Marie Bonnin
email: marie.bonnin@univ-angers.fr

Catherine Azzaro-Pantel

Serge Domenech

Optimization of natural resource management: Application to French copper cycle

Keywords:

An innovative resource flow optimization model is proposed that aims at helping decision makers to choose the best resource management policies at national and international scales. This model has been developed and validated on French copper cycle, but can easily be extended to any country or metal. A mathematical formulation of all the in and outflows of the resource, as well as stocks in the techno sphere and waste management, including recycling, has been developed. The complexity of resource cycle led to the introduction of 47 decision variables and resulted in a Mixed Integer Non Linear Pro gramming formulation. The resource cycle efficiency has been assessed through four indicators regarding costs, greenhouse gas emissions, energy consumption and resource losses. The NSGA II genetic algorithm methodology has been selected as an optimization strategy. Monobjective optimizations have firstly been conducted for each of the four criteria: the results showed that very different management stra tegies are needed depending on the targeted criteria. Multiobjective optimizations have thus been conducted coupled with the decision support tool TOPSIS to find an optimal compromise solution. As expected, the selected solution highlights the importance of developing a recycling channel for Waste from Electrical and Electronic Equipment in France.

Introduction

Economic development is strongly dependent on the use of natural resource and the growing demand creates a permanent pressure on the resource base, so that natural resource manage ment is an important issue that has to be treated carefully. Indeed, many materials, including metals, are essential to our lifestyle, while their availability is limited and their exploitation is both capital and energy intensive. The growing metal stocks in our so ciety can thus be seen as huge mines, which has been democratized with the "urban mining concept", defined as the "process of reclaiming compounds and elements from any kind of anthropo genic stocks, including buildings, infrastructure, industries, prod ucts (in and out of use), environmental media receiving anthropogenic emissions, etc." [START_REF] Cossu | Urban mining: concepts, terminology, challenges[END_REF]. Metals possess the advantage that they are infinitely recyclable with no loss of quality. In that context, scrap metal recycling, that provides resources to the basic manufacturing sector, plays a pivotal role while conserving natural resources and protecting the environ ment. Actually, recycling can be viewed as a way to mitigate negative impacts on increasing metal demand and to assure the potentials of economic growth. Scrap recycling facilities are rich with resources that can be reused, at a fraction of the cost to mine and refine metals from virgin ores. The utilization of these growing metal stocks through recycling is expected to be an important source for future metal supply. [START_REF] Graedel | Recycling Rates of Metals[END_REF] conducted a global study on metal recycling rates and concluded that most metals have too low recycling rates regarding their importance in crucial new technologies (for instance battery for electric cars), with significant potential for improvement. However, regarding for instance copper, the recycling input rate is continuously decreasing since 2011 (ranging from 36% in 2011 to 29% in 2016), while the secondary refined production is quite stable over the same period (ICSG, 2018). This shows that there is still room for improvement. In that context, the objective of this work is to propose a management strategy that could be implemented to support the deployment of a circular economy.

French copper cycle has been chosen as an application case because of copper importance in today's world as the third metal used in the world (after iron and aluminum) and used in many areas [START_REF] Muchova | End-of-Waste Criteria for Copper and Copper Alloy Scrap: Technical Proposals[END_REF]. The case of copper is also very inter esting because of the important available copper deposit. Indeed, it is estimated that 80% of the copper extracted since prehistory is still in use, immobilized in construction (55%), infrastructure (15%), industry (10%), transport (10%) and equipment (10%), with an average 30 year use duration (from a few years for electronic equipment until hundreds years for buildings) [START_REF] Scf | France Chemical Society -Copper Data[END_REF]. How ever, in 2016, about 29% of the world copper consumption came from recycled wastes while only about 30% of available copper wastes have been recycled (ICSG, 2018) (against nearly 36% in 2014 (ICSG, 2016)). France does not take part in most of copper cycle, in particular in metallurgy and refining, but has an important copper primary processing industry from refined copper and is an impor tant producer of semi finished products [START_REF] Scf | France Chemical Society -Copper Data[END_REF]. Moreover, [START_REF] Gie | Recycling Report 1999 -2008 -Synth ese G en erale[END_REF] showed that, in 2008 in France, most of copper losses occurred during the waste management step, as France only recy cled 3.5% of collected wastes and exported most of the remainder. In 2014 in France, according to an ADEME report (Bio by Deloitte, 2017), 183 kt of copper were collected in the waste and 56 kt of copper in waste were imported, while 197 kt were exported and 42 kt were recycled by fusion, which leads to a recycling input rate of 17% (against 39% in 2011). This high exportation flow is composed of complex wastes that cannot be treated in France with the existing facilities, adapted only for high grade scraps. Please note that a high variability of the recycling input rate has also been highlighted due to data uncertainties and confirms that copper waste situation in France has been observed as quite stable since 2009.

According to [START_REF] Giurco | Strategies for reducing the carbon footprint of copper: new technologies, more recycling or demand management?[END_REF], innovative technologies have only a limited role on the reduction of carbon footprint of copper, and the optimization of copper management should cover both technology and flowrate management optimization. To reach a more sustainable system, the management of copper recycling processes is addressed in this work.

For this purpose, a cartography of the current French copper cycle has been carried out in a previous work [START_REF] Bonnin | Development and validation of a dynamic material flow analysis model for French copper cycle[END_REF]. This cartography has shown that most of copper losses occur during the waste treatment step. Indeed, most of French copper scraps are exported or discarded, while only a low highly concentrated frac tion is recycled. Following this observation, a second study has been conducted that focused on copper scrap recycling processes [START_REF] Bonnin | Multicriteria optimization of copper scrap management strategy[END_REF]. This second study led to the proposal of a mathematical formulation that aimed to optimize copper scrap management and that was illustrated by the choice of the optimal process for the recycling of printed wiring board. This previous study also showed the interest of using genetic algorithms (GA) to solve this kind of optimization problems. The idea here is to use the results obtained in these two first works to propose a superstruc ture that encompasses the French copper cycle model and the scrap management optimization method to develop an optimization methodology for integrated resource management. The model formulation is generic enough so that data can be easily updated if necessary. Yet as aforementioned, the copper situation in France is fairly stable.

This paper presents firstly an inventory of the work carried out on copper mapping, management, recycling and environmental impact assessment 2.

Then the formulation and implementation of the optimization problem is described (part 3): a copper management superstruc ture is proposed, including as decision variables all possible man agement options. The specific parameters to this case study are specified: definition of model input data and of decision variable bounds. The involved algorithm and the formulation of the problem are developed. The choice of software and program structure are described. Finally, single and multi objective optimization are conducted to determine a compromise solution.

Lastly, section 4 provides a critical analysis and perspective to go further.

Literature review

Copper in literature

Many studies have already focused on copper. This part presents some of the main works regarding the mapping of copper flow, the extraction and mining management assessment and the produc tion and recycling processes evaluation.

Copper flow cartography

A huge amount of works has been performed on the assessment of copper flow, whether at city, country or world scale. This issue has been more widely explored in our first work [START_REF] Bonnin | Development and validation of a dynamic material flow analysis model for French copper cycle[END_REF], but some of the main and more recent works are still worth being presented here.

"The contemporary European copper cycle" study (Spatari et al 2002) can probably be considered as one of the most significant works, and the methodology that has been carried out has then been adopted for developing similar studies in Asia [START_REF] Kapur | The contemporary copper cycle of Asia[END_REF], Africa (van Beers et al., 2003), Latin American and Carib bean [START_REF] Vexler | The contemporary Latin American and Caribbean copper cycle: 1 year stocks and flows[END_REF], China [START_REF] Guo | Substance flow analysis of copper in China[END_REF], United Kingdom [START_REF] Jones | Material flows and mass balance analysis in the United Kingdom[END_REF], Brazil [START_REF] Tanimoto | Material flow accounting of the copper cycle in Brazil[END_REF], etc. as well as for studies on other chemicals (for instance silver [START_REF] Lanzano | The contemporary European silver cycle[END_REF]). These studies used the material flow analysis methodol ogy that gives a picture of the situation at a specific time.

