Alexandre Boutoute

Nathalie Di

Miceli Raimondi

Richard Guilet
email: richard.guilet@iut-tlse3.fr

Michel Cabassud

Corrado Amodeo

Hassen Benbelkacem

Pierre Buffiere

Ruben Teixeira Franco

Stéphane Hattou

Development of a Sensitivity Analysis method to highlight key parameters of a dry Anaerobic Digestion reactor model

Keywords: Dry anaerobic digestion, Modelling, Sensitivity analysis, Definitive screening design method

d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Anaerobic digestion (AD) is known as an alternative way to treat and to recycle organic wastes while producing biogas. AD is a natural process carried out by anaerobic microorganisms and led by biological and physicochemical phenomena. Biogas is mainly composed of CH4 and CO2 and is the result of the organic matter breakdown through a cascade of enzymatic reactions namely hydrolysis, acidogenesis, acetogenesis and methanogenesis [START_REF] Batstone | Anaerobic Digestion Model N°1 (ADM1)[END_REF]. Various anaerobic process technologies exist but due to the coupling between the phenomena involved and the high sensitivity of the microbial flora, these processes may present a low robustness [START_REF] Chen | Toxicants inhibiting anaerobic digestion: A review[END_REF][START_REF] André | Solid anaerobic digestion: State-of-art, scientific and technological hurdles[END_REF].

The mathematical modelling of AD process enables to understand and to describe biological, as well as mass transfer phenomena. Models are also predictive tools used to design processes and to optimise process control. In order to propose a generic model that would be a common basis, the IWA Task Group for Mathematical Modeling of Anaerobic Digestion Processes developed the Anaerobic Digestion Model No.1 (ADM1) [START_REF] Batstone | Anaerobic Digestion Model N°1 (ADM1)[END_REF]. The ADM1 is a very complete structured biological model that considers the major physical and biochemical mechanisms describing the dynamics of 24 species including 19 bioconversion processes associated to 80 kinetic and mass transfer parameters. These parameters compose the set of input model parameters that have to be defined to correctly describe the dynamic behaviour of a particular digestion medium in a given digester technology. The ADM1 was initially based on the AD of sewage sludge [START_REF] Batstone | Anaerobic Digestion Model N°1 (ADM1)[END_REF]. Since its publication, modified ADM1 and adapted ADM1 models have emerged in order to consider specific processes taking place during the digestion of complex substrates such as organic substrate with high solid content [START_REF] Abbassi-Guendouz | Total solids content drives high solid anaerobic digestion via mass transfer limitation[END_REF][START_REF] Pastor-Poquet | High-solids anaerobic digestion model for homogenized reactors[END_REF][START_REF] Zhao | Modified Anaerobic Digestion Model No. 1 for modeling methane production from food waste in batch and semi-continuous anaerobic digestions[END_REF][START_REF] Tartakovsky | Anaerobic digestion model No. 1-based distributed parameter model of an anaerobic reactor: II. Model validation[END_REF][START_REF] Liotta | Modified Anaerobic Digestion Model No.1 for dry and semi-dry anaerobic digestion of solid organic waste[END_REF]. Various works have also discussed the development of simplified ADM1 models [START_REF] Bollon | Development of a kinetic model for anaerobic dry digestion processes: Focus on acetate degradation and moisture content[END_REF][START_REF] Donoso-Bravo | Model selection, identification and validation in anaerobic digestion: A review[END_REF][START_REF] Arzate | Anaerobic Digestion Model (AM2) for the Description of Biogas Processes at Dynamic Feedstock Loading Rates[END_REF][START_REF] Pommier | A logistic model for the prediction of the influence of water on the solid waste methanization in landfills[END_REF][START_REF] López | A simple kinetic model applied to anaerobic digestion of cow manure[END_REF][START_REF] Hassam | A generic and systematic procedure to derive a simplified model from the anaerobic digestion model No. 1 (ADM1)[END_REF]. Although these models are less generic, they can be sufficient to model particular AD operations, reducing the number of parameters to be calibrated.

Nevertheless, whatever the complexity of the model is, it is interesting to know which parameters have the most influence on model outputs to obtain a reliable model while reducing the estimation effort [START_REF] Fortela | Computational evaluation for effects of feedstock variations on the sensitivities of biochemical mechanism parameters in anaerobic digestion kinetic models[END_REF]. In some adapted ADM1 models, parametric identification is typically based on the knowledge of the researcher who selects the set of parameters to be calibrated among the existing parameters in the ADM1 [START_REF] Abbassi-Guendouz | Total solids content drives high solid anaerobic digestion via mass transfer limitation[END_REF][START_REF] Pastor-Poquet | High-solids anaerobic digestion model for homogenized reactors[END_REF]. Also, sensitivity analysis consisting in the investigation of the change in model outputs resulting from a change in model parameters can be helpful to select the most relevant parameters to be identified [START_REF] Zhao | Modified Anaerobic Digestion Model No. 1 for modeling methane production from food waste in batch and semi-continuous anaerobic digestions[END_REF][START_REF] Tartakovsky | Anaerobic digestion model No. 1-based distributed parameter model of an anaerobic reactor: II. Model validation[END_REF][START_REF] Donoso-Bravo | Identification in an anaerobic batch system: global sensitivity analysis, multi-start strategy and optimization criterion selection[END_REF][START_REF] Schroyen | Modelling and simulation of anaerobic digestion of various lignocellulosic substrates in batch reactors: Influence of lignin content and phenolic compounds II[END_REF][18]. Sensitivity analysis can also help to verify the validity of model assumptions and to check the identifiability of the parameters [START_REF] Pastor-Poquet | Assessing practical identifiability during calibration and cross-validation of a structured model for high-solids anaerobic digestion[END_REF]. The most widely used sensitivity analysis technique, especially for adapted ADM1 model, is the local sensitivity method that consists in analysing how a small perturbation near a central parameter value influences a model output [START_REF] Zhao | Modified Anaerobic Digestion Model No. 1 for modeling methane production from food waste in batch and semi-continuous anaerobic digestions[END_REF][START_REF] Tartakovsky | Anaerobic digestion model No. 1-based distributed parameter model of an anaerobic reactor: II. Model validation[END_REF]. The drawbacks of this method are the small range of variation of the parameters and the fact that interaction effects are not considered [START_REF] Donoso-Bravo | Model selection, identification and validation in anaerobic digestion: A review[END_REF]. Because of the complexity of the phenomena involved during AD, the values of the kinetic and mass transfer parameters strongly depend on a large number of conditions such as inoculum, nature of the substrate [20], temperature [START_REF] Buffière | The hydrolytic stage in high solids temperature phased anaerobic digestion improves the downstream methane production rate[END_REF], water content of the media [START_REF] Pommier | A logistic model for the prediction of the influence of water on the solid waste methanization in landfills[END_REF] or mixing efficiency [START_REF] Van Hulle | Importance of scale and hydrodynamics for modeling anaerobic digester performance[END_REF]. This is accentuated in the case of simplified models where phenomena are described through fewer parameters. Thus, it can be necessary to conduct sensitivity analysis on large ranges of parameter values. Some authors have sought to measure the effect of large parameter variations by changing the value of each parameter "one at a time" (OAT) while leaving the other fixed and calculating the relative difference in outputs over time [18,[START_REF] Mendes | Application of Anaerobic Digestion Model No. 1 for simulating anaerobic mesophilic sludge digestion[END_REF]. This methodology was applied by Fatolahi et al. [START_REF] Fatolahi | Calibration of the Anaerobic Digestion Model No. 1 for anaerobic digestion of organic fraction of municipal solid waste under mesophilic condition[END_REF] to identify important parameters of ADM1 to simulate the digestion of an organic fraction of municipal solid wastes. In their work, Shannon entropy was applied as a sensitivity index to interpret the sensitivity analysis screening results.

The major flaws of the OAT method are the large number of runs or experiments required and again the fact that the interaction effects are not considered [START_REF] Donoso-Bravo | Model selection, identification and validation in anaerobic digestion: A review[END_REF]. On the other side, global sensitivity analysis not only provides quantitative approach to assess the significant influences of several kinetic parameters at a time on model outputs but also allows a focus on how the variability of each parameter influences the variance of model outputs [START_REF] Donoso-Bravo | Model selection, identification and validation in anaerobic digestion: A review[END_REF]. Thus, more and more works underline the usefulness and necessity of applying reliable global sensitivity analysis methods to AD models. For instance, Donoso et al. [START_REF] Donoso-Bravo | Identification in an anaerobic batch system: global sensitivity analysis, multi-start strategy and optimization criterion selection[END_REF], have developed a two steps model where 12 kinetic and mass transfer parameters are involved. Monte-Carlo method has been used to generate random parameter values and the Sobol analysis has allowed to decompose variances of several model outputs into fractions that can be attributed to parameter variances [START_REF] Donoso-Bravo | Identification in an anaerobic batch system: global sensitivity analysis, multi-start strategy and optimization criterion selection[END_REF]. In their work, Schroyen et al. [START_REF] Schroyen | Modelling and simulation of anaerobic digestion of various lignocellulosic substrates in batch reactors: Influence of lignin content and phenolic compounds II[END_REF] performed global sensitivity analysis on an ADM1 simplified model using Monte-Carlo simulations and linear regression to analyse the effects of kinetic parameter variations on biomethane production. In another study, Pastor-Poquet et al. [START_REF] Pastor-Poquet | Assessing practical identifiability during calibration and cross-validation of a structured model for high-solids anaerobic digestion[END_REF] used global sensitivity analysis to highlight the most influential parameter of an adapted ADM1 model to be calibrated with an available set of experimental data. In this aim, Latin-hypercube sampling technique was used and the individual and global effects of each parameter upon the global model output variance were calculated. Moreover, this work also helped to evaluate the suitability of the ammonia inhibition function used in the model by performing sensibility analysis based on experimental data. Recently, a new approach of global sensitivity analysis has enabled to assess the effect of feedstock variations on parameter sensitivities of two models [START_REF] Fortela | Computational evaluation for effects of feedstock variations on the sensitivities of biochemical mechanism parameters in anaerobic digestion kinetic models[END_REF]. This methodology is based on the coupling between the Morris method and the functional principal component analysis and enables the interpretation of time-dependent outputs.

