Other useful expressions:

Qw Xr
1   mS


 kd 
VX
c  K s  S


r


1
  Y su  k d 
 c 
X

But
rg = - Y rsu - kdX
rg/X =  = - Y rsu /X - kd
where
 is the specific biomass growth rate (gVSS/g VSS●d)
1

therefore
c
Book defines Specific Substrate Utilization Rate U (g COD/g VSS●d)
r
Q(So  S) (So  S)
U  su 

X
VX
 X
Notes: Book gives
F/M as QSo/VX
Minimum SRT (SRTmin or min) is given by:
1
 min
 m  kd  Y k  kd
Mixed Liquor Solids Production
The total MLVSS in the aeration tank equals the biomass concentration X and the nonbiodegradable VSS (nbVSS)
concentration Xi
XT
=
X + Xi
Using a mass balance, we have the following:
   Y(S o  S) 
X T   c 
  (f d )( k d ) X  c 
    1  ( k d ) c 
Heterotrophic
Biomass (A)
Where
Xo,i
fd
cell
debris (B)

Nonbiodegradable VSS
in influent (C)
= nbVSS (nonbiodegradable VSS) concentration in influent
= fraction of biomass that remains as cell debris (0.10 - 0.15 gVSS/gVSS)
XTV
c
= total solids wasted daily (g VSS/day)
= total MLVSS concentration in aeration tank (g VSS/m3)
= volume of reactor (m3)
Total Sludge Produced daily
where
X o, i  c
PXT,VSS
XT
V
= PXT , VSS 
Daily VSS production rate:
 Q Y (S o  S) 
(f d )( k d )YQ (S o  S) c
PX, VSS  
 Q X o, i
 
1  k d c
 1  (k d ) c 
Heterotrophic
Biomass (A)
cell
debris (B)
Nonbiodegradable VSS
in influent (C)
If nitrification is involved, add the following term
+
where
NOx
kd,n
Q Y ( NO x )
1  k d, n  c
= concentration of NH4-N in the influent flow that is nitrified
= endogeneous decay for nitrifying organisms (g VSS/g VSS●d)
If the reactor is a plug flow reactor:
Similar analysis can be made and the final equations are as follows:
 cY(So  S )
X
(1  k dc )
_
where X = average biomass concentration in the reactor, i.e., for c/ > 5
1

c
Y m (S o  S)
S
(S o  S )  (1  r )( K s ln i )
S
 kd
r = recycle ratio Qr/Q
Si = concentration of substrate after mixing with recycled sludge (mg/L) = (So+ rS)/(1+r)
Oxygen Requirement
- needed to
(i) satisfy BOD requirements
(ii) satisfy the endogeneous respiration
(iii) provide adequate mixing
(iv) maintain a minimum dissolved oxygen of 1 to 2 mg/L throughout the tank.
Air is supplied with submerged porous diffusers or air nozzles or wastewater is agitated mechanically to promote
turbulence and dissolution of air from the atmosphere (see handout of different aerators)
How do we determine the oxygen requirements?
Rule of Thumb
Conventional systems - assume 1 lb of O2 /lb of BOD5 removed
Diffused air aeration
500 - 900 ft3 air/lb BOD5
3.7 - 15 m3 air/m3 wastewater
Ten States Standard
1000 ft3 air/lb BOD5
Extended Aeration
2000 ft3 air/lb BOD5
Theoretical calculations
-oxygen demand is equal to the BODL (the ultimate oxygen demand)
lb O2/d = Q(So - Se)8.34/f - 1.42 Px
where
Q
So
Se
f
8.34
Px,bio
= flow (mgd)
= influent BOD5 (mg/L)
= effluent BOD5 (mg/L)
= factor to convert BOD5 to BODL (0.45 - 0.68)
= conversion factor [(lb/mgd)(mg/L)]
= mass of sludge as VSS wasted (lb/d) = QwXvr
1.42
= amount of O2 needed to convert 1 lb of cells to CO2, H2O during endogeneous
decay
(example, C5H7NO2 + 5O2 == > 5CO2 + 2H2O + NH3 + energy
112
160
1
1.42
Book equation
kg/d
=
Q(So - S) - 1.42 Px,bio
where So, S are expressed as biodegradable COD or bCOD
If nitrification is occurring, have to account for conversion of NH 3 => NO3lb O2/d for nitrification = 4.33Q(No - N) x 8.34
No
N
4.33
= influent Total Kjeldahl nitrogen, TKN
= effluent TKN
= conversion factor for amount of oxygen required for complete oxidation
of TKN
Note that the total amount of oxygen needed is usually designed with a safety factor of at least 2 times the average
BOD load, to account for peak organic loading and to maintain the minimum DO level during peak loading.
Wastewater Characterization (Table 8-2, Figure 8-4)
Total COD
(COD or tCOD)
Carbonaceous materials in wastewater
Biodegradable COD
(bCOD)
Nonbiodegradable COD
(nbCOD, uCOD)
Carbonaceous materials which can be
degraded biologically
Typically 50 – 70%
Carbonaceous materials which are inert and
not processed biologically
Typically 30 – 50%
Readily Biodegradable
(soluble)
rbCOD
Slowly Biodegradable
(particulate)
sbCOD
Carbonaceous materials of
low molecular size,
important in high rate
denitrification and P
removal
Typically 8 – 25%
Usually the main
biodegradable carbonaceous
fraction, require enzymatic
or hydrolytic conversion,
important in slow rate
denitrification
Typically 75 – 90%
Nonbiodegradable
(soluble)
nbsCOD
Nonbiodegradable
(particulate)
nbpCOD, upCOD
Always present in
influent, passes through
plant unchanged, become
effluent soluble COD
(sCODe, usCODe)
Inert particulate material
assumed entrapped by
activated sludge flocs,
removed by wasting of
sludge
Analogous to nbVSS
COD
=
bCOD + nbCOD
bCOD consists of soluble (dissolved), colloidal and particulate biodegradable
materials

