Ulysse Brémond
email: ulysse.bremond@airliquide.com

Aude Bertrandias

Jean-Philippe Steyer

Hélène Carrere
email: helene.carrere@inra.fr

Post-treatments and recirculation of agricultural solid digestates: impact on full-scale methane yield

Keywords: Solid digestate, Post-treatment, Recirculation Session -Post-treatments anaerobic effluents/digestates

In order to enhance agricultural biogas plant efficiency, impact of solid digestate post-treatments and recirculation on methane yield were evaluated at lab scale. Several full-scale solid digestates were characterized to determine their residual methane potential. Subsequently, effects of thermo-alkaline or short-term aerobic post-treatments on solid digestate methane potential were measured. Results show that direct recirculation of 50% of agricultural solid digestate leads to a low increase on plant methane yield (less than 3%). Therefore, post-treatment cost has to be carefully taken into account as potential gains are weak. Thermo-alkaline treatment leads to a 30-45% increase of the solid digestate methane yield but its cost at full scale is not profitable. On the contrary, short-term aeration posttreatment can be performed at low cost at industrial scale but it leads to methane losses since the remaining easily biodegradable fractions are degraded instead of lignocellulosic ones.

Introduction

At full scale, Hydraulic Retention Time (HRT) and feedstock type are the two key parameters affecting biogas plant efficiency [START_REF] Ruile | Degradation efficiency of agricultural biogas plants-a full-scale study[END_REF]. To ensure a high efficiency, HRT has to be adapted as a function of the feedstock [START_REF] Muha | A dynamic model for calculating methane emissions from digestate based on co-digestion of animal manure and biogas crops in full scale German biogas plants[END_REF]. However, current co-digestion processes and empirical selection of the HRT in agricultural biogas plants often lead to remaining methane potential in the digestate. Therefore, a good management practice of digestates has to be identified in order to enhance efficiency and environmental footprint of agricultural biogas plants. For liquid digestates, coverage and heating of the storage tank were identified as good practices [START_REF] Bacenetti | Agricultural anaerobic digestion plants: What LCA studies pointed out and what can be done to make them more environmentally sustainable[END_REF]Lijo et al., 2017) and they are often implemented at the industrial scale. However, for solid digestate, there is currently no good management clearly advised. This study focuses on increasing agricultural biogas plant efficiency by recirculating part of the solid digestate. Additionally, two post-treatments were tested to enhance biodegradability and methane yield of solid digestates: (i) a thermo-alkaline post-treatment using soda, as it was proven to be an efficient pretreatment to degrade lignin [START_REF] Carrere | Review of feedstock pretreatment strategies for improved anaerobic digestion: From lab-scale research to full-scale[END_REF], (ii) a short-term and controlled aerobic post-treatment, as long-term composting of solid digestate leads to low methane yields (Menardo et al., 2010). Impact and interest of such practices are evaluated regarding potential economic gains at full scale.

Material and Methods

Origin and characterisation of solid digestates Solid digestates were sampled from screw-press facilities in six agricultural biogas plants located in France. Total solids (TS) and volatile solids (VS) were measured according to standard protocols (APHA method) and BMPs were prepared similarly to [START_REF] Rouches | White-Rot Fungi pretreatment of lignocellulosic biomass for anaerobic digestion: Impact of glucose supplementation[END_REF] and performed following standardized practices [START_REF] Holliger | Towards a standardization of biomethane potential tests[END_REF].

Evaluation of direct recirculation strategy Two hypotheses were made: (1) solid digestate was not replacing substrate; (2) a reasonable quantity of solid digestate that can be recirculated corresponds to 50% of the total amount produced. Indeed, part of it needs to be returned to the soil and a higher amount would probably increase digester total solids too much. Direct recirculation consists in the farmer picking up solid digestate at the outlet of the screw press and reincorporating it into the hopper. BMP values, corrected by a 0.8 factor [START_REF] Holliger | Methane Production of Full-scale anaerobic Digestion Plants calculated from substrate's Biomethane Potentials compares well with the One Measured On-site[END_REF], were used to simulate recirculation process at full scale. Soda post-treatment Thermo-alkaline soda post-treatment was performed on three of the digestates. Soda was added to solid digestate at 2%w and maintained at 55°C for 3 days at 120 rpm. Then, inoculum was added and BMP tests were started. Short-term aerobic post-treatment Short-term aerobic post-treatment was evaluated on two solid digestates. Solid digestates were placed inside 2.5L bioreactors equipped with an aeration system. Several short duration (1.5 to 6 days) and airflow (1.5 to 30 L/h/kg of TS) were tested at 30°C. Finally, mass loss due to respiration was evaluated by trapping the emitted CO 2 in a soda solution, of which conductivity was measured. It was considered that all carbon losses under the form of CO 2 during the post-treatment would have otherwise given biogas (ratio 60% CH 4 /40% CO 2 ). BMPs and matter fractionating method [START_REF] Jimenez | A new organic matter fractionation methodology for organic wastes: Bioaccessibility and complexity characterization for treatment optimization[END_REF] were performed on treated solid digestates.

