6. Dynamic Modeling
6.1 Model Development
6.1.3 Microbial Inhibition
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0.000 0.200 0.400 0.600 0.800 1.000 1.200 1.400
0 10 20 30 40 50 60
Temperature [oC]
Inhibition Function
Arrhenius
Double Sided
Figure 6.4, Inhibition of Mesophillic Anaerobic Digestion as a Function of Temperature with Arrhenius Law and “Double Sided” Inhibition function.
From Figure 6.4, it can be noted that for temperatures >37 oC, the Arrhenius law predicts a inhibition
> 1, which shows this function is not suitable for the prediction of mesophillic anaerobic digestion’s response to high temperature. Thus a double sided sine function was chosen for the dynamic AD- FTRW model. It should be emphasized that this is nothing more than a crude approximation for the system’s response to temperature and requires further investigation. Since no literature could be found on how the individual trophic groups of anaerobic digestion responds to temperature, all the groups were modeled with one temperature inhibition function.
Unlike temperature, the modeling of pH inhibition is well studied and fairly well understood. pH often inhibits the biological activity due to non-dissociated acids and bases in the mixed liquor (Dochain & Vanrolleghem, 2001). Free acid and base inhibition has been defined as the disruption of homeostasis by changes in pH, caused by the passive transport of the free acid/base over the cell membrane and subsequent dissociation. However the actual proton activity in the bulk liquid also appears to contribute to the inhibitory nature of this environmental parameter. Batstone et al. (2002) suggested the following pH inhibition function for anaerobic digestion:
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( )
( ) ( )
1 10
1 10 10
pHj LLZij ULZj
r ULZj LLZj r
K pH pH
pHZj pH pH pH pH
I
−
− −
= +
+ + (6.32) Where
IpHZj = pH inhibition function of FOGi [-]
pHULZj = Upper pH level of 50% inhibition of FOGi [-]
pHLLZj = Lower pH level of 50% inhibition of FOGi [-]
pHr = Reactor pH [-]
KpHj = pH inhibition constant [-]
Because of the high acidity of FTRW and the fact that a strong base (NaOH) is dosed for pH control, it was experimentally observed that the on-line pH control system (Section 3.4.1) can easily over/undershoot the desired pH level. Thus, similar to temperature, a double sided pH inhibition function was selected. Eq 6.32 yields a bell shaped curve around a specified mean ((pHUL+pHLL)/2).
Figure 6.5 represents the pH inhibition curves for the various FOGs.
0.00 0.20 0.40 0.60 0.80 1.00 1.20
0 2 4 6 8 10 12 14
pH
Inhiition
IpHZadZac IpHZamZmm IpHZhm
Figure 6.5, pH Inhibition Functions for Dynamic AD-FTRW
From Figure 6.5 it can be noted that three pH inhibition functions describe all of the FOGs in the dynamic model. It was found from literature that acetogenesis and acidogenesis has very similar responses to pH, thus one function describes all the FOGs in these two trophic groups (IpHZadZac). No
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information was found in the literature about the response of methanol utilizing methanogens to pH, thus it was assumed that these organisms had the same response to pH as the acetoclastic methanogens (IpHZamZmm) (Batstone etal., 2002).
Note the acidogenic (Zad) and acetogenic (Zac) trophic groups have the widest activity range with variation in pH. This implies that as the pH goes out of bounds, the acetic acid and H2(gas)
concentrations will increase in the effluent and correspondingly, the methane fraction in the biogas will decrease. Both SCFA and H2(gas) increases can have adverse effects on anaerobic digestion. The first of which is hydrogen inhibition.
The most inhibitory metabolic intermediate produced in anaerobic digestion is dissolved hydrogen gas (H2(aq)). This compound has a detrimental effect on the activity of the H2 producing organisms even at a micro-mol concentration. FOGs adversely affected by H2(aq) is Acidogenesis (Zam), Acetogenesis (Zac) and most importantly the propionate reducing Acetogens (ZacPr). Sötemann et al.
(2005) suggests the following inhibition function for acidogenesis (Zad) (Eq 6.33):
2
2
2( ) 2( )
[ ]
1 [ ]
aq H Zad
IH Zad aq
I H
k H
= − + (6.33)
Where
IH2Zad = The inhibition of acidogenesis (Zad) by H2(aq) [-]
H2(aq) = Dissolved hydrogen gas concentration [mol/L]
kIH2Zad = Hydrogen inhibition constant. [mol/L]
Batstone et al. (2002) suggested the following inhibition functions for acetogenesis (Zac) (Eq 6.34):
2
2
2( )
1
[ ]
1
H Zacj
aq IH Zacj
I
H k
=
+
(6.34)
Where
IH2Zacj = The inhibition of the jth acetogenic (Zac) group by H2(aq) [-]
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kIH2Zacj = The inhibition constant for the jth Zac by H2(aq) [mol/L]
0.00 0.20 0.40 0.60 0.80 1.00 1.20
0 200 400 600 800 1000
H2(aq) Concentration [micro mol/L]
Inhibition (IpH)
IH2Zad IH2Zacj IH2ZacPr
Figure 6.6, H2(aq) Inhibition of Zad and Zac
From Figure 6.6 it can be noted that the same H2(aq) inhibition function is used to describe all of the acetogenic (Zac) FOGs except for propionate reducing acetogenesis (ZacPr). This group is so adversely affected by H2(aq) that it requires its own inhibition constant in Eq 6.34. The effect of H2(aq)
inhibition on the methanogenic groups appears to be negligible compared to the that of acidogenesis (Zad) and acetogenesis (Zac).
The final inhibitory compound to be modeled is the total SCFA concentration (SCFAe). SCFAe has an inhibitory effect on both acetoclastic methanogenesis Zam and the propionate reducing acetogens (ZacPr). The SCFA inhibition functions can be described as follows:
e
1 [SCFA ] 1
t am
t am
A Z
IA Z
I
k
=
+
(6.35)
And
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Pr
Pr
1
[ ]
1
t ac
t ac
A Z
e IA Z
I
SCFA k
=
+
(6.36)
Where
IAtZam/IAtZacPr = Inhibition of Zam & ZacPr by SCFAe [-]
SCFAe = Total SCFA concentration [mol/L]
kIAtZam & kIAtZacPr = Inhibition constants [mol/L]
0.00 0.20 0.40 0.60 0.80 1.00 1.20
0 500 1000
Concentration [mgAc/L]
Inhibition Function
IZamAt IZacPrAt
Figure 6.7, Zam & ZacPr Inhibition as a Function of SCFAe
Figure 6.7 shows that the inhibition of both acetoclastic methanogenesis (Zam) and propionate reducing acetogens (ZacPr) is almost linear with an increase in Effluent Short Chain Fatty Acids (SCFAe). However, ZacPr is much more strongly affected by an SCFA increase than Zam, with a 50%
decrease in activity occurring at a concentration of 0.0175 mol/L or 1050 mgAc/L (as compared to 0.6 mol/L for Zam).