These methods can be time-consuming as they can require a large number of runs. An alternative method is the use of screening design methods to assess the influence of parameter variations on model outputs. Definitive Screening Design (DSD) is particularly adapted for this purpose. Indeed, this is a three-level screening design that enables to estimate the main effects of parameter variations on a given variable. Moreover, compared to classical fractional factorial designs, DSD has the advantage to provide estimates of main effects that are orthogonal to other main effects and that are unbiased by any second-order effect [START_REF] Phoa | A systematic approach for the construction of definitive screening designs[END_REF][START_REF] Jones | A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects[END_REF]. On top of that, this design requires a relatively low number of runs, only one more run than twice the number of parameters. DSD has been mainly used for operating parameter optimisations because of its capacity to also estimate quadratic effects without confounding with two-factor interactions [START_REF] Libbrecht | Optimization of soft templated mesoporous carbon synthesis using Definitive Screening Design[END_REF][START_REF] Felix | Investigation of direct biodiesel production from wet microalgae using definitive screening design[END_REF][29]. However, the literature lacks information on the application of DSD on numerical modelling. Therefore, the aim of the present work is to show the relevancy of the application of DSD coupled with multiple linear regression analysis to global sensitivity analysis to assess the key parameters that significantly influence AD model outputs. The methodology is applied to an ADM1 simplified model for thermophilic dry anaerobic digestion of agricultural wastes which is firstly presented. A literature review is carried out to define realistic ranges of the model parameters in relation to the process studied. This choice is essential to ensure the consistency of the results obtained from the sensitivity analysis. The global sensitivity analysis based on DSD is then described and applied to highlight the model parameters that have the most significant impacts on the simulation outputs in the case study considered. The results obtained are compared to trends observed in literature for similar cases.

Model description

Reaction scheme

The model considered in this paper is a dynamic model developed for process control purpose and more precisely to prevent failures of high solid anaerobic digestion, over 15% total solid (TS) of agricultural and livestock wastes. This is a simplified ADM1 model intended to describe major phenomena involved during dry anaerobic digestion of different substrates.

In the present study, the anaerobic biological processes are described through two steps. The disintegration, hydrolysis and acidogenesis stages are gathered in a single solubilisation step named DHA. Hydrogenotrophic methanogenesis is also included in this step to consider the consumption of H2 and inorganic carbon (IC) resulting from the acidogenesis stage ( Table 1). During DHA, hydrolytic biomass (Xbha) degrades the readily (Xr) and the slowly (Xs) biodegradable fractions of the particulate substrate into soluble matter such as acetate (SA), methane (SCH4), inorganic carbon (SIC), and inorganic nitrogen (SN). The division of particulate matter into two fractions enables to consider the complexity of various substrates. The acidogenic step of anaerobic digestion produces various volatile fatty acids (VFA) represented by acetate. Inorganic nitrogen production appears in the DHA step because ammonia is a byproduct of both hydrolysis and acidogenesis of nitrogen rich compounds such as proteins or urea [START_REF] Batstone | Anaerobic Digestion Model N°1 (ADM1)[END_REF]. The reaction equations of the DHA step are defined as follows:

X r → α 1,A S A + 1 -α 1,A -α 1,CH4 X bha + α 1,IC S IC + α 1,N S N + α ,CH4 S (1)
X → α , S + 1 -α , -α ,CH4 X + α , S + α , S + α ,CH4 S

where αj,i are the stoichiometric coefficients of the component i in the reaction j.

The methanogenic pathway of the conversion of acetate (SA) into dissolved CH4 (SCH4) and inorganic carbon (SIC) by methanogens (Xbm) is described by the following equation:

S → α , S + α , S + (1 -α , )X (3)
The biomass decay is also accounted for. According to the ADM1, death of biomass (Xbha and Xbm) leads to the formation of slowly degradable particulate matter, particulate inert (XI) and soluble inert (SI):

X → α , X + 1 -α , -α , X + α , S (4)
X → α , X + 1 -α , -α , X + α , S

Thus, the simplifications made on degradation pathways lead to 5 stoichiometric reactions in which 10 variables are involved.

Model units and notations

As suggested in the ADM1, chemical component base unit is the chemical oxygen demand (COD). Molar basis is used for components with no COD such as inorganic carbon (CO2 and HCO3 -) or inorganic nitrogen (NH3 and NH4 + ). Concentrations are expressed according to the wet medium mass unit: gCOD.kg -1 (or mol.kg -1 ).

Stoichiometric coefficients

The stoichiometric coefficients are estimated based on assumptions made on biochemical reaction schemes and experimental data.

In DHA step, the solubilisation of carbohydrate and fats contained in the particulate matter mainly leads to monomers like monosaccharides [START_REF] Batstone | Anaerobic Digestion Model N°1 (ADM1)[END_REF]. Glucose is used as the model monomer to calculate the stoichiometric parameters of the DHA reactions, for both readily and slowly degradable particulate matters. According to the acidogenesis equation of glucose (Step The stoichiometric coefficients are estimated from Step 3 in Table 1. As in the ADM1, it is suggested that 10% of the transformed COD is turned into biomass [START_REF] Batstone | Anaerobic Digestion Model N°1 (ADM1)[END_REF]. Stoichiometric coefficients of the DHA step are calculated from the following equations:

α , = α , = (1 -Y ) ν , = 0.3 g . g (6)
α , = α , = (1 -Y ) ν , = 0.6 g . g

α , = α , = (1 -Y ) ν , = 0.00468 mol . g

where YXbha is the percentage of COD consumed for hydrolytic biomass growth (0.1 gCOD_Xbha.gCOD_Glucose -1 ), 3,i is the stoichiometric coefficient of component i from Step 3 in Table 1, CODGlucose is the COD of one mole of glucose (192 gCOD.mol -1 ), CODCH4 is the COD of one mole of methane (64 gCOD.mol -1 ), CODAcetate is the COD of one mole of acetate (64 gCOD.mol - 1 ), molCO2 corresponds to a mole of inorganic carbon.

In this study, organic nitrogen biodegradability is assumed equal to the organic carbon biodegradability of the particulate substrate. Hence, stoichiometric coefficients of inorganic nitrogen, α1,N and α2,N (Eq. (1) and Eq. ( 2)) are estimated from biochemical methanogenic potential (BMP) tests carried out on the influent. The total nitrogen content (TKN) of the raw substrate considered in this work is about 0.50 molN.kg -1 and the total ammonia concentration (TAN) is 0.18 mol.kg -1 . The organic carbon biodegradability of the substrate is estimated at 62.7% (see 2.6.1) which leads to stoichiometric coefficients of inorganic nitrogen (α1,N and α2,N) of 0.0009 mol.gCOD_X -1 .

α , = α , = % , ( )
( ) (9)
where %BD,N is the biodegradability of the organic nitrogen.

Stoichiometric coefficients of the methanogenic step are calculated from the methanogenesis balance equation (Eq. ( 4), Table 1). As in ADM1, it is proposed that 5% of the acetate is turned into methanogenic biomass [START_REF] Batstone | Anaerobic Digestion Model N°1 (ADM1)[END_REF].

α , = (1 -Y ) ν , = 0.95 g . g (10)
α , = (1 -Y ) ν , = 0.0148 mol . g [START_REF] Arzate | Anaerobic Digestion Model (AM2) for the Description of Biogas Processes at Dynamic Feedstock Loading Rates[END_REF] where YXbm is the percentage of COD consumed for methanogenic biomass growth (0.05 gCOD_Xbm.gCOD_A -1 ) and 4,i is the stoichiometric coefficient of component i from the Step 4 in Table 1.

Finally, stoichiometric coefficients of the biomass decay balance equations (Eq. ( 4) and Eq. ( 5))

are taken from the suggested values of ADM1 where α4,Xi = α5,Xi = 0.25 gCOD Xi.gCOD Xbiomass -1 and α4,Si = α5,Si = 0.1 gCOD Si.gCOD Xbiomass -1 .

Kinetics and mass transfer

In dry anaerobic digestion, the rate-limiting step is usually considered to be the hydrolysis [START_REF] Pommier | A logistic model for the prediction of the influence of water on the solid waste methanization in landfills[END_REF][START_REF] Vavilin | Hydrolysis kinetics in anaerobic degradation of particulate organic material: An overview[END_REF], modelled by first order kinetics in ADM1. Therefore, in this work DHA step is modelled by first order kinetics and characterised by two kinetic parameters, k1, k2, respectively for the degradation of the readily (Xr) and the slowly (Xs) degradable fractions of the particulate substrates. As in the ADM1, a Monod kinetic law describes the methanogenic step and the decay rates of the biomass are modelled by first order kinetics. All these bioconversion rates rj are shown in the Petersen matrix given in Table 2.

According to the ADM1, pH inhibition on both DHA step and methanogenesis are accounted for in this model as well as ammonia inhibition on the methanogenic step. pH and ammonia inhibitions are described by the following equations [START_REF] Batstone | Anaerobic Digestion Model N°1 (ADM1)[END_REF]:

I pH,i = 1+2•10 0.5(pH LL,i -pH UL,i ) 1+10 (pH-pH UL,i ) +10 (pH LL,i -pH) (12)
I NH 3 = 1 1+ S NH 3 MC K i ( 13
)
where IpH,i is the pH inhibition factor affecting biomass i, pHLL,i and pHUL,i are respectively the lower and upper limits of pH for 50% inhibitory effect on biomass i. INH3 is the free ammonia inhibition factor affecting methanogens activity, SNH3 is the molar concentration of free ammonia in the media (mol.kg -1 ) and MC is the moisture content, which is equal to 1-TS (Lliquid.kg -1 ). Besides kinetics, the model includes mass transfer of components from the liquid to the gaseous phase for CH4, CO2 and NH3. Resistance to liquid-gas mass transfer is characterised by the two-film theory of Whitman [START_REF] Whitman | The two film theory of gas absorption[END_REF]. Since resistance to transfer is mainly in the liquid phase and because diffusivity of CH4, CO2 and NH3 are similar, liquid-gas mass transfer coefficients (kL,ia) are supposed to have the same value kLa. Thus, biogas production (CH4, CO2 and NH3) is calculated from soluble concentrations through dynamic liquid-gas transfer equations as follows:

Process XI Xr Xs Xbha Xbm SA SCH4 SIC SN SI 1 Fast hydrolysis -1 1-α1,A-α1,CH4 α1,A α1,CH4 α1,IC α1,N k1 Xf IpH,Xbha 2 Slow hydrolysis -1 1-α2,A-α2,CH4 α2,A α2,CH4 α2,IC α2,N k2 Xd IpH,Xbha 3 Methanogenesis 1-α3,CH4 -1 α3,CH4 α3,IC μ max 1-α 3,CH4 X bm S A K s MC+S A I pH,Xbm I NH3
r , = k a(S -MC • H • P ) (14)
where rliq-gas,I is the liquid to gas rate transfer of the gaseous component i (gCOD.kg -1 .d -1 for CH4 and mol.kg -1 .d -1 for CO2 and NH3). It is necessary to correct Hi by the moisture content (MC) to account for the substrate wet mass unit basis of Si. Furthermore, to change HCH4 from M.atm - 1 to gCOD.L -1 .atm -1 , the methane Henry constant is multiplied by a factor of 64.

Gathered in Table 2, 12 kinetic and mass transfer parameters are required to use the biochemical model considered in the present study. The reliability of the anaerobic digestion process modelling depends obviously on the consistency of these parameters.

Model implementation

The biological model is integrated in a continuous stirred tank reactor (CSTR) model as CSTR are the more commonly used reactors in the industrial treatment of livestock wastes [START_REF] André | Solid anaerobic digestion: State-of-art, scientific and technological hurdles[END_REF].