More recently, some authors have emphasized the importance of dynamic analysis that allow to define indicators and draw ten dencies that can be used for decision making [START_REF] Gloser | Dynamic analysis of global copper flows. Global stocks, postconsumer material flows, recycling indicators, and uncertainty evaluation[END_REF]Soulier et al., 2018a,b;Pfaff et al., 2018), etc.). All these studies address in particular the issue of secondary copper availability, which can be calculated thanks to dynamic analysis by combining the in use stocks with end use lifetime assumptions, and the recycling efficiency, that varies a lot from one country to the other. For instance, France has a good copper waste collection rate but exports nearly all of it, while China recycles a high amount of im ported copper waste but has a relatively low domestic recycling efficiency.

Extraction and mining

The long term availability of copper being of crucial importance for our lifestyle, many studies focus on the extraction and mining issues. A paper from [START_REF] Northey | Modelling future copper ore grade decline based on a detailed assessment of copper resources and mining[END_REF] on the modeling of future copper ore grade, whose expected decline will have important impacts on cost and environmental impacts of copper extraction, is a good example of these issues. On a complementary topic, [START_REF] Memary | Life cycle assessment: a timeseries analysis of copper[END_REF] conducted time series life cycle assessment to deter mine environmental impacts of copper mining and smelting in Australia, and showed that LCA models are interesting tools to help decision makers choose technology and energy strategies in the mineral sector. Finally, [START_REF] Govindan | Application of multi-criteria decision making/operations research techniques for sustainable management in mining and minerals[END_REF] reviewed eleven paper dealing with multi criteria decision making or operations research in the implementation of sustainability in mining and minerals sector, and concluded that these new tools and techniques are of high interest for future research in sustainable mining.

Production and recycling processes

Once again, studies on copper production and recycling process are widely present in literature. This issue was explored in more details in [START_REF] Bonnin | Multicriteria optimization of copper scrap management strategy[END_REF], and those with specific focus on the work explored here are recalled for the sake of clarity.

In an environmental impact assessment perspective, [START_REF] Norgate | Assessing the environmental impact of metal production processes[END_REF] proposed an important review of metal production processes, including copper, and performed LCA for comparative purpose. Similarly, [START_REF] Farjana | Life cycle analysis of copper-gold-leadsilver-zinc beneficiation process[END_REF] carried out a life cycle analysis of copper gold lead silver zinc beneficiation process that shows the interests and limits of recycling regarding environmental impacts and that gives keys for comparison with primary production.

However, most of the works on copper recycling focus on Waste from Electrical and Electronic Equipment (WEEE) with the highest copper content and ignore other wastes. Some interesting works on WEEE recycling optimization can be cited: [START_REF] Johansson | Material hygiene: improving recycling of WEEE demonstrated on dishwashers[END_REF]; [START_REF] Kasper | Printed wiring boards for mobile phones: characterization and recycling of copper[END_REF][START_REF] De Souza | Sustainability assessment and prioritisation of ewaste management options in Brazil[END_REF]; [START_REF] Dias | Waste electric and electronic equipment (WEEE) management: a study on the Brazilian recycling routes[END_REF]; [START_REF] Meester | Using material flow analysis and life cycle assessment in decision support: a case study on WEEE valorization in Belgium[END_REF].

Copper literature review conclusion

In these studies, depending on the objectives, mono or multi criteria optimization strategies are sometimes used to find the best compromise between costs, environmental impacts, risks, etc.

Multicriteria strategies used in these different works proved their efficiency to solve complex decision making problems. For instance, [START_REF] Minciardi | Multi-objective optimization of solid waste flows: environmentally sustainable strategies for municipalities[END_REF] proposed a strategy for the optimization of solid waste flows treatment at urban scale. In another field of application, [START_REF] Sharif | Simulation-based multi-objective optimization of institutional building renovation considering energy consumption, life-cycle cost and life-cycle assessment[END_REF] showed the interest of coupling life cycle assessment and multicriteria optimization for building renovation. However, there is no study aiming at per forming a multicriteria optimization of the whole cycle of a given resource. Indeed, the optimization of a resource management is not only a multiobjective problem (aiming at minimizing simulta neously cost, energy consumption, environmental impacts, etc.), but also a mixed problem with many continuous (such as flowrates) and integer variables (for example the choice between different process alternatives) (Giurco, 2009). The aim of this work is to propose a strategy to optimize the copper cycle encompassing resource supply to waste management, considering both environ mental and economic issues with a life cycle approach. This is consistent with the works of [START_REF] Jeswani | Options for broadening and deepening the LCA approaches[END_REF], [START_REF] Petrillo | Life cycle assessment (LCA) and life cycle cost (LCC) analysis model for a stand-alone hybrid renewable energy system[END_REF] and many others that show how Life Cycle Assessment method can be improved by being combined with economic studies. A review that showed the interest of coupling economic models and environmental assessment methods has been pro posed by [START_REF] Beaussier | Coupling economic models and environmental assessment methods to support regional policies: a critical review[END_REF].

Multicriteria optimization strategy and support decision making tool

Resource consumption leads not only to depletion of abiotic resources, but also to indirect impacts on health and environment such as energy consumption, pollutant emission, etc. Moreover, resource extraction is expensive. The objective is to mathematically model all the copper flows and to identify the decision variables that can act as key drivers to improve resource management.

In a sustainable development perspective, economic, environ mental and social criteria have to be taken into account. The diffi culty is that each of these sustainable pillars might be evaluated by a large amount of indicators [START_REF] Milutinovic | Multicriteria analysis as a tool for sustainability assessment of a waste management model[END_REF]. For instance, environmental impacts can be estimated considering pollutants emission, waste generation, energy consumption, etc. Each impact could also be estimated with many "sub indicators": for instance, to help policy decision making on energy management, the International Atomic Energy Agency (2005) proposed a set of about 30 "Energy Indicators for Sustainable Development". Furthermore, considering environmental impacts, a life cycle assessment (LCA) leads to 5 to about 20 different impacts (global warming potential, toxicity, eutrophication, resources depletion, etc.), which can also constitute a set of sub indicators for the environmental impact evaluation.

The complexity of the decision making process increases yet with the number of decision criteria. How could an optimal compromise solution be found when more than ten antagonist objectives have to be optimized simultaneously? To limit complexity, different works on specific waste management opti mization have adopted to work on a limited number of optimiza tion criteria. [START_REF] Minciardi | Multi-objective optimization of solid waste flows: environmentally sustainable strategies for municipalities[END_REF] have chosen four decision variables for the optimization of solid waste flows: economic costs, unrecycled waste, sanitary landfill disposal and environmental impact. [START_REF] Zaman | A comprehensive study of the environmental and economic benefits of resource recovery from global waste management systems[END_REF] attempted to measure the waste manage ment system efficiency in different countries with a new indicator, i.e. the Zero Waste Index (ZWI). The ZWI accounts for the potential amount of virgin material that can be offset by recycling, mini mizing energy and water consumption, as well as greenhouse gas (GHG) emissions, by offsetting virgin materials and recovering energy from waste. Another set of indicators, including manage ment costs and reuse time span as well as different objectives of economy, perceived risk and environmental impact, has been used by [START_REF] Ahluwalia | A life cycle based multi-objective optimization model for the management of computer waste[END_REF] for optimizing computer waste management.

Regarding the tool choice, the model developed here encom passes the formulation of the copper scrap management model proposed in [START_REF] Bonnin | Multicriteria optimization of copper scrap management strategy[END_REF]: optimization and decision making strategies use the same tools, which are the Genetic Algorithm (GA) for the multiobjective optimization and TOPSIS (Technique for Or der Preference by Similarity to Ideal Solution) decision support tool. The interested reader will find more information on multiobjective optimization in [START_REF] Mahdi | A holistic review on optimization strategies for combined economic emission dispatch problem[END_REF]; [START_REF] Qu | A Survey on Multi-Objective Evolutionary Algorithms for the Solution of the Environmental/Economic Dispatch Problems[END_REF] literature re views and on multi criteria decision making in [START_REF] Mardani | A review of multi-criteria decision-making applications to solve energy management problems: two decades from 1995 to 2015[END_REF]; [START_REF] Govindan | Multi criteria decision making approaches for green supplier evaluation and selection: a literature review[END_REF]; [START_REF] Kumar | A review of multi criteria decision making (MCDM) towards sustainable renewable energy development[END_REF] literature reviews.

