5. Steady State Modeling
5.1 Steady State Model Development
5.1.1 Kinetic Part
In steady state models the organism growth process is governed by the slowest step in the sequence.
For sewage sludge digestion, this was the hydrolysis/acidogenesis step. With FTRW, all the influent organics are readily biodegradable and do not require hydrolysis. The rate of utilization is therefore very fast, especially at long sludge ages, which will be required to provide bio-process stability and capacity to absorb small variations in Organic Loading Rates (OLR). The rapid rate of utilization will result in virtually complete consumption of influent organics, which was in fact observed to be the case in the experimental AnMBR (99.8% COD removal) (Section 4.6.1). It can therefore be assumed that all the influent organics are completely utilized by three groups of anaerobic organisms, acetogens (Zac), acetoclastic methanogens (Zam), and hydrogenotrophic methanogens (Zhm), with the result that kinetics of the growth processes are not required in the steady state model – they can be assumed to be instantaneous. The effluent COD concentration (Sbe) will be assumed zero for this steady state AD-FTRW model.
The three groups of organisms undergo endogenous respiration in the reactor. This endogenous process generates biodegradable particulate organics (Sbp) which will undergo hydrolysis/
acidogenesis (Zad) to produce acetic acid and hydrogen. So while no acidogens grow from the influent organics, they will nevertheless be part of the biocenosis, and undergo endogenous respiration themselves also. Because the endogenous process is very slow ~0.04/d for all four organism groups, the acidogens will be a small proportion of the total biomass. Even though the rate of hydrolysis of biomass complex organics is slow compared with the growth rate, the generation rate of these organics by endogenous respiration is much slower than hydrolysis, i.e. the endogenous
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respiration rate (b) is the rate limiting step in endogenous-hydrolysis process sequence. Therefore, only the endogenous respiration rate (b) needs to be considered in the steady state model.
In the interests of keeping the steady state model simple, only a single anaerobic organism will be modeled representing all four organism groups. The yield coefficient of this representative organism (YAR) will be close to the yield of the acetoclastic methanogens (0.04 gCODbiomass/gCODutilized), which will dominate the biocenosis due to the high proportion of acetic acid in the influent (~50%) and relative to the acetoclastic methanogens, the hydrogenotrophic methanogens have a low yield value and the acidogens have a high yield value. Starting from YAR = 0.04 gCODbiomass/gCODutilized, this value will be calibrated against the steady state experimental data
With sewage sludge digestion, the effluent COD concentration is mostly particulate unbiodegradable organics (~35% of influent COD) and biomass. Endogenous residue generation, which is negligible compared with the particulate unbiodegradable organics, could therefore be ignored by Sötemann et al. (2005). However, for completely biodegradable organics and the long sludge age at which the AnMBR operates, endogenous residue generation becomes significant and no longer can be regarded a negligible part of the reactor VSS concentration, particularly with low growth yield values of the anaerobic biomass. Thus, endogenous residue accumulation needs to be included in the AnMBR model to predict the sludge production accurately. The endogenous respiration rates of the four anaerobic organisms are quite similar (~0.04/d) so an average value of 0.0377/d (bAR) will be used for the representative anaerobic organism in the steady state model (Sötemann et al., 2005). The unbiodegradable fraction of the biomass (fAR) was taken as 0.08 from activated sludge models (Dold et al., 1980).