Modelling of CSTR implies the hypothesis of a homogeneous media. Concentrations in the output flowrate (Wout) are equal to the concentrations in the reactor. Reactor feeding is assumed continuous and constant. The global volume of the CSTR is separated into a working volume (Vd) and a gas volume (VGas) as illustrated in Figure 1. The working volume is the medium (digestate) where all the bioconversion processes take place. The gas volume is supposed to be at atmospheric pressure and the global outlet biogas flowrate of the reactor is equal to the inlet biogas flowrate in VGas. This biogas production is therefore depending on the dynamical mass transfer equations Eq. ( 14). The partial pressures of CH4, CO2 and NH3 in the reactor gas volume are expressed as follows:

P = G • R • T ( 15
)
where Pi is the partial pressure of the gaseous species i (CH4, CO2 or NH3) (atm), Gi is the molar concentration of the gaseous specie (mol.L -1 ), R is the ideal gas constant (L.atm.K -1 .mol -1 ) and T is the digester temperature (K). Finally, the biogas production is expressed as follows:

q = 10 M , + r , + r , ( 16
)
where qG is the total biogas production (m 3 .d -1 ), and Md is the mass of digestate in the reactor (kg). No mass balance on water is accounted for in this model because a preliminary study has shown that with a mass balance on water considering a saturated gas phase, the water steam represents less than 4% of the total biogas production. The total biogas mass flow is calculated as follows:

W iogas = q G RT ∑ P i M i i ( 17
)
where Wbiogas is the outlet mass flow of biogas (kg.d -1 ), and Mi is the molar mass of the gaseous component i (g.mol -1 ). The output mass flowrate (Wout) of digestate is then obtained from the global mass balance on the CSTR:

W ut =W in -W iogas (18)
In the working volume, partial mass balances lead to a set of 10 differential equations:

= W X _ -W X /M -r (19) = W X _ -W X /M -r + 1 -α , -α , r + (1 -α , -α , )r (20) = W X _ -W X /M + α , r + α , r (21)
= W X _ -W X /M + (1 -α , -α , )r + 1 -α , -α , r -r (22) = W X _ -W X /M + (1 -α , )r -r (23)
= W S _ -W S /M + α , r + α , r -r (24)

= W S _ -W S /M + α , r + α , r + α , r -r , (25)
= W S _ -W S /M + α , r + α , r + α , r -r , (26)
= W S _ -W S /M + α , r + α , r -r , (27)
= W S _ -W S /M + α , r + α , r (28)
In the gas phase, partial mass balances lead to the 3 following differential equations:

= r , -G (29) = r , -G (30) = r , -G (31)
A set of 4 algebraic equations corresponding to the acid-base equilibria (H + /OH -, CO2/HCO3 -, NH3/NH4 + , acetic acid/acetate) are used to calculate the concentrations of the dissociated species. These equations are gathered in the electroneutrality equation to calculate SH+ and subsequently pH.

S N •S H + (MC•K a, NH 4 + +S H +) + S H + +S cations - MC•K a, CO 2 •S IC (MC•K a, CO 2 +S H +) - MC•K a,S A • S A 64 (MC•K a,S A +S H +) - K a, H 2 O • MC² S H + -S anions =0 (32)
Acid-base constants (Ka,i) are determined from volumetric molar concentrations. The use of moisture content (MC) enables to change the base unit of Ka,i, from volumetric concentrations to mole per kilogram of wet substrate. Also, the moisture content is introduced to express the pH related to the liquid phase concentration.

Sions is defined as the difference between the concentration of cations and anions (Scations -Sanions) that are not individually calculated in this model but that are necessary for pH resolution. It implies that Sions can be positive or negative. The dynamical modelling approach leads to a last differential equation for Sions:

= W S _ -W S /M ( 33
)
This model is implemented in Matlab R2019a and solved using the ode15s solver.

3. Simulation of a case study

From feedstock characterisation to model input variables

Composition and flowrate of raw substrate in the digester are taken from a potential running condition of digester treating agricultural wastes in Occitanie region in France, mainly composed of grass silage, straw and cattle manure (Table 3). The influent is diluted with water to reach a TS of 30%. This leads to a total influent mass flow (Win) of 62.4 t.d -1 . Since, in the present biological model, the DHA step directly leads to acetate formation, VFA in Table 3 are supposed to be acetate equivalent (SA). The COD biodegradability of the soluble organic matter is assumed to be equal to 80%, within the range of values found in literature [START_REF] Franco | An improved procedure to assess the organic biodegradability and the biomethane potential of organic wastes for anaerobic digestion[END_REF][START_REF] Moretti | Characterization of municipal biowaste categories for their capacity to be converted into a feedstock aqueous slurry to produce methane by anaerobic digestion[END_REF]. This means that in the soluble fraction, 53 gCOD.kg -1 are biodegradable, among which are the 20 gCOD.kg -1 of VFA. The soluble COD that is not VFA is considered to be easily hydrolysable compounds (Xr) like soluble polymers. The slowly degradable particulate matter (Xs) is assumed as the total biodegradable particulate matter. Knowing the TS and the volatile solid content (VS) of the raw substrate (particulate and soluble), the BMP of the raw substrate is 69.66 NL.kgraw substrate -1 . According to the COD concentration of the raw substrate, this BMP is also equal to 0.204 NL.gCOD -1 . Theoretically, the methane production from total degradation of one gram of COD is equal to 0.350 NL.gCOD -1 [START_REF] Angelidaki | Assessment of the anaerobic biodegradability of macropollutants[END_REF]. Assuming that about 7% of the biodegradable COD is converted into biomass during AD processes, the biodegradability of the organic matter in the raw substrate can be calculated as follows:

% = . . * (
. ) * 100 = 62.7%

The biodegradable organic matter concentration in the raw substrate is thus equal to 214 gCOD.kg -1 . Since the biodegradable soluble organic matter concentration is equal to 53 gCOD.kg - 1 , the total biodegradable particulate matter is equal to 161 gCOD.kg -1 . The global anions and cations concentration (Sions) is calculated before running simulations in order to fit initial pH of the media through the electroneutrality equation (Eq. ( 32)). Model input values are gathered in Table 4. Concentrations of hydrolytic and methanogenic biomasses as well as the concentration of dissolved IC in the influent are supposed to be negligible compared to the concentrations in the digester.

Results

The model previously introduced is a dynamic model that enables to follow the evolution of the different variables over time. This work is based on the results obtained in steady state conditions (after 400 days). The reactor is working at 55°C and has a working volume (Vd) of 1200 m 3 , corresponding to a digestate mass (Md) of 1 200 tons, and has a gas volume (VGas) of 300 m 3 . In order to simulate the anaerobic digestion of the agricultural substrate presented in Table 3 and Table 4, the 12 kinetic and mass transfer parameters are those presented in Table 5. These typical values are chosen within the limits found in the literature and are used to achieve the simulation that gives the model outputs presented in Table 6. Ki (mol.L -1 ) 0.098 0.0028-0.18 [START_REF] Capson-Tojo | Unraveling the literature chaos around free ammonia inhibition in anaerobic digestion[END_REF] The initial conditions in the digester are the ones of the influent except biomass concentrations (Xbha and Xbm). In order to model a seeded digester and to prevent pH inhibition and biomass decay due to the low initial pH (Table 3), the initial concentrations Xbha and Xbm are set to relatively high values, respectively 30 gCOD.kg -1 and 100 gCOD.kg -1 .

For the chosen substrate (Table 4), the raw methane yield from the digestion of the agricultural substrate is about 0.17 Nm 3 CH4.kgVS -1 which corresponds to a degradation of the feedstock VS of 63%. This degradation percentage is of the same order of magnitude as the percentage encountered in the literature where values between 60% and 80% correspond to degradation percentage observed on full-scale plants treating agricultural wastes without a second digester [START_REF] Ruile | Degradation efficiency of agricultural biogas plants -A full-scale study[END_REF]. Finally, the methane percentage in the biogas observed during the AD simulation is 53.14%. This result is consistent with values found in the literature, which are between 50% and 70% for full-scale AD of agricultural wastes [START_REF] André | Solid anaerobic digestion: State-of-art, scientific and technological hurdles[END_REF][START_REF] Cavinato | Thermophilic anaerobic co-digestion of cattle manure with agro-wastes and energy crops: Comparison of pilot and full scale experiences[END_REF]. Thus, the proposed simplified model enables to obtain typical results observed in AD processes similar than that considered in the present case study. The previous part shows the consistency of the model to represent the considered dry AD of a mixture of agricultural substrates. A global sensitivity analysis is implemented to determine the key model parameters that may strongly affect the simulation results and, therefore, to highlight the parameters that have to be carefully determined for the model to be reliable. In this work definitive screening design (DSD) method is used.

To perform the DSD method, three parameter levels are defined. These three levels (-1, 0, 1) correspond to parameter values (minimal, central, maximal) that allow to describe the range of investigation. A bibliographical study (Table 5) has been carried out to choose reasonable ranges of the parameter values corresponding to the case studied in this work. The setting of the parameter levels is a delicate task since kinetic constants, especially hydrolysis constants (k1 and k2) and the maximum growth rate of methanogens (µmax), depend on large extent of experimental conditions such as the inoculum [20], the moisture content [START_REF] Abbassi-Guendouz | Total solids content drives high solid anaerobic digestion via mass transfer limitation[END_REF][START_REF] Liotta | Modified Anaerobic Digestion Model No.1 for dry and semi-dry anaerobic digestion of solid organic waste[END_REF][START_REF] Pommier | A logistic model for the prediction of the influence of water on the solid waste methanization in landfills[END_REF], the temperature [START_REF] Ge | Relative kinetics of anaerobic digestion under thermophilic and mesophilic conditions[END_REF] or the mixing condition [START_REF] Van Hulle | Importance of scale and hydrodynamics for modeling anaerobic digester performance[END_REF]. Among the large amount of published works on anaerobic digestion, the parameter ranges, presented in Table 7, have been determined using data identified on similar experimental conditions than that of the operating conditions of the process considered in this work i.e. thermophilic (55°C) condition, high solid content (>15%) and digestion of agricultural wastes. The central values correspond to those used in the case study presented in the previous part.

In details, the hydrolysis constants (k1 and k2) must be consistent with the two fractions of particulate matter considered in this work, namely readily and slowly degradable (Xr and Xs).

