Q(ΔO2) = 380 g 70 m^3 (1440 min) 10^-3 kg/g = 3.83×10^4 kg O2/d

R_S = -3.83×10^4 kg COD/d

a.

R_O2 = (1 - Y) R_S = 0.65(3.83×10^4) = 2.49×10^4 kg O2/day

(seen 1 kg COD = 1 kg O2)

R_X = Y R_S = 0.65(3.83×10^4) = 1.34×10^4 kg COD_X/d

R_X = 1.34×10^4 kg COD_X/d · (1 kcal/s, 365 d)/(142 kg COD/yr)

b.

R_X = 3.45×10^6 kg cells/yr

2. Compare O2 and NO3 as electron acceptors in respiration of 1 mole of CH2O

O2:

1 CH2O + 1 O2 → 1 CO2 + 1 H2O

NO3^-:

1 CH2O + 0.8 NO3^- + 0.8 H^+ → 1 CO2 + 1.4 H2O + 0.4 N2

ratio

1 mole (32 g/mole) O2 / 0.8 mole (14 g/mole) NO3-N = 2.86 g O2/g NO3-N

(or -2.86 g OD/g NO3-N)

a. meant to say 30% of lost cells (Y - Y_obs) are lysed and available as substrate

Lost cells = 0.4 - 0.32 g COD_x/g COD_s = 0.08 g COD_x/g COD_s

lysed cells recycled = 0.3(0.08) = 0.024 g COD_l/g COD_s

b. then COD_d (debris) is

COD_d = 0.7(0.08) g COD_d/g COD_s = 0.056 g COD_d/g COD_s

So for biodegradation of 1 gram COD_s you get

0.32 g COD_x (viable cells)

0.024 g COD_l (lysed COD recycled)

0.056 g COD_d (debris COD)

neglecting further metabolism of COD_d etc. etc. ...

a)

1 CH3COO^- + 0.022 CO2 + 0.006 NH4^+ + 0.281 H2O →

→ 0.258 CH1Y + 0.038 C5H7NO2 + 1.01 HCO3^-

b) (COD)

Y1 = 1, Y3 = 0.258(4)/(1(1.08)) = 0.956, Y4 = 0.038(1.42)/(1(1.08)) = 0.05

NOTE: NH4^+ has no COD equivalents in this reaction since NH4^+ is not oxidized during cell synthesis

CO2 also assumed to have no COD even though it is e^- acceptor since it is also a product of CH3COO^- oxidation: CH3COO^- + H^+ → CO2 + CH4

to CH4

1 COD_CH3COO^- → 0.956 COD_CH4 + 0.05 COD_C5H7NO2

1 - 0.956 - 0.05 = -0.006 close enough

c)

500 kg CH3COO^- / d (0.258 kg CH4 / kg CH3COO^-) = 129 kg CH4/d

129 kg CH4 = 8.06 kmol CH4/d, assume CH4 is ideal gas

PV = nRT

V = 8.06 kmol (82.05 L-atm/kmol)(273.35 K)/(1 atm) 10^-3 m^3/L

= 204 m^3 CH4/d

d)

500 kg CH3COO^- / d (0.038 kg VSS / kg CH3COO^-) = 19 kg VSS/d

COD AND NITROGEN STOICHIOMETRIC AND KINETIC MATRIX FOR GROWTH AND

Components

Soluble COD S_s (mg/L COD)

Soluble NH4-N S_NH (mg/L N)

Dissolved O2 S_O (mg/L O2)

Heterotrophic biomass, X_BH (mg/L COD)

Autotrophic (Nitrifying) Biomass, X_BA (mg/L COD)

Debris, X_D (mg/L COD)

Process

Aerobic Heterotrophic Growth

Aerobic Growth of Autotrophs (Nitrification)

Decay and Lysis of Heterotrophs

Aerobic Heterotrophic Growth:

-1/Y_H

- i_XB

- (1 - Y_H)/Y_H

Aerobic Growth of Autotrophs (Nitrification):

-1/Y_A

- 1/Y_A

- (4.57 - Y_A)/Y_A

Decay and Lysis of Heterotrophs:

1 - f_D

And reaction rates are

μ_H * X_BH = growth rate for heterotrophs (d^-1)

μ_A * X_BA = growth rate for autotrophs (d^-1)

b_H * X_BH = decay rate for heterotrophs (d^-1)

c. Give the total rate expressions for ammonia nitrogen, heterotrophic bacteria, autotrophic bacteria, and dissolved oxygen considering the reactions 1, 2, and 3

r_XBA = μ_A X_BA (neglect decay of X_A)

r_XD = f_D b_H X_BH

r_S = -1/Y_H μ_H X_BH + (1 - f_D) b_H X_BH

r_O2 = -((1 - Y_H)/Y_H) μ_H X_BH - ((4.57 - Y_A)/Y_A) μ_A X_BA