Problem formulation and implementation of the optimization process

Choice of the criteria

Considering the reported works in the literature review section, it was decided for this study to focus only on environmental and economic objectives, which can be more easily and objectively estimated than social impacts. The efficiency of the resource management system has thus been assessed by four criteria: economic efficiency is evaluated by calculating the costs of the resource cycle; environmental impacts are determined via: e energy consumption; e greenhouse gases emissions; e abiotic resources depletion, taken into account by calculating copper losses.

For each of these criteria, the total impact is calculated consid ering waste collection (either selective or not), sorting and disposal (either landfilling or incineration), as well as scrap recycling and import/export flows.

Mathematical formulation of the model

Fig. 1 presents the superstructure that can be used for the management optimization of any natural resource that embeds all the options that can be explored by the solution algorithm. Two constraints are considered in this model formulation: the former one involves the satisfaction of the demand in refined copper and in refined alloys (both are estimated from copper use), and the latter involves a fixed input data set based on the waste deposit. These parameters can be determined from national statistics as well as from company and association data reports: this has been the core of another study [START_REF] Bonnin | Development and validation of a dynamic material flow analysis model for French copper cycle[END_REF]. All the other flows are free and thus considered as decision variables.

The decision process starts with the total amount of produced waste; then the decisions are made according to the waste flow circulation (Table 1):

Wastes can be collected (wholly or partly) either selectively or not (d1). It is assumed that non selectively collected waste are landfilled; Selectively collected wastes are sorted into six streams: con struction and demolition wastes (C&D), End of Life Vehicles (ELV), Waste from Electric and Electronic Equipment, Municipal Solid Waste (MSW), Sewage Sludge (SS) and Industrial and Hazardous Wastes (I&HW). If discarded, MSW, SS and I&HW can be either landfilled or incinerated (d2), while ELV, WEEE and C&D can only be incinerated (because of French legislation); It is possible to import mixed wastes (d3), but imported waste are assumed to be recycled, thus they are sorted and mixed with selectively collected wastes; Then the decisions concerning each stream are made indepen dently from each other: it is possible to import or export a specific stream (d4 d9), then for each remaining stream there is a choice between discarding, recycling and sorting (d10 d15); Sorted streams are divided into six scrap categories: No.1 scrap (>99% Cu), No.2 scrap (88e99% Cu), low grade scrap (LGS) (10e88% Cu), alloys and remaining scrap (<10% Cu). Each scrap stream can either be discarded or recycled (d20 d23). Waste streams that are recycled without being sorted are mixed with

LGS or remaining scrap depending on their copper content; Scrap streams can also be imported or exported (d16 d19), but as for mixed wastes, imported scraps are assumed meant to be recycled and can thus not be discarded; Then all recycled scrap streams enter the recycling flowsheet construction process: it is possible to import copper from pri mary industry (concentrate, mate, etc.; d27 d29) and then the flowsheet is selected (d24 d26). It was assumed that, on the lifetime of the facilities, capital construction costs are insignifi cant compared to running costs; Finally refined copper and alloys importation or exportation flowrates are calculated in order to meet the demand.

It has to be highlighted that the recycling of copper scrap has been an important issue of this work: an innovative recycling flowsheet construction methodology has been developed and presented in detail in [START_REF] Bonnin | Multicriteria optimization of copper scrap management strategy[END_REF]. The method aims at finding all the possible combinations of process, i.e. flowsheets, that can be used to transform a copper scrap into refined copper, associated with their costs, energy consumption, greenhouse gases emissions and copper losses.

Two main routes exist for copper recycling: the pyrometallur gical and the hydrometallurgical technologies. The pyrometallur gical alternative can be divided into six steps from ore or low grade scraps to refined copper: pre treatment, smelting, converting, fire refining, electrorefining and smelting for form casting. Nine pro cesses can be used, alone or associated with each other, for these steps, depending on the recycled metal characteristics: anode furnace (A), direct to blister flash smelter (DTB), electric furnace (Elec), electrolytic refinery (ER), Noranda furnace (NOR), Out ukumpu flash smelter (OUT), Pierce Smith converter (PS), Shui koushan bath furnace (SKS) and Teniente furnace (TEN). The hydrometallurgical method is based on leach solvent extraction electrowin (LSXEW) technology and is described here as a unique step from scrap to refined copper. More details on these ten pro cesses are given by [START_REF] Suljada | A Decision Process Guiding Flowsheet Development for Recycling Copper-Containing Materials[END_REF]. For readability reasons, Fig. 1 only shows the different steps of the pyrometallurgical process. It would be similar with hydrometallurgical process but simpler as all six steps of the recycling process would be condensed in one pro cess. The best flowsheet (that can embed one to five of the 10 cited processes) for a specific kind of scrap is determined based on data such as copper, lead, iron, zinc and tin contents, scrap sized, moisture, etc.

Finally, as shown in Table 1, the whole formulation involves 47 variables, either continuous (imports minus exports, rate of selec tive collection, etc.) or integer (choice between processing, sorting and discarding, etc.). Moreover, mainly because of the recycling process construction formulation, the problem is also nonlinear, so that a Mixed Integer NonLinear formulation of the problem is involved [START_REF] Bonnin | Multicriteria optimization of copper scrap management strategy[END_REF].

Model parameters

As seen in the definition of the superstructure of the problem, the objective is to determine the set of the decision variables (47) that optimizes simultaneously costs, environmental impacts, en ergy consumption and losses due to copper management during a year, to meet demand without importing refined copper or alloys from primary industry. The problem formulation is based on the determination of the model input parameters (demand for refined copper and alloys, waste deposit), as well as bounds between which the decision variables may vary.

Input parameters

The input parameters of the model have been taken from [START_REF] Bonnin | Development and validation of a dynamic material flow analysis model for French copper cycle[END_REF], in which a cartography of the copper cycle in France from 2000 to 2009 is presented. This study showed that the copper amount contained in the waste has been fairly stable since the early 2000's: around 300 kt Cu =year, contained in a total amount of waste of about 192,000 kt, with more than two thirds of copper embedded in waste from electrical and electronic equipment (WEEE).

Moreover, as previously mentioned, the recycling flowsheet construction requires, in addition to copper content, iron, lead, tin and zinc concentrations, as well as the quantity of each type of scrap that can be extracted by sorting the wastes. Some charac terizations were performed using a compilation of data from ADEME (French Environment and Energy Management Agency) and BRGM (French Geological Survey) reports, as well as reports on the different types of waste [START_REF] Richer | Demolition materials in the Nord -Pas-de-Calais region -Storage and recycling recommendations[END_REF][START_REF] Bremond | Inventory of the recovery of materials from the treatment of end-of-life vehicles[END_REF]ADEME, 2019;[START_REF] Fangeat | National Campaign for the Characterization of Household Waste -2007 Results[END_REF][START_REF] Brahmst | Copper in End-Of-Life Vehicle Recycling[END_REF] and are presented in Tables 2 and3.

Regarding demand, flow modeling has shown that between 2000 and 2009 the difference between the amounts of refined copper imports and exports decreased from about 580 kt in 2000 to 375 kt in 2008. In addition, France is a major importer of copper in finished and semi finished products. The amount of imported and exported copper in finished and semi finished products has been assumed to be constant. This hypothesis could be questioned but has been adopted because of the lack of data. Thus, recycling is only used to meet the refined copper demand, which was set at 400kt=year.

Regarding alloys, the amount used in France by the process in dustries is not known in detail, which is why the demand was set equal to the amount of alloys present in the finished products manufactured in France, i.e. about 100 kt=year. It should be high lighted that many types of alloys are used in various sectors, and an accurate counting would be very difficult to drive. The alloys have been considered in this study as only one type of scrap containing about 60% of copper, which is the concentration in many brasses and bronzes that are the most commonly used alloys.

