5. Steady State Modeling
5.2 Model Calibration
The stoichiometric model developed for the anaerobic digestion of FTRW was calibrated against data measured on the AnMBR. The dataset spanned from day 572 to 606 of the experimental period.
Over this period the AnMBR was operated at an OLR of ± 15 kgCOD/m3Vr/d, with three membranes and operational fluxes below critical (i.e. normal operating conditions). Because of the extremely long sludge ages at which the AnMBR operates(> 100 days) and the large amount of parameters that have an effect on the system performance, a true steady state (constant OLR for > 3 sludge ages) could never be attained. However, the average sludge age over the 300 day period before the steady state investigation was estimated from the measured daily waste flow rate (Qw) and reactor volume (Vr), which varied somewhat with the flux through the membranes, at ~ 200 days. 10 days before day 572 the sludge age was specifically controlled to this value (200 days) for the constant OLR (15 kgCOD/m3Vr/d ). Thus it will be assumed that the system was at virtual steady state.
Although one of the underlying assumptions of this steady state anaerobic digestion model is that the biodegradable substrate is all utilized (Sbe = 0), in order to calibrate the representative organism mass yield value (YAR) correctly, the effluent COD concentration will be subtracted to give the COD utilized in the system. Thus for model calibration Sbe was used as an input parameter obtained from the experimental data obtained from the AnMBR, viz.
( )
b utilized bi be
S =S −S (5.16)
The model was calibrated by changing the yield value (YAR) of the representative anaerobic organism until an optimal fit to the measured data was obtained. A COD, N and C balance could be done on the system because the COD entering the system and the COD exiting is known (assuming sludge is C5H7O2N), likewise the N and C. If these balances do not close (not 100%), then the margin of error in the calibration will be greater. Table 5.1 shows the COD, C and N mass balance
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that was done on the experimental dataset. It can be noted that the COD and N balance was fairly low (83% and 88%) and calibration on this data would probably yield unreliable model parameters.
However, the C balance was very good (99%).
Table 5.1, Average COD, C & N Mass Balance Day 572-606
Influent Biogas Waste Effluent Mass
Balance [%]
COD [mgCOD/L] 344.4 278.2 2.8 3.5 82.6
C [mol/L] 9.4 8.3 0.087 0.89 98.9
N [mol/L] 0.082 0.000 0.017 0.055 87.9
The F, x, y and z values for the synthetic FTRW were 0.091, 2.76, 5.61 and 1.97 respectively. A possible reason for the low COD balance is preferential escape of methane through the membranes.
Being a smaller molecule than CO2, it is possible that methane gas selectively passes through the membranes. The escape of some gas bubbles via the effluent manifold was observed on the AnMBR.
However to account for the COD shortfall (60 gCOD/d), some 21 LCH4/d is required to have escaped, which would reduce the carbon balance by 0.9 mol carbon or ~10%. This is too high in relation to the good C balance which was very close to 100% (98.9). Secondly, dissolved methane escaping in the effluent could also not account for the loss in COD since the saturation point is ~100 mgCH4/L, this would amount to less than 2 gCOD/d. The third option might be high COD-low carbon EPS in the biomass, but this would have been detected in the COD tests done on the waste sludge which was conducted on a regular basis. It was therefore concluded that the low COD balance, but accurate carbon balance was due to the methane fraction in the biogas measured too low by the gas chromatograph (GC1) on which it was analyzed.
Because the C balance was close to 100%, it was decided to calibrate the steady state AD-FTRW model against the carbon instead of the COD data. The method used to observe the model’s fit to the experimental data was done in much the same manner as discussed in Section 5.1.4. This was done by observing how the % Error between the predicted and experimental (i) biogas, (ii) biomass and (iii) effluent carbon compared with change in YAR .
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( )
2 100%
Exp SS
Exp
x x
Err x
−
= (5.17)
Where
xExp = Actual experimental measurement
xSS = Corresponding steady state model prediction varying with a variation in YAR
The average sludge age and OLR of the 35 day steady state period was 195 days and 15 kgCOD/m3Vr/d respectively, these values were used as input for the steady state AD-FTRW model.
The YAR was then varied and the predicted carbon exiting the system as (i) biogas, (ii) biomass and (iii) bicarbonate (HCO3-
) in the effluent in relation to the actual measured carbon exiting the experimental system and was compared via Eq 5.17 (Figure 5.4 A, Figure 5.4 B being a magnification of the square in Figure A).
[A] [B]
Figure 5.4, % Squared Error for Predicted & Actual Carbon vs. Yield
It was found that the initial yield of 0.04 [gCOD/gCOD] (acetoclastic methanogenesis) had to be
increased by 10% to 0.044 [gCOD/gCOD] to give a best fit to the experimental data. This was indicated by the minimum in the Total Error in Figure
5.4B which is the sum of the errors between the experimental and predicted values for (i) biogas, (ii) biomass and (iii) effluent carbon. This technique ensures that one parameter, like biogas prediction, is not preferentially calibrated which might negatively affect the estimations of effluent and biomass
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carbon predictions. The death rates for most anaerobic organisms are quite similar so this value was kept constant at bAR = 0.0377 [/d]. Furthermore, it was assumed that the un-biodegradable particulate fraction of the representative organism mass is the same as that of activated sludge; f = 0.08 (Dold et al., 1980). A graphical presentation of the calibrated predictions and measured data is given in Figure 5.5 to 5.9.