Xs can be considered as lignocellulosic wastes for their low bioaccessibility [START_REF] Li | Methane production through anaerobic digestion: Participation and digestion characteristics of cellulose, hemicellulose and lignin[END_REF]. Therefore, the value of k2 is associated to manure hydrolysis rates because of high concentration of undigested lignocellulosic material in this kind of substrate. As Xr is assimilated to simple polymers, k1 is associated to cellulose hydrolysis constants or more generally to hydrolysis constants of substrates with higher concentrations of more accessible carbohydrates such as corn silage or grass silage [START_REF] López | A simple kinetic model applied to anaerobic digestion of cow manure[END_REF][START_REF] Buffière | The hydrolytic stage in high solids temperature phased anaerobic digestion improves the downstream methane production rate[END_REF]. Acetoclastic methanogenesis kinetics (µmax and Ks) are set as recommended by the ADM1 for liquid anaerobic digestion. Nevertheless, several papers reveal that mass transfer limitation caused by a decrease in moisture content results in a diminution in the apparent methanogenesis rate [START_REF] Abbassi-Guendouz | Total solids content drives high solid anaerobic digestion via mass transfer limitation[END_REF][START_REF] Liotta | Modified Anaerobic Digestion Model No.1 for dry and semi-dry anaerobic digestion of solid organic waste[END_REF][START_REF] Pommier | A logistic model for the prediction of the influence of water on the solid waste methanization in landfills[END_REF][START_REF] Hyaric | Influence of moisture content on the specific methanogenic activity of dry mesophilic municipal solid waste digestate[END_REF]. An increase in TS from 20% to 35% may result in a decrease in methanogenic activity of 66% [START_REF] Hyaric | Influence of moisture content on the specific methanogenic activity of dry mesophilic municipal solid waste digestate[END_REF]. The value of µmax proposed by the ADM1, 0.8 d -1 , is thus chosen as the upper level for the maximum specific growth rate for methanogens. Reductions of respectively 25 % and 50% are assumed to set the central value and the minimal value in the case of very high solid content causing mass transfer limitations [START_REF] Hyaric | Influence of moisture content on the specific methanogenic activity of dry mesophilic municipal solid waste digestate[END_REF]. The upper and lower levels of the first order decay constants (k4 and k5) and the pH inhibition limits correspond to the limits given by the ADM1. The values of the free ammonia inhibition constant (Ki) exhibit a large disparity in the concentration threshold of ammonia (FAN) that degrades methanogens activity. A review has highlighted the existence of six different clusters corresponding to six Ki values [START_REF] Capson-Tojo | Unraveling the literature chaos around free ammonia inhibition in anaerobic digestion[END_REF]. The values of Ki corresponding to livestock waste vary from 0.015 mol.L -1 to 0.18 mol.L -1 . Finally, mass transfer coefficient (kLa) has been less studied or even considered as non-limiting, which gives rise to a large range of values [START_REF] Abbassi-Guendouz | Total solids content drives high solid anaerobic digestion via mass transfer limitation[END_REF]. Moreover, the kLa value is directly linked to the moisture content, to the digester technology, to the medium physical properties and to the mixing condition of the system. Liquid-gas mass transfer coefficient of CO2 of about 3 d -1 has been measured in a CSTR during liquid AD of activated sludge [START_REF] Pauss | Liquid-to-Gas Mass Transfer in Anaerobic Processes: Inevitable Transfer Limitations of Methane and Hydrogen in the Biomethanation Process[END_REF]. Similar kLa value has been found during the dry AD of municipal solid wastes (80% of moisture content) mixed by biogas injections [START_REF] Bollon | Etude des mécanismes physiques et de leur influence sur la cinétique de méthanisation en voie sèche: essais expérimentaux et modélisation[END_REF]. Since a decrease of moisture content has a strongly negative impact on mass transfer phenomena [START_REF] Bollon | Measurement of diffusion coefficients in dry anaerobic digestion media[END_REF], the value of 3 d -1 is here set as the upper level of kLa. The minimal value of 0.5 d -1

corresponds to kLa value calculated in the case of dry AD of municipal solid wastes without mixing system [START_REF] Bollon | Etude des mécanismes physiques et de leur influence sur la cinétique de méthanisation en voie sèche: essais expérimentaux et modélisation[END_REF].

Screening design of running simulations

The DSD has been constructed from the systematic approach developed by Phoa and Lin [START_REF] Phoa | A systematic approach for the construction of definitive screening designs[END_REF].

This construction method is based on the D-efficiency optimisation and provides design for any number of parameters. As the number of parameters is 12, the screening design matrix, noted X, presented in Table 8, implies 25 runs. Among the model outputs, the responses considered in the DSD are biogas production (qG), pH and percentage of CH4 in the biogas (%CH4) because these variables are usually monitored on industrial digesters as indicators of productivity and stability of the system. The further work is to assess the main effects of variations in the parameter levels on these model outputs.

Model outputs interpretation

For each model output of interest, multiple regression analysis is used to assess the main effect of each parameter present in the DSD. From the multiple regression, each model output value obtained from the running simulations, can be expressed as a function of the parameter values. The corresponding multiple linear regression model of each model output can be written as follows:

Y = β + ∑ β x ( 35
)
where Y is the response given by multiple linear regression for a model output Y (qG, pH or %CH4), β0 a constant, βk is a constant giving the main effect of parameter k on Y and xk is the level of parameter k. The coefficient βk can be interpreted as the average growth rate of the model output Y depending on the level parameter xk when all other regressors remain fixed.

Coefficients βk would be obtained with an infinite number of runs by continuously varying the parameters xk in the considered intervals defined in Table 7. Since the present DSD matrix (Table 8) includes 25 runs, it is only possible to calculate estimates of the coefficients βk namely β k which are obtained by multiple regression on each model output for the 25 runs. The response given by the multiple regression can be written as follows:

Y = β + ∑ β x (36)
where β is an estimate of β0, β is an estimate of the main effect of the parameter k on Y and xk is the level of parameter k. For each run, each model output value Yi can be expressed from the multiple regression and a residual term reflecting the difference between the value of the response given by the AD model and the value resulting from multiple linear regression:

Y = Y + ε ( 37
)
where Yi is the observed AD model output value (qG, pH or %CH4) for the i th run, Y is the response given by the multiple linear regression (qG, pH or %CH4) for the i th run and ε is the residual term for the i th run. The least square method is used to estimate the constants of each multiple linear regression carried out on each model output. Based on the assumption that the residual term follows a normal distribution N(0,σ ²), it is established that the estimate β follows a normal distribution N(βk,σβ,k²). The variance σβ,k² is unknown but can be estimated from the experimental design matrix (X) and the calculation of the variance of the residual term (σ ²)

σ , = (X X) , σ (38)
where σ , is the estimate of the variance of β k , (X T X) k,k -1

is the diagonal term of the matrix

(X T X) -1
corresponding to the parameter k and σ is the estimate of the residual term variance.

Once the multiple regression is done, estimates of the effects (β ) and the residual term are known. Because σ , is an estimate of the real variance of β , the standardised probability density function of β a Student t-distribution. The degrees of freedom of the Student t-distribution is 12 since the screening design includes 25 runs for 13 constants to set (from β 0 to β 12 ). The standardised probability density function can be written as follows:

L , = t (39)
where t12 is the Student t-distribution with a degree of freedom equal to 12.

The significance of each coefficient β on the corresponding model output Y is tested, based on the H0 hypothesis which assumes that a given coefficient is not significant. Under the H0 hypothesis, the main effect βk of the parameter k on the model output Y is assumed to be null (in Eq. ( 39)). The corresponding t-value is calculated from Eq. ( 39) and its p-value is estimated.

The p-value is the probability that the H0 hypothesis is true: an effect is considered to be significant when p < 0.05 [START_REF] Wasserman | All of Statistics: A Concise Course in Statistical Inference[END_REF]. However, if a parameter effect had a p-value higher than but close to 0.05, the parameter would not be disregarded and its effect would be discussed.

All multiple linear regressions were performed using the MATLAB R2019a software with the "stepwiselm" function allowing to directly estimate the parameters with significant effect (pvalue < 0.05) and to set the corresponding regression equation for each model output. For each regression, the Durbin-Watson test and the Shapiro test (p-value > 0.05) are performed on residuals terms to respectively detect the presence of autocorrelation and to confirm that the residuals are normally distributed.

Results and discussion

The DSD method is applied to the parameters defined in Table 7 resulting in 25 simulation runs. The parameter settings and the associated model outputs are listed in Table 8.

Table 8: Screening design matrix obtained for variable parameters from the application of the construction method of Phoa and Lin [START_REF] Phoa | A systematic approach for the construction of definitive screening designs[END_REF] and the associated model outputs values for the biogas flowrate, the percentage of methane in the biogas and the pH.

Kinetic and mass transfer parameter levels (xi,j) Model outputs (Yi) To ensure that the results do not depend on the chosen set of runs presented in Table 8, several tests were carried out by varying the order of parameters in the DSD matrix. Despite slight differences in the coefficients values, conclusions of the sensitivity analysis were identical revealing the same significant parameters.

Runs x k 1 x k 2 x μ max x K s x k x k x k L a x pH , x pH UL,Xbha x pH LL,Xbm x pH UL,Xbm x K i qG (Nm 3 .d -1 ) %CH4 pH 1 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 2896 54.2 6.58 2 1 0 -1 -1 -1 -1 -1 1 1 1 1 1 4896 53.2 6.48 3 1 1 0 -1 -1 1 1 -1 -1 1 -1 1 4923 53.1 7.15 4 1 1 1 0 -1 -1 1 -1 1 -1 1 -1 5961 52.8 7.13 5 1 1 1 1 0 -1 -1 1 -1 1 -1 -1 5608 53.0 6.46 6 1 1 -1 1 1 0 -1 -1 1 -1 -1 1 5678 53.0 6.46 7 1 1 -1 -1 1 1 0 1 -1 -1 1 -1 5583 53.0 6.94 8 1 -1 1 1 -1 1 -1 0 -1 -

Biogas production

Over all the simulations, the value of biogas production varies between 2360 Nm 3 .d -1 and 6066 Nm 3 .d -1 for a mean value of 4284 Nm 3 .d -1 . Lowest and highest specific methane yields correspond the minimum and the maximum biogas productions and are respectively of 0.08 and 0.20 Nm 3 CH4.kgVS -1 . The statistical analysis reveals that only variations in the kinetic parameters related to the hydrolysis step have significant effects on the overall biogas production values (Table 9). These parameters are the first order hydrolysis constants k1, k2 and the upper pH inhibition limit of the hydrolytic biomass pHUL,Xbha. Effects of the other parameters of the model have a p-value greater than 0.05 and are therefore not considered to have a significant impact on the biogas production.

Table 9: Parameters with significant effect on the biogas production, each with its coefficient value (main effect) and the corresponding p-probability.

Model output

Parameter main effects

β 0 β k 1 β k 2 β pH ,
The Durbin-Watson test and the Shapiro test performed on the residuals that residuals are independent and follow a normal distribution.

