Page 738 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

Biological Reactions and Kinetics 693

where C 5 H 7 O 2 N þ 5O 2 ! 5CO 2 þ NH 3 þ 2H 2 O (22:20)
X is the cells synthesized by the biochemical reaction (e.g., 113 5 32
mol cells, kg cells, COD cells, etc.) f(cell COD) ¼ (5 32)=(113) ¼ 1:42 g COD=g cells
S is the substrate, which is degradable organic matter,
ammonia, etc., utilized by the bacterial enzymes that a. Cell yield as COD of cells per unit of substrate COD
enable a reaction (mol substrate, kg substrate, COD
substrate, etc.) Y(COD cells=COD substrate)
Y is the stoichiometric coefficient, usually called the ‘‘true ¼ Y(cells=substrate COD) f(cell COD)
yield’’ (e.g., mol cells synthesized=mol substrate ¼ 0:44 g cells synthesized=
degraded)
g substrate COD 1:42 g cell COD=g cells
Equation 22.19 is utilized often in the literature as an empir- Discussion
ical relation. As noted, the units for X and S may be selected The COD equivalent of the substrate, i.e., CH 2 O,
based on their utility for a given problem. expended for energy and biomass is 8O 2 , with 3O 2 used
in the oxidation of CH 2 O for energy; the rest is converted
to cells, i.e., C 5 H 7 O 2 N, which has a COD equivalent of
Example 22.2 Convert Cell-Yield to Y(COD 3O 2 (Orhon and Artan, 1994, p. 89). Eckenfelder and
Cells=COD Substrate); Orhon and Artan (1994, p. 88) Weston (1956, p. 19) also calculated, based on stoichio-
metric equations, 1.42 g cell COD=g cells based on cell
material, C 5 H 7 O 2 N. Further, they plotted experimental
Given
data (1956, p. 20) for sludge COD versus sludge VS for
Reaction equations as listed in sequence.
domestic sewage, pulp and paper waste, and pharmaceut-
Required ical wastes; the plot showed 1.42 g sludge COD=g VS (the
Determine cell yield with units (g cell COD)=(g substrate 19 data points showed very little scatter about the about
COD) the best fit line).
Solution
The procedure is given by Orhon and Artan (1994, p. 66). 22.4.2 CELL MAINTENANCE AND ENDOGENOUS
The units give identity to each term and following their
cancellations facilitates explanation. RESPIRATION
Simultaneously with cell synthesis a fraction of the cells are
1. Cell synthesis
consumed by ‘‘endogenous-respiration.’’ This occurs espe-
cially when the cells are in a ‘‘starved’’ condition, which
8CH 2 Oþ3O 2 þNH 3 ! C 5 H 7 O 2 Nþ3CO 2 þ6H 2 O
may be defined as a substrate concentration that results in a
8 30 g=mol 113 g=mol (22:8)
cell-division rate significantly lower than the ‘‘enzyme cap-
acity.’’ On the other hand, ‘‘cell maintenance’’ seems to be a
Associated calculated quantities include necessary function of a cell, as opposed to a cell death. The
Y ¼ 113=(8 30) ¼ 0.47 g cell VSS synthesized=g two aspects are discussed in separate paragraphs to allow for
substrate utilized
2. Oxidation of substrate the possible distinction.
For carbohydrate substrate, i.e., CH 2 O, the oxi-
dation equation is (Table 22.3) 22.4.2.1 Cell Maintenance
The maintenance function includes cell motility, rebuilding of
8CH 2 O þ 8O 2 ! 8CO 2 þ 8H 2 O
proteins, transfer of solutes across the cell wall, etc. (Orhon
8 30 8 32 and Artan, 1994, p. 74; Rittman and McCarty, 2001, p. 131).
In this reaction the cells in suspension may consume a portion
f(substrate COD) ¼ (8 32)=(8 30)
of the ATP energy available for cell synthesis (keep in mind
¼ 1:06 g COD=g substrate
that the ATP is present within the cell as a part of the
biochemical cycles). Or the cells could oxidize a fraction of
a. Cell yield mass per unit of substrate COD
their own cell matter. It is not clear whether the energy comes
Y(cells=substrate COD) ¼ Y=f(substrate COD) from a fraction of the ATP energy available for synthesis or
from the oxidation of the cell’s own matter (Benefield and
¼ (0:47 g cell synthesized=g substrate utilized)=
Randall, 1980, p. 54).
(1:06 g COD=g substrate)
¼ 0:44 g cells synthesized=g substrate COD
22.4.2.2 Endogenous Respiration
3. Oxidation of cells As described by Porges et al. (1956, p. 44), ‘‘After the cells
For biomass COD, the oxidation equation is are formed, there is a slow continuous oxygen requirement.