As previously mentioned, France recycles today about 50 kt per year of high grade scrap. Nearly all of it is imported scrap, while most of copper waste collected in France is exported. Only one company can recycle No.2 scrap, three companies can only treat No.1 scrap, and about ten companies use high quality recycled copper in their semi products and products production process (J erôme Betton, 2014). To test the potential of the optimization strategy, the optimization process has been initialized with a "blank" page and no information on the current used technologies was implemented. Moreover, industrial confidentiality makes this kind of information difficult to obtain.

Variable boundaries

As presented in Table 1, the problem consists of 18 continuous variables, 9 integer variables and 20 binary variables.

For the binary variables, which represent the choice between recycling and disposal for each scrap from each waste, no bound is fixed.

For integer variables, the bounds depend of the variable type:

the six variables concerning the future of each waste category can vary from 1 to 3: if di 1 the category is sent directly to recycling, if di 2, it is sorted and if di 3, it is discarded. the selection of three recycling flowsheet choice variables returns di, the index of the flowsheet adopted and therefore varies between 1 and the number of useable flowsheet for each scrap. The number of flowsheets was calculated with the method mentioned in part 3 and described in [START_REF] Bonnin | Multicriteria optimization of copper scrap management strategy[END_REF]: 7 flowsheets can be used for No.2 scrap, 127 for LGS and only one for the remaining scrap, which simplify the problem by removing one integer variable. The problem in cludes finally 46 variables. Regarding continuous variables, there are also two categories: those representing a sharing rate, which are between 0 and 1, and those representing the difference between imports and exports, defined on \mathdsR.

Concerning the seven "sharing rate" variables used, to find treatment solutions consistent with the French situation, given the compositions and characteristics of WEEE, ELV and C&D, it was decided to prohibit incineration.

Finally, for continuous "imports minus exports" variables, bounds must be defined. For lower bounds, i.e. export limitations, the maximum amounts that can be exported of each waste or scrap were calculated. For example, the maximum amount of household waste (MSW) that can be exported is calculated by assuming that all waste is collected selectively and imports of mixed waste are at their maximum (remembering that, by definition, imported mixed waste are sorted and divided into the six waste categories). The quantity of available MSW is then calculated and this sets the maximum amount that may be exported. Regarding the upper limit, i.e. the highest imports, its value has been fixed so that the maximum imports of a flow is sufficient to cover the demand for refined copper, with a maximum set at the amount of (each) waste produced in France.

Table 4 summarizes the bounds used for the decision variables corresponding to imports minus exports of each category of waste or scrap ("di" indexes correspond to those presented in Fig. 1).

The model formulation offers a superstructure that can be adapted to different situations in different countries. For all the other streams, flowrates are calculated in accordance with what is presented in part 3 and with the data presented in Appendix A.

Impact evaluation

As detailed in the formulation of the problem, imported flows intended a priori to be recycled. The following assumptions have been adopted: mixed waste imports are necessarily sorted into the six cate gories of waste selective collection; waste imported by category is mixed with flows from selective collection and from mixed wastes sorting; imported scrap, concentrate, matte and blisters are necessarily sent to the recycling process and are mixed with sorted scrap sent for recycling (depending on their content); if a scrap coming in the recycling chain cannot be treated by any flowsheet, it is discarded.

Then the four objective functions (Costs, GHG Emissions, Energy consumption and Losses) are calculated according to the following equations (Eqs. (1)e(4)), using data presented in Appendix A:

C Total C recycling þ C disposal þ C sorting þ C IÀE (1) EI Total EI recycling þ EI disposal þ EI sorting þ EI IÀE (2) NRJ Total NRJ recycling þ NRJ disposal þ NRJ sorting þ NRJ IÀE (3) L Total L disposal þ L recycling þ L E (4)
with:

C Total : total costs in monetary units; C recycling : costs related to recycling processes, calculated from energy and material consumption (these costs do not take into account the investment costs, like infrastructures, etc.); C disposal : costs of waste disposal (landfill or incineration) [START_REF] Andrup | National cost framework for the management of the public waste disposal service in 2007/ 2008[END_REF]; C sorting : costs of sorting waste (to extract scraps); C IÀE : costs of imports and exports. EI Total : total environmental impacts, simplified to GHG emis sions, expressed in equivalent CO 2 ; EI recycling : impacts related exclusively to recycling processes, calculated from the energy consumption and material processes with impact factors extracted from SimaPro software and using the database EcoInvent (Classen et al., 2007); EI disposal : impacts associated with waste disposal (landfill or incineration);

Optimization strategy

Many different optimization algorithms can be used depending on the model formulation. According to a previous study dedicated to the optimization of the recycling of copper waste [START_REF] Bonnin | Multicriteria optimization of copper scrap management strategy[END_REF], genetic algorithms have been identified as one of the most suited methods for addressing multi criteria, mixed and non linear problems, despite their known limits regarding computational time and absence of convergence properties for monobjective optimi zation problems. The analysis of available optimization methods led us to choose a genetic algorithm from MULTIGEN library, developed by [START_REF] Gomez | Multiobjective Technico-Economic Optimization of Energy Conversion Systems: Hydrogen and Electricity Cogeneration from IVth Generation Nuclear Reactor[END_REF] and written in VBA with Excel ® interface. The criteria that have to be optimized were calculated using Matlab ® software.

A function called "optimization" was written to calculate the flowrates in each stream, evaluate the impacts associated with these flows and determine the amount of recycled copper, copper losses, etc., all depending upon the decision variables. The code is too long to be included here but it follows the process described in part 3.2 and Fig. 2 presents the architecture of the Matlab ® program developed. The Matlab ® function optimization was converted using the MATLAB Builder™ EX supplement into Excel ® coding, so that the NSGA II Continuous Mixed Integer Boolean algorithm from MULTIGEN library can be used.

In a first step, monobjective optimizations have been performed for each criterion, in order to analyze their behavior. This allows to study the possible antagonism of the criteria and compare the decision variables to be optimized. If some criteria are redundant, it will be possible to reduce their number in the following multiobjective optimization procedure.

As recommended by [START_REF] Gomez | Multiobjective Technico-Economic Optimization of Energy Conversion Systems: Hydrogen and Electricity Cogeneration from IVth Generation Nuclear Reactor[END_REF], the genetic algorithm NSGA II Mixed Integer Continue Boolean is used independently for each of the objective functions with the parameters presented in Table 5.

Results and discussion

Each function has been minimized by keeping free the other functions and setting the constraint relative to imports of refined copper and alloys at 0. The results are summarized in Table 6: each row corresponds to the monobjective optimization of the criterion mentioned in the first column, and the other columns give the costs, environmental impacts, energy consumption, copper losses and export flows of refined copper and alloys obtained with each monobjective optimization (the value in bold being the minimized criterion).

The four rows present quite different results: depending of the minimized criterion, the cost varies from 21 to 58 GV=an, envi ronmental impacts from 35 to 103 Mt eqCO 2 =an, energy consumption from 41 (production of 41 TWh=an due to waste incineration) to 148 TWh=an and copper losses from 38 to 302 kt=an. Moreover, the values of the exported flows of refined copper and alloys are clearly different for each optimization run, highlighting that copper management strategy depends on the targeted criterion. Indeed, a more extensive study of the variables of decision proves that all four criteria are clearly antagonists with very different strategies obtained depending on the studied criterion. These results are presented in detail in the following paragraphs.

Monobjective optimization

Cost minimization

Cost optimization shows that minimum copper management costs could be 21 GV=an. The required strategy to reach this result is characterized by: a rate of selective collection of 100%; significant imports of copper from primary industry (concen trates, mattes and blisters), No.1 scrap, LGS and WEEE; sorting of the most concentrated copper waste (WEEE), direct recycling of ELV and SS and disposal of other waste (C&D, I&HW et MSW); recycling of all scrap categories; incineration of I&HW and MSW. Fig. 3 shows this management strategy, the size of the arrows is proportional to the flow of copper. 1 The high cost of refined copper can explain these results so that it is interesting to produce as much copper as possible to sell the overflow once the demand is satisfied. Thus, all waste and scrap with recycling costs lower than refined copper price are recycled. Others are incinerated (if possible, as explained in part 3.3.2) because, under the assumptions, it is the cheapest treatment through the sale of produced energy (see Appendix A.1). With regard to recycling, no No.2 scrap import is involved to reach the minimum cost. No.2 scrap from WEEE is recycled with imported blister by a process comprising an electric furnace and an anode furnace. For LGS, a flowsheet consisting of three processes is used: a Teniente furnace, a Peirce Smith converter and an anode furnace.