It can be deduced from this equation that a variation in the level of k2 (from 0 to -1 or from 0 to 1) is responsible for a variation in biogas production of 30% around the mean value while a variation in the levels of pHUL,Xbha and k1 would be respectively responsible for variations of 6% and 3%. The positive sign in front of levels of the kinetic constants k1 and k2 in Eq. [START_REF] Feng | Coensiling of cover crops and barley straw for biogas production[END_REF] indicates that an increase in hydrolysis rates, implying an increase in the acetate production, causes an increase in biogas production. An increase in the level of pHUL,Xbha has a positive impact on the biogas production. In fact, simulations demonstrate that, under the hypothesis of a perfectly stirred reactor, the pH of the media at steady state resulting from the degradation of the influent used in this study is around 7 (Table 8). As the pH value is closed to pHUL,Xbha which gives the value of Iph,Xbha in Eq. ( 12), the higher the value of pHUL,Xbha is, the closer to 1 the of Iph,Xbha is. Furthermore, variations in methanogenesis kinetic parameters do not appear to affect significantly biogas production. It shows that, within the limits of the sensitivity study (substrate characteristics and parameter variation ranges), almost all the acetate is converted by methanogens and that little or no inhibition occurs during the methanogenesis.

The results of the global sensitivity analysis performed on the biogas production have been compared to data from the literature. Schroyen et al. [START_REF] Schroyen | Modelling and simulation of anaerobic digestion of various lignocellulosic substrates in batch reactors: Influence of lignin content and phenolic compounds II[END_REF] carried out a global sensitivity analysis on the kinetic parameters of their simplified ADM1 model using Monte-Carlo sampling method. They reported that, the hydrolysis constant was the most influential parameter to simulate the methane production during the anaerobic digestion of lignocellulosic substrates. Weinrich et al. [START_REF] Weinrich | Critical comparison of different model structures for the applied simulation of the anaerobic digestion of agricultural energy crops[END_REF] have compared the complex structure of the ADM1 to different simplified model structures to simulate experimental data of AD of agricultural waste. They have proved that hydrolysis is the rate-limiting step during the uninhibited anaerobic digestion of complex particulate substrates since the reduction of the kinetics of the methanogenesis, acidogenesis and acetogenesis only have a little effect on the simulated biogas production. However, no similar results were found in the literature regarding the influence of pHUL,Xbha on the biogas production.

Thus, the first order kinetic constant k2 has the larger impact on the biogas production. To rightly describe and predict biogas production from the anaerobic digestion of the previously presented substrate, this kinetic parameter as well as pHUL,Xbha should be precisely identified.

The constant k2 is substrate dependant but the large influence of its value on qG suggests that it can be identified from experiments conducted in continuous flow for various substrates by following the biogas production.

Methane percentage in the biogas

Execution of the DSD matrix developed in Table 8 reveals the low variability of the methane percentage in the biogas (%CH4) given by the biological modelling. Among the values obtained from the DSD application, the minimum, maximum and the mean value of %CH4 are respectively 52.77%, 54.66% and 53.52%. In the biological model presented in this study, the same number of moles of inorganic carbon and methane is produced during the hydrolysis and methanogenic steps. This leads to values of %CH4 close to 50%. The parameter variations of the first order hydrolysis constant k2 and the upper pH inhibition limit of the hydrolytic biomass pHUL,Xbha are significantly responsible for the %CH4 variability (Table 10).

Table 10: Parameters with significant effect on the methane percentage in the biogas, each with its coefficient value (main effect) and the corresponding p-probability.

Model output

Parameter main effects

β 0 β k 2 β pH , %CH4 53
The Durbin-Watson test and the Shapiro test carried out on the residuals terms of the regression reveal that residuals are independent and follow a normal distribution. Differences in concentration in the gas phase are mainly due to differences in Henry's law constants of CO2 and CH4 (at 55°C, HCH4= 0.0009 mol.atm -1 .L -1 [START_REF] Sander | Compilation of Henry's law constants (version 4.0) for water as solvent[END_REF] and HCO2=0.0180 mol.atm - 1 .L -1 and to the proportion of inorganic carbon produced as bicarbonate. Increases in k2 and pHUL,Xbha result in a combined increase in inorganic carbon production and a decrease in pH. However, as the pH decreases, the concentration of inorganic carbon in acid form, namely CO2, increases and therefore the quantity of CO2 that desorbs is greater, which means that the proportion of CO2 in the gas increases to the detriment of %CH4. Nevertheless, as said before, methane percentage in biogas is not significantly influenced by the model parameter values in the investigated ranges: this output is therefore not relevant, in the range of this study, to identify the parameters of the model.

pH

The pH values observed during the simulations range from 6.46 to 7.24 around a mean value of 6.86. No pH value falls into an acidic range which explains the low impact of pHLL values on the different model outputs. Variations in the level of parameters k2 and kLa have significant effects on the pH value observed in steady state (Table 11).

Table 11: Parameters with significant effect on the pH in the reactor, each with its coefficient value (main effect) and the corresponding p-probability.

Model output

Parameter main effects

β 0 β k 2 β k L
The Durbin-Watson test performed on the residuals terms of the regression reveals that residuals are independent. However, the Shapiro test (not detailed) has shown that residuals do not follow a Gaussian distribution. By adding the square term of only one of the two selected parameters (xkLa²), the Shapiro test reveals that residuals follow a normal distribution.

This confirms that the screening analysis of the pH can be carried out by these parameters alone This shows that the main effect of k2 is 8 times lower than the main effect of kLa. The main effect of k2 is a combination of the influences of the inorganic nitrogen, acetate and inorganic carbon productions on the pH. Since no inhibition of the methanogenesis occurs, the acetate is mostly consumed by methanogens. Thus, the concentrations of inorganic carbon and nitrogen insure the medium alkalinity. An increase in k2 leads to a slight increase in the proportion of inorganic carbon to inorganic nitrogen and thus a decrease in pH. In the observed pH range (between 6.49 and 7.25), the free ammonia (NH3) fraction is extremely low. It means that the positive main effect of the kLa is linked to a higher CO2 desorption when kLa increases.

The volumetric liquid/gas mass transfer coefficient value suggested in the ADM1 is 200 d -1 [START_REF] Abbassi-Guendouz | Total solids content drives high solid anaerobic digestion via mass transfer limitation[END_REF].

This reflects the low mass transfer limitation that may occur in wet anaerobic digestion.

However, it has been demonstrated in several papers that a limitation to the transfer of gaseous species due to the high TS or to mixing problems may occur in the case of dry anaerobic digestion [START_REF] Abbassi-Guendouz | Total solids content drives high solid anaerobic digestion via mass transfer limitation[END_REF][START_REF] Hyaric | Influence of moisture content on the specific methanogenic activity of dry mesophilic municipal solid waste digestate[END_REF]. The sensitivity analysis highlights that for low ranges of kLa value the CO2 oversaturation has the greater impact on the media alkalinity. This result is consistent with the work of Pauss et al. [START_REF] Pauss | Liquid-to-Gas Mass Transfer in Anaerobic Processes: Inevitable Transfer Limitations of Methane and Hydrogen in the Biomethanation Process[END_REF] which shows that low kLa values imply insoluble gas overconcentrations such as CH4 and H2 but also CO2 responsible of medium acidification. In order to simulate the inhibitory effects of pH, caused by CO2 accumulation, occurring during the dry anaerobic digestion of cardboards, Abbassi-Guendouz et al. [START_REF] Abbassi-Guendouz | Total solids content drives high solid anaerobic digestion via mass transfer limitation[END_REF] had to drastically reduced the kLa value of the ADM1. These literature data confirm that the kLa value can be significant to model the pH evolution of digestion media of high solid content substrates.

Since the mass transfer coefficient has the most significant impact on the pH media, it can be deduced that kLa could be identified by fitting the pH of experiments conducted in continuous flow.

Conclusion

The present work shows the reliability of a global sensitivity analysis methodology to assess model parameters that significantly influence anaerobic digestion model outputs. This method uses Definitive Screening Design technique, as its major advantage is the estimation of unbiased main effects of parameter variations on model outputs from a low number of runs. The global sensitivity analysis method is performed on the kinetic and mass transfer parameters of a simplified ADM1 model for dry AD of agricultural wastes. The statistical multiple regression analysis is used to estimate the significant main effects of the parameters on chosen significant model outputs (biogas flowrate, methane percentage in the biogas and pH).

The implementation of this global sensitivity analysis method reveals that hydrolysis constant k2 as well as pHUL,Xbha should mainly be targeted for identification due to their significant influences on the biogas production given by the model. The mass transfer coefficient kLa found to have a significant impact on the pH of the media whereas the methane percentage given by the model presents a low variability whatever the parameter values are.

Furthermore, the low impact of the hydrolysis constant k1 on model outputs suggests that the model could be further simplified. Results of the global sensitivity analysis also highlight that there is no significant inhibition of methanogenesis during the AD of the agricultural waste considered in the study. Complementary work should be addressed on the simplified model to measure the influence of input conditions, notably the organic nitrogen content, on the global sensitivity analysis results. It would allow to check if potential inhibition issues modify the global sensitivity analysis results. Finally, the low number of runs required for the present method makes its application easy to any type of model from simplified to more complex models. The low computational time and reliability of the method presented enables its application to any type of digestion model.

Figure 1 :

 1 Figure 1: Representation of the continuous stirred tank reactor, influent mass flowrate (Win), biogas mass flowrate (Wbiogas), digestate mass flowrate (Wout), mass of media in the reactor (Md) and volume of the gas phase of the reactor (VGas).

  linear equation of the biogas production as a function of x k 1 , x k 2 and x pH UL,Xbha can be written as follows: q = 4284 + 136 x + 1261 x + 276 x ,

  0.0019) Estimates of the main effects of these parameters on the %CH4 can be transcribed in the multiple linear equation of the methane percentage. %CH = 53.52 -0.57 x -0.14 x ,

  0.0001)The equation corresponding to the multiple linear regression made on the pH values is: pH = 6.86 -0.04 x + 0.33 x

Table 1

 1

	1,

Table 1 :

 1 ). Reaction schemes of the bioconversion processes.

	Step	Balance equation
	1 Acidogenesis from monosaccharides C H O + 2 H O → 2 CH COOH + 2 CO + 4 H
	2 Hydrogen-utilising methanogenesis 4 H + CO → CH + 2 H O
	3 DHA of glucose	C H O → 2 CH COOH + CO + CH
	4 Methanogenesis	CH COOH → CO + CH

Table 2 :

 2 Peterson matrix of the model state variables.

		Rate rj (gCOD.kg -1 .d -1 or
	Component i	mol.kg -1 .d -1 for SIC and SN)

Table 3 :

 3 Influent characteristics.

		Particulate + Soluble				Soluble fraction
	Substrate	Flow	TS 1	VS²	BMP 3	COD	TKN	COD	VFA	N-NH4	pH
		(t.d -1 )	(%)	(%)	(NL.kgVS -1 )	(g.kg -1 )	(mol.kg -1 )	(g.kg -1 )	(gCOD.kg -1 )	(mol.kg -1 )
	Cattle manure 6.3	25%	81%	203	310	0.4	30	5	0.00	8.0
	Cattle slurry	0.6	9%	80%	222	108	0.3	19	2	0.06	8.0
	Pig slurry	2.2	5%	69%	261	51	0.4	10	1	0.21	8.0
	Poultry manure	4.4	58%	73%	286	680	2.5	61	11	1.24	8.0
	Straw	8.2	89%	91%	248	1070	0.6	33	0	0.00	7.5
	Grass silage	28.5	25%	87%	303	260	0.4	119	40	0.18	4.5
	Influent	50.2	37%	86%	270	424	0.6	83	24	0.22	4.6
	Total influent 62.4	30%	86%	270	341	0.5	66	20	0.177	4.6
	1 gTS.graw substrate -1
	2 Volatile solid content expressed in gvolatile solids.gTS -1
	3 Biochemical Methane Potential.

