Comparison of different modelling approaches to better evaluate
greenhouse gas emissions from whole wastewater treatment plants
(SUPPLEMENTAL INFORMATION)
Lluís Corominas1,2, Xavier Flores-Alsina1,3, Laura Snip1 and Peter A. Vanrolleghem1
1)
modelEAU, Département de génie civil et de génie des eaux. Université Laval, 1065, Avenue de
la Médecine. Québec G1V 0A6, QC, Canada.
2)
ICRA, Catalan institute for water research, Carrer Emili Grahit, 101, E- 17003 Girona, Spain.
3)
Div. of Industrial Electrical Engineering and Automation (IEA), Lund University, Box 118, SE-
221 00 Lund, Sweden.
Corresponding author: Lluís Corominas
Pavillon Pouliot, 1065 av. de la Médecine, Quebec (QC) G1V 0A6, Canada. (E-mail: lcorominas@icra.cat,
telephone: +1 418 656 5085, fax: +1 418 656 2928)
1. ESTIMATION OF GREENHOUSE GAS (GHG) EMISSIONS (Bridle approach)
1.1. Direct secondary treatment emissions
1.1.1. CO2 generated from biomass respiration
The proposed model calculates the biomass decayed following equation (Eq1)
Xdecayed = Qinfluent * HRT * MLVSS * kd
Eq1
where Xdecayed is the biomass decayed per day (kgVSS day-1), Qinfluent is the average daily flow (m3 day-1),
HRT is the hydraulic retention time (days), MLVSS is the concentration of mixed liquid volatile suspended
solids (kg m-3) and kd is the endogenous decay coefficient (day-1)
The conversion from the biomass decayed to the CO2 produced is based on reaction (R1). The elemental
composition of biomass is C5H7O2N
C5H7O2N + 5 O2  5 CO2 + 2 H2O + NH3
R1
The biomass to CO2 ratio is 113 : 5*44 which equals 1 : 1.947. This means that for the decay of one kg of
biomass 1.947 kg of CO2 is produced as states Eq 2
CO2,decay = Xdecayed * 1,947
Eq2
Further information can be found in Monteith et al. (2005).
1.1.2. CO2 generated from BOD oxidation
During biomass production CO2 is emitted. Thus, the proposed approach first calculates the observed
biomass yield (Eq 3)
Yobs = Y /(1+ kd * SRT)
Eq3
Where Yobs is the observed biomass yield (kg VSS kg BODremoved-1), Y is the yield (kg VSS kg BODremoved-1),
SRT is the sludge retention time (days) and kd is the endogenous decay coefficient (day-1).
The net biomass produced is calculated from is summarized in Eq 4
Xnet,produced = Yobs * BODox
Eq4
where Xnet,produced is the net biomass produced per day (kg VSS day)
The oxidized BOD is calculated from (Eq5):
BODox = Qinfluent * ((100-BODrem)/100 * BODinfluent –BODeffluent )
Eq5
BODox is the oxidized BOD5 by the biomass (kg BOD day-1), BODrem is the BOD removal efficiency of the
primary clarifier (%), BODinfluent is the influent BOD (kg BOD m-3), BODeffluent is the effluent BOD (kg BOD
m-3)
With the net biomass produced the rate of oxygen used can be calculated (Eq6):
RO2 = BODox / (f) – 1,42 * Xnet,produced
Eq6
Where RO2 is the rate at which oxygen is used by the biomass (kg O2/day) and f (=0.65) is the BOD5/BODu
ratio
When the rate of oxygen used is known the amount of CO2 produced per day can be calculated (Eq7).
CO2, BODox = RO2 * CO2fromBODox
Eq7
CO2, BODox is the amount of CO2 produced per day by BOD oxidation (kg CO2 day-1)
CO2fromBODox is a conversion factor which is calculated from the chemical reaction in which C 10H19O3N
is the elemental composition of wastewater BOD (R2):
2 C10H19O3N + 25 O2  20 CO2 + 16 H2O + 2 NH3
R2
The ratio between O2 and CO2 is then 25 * 32 : 20 * 44 which is 1 : 1.1. Thus for 1 kg of O2 1.1 kg of CO2 is
produced.
Further information can be found in Monteith et al. (2005).
1.1.3. CO2 credit from ammonium oxidation
While nitrifying ammonium, CO2 is consumed for biomass production, leading to a CO2 credit.
