Model development

Since the late 1970’s, many models were developed to describe and predict the behavior of various organic wastes during composting. As noted by Ndegwa et al. (2000), composting models are generally based on three main considerations : (1) Mass balances (solid, OM and water); (2) energy and heat balances, and; (3) microbial kinetics. In modeling the composting of an organic waste, microbial activity plays a key role in heat generation and it must therefore be accurately predicted. Indeed, in many composting models, biologically generated heat is calculated from respiration kinetics (O₂ consumption rates or CO₂ production rates) (Kaiser, 1996; Nakasaki et al., 1987). Nevertheless, the level and extent of microbial activity must first be determined from the biodegradability of the waste, or the evolution of its different OM fractions. Only then can heat generation be estimated. The present study will therefore only focus on the fundamentals of organic waste aerobic biodegradation kinetics, setting aside energy and heat balances of the whole composting model. The biodegradation kinetics in the developed model will pertain to the evolution of the OM fractions, along with microbial growth and respiration rate. The results of such microbial activity model can later

72 on be integrated into a more global composting model also computing heat generation and moisture evaporation.

2.1.2.2.1.State of the art for the modeling of OM evolution under aerobic biodegradation

Respiration can provide a reliable, repeatable and scientifically sound assessment of microbial activity (Gomez et al., 2006). Respiration rates are usually calculated as a function of the organic waste degradation rate, using first order (Das & Keener, 1997; Higgins & Walker, 2001) or Monod-type equations (Kaiser, 1996; Liang et al., 2004; Oudart et al., 2012;

Stombaugh & Nokes, 1996; Tremier et al., 2005; Zhang et al., 2012). By integrating microbial basic principles, the Monod-type approach permits to develop more universal models than that of first order. Generally, first order constants apply only to specific organic waste and most of the Monod-type approaches are based on single microbial population. However some recent respiration kinetics studies for the aerobic biodegradation of diverse organic wastes showed that several successive respiration peaks could occur and these were not explained by variations in the environmental conditions such as temperature or moisture (Dabert et al., 2010; Esteve et al., 2009). Also, Esteve et al. (2009) showed that various microbial communities could alternate during biodegradation, although most of the models considering a single population of microorganisms growing on a single-pool waste were not adapted for the simulation of these double-peak respiration curves.

Moreover, substrate hydrolysis by extracellular enzymes was suggested to be an important process limiting substrate degradation, as shown in the modeling of activated sludge treatments by Insel et al. (2002). Thus, substrate hydrolysis and substrate assimilation must be considered as being different processes. According to Sole-Mauri et al. (2007), only few recent models have explicitly included the equations of substrate hydrolysis (Oudart et al., 2012; Sole-Mauri et al., 2007; Tremier et al., 2005; Zhang et al., 2012). To consider substrate hydrolysis and substrate assimilation in aerobic biodegradation models, an appropriate OM fractionation of the waste has to be proposed. Evolutions of OM fractions have to be linked to different stages of biodegradation. The assessment of the biodegradation stage and the quantification of the biodegradable fractions was proposed through different methods among which: fractionation of the Chemical Oxygen Demand (COD) for Activated Sludge Models (Gujer et al., 1999) and for composting Tremier et al. (2005); and solubility of organic matter in diverse extraction solvents (Esteve et al., 2009; Zhang et al., 2012). Aerobic biodegradation models based on the evolution of OM fractions, expressed as COD, are interesting because of

73 the direct link between degradation and O₂ consumption rates. Accordingly, Esteve et al.

(2009) linked O₂ consumption rate to the chemical composition of different OM fractions during the biodegradation of organic waste which permitted to propose a biodegradation model including a solid fraction of OM, two water soluble fractions and two microbial communities, expressed as COD compartment. The weakness of this model is that these OM fractions are experimentally difficult to measure and do not predict variations in the agronomic quality of the compost. Only a few composting models have an appropriate OM characterization predicting the agronomic evaluation of the compost (Kaiser, 1996; Sole-Mauri et al., 2007; Zhang et al., 2012).

Zhang et al. (2012) developed an innovative model with the explicit aim of predicting compost quality in regards to agronomic uses. In this model, OM was divided into six fractions, where five solid fractions corresponded to the biochemical fractions described using the Van Soest fractionation method. Their evolution was calculated using first order kinetics, thus supplying a sixth fraction: the water soluble OM fraction. The evolution of this OM fraction available for microbial growth was calculated using the Monod-type approach. Only one microbial population was represented in this model. Calibrated using experimental data on each OM fraction and the total carbon (TC) degradation rate, the model was validated with a new dataset by Lashermes et al. (2013). The model predicted relatively well the evolution of the OM fractions during composting but was not validated with respect to microbial growth.

