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3.1. Initial state for simulation of batch experiments

The initial conditions based on continuous steady state modelling of the continuous digesters are given in Figure 37. Both the total biomass concentrations and the proportions differ due to the differences in the feed mixtures. To normalise, results in Figure 37 are expressed as a % of the total biomass contained in the inoculum concerned. Methanogenic and acetogenic biomass proportions were predicted to be similar for WAS and PS acclimated inoculums. Indeed, as these reactions occur at the end of the degradation chain, biomass proportions are not strongly dependent on the biochemical characteristics of the feed.

However, PS acclimated inoculum was better suited for saccharide acidogenesis than WAS acclimated inoculum and WAS acclimated inoculum was better suited for LCFA and AA acidogenesis. These differences are directly correlated with differences in feed composition.

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10%

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30%

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Sugar acidogenesis AA acidogenesis LCFA acetogenesis C4 acetogenesis Propionate acetogenesis Acetotrophic methanogenesis Hydrogenotrophic methanogenesis

Specific biomass according to ADM1 Specific biomass concentration (% of total biomass)

WAS-acclimated inoc. PS-acclimated inoc.

Figure 37 : Specific biomass fractions for WAS and PS acclimated inoculums obtained by static simulation of both continuous reactors using the ADM1 (table at top right).

Xpr Xch Xli Xi

% of the totalCOD

WAS acclimated inoc. 11% 10% 8% 71%

PS acclimated inoc. 7% 33% 15% 45%

Influent fractionation for the simulation of both CSTRs.

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3.2. Degradation of acetate

Within the ADM1, the reaction rate for acetotrophic methanogenesis (ρXac) is defined as follows: half-saturation constant for acetotrophic methanogens, Sac is the concentration of acetate, Xac is the concentration of acetotrophic methanogens and INH3,Xac; IpH; IIN,lim are respectively the inhibition factors by high free ammonia concentration, pH (equal to 1 in our case) and low inorganic nitrogen concentration (equal to 1 in our case).

Figure38 shows a comparison of the experimental data obtained with an acetate pulse into WAS and PS acclimated inoculum and the simulated results obtained with default parameters proposed by Batstone et al. (2002) (km_ac=8kgCOD.kgCOD-1.d-1 and Ks_ac.0.15 kgCOD.m-3). Whatever the inoculum, initial MPR values were significantly overestimated with ADM1 default parameters if no ammonia inhibition was incorporated. Default ammonia inhibition factor was then considered as follows (Batstone et al., 2002):

3

where SNH3 is the free ammonia concentration calculated from measured TAN concentration considering pKa(NH3/NH4+)=8.9 at 37 °C and KI,NH3 is the default inhibition constant for free ammonia (0.0018 kmol.m-3) from Batstone et al. (2002). Hence, the default ammonia inhibition factor was 0.37 and 0.090 for WAS and PS acclimated inoculums respectively.

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0 Figure 38 : Comparison of the experimental MPR data for acetate pulses and simulation

results before and after calibration (A: pulse in PS-acclimated inoculum; B: pulse in WAS-acclimated inoculum). MPR due to the inoculum has been subtracted.

The simulation of the MPR related to acetate degradation matched experimental data for WAS acclimated inoculum but significantly underestimated data for PS acclimated inoculum. Optimal (INH3×km_ac)/Ks_ac sets were estimated considering a confidence interval of 95% (see Figure 39). For each inoculum, after parameter optimisation, simulated MPR curves fitted the experimental data much better (figure 38).

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Figure 39 : Comparison of the confidence regions, indicating confidence in km_ac and Ks_ac , for optimal simulation of MPR curves obtained after acetate pulses in WAS and

PS acclimated inoculum

Inoculum source, intensity of the substrate pulse and sampling date are shown in the diagram ; *: simulation results are shown in fig. 38A ; **: simulation results are shown in

fig. 38B.

A B

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Two different amounts of acetate added (3gCOD.Linoculum-1

and 1.5 gCOD.Linoculum-1

) resulted in very similar, though statistically different, regions. This was due to an increase in INH3×km_ac with the lower amount of substrate added, possibly related to minor acetate inhibition (not incorporated in the model).

Temporal variability of the results was also assessed. PS acclimated inoculum samples taken at a later date (10 months and 12 months) varied significantly in both INH3×km_ac and KS_ac values, but particularly in KS_ac. The three ( INH3×km_ac)/Ks_ac parameter sets were respectively 2.51/0.30, 2.24/0.43 and 2.85/0.69. For WAS-acclimated inoculum, INH3×km_ac)/Ks_ac estimated parameter sets were very close at two sampling dates (2.79/0.089 and 2.73/0.088, see Figure 39), but with a consistently lower apparent KS value than with PS acclimated inoculum. This suggests that the inoculum shifts significantly (though not enormously) over time, particularly PS acclimated inoculum.