Results

Data on biogas plants, solid digestates characterization and the impact of the direct recirculation are summarized in Table 1. For all plants, recirculation of 50% of the total amount of solid digestate produced leads to an increase in plant methane yield as solid digestate still contains biodegradable organic matter. However, this increase is relatively low (1-2.6%). Economic gains from this additional methane are between 8.5 and 28 k€/year. Even with the added operational costs, such strategy should be beneficial for biogas plants. The following question is raised: can additional post-treatment be economically viable? Thermo-alkaline post-treatment using soda was tested on plant A, B, C and had a positive impact on the solid digestate methane yield. BMP values indeed increased respectively by 45%, 35% and 30% (see Table 2). However, additional gains towards direct recirculation, around 5000 €/year, are too small regarding additional CAPEX (treatment tank) and OPEX (soda, heating & mixing). Therefore, thermo-alkaline post-treatment is too expensive and not viable at full scale. Thus, low-cost post-treatments have to be considered such as short-term aeration posttreatment. This post-treatment was performed on solid digestates of plants B and C. Carbon loss due to respiration was always detected and taken into account when methane yield was calculated. For plant B (Figure 1), when a strong aeration was applied (10 or 20 L/h/kg TS), methane yield was 10-20% lower than the control (untreated blank). Even for lower airflow (1.6 L/h/kg TS) but longer duration, the methane yield was not significantly enhanced. For plant C solid digestate, similar results were found (data not shown). Methane loss was around 15% whatever the applied airflow and duration. Such results can be explained by the composition of the organic matter of solid digestate (Figure 2). Indeed, a fraction of easily biodegradable organic matter (solubles, proteins, sugars) remains in the solid digestate; for instance, 19% in plant B solid digestate (SPOM+SEOM). During the short-term aeration post-treatment, lignin and holocelluloses fractions are not degraded by aerobic endogenous microorganisms. Instead, easy-to-degrade fractions, which would have given methane in a direct recirculation strategy, are respired under the form of CO 2 . Thus, in the case of a solid digestate aerated 6 days at low air flow, the easily biodegradable fraction (SPOM+SEOM) was reduced by 20%. Endogenous microorganisms do not display naturally, under aerobic conditions, ligninolytic activities and they only degrade the easily degradable matter. Lower methane yields obtained can be explained by: (1) almost no gain in solid digestate biodegradability as lignin fraction is not degraded;

(2) matter loss due to respiration. Thus, despite its interesting lower cost, a shortterm aeration post-treatment does not permit to enhance methane yield of solid digestate.

Conclusions

We have shown, at lab scale, that direct recirculation of solid digestate can be a good strategy to slightly enhance agricultural plant methane yield by 1-2.6%. For farmers, such increases are interesting as this strategy is easy to implement at full scale. Some agricultural biogas plants in France are already performing this strategy but a full-scale study is still needed to clearly evaluate its economic interest (OPEX determination).

Thermo-alkaline and short-term aerobic post-treatments do not appear to be beneficial in comparison to direct recirculation as methane yield or/and economic gains are weaker.

Figure 1

 1 Figure 1 Effects of several short-term aerations on methane potential of plant B solid digestate (mass loss included)

Figure 2

 2 Figure 2 Example of the effect of short term aerobic post-treatment on organic matter bioaccessibility

Table 1 Agricultural biogas plant features and effect of direct recirculation strategy on plant methane yield.

 1

	Plant name	Plant A	Plant B	Plant C	Plant D	Plant E	Plant F
	Main type of waste	Catch crop beet pulp	Bovine manure & cereal waste	Bovine manure & straws	Swine manure & beet pulp	bovine manure & food waste	Green waste
	HRT (days)	120	100	120	25	80	18
	Type of valorization	upgrading	upgrading	CHP	CHP	upgrading upgrading
	Methane production (Nm 3 /year)	1 060 000	1 060000	1 201 000	775 000	1 020 000 1 020 000
	Incomes (k€/year)	1130	1130	745	500	1088	1090
	Quantity of solid dig. produced (tons/year)	1100	1500	2000	1600	2400	2600
	Volatile solids (% fresh matter)	21	16	20	20	19	29
	BMP of solid dig. without treatment (Nml CH4/g VS)	129	150	145	155	158	67.5
	Plant methane yield increase
	if 50% solid dig. directly	0.98	1.34	1.85	2.6	2.58	1.87
	recirculated (%)
	Economic gains from methane (k€/year)	11.2	15	13.8	8.5	28	20.5

