Model development

6.2.2.1 Model structure

6.2.2.1.1 Structure based on modified ADM1 model

The model structure used in this work was based on the modified model presented in Chapter 5. This model was elaborated from the ADM1 model (Batstone et al., 2002).

The reactions such as hydrolysis, acidogenesis, acetogenesis and methanogenesis are identical to those present in the model proposed in Chapter 5. In order to better represent the hydrolysis limiting effect of WAS anaerobic digestion, we integrated the Contois model to represent the disintegration and hydrolysis steps as described in detail in Chapter 5 (Section 5.2.2.1.1).

However, we showed that the Hill function for modeling the aceticlastic methanogenesis inhibition by ammonia was not appropriated since experimental data of NH4+

and NH3 did not

validate this approach. Moreover, the inhibition threshold varied from 4.5.10^-3 to 6.10^-3 kmole_N.m^-3. These values were very low and were not in agreement with the literature

(Chen et al., 2008). The Hill function was thus changed by the standard non-competitive form.

In the modified model, three coefficients of liquid/gas transfers were used, one for each gas:

kLaCH4, kLaCO2and kLaH2 for methane, carbon dioxide and hydrogen respectively. This was described in Chapter 5 (Section 5.2.2.1.3).

6.2.2.1.2 Two different hydrolysable fractions of particulate organic matter

The previous experimental data, presented in Chapter 4 (Section 4.3.2.2) and Chapter 5 (Section 5.4), on the methane and inorganic nitrogen variations, showed two distinct phases of production between around day 0 to day 6-9 and day 6-9 to day 12-15. The Figure 6.1 presents the methane production from WAS untreated and pretreated at 165°C and 220°C monitored during the second feed of batch reactors (data from Chapter 4, section 4.3.2.2). In the case of untreated and pretreated at 165°C WAS, the methane production showed two phases: the first production phase from day 1 to day 6 corresponds to the degradation of readily hydrolysable organic matter, the second production phase from day 6 to day 12 corresponds to the degradation of slowly hydrolysable organic matter. Thanks to the thermal pretreatment, the slowly hydrolysed organic matter concentration was higher and the uptake rate of the slowly hydrolysable organic matter was improved. Indeed, at a standard sludge retention time of around 15 d, usually applied in full scale digester, the methane specific production was equal to 198 mL_CH4.g_CODintro^-1 for the WAS thermally pretreated against 166 mLCH4.gCODintro-1

for the untreated WAS. With the thermal pretreatment, the organic matter therefore became more accessible that improved the uptake rates and decreased the quantity of slowly hydrolysable organic matter. At 220°C, the production of hardly and slowly biodegradable compounds as melanoidins, strongly decreased the uptake rates of the two hydrolysable organic matter fractions. The final methane production was also decreased.

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0 50 100 150 200 250

0 5 10 15 20

Methane specific production (mLCH4.gCODintro-1)

Time (d) Readily hydrolysed

matter

Slowly hydrolysed matter

Untreated

Pretreated at 165 C Pretreated at 220 C

Figure 6.1: Methane specific production of WAS untreated and pretreated at 165°C and 220°C during the second feed of batch reactors (data from Chapter 4).

Thus, the WAS structure brings more or less accessible organic matter to the anaerobic biomass. In the proposed model, the initial variable Xc is divided into two different fractions:

a readily hydrolysable fraction X_cr and a slowly hydrolysable fraction X_cs. Then, each fraction is degraded into particulate proteins Xpr, carbohydrates Xch and lipids Xli, and into particulate and soluble inert fractions. The Contois function is used to represent the disintegration reaction which is associated to hydrolytic biomass: XXcr for the degradation of readily hydrolysable fraction and XXcs for the degradation of slowly hydrolysable fraction. The disintegration COD fractions of the proposed model are illustrated in Figure 6.2.

To summarise, the new structure of the disintegration step involves some additional parameters: six disintegration biochemical parameters of Xcr and Xcs: km,Xcr, KS,Xcr, kdec,Xcr, km,Xcs, KS,Xcs, kdec,Xcs and two stoichiometric parameters: YXcr, YXcs. These additional process rates of the modified ADM1 can be found in appendix I, where only disintegration, hydrolysis and decay reactions are described.

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Xcr Xcs

X_Xcr1 Contois X_Xcs2

Disintegration

Particulate compounds

Soluble monomers Hydrolysis

Acidogenesis Acetogenesis

Acetate H₂and CO₂

Acetoclastic methanogenesis

Hydrogenotrophic methanogenesis

Methane

Death of biomass

1 Hydrolytic biomass associated to the disintegration step of readily hydrolysable fraction

2 Hydrolytic biomass associated to the disintegration step of slowly hydrolysable fraction Figure 6.2: COD flows for a particulate substrate in dual-pathway disintegration modified ADM1 model structure.

