Page 739 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

The organisms oxidize their own tissue to supply the energy 22.4.3 NET CELL YIELD, Y(net)
of maintenance.’’ The equation was given as
The mathematical relations for net cell yield, Y(net) are given,
C 5 H 7 O 2 N þ 5O 2 ! 5CO 2 þ NH 3 þ 2H 2 O (22:20) first, in terms of a mass relation and, second, in terms of a rate
relation. Regarding nomenclature, the DX(net) and DX(obs)
Based upon oxygen utilization rate studies with a ‘‘Warburg’’ are the same, i.e., the net change in cell mass is the observed
apparatus, they determined that d(O 2 )=dt ¼ 14.3 mg O 2 =g change.
cell=h, which converts to dX=dt ¼ 10.2 mg cell=h, or about
0.01 fraction of cell mass consumed per hour. Although 22.4.3.1 Cell Mass Relations
endogenous respiration has been a continuing consideration The idea of net cell synthesis that was tied to cell synthesis
in biological treatment, the foregoing description by Porges and endogenous respiration was given by Eckenfelder and
et al. (1956) remains valid. Weston (1956, p. 21), i.e.,
In a later article, McKinney and Symons (1964, p. 441)
refer to maintenance energy as ‘‘endogenous respiration,’’ DX(obs) ¼ Y S b X(obs) (22:21)
0
indicating that they are the same. To confirm this point they
cite research based on C-14 labeled organisms that endogen- where
ous respiration proceeds uninterrupted at the same rate in the X(obs) is a viable cell concentration as observed (mg cells
presence of an external source of substrate as in its absence. that can reproduce=L)
They further state that they require ‘‘a basic amount of energy S is the substrate concentration (mg cells=L)
per unit of active mass per unit time during growth as during Y is the cell yield (mg cells synthesized=mg substrate
starvation,’’ which is sometimes called ‘‘basal metabolism.’’ degraded)
Another depiction of endogenous respiration that is com- b is the fraction of cells rendered nonviable (mg cells
0
plementary to the foregoing was given by Grady et al. (1999, rendered nonviable=mg viable cells)
p. 98); the following summary is excerpted:
Dividing both sides of Equation 22.21 by DS gives
b X(viable cells) ! X(nonviable cells)
DX(obs) X(obs)
X(nonviable cells) ! X(lysed cells) þ X(debris cells) ¼ Y b (22:22)
0
DS DS
X(lysed cells) ! X(lysed-cell substrate)þX(lysed-cell debris)
to give an expression for Y(obs), i.e.,
X(lysed-cell substrate) þ E(bacteria) þ O 2
X(obs)
! X(new cells) þ E(bacteria) þ CO 2 0 (22:23)
Y(obs) ¼ Y b
DS
To summarize, a fraction of the cells lyse, with a portion of
the matter becoming substrate, and a portion becoming inert where Y(obs) ¼ DX(obs)=DS (observed mg cells synthesi-
‘‘debris.’’ Also, some fraction of the viable cells is consumed zed=mg substrate degraded).
by predation (e.g., by protozoa or rotifers). To illustrate In other words, the ‘‘observed’’ yield, Y(obs), is the true
another facet of endogenous respiration, if the substrate level yield of viable cells, Y, minus the cells lost to endogenous
declines to zero, the cell protoplasm is the only source of decay. As seen in Equation 22.22, if DX(obs) ¼ 0, then
energy and the net rate of cell growth is zero; it then declines Y ¼ b X(obs)=DS.
0
in proportion to the remaining viable cell concentration (see
also, Sherrard, 1977, p. 1969). 22.4.3.2 Cell Mass Rate Relations
The actual observed cell growth per unit of substrate, also
22.4.2.3 Microbial Growth Curve and Debris
called the ‘‘net’’ growth, X(net), was expressed in terms of rate
Accumulation by Rittman and McCarty (2001, p. 131),
In the context of reactors, if the system is a batch reactor with
zero inflow and zero outflow, and if the system starts ‘‘fresh,’’
dX(net) dS
i.e., with adequate substrate, then a typical ‘‘growth curve’’ ¼ Y b X(net) (22:24)
dt dt
results, which includes a lag phase, exponential growth,
declining growth and stationary growth. Both the concentra-
tions, X(debris cells) þ X(lysed-cell-debris), increase along Dividing each term by ( dS=dt),
the growth curve. If the system is a steady-state continuous-
flow reactor the concentration sum, X(debris cells) þ X(lysed- dX(net)=dt
(22:25)
cell-debris), is constant with value depending on the u c , the Y(net) ¼ dS=dt
cell retention time in the system, as is X(net), which is the
X(net)
observed cell mass concentration. In other words, the cell (22:26)
¼ Y b
debris accumulates to some equilibrium value. dS=dt