For WAS acclimated inoculum, default parameters (INH3×km_ac = 0.37×8 = 3.0COD.kgCOD-1.d-1 and Ks_ac.0.15 kgCOD.m-3) were close to optimal parameters. Thus, default ADM1 parameters and ammonia inhibition enabled very accurate simulation of biomass activity related to acetate degradation for WAS acclimated inoculum.

For PS acclimated inoculum, default parameters (INH3×km_ac = 0.087×8 = 0.70COD.kgCOD-1.d-1 and Ks_ac.0.15 kgCOD.m-3) differed significantly from optimal parameters. Biomass activity related to acetate degradation was significantly underestimated.

Underestimation of INH3×km_ac was probably due to the fact that the default ammonia inhibition incorporated in ADM1 was not valid for such a high concentration of free ammonia. The reasons for these inconsistencies, as well as for the higher KS values (compared to WAS) are likely linked with biomass acclimation to ammonia. In particular, high ammonia concentrations are known to cause a shift from Methanosaetaceae to Methanosarcinaceae (Karakashev et al., 2005), which generally have higher KS values (Conklin et al., 2006). In addition, high ammonia concentrations (>3gN.L-1) cause a shift from the acetoclastic pathway to the syntrophic acetate oxidation pathway (Schnürer and Nordberg, 2008).

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3.3. Degradation of propionate concentration of propionate acetogenesis biomass and Ih2, IpH, and IIN,lim are respectively the inhibition factors by high hydrogen concentration, pH (equal to 1 in our case) and low inorganic nitrogen concentration (equal to 1 in our case).

Figure 40 shows a comparison of experimental data obtained after a propionate pulse in WAS and PS acclimated inoculum with simulated results obtained with the default parameters (km_pr = 13 kgCOD.kgCOD-1.d-1 and Ks_pr = 0.3 kgCOD.m-3; Batstone et al., 2002). For PS acclimated inoculum (Figure40A), simulation of the MPR curves with default parameters led to overestimation of methane production (inhibition of acetogenesis by H2 reduced apparent kinetics by 25%). With WAS acclimated inoculum, the results were very different because methane production was greatly underestimated by the model (Figure40B).

This was still true when inhibition of acidogenesis by H2, which reduced the apparent degradation kinetics by 36%, was inactivated.

0 Simulated propionate pulse w ith ADM1 def ault parameters

Simulated propionate pulse after calibration and an increase of initial Xpro concentration (multiply by 3)

Figure 40 : Comparison of the experimental MPR data for a propionate pulse and simulation results before and after calibration (A: pulse in PS sludge; B: pulse in WAS

sludge)

MPR due to the inoculum has been subtracted.

A B

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For PS acclimated inoculum, parameter optimisation led to accurate simulation of the experimental data. Figure 41 shows all the optimum km_pr/Ks_pr parameter sets with a confidence interval of 95%. Calibration thus reduced km_pr by more than 39% (optimum km_pr = 7.80 kgCOD.kgCOD-1.d-1). For Ks_pr the default value decreased from 0.3 to 0.077 kgCOD.m-3.

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

6.5 7 7.5 8 8.5

km_pro (kgCOD.kgCOD-1.day-1) Ks_pro (kgCOD.m-3 )

Figure 41 : Comparison of the confidence regions, indicating confidence in km_pro and Ks_pro , for a optimal simulation of MPR curves obtained after acetate pulses in PS

acclimated inoculum.

For WAS acclimated inoculum, the experimental MPR curve can be divided into two parts. During the two first days, propionate acetogenesis occurred and the MPR value was high due to the sum of the methanogenesis of the acetate and the hydrogen produced by propionate uptake. After two days, the MPR dropped sharply because only the residual accumulated acetate continued to be converted into methane. As shown in Figure 40B, it is possible to modify the km_pr/Ks_pr set to improve the simulation. However, the simulation of the MPR values during the two first days of the substrate pulse did not match experimental values. Moreover, a significant modification of the km_pr parameter was necessary (km_pr = 28 kgCOD.kgCOD-1.d-1 and Ks_pr = 0.15 kgCOD.m-3). Inhibition of acidogenesis due to H2 concentration decreased the degradation rate by 42%. The simulation results can be improved by increasing the initial concentration of propionate acetogenic biomass. Hence, as shown in Figure40B, the simulation is improved if km_pro value is kept at 13 kgCOD.kgCOD-1.d-1 (Ks_pr

= 0.15 kgCOD.m-3) and the initial concentration of propionate acetogenic biomass is increased by 200%.