Table 2 Effect of thermo-alkaline post-treatment on plant methane yield and economic gains

 2

	Plant Name	Plant A	Plant B	Plant C
	BMP of solid dig. without treatment (Nml CH4/g VS)	129	150	145
	Plant methane yield increase if 50% solid dig. directly recirculated (%)	0.98	1.34	1.85
	BMP of solid dig. with thermo-alkaline treatment (Nml CH4/g VS)	188	209	195
	Plant methane yield increase if 50% solid dig. is post-treated & recirculated (%)	1.43	1.86	2.48
	Economic gains from methane (k€/year)	16.3	21.1	18.5
	Net gains towards direct recirculation (k€/year)	5	6.1	4.7


Akli Fundo

Jean-Benoist Leger
email: jbleger@hds.utc.fr

Dritan Nace
email: dnace@hds.utc.fr

Chenghao Wang

Dealing with uncertainty in ATM -the Flight Level Assignment problem

Keywords: Robust Optimization, Flight Level Assignment, Gaussian Mixture Distribution

Introduction

The aircraft will be required to follow a negotiated conflict-free trajectory in the future ATM (Air Traffic Management) system, accurately defined in 4 dimensions (Waypoint composed of longitude and latitude, Altitude and Time) in order to reduce the need of controller's intervention during the tactical phase. Instead of rerouting aircraft's trajectory (new waypoints may be required) in a resolution of potential conflicts, the FLA (Flight Level Assignment) problem aims at optimally assigning flight level to reduce the total number of potential en-route conflicts and most importantly the induced cost (generally expressed as delays). In practice, flights are continously impacted by delays in departure time as well as en-route delays. Unfortunately, a very small deviation of flight departure time may lead to important adittional en-route delays due to unpredicted conflicts. Therefore, leveraging the tractable algorithms proposed in [START_REF] Klopfenstein | Tractable algorithms for chance-constrained combinatorial problems[END_REF], a first robust approach to solve the FLA is proposed to tackle the issue of data uncertainty in [START_REF] Fundo | A Heuristic Approach for the Robust Flight Level Assignment Problem[END_REF]. Optimization problems in ATM have been widely studied these last decades. We focus on some works related to a certain extent to the flight level assignment problem. Let us firstly refer to [START_REF] Cook | Applying complexity science to air traffic management[END_REF], Cook et al. have shown how the uncertainty affects the ATM system and its importance in building a proper model, control it and improve its performance. We focus on an important facet of ATM, namely the flight level assignment, and report some new considerations on this issue and more generally on robust optimization. This work is in continuation of [START_REF] Fundo | A Heuristic Approach for the Robust Flight Level Assignment Problem[END_REF][START_REF] Klopfenstein | The robust flight level assignment problem[END_REF].

Dealing with uncertainty in FLA

Let be given a general problem : max Cx such that Ax ≤ b and x is binary. A typical constraint in A is expressed as : j x j a i,j ≤ a i,0 and we consider the probabilistic separated constraint problem which gives constraints as : P r( j x j a i,j ≤ a i,0 ) ≥ 1 -ε. Following the idea of Klopfenstein in [START_REF] Klopfenstein | Tractable algorithms for chance-constrained combinatorial problems[END_REF], one may relax the initial set of uncertain variables into a subset of variables (I u ) that we intend to control while the other variables are assumed to take their worst-case values. The corresponding constraint will be : P r( j∈Iu a ij x j + j / ∈Iu a ij x j ) ≥ 1-ε. Comming to our FLA problem, all above is written as :

P r   j∈S il p ij x l j ≤ P l i   ≥ 1 -⇔ P r   j∈S il ∩Iu p ij x l j + j∈S il \Iu pij x l j ≤ P l i   ≥ 1 -ε, (1)
where x l j is a binary variable taking 1 if an aircraft j is assigned at level l, 0 otherwise. S il denotes a set of flights having a potential conflict with flight i at level l. P l i specifies the admissible induced cost for a given flight i at level l. The induced cost (is a random value due to uncertainty of flight departure times) of flight i when resolving a potential conflict (a conflict happens when two flights at some moment have a separation distance less to a security given distance) with j is denoted by p ij . This random variable takes its values in [0, pij ], where pij takes the worst-case value in case of conflict.

