Steady State Calibration

6. Dynamic Modeling

6.2 Model Verification and Calibration

6.2.1 Steady State Calibration

For a constant flow and load bio-reactor with sludge age control, steady state is typically reached after three sludge ages. If this constant flow and load state is applied for longer than 3 sludge ages, then the dynamic and steady state models should yield virtually identical outputs for the same set of input parameters.

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Provided the above criteria are met, the steady state model results can be used to calibrate some of the stoichiometric constants required in the dynamic model. However, since the number of parameters required is more than the number of stoichiometric relationships, only ratios between parameters can be explicitly identified. Thus prior knowledge about some parameters is required to identify of each individual parameters.

Under steady state conditions with effluent COD concentration (Sbe) = 0 i.e. eliminating process rates and reducing the model to stoichiometry on the basis that the observed yield (Yobs) = Ymetabolic/(1+b.Rs), the influent biodegradable COD (Sbi) can only exit the system in the form of biogas (Sm) or biomass (ZVSS). The ratio between the COD exiting as biogas vs. the COD entering the system is governed by the net yield (Yobs), which is a fraction of the metabolic yield (Ymetabolic) and the endogenous respiration rate (bi) for a fixed unbiodegradable biomass residue f = 0.08 and sludge age (Rs). Since the endogenous respiration rates of the anaerobic organism groups are fairly similar, a literature survey was done to obtain the bj values. Thus the steady state parameter optimization was only done on the stoichiometric yield (Ymetabolic) values for each of the FOGs.

The parameters optimization in West^® requires lower- and upper-bound values for each of the parameters to be optimized. These (Ymetabolic) values were obtained from literature and the lowest and highest quoted values for each of the organism yield values were taken as the upper and lower-bound values respectively. To avoid the issues around using a ‘Simplex’ optimizer to fins the optimim Yield values, a constrained ‘Praxis’ optimizer with a covariance and perturbation factor set to 1E-6 was used for a high degree of accuracy. Table 6.2 displays the upper and lower-bound and the optimized Y value for each of the functional organism groups as optimized for a sludge age of 300 days:

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Table 6.2, Steady State Metabolic Yield (mol_Biomass/mol_substrate) Optimization

Metabolic Yield

Lower- Bound

Upper- Bound

Optimized Value

Yad 0.03 ⁴ 0.15 ³ 0.1074

YacHx 0.03 ¹ 0.1027 ¹ 0.0474

Y_acVa 0.0338 ³ 0.1027 ³ 0.0496 Y_acBu 0.02875 ¹ 0.125 ¹ 0.0558 Y_acPr 0.0278 ² 0.0632 ³ 0.0376 YacEt 0.0125 ¹ 0.125 ¹ 0.0832 Yam 0.0056 ³ 0.0304 ³ 0.0157 Ymm 0.0056 ¹ 0.0304 ¹ 0.0127

Yhm 0.0014 ³ 0.0183 ³ 0.004

1. Kalyuznhyi, 1997b 2. Sötemann et al., 2005 3. Batstone et al., 2002 4. Sam-Soon et al., 1989

Table 6.2 shows that optimized yield values for all of the functional groups could be found between the lower and upper bounds indicating that none of the Ymetabolic values found compensated for another one constrained by the upper and lower bounds. After the yield optimization the dynamic model was compared to the steady state model for a constant load of 346 gCOD/d (i.e 19.23 L/d at 18 000 mgCOD/L) for a 23 L reactor volume for a sludge age of 100, 300 and 500 days (Table 6.3):

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Table 6.3, Steady State and Dynamic AD-FTRW Model Comparison for a constant influent flow rate of 19.23 L/d and a reactor volume of 23 L

Sludge Age Rs = 100 days Rs = 300 days Rs = 500 days

Parameter SS Dyn %

Error SS Dyn %

Error SS Dyn % Error Sti [mgCOD/L] 18000 18000 18000 18000 18000 18000

Ste [mgCOD/L] 0 9.60 0 7.83 0 7.50

CH4 [L/d] 135.0 134.8 0.1 135.8 135.7 0.0 135.9 136.0 -0.1 CO2 [L/d] 75.5 78.4 -3.8 76.0 79.0 -3.9 76.1 79.2 -4.1 Alk [mgCaCO3/L] 2642 2593 1.9 2674 2644 1.1 2681 2660 0.8 MLVSS [mgVSS/L] 12.48 13.28 -6.3 21.17 21.17 0.0 28.80 23.40 18.8

pH 7.1 7.09 0.1 7.1 7.1 0.0 7.1 7.1 0.0

Nti [mgN/L] 85.3 85.3 0.0 85.3 85.3 0.0 85.3 85.3 0.0 Nte [mgN/L] 70.4 69.4 1.3 76.9 76.9 0.0 78.4 79.7 -1.6

COD_Methane/COD_Influent [%] 98.7 98.6 0.1 99.3 99.2 0.0 99.4 99.5 -0.1

CODBiomass/CODInfluent [%] 1.3 1.4 -10.6 0.7 0.8 -6.2 0.6 0.5 11.6

COD 100.0 100.0 0.0 100.0 100.0 0.0 100.0 100.0 0.0

C 100.0 100.0 0.0 100.0 100.0 0.0 100.0 100.0 0.0

H 100.0 100.0 0.0 100.0 100.0 0.0 100.0 100.0 0.0

O 100.0 100.0 0.0 100.0 100.0 0.0 100.0 100.0 0.0

N 100.0 100.0 0.0 100.0 100.0 0.0 100.0 100.0 0.0

Charge 100.0 100.0 0.0 100.0 100.0 0.0 100.0 100.0 0.0

Note: Since the gas temperature was assumed to be 37 ^oC, the molar volume of the biogas was taken as 25.285 L/mol

Table 6.3 shows that all the masses again balanced and after optimization a large degree of correlation (< 4 % error) exists between the steady state and dynamic AD-FTRW model on most of the parameters evaluated. However, the dynamic model tends to under-predict reactor MLVSS by as much as 19% as the sludge age increases from 300 to 500 days and under predicted the MLSS by 6% by decreasing the sludge age to 100 days. The resultant effect is also an over (or under) - prediction of the effluent N concentration (Nte). However, to place this error into interest, the % of the influent COD exiting as MLVSS is ~1% and of methane is ~99%. The 19% error on the reactor VSS concentration estimate results in a 0.04 % error on the mass of VSS wasted per day (i.e.

19%/500 = 0.04%). This is because the mass of VSS wasted per day is 1/500^th of the mass of VSS in

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the reactor at a 500 d sludge age. Clearly this error is acceptable from a sludge production point of view. Figure 6.8 gives a presentation of how the VSS is distributed between the various FOGs and also endogenous mass.

0 1000 2000 3000 4000 5000 6000 7000 8000

Zad ZacHx ZacVa ZacBu ZacPr ZacEt Zam Zmm Zhm Ze

Concentration [mgVSS/L]

Figure 6.8, FOG and Z_e Mass Distribution (OLR = 15 kgCOD/m³/d & R_s = 300 days)

From Figure 6.8 it can be noted that the major part of the VSS consists of acetogenic biomass with especially the propionate (ZacPr) and valeric acid (ZacVa) reducers contributing a significant amount to the total VSS due to their high yields. As expected the acetoclastic methanogens (Zam) are also a major contributor to the reactor VSS. Interestingly, even at a sludge age of 300 days the endogenous mass fraction (Ze) is only ~5% of the total VSS.