0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00
572 574 576 578 580 582 584 586 588 590 592 594 596 598 600 602 604 606
Time [days]
Biogas Production [l/d]
Predicted Actual
Figure 5.5, Predicted & Actual Biogas vs. Time
A good correlation between the predicted and actual biogas production was observed for the entire steady state test period (Figure 5.5). The measured and predicted averages were 210 L/d and 212 L/d respectively with 90% of the model predictions showing less than 6% variance form the experimental measurements (P90 = 6%) and 50% of the model predictions showing less than 1.7%
variance from the experimental (P50 = 1.7 %). The coefficient of determination for this dataset was calculated at R2 = 0.54, implying that the model does not fit the experimental very well (ideally R2 >
0.85). On the other hand, visually and there are a relatively good fit and low P90 and P50 also implying a good fit. This highlights the problems with using the coefficient of determination to evaluate the model performance compared to visual and the error percentile method. If the biogas composition predicted by the model is compared to biogas samples analyzed with the gas chromatograph (GC1) it can be noted that the model predictions are consistently higher than the measured by about 10% (Figure 5.6):
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0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
572 574 576 578 580 582 584 586 588 590 592 594 596 598 600 602 604 606 Time [days]
Biogas: Methane Fraction [%]
Predicted Actual
Figure 5.6: Predicted and Actual Biogas Methane Fraction vs. Time
The average measured and predicted methane fractions were 52.3 and 63 respectively with P90 = 26% and P50 = 20%. Thus the experimental analysis was consistently low by 10% (Figure 5.6). This difference in the predicted and actual methane fraction of the biogas adds weight to the argument of low GC results.
Figure 5.7: Predicted & Actual Alkalinity vs. Time
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The predicted and measured (H2CO3*) Alkalinity is shown in Figure 5.7. The model predicts the measured data quite well, the average measured and predicted alkalinities are 2288 mgCaCO3/L and 2198 mgCaCO3/L (P90 = 18% & P50 = 5%). If no biological utilization of the organics in the FTRW stream took place ~10 000 mgCaCO3/L alkalinity or ~6.7 gNaOH/L would have been required for neutralization to a pH of 7. The alkalinity dosed (~1000 mg/L as CaCO3) is therefore only about 10% of the FTRW neutralization demand because the anaerobic biomass utilize the acid (undissociated) form of the SCFAs.
The contributors to the alkalinity in the AnMBR are (i) hydroxide dosed, (ii) urea dosed and (iii) FTRW influent alkalinity (Section 5.1.3). These contribute 57%, 38% and 5% to the total alkalinity respectively. It can be seen that the OH dose is the largest contributor (Figure 5.7 Alk-OH), but the influent alkalinity (Alk-AD) despite the pH being 3.77, is not insignificant and cannot be ignored to predict the reactor pH correctly. The increase in OH dosing from day 596 onwards shows how sensitive the system is to the amount of hydroxide dosed. Since the influent alkalinity and the amount of urea in the feed remains virtually constant, it is the OH dosing that is the most sensitive contributor to reactor alkalinity. Interestingly urea decomposition to form NH4+
also adds a significant amount of alkalinity (~120 mgCaCO3/L) and thus cannot be ignored, hence the inclusion of urea decomposition in Eq 5.8.
6.90 6.95 7.00 7.05 7.10 7.15 7.20
572 574 576 578 580 582 584 586 588 590 592 594 596 598 600 602 604 606
Time [days]
pH
Predicted Actual
Figure 5.8, Predicted & Actual pH vs. Time
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Because of the slight under-prediction of the alkalinity, the predicted pH is also slightly lower than the actual (Figure 5.8). The measured and predicted averages are 7.01 and 6.99 respectively with P90
= 0.3% and P50 = 0.1%. If the alkalinity measured in the 5-pt titration and the CO2 partial pressure measured on the gas chromatograph is used in Eq 5.14, the pH is predicted consistently low at 6.89.
However if the experimental PCO2 is substituted for the PCO2 calculated from the COD balance (Eq 5.13), the model predicts the pH accurately. This further ads weight to the questionable gas chromatograph measurements as discussed in earlier in Section 5.2.
The sludge age (Figure 5.9A) was calculated from the measured volume of biomass wasted per day from the AnMBR divided into the actual operational volume of that day (Rs = Vr/Qw), as was discussed in detail in Section 3.3.
[A] [B]
Figure 5.9, AnMBR Sludge Age [A] and Predicted and Actual MLSS [B] vs. Time
The predicted and measured reactor TSS is shown in Figure 5.9B. The predicted reactor TSS concentration show significantly more variance that those measured. The predicted and measured averages are 20gTSS/L and 19.84 gTSS/L with P90 = 22% and P50 = 11%, implying a large amount of variance in the data even though the averages are statistically similar. Because of the long sludge age and its significant variation over a wide range, resulting from controlling reactor concentration at
~20 gTSS/L and not sludge age, the MLSS concentration is not strongly dependant on the chosen
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yield and death rates. Thus it appears that the generic C5H7O2N biomass composition correlates to within the margin of experimental error. If Figure 5.9A and B are compared it can be seen that – for a constant OLR (in this case 15 kgCOD/m3Vr/d) – the reactor MLSS is directly proportional to the sludge age. Table 5.2 gives a summary of the results obtained in the model calibration:
Table 5.2, Stoichiometric Model Calibration
Comparison Predicted Average
Actual Average
P90
[%]
COD Balance 93
COD/VSS 1.53
VSS/TSS 0.78
TKN/VSS 0.11
Sludge Age [days] 195* 195
Nitrogen Requirements [mgN/L] 17 16.6 40 Biogas Production [L/d] 212 210 6.0
CH4 Fraction [%] 63 52 26
Alkalinity [mgCaCO3/L 2125 2288 18
pH 6.99 7.01 0.30
MLSS [gTSS/L] 20 19.8 22.0
* Per definition same as measured
Note: since the steady state AD-FTRW over-predicts the sludge production (slightly by ~1%) there is a corresponding over-prediction in the nitrogen requirements for biomass growth.