The amount of ammonia oxidized is calculated by the following equation:
NHox = Qinfluent * (TKNp.c. effluent – TKNeffluent) - Nbiomass
Eq8
TKNp.c. effluent is the total nitrogen in the effluent of the primary clarifier (kg N m-3) and TKNeffluent is the total
nitrogen in the effluent (kg N m-3),
The amount of N assimilated in the heterotrophic biomass is calculated from the elemental composition. The
molar weight of N is 14 and that of biomass 113, as seen above. Thus, the amount of N incorporated in the
net produced heterotrophic biomass is:
N biomass = Xnet,produced * 14/113
Eq9
Nbiomass is the amount of nitrogen in the biomass (kg N day-1)
The CO2 credit from the ammonia that is oxidized is calculated with:
CO2, credit = NHox * CO2, consumed
Eq10
The CO2 to N ratio is obtained from R3. 1/[(1/0.098)*14/44] which leads to 0.308 and thus the amount of
CO2,consumed is 0.308 kg per kg of N nitrified.
NH4+ + 1.863O2 + 0.098CO2  0.0196C5H7NO2 + 0.98NO3- + 0.0941H2O + 1.98H+
R3
The credit from nitrification is calculated using the factor 0.308 kg of CO2 consumed·(kg N nitrified)-1
(calculated from Tchobanoglous et al., 2003) instead of the factor 4.49kg of CO 2 consumed·(kg N nitrified)-1
suggested in Bridle et al. (2008). The explanation is the following:
The factor 4.49 is obtained from the following reactions (R4 and R5) given in the EPA “Process design
manual for nitrogen control”:
15CO2 + 13NH4+  10NO2- + 3C5H7NO2 + 23H+ + 4H2O (Nitrosomonas)
R4
5CO2 + NH4+ + 10NO2- + 2H2O  10NO3- + C5H7NO2 + H+ (Nitrobacter)
R5
The yield of reaction 4 is 3*113/(13*14)=1.8626 g biomass/g N nitrified. Adding another mole of biomass
from reaction 5, the yield is 4*113/(14*14) = 2.306 g biomass/g N nitrified.
In comparison, the yield obtained from reaction 3 in Tchobanoglous et al. (2003) is 0.0196*(113/14) =
0.1582 g biomass/g N nitrified, which is a value that is the now accepted value for this process. In the mid70s knowledge of the nitrification process was still being developed, explaining the 10 times higher value
reported in the 1975 EPA manual (Parker et al., 1975). Hence, the value used for the credit for nitrification
should be replaced by 0.308 kg of CO2 consumed·(kg N nitrified)-1
1.2. Sludge processing
a) calculation of the difference between volatile suspended solids that enter and that leave the
anaerobic digestion
VSSdestroyed = VSSAD,in - VSSAD,out
Eq 10
where VSSAD,in are the volatile suspended solids entering the AD and VSSAD,out the volatile suspended solids
leaving the AD. These values are obtained from the BSM simulations.
b) Calculation of mass of biogas produced in the anaerobic digester, using a fraction of VSS converted
into biogas
Biogasmass = VSSdestroyed · fbiogas/VSS
Eq 11
Where fbiogas/VSS is equal to 1 kg biogas·kg VSS-1
c) Estimation of the CH4 and CO2 mass produced, assuming that the methane in the biogas is 65% by
volume and the remainder of the biogas is CO2
The methane concentration in mass percentage (MP) is calculated
CH4,MP = (100 · CH4,VP · MWCH4 / MV) / (CH4,VP * MWCH4 / MV + (100 - CH4,VP) * MWCO2 / MV)
CH4,MP is the mass percentage of methane in the biogas
[%]
CH4,VP is the volume percentage of methane in the biogas
[%]
MWCH4 is the molar weight of methane
[16 g/mole]
MV is the volume of 1 mole at a temperature of 20 °C
[24.7 m3/mole]
MWCO2 is the molar weight of carbon dioxide
[44 g/mole]
Eq 12
The quantity of methane and CO2 per day emitted in the AD is calculated using the following equations.
CH4,AD = Biogasmass * CH4,MP/100
Eq 13
CO2,AD = Biogasmass – CH4,AD
Eq 14
d) Calculation of the CO2 generated by combustion of biogas (CO2combustion, kg CO2/day)
CO2 combustion = CO2,AD + CH4,AD · MWCO2/MWCH4
Eq 15
1.3. Net power
The energy variables, in kWh·d-1, are calculated by using the benchmark criteria (Gernaey et al., 2011).