The main difficulty of handling this kind of constraints stands in measuring the probability of sum of independent induced cost p ij , knowing that they follow a mixture Gaussian distribution (as shown in [START_REF] Tu | Estimating flight departure delay distributions-a statistical approach with long-term trend and short-term pattern[END_REF]) and are censored in [0, pij ]. More precisely, the distribution of p ij can be represented by a linear mixture of dirac distribution and a set of truncated Gaussian distributions which are outcome of mixture Gaussian distribution of flight departure time.

There may be several ways to deal with the model above. A general method is to treat the induced cost as independent random variables and compute a lower bound probability of their sum in (1) by using Hoeffding's inequalities [START_REF] Hoeffding | Probability inequalities for sums of bounded random variables[END_REF]. However, this method provides quite weak bounds as shown in [START_REF] Fundo | A Heuristic Approach for the Robust Flight Level Assignment Problem[END_REF]. Another common method is using Monte-Carlo Simulation method as shown also in [START_REF] Fundo | A Heuristic Approach for the Robust Flight Level Assignment Problem[END_REF]. MC simulation gives very good results but it scales not well with large instances. Inspired of closed-form proposed by Beauchamp [START_REF] Beauchamp | On numerical computation for the distribution of the convolution of N independent rectified Gaussian variables[END_REF] for the pdf of the sum of independent Gaussian random variables which are censored in [0, ∞), we are working to adapt this model to Robust FLA. The first drawn conclusions show that from the problem becomes computationally intractable. We are working on approximation of this form through 1) approximating mixture Gaussian model and 2) approximating convolution of truncated Gaussian distribution.

Conclusions and perspectives

In this work, we try to conduct a tractable and analytical form to evaluate the probability of feasibility of given robust solution, however such evaluation may have exponential number of items to compute. A first approximation herein is made to reduce the number of item during evaluation. A more tight approximation will be investigated in the future work. Some numerical results will be shown in trhe conference. This work is in progress.


Anne-Geneviève Bagnères

Cuticular Hydrocarbons in Social Insects

come

Cuticular Hydrocarbons in Social Insects

Author: Anne-Geneviève Bagnères CEFE, UMR CNRS 5175, Montpellier France Email: ag.bagneres@cefe.cnrs.fr All insects are covered by an epicuticular lipid layer comprising of long hydrocarbon chains generally termed cuticular hydrocarbons (CHCs)(2). In social insects, CHCs play multiple roles: they primarily serve structural and anti-desiccation functions, but they are also involved in various forms of signalling. More specifically, starting in the 1980s, researchers began to discover that CHCs play a role in interspecific, intercolonial, and interindividual recognition. Within colonies, they can convey information about nestmate status, kinship, caste, and fertility. They also act as sexual pheromones. In large part, they form signature mixtures, but they can also function as contact pheromones and primer pheromones.

CUTICULAR HYDROCARBONS AS SIGNALS

Extensive research has examined the semiochemical role of CHCs in ants and other social insects. Using behavioural tests employing covered dummies and electrophysiological data, studies have shown that individuals can recognise alien CHC mixtures, i.e., mixtures associated with other colonies or species. While the bodily location of the CHC signal varies among insects, the antenna seems to be the main organ involved in signal perception (Fig. 1). More specifically, the antenna's basiconica sensilla act as receptors for the sensory signals conveyed by CHCs, and via their multiple olfactory receptor neurons (ORNs) then transmit the information to the central nervous system, allowing individuals to differentiate between CHCs from nestmates versus non-nestmates or from queens versus workers (Fig. 2). Social insects can also distinguish among hydrocarbon types (e.g., linear alkanes, alkenes, methyl-branched alkanes). It was traditionally consensual that the olfactory receptors (ORs) in the 9-exon subfamily, which are part of a specialised olfactory subsystem in the antennal lobe (T6 glomeruli), are responsible for CHC discrimination. However, recent discoveries revealed that many other glomeruli and ORs in the antennal lobe may also be involved. Regardless of the specifics, OR neurons can differentiate between enantiomers methyl-branched hydrocarbons that act as pheromones and, in some cases, can distinguish among primer pheromones regulating colony reproduction. Social insects employ (R) methyl-branched enantiomers, a configuration that is highly conserved within this group. That said, both (R) and (S) enantiomers exist and could play a role in regulating social behaviour (1). It has been found that, over the course of honeybee development (pupae to mature adults), there are differences in the expression of the various genes involved in CHC biosynthesis, which results in stage-specific differences in CHCs.