Fig. 4 presents the impact distribution between the different steps for each studied impact. The copper life cycle steps have been combined in five main stages: copper waste collection, recycling processes, waste sorting into scraps, elimination of wastes and scraps and import/export flows (sum of all flows, whatever they are.).

The collection and disposal of wastes are the most expensive steps, due to the very large flows involved. The remainder is due to recycling. The cost of waste sorting is insignificant here because only the WEEE are sorted, which represents a small amount. The exports of refined copper and sales cover about 20% of expenditures.

With regard to the other criteria, that are not optimized for this monobjective optimization run, the environmental impacts are approximately 3 times higher than their minimum (103 instead of 35 Mt eqCO 2 =year) and are mainly due to waste incineration (I&HW, MSW and SS, which represents a large volume). Cost minimization leads to a small energy production through waste incineration. Energy consumption is divided between collection (50%), recycling (25%) and international trade (25%), but waste incineration pro duces so much energy than finally there is an energy gain rather than a consumption. Losses are shared equally between recycling and disposal. Indeed, the copper content of the waste disposed is very low, while large quantities of low copper are recycled.

Minimization of environmental impacts

The minimization of the environmental impacts leads to a strategy producing about 35 Mt eqCO 2 =year. This requires (Fig. 5): a rate of selective collection of 100%; importing a small amount of WEEE and sorting and exporting all other waste; importing of copper from primary industry (mattes and blis ters), recycled with scrap from WEEE.

These results are explained by the fact that, for exported waste, only transportation impacts were considered (once exported, it is not known whether the waste is recycled, discarded, etc.). These impacts are less important than those related to the disposal or recycling of waste: low grade waste are mainly exported. Only WEEE are fully preserved to be sorted and recycled. Copper from primary industry is imported to meet the constraints of non importation of refined copper and alloys. This result shows the negative effects of taking into account only direct impacts: not charging impacts on exported waste makes it "cleaner" to export Legend: EI: environmental impacts -Exp.: exportation -RC: refined copper. a Please note that negative value means that there is production of energy instead of consumption. waste rather than recycling it. To mitigate this effect, the copper content in the waste exported was recorded as lost, so that, in the multiobjective problem, exportation is not favored. Fig. 6 shows that the environmental impacts, costs and energy consumption are mainly due to imports and exports, which is explained by the large exported quantities. The second rank for these three criteria is due to collection, which also involves a significant amount of waste. The small amount of waste recycled leads to negligible impacts to these three criteria.

Regarding losses, however, a substantial contribution is due to recycling. These huge losses can be explained by the fact that all recycled No.2 scrap and LGS, as well as matte and blister imported, are mixed and recycled as "residuals" (scrap containing 10% of Cu) using the hydrometallurgical process. Exported wastes also repre sent copper losses, but are less important because of their low content.

Minimizing energy consumption

Minimizing energy consumption actually leads to energy pro duction of 41 TWh=year. This is explained by the assumption that the energy released during incineration of waste is recovered by electricity production.

The following parameters allow such a result (Fig. 7):

a rate of selective collection of 100%; WEEE sorting and disposal of other waste; incineration of I&HW, disposal of MSW and SS; import of No.1 scrap to meet demand and recycling of No.1 scrap and alloys only.

Waste incineration produces energy, so the model proposes to incinerate as much waste as possible.

Since the recycling of other wastes and scraps consumes more energy than landfilling, only electronic waste is recycled in order to satisfy the constraint of non importation of refined copper. The difference between the amount of copper contained in WEEE and demand is imported as No.1 scrap.

The study of impact sources, as shown in Fig. 8, shows that the energy consumption (about 20 TWh=year) is almost entirely due to waste collection. The impacts on the environment and resource losses are mainly caused by waste disposal. Costs are mainly related to waste collection (55% of costs) and disposal (40% of costs).

Minimizing losses

The optimal value of losses flow, when considering this criterion alone, results in 40 kt=year copper lost (about 10% of needs), which is far from being insignificant. This is explained by the fact that flows with very low copper content are important, and they cannot currently be recycled. Thus, minimizing losses requires the recy cling of the largest possible amount of waste (Fig. 9): a rate of selective collection of 100%; sorting and recycling of all waste with a sufficient content (i.e. all scrap, except the remaining whose content is less than 0.03%); import of No.1 scrap, sufficient amount to meet demand.

It should be noted that the remaining scrap from the WEEE can be recycled by being mixed with new scrap from low grade scrap recycling.

As previously explained, having no information on the fate of exported wastes, only transportation impacts are allocated, thus favoring the exportation pathway. To mitigate this advantage, ex ports have been considered as losses, as they leave the considered cycle. Given these assumptions, the choice between export and disposal of waste that cannot be recycled does not impact this criterion. Similarly, import of No.1 scrap, for which recycling does not cause losses, may vary. Different values for these decision var iables are therefore possible to reach this result, a variant without export is used for Figs. 9 and 10. With regard to recycling, two flowsheets can be used for No.2 scrap resulting in a similar result in terms of losses. A flowsheet consisting of an electric furnace and an anode furnace can be used, with the importation of a small amount of blister to slightly improve the copper content of the scrap. A similar flowsheet but with an electrorefining step is used in addi tion if no blister is imported. LGS are treated by means of an electric furnace, a Peirce Smith converter and an anode furnace.

As it can be seen in Fig. 10 and 88% of the losses are due to the elimination of waste that can not be recycled, the remainder 12% being lost in the recycling process. In this configuration, the costs are mainly due to the large volumes of low grade waste which are sorted, while the environmental impacts are mainly due to the disposal of waste. This is consistent with the results obtained with the other monobjective optimizations. Energy consumption is mainly due to waste collection.

Discussion

The monobjective optimizations have therefore allowed to determine the best management strategy for each objective, and showed the greatest impact areas for each criterion. However, these results should be considered with caution: the model formulation provides an assessment of impacts associated with the copper cy cle, with a penalizing assumption, i.e., all costs of collection and sorting, among others, are due to the copper flow management. However, in reality, through selective collection and sorting of waste, metals and many other materials can be recycled, which could lead to an allocation of impacts. The real benefit of the approach is not the absolute values but the comparison of results between the different management strategies.

These results demonstrate the need for the establishment of a multiobjective optimization strategy to study the behavior of the criteria with respect to each other and determine a compromise solution. However, given the size of the problem, with the GA pa rameters presented above, the computation time for each mono bjective optimization is particularly high (about 20:30 for 900 individuals and 1800 generations). Some trials with less individuals or less generations have been run, but in these conditions the re sults were not reproducible: the best solution was not always found as the model tends to get trapped in local optimums. Considering this, the implementation of a quadriobjective optimization may be viewed as difficult. For this reason, biobjective optimizations have been carried considering the six antagonistic pairs to be separately studied: environmental impacts/costs, environmental impacts/en ergy, environmental impacts/losses, costs/energy, costs/losses and energy/losses. In this work, only results related to costs and GHG emission minimization will be detailed, as they are both of high priority in view of current issues (United Nation Conference on Climate Change (COP21), 2016).

Biobjective optimization

Implementation of the biobjective optimization environmental impacts versus costs

A biobjective optimization run has been conducted with the same parameters as the monobjective optimizations. However, due to the mathematical complexity of the problem (e.g. large number of variables, involvement of mixed variables, and especially the equality constraints associated with mass balances that must be rigorously solved), several runs have been implemented to obtain a Pareto front with uniformly distributed solutions. Indeed, as already observed for monobjective optimization with a smaller number of individuals or generations, the model tend to get trap ped in local optimums. Some runs with more individuals and more generations have thus been implemented, leading to the following Pareto front (Fig. 11) exhibiting an important set of non dominated solutions.