Table 4 :

 4 Model input variables characteristic of the influent described in Table3.

	Variable	Value	Units
	XI	114	gCOD.kg -1
	Xs	161	gCOD.kg -1
	Xr	33	gCOD.kg -1
	Xbha	0	gCOD.kg -1
	Xbm	0	gCOD.kg -1
	SI	13	gCOD.kg -1
	SA	20	gCOD.kg -1
	SCH4	0	gCOD.kg -1
	SIC	0	mol.kg -1
	SN	0.177	mol.kg -1
	Sions	-0.0488	mol.kg -1
	Win	62 408	kg.d -1
	pH	4.6	-
	TS	30	%

Table 5 :

 5 Setting of the model parameters values for the simulation of AD of agricultural substrate.

	Kinetic parameters Values	Bibliographical study Sources
	k1 (d -1 )	0.43	0.16-0.7	[35-38]
	k2 (d -1 )	0.07	0.015-0.12	[20,30,37,39-42]
	μmax (d -1 )	0.6	0.4-0.8	[8,43]
	Ks (gCOD.L -1 )	0.3	0.2-0.4	[8,43]
	k4 (d -1 )	0.02	0.01-0.03	[1]
	k5 (d -1 )	0.02	0.01-0.03	[1]
	kLa (d -1 )	1.75	0.02-5	[4,44]
	pHLL.Xbha	5	4.5-5.8	[1]
	pHUL.Xbha	7.5	7-8.5	[1]
	pHLL_Xbm	6	5.5-6.7	[1]
	pHUL.Xbm	8.5	8-8.5	[1]

Table 6 :

 6 Model output variables resulting from the simulation of the case study.

	Particulate matter
	XI (gCOD.kg -1 )	128.66
	Xr (gCOD.kg -1 )	4.20
	Xs (gCOD.kg -1 )	80.23
	Xbha (gCOD.kg -1 )	9.54
	Xbm (gCOD.kg -1 )	3.63
	Soluble matter
	SA (gCOD.kg -1 )	0.03
	SN (mol.kg -1 )	0.32
	SH+ (mol.kg -1 )	7.70E-08
	SIC (mol.kg -1 )	0.31
	Sions (mol.kg -1 )	-0.05
	SCH4 (gCOD.kg -1 )	3.64
	SI (gCOD.kg -1 )	15.51
	Gas
	qG (Nm 3. d -1 )	5007
	GCH4 (mol.L -1 )	0.02
	GCO2 (mol.L -1 )	0.02
	GNH3 (mol.L -1 )
	%CH4	53.14%
	%CO2	46.78%
	%NH3	0.08%
	Digester outputs
	pH	6.96
	Wbiogas (kg.d -1 )	6505
	Wout (kg.d -1 )	55903
	4. Method for global sensitivity analysis of the model by Definitive Screening Design
	4.1. Kinetic and mass transfer parameter levels

Table 7 :

 7 Kinetic and mass transfer parameters and the associated levels for the DSD.

	Kinetic
		Min (-1) Central (0) Max (1)
	k1 (d -1 )	0.16	0.43	0.7
	k2 (d -1 )	0.02	0.07	0.12
	μmax (d -1 )	0.4	0.6	0.8
	Ks (gCOD.L -1 )	0.2	0.3	0.4
	k4 (d -1 )	0.01	0.02	0.03
	k5 (d -1	0.01	0.02	0.03
	kLa (d -1 )	0.5	1.75	3
	pHLL.Xbha	4.5	5	5.5
	pHUL.Xbha	7	7.5	8
	pHLL_Xbm	5.5	6	6.5
	pHUL.Xbm	8	8.5	9
	Ki (mol.L -1 )	0.015	0.098	0.18

Acknowledgments

The authors are grateful for financial support provided by the regional council of Occitanie, France and the European Regional Development Fund under grant agreement n°17010098 (OCCIMETHA project).

Notations d

Density of the digestion media

Ks

Half saturation constant of methanogens for acetate (mol.L -


Reducing Risk: Landscape Approaches to Sustainable Sourcing. EcoAgriculture


domain: sdv sde sdv.bv

text:
Christian Mougin
email: christian.mougin@versailles.inra.fr

Agnes Bouchez

Laurence Denaix

Francois Laurent

Fabrice Martin-Laurent

Agnès Bouchez

François Laurent

Fabrice Martin- Laurent

ECOTOX, the INRA's network of ecotoxicologists, a major structure involved for the coordination and structuring of the French research in ecotoxicology

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

A great number of chemicals (metallic and synthetic compounds) are used by human activities. Most of them enter our environment, and lead to its contamination, as well as to adverse effects on wildlife and humans. One challenge for ecotoxicologists remain to understand and predict the long-term impact of these mixtures of chemicals, often on trace concentrations, on living organisms. This implies to develop tools and assessment strategies at different biological levels: individuals, populations and communities.

In that context, this Special Issue of Environmental Science and Pollution Research highlights selected papers from members of ECOTOX, the network of ecotoxicologists of the National Institute for Agricultural Research (INRA) (http://www6.inra.fr/ecotox). Set up in 2009 to stimulate research on ecotoxicology within INRA, and to unify the teams involved in the field, the network now brought together academics of other French research institutes and universities, as well as professionals. A total of 140 scientists over 44 laboratories or companies subscribes to the mailing list of the network. The EXOTOX network is sponsored by the National Institute for Agricultural Research, and particularly the scientific divisions: "Forest, Grassland and Freshwater Ecology", "Plant Health and the Environment" and "Environment and Agronomy", as well as from the "Sustainable Management of Crop Health" metaprogramme (SMaCH).

The network has three main priority objectives: (i) to encourage scientific thinking within the community of ecotoxicologists, whether they are dealing with aquatic or terrestrial ecosystems, (ii) to contribute to defining a national research strategy in this field, and (iii) to favour scientific production. For many years, the network offers opportunities for exchanges within the French community of ecotoxicologists, especially through regular scientific seminars They were held in Thonon les Bains (1999), Antibes (2002), Dinard (2006), St-Lager (2011) and Biarritz (2014), see the Conference Report on the last seminar in the present Special Issue.

The network is also involved in the coordination and structuring of the national research in ecotoxicology, by interacting with other French networks and structures. In addition, the network has also set up a watch strategy (http://www6.inra.fr/ecotox/Veille), providing to numerous partners a bimonthly newsletter. Finally, the network provides means to present and publish the results and highlights from the research developed by its scientists. That Special Issue is one illustration of that objective.

Twenty-three papers were included in this Special Issue. These papers highlighted current research on the fate, mode of action and adverse outcomes for a variety of environmental contaminants, on a variety of biological targets. Some of these results were presented during the last seminar in Biarritz. They aimed at establishing the relationships between environmental factors, toxic chemicals, and their effects on eukaryotic organisms.

The first papers concerned: the assessment of the bioavailability of chemicals to invertebrates and plants. In that context, a mild extraction method was proposed by Nélieu et al. to study the bioavailability of the fungicide epoxiconazole to the earthworm Aporrectodea icterica.

Amounts of epoxiconazole extracted by an hydroxypropyl-β-cyclodextrin solution were identical to these determined in A. icterica exposed in real spiked soil. This mild method was sensitive to soil sorption capacity and to ageing. The study could be expanded to other organic contaminants in order to tend towards a reliable predictability of the ecotoxicological risks which would take bioavailability in consideration Pauget at al. were interested in determining the environmental parameters influencing the metal bioavailability and transfer to snails exposed to multiple contamination sources. They showed the great contribution of lettuce in Cd assimilation by snails, reinforcing the fact that measuring only the total soil concentration was not sufficient to accurately assess Cd bioavailability. They concluded that improving biodynamic model data on sources contribution under a complex exposure remain necessary to assess metal bioavailability to snails for risk assessment purpose.

Predicting the soil-to-plant transfer of metals in the context of global warming has become a major issue for food safety. It requires a better understanding of how the temperature alters the bioavailability of metals in cultivated soils, as studied by Cornu et al. The soil-to-plant transfer of Cd and Zn was promoted at higher soil temperatures despite a parallel decrease in Cd and Zn bioavailability. Warming is thus suspected to promote the soil-to-plant transfer of metals by facilitating the capture of metals by plant roots and, in agricultural soils, may lead to an over concentration of metals like Cd in the edible parts of crops.

Then, the assessment of the relevance of innovative processes and exogenic materials in modifying the exposome of fauna and plants to ensure appropriate remedial solutions of polluted soils. Mixed effluents of urban and hospital effluents were tested by Wigh et al. before treatment, after biological treatment alone and after biological treatment followed by a tertiary ozonation. Contrary to the lack of toxicity observed with normalized ecotoxicity tests, endpoints measured on zebrafish embryos such as mortality, developmental abnormalities and genotoxicity demonstrated a residual toxicity of wastewaters after biological treatment, followed or not by ozonation. This work highlighted the long way to dispose of a valuable ecotoxicity bioassays battery adapted to the peculiarities of treated wastewater effluents.

In a similar way, the eco-genotoxicity of sludge was assessed in a laboratory soil test before their use for remediation in real conditions (Chiochetta et al.). They have shown that biotests (microbiological enzymes, earthworms, and higher plants including Vicia faba genotoxicity test) help to determine the most appropriate higher plants for this later purpose and to ascertain the application rates of sludge to promote soil revegetation and ecological restoration of a site impacted by anthropic activities.

Finally, Rorat et al. used specific biomarkers to assess the influence of exposure to sewage sludge on the composting earthworms Eisenia fetida and Eisenia Andrei, also recommended by OECD as test organisms in ecotoxicology. Considering specific biomarkers, they showed that contaminants present in sewage sludge did not affect earthworm's immune system, but the mechanisms of accumulation and detoxification of particular metal fractions by earthworms should be explained.

Research was also designed to assess the impact of chemical stressors encountered in agroecosystems (organic contaminants, trace elements, and biological control agents). They concerned different model organisms of aquatic and terrestrial ecosystems. In particular, these age-dependent differences reflected the variability of the individual hatching success and varying expression levels of the Ca-CdMT gene in response to Cd exposure. Cd sensitivity was found to decrease with the age and developmental stage of C. aspersus embryos at the time of Cd exposure. In a second study, they showed that exposure to Cd and Cu in developing snail embryos can lead to the expression of all three snail-specific MT isoform genes. The investigation shows that the kind of metal exposure (duration of exposure, concentration levels of metals involved) may have a strong impact on the upregulation pattern of the three snail MT genes.