Net power = Aeration Energy + pumping energy + mixing energy + heating energy – energy credit
Eq 16
Aeration Energy is obtained from KLa values of the simulation. Pumping energy includes internal recycle
flow rate, the external recycle flow rate, the waste sludge flow rate, the primary clarifier underflow rate, the
thickener unit underflow rate, and the dewatering unit overflow flow rate. Mixing energy combines energy
used for mixing the activated sludge tanks and energy used for mixing the anaerobic digester. Heating energy
takes into account the energy demand to heat the anaerobic digester. The energy credit refers to the
electricity generated by the turbine and it is calculated as follows:
Energy credit = CH4,AD · ECH4 /3600 · Ef
Eq 17
ECH4 is the Energy content of methane gas = 50014 MJ·(kg CH4)-1)
3600 is a factor to convert from MJ to kWh
Ef is the efficiency for electricity generation assumed in the energy credit. In this case, 43% efficiency is
assumed. With the remaining energy content, 50% is usable heat and 7% are losses.
Finally, energy units are converted to CO2 units by using equation 18.
CO2 Net power = Net power · fCO2/kWh
fCO2/kWh = 0.94 kg CO2·kWh  Taken from Bridle et al. (2008)
Eq 18
1.4. Embedded GHG emissions from chemical use
The calculation of CO2 emissions generated from the production of external carbon source that is used in the
WWTP is conducted as follows.
CO2 Methanol = Qcarb * fMethanol/CO2
Eq 19
where CO2 Methanol is the CO2 emitted because of the use of methanol
[kg CO2/d]
Qcarb is the amount of methanol added to the wastewater treatment plant
[kg methanol/d]
fMethanol/CO2 is the g CO2 emitted per g of methanol produced
[g CO2/g methanol as COD]
fMethanol/CO2 = 1.54 g CO2e·g methanol as COD-1 (Dong and Steinberg, 1997).
1.5. Sludge disposal and reuse
After treatment, the sludge can be reused in different ways. The Bridle approach gives four different options:
reuse for agriculture, reuse for composting, reuse for forestry, and reuse for other options. For each
wastewater treatment plant different fractions of the reuse of the sludge may be given: f agri, fcomp, fforest, fother.
Calculation of the carbon in the sludge is evaluated from an empirical relationship.
Csludge = 0.3962 · VSSAD,out + 9.4548
Eq 20
The values 0.3962 and 9.4548 are from the Bridle consulting data
With the amount of carbon in the sludge known the total CO2 emissions can be calculated:
CO2disposal = MWCO2/MWC · Csludge · VSSAD,out · fC/CO2
Eq 21
MWC is the molar weight of carbon
[g/mol]
MWCO2 is the molar weight of CO2
[g/mol]
fC/CO2 is the sludge carbon that is mineralized to CO2
[80 %]
The transport is determined by the number of truck movements per day for each site that is calculated by
dividing the biosolids volume by the truck volume. To determine the total kilometres travelled per day the
number of truck movements is multiplied by the distance (times two, for the return trip) to each reuse site.
This value is then multiplied by the truck CO2 emission factor (kg CO2/km travelled) to determine the total
CO2 emissions for each reuse site, which are then combined to provide a total GHG emission for biosolids
transport.
CO2truck = VVSSout / Vtruck · D · 2 · fkm/CO2
Eq 22
CO2truck is the amount of CO2 emissions from truck use
[kg CO2/day]
fkm/CO2 is the amount of kg CO2 emitted per kilometer
[1 kg CO2/km]
D is the distance of the wastewater treatment plant to the disposal site
[314 km]
Vtruck is the volume of sludge the truck can transport
[40 m3]
For this study it is assumed that 38% of sludge goes to agriculture, 45% to a compost site and 17% to
forestry (Bridle et al., 2008). The distances(D) are: 150 km to agriculture, 20 km to compost and 144 km to
forestry.
where
VVSSout = VSSAD,out / solidscake / dsludge
solidscake is the fraction of solids of the dewatered cake (kg solids / kg cake, 0.19 in this study)
dsludge is the density of the sludge (1g / cm3)
Eq 23
2. ESTIMATION OF GREENHOUSE GAS (GHG) EMISSIONS (BSM2G approach)
2.1. Biokinetic activated sludge model
The BSM2G activated sludge model incorporates two nitrifying populations – ammonia oxidizing bacteria
(AOB) and nitrite oxidizing bacteria (NOB) – using free ammonia and free nitrous acid, respectively as their
substrates. The model also incorporates four step denitrification, (sequential reduction of nitrate to nitrogen
gas via nitrite, nitric oxide, and nitrous oxide), using individual reaction specific parameters. The parameter
values suggested in Hiatt and Grady (2008) were used, except for the K FNA (inhibition constant for free
nitrous acid) that was reduced from 1 10-4 (used for high nitrogen loads) to 1 10-6 g m-3 (used for low nitrogen
loads) to promote NOB growth. Kinetic and stoichiometric expressions can be found in Table 1 and 2. The
Ratkowsky temperature functions (Ratkowsky et al., 1982) were used for the temperature effect on AOB and
NOB.