Choice of the best compromise solution

To choose a compromise solution from the Pareto front, a multicriteria decision making tool method was used. M TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method, which is a synthetic evaluation method based on the concept of the original TOPSIS [START_REF] Ren | Comparative analysis of a novel M-TOPSIS method and TOPSIS[END_REF], has been adopted. This method makes a classification of the points of the Pareto front according to their distance with the point Utopia ("optimized ideal reference").

The top three points according to M TOPSIS, shown in Fig. 11, are very close to each other, which is consistent given that the front is continuous. Table 7 presents the criteria values for these three points.

Fig. 12 shows the distribution of the different impacts for the best M TOPSIS solution. Since the distribution is very similar for points 2 and 3 for the abovementioned reason, these will not be presented in detail.

The decision variables that allow to reach this solution are given in Table 8. They lead to an intermediate solution between indi vidual optimization of costs and environmental impacts (Fig. 13): export of low grade wastes (all except WEEE) that will be treated outside the national territory; import large quantities of WEEE, concentrates, mattes, blisters and scrap (excluding remaining scrap) for recycling and sale of the refined copper produced.

Towards a quadriobjective optimization

A first attempt towards quadriobjective optimization has been conducted with NSGA II as an optimization strategy for the already mentioned reasons. Yet the complexity of the problem already observed in the biobjective case was confirmed in the quad riobjective case, leading to a failure in the optimization process. To envision this antagonist behavior, a Pareto front combining the six obtained biobjective fronts (environmental impacts/cost, environ mental impacts/energy, environmental impacts/losses, costs/en ergy, costs/losses and energy/losses) has been built. Fig. 14 illustrates the new environmental impacts versus costs Pareto front for this quadriobjective optimization. The biobjective opti mization considering environmental impacts and costs that has been previously presented is clearly visible.

A best compromise solution has been obtained according to the previously detailed M TOPSIS method: Table 9 presents the decision variables used to reach this optimal solution compared to the best compromise of the biobjective optimization and Fig. 15 shows the distribution of impact sources for this solution.

It is also possible to compare the best compromise solution obtained by bi and quadriobjective optimization. Table 10 presents the differences between the objective function final values for both M TOPSIS best ranked solution. In addition, by comparing the de cision variables and the impact distribution, the resulting strategies are quite different: the rate of landfilled waste is highly decreased with the quadriobjective solution, and importation and exportation strategies are quite different in both solutions. For instance, the quadriobjective solution includes quite large imports of No.1 ad No.2 scrap, which was not the case in the biobjective optimization because of the important cost of these kinds of scraps. These dif ferences in the strategies mainly leads to an increase in the elimi nation stage and a decrease in the import/export stage in the impact distribution. Regarding objective function values, environ mental impacts and costs are slightly more important in the quadriobjective function, while energy consumption is reduced and losses are greatly increased.

Discussion and perspectives

The use of genetic algorithm has led to propose waste man agement solutions that optimize costs, GHG emissions, energy consumption and resource losses, as well as a biobjective optimi zation leading to a compromise solution between cost and envi ronmental impacts. A first quadriobjective optimization result is also proposed, however, given the number of variables and criteria as well as the presence of equality constraint, the GA failed to directly solve this quadriobjective problem. Some trials on smaller instances of the problem had been suc cessfully solved all along the implementation of this work and no operational alternative was found.

Despite the impossibility to carry out the quadriobjective opti mization, biobjective optimizations successfully result in large Pareto fronts that allow to find a compromise for this quad riobjective problem. Regarding these results, different perspectives can be highlighted. The same importance has been given to all four criteria in the decision making process: this can easily be modified and other strategies could be deduced. To overcome the problem complexity and reduce the subsequent computational time, a linearization of the problem formulation is currently being studied to be able to solve it via a mixed integer linear programming solver.

Conclusion

A global methodology of resource management optimization at a national scale is proposed, considering all the resource cycle from supplying to waste management. This methodology has been developed and validated on the example of copper management in France involving a multioptimization framework based on a genetic algorithm. Considering all the in and outflows of the resource, as well as stocks in the technosphere and wastes, the environmental impacts, energy consumption, resource losses and costs have been evaluated and optimized for all possible management strategies.

Mono and biobjective studies have been conducted through a genetic algorithm for copper waste management. This methodo logical framework has been used to find a compromise solution optimizing simultaneously costs, environmental impacts, energy consumption and losses.

The quadriobjective study could not be performed using directly the genetic algorithm. Indeed, this article has highlighted the dif ficulty of solving multiobjective problems with many decision variables. The genetic algorithm optimization, which seemed most appropriate given the ability of this method to construct Pareto fronts for multiobjective problems, has finally reached its limits on this complex problem involving strong equality constraints.

The proposed model is a first step in natural resource manage ment and efforts are to be made to make this model really reliable. Some preliminary conclusions can yet be drawn regarding the establishment of a sustainable resource management. Under cur rent conditions, it appears that the recycling of most highly concentrated copper waste is the only interesting strategy that optimizes all the criteria. The compromise solutions obtained fa vours the development of the recycling of waste from electrical and electronic equipment. However, if the cost of resources (raw ma terials) increases or if new recycling processes of waste with low copper content are to be developed, changes may be expected. It should also be emphasized that, according to the different simu lations that have been performed, even if all the wastes are recy cled, the current amount of copper contained in the waste does not meet demand, and that imports are necessary in all scenarios. This model should thus be extended at the world scale to define if it is possible to reach a sustainable cycle only through a good man agement strategy, or if in the future copper will have to be replace with other materials for given use to avoid scarcity.

Once the aforementioned perspective implemented, longer term perspectives to this work will be to vary the system input data, especially economic data, to identify the value of primary copper cost that makes the recycling of all waste flows interesting. The model developed here can therefore be adapted very easily, by adding or removing constraints and criteria to evaluate manage ment scenarios based on economic, regulation and environmental constraints. Another study could focus on opportunities to reduce the copper demand and the effects it would have, for example by replacing it by other materials in some applications.

Finally, in this study all impacts have been allocated to copper while recycling of scrap will lead to the recovery of other metals. An even more systemic approach should be performed to implement and interconnect different metal cycles.

Fig. 1 .

 1 Fig. 1. Superstructure of copper processing pathways.

Fig. 2 .

 2 Fig. 2. Architecture of the impact calculation Matlab ® program.

Fig. 3 .

 3 Fig. 3. Representation of flows in the cost minimization.

Fig. 4 .

 4 Fig. 4. Distribution of the different impacts at the cost minimization.

Fig. 5 .

 5 Fig. 5. Representation of flows when minimizing environmental impacts.

Fig. 6 .

 6 Fig. 6. Distribution of the different impacts when minimizing environmental impacts.

Fig. 7 .

 7 Fig. 7. Representation of flows during minimization of the energy consumption.

Fig. 8 .

 8 Fig. 8. Distribution of the various impacts during the minimization of the energy consumption.

Fig. 9 .

 9 Fig. 9. Representation of flows when minimizing losses.

Fig. 11 .

 11 Fig. 11. Cost-Environmental impacts biobjective optimization results: Pareto front.

Fig. 12 .

 12 Fig. 12. Distribution of impacts for the best ranked M-TOPSIS of the biobjective optimization.

Fig. 13 .

 13 Fig. 13. Representation of flows for the compromise solution obtained with biobjective optimization.

Fig. 14 .

 14 Fig. 14. Pareto fronts of the quadriobjective optimization: EI vs costs with M-TOPSIS results for the bi-and quadriobjective optimizations.

Fig. 15 .