Then, the effects of low doses of insecticides were assessed on both targeted crop pests and beneficial insects. These doses could induce unexpected hormetic effects on insects. Siaussat et al. aimed at examining the effects of sublethal doses of deltamethrin on the peripheral olfactory system and sexual behavior of the cotton leafworm Spodoptera littoralis. They highlighted a hormetic effect of sublethal dose of deltamethrin on the male responses to sex pheromone, without any modification of their response to host-plant odorants. That effect can potentially contribute to the adaptation of this pest insect to pesticide treatment. They studied also the effects of sublethal doses of methomyl and chlorpyrifos on S. littoralis. A metabolomic approach evidenced that these insecticides had a systemic effect on the treated insects. The metabolic disruption and the info-disruption of the chemical communication they reported participated to a better understanding of the subtle effects of environmentally relevant sublethal pesticide concentrations on a target species.

Moreover, beside conventional organic pesticides, biological control agents are used for crop protection. Amichot et al. evidenced, as side effect, an acute toxicity of Bacillus thuringiensis on Trichogramma chilonis females. After ingestion of B. thuringiensis at sublethal doses, life history traits of T. chilonis such were differently affected. These effects, taken together, exemplify the difficulty to address ecological risks of an active compound.

Several studies were concerned with higher plants. Marchand et al. studied the foliar ionome, photosystem II activity, and leaf growth parameters of Ranunculus acris L., a potential biomonitor of trace element contamination and phytoavailability in two riverbank soils. They showed that the foliar ionome of R. acris was only effective to biomonitor total and soluble soil Na and Mo concentrations in soil series. In a second study, they considered the plant responses to a phytomanaged urban technosol contaminated by trace elements and polycyclic aromatic hydrocarbons. They showed as necessary to characterize the whole pollutant linkage when estimating the risks associated to high trace elements/PAH concentrations in a soil. Because the phytotoxicity may be, as in their study, relatively low in spite of high total contaminant concentrations, the implementation of phytomanagement strategies will limit in a long-lasting way the solubilization and/or mobility of contaminants at lower cost than techniques of civil engineering used for soil decontamination. The study of crossed-effects between chemical pollution and climate change was identified as an increasing relevant concern for ecotoxicologists, by possibly modifying community structure and ecosystem functioning. Gandar et al. assessed the individual and crossed-effects of pesticide exposure and temperature rising on Goldfish, Carassius auratus. They found that combined chemical and thermal stresses impaired the capacity of the fish to setup an efficient adaptive response, and suggested that temperature will make fish more sensitive to water contamination by pesticides. These results raised concerns about wild fish conservation submitted to global changes.

To conclude that Special Issue, we present the infrastructure for Analysis and Experimentation on Ecosystems (AnaEE-France), an integrated network of the major French experimental, analytical, and modeling platforms dedicated to the biological study of continental ecosystems (both aquatic and terrestrial). AnaEE-France offers adequate services to tackle the new challenges of research in ecotoxicology, positioning its various types of platforms in an ecologically advanced ecotoxicology approach.

We hope that you will enjoy reading this Special Issue, presenting some challenging questions in ecotoxicology, from bioavailability of pollutants to remediation and ecological engineering.

Firstly,

  Lebrun et al. conformed that soil fungi of different phyla secreted hydrolases and oxidoreductases involved in various environmental processes. They demonstrated that, unlike the great variability of the response of hydrolases, the secretion of oxidoreductases was increased or specifically produced following exposure of fungi to Cu and Cd. Because of the genericity of these responses, the fungal oxidoreductases appear relevant tools for metal ecotoxicity assessment in soils.The choice of incoming data for building Species Sensitivity Distributions (SSD) play a crucial role and may change greatly the values of the Hazardous Concentrations thresholds. In their study considering planktonic species, Larras et al. showed that SSD based on literature data were more sensitive than the one obtained with specific data. They conclude that in SSD models based on data that underestimate the sensitivity of species, the Hazardous Concentration 5 (that affect 5% of the species of a community) thresholds less protective than expected. Additional studies on communities are important to increase the predictive power of the threshold defined for risk assessment.Effects of pollutants were also assessed on invertebrates. Pelosi et al. showed that the commercial formulation of the fungicide epoxiconazole (Opus®) exerted more negative effects on the earthworm Aporrectodea icterica than this observed on Eisenia fetida., a species commonly used in assays for ecotoxicity assessment. They highlighted the importance of considering exposure duration and kinetic measurements when studying biochemical biomarkers.Developmental stage was shown to govern snail sensitivity to Cd by Baurand et al. They evidenced differential sensitivities in early life stages of Cd-exposed terrestrial snail embryos.

  Understanding the developed by organisms to tolerate pollutants remains of great concern. Bernard et al. analyzed the expression of antioxidant defense genes in Brassica oleracea and Trifolium repens. Plants exposed suburban soil spiked by low concentrations of Cd and Pb were analyzed for metal accumulations, expression levels of genes encoding proteins involved and/or related to antioxidant defense systems. The results presented suggested a benefit to use complementary species to better apprehend the biological effects in ecotoxicology, because distinct species do not mobilize exactly the same mechanisms to manage with metal contamination. This must be kept in mind when gene variations and in a larger extent biomarkers are used to assess soil quality. Several papers were also concerned with the transfer of contamination within feed or food chains in a context of agricultural practices. The work presented by Nguyen et al. considered the exposure of maize plant to low Cd concentrations. The Cd, Cu and Zn concentrations in shoots decreased with time at the vegetative stages. Shoots of young plants were enriched in micronutrients Cu and Zn but also in toxic Cd, illustrating the challenge to consider plants containing both nutritional value and levels of toxic elements. The xylem sap analysis is a potential valuable tool to precociously compare different soil conditions with respect to both the phytoavailability of the trace elements and their allocation to shoots. The high tolerance of the herbivorous snail Cantareus aspersus to Hg when exposed through food or soil contamination was demonstrated by Gimbert et al. The ecotoxicological metrics provided by their study will contribute to the databases for Hg, remaining still sparse concerning the terrestrial environment. Their results made snails of interest for the biomonitoring and thus, as they may represent a non-negligible source of Hg transfer to their consumers, for the risk assessment of Hg contaminated sites. Livestock reared on polluted areas are involuntary contaminated by chemicals. Their level of contamination may exceed the threshold values set by the European Union. In their study, Lastel et al. aimed at characterizing chlordecone disappearance in the empty carcass, the liver, the adipose tissues and the serum in growing ruminants. Their suggesedt that sustainability of farming and rearing practices used in the French West Indies remained possible when the contaminated animals underwent a sufficient period of decontamination. That period of decontamination needs to be adjusted to each kind of animals and their initial level of contamination.

Dr

  Christian Mougin is a senior scientist at the National Institute for Agricultural Research (INRA) in the "Functional Ecology and Ecotoxicology of Agro-Ecosystems" joint research unit in Versailles, France. His main interests combine the fate of contaminants (metals, pesticides, cyanotoxins and emerging compounds) in soils, and the responses of microorganisms and macrofauna exposed to these chemicals, both in situ and through laboratory experiments. His work focuses actually on the development of innovative tools for the biochemical characterizations of soils, sediments, and living micro-macro-organisms, in relation to the assessment of ecosystems functioning under anthropic constraints. Christian Mougin is in charge of French research platforms open to research in ecotoxicology, and leads the INRA's national network of Ecotoxicologists, ECOTOX (http://www6.inra.fr/ecotox). Dr Agnès Bouchez is a senior scientist at the National Institute for Agricultural Research (INRA) in the "Alpine Center for Research on Lake Ecosystems and Food Webs" research unit in Thonon-les-bains, France. She is mainly involved in the functional evaluation of the ecological quality of lakes and rivers using genomic, taxonomic and ecotoxicological tools. Based on these tools, she develops innovative metrics and methodologies to assess the impacts of xenobiotics on the structure and functioning of freshwater microbial communities. Her work focused on bringing more ecological realism in risk or impact assessment, regarding contaminants (low doses, mixtures), biological organisms (species or communities from the environment) and experimental approaches in micro-mesocosms or in the field. Agnès Bouchez is co-leading the INRA's national network of Ecotoxicologists, ECOTOX (http://www6.inra.fr/ecotox).

Acknowledgments: The network extends its sincere thanks to Environmental Science and Pollution Research editor-in-chief Prof Philippe Garrigues and to Springer, the journal's publisher, for their full support to that special issue. We are also grateful to the ESPR Editorial Board and reviewers for undertaking careful review of manuscripts submitted to this special issue.

Dr Laurence Denaix is a senior scientist at the National Institute for Agricultural Research (INRA) in charge of the direction of the research Unit "Interactions of Soil-Plant Atmosphere" in Bordeaux, France. Her main research topics are the bioavailability of trace elements, their speciation in soil solution and the quantification of their soil-root flows, using passive samplers.

She is working on diffuse contamination of agro-ecosystems and also manages transfer projects with technical institutes and participates to the management of the RMT QUASAPROVE. She


Antonis A Zorpas
email: antoniszorpas@yahoo.com

Maria K Doula
email: mdoula@otenet.gr

Mejdi Jeguirim
email: mejdi.jeguirim@uha.fr

Waste Strategies Development in the Framework of Circular Economy

Introduction

Current studies proposed that more that 2bn tons of solid waste/year are produced globally [START_REF] Kazamias | Cutting drilling waste from oil & gas exploitation management through end-of-waste criteria in the framework of circular economy strategy[END_REF][START_REF] Loizia | Measuring the Level of Environmental Performance on Coastal Environment before and during the COVID-19 Pandemic: A Case Study from Cyprus[END_REF][START_REF] Voukkali | Evaluation of Urban Metabolism assessment methods through SWOT Analysis and Analytical Hierocracy Process[END_REF]. Waste, in its general definition (solid and/or liquid), is among the most challenging environmental concerns in many communities. Considering the goals that are raised in the context of the circular economy (which focuses on the recycling of at least 65% of communal waste by 2035, and up to 70% by 2030, according to the common EU target), several strategies are needed. To propose any answer to waste management, strategies related to the hierocracy, as mentioned in the waste framework directive (WFD), must be developed. This special issue invited submissions connected to strategy development at the horizontal level, i.e., solid waste, wastewater, agri-waste, etc. .

The responses to our invitation had the following statistics: The authors' geographical distribution (published papers) is:

• Cyprus (3) • Greece (2) • Kazakhstan (2) • Australia (1) • China (1) • Oman (1) • Palestine (1) • Spain (1) • Tunisia (1) • United Kingdom (1)
The published submissions, without limitation, are related to waste strategies management, air pollution, waste valorization, environmental impact evaluation, life cycle analysis and wastewater treatment.