2.2. Anaerobic digestion model
The emissions of GHG during sludge treatment are mainly generated in the anaerobic digester. Direct biogas
CO2 and CH4 emissions are quantified using ADM1. Please, refer to Batstone et al. (2002) for model details
and for parameter values used in this work check Gernaey et al. (2011).
2.3. Stripping equations
Stripping equations are implemented as Foley et al. (2010). N2O emissions are calculated by implementing
the stripping equations in process rate 4 (Table 1)
K L a N 2O ( S N 2O sat  S N 2O )
Eq 24
Where KLaN2O is calculated using Eq2
K L a N 2O 
DO 2
D N 2O
Eq 25
K L aO 2
SN2Osat is the saturation concentration of N2O in water, DO2 is the diffusion coefficient of oxygen in water at
20 °C (m2 s-1), DN2O is the diffusion coefficient of dinitrogen oxide in water at 20 °C (m2 s-1) and KLaO2 is the
oxygen transfer coefficient (days-1).
Stripping equations for ADM1 model were implemented according to Rosen et al. (2012).
2.4. Parameter values
The parameter values suggested in Hiatt and Grady (2008) were used, except for the KFNA that was reduced
from 1·10-4 (used for high nitrogen loads) to 1·10-6 g·m-3 (used for low nitrogen loads) to get reasonable
NOB growth in the modelled system.
Table 1. Process rates for the biological model
Process Process name
1
2
3
4
5
6
7
Process rate
The
aerobic
growth
heterotrophic biomass
 max, OHO
S B ,Org
K S 1  S B ,Org
The anoxic growth of
heterotrophic
biomass,
reducing NO3- to NO2The anoxic growth of
heterotrophic
biomass,
reducing NO2- to NO
The anoxic growth of
heterotrophic
biomass,
reducing NO to N2O
 max, OHO g 3
The anoxic growth of
heterotrophic
biomass,
reducing N2O to N2
 max, OHO g 5
 max, OHO g 2
 max, OHO g 4
The decay of heterotrophic b
OHO X OHO
biomass
The autotrophic growth of
 max, A1
AOB
S B ,Org
The autotrophic growth of
NOB
S B ,Org
K S 3  S B ,Org
The decay of AOB
10
The decay of NOB
11
The
ammonification
soluble organic nitrogen
12
The hydrolysis of particulate
organics
S NO
K S 4  S B ,Org
2
K NO  S NO 
S B ,Org
S NO
K I 4 NO
K OH 4
X OHO
K OH 4  S O 2
S N 2O
K OH 5
K I 5 NO
X OHO
K N 2O  S N 2O K OH 5  S O 2 K I 5 NO  S NO
K S 5  S B ,Org
S FA
2
S FA
K I 9 FA
SO 2
K I 9 FNA
X A1
S O 2  K OA1 K I 9 FNA  S FNA
S FNA
 max, A2
2
S FNA
K I 10 FNA
SO 2
K I 10 FA
X A2
S O 2  K OA2 K I 10 FA  S FA
bA1 X A1
bA2 X A2
of k S X
a BN OHO
XCB


X OHO
SO 2
K OH1
S NOX
·
 h
X OHO 
K OH1  SO 2 K NO 3  S NOX
 K OH1  SO 2

K X  XCB
X OHO
The hydrolysis of particulate
XCB
organics nitrogen


X OHO
SO 2
K OH 1
S NOX
X BN
kh
·
 h
X OHO 
K OH 1  SO 2 K NO 3  S NOX XCBS
 K OH 1  SO 2

K X  XCB
X OHO
kh
13
S NO 2
K OH 3
K I 3 NO
X OHO
K NO 2  S NO 2 K OH 3  S O 2 K I 3 NO  S NO
S B ,Org
K FNA  S FNA 
9
S NO 3
K OH 2
X OHO
K NO 3  S NO 3 K OH 2  S O 2
K S 2  S B ,Org
K FA  S FA 
8
SO2
X OHO
K O,H 1  S O 2
Table 2. Stoichiometry matrix
SB,Org
SO2
SNO3
SNO2
SNO
SN2O
SN2
SNH
S
SALK
XCB
XOHO
XA1
XA2
XP
XBN
BN
1
1
2
-A
3
A
-B
4
1
B
-B
5
C
1
B
-B
1
B
1
6
1-fD
7
D
-1
fD
1
8
1
9
1-fD
10
1-fD
11
12
13
14
1
-1
1
-1
fD
-1
fD
1/14
-1
1
-1
The letters A, B, C, D, E and F represent:
References
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