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Figure 5.1, AnMBR Steady State Mass Balance
Applying the above considerations in a COD balance over the AnMBR (Appendix 5.3) at a defined sludge age (RS), established hydraulically by a waste flow rate (QW = Vr/RS) directly from the reactor (Figure 5.1), the following kinetic model equations are obtained:
( )
( )
( )
(
1 1 1)
AR bi be s
AR
AR s AR AR h
Y S S R
Z
b R Y f R
= −
+ − − (5.1)
ER AR AR s AR
Z =f b R Z (5.2)
( )
( )
( )
( )
(1 )
1 1 1
AR bi be s AR AR s
VSS AR ER
AR s AR AR h
Y S S R f b R
Z Z Z
b R Y f R
− +
= + =
+ − − (5.3)
( ) ( )
( )
( )
( )
1 1
1 1 1
AR AR s
m
AR s AR AR
Y b R
S
b R Y f
− +
=
+ − − (5.4)
Where
ZAR = representative active organism concentration [gCOD/Lreactor]
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YAR = yield coefficient of the active
organism concentration = 0.04 (provisionally) [gCODbiomass/gCODutilized] bAR = representative active organism
endogenous respiration rate = 0.038 [1/d]
fAR = unbiodegradable fraction of
representative active organism = 0.08
ZER = endogenous residue concentration [gCOD/Lreactor] Sbi = influent COD concentration [gCOD/Linfluent] Sbe = effluent COD concentration =0 [gCOD/Leffluent]
RS = sludge age (=Vr/Qw) [d]
Rh = hydraulic retention time (=Vr/Qi) [d]
Vr = reactor volume [L]
ZVSS = reactor organic suspended solids concentration [gCOD/Lreactor]
Sm = methane production [gCOD/Linfluent]
The reactor suspended solids COD concentration (ZVSS, gCOD/L Eq 5.3) and the methane gas Eq 5.4 and sludge (Eq 5.3*Qw) production as a % of the influent COD (Sbi) are plotted versus sludge age for an OLR (= Qi Sbi/Vr) of 15kgCOD/m3/d in Figure 5.2, where Qi is the influent flow rate and Vr the volume of the membrane reactor. It can be seen that (i) a very high proportion of influent COD is converted to methane (>98% for sludge age > 40d), (ii) this percentage increases with sludge age (due to endogenous respiration of biomass) and is 99% at 80d sludge age with the result that (iii) the sludge production is very low, i.e. 100-99 = 1% of influent COD mass at 80d sludge age and (iv) the reactor solids COD concentration increases with sludge age and >12 gTSS/L required for membrane scour for sludge ages longer than 60d. If the OLR is increased to 25 kgCOD/m3/d, the reactor concentration exceeds 15gCOD/L for >50d sludge age. Long sludge ages, high reactor solids concentration for membrane scour and high % influent COD conversion to methane work together in the AnMBR system.
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Figure 5.2: Reactor solids COD concentration and % influent COD converted to methane (1-E) versus sludge for the AnMBR system.
The net proportion (E) of the influent biodegradable organics load [Qi (Sbi-Sbe)] that remains as sludge mass and is harvested daily from the reactor to maintain the sludge age [Qw (ZAR+ZER)] can be calculated from Eq 5.3. From Figure 5.2, it can be seen that this E value decreases as sludge age increases. From Eq 5.3,
( )
( )
( )
( )
( )
( )
1 . .
1 . . 1 1
w AR ER AR AR AR s
i bi be AR s AR AR
Q Z Z Y f b R
E Q S S b R Y f
+ +
= =
− + − − (5.5)
The link between the reactor MLSS (kgTSS/m3 or gTSS/L), reactor volume (Vr, m3), sludge age (Rs, d) and influent flow and load is given by combining Eqs 5.3 and Eq 5.5, viz.
( )
.( )
. . . .. . . .
AR ER i bi be s s
cv i r cv i cv i
Z Z Q S S E R OLR E R
MLSS f f V f f f f
+ −
= = = [gTSS/L] (5.6)
where
fcv = COD/VSS ratio of the sludge in the reactor and [gCOD/gVSS]
fi = VSS/TSS ratio of the sludge in the reactor [gVSS/gTSS]
OLR = Organic Loading Rate [kgCOD/m3Vr/d]
Both COD/VSS and VSS/TSS ratios were measured on the experimental AnMBR system and were fcv = 1.53 and fi = 0.78. While the former (fcv) is close to the value accepted for activated sludge (1.48), the latter (fi) seems unexpectedly low for a purely biodegradable organic feed – fi values for activated sludge fed pure organic substrates are around 0.90. Possibly the low fi value is due to the municipal anaerobic digester sludge used for seeding of the experimental AnMBR, which had a fairly large ISS component. Thus because of the large initial ISS concentration, which combined
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with the extremely long sludge ages in the AnMBR, resulted that the ISS was not fully harvested from the AnMBR by the time the steady state experimental investigation was commenced.
The nitrogen for sludge production (growth) can also be determined from Eq 5.3. With the N content of the VSS in the reactor (fn) known from measurement (0.11 gN/gVSS – also close to 0.10 measured on activated sludge), the minimum N concentration in the influent required for sludge production (Ns) [mgN/L] is given by
( )
r VSS n
s n bi be
cv s i cv
V Z f
N f S S
f R Q f
= = − [mgN/L] (5.7)
Where fn = TKN/VSS ratio of the sludge [gN/gVSS]. However, usually a back ground (non-utilized) ammonia concentration (Nb) is required so the ammonia dosed Nd = Ns + Nb [mgN/L], Eq 4.1 as discussed in Section 4.3.