Short Review of the Contributions in This Issue

Although waste will continue to grow, and despite several efforts to reduce waste in many levels, there is a total absence of a holistic approach at the political level to solve the crisis of waste management in depth. In fact, since the treaty of Rome, back in 1957, there was no common statement from the leaders to take action on environmental protection. For more than 60 years, there were no specific initiatives at the European level. A strategic approach is needed and is essential to solve the problem .

Ciu et al. [START_REF] Cui | Study on Compulsory Classification Management and Behavior Synergy of Municipal Solid Waste[END_REF] presented the subject-object-process model, within the waste classification management system, and proposed a model focused on municipal solid waste (MSW), which also uses several KPIs (Key Performed Indicators)-considering Beijing, China, as an example, and the citizens' behaviors in several household waste management systems (WMS). The proposed research indicates that in the existing WMS the interaction between government management and residents' domestic waste classification behavior varies from 0.40 to 0.68, compared with the behavior between companies and residents, which varies from 0.45 to 0.75. Social behavior is considered a vital issue in any waste strategy plan, as through the analysis of the social attitude and behavior of the participants several weaknesses have been defined in order to improve the existing management system and the appropriate strategy.

Food waste prevention is on the top of the stakeholders' priority list at the global level [START_REF] Zorpas | A prevention strategy plan concerning the waste framework directive in Cyprus[END_REF][START_REF] Zorpas | Waste prevention campaign regarding the Waste Framework Directive[END_REF]. Several studies mentioned that the households are the main food waste producers. Among the main issues concerning food waste and the predictability of consumers' behavior, Kritikou et al. try to analyse, in their last report, the main factors that affect food waste generation in Greece [START_REF] Kritikou | Investigating the Determinants of Greek Households Food Waste Prevention Behaviour[END_REF]. The authors have used 921 households from Greece based on a structured questionnaire considering all ethical issues. Using the Theory of Planned Behavior, they examined the relations between the attitude to food waste, subjective norms, perceived behavior at intention, control, and self-reported behavior, considering the knowledge on prevention control in general. The proposed research indicates that the food waste prevention was mainly determined by a general environmental attitude. This has a direct effect on environmental education and food waste prevention behavior. Furthermore, the results of the proposed study can act as a reference point for policy makers and the implantation of a campaign focused on food waste prevention.

Conventional policies and practices cannot be resolved during the COVID-19 pandemic. Furthermore, COVID-19 has a direct impact on many industrial activities, like construction and demolition (C&D) waste management. More than that, Extended Producer Responsibility (EPR) may prevent waste development and promote a circular economy strategy, to be adopted in the construction industry. Shooshtarian et al. [START_REF] Shooshtarian | Extended Producer Responsibility in the Australian Construction Industry[END_REF] reviewed the Australian regulatory environment and practice in order to distinguish barriers to implement a relative strategy on C&D considering EPR. Using multiple selection criteria and 59 diverse causes, the presented results point out that there is an extensive support among diverse stakeholders to develop EPR and extend the existing regulation to other materials. The main obstacles remain the relevant cost and the time implications for the EPR policy. The result of this research could be useful for policy makers dealing with EPR policies.

In a strategic approach to help communities and local economies, the entire hospitality industry plays a fundamental role. At the same time, the entire hospitality industry led to opposing environmental effects, particularly in coastal regions which are documented as being of strategic importance. In addition, coastal areas are facing lots of pressure from the hospitality industry due to the massive amount of waste production. Loizia et al. [START_REF] Loizia | Measuring the Level of Environmental Performance on Coastal Environment before and during the COVID-19 Pandemic: A Case Study from Cyprus[END_REF] provided responses to the hypothesis that the COVID-19 pandemic lockdown scenario would advance the environmental performance in this area. Until now, there are very few studies focused on the environmental dimensions in any coastal area due to the pandemic. Using a number of KPIs, the environmental performance was measured considering the clean coast index (CCI), waste accumulation index (WAI) and waste accumulation rate (WAR), as well as through micro-, meso-and macroplastic concentrations on the beach. The proposed research could serve as a reference point for competent authorities in order to reorganize their waste management plan, by expanding their waste infrastructures to defend the coastal environment.

Air quality is considered a vital indicator for human health. The World Health Organization pointed out that, on a yearly basis, approximately 7-9 million citizens are dying due to air pollution issues. In general, air pollution is strictly related to energy production, climate change and human health. Especially in modern cities, air pollution plays a fundamental role in human health, and especially the concentration of PM10, PM2.5 and PM1 µm. The PM concentrations were measured in the city of Limassol in Cyprus from natural (e.g., dust events) and anthropogenic (i.e., traffic, cement works, restaurants) activities in two seasons: summer and spring [START_REF] Petsas | Measurements of Local Sources of Particulates with a Portable Monitor along the Coast of an Insular City[END_REF]. The results were useful to monitor the air quality in cities.

A Life Cycle Analysis (LCA) is an environmental tool that is very useful to assess any strategy put in place [START_REF] Litskas | Sustainable Viticulture: First Determination of the Environmental Footprint of Grapes[END_REF][START_REF] Banti | LCA of a membrane bioreactor compared to activated sludge system for municipal wastewater treatment[END_REF][START_REF] Tsangas | Life cycle analysis in the framework of agricultural strategic development planning in the Balkan region[END_REF]. Litskas et al. [START_REF] Litskas | Sustainable Viticulture: First Determination of the Environmental Footprint of Grapes[END_REF], using an LCA approach, assess grapes' environmental footprint (EF). Using data from three several production systems from wineries in Cyprus and the database from AGRIBALYSE (life cycle inventory-LCI data), they calculate the EF of the vineyards through the Open LCA software. The system boundaries were chosen from "cradle to winery door", and 1 ton of grapes carried to the winery was chosen as the functional unit. Machinery, oil and sulfur production were recognized as EF hotspots for organic grapes, while the production of fertilizer was recognized as the EF hotspot for high-input grape manufacture. This research points out that future studies need to enrich the LCI databases.

Considering the effectiveness of wastewater treatment technologies on real conditions is vital for the effective monitoring of wastewater [START_REF] Nikologianni | New Integrated Approaches to Climate Emergency Landscape Strategies: The Case of Pan-European SATURN Project[END_REF]. Poultry slaughterhouse wastewater generated from defeathering, cooling and evisceration processes was preserved using a electrochemical method with Fe-Gr, Fe-Fe and Al-Gr electrode groupings [START_REF] Zorpas | Municipal Sewage Sludge Characteristics and Waste Water Treatment Plant Effectiveness under Warm Climate conditions[END_REF]. In addition, water and sanitation is considered as one of the main SDGs-more specifically, the SDG 6. There are many studies focusing on the competence of the wastewater treatment. For this special issue, Meiramkulova et al. [START_REF] Meiramkulova | Evaluation of Electrochemical Methods for Poultry Slaughterhouse Wastewater Treatment[END_REF][START_REF] Meiramkulova | The Effect of Scale on the Performance of an Integrated Poultry Slaughterhouse Wastewater Treatment Process[END_REF] examined the effect of wastewater behavior in a poultry slaughterhouse. The proposed systems include membrane filtration, electrolysis and ultraviolet irradiation. The study took place in a poultry farm slaughterhouse in Kazakhstan. The water quality index (WQI) was used to provide answers on the quality of the drinking water that were used as a reference point. The engineering plants exposed a high purification productivity for most of the parameters.

Jellali et al. [START_REF] Jellali | Investigations on Biogas Recovery from Anaerobic Digestion of Raw Sludge and Its Mixture with Agri-Food Wastes: Application to the Largest Industrial Estate in Oman[END_REF] assessed the environmental, technical and economic viability of the anaerobic digestion (AD) sludge formed in a wastewater treatment plant (WWTP). Based on the characterization of the sludge samples, it was mentioned that for a 20-year project the production of electricity through AD was 43.9 GWh, while at the same time the reduction of greenhouse gas (GHG) emissions was greater than 37,000 ton. equivalent CO 2 .

Hindiyeh et al. [START_REF] Jellali | Investigations on Biogas Recovery from Anaerobic Digestion of Raw Sludge and Its Mixture with Agri-Food Wastes: Application to the Largest Industrial Estate in Oman[END_REF] proposed a valuable explanation for avoiding the predicted Sea Level Rise (SLR) by the seawater desalination and storage within the des-plants distributed globally, which in a strategic approach is considered as a very promising scenario.

The agri-sector plays an important part concerning the food safety and scarcity. In addition, the agri-sector contributes to air quality contamination and the associated effects on the human health, and produces huge numbers of several waste types [START_REF] Tsangas | Life cycle analysis in the framework of agricultural strategic development planning in the Balkan region[END_REF]. Olive mill wastes received huge attention due to the high waste volumes, mainly due to their toxicity and their negative impacts on the environment [START_REF] Vlyssides | Characteristics of solid residues from olive oil processing as a bulking material for co-composting with industrial wastewater[END_REF][START_REF] Doula | Evaluation of the application of Olive Mill Waste on soils; The case study of disposal areas in Crete, Greece[END_REF]. The oil extraction process produces huge seasonal quantities of olive by-products that require noteworthy attention because of their high organic content and significant toxicity due to the phenolic substances with extremely vital environmental issues [START_REF] Zorpas | Combination of Fenton Oxidation and Composting for the treatment of the olive solid residue and the olive mile wastewater from the olive oil industry in Cyprus[END_REF][START_REF] Zorpas | Intergraded Applied Methodology for the Treatment of Heavy Polluted Waste waters from the olive oil industries[END_REF][START_REF] Jeguirim | Olive mill wastewater: From a pollutant to green fuels, agricultural water source and bio-fertilizer-1. The drying kinetic[END_REF][START_REF] Marks | Potential for Production of Biochar-Based Fertilizers from Olive Mill Waste in Mediterranean Basin Countries: An Initial Assessment for Spain, Tunisia, and Greece[END_REF][START_REF] Hadroug | Static and Dynamic Investigations on Leaching/Retention of Nutrients from Raw Poultry Manure Biochars and Amended Agricultural Soil[END_REF]. A promising strategic approach beside composting [START_REF] Zorpas | Combination of Fenton Oxidation and Composting for the treatment of the olive solid residue and the olive mile wastewater from the olive oil industry in Cyprus[END_REF][START_REF] Zorpas | Intergraded Applied Methodology for the Treatment of Heavy Polluted Waste waters from the olive oil industries[END_REF] is the thermal conversion of olive mill solid wastes and olive mill wastewaters into a rich nutrient biochar.

Sustainability 2021, 13, 13467. https://doi.org/10.3390/su132313467 https://www.mdpi.com/journal/sustainability

Funding: This research received no external funding.

Institutional Review Board Statement: Not applicable.

Data Availability Statement: Not applicable.

Conflicts of Interest:

The authors declare no conflict of interest.

Author Contributions: The authors contributed equally to the manuscript. All authors have read and agreed to the published version of the manuscript.

Informed Consent Statement: Not applicable.