FACTORS RESPONSIBLE FOR CUTICULAR HYDROCARBON VARIATION

In social insects, there are chemosystematic differences among orders and genera. In the termite genus Reticulitermes, chemosystematic data have yielded helpful insights on species delimitation, which correspond fairly well to phylogeographic data obtained via analyses of nuclear and mitochondrial DNA. However, in other taxa, such as the ant genus Crematogaster, only species-level variation has proven useful. Indeed, it is important to understand that external selection pressures exerted on social insects may often result in rapid adaption in terms of their chemical signatures. Furthermore, biotic and abiotic factors can shape CHC patterns. For example, social parasites, stress, geographical features, climate change, status as an invader, and microbial symbionts can also affect a social insect's chemical signature. Furthermore, such variation can then scale up: in paper wasps, nest odour can change following the state (parasitized or not) and the scale of parasitism.

HORMONAL AND ENZYMATIC REGULATION OF CUTICULAR HYDROCARBONS

CHCs are associated with juvenile hormone (JH) titres, behaviour, caste status, and reproduction. In the last few years, research in various social insect taxa has looked at how endocrine factors affect the release and the relative proportions of the compounds that serve as primer pheromones. It has been found that cuticular changes, notably those occurring during development and reproduction, are under the direct or indirect control of JH and various enzymes [START_REF] Falcón | Exoskeleton formation in Apis mellifera: Cuticular hydrocarbons profiles and expression of desaturase and elongase genes during pupal and adult development[END_REF].

KEY ROLES IN RECOGNITION

In the 1990s, CHCs were discovered to play a role in recognition. Since then, further research has demonstrated that CHCs are influenced by lifestyle (e.g., social parasitism) and are involved in caste and brood discrimination, task allocation, and behaviour (e.g., the honeybee waggle dance). It is clear that one of the main roles of CHCs in social insects is to convey reproductive status-within colonies, individuals are highly specialised, and most do not reproduce. In social species, it has been demonstrated that workers recognise reproductives based on their CHCs. In particular, the queen pheromone seems to have been conserved across diverse taxa. Non-volatile saturated hydrocarbons, and sometimes unsaturated hydrocarbons, are used to advertise queen fecundity and/or suppress worker reproduction [START_REF] Conte | Primer Pheromones in Social Hymenoptera[END_REF]; they can also serve to differentiate virgin, egg-laying, and non-egg-laying females. Such fertility signalling has been documented in native ants as well as in invasive ants, such as the Argentine ant. In wasps the role of CHCs as fertility signals is less clear Although reproduction-related patterns in CHCs have been observed, strong evidence of fertility signalling has yet to be obtained. As mentioned above, variation in CHCs is linked to hormonal changes. The relationship between CHCs and reproductive status has been demonstrated in different social insects, such as drywood termites [START_REF] Korb | Chemical fertility signaling in termites: Idiosyncrasies and commonalities in comparison with ants[END_REF], and the existence of cuticular royal pheromones was recently described in a subterranean termite. This reproductive signal can also convey dominance, as has been seen in social parasites. In most social insects and regardless of colony size, the earliest-described and most prominent role of CHCs is in nestmate recognition. However, more recently, it was shown that CHCs could also help to appease non-nestmates (4).

CUTICULAR HYDROCARBONS AND SOCIOBIOLOGY: A CONCLUSION

In social insects, the antenna is the organ that perceives and decodes the signal conveyed by CHCs, often resulting in changes in social behaviour. For example, social insects rely on CHCs to transmit information about factors such as reproductive status, group membership, and resource location, among others. Queen pheromones seem to have evolved from signals used in solitary ancestors (particularly in Hymenoptera), but there is a need for research comparing CHCs in solitary and social species to determine if the relationship of CHCs with physiology, behaviour, and reproductive status is also ancestral [START_REF] Oi | The origin and evolution of social insect queen pheromones: Novel hypotheses and outstanding problems[END_REF]. The debate over the signal honesty of queen pheromones is ongoing. Regardless, most forms of communication in social insects (e.g., regarding nestmate status, kinship, food location, recruitment, trail establishment, and alarm signalling) probably evolved from ancestral forms of communication. It has been shown that solitary insects and more basal social insects invest less in communication [START_REF] Wittwer | Solitary bees reduce investment in communication compared with their social relatives[END_REF]. Many interesting questions remain to be explored when it comes to the evolution of communication systems that use contact semiochemicals such as cuticular hydrocarbons. Also, many studies have focused on just a few models, such as honeybees or certain ant species. Although efforts have been made over recent years to improve model diversity, it is important to consider even a broader range of social insect taxa.

Figure 1 -Figure 2

 12 Figure1-Specificity of the antenna as the main organ involved in CHC perception. From Wang et al.[START_REF] Wang | Location-specific cuticular hydrocarbon signals in a social insect[END_REF]