**Chapitre 2 : Evolution des matières organiques en compostage**

**2.1. Etude de la biodégradation aérobie des matières organiques en conditions contrôlées**

**2.1.2. Modélisation de la biodégradation aérobie de déchets organiques : une nouvelle**

**2.1.2.3. Materials and methods**

*2.1.2.3.1. Experimental design *
*Respirometric devices *

Four organic wastes were studied: solid manure from a finishing steer feedlot (MAN); the solid phase of the digestate from the anaerobic treatment of this manure (ADMAN); a biowaste mixed with green waste (BIO); and the solid phase of the digestate from the anaerobic digestion of this latter waste (ADBIO).

To study the aerobic biodegradation of these organic wastes under controlled and optimal
microbial conditions, a respirometric method was used (Tremier et al., 2005). A 1.2 kg sample
of each waste was mixed with 300 g of structuring plastic rings and placed in a respirometric
cell maintained at 40 °C and aerated continuously with an air flow of 70 to 80 L/h as
described in Adhikari et al. (2012). The inlet and outlet aeration air flows were continuously
monitored for CO_{2} concentration using gas analyzers (Multor 610 and Finor). The CO_{2}
production rates were computed by multiplying the dry air molar flow rate by the difference
in CO_{2} concentration between inlet and outlet air flow and was expressed as gC.100g^{-1} initial
TC.day^{-1}. The whole CO2 production was presumed to be due to aerobic mineralization of
organic carbon.

A first set of duplicated experiments performed in respirometric cells degraded each organic waste to determine the total CO2 production and the result reproducibility. The end of the

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biodegradation process was determined for each waste when no additional CO_{2} production
was measured after mixing the cell content. Experiment reproducibility was assessed by
calculating the mean absolute percentage difference for CO_{2} production between duplicates of
each organic waste (Equation 7).

**Equation 7 ** = ∑ ^{|X}_{Y.$ZY5$}^{.$}^{JX}^{5$}^{|}

5 ∗ 100

!

With: : Mean absolute percentage difference in CO2 production between the
duplicates (%) ; P: Number of CO_{2} measurements ; : Measured CO_{2 }value for cell 1 at time
t; : Measured CO_{2 }values for cell 2 at time t.

A second set of experiments was performed by stopping the biodegradation process at
different stages to sample and quantify the OM fractions. Thus, for each waste, five (MAN,
ADBIO) or four (ADMAN, BIO) respirometric cells were monitored in parallel and sampled
at different time intervals for OM analyses. Depending on the shape of the CO_{2} production
rate curve, OM chemical analyses were performed after: 0.4, 1.5, 6.6, 8.9 and 34.6 days of
biodegradation for MAN; 8.8, 13, 25, 33.8 days for ADMAN; 2, 3.8, 6.3 and 22.4 days for
BIO, and; 0.4, 3.7, 7.5, 12.6 and 30 days for ADBIO.

*Chemical analyses *

Overall flowchart of the biochemical fractionation procedure is presented in Figure 13.

Organic waste samples were ground to 2mm after being solidified by immersion in liquid nitrogen (-196°C). The water soluble fraction (SOLH2O) was then extracted from the 2 mm global samples in boiling water during 1 hour at a residue/water ratio of 2/17 (w/w) followed by centrifugation (20 min, 17700 rpm). The non-soluble fraction (NSOL) was then dried at 38°C before further analysis. The OM, C, and N analyses were performed on global (non-water extracted) and NSOL samples.

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**Figure 13 : Flow chart of the biochemical fractionation. The method was adapted from French standard XPU 44-162 **
**(AFNOR, 2009). Dry matter, organic matter and total carbon analysis were performed on the global and on each insoluble **
**fraction. NSOL: Insoluble in hot water fraction; SOLH2O: Soluble in hot water fraction; SOLnd: Soluble in neutral **

**detergent fraction; HEM: Hemicellulose-like fraction; CEL: Cellulose-like fraction; LIC: Lignin and cutin-like fraction. **