 15 Fig. 15. Distribution of impacts for the best ranked M-TOPSIS of the quadriobjective optimization.

  .,

	Nomenclature	LCA	Life Cycle Assessment
			LGS	Low Grade Scrap
	A	Anode (furnace)	LSXEW	Leach Solvent eXtraction ElectroWin
	ADEME	French Environment and Energy Management	MSW	Municipal Solid Waste
		Agency	MILP	Mixed Integer Linear Programming
	BRGM	French Geological Survey	MINLP	Mixed Integer NonLinear Program
	C&D	Construction and Demolition Waste	NOR	Noranda (furnace)
	DTB	Direct to blister (flash smelter)	OUT	Outukumpu (flash smelter)
	EC	Energy Cost	PS	Pierce Smith (converter)
	Elec	Electric (furnace)	RC	Refined Copper
	EI	Environmental Impact	SKS	Shuikoushan (bath furnace)
	ELV	End of Life Vehicles	SS	Sewage Sludge
	ER	Electrolytic Refinery	TEN	Teniente (furnace)
	GA	Genetic Algorithm	TOPSIS	Technique for Order Preference by Similarity to Ideal
	GHG	GreenHouse Gas		Solution
	I&HW	Industrial and Hazardous Waste	WEEE	Waste from Electrical and Electronic Equipment

Table 1

 1 Decision variables for problem formulation.

	di	Variable

Legend: P: processing -S: sorting -D: discarding -I-E: imports minus exports.

Table 2

 2 Composition of the different categories of waste.

		WEEE	ELV	C&D	I &HW	MSW	SS
	Copper	13%	2.5%	0.07%	0.02%	0.0065%	0.037%
	Iron	43%	62.1%	0.36%	10.00%	0%	0%
	Zinc	3%	1.0%	0.35%	0.02%	0.0301%	0%
	Lead	3%	1.3%	0.35%	0.02%	0%	0%
	Tin	1%	1.0%	0.35%	0.02%	0%	0%
	Residuals	37%	32.1%	98.52%	89.92%	99.9634%	99.963%

Table 3

 3 Scrap content in the different categories of waste.

		WEEE	ELV	C&D	I &HW	MSW	SS
	No.1	1%	0.50%	0.001%	0%	0%	0%
	No.2	1%	0.05%	0%	0%	0%	0%
	LGS	15%	5.00%	0.080%	0.01%	0.005%	0.1%
	Alloys	5%	0.50%	0.010%	0%	0%	0%
	Residuals	78%	93.95%	99.909%	99.99%	99.995%	99.9%

Table 4

 4 Bounds of imports and exports decision variables.

	di	Variable	Lower bounds	Upper bounds
			(kt=an)	(kt=an)
	d3	I-E of mixed waste	À192,000	192,000
	d4	I-E of I&HW	À204,288	102,144
	d5	I-E of SS	À1920	960
	d6	I-E of MSW	À62,976	31,488
	d7	I-E of WEEE	À3072	1536
	d8	I-E of ELV	À3456	1728
	d9	I-E of C&D	À108,288	54,144
	d16	I-E of remainder waste (Residual)	À96,341	192,000
	d17	I-E of low grade scrap (LGS)	À1119	1600
	d18	I-E of high grade scrap (No.2)	À49	416
	d19	I-E of pure scrap (No.1)	À51	400
	d27	I-E of copper concentrate	0	1600
	d28	I-E of matte	0	548
	d29	I-E of blister	0	417
	Legend: I-E: imports minus exports.

Table 5

 5 Parameters used for the genetic algorithm.

	Parameter	Value
	Population size ( 20Â number of variables)	920 individuals
	Number of generations ( 2Â number of individuals)	1840
	Crossover probability	0.9
	Mutation probability	0.5

1 With the exception of imports of low debris flow concentrates and mattes that is too large in relation to others and is divided by two.

Table 6

 6 Results of monobjective optimizations.

	Minimized criterion	Costs (G=an)	E I ( Mteq CO 2 =an)	Energy a (TWh=an)	Losses (kt=an)	Exp. RC (kt=an)	Exp. alloys (kt=an)
	Costs	21	103	À15	162	1806	115
	EI	31	35	148	302	0	11
	Energy	30	94	¡41	220	0	8
	Losses	58	68	35	38	6	2 2

Table 7

 7 Best ranked M-TOPSIS solutions for the biobjective optimization.

	Minimized function	Costs (GV=an)	E I ( Mteq CO 2 =an)	Energy (TWh=an)	Losses (kt=an)	Exp. RC (kt=an)	Exp. alloys (kt=an)
	TOPSIS 1	24.3	46.2	157.2	154.6	1422.5	114.7
	TOPSIS 2	24.3	46.4	156.7	154.3	1432.9	114.9
	TOPSIS 3	24.3	46.5	156.2	154.9	1426.6	114.9
	Legend: EI: environmental impacts -Exp.: exports -RC: refined copper.

Table 8

 8 Decision variables to reach the four identified optimal solutions.

	di	Variable

Table 9

 9 Decision variables to reach the four identified optimal solutions.

	di	Variable

Table 10

 10 Comparison of best ranked M-TOPSIS solutions for the bi-and quadriobjective optimizations. Very low energy consumption, only to feed trucks: 10 km to raise Incineration À550 kWh=t Power generation by incineration: PCI of waste is such that 2.2 MWh thermal =t are recovered, if electric energy is considered, this is multiplied by a yield of 25% Energy consumption associated with waste sorting to extract scrap Sorting 1 kWh=t Manual sorting, negligible energy Energy consumption attributed to imports and exports (copper, waste, etc.). All wastes 600 kWh=t EcoInvent: 0.0272 L oil =tkm or 54.4 L=t for 2000km, with a calorific value of 38,080 kJ=L or 10.58kWh=L, so 575 kWh=t Energy consumption attributed to imported products (besides transport) Refined copper 8300 kWh=t Average of different studies: Jdid and Blazy (2002): production from ore 105 to 110MJ=kg Cu , or 29,166.67 to 30,555.56kWh=t Cu , but in many other studies, it is rather between 25 and 30 MJ=kg Cu (for example Fthenakis et al. (2009)), about 8300 kWh=t Cu Concentrate 166 kWh=t EcoInvent "copper concentrate, at beneficiation" Matte 2324 kWh=t Energy between that of the concentrate and the blister Blister 6354 kWh=t EcoInvent "copper, blister-copper, at primary smelter/kg/RER"

	Minimized function	Costs (G=an)	E I ( Mteq CO 2 =an)	Energy (TWh=an)	Losses (kt=an)	Exp. RC (kt=an)	Exp. alloys (kt=an)
	TOPSIS bi	24.3	46.2	157.2	154.6	1422.5	114.7
	TOPSIS quadri	30.5	59.8	82.1	1086.4	424.9	59.3

Legend: EI: environmental impacts -Exp.: exports -RC: refined copper.

Acknowledgments

The authors would like to thank all the reviewers for their wise and useful comments. They helped us increase the clarity and quality of this paper.

Appendix A. Data used for impact calculation

Funding

This work was supported by the French National Research Agency as part of the ESPEER project (ANR 10 ECOT 008).

Appendix A.1. Data used for economic impact calculation Following data and hypothesis have been used for calculation of the copper cycle cost.

Appendix A.2. Data used for environmental impacts calculation

The following data and assumptions were used to calculate the total environmental impact expressed in equivalent CO 2 mainly taken from the database EcoInvent [START_REF] Classen | Life Cycle Inventories of Metals[END_REF]. It should be noted that the impacts of recycling processes have been calcu lated from the energy and material consumption of the processes.

Appendix A.3. Data used for energy consumption calculation

Following data and hypothesis have been used for calculation of energy consumption linked to copper cycle.


Vincent Escande

Alicia Velati

Claude Grison
email: claude.grison@cnrs.fr

Ecocatalysis for 2H-chromenes synthesis: an integrated approach for phytomanagement of polluted ecosystems

Keywords: Metal hyperaccumulating plants, Phytoextraction, Biopesticides, Chromenes, Ecocatalysis, Green chemistry

A direct, general and efficient method to synthesize 2H-chromenes (2H-benzo[b]pyrans), identified as environmentally friendly pesticides, has been developed. This approach lays on the new concept of ecocatalysis, which involves the use of biomass from phytoextraction processes, as a valuable source of metallic elements for chemical synthesis. This methodology is similar or superior to known methods, affording 2H-chromenes with good to excellent yields (60-98 %), including the preparation of precocene I, a natural insect growth regulator, with 91 % yield. The approach is ideal for poor reactive substrates such as phenol or naphthol, classically transformed into 2H-chromenes by methodologies associated with environmental issues. These results illustrate the interest of combining phytoextraction and green synthesis of natural insecticides.