Moreover, the experimental data set for validation only concerned four dates along 100 days composting and no experimental CO2 measurements were available for a relevant validation of the respiration rate. Authors also underlined that the fractionation of the water soluble organic matter would have to be improved.

The aim of the present work was then to couple the organic matter fractionation approach proposed by Zhang et al. (2012) and the respiration approach proposed by Esteve et al. (2009) to develop and calibrate a model capable of predicting the optimal biodegradation point and OM quality for various types of organic wastes.

2.1.2.2.2.Mathematical development of the OM-biodegradation model

Figure 12 shows the general scheme of the biodegradation model developed and Tableau 7 describes the OM fractions and kinetics parameters used.

74

Figure 12 : General scheme of the biodegradation model. Model fractions and parameters are described in Tableau 7.

The water non-soluble OM fraction was divided into five compartments (R, SOLnd-B, HEM, CEL and LIC) as shown in Figure 12, corresponding to the fractions measured by laboratory analyses using the standard Van-Soest extraction method recognized in France (AFNOR, 2009). As for the Zhang et al. (2012) model, the soluble OM fraction extracted using a neutral detergent (SOLnd) is divided into an easily biodegradable fraction (SOLnd-B) and a recalcitrant fraction (R). Only the B is hydrolyzed, whereas the SOLnd-R is assumed inert. The hydrolyzed products of these water non-soluble OM fractions contribute to the water soluble OM fraction. As observed during biodegradation by Esteve et al. (2009) and Dabert et al. (2010) using a high performance size exclusion chromatography system, the variation in particle size distribution of the soluble carbohydrates is linked to respiration kinetics. Thus, the hot water soluble OM fraction (SOLH2O) of the present model was divided into two compartments, SOLH2O2 and SOLH2O1, which correspond respectively to heavy molecules requiring further hydrolysis and light molecules directly available for microbial degradation and growth. Two biomass compartments, X1 and X2, were included in the present model, corresponding respectively to a slow-growing biomass and a fast-growing biomass. As proposed by Sole-Mauri et al. (2007), fungi have lower growth rates than bacteria. Furthermore, during biodegradation of organic waste, Dabert et al. (2010) measured

SOLnd-R SOLnd-B HEM CEL LIC

SOLH2O₁ SOLH2O₂

X₂ X₁

O₂

O₂

O₂

CO₂ CO₂

CO₂

K_SOLnd-B . SOLnd-B K_HEM. HEM K_CEL. CEL K_LIC. LIC

K_h, K_MH,f(X₂,SOLH2O₂)

1/Y2 1/Y1

1/Y₁ - 1 1/Y₂ - 1

1- f₁ b₂.X₂

f₁

b₁.X₁

µ₂, K_B2,f(SOLH2O₁) µ₁, K_B1,f(SOLH2O₁)

75 a maximum concentration of bacteria occurring before that of fungi. Thus X₁ might be mostly fungi whereas X₂ might be mostly bacteria.

Tableau 7 : Model compartments, parameters and values used for calibration. 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. TC: Total Carbon.

In this model, two hydrolysis steps are proposed. The first step concerns the solid OM fractions which are assumed to be hydrolysed through enzymatic activity of biomass X₁. Nevertheless, in order to simplify the model and the determination of model parameters, first order kinetics are described, and not microbial kinetics, with different rate coefficients for each compartment (Eq 1).

Equation 1 ^"#$

"% = −& × (

with i representing respectively SOLnd-B, HEM, CEL and LIC. This hydrolysis leads to the formation of heavy OM molecules soluble in hot water (SOLH2O2).

The second hydrolysis degrades, through the action of biomass X2, the soluble OM fraction SOLH2O2 into low-size molecules (SOLH2O1). This hydrolysis is described by a Monod-like equation limited by the substrate-to-biomass ratio (first term of Eq 2).

