Page 769 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

23.2.1.2 From Empiricism to Science 5. Cell synthesis from substrate. In 1951, Heukelekian
In sizing aeration tanks, Fair and Geyer (1954, p. 720) et al. proposed the equation (Goodman and Englande,
mention several sizing parameters including detention 1974),
3
time, u; volumetric loading (lb BOD=day=ft tank volume);
and BOD solids loading (lb BOD=day=1000 lb suspended DX v ¼ a S o b X v (23:1)
solids per hour of aeration). The latter is called the F=M ratio
(see Section 22.5.7.2). Detention time and F=M remain in
where
practice for sizing the tank volume and substrate loading,
DX v is the volatile suspended solids (VSS) accu-
respectively.
mulation rate in aeration basin
While reactor modeling was not underway until the mid-
(kg VSS synthesized=day)
1950s, the biological character of activated sludge was recog-
S o is the mass flow of BOD in influent flow (kg
nized at inception and extended over the decades. Fair and
BOD flux-in.=day)
Geyer (1954, p. 506), for example, describe activated sludge
X v is the mixed liquor volatile suspended solids in
as an ecological system consisting of a variety of species of
suspension (kg VSS)
bacteria, fungi, protozoa, and rotifers. The 1950s at MIT saw
a is the VSS synthesis rate (kg VSS synthesi-
the sciences, organic chemistry, biochemistry, and physical
zed=day=kg BOD flux-in.)
chemistry, integrated into graduate studies. Books with the
b is the VSS oxidation rate kg VSS destroy-
modern science orientation had MIT roots, e.g., Microbiology
ed=day=kg VSS in aeration basin)
for Sanitary Engineers (McKinney, 1962) and Chemistry for
Sanitary Engineers (Sawyer and McCarty, 1967). Another
milestone was the paper ‘‘Mathematics of complete mixing The Heukelekian equation was a first-order equation
activated sludge’’ (McKinney, 1963). In 1962 MIT terminated with respect to substrate, showing that cell synthesis
its program in sanitary engineering; by that date, however, the is proportional to BOD, with endogenous respiration
transition was essentially complete. Its influence had spread, proportional to cell mass present (the units were
dating from perhaps 1948 and its graduates had disseminated changed to metric).
to other universities. 6. Chemical formula for microorganisms. In 1952,
Hoover and Porges reported an empirical formula
23.2.1.3 Milestones for the composition of activated-sludge microorgan-
Activated sludge theory and practice have evolved from about isms. The formula, C 5 H 7 O 2 N, yields a molecular
1880. Milestones are enumerated as follows, taken from ref- weight of 113, which is corrected to 124 to account
erences indicated. for the ash content of the organisms (Goodman and
Englande, 1974).
1. Lawrence. In 1912, H.W. Clarke, at the Lawrence 7. Eckenfelder. In 1954, Eckenfelder and O’Connor
Experiment Station, Massachusetts, studied waste proposed a mathematical model for activated sludge
purification through its aeration in the presence of which established a systematic mathematical approach
microorganisms. Dr. G.J. Fowler, consulting chem- to activated-sludge process design (Goodman and
ist for the Rivers Committee of the Manchester Cor- Englande, 1974).
poration, observed some of the Lawrence 8. Kinetic model search at Berkeley. In 1956, Mervin
experiments and suggested to Edward Ardern and Stewart made a thorough appraisal of the kinetic
William Lockett of the Davyhulme Sewage Works, descriptions of biological systems and from this
Manchester Corporation that they carry out similar study, selected the Michaelis–Menten kinetic model
experiments (Goodman and Englande, 1974). (Pearson, 1968). Stewart was doing doctoral research
2. Ardern and Lockett. Ardern and Lockett (1914) found in methane fermentation kinetics under Erman Pear-
high removals of organic matter as measured by oxy- son. The research was continued by Frank J. Agardy
gen absorption after only several hours of aeration and John F. Andrews. In addition, Andrew Gram
with activated sludge. The term activated sludge was (1956a,b) completed a doctoral dissertation incorp-
given, for lack of another term, for the deposited orating Monod kinetics and a mass balance reactor
solids resulting from the oxidation of sewage. model in an experimental study.
3. Michaelis–Menten. In 1913, Leonor Michaelis and 9. Complete-mix model and F=M. In 1962, McKinney
Maud Menten (see Appendix 22.B) developed an (1962) proposed a complete-mixing model.
expression for enzyme kinetics (Stryer, 1981). This Although the focus was on complete mixing, the
was the same expression as the one later developed approach was based upon a kinetic formulation of
through empirical observations by Monod (Pearson, substrate utilization in the declining growth phase (of
1968). the growth curve) combined with a material-balance
4. Monod. In 1942, Monod (1949) published the results description of the reactor. McKinney used the food-
of his studies on continuous bacterial cultures, with to-microorganism ratio, i.e., F=M, and tied bacteria
an empirical equation describing results. synthesis to substrate degradation. McKinney also