Page 741 - Fundamentals of Water Treatment Unit Processes : Physical, Chemical, and Biological

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

TABLE 22.8
Examples of Calculation of Cell-Yield and Other Values for Stoichiometric Equation for Oxidations
of Substrates to Obtain Microbial Cells
Substrate Domestic Wastewater, Formula: C 10 H 19 O 3 N

Reaction equation obtained from Orhon and Artan (1994, p. 101) based on half-reactions compiled in their Table 2.12
Assumption: Y ¼ 0.67 e-eq. cells=e-eq. substrate
1=50C 10 H 19 O 3 N þ 1=12O 2 þ 1=75NH 4 þ 1=75HCO 3 ! 1=30C 5 H 7 O 2 N þ 7=150CO 2 þ 25=150H 2 O(equation for one e eq)

þ

1=50 201 1=12 32 1=30 113
Cell yield and other values
(1) Y(C 10 H 19 O 3 N-stoichiometric) ¼ 0.64 g cell COD=g substrate COD (Orhon and Artan, 1994, pp. 98)
(2) Y(C 10 H 19 O 3 N-experimental) ¼ 0.66 g cell COD=g substrate COD (Orhon and Artan, 1994, pp. 98)
(3) Y(C 10 H 19 O 3 N-experimental) ¼ 0.46 g cell VSS=g substrate COD (Orhon and Artan, 1994, pp. 98)
(4) f(conversion) ¼ (1.42 g cell COD=g cell VSS) (Grady et al., 1999, p. 70)
(5) Y(C 10 H 19 O 3 N-stoichiometric) ¼ 0.94 g cells synthesized=g substrate degraded (calculated)
(6) Y(O 2 -stoichiometric) ¼ 0.66 g O 2 used=g substrate degraded (calculated)
(7) Calculation of substrate COD based on one e-eq electron transfer in reaction:
(1=50 201 g substrate=e-eq)=(8 g COD=e-eq) ¼ 0.5025 g substrate=g substrate COD
¼ 1.99 g substrate COD=g substrate
Substrate Pentose, Formula: C 5 H 10 O 5
1. Cell synthesis reaction equation
Obtained from Orhon and Artan (1994, p. 103) based on half-reactions compiled in their Table 2.12.
Assumption: Y ¼ 0.67 e-eq. cells=e-eq. substrate.
1=20C 5 H 10 O 5 þ 1=12O 2 þ 2=60NH 4 þ 2=60HCO 3 ! 2=60C 5 H 7 O 2 N þ 7=60CO 2 þ 13=60H 2 O

þ
1=20 150 1=12 32 2=60 113
2. Cell yield and other values
(1) Y(C 5 H 7 O 2 N-stoichiometric) ¼ 0.50 g cells synthesized=g substrate degraded
(2) Y(O 2 -stoichiometric) ¼ 0.36 g O 2 used=g substrate degraded
3. Oxidation of cells to get f (cell COD=g cells)
Oxidation reaction for cells to get COD equivalent. Overall equation from half-reactions by Orhon and Artan (1994, p. 88); equation coefficients are for
transfer of one e-eq needed to balance the two half-reactions.
1=20C 5 H 7 O 2 N þ 5=20O 2 ! 5=20CO 2 þ 1=20NH 3 þ 2=20H 2 O
1=20 113 5=20 32
f(cell COD=g cells) ¼ (5=20 32)=(1=20 113) ¼ 1.42 g cell COD=g cells
4. Oxidation of pentose substrate to get f (substrate COD=g substrate)—(see also Benefield and Randall, 1980, p. 73)
1=20 C 5 H 10 O 5 þ 1=4O 2 ! 1=4CO 2 þ 1=4H 2 O
1=20 150 1=4 32
f(substrate COD=g substrate) ¼ (1=4 32)=(1=20 150) ¼ 1.07 g substrate COD=g substrate
5. Calculation of Y (g cell COD=g substrate COD)
Y(g cell COD=g substrate COD) ¼ f (g cell COD=g cells) [1=f (substrate COD=g substrate)] Y(g cells=g substrate)
¼ (1.42 g cell COD=g cells) [1=(1.07 g substrate COD=g substrate)] (0.50 g cells=g substrate)
¼ 0.66 g cell COD=g substrate COD

22.5.3 NET SPECIFIC GROWTH RATE, m(net) Dividing both sides of Equation 22.35 by X gives (Lawrence,
1975, p. 223)
The net increase [dX=dt] net , in viable cell mass is the differ-
ence between growth rate and depletion rate:
½ dX=dtŠ net ¼ m b (22:36)
X

dX dX dX
(22:33)
dt ¼ dt dt And if we define,
net g d
¼ mX bX (22:34)
½ dX=dtŠ net (22:37)
¼ (m b)X (22:35) m(net) X