bCOD
(1.6 to 1.7) (BOD)
[note for domestic wastewater UBOD  1.5 (BOD)]
(see Equation 8-1 for relationship between bCOD, UBOD, and BOD)
nbCOD =
sCODe + nbpCOD
bCOD
=
rbCOD + sbCOD
In addition to the above COD can be divided into soluble or dissolved COD and particulate COD. This is found by
filtering the sample with a 0.45 micron filter.
COD
=
sCOD + pCOD
sCOD
=
rbCOD + nbsCOD + a small fraction of colloidal COD
Another term that is used is biodegradable soluble COD (bsCOD) to quantify
the fate of soluble biodegradable organic compounds
rbCOD is determined from the oxygen uptake rate (OUR) or estimated by physical separation technique.
(1) OUR – The wastewater sample and an acclimated activated sludge are mixed in a batch reactor with separate
mixing and aeration. Initially with mixing but no aeration, the DO in the mixture will decline until the DO is about
3 mg/L. The OUR can be determined for the initial mixing but no aeration in terms of mg/L/h. Vigorous aeration is
applied and the DO elevated to 5 to 6 mg/L. Aeration is stopped and the OUR measured. The initial OUR is used to
estimated the rbCOD.
rbCOD 
 VAS  Vww 
OA


1  YH ,COD 
Vww

Where OA
YH,COD
= oxygen consumed in area A of OUR plot
= synthesis yield coefficient for heterotrophic bacteria,
g cell COD/g COD used
= volume of activated sludge used in test, mL
= volume of wastewater sample, mL
VAS
VWW
(2) By floc/filtration method on both wastewater sample and a secondary effluent sample or a settled supernatant
sample after sufficient contact and aeration of the wastewater sample with activated sludge. Zinc sulfate solution is
added to a sample, pH raised for floc formation, flocs are settled, and supernatant filtered with 0.45 micron filter and
filtrate analyze for COD concentration. The difference between the COD concentration between the wastewater and
activated sludge treated wastewater sample is the rbCOD.
Nitrogen Compounds
TKN
=
NH4-N + Organic Nitrogen (ON)
ON
=
bON
nbON
=
nbsON + nbpON
+ nbON
The nonbiodegradable particulate organic nitrogen (nbpON) can be estimated by an analysis of the influent VSS for
organic nitrogen and the estimated amount of nbVSS. The fraction of nitrogen in the VSS is as follows:
fN 
(TKN  sON  NH 4asN)
VSS
nbpON =
fN (nbsVSS)
Biomass solids
TSS
-
total suspended solids
VSS
-
volatile suspended solids
MLSS -
mixed liquor suspended solids (mixture of solids resulting from combining recyled sludge with
influent wastewater in bioreactor)
MLVSS -
mixed liquor volatile suspended solids
nbVSS -
nonbiodegradable volatile suspended solids
(derived from influent wastewater and is also produced as cell debris from endogeneous decay)
iTSS
inert inorganic total suspended solids (originated from influent wastewater)
-