The SOLH2O fraction was calculated as the difference between the OM, C or N content of the global and NSOL samples. The dry matter of the global samples was determined by drying at 80°C to constant weight. The OM content was determined as loss by ignition at 250°C for 2h followed by 550°C for 3h. The Total carbon (TC) content was determined by oxidizing C to CO2 at 1 800 °C and CO2 was detected by a thermal detector (FLASH 2000 Organic Elemental Analyzer, THERMO SCIENTIFIC). The NSOL fraction was characterized as SOLnd, hemicellulose, cellulose and lignin, using a procedure derived from the Van Soest method (AFNOR, 2009). To obtain the four fractions, successive extractions were achieved:

hot extraction in a neutral detergent (1.86% disodium ethylene diamine tetraacetate, 3%

aqueous solution of sodium dodecyl sulfate, 0.68% decahydrate sodium tetraborate, 0.45%

disodium hydrogen phosphate and 1.0% triethylene glycol); hot extraction in a weak acid (2.6% sulfuric acid and 2.0% centrimonium bromide), and ambient extraction in a strong acid (72 % sulfuric acid). The obtained fractions were analyzed using an elemental analyzer (FLASH 2000 Organic Elemental Analyzer, THERMO SCIENTIFIC) to quantify TC and were expressed as a percentage of the initial TC.

The microbial biomass X1 and X2 were not specifically measured (initial values were estimated by fitting on the CO2 production rates; see paragraph 3.2.2). The total microbial biomass generally represents only a very small portion of TC in organic wastes: Gattinger et

NSOL = HEM+ CEL+ LIC

SOLnd HEM + CEL + LIC

Neutral detergent extraction

HEM CEL + LIC

Cold strong acid extraction

CEL LIC

Hot weak acid extraction Global sample (grounded to 2mm) = SOLH2O + NSOL

SOLH2O 100 – NSOL

Hot water extraction (100°C, 1 h) + centrifugation (20 min, 17700 rpm)

80 al. (2004) found a total microbial biomass of 2.5% TC in cattle manure and 0.5% TC in a biowaste. The microbial biomass was thus presumed to have little influence on the C content measured within the Van Soest fractions. The initial characteristics of the organic wastes are summarized in Tableau 8.

**Tableau 8 : Initial characteristics measured on the four experimental wastes. MAN: finishing steer solid manure. ADMAN: **

**solid phase of the finishing steer solid manure anaerobic digestate. BIO: biowaste and green waste mixture. ADBIO: solid **
**phase of the digestate from the biowaste and green waste mixture. DM: Dry matter; OM: Organic matter; TC: Total **
**Carbon; TN: Total Nitrogen; LIC: Lignin and cutin-like fraction; CEL: Cellulose-like fraction; HEM: Hemicellulose-like **
**fraction; SOLnd: Soluble in neutral detergent fraction; SOLH2O: Soluble in hot water fraction. **

*2.1.2.3.2.Model initialization and calibration *
*Initialization of the model compartments *

The HEM, CEL and LIC fractions were measured in the laboratory using the experimental protocol described above. The SOLnd-R fraction was initially set at 0 as little if any recalcitrant compounds were presumed present in this fraction before starting the aerobic degradation process. Thus, the SOLnd-B fraction in the model was initially set equal to that of the experimental compartment SOLnd. The SOLH2O fraction was experimentally obtained by mass balance and corresponded to the sum of SOLH2O1, SOLH2O2, X1 and X2. The SOLH2O1 / SOLH2O2 ratio and the initial microbial biomasses X1 and X2 were optimized, as described below.

*Optimization procedure *

Linear regression after logarithmic transformation was used to directly estimate KHEM, KCEL

and KLIC from the measured evolution of their respective fractions during biodegradation. The others parameters, i.e. the SOLH2O1 / SOLH2O2 ratio and the initial microbial biomasses X1

and X2, were optimized from the measured CO2 production rate and the SOLnd fraction dynamics, by minimizing the total root mean squared error (RMSEt) as defined by Eq 8.

**Equation 8 ** NU] =^{^}
measured value of the SOLnd fraction (gC.100g^{-1 }initial TC) at time t ; rq_{p}: simulated value of

DM (%) OM (% DM) TC (g.kg^{-1} OM) TN (g.kg^{-1} OM) SOLH2O (% TC) SOLnd (% TC) HEM (% TC) CEL (% TC) LIC (% TC)

MAN 31.2 84.3 534 44.2 26.0 12.2 18.1 28.6 15.2

ADMAN 26.2 77.7 511 39.8 13.2 20.0 16.8 30.2 19.7

BIO 39.3 61.9 626 28.1 7.30 21.7 17.5 21.1 32.5

ADBIO 39.9 52.5 688 26.7 0 18.5 12.0 33.6 35.9

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the SOLnd fraction (gC.100g^{-1 }initial TC) at time t ; s: number of sample SOLnd fraction
measurements.

