia Desulfomonite Pseudomonas Enterobacter Rhodococcus Morganeela Xanthobacter Mycobacterium
*Fungi; †yeast.
Trang 13grades the metabolites of the first The number and types of microbes requiredfor a successful consortium depends on the contaminant classification, complex-ity, and concentration.
Natural mixed populations (i.e., consortiums) can be viewed as an tive community that require each individual presence in order to thrive Whenunmanipulated, the mixed population will contain one or two species thatdominate the culture These species are the most adaptable to the surroundingenvironment, have the most efficient energy utilization, and often facilitate thefirst step in the metabolic pathway As time progress, the population may shift toone in which a different species dominates to continue the metabolic pathway oradjust for changes in substrate, nutrients, or terminal electron acceptor (82–84).The microbes used for waste minimization applications have three basicmodes of growth: attached (fixed), suspended, or free growth Attached growth
interac-is similar to the biofilms used in wastewater treatment (trickling filters) and airemissions Bioflims are surface aggregates composed of layers of bacteria thatare embedded in a polysaccharide matrix Biofilms differ from suspended growth
in that they are fixed in a stationary place Suspended growth systems (i.e.,activated sludge) still have the bacteria attached to a surface, but the surface isfreely moving within the reactor Free growth systems are similar to slurrytreatments where the bacteria can sorb and desorb from a surface
2.2 Terminal Electron Acceptor
Without an adequate supply or specific type of TEA, biological treatment willfail Table 4 includes the primary electron acceptors used Aerobic microbesutilize O2 as the TEA For strict aerobes, the oxygen source is typically obtainedfrom air or H2O2 Incorporation of alternative TEA sources provide another name
to identify the respiration–microbe interaction For instance, denitrifying bacteriautilize nitrate (NO3−→ NO2 −→ N2) as the TEA Nitrobacter sp is one of the
microbes capable of nitrification, the conversion of NH3-N to nitrates and
nitrates Sulfate reducers, such as Desulfovibrio, utilize SO42– and generate
T ABLE 4 Typical TEAs and Their Associated Respiration Modes
Carbon dioxide CO2 Methane fermentation
Organic compound Various Aerobic, anaerobic, fermentation