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These results highlight uncertainties in the estimation of initial states, since errors can result in major differences in assumed initial conditions. Default ADM1 underestimated biomass activity related to propionate degradation by 56% in WAS acclimated inoculum. In PS acclimated inoculum, default ADM1 overestimated biomass activity related to propionate degradation by 33%. These inconsistencies could be due to uncertainty in the calculation of the initial state of batches related to uncertainties in the biochemical fractionation of the input into the CSTRs from which sample inoculums were taken. Indeed, according to ADM1 stoichiometry, degradation of carbohydrates leads to more propionate degrading biomass growth than do degradation of proteins and lipids. This could explain inconsistencies in propionate degradation in PS acclimated inoculum. But not in the case of WAS acclimated inoculum. The maximum theoretical error induced by the biochemical fractionation of the CSTR feed led to an increase of +69% in the initial propionate degrader concentration in WAS acclimated inoculum. Nevertheless, the initial propionate degrader concentration needs to be increased even more (+200%). Other hypotheses may explain the underestimation of the initial concentration of propionate degraders, e.g. incorrect model stoichiometry or incorrect definition of the specific acetogenic biomass.

3.3. Degradation of particulates and corresponding monomers

For more complex substrates, including hydrolytic and acidogenic substrates, parameter estimation only using MPR curves was difficult due to the lack of information on intermediate dynamics (H2, VFAs, etc.). Consequently, in this section, only the ability of default ADM1 acidogenic parameter set was evaluated.

3.3.1. Degradation of glucose and cellulose

MPR curves obtained after addition of glucose in WAS and PS acclimated sludge are shown in Figure 42. This figure compares these results with ADM1 simulation results using the default parameter set (km_su =30 kgCOD.kgCOD-1.d-1 and Ks_su = 0.5 kgCOD.m-3). For both anaerobic inoculums, the first MPR peak was due to a very rapid acidogenesis leading to production of H2, which is rapidly converted into methane. The rest of the MPR curve corresponds to the conversion of VFAs produced into methane. First, the total volume of

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methane produced by glucose degradation in the batch experiments was 38 and 28% lower than the volume of methane produced in the simulation of PS and WAS acclimated inoculums respectively. These differences may be due to stoichiometric issues related to the production of alternative products (ethanol for example) or long-term storage phenomena (at the end of the batch experiment, HPLC analysis detected no residual glucose in the soluble phase of the media). Consequently, in the simulation, the initial concentration of Ssu in batch experiments was modified to induce total methane production consistent with that in the experiments. The glucose acidogenesis rate was significantly overestimated by default ADM1 parameters for PS acclimated sludge and underestimated for WAS acclimated sludge. Nevertheless, in Figure 42, the comparison of the MPR curves due to cellulose, glucose, propionate and acetate addition (main intermediate compounds for carbohydrate degradation) shows that, for two inoculums, the rate-limiting stages in saccharide degradation are cellulose hydrolysis, acetotrophic methanogenesis and, to a lesser extent, propionate acetogenesis for PS acclimated inoculum. Problems in simulating glucose degradation were already highlighted by Batstone et al. (2006). There are many possible reasons for these difficulties including variable stoichiometry (Rodriguez et al., 2006), and pH and H2 regulation. As glucose acidogenesis is not rate limiting, these simulation problems do not arise during modelling of a continuous reactor. However, they can strongly impact the simulation of batch systems.

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Figure 42 : MPR curves obtained for batch experiments related to carbohydrate degradation in PS acclimated inoculum (A) and WAS acclimated inoculum (B).

Simulation of MPR curve due to glucose addition with ADM1 default parameters for acidogenesis.

A B

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3.3.2. Degradation of amino acids (AA) and casein

The MPR curves obtained after addition of an amino acid in WAS and PS acclimated sludge are shown on Figure 43 with the main intermediate compounds for protein degradation. This figure compares these results with simulation results with ADM1 using the default parameter set (km_aa =50 kgCOD.kgCOD-1.d-1 and Ks_aa = 0.3 kgCOD.m-3). For the two inoculums, the first MPR peak was again due to the production of hydrogen and its immediate conversion into methane. This MPR peak was not as clear in the experimental MPR curves.

For this reason, the AA degradation kinetics of both inoculums was overestimated by the model. In contrast to glucose fermentation, the volume of methane produced by AA degradation in batch experiments matches that produced in the simulation of both inoculums.

For the WAS acclimated inoculum, the MPR curve obtained after amino acid addition showed several production peaks. In particular, an additional MPR peak occurred at day 3. This phenomenon can be explained by different amino acid degradation rates. Indeed, Ganesh Kumar et al. (2008) identified lower acidogenesis rates for aromatic AA, which represent about 10% of the amino acids from casein, than for non-aromatic AA. In addition, casein hydrolysis and amino-acid acidogenesis are not rate-limiting stages in the anaerobic degradation of proteins. Acetotrophic methanogenesis was strongly rate limiting for both inoculums and propionate degradation was slightly rate limiting for PS acclimated sludge.