The minimization was performed in four steps to reduce the risk of determining local minima
for RMSEt. The first step consisted in optimizing the SOLH2O_{1 }/ SOLH2O_{2} ratio and the
initial microbial biomasses (X1 and X2), with all others parameters kept constant. Optimized
values were then used in the second step that consisted in optimizing the microbial growth
and death rate parameters (μ_{1}, μ_{2}, b_{1}, b_{2}), with all other parameters kept constant. Optimized
values were used in the third step that consisted in optimizing the assimilation yields
constants (Y1 and Y2) and the f1 ratio, with all other parameters kept constant. Optimized
values were then used in the final optimization step that consisted in optimizing all the
parameters simultaneously, including those which were not optimized in the previous steps.

Parameters values were constrained to a range obtained in the literature (presented and
discussed in section 4.2.2) to avoid aberrant parameter values and the sum of the initial
compartments of the model was constrained to 100 gC.100g^{-1} initial TC. These threshold
values are presented in the Tableau 9 and the sum of the initial compartments of the model
was constrained to 100 gC.100g^{-1} initial TCParameters optimization was performed with the
R software using the Nelder-Mead algorithm (Nelder & Mead, 1965).

**Tableau 9 : Calibration procedure and constraints applied to the parameters. Parameters meanings are described in **
**Tableau 7. **

**Parameters** **Step 1** **Step 2** **Step 3** **Step 4**

SOLH2O1/SOLH2O2 SOLH2O1 + SOLH2O2 = SOLH2O - - -

X2 [0:1.75] - - -

X1 [0:1.75] - - -

KSOLnd-B - - - [0:0.12]

Kh - - - [0:20]

KMH - - - [0:20]

µ_{1} - [0:5] - [0:5]

KB1 - - - [0:1.5]

b1 - [0:5] - [0:5]

µ_{2} - [0:10] - [0:10]

KB2 - - - [0:1.5]

b2 - [0:5] - [0:5]

Y1 - - [0.6:0.7] [0.6:0.7]

Y2 - - [0.6:0.7] [0.6:0.7]

f1 - - [0.1:0.45] [0.1:0.45]

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*2.1.2.3.3.Evaluation of the model performance *

The performance of the model was evaluated by comparing the predicted versus measured values of all measured variables (eg. dCO2, SOLH2O, SOLnd, HEM, CEL and LIC) by calculating the RMSE and the mean absolute percentage error (MAPE), using respectively Eq 9 and Eq 10. The former is basically the standard deviation of the difference between the predicted and measured values and is expressed in the same unit as the variable, whereas the latter is the mean relative difference between the predicted and measured values and is expressed as a percentage.

**Equation 9 ** NU = ^^{∑}^{u}^{$f.}^{F}_{v}^{$}^{JF}^{t ²}^{a}

**Equation 10 ** wxU =_{v}∑ ^{|F}^{$}_{F}^{JF}^{t|}^{a}

$

v! 100

With: :: measured value of the fraction (or production rate) X (X representing CO2

production rate (dCO_{2}), SOLH2O, SOLnd, HEM, CEL or LIC) at time t ; :y_{p}: simulated value
of the fraction (or production rate) X at time t ; z: number of fraction measurements for the
fraction (or production rate) X; : : mean value of the measured fraction (or production rate) X
(X representing dCO2, SOLH2O, SOLnd, HEM, CEL or LIC).

*2.1.2.3.4.Sensitivity analysis *

The model sensitivity to variation in the parameters values and initial fractions values has been estimated by computing the sensitivity coefficients, as described in Zhang et al. (2012).

Basically, it consists in performing new simulations by varying successively each parameter
or initial fraction by +20 % of its default value. Influence of these variations was tested
against cumulated amounts of CO2.Default parameters values (or initial fractions) were the
optimal ones for MAN (Tableau 7). As the sum of initial fractions was constrained to 100
gC.100g^{-1 }initial TC, each increase of 20% in the initial value of a fraction was associated
with an equivalent decrease in each of the other fractions (excepted X1 and X2). As SOLnd-R
is assumed to be initially null (paragraph 3.2.1), the sensitivity analysis was not performed on
this fraction.

**Equation 11 ** N { =_{v}∑ |^{#+}^{5} ^{},}•}_{#+}^{$}^{J#+}_{5} _{},}•}^{5} ^{}9 •%,}•}^{$}

$ |

v! × 100

With: S(p): sensitivity coefficient for parameter or initial fraction p (%); ( {, {0 :
cumulated amounts of CO2 (gC.100g^{-1} initial TC) as simulated with the optimal parameters
(or initial fractions) (Tableau 7); ( { + 20% : cumulated amounts of CO_{2} (gC.100g^{-1}
initial TC) as simulated with the parameter (or initial fraction) p 20 % higher than its optimal
value (all other parameters and initial fractions being optimal).

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