Sensitivity analysis

km,Xcr, km,Xcs, km,pro, km,ac could be considered as the most sensitive parameters since they were main modified parameters for fitting well the experimental data of untreated WAS degradation. Thus, a sensitivity analysis was carried out to determine effects of these parameter variations on the acetate and propionate kinetics and on the methane production kinetic. The sensitivity of decay rates of these biomass were also studied since the initial values were modified compared with the standard ADM1. The batch test 2 data were arbitrarily chosen to perform the sensitivity analysis. Thus, eight parameters (km,Xcr, km,Xcs, k_m,pro, k_m,ac, k_dec,Xcr, k_dec,Xcs, k_dec,pro, k_dec,ac) were changed with a variation of ± 50 % compared with the initial value. The model parameters were independent and they were investigated individually. Twenty seven simulations were run at each of those values to generate new acetate, propionate and methane profiles. The results are presented from Figure 6.7 to Figure 6.10. Sensitivity coefficients, σ_+∆p and σ_-∆p, were determined for each parameter changes in order to evaluate the deviation involved by a change of ± 50 %. The calculation was in agreement with the expression of the variance as following:

∫

= _±

∆

±

tf

ion concentrat initial with

simulation

p X X

n ₀( ^50% )

σ 1

Where,

σ_±∆p is the sensitivity coefficient for a positive or a negative variation of 50 % of model parameters,

X is the simulated variable with initial parameter or when the parameter was changed by a variation of ±50 %,

n is the sample size,

tf is the experiment duration.

The sensitivity coefficient is expressed in kg_COD.m^-3 for acetate and propionate concentration variations and in mL for the methane productions. The effect of the parameter change is significant when an important deviation is observed between the simulation with initial values and the simulation with a variation of ± 50 %. The threshold is therefore arbitrarily chosen.

166

Figure 6.7: Sensitivity of acetate, propionate concentrations and methane production in batch test 2 to X_cr disintegration parameters. (red circles and blue thin dotted line: experimental data points; red thin plain line: simulation with initial values; red thick wide dotted line:

simulation with an increment of +50 % on model parameter values; blue thick small dotted line: simulation with a variation of –50 % on model parameter values).

167

Figure 6.8: Sensitivity of acetate, propionate concentrations and methane production in batch test 2 to Xcs disintegration parameters. (red circles and blue thin dotted line: experimental data points; red thin plain line: simulation with initial values; red thick wide dotted line:

simulation with an increment of +50 % on model parameter values; blue thick small dotted line: simulation with a variation of –50 % on model parameter values).

168

Figure 6.9: Sensitivity of acetate, propionate concentrations and methane production in batch test 2 to propionate degradation parameters.

(red circles and blue thin dotted line: experimental data points; red thin plain line: simulation with initial values; red thick wide dotted line: simulation with an increment of +50 % on model parameter values; blue thick small dotted line: simulation with a variation of –50

% on model parameter values).

169

Figure 6.10: Sensitivity of acetate, propionate concentrations and methane production in batch test 2 to acetate degradation parameters.

(red circles and blue thin dotted line: experimental data points; red thin plain line: simulation with initial values; red thick wide dotted line: simulation with an increment of +50 % on model parameter values; blue thick small dotted line: simulation with a variation of –50

% on model parameter values).

170 6.3.2.1 Acetate concentration variation

The most sensitive parameters on the predicted acetate concentration are km,Xcr, km,ac, and kdec,ac. The effect of the parameter change is very significant when the sensitivity coefficient value is higher than 0.06 kg_COD.m^-3. No significant effects are observed when the sensitivity coefficient value is inferior to 0.01 kgCOD.m^-3. A ± 50 % change of acetate degrader kinetic parameters strongly modified the dynamic of acetate concentration (Figure 6.10). It is coherent since these parameters drive the degradation rates of acetate. The kinetic parameter of readily hydrolysable fraction degraders (km,Xcr) has also an effect on the acetate degradation rate (Figure 6.7). Indeed, as acetate is the main intermediate coming from the degradation of Xcr, a decrease of 50 % of this parameter reduced the degradation rate of Xcr and the acetate production. As the acetate degradation rate remained similar, a low acetate increase was observed. Thus, the parameter km,Xcr must be well defined for representing the behavior of acetate kinetic. The decay rates for Xcr and Xcs are not sensitive (Figures 6.7 and 6.8).

6.3.2.2 Propionate concentration variation

From the results of the sensitivity analysis on propionate dynamic, a value of sensitivity coefficient inferior to 0.015 kg_COD.m^-3 can be considered as non significant whereas a value superior to 0.04 kg_COD.m^-3 indicated a very important effect. The kinetic parameter of the slowly hydrolysable fraction degraders (km,Xcs) has a significant effect on the propionate variation since a decrease of this parameter leads to a sensitivity coefficient equal to 0.044 kgCOD.m^-3 (Figure 6.8). We observed a lower propionate accumulation since a low km,Xcs

did not allow a complete degradation of X_cs. This confirms that the implementation of X_cs is a good strategy to represent a COD flow that corresponds to a degradation of slowly hydrolysable organic matter between day 10 to day 20. The propionate dynamic is strongly dependent on kinetic parameters, km,pro, and kdec,pro, as can be observed in Figure 6.9.

6.3.2.3 Methane production variation

The ± 50 % variations of parameters on predicted methane productions showed that the parameters can be considered as significant when the sensitivity coefficient is superior to 150 mLCH4. In this way, the maximum specific uptake rates of each variable have an effect on the methane production dynamic. k_m,Xcr drives the degradation of the main organic matter fraction. The decrease of k_m,Xcr involved a slower degradation rate of the readily hydrolysable fraction which indicates that the limiting effect of hydrolysis is amplified. Indeed the methane production shows a delay since the higher methane production rate is reached at day 8. The variation of km,Xcs and kdec,Xcs impacted the final value of predicted methane volume. A decrease of k_m,Xcs or an increase of k_dec,Xcs reduced the activity of X_cs degraders and thus the fraction X_cs was not degraded which involves that the second phase of methane production was not observed (Figure 6.8). Thus the implementation of a slowly hydrolysable fraction Xcs

in order to represent the second phase of methane production is succeeded. The kinetic parameter changes of acetate and propionate degraders showed that the propionate degradation is slow and mainly impacts the second phase of methane production and the acetate degradation is fast and mainly impacts the first phase of methane production (Figures 6.9 and 6.10). This confirms the results described in section 4.3.2.2.

171 Table 6.4 summarises the significant effect of kinetic parameter changes on the variations of acetate, propionate and methane production. These results showed that the simulated methane production kinetic strongly depends on km,Xcr, km,Xcs, km,pro, km,ac, kdec,Xcs, kdec,pro. It confirms that the particulate organic matter disintegration and propionate and acetate degradation are important conversion steps during the WAS anaerobic digestion.

Kinetic

1 Value in parenthesis is the variation applied on the kinetic parameter +++: significant effect

0: no significant effect

Table 6.4: Significant effect of kinetic parameter changes on the dynamic evolution of acetate, propionate and methane production.