Model compartments Descritpion Unit MAN ADMAN BIO ADBIO

SOLnd-R Soluble in neutral detergent (Recalcitrant) gC.100g^-1 initial TC 0 0 0 0

SOLnd-B Soluble in neutral detergent (Biodegradable) gC.100g^-1 initial TC 12.2 20.0 21.7 18.5

HEM Hemicellulose-like gC.100g^-1 initial TC 18.1 16.8 17.5 9.80

CEL Cellulose-like gC.100g^-1 initial TC 28.6 30.2 21.1 33.6

LIC Lignin-like gC.100g^-1 initial TC 15.2 19.7 32.5 35.9

SOLH2O2 Soluble in boiling water (high molecular weight) gC.100g^-1 initial TC 21 11 4.0 0.80 SOLH2O1 Soluble in boiling water (low molecular weight) gC.100g^-1 initial TC 3.2 1.2 3.1 2.0

X2 Biomass (fast growing) gC.100g^-1 initial TC 0.7 0.5 0.1 0.2

X1 Biomass (slow growing) gC.100g^-1 initial TC 0.6 0.5 0.1 0.2

KSOLnd-B Rate coefficient for SOLnd-B degradation day^-1 0.061 0.092 0.088 0.092

KHEM Rate coefficient for HEM degradation day^-1 0.034 0.039 0.057 0.0054

KCEL Rate coefficient for CEL degradation day^-1 0.046 0.057 0.035 0.021

KLIC Rate coefficient for LIC degradation day^-1 0.010 0.029 0.012 0.0093

Kh Rate coefficient for SOLH2O2 hydrolysis day^-1 4.7 5.0 12 5.0

KMH Michaelis-menten limitation coefficient for SOLH2O2 hydrolysis dimensionless 1.8 18 2.0 4.0 µ1 Specific maximum growth rate for the microbial biomass X1 day^-1 5.3 4.8 2.8 4.5 KB1 Monod saturation coefficient for the microbial biomass X1 gC.100g^-1 initial TC 0.49 0.38 0.17 0.15

b1 Constant for the microbial biomass X1 death day^-1 0.53 0.20 0.85 1.2

µ2 Specific maximum growth rate for the microbial biomass X2 day^-1 6.5 8.1 2.0 3.0 KB2 Monod saturation coefficient for the microbial biomass X2 gC.100g^-1 initial TC 0.54 0.15 0.14 0.22

b2 Constant for the microbial biomass X2 death day^-1 0.65 1.3 0.75 0.60

Y1 Growth yield for the microbial biomass X1 dimensionless 0.65 0.70 0.70 0.60

Y2 Growth yield for the microbial biomass X2 dimensionless 0.70 0.70 0.60 0.60

f1 Part of the dead biomass X1 recycled into SOLnd-R dimensionless 0.38 0.45 0.40 0.40

76 kinetics, taking into account biomass growth and death, (Eq 3).

Equation 3 ^"F$

"% = < ×₇ ^{*+,- +.}

=G9*+,- +.× : − H × : with I = 1 or 2 The production of CO₂ is generated by the respiration of the unassimilated portion of the substrate SOLH2O₁ plus part of the dead biomass X₁, leading to the Equation 4.

Equation 4 ^"#+5

"% = ^J;_;.^.× < ×_7=.^{*+,- +}_{9*+,- +}^. _.× : + ^J;_;5⁵× < ×

*+,- +.

7=59*+,- +.× : + 1 − K × H × :

Formed during biodegradation, the recalcitrant fraction of the soluble neutral detergent OM is the residual part of the dead biomass X1 (Eq 5).

Equation 5 "*+, "JL

"% = K × H × :

The dead biomass X₂ is recycled into the SOLH2O₂ fraction leading to Equation 6.

Equation 6 "*+,- +5 (including the both biomasses) which require initialization and 15 kinetics parameters. These parameters are:

• 4 first order coefficients for solid OM hydrolysis (Ki)

• 2 parameters describing the soluble OM hydrolysis (K_h and K_MH)

• 6 parameters for microbial kinetics (µ_i, b_i and K_Bi)

• 2 assimilation yields (Yi)

• 1 coefficient for the recycling of the dead biomass X1 in SOLnd-R.

77 Fractions initialization is based on the initial characterization of the organic waste. Parameter identification was achieved by fitting with measurement of the evolution of the OM fractions during biodegradation.

Microbial kinetics are known to vary with temperature (Richard & Walker, 2006). In composting models, temperature functions are usually included to account for temperature variations that may limit microbial growth and/or activity (Hamelers, 2004). The present model considers optimal kinetics defined at optimal constant temperature point for biodegradation, as defined by Tremier et al. (2014). When included in a whole composting model, this biodegradation model will thus be corrected by temperature limiting functions, as the one proposed by Rosso et al. (1995). Previous work published by Tremier et al. (2005) proved that a biodegradation model established at the optimal temperature of 40°C was valid for other temperature using the Rosso temperature correction model.