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Figure 43 : MPR curves obtained for batch experiments related to protein degradation in PS acclimated inoculum (A) and WAS acclimated inoculum (B).

Simulation of MPR curve due to amino acid addition with ADM1 default parameters for acidogenesis.

A B

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3.3.3. Degradation of oleate and triolein

MPR curves obtained after addition of oleate to WAS and PS acclimated inoculums are shown in Figure 44. Results showed that with PS acclimated inoculum, total methane production due to oleate degradation was 17% lower in the experiment than in the simulation.

Incomplete COD degradation may be due to the adsorption of this substrate onto biomass aggregates and other components. For PS acclimated inoculum, the MPR dynamics during oleate degradation were quite satisfactorily simulated. But some phenomena were not represented: the first slow increase in MPR and the slow decrease in MPR at the end of the curve which was probably due to low substrate accessibility (hydrophobic material) and the fact that the substrate attached to the glass surface of the reactor. Concerning WAS acclimated inoculum, the degradation kinetics was significantly underestimated. The delay in uptake at the start of the pulse, which could be due to adaptation by the biomass, was again related to issues not included in the model. Figure 44 compares MPR curves due to triolein, oleate and acetate. With PS acclimated sludge, oleate acidogenesis was the only rate-limiting stage in the degradation of triolein. With WAS acclimated sludge, inhibition of triolein degradation occurred and acetotrophic methanogenesis appears to be the rate-limiting stage for oleate degradation.

Figure 44 : MPR curves obtained for batch experiments related to lipid degradation in PS acclimated inoculum (A) and WAS acclimated inoculum (B).

Simulation of MPR curve due to oleate addition with ADM1 default parameters for acidogenesis.

A B

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4. Discussion

ADM1 default parameters from Batstone et al. (2002) was shown to be suitable for acetotrophic methanogenesis if the concentration of free ammonia does not cause significant biomass shifts. However, for acetogenesis and acidogenesis, ADM1 default parameters did not allow accurate simulation of the methane production kinetics related to degradation of propionate and monomers. These stages are more difficult to calibrate than methanogenesis.

Indeed, metabolic pathways are more complex because of the number of potential substrates and the number of potential intermediary compounds (especially for acidogenesis). In addition, simulation results of batch experiments are strongly dependent on the initial concentration of specific biomass. For batch simulations, this initial state is highly sensitive to the quality of the simulation of the anaerobic digester in which the inoculum was sampled. In particular, the biochemical fractionation of the biodegraded COD has a major impact.

To improve calibration of the acetogenic and acidogenic stages, other data than methane production rates during the degradation tests would be useful. To this end, the concentration of VFAs and monomers could be monitored to provide additional data for calibration and to help understand the degradation mechanism.

The relevance of using methane production kinetics resulting from simple monomer degradation can be questioned. Indeed, concerning monomer degradation tests, batch experiments related to the degradation of simple substrates are not suitable for parameter estimation. Inoculums are acclimated to the degradation of complex substrates during acidogenesis and the degradation of pure substrates can thus be considered as not representative of total acidogenic activity. Consequently, the determination of acidogenesis parameters is difficult, even though indispensable for accurate simulation of accumulation of VFA which is tightly linked to process stability. To solve this problem, it would be necessary to run batch degradation tests using the complex substrate to which the inoculum is acclimated. However, this would require previous calibration of acetogenesis and hydrolysis at the very least (default parameters for acetotrophic methanogenesis can be considered as suitable if the concentration of ammonia is not too high). In addition, accurate COD fractionation of the complex substrate would be required. Thereafter, acidogenesis parameters could be estimated so that simulated VFA accumulations matched the experimental data.

Nevertheless, such a method is only able to determine mean acidogenesis parameters but not specific parameters for the acidogenesis of sugars, amino acids, and LCFAs.

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On the other hand, our results highlight the sensitive points related to the use of batch experiments for model calibration. The determination of initial conditions in terms of biomass concentration is crucial. Indeed, maximum growth rates are tightly correlated with the initial concentration of biomass in the inoculum. In this study, this point has been highlighted for propionate acetogenesis. However, the determination of the initial biomass concentration is quite tricky because it requires a lot of analyses using the reactor in which the inoculum was sampled to obtain the overall COD balance and the biochemical fractionation of the degraded COD. Hence, uncertainty in the determination of the initial state for batch experiments leads directly to a proportional uncertainty in determined km values.

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