6.2.2.2 Implementation of initial variables

The modeling of anaerobic degradation of the untreated and pretreated sludge samples was carried out on the four successive batch experiments. Initial condition values of the model variables were obtained from the characterization methods applied on WAS samples as already presented in Chapter 5 section 5.2.2.2.

6.2.2.2.1 Fractionation of X_c

In our approach, the particulate organic matter was assumed to be initially present in the both fractions of composite X_cr and X_cs. The concentrations of organic matter present in each fraction were determined from the methane production curves. The content of particulate organic matter involved in the readily hydrolysable fraction is calculated from the produced methane volume during the first phase divided by the produced total methane volume. Then, the content of particulate organic matter involved in the slowly hydrolysable fraction was similarly determined from the produced methane volume during the second phase.

For instance, in the case of the second batch test with the untreated sludge (Figure 6.1), the first phase of methane production represented 78 % of total produced methane and the second

156 phase production represented 22 % of total produced methane. The fed particulate COD which was equal to 3.9553 kg_COD.m^-3, is divided into X_cr equal to 3.0851 kg_COD.m^-3 and X_cs equal to 0.8702 kgCOD.m^-3.

Then, the COD coming from Xcr and Xcs were fractionated following yield coefficients into proteins, carbohydrates, lipids and inerts. These parameters are strongly correlated to the sludge composition and intrinsic characteristics and, as a consequence, they have to be specified for each sludge. However, it is difficult to clearly determine the COD fractions coming from Xcr and Xcs. We assumed that the Xcr yield coefficients, i.e. fch_Xcr, fpr_Xcr, fli_Xcr

and the Xcs yield coefficients fch_Xcs, fpr_Xcs, fli_Xcs, were equal and were calculated from the particulate carbohydrate, proteins and lipids content of the WAS. The yield coefficients were directly worked out from the ratio of the COD concentration of each component over the total COD particulate concentration. The inert composite fractions from X_cr and X_cs, i.e. f_{Xi_Xcr} and fXi_Xcs, were also assumed to be equal since it was not possible to determine the inert matter in the readily and in the slowly hydrolysable fractions. The particulate inerts yield coefficients were determined from the final measured biodegradability (BD) of each batch reactor test.

The inert fraction is 1-BD. Since our objective is to analyze the dynamics of non-inert materials, it was decided for simplicity to set all inert material to the particulate variable and fSi_Xcr and fSi_Xcs were taken equal to 0. The hypothesis was used in Chapter 5. The results are presented in Table 6.1.

Yield of product on substrate (kg_COD.kg_COD^-1)

Table 6.1: Yield of product on substrate determined from experimental data through the four successive degradation batch tests with untreated WAS.

6.2.2.2.2 Implementation of soluble initial variables

For the soluble fraction, initial values of Ssu and Saa were taken equal to the measured sugar and amino acids concentrations at time t = 0. The initial values for the different VFAs (i.e., S_ac, S_pro, S_bu and S_va) were also obtained from the measurements performed just after feeding the reactor. The pH was calculated from the ionised forms of VFAs, bicarbonate, ammonia and cation/anion concentrations. Ammonia (SIN) and bicarbonate (SIC) were measured by Kjeldahl method and TOCmeter, respectively. Anion concentration (San) was taken equal to S_IN according to Rosen and Jeppsson (2002) and cation concentration (S_cat) was adjusted in each case according with experimental pH. Initial values of the different biomass concentrations were determined to fit to the VFAs curves obtained from each batch reactor.

157 Thus the initial conditions of the four successive batch tests were based on the characterization of WAS samples and reactor composition.

6.2.2.2.3 Implementation of biomass initial variables

The biomass initial variables are key parameters in the implementation of ADM1. In the literature, the determination of biomass initial concentrations is usually not explained. In this work, thirteen anaerobic biomass were present and determined from a strategy which is based on the bacterial growth in batch culture. In batch condition, microorganisms have a typical growth curve which is represented by a latency period, an exponential growth phase, a stationary phase and a death phase. Thus, during the modeling of each batch test, the biomass concentrations variations must have the same growth curve as the bacterial growth.

0 2 4 6 8 10 12 14 16 18 20 successive batch tests (A: batch test 1; B: batch test 2; C: batch test 3; D: batch test 4).

In the first degradation batch of untreated sludge, the biomass initial values were arbitrarily chosen. Several simulations of this first batch were carried out until to obtain a typical bacterial growth and similar values between the initial and final biomass concentrations.

Then, the final biomass concentrations of the first batch test were used as initial biomass concentrations for the second batch test. We similarly performed for the next batch tests, i.e.

the batch test 3 and 4. Thus, the biomass values through the modeling of each batch test were predicted by the model. Their variations were dependent on the operating conditions and substrate composition. The behavior of biomass concentrations for untreated WAS through the four successive batch test are illustrated in Figure 6.3.

A B

C D

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