Introduction

According to Freedonia Group (2010), global demand for pesticides will rise 2.9 % annually to 2014. Gains will reflect a reversal of declines in 2009, caused in part by a price drop for the leading herbicide, glyphosate. Herbicides and insecticides will remain the largest types. Asia and South America will offer the best growth opportunities. Demand for formulated pesticides in the agricultural market in China is forecast to rise 5.3 % per annum to 2.3 million metric tons in 2015. In value terms, formulated pesticide demand is expected to rise 7.1 % per year to 60 billion Yuan. Market gains will be driven primarily by increases in agricultural production as measured by the total area of sown land and ongoing expansions in the production of fruits and vegetables, which are by far the most intensive users of pesticides relative to most other crops.

This study analyzes the $45 billion pesticide industry at the global scale. It presents historical demand data for the years 1999, 2004, and 2009 and forecasts it for 2014 and 2019 byproduct (herbicides, insecticides, and fungicides), market (wheat, corn, rice, soybeans, consumer, and commercial), and world region and for 39 major countries.

According to these data, globalization promotes the development of invasive species. For instance, devastation caused by the Asian Formosan subterranean termite (Coptotermes formosansus, Rhinotermitidae) in North America has been estimated to cost $US 1 billion a year. Over the past two decades, organochlorines and organophosphates, the two prominent classes of termite control agents, have been banned, owing to environmental and human health concerns [START_REF] Meepagala | New class of algicidal compounds and fungicidal activities derived from a chromene amide of Amyris texana[END_REF]. In each case, there is an increased need to discover effective, environmentally friendly, and safe insect control agents with minimal human and environmental toxicity.

In addition, the pesticide pollution is sometimes exacerbated by metallic pollution of soils. Indeed, mining activities and agriculture practices lead to the contamination of soils and surface waters by metallic trace elements and pesticides. It is admitted that significant levels of pollution have been reached, inducing food contamination and human health risks.

On the other hand, Zn phytoextraction provides coherent and workable responses to the problems of large-scale revegetation and phytoremediation and may, ultimately, contribute to the ecological restoration of contaminated mine sites [START_REF] Wu | Effects of organic amendments on Cd, Zn and Cu bioavailability in soil with repeated phytoremediation by Sedum plumbizincicola[END_REF]. The development of these advanced techniques will help accomplish the remediation of marginalized lands polluted by heavy metals. For example, in France and southern China, our group and collaborators are performing phytoextraction of Zn-polluted soils [START_REF] Saunier | Trace elements biomonitoring in a historical mining district (les Malines, France)[END_REF][START_REF] Wu | Wu (Crassulaceae): a new species from Zhejiang Province, China[END_REF]. A similar methodology is developed for Mn phytoextraction in New Caledonia on degraded mining sites, thanks to accumulation abilities of local plants [START_REF] Brooks | Studies on manganese-accumulating Alyxia species from New Caledonia[END_REF][START_REF] Jaffre | Manganese accumulation by plants on ultrabasic rocks in New Caledonia[END_REF][START_REF] Jaffre | Manganese accumulation by New Caledonian Proteaceae[END_REF]. However, phytoextraction generates a new waste, namely the contaminated biomass. The treatment of contaminated leaves appears thus as an environmental problem again.

This paper has the ambition to propose an innovative technology to tackle these two types of pollution. The concept is based on the pioneering idea that metallic wastes recycled from hyperaccumulating plants can be used for the production of green, bioinspired pesticides. Our group already established a new concept that the biomass from phytoextraction can receive a new value, thanks to its transformation into ecocatalysts for the synthesis of organic molecules (Escande et al. 2014a, b, c;[START_REF] Grison | Psychotria douarrei and Geissois pruinosa, novel resources for the plant-based catalytic chemistry[END_REF]Losfeld et al. 2012a, b, c;[START_REF] Thillier | Metallophyte wastes and polymetallic catalysis: a promising combination in green chemistry. The illustrative synthesis of 5[prime or minute]-capped RNA[END_REF]. In this paper, we planned to study the use of these ecocatalysts for the synthesis of green pesticides, reinforcing the ecological interest of the technology. Our aim is to demonstrate that ecocatalysis represents an extraordinary environmental opportunity for the plant-based synthesis of bioinspired and green pesticides. By combining phytoextraction and ecocatalysis, we describe a novel access to emerging biopesticides, eco-friendly substitutes to toxic pesticides.

Model candidate molecules have been chosen in order to limit their human and environmental toxicity. We focused on juvenile hormone inhibitors in insects such as cockroach (Periplaneta americana Blattidae) [START_REF] Pratt | Precocene II inhibits juvenile hormone biosynthesis by cockroach corpora allata in vitro[END_REF] and milkweed bug (Oncopeltus fasciatus Lygaeidae) [START_REF] Brooks | The action of precocenes in milkweed bugs (Oncopeltus fasciatus) and locusts (Locusta migratoria)[END_REF]. Such juvenile hormonal inhibitors of natural origins include plant-based 2H-chromenes with insecticidal activities (Proksch et al. 1983;Proksch and Rodriguez 1983).

Several articles and patents have been published, concerning the biological activity, mechanism of action, and metabolism of natural 2H-chromenes, specifically precocenes [START_REF] Adler | Direct, regioselective synthesis of 2,2dimethyl-2H-chromenes. Total syntheses of octandrenolone and precocenes I and II[END_REF][START_REF] Brooks | The action of precocenes in milkweed bugs (Oncopeltus fasciatus) and locusts (Locusta migratoria)[END_REF]Lv et al. 2012;[START_REF] Timar | 7-Alkoxy-8-methoxy-2,2-dimethyl-2H-chromenes; insecticides, nematocides[END_REF]. Exposure of young larval stages of test insects to precocenes leads to precocious metamorphosis into unviable adults. Precocenes constitute a new type of insect growth regulator and have been referred to as fourth-generation insecticides. They are considered as environmentally friendly and have been postulated as biocontrol agents [START_REF] Bowers | Discovery of insect antijuvenile hormones in plants[END_REF][START_REF] Lévai | Synthesis of benzopyran derivatives, XV preparation of arylsulfonyloxy-2,2-dimethyl-2Hchromenes[END_REF][START_REF] Triseleva | Effect of plants synthesizing biologically active substances-precocenes-on insects[END_REF]. Our objective will be to develop a green process based on the use of ecocatalysts, which are efficient and low cost and can be used on an industrial scale.

The retrosynthetic strategy revealed that these molecules can be accessed by a cascade reaction, which involves the electrophilic addition of a phenol aromatic ring to an enal, followed by the dehydration of adduct and then by an intramolecular 6π-electrocyclization [START_REF] Adler | Direct, regioselective synthesis of 2,2dimethyl-2H-chromenes. Total syntheses of octandrenolone and precocenes I and II[END_REF][START_REF] Dintzner | Microwave-assisted synthesis of a natural insecticide on basic montmorillonite K10 clay. Green chemistry in the undergraduate organic laboratory[END_REF]) (Scheme 1).

Materials and methods

Ecocatalyst preparation

The selection of hyperaccumulating plants was undertaken in the context of our ongoing phytoremediation programs. Znhyperaccumulating plant leaves were derived from Noccaea caerulescens (Brassicaceae). They were collected from plants growing on the Les Avinières mine site, at Saint-Laurent-le-Minier (Gard) in the Mediterranean climate region of southern France. Mn-hyperaccumulating plant leaves derived from Grevillea exul rubiginosa were collected from plants growing in the southern province of New Caledonia (Thio).

Leaves were harvested before flowering, air-dried, and grounded. The obtained solid (30 g) was calcinated at 400 °C for 5 h, and the resulting powder (5 g) was added to 50 mL of a solution of hydrochloric acid (∼1 M). The solution was heated at 60 °C and stirred for 2 h. The reaction mixture was then filtered on celite. The resulting solutions were then concentrated under vacuum. The resulting ecocatalysts were stored under nitrogen atmosphere. Purification steps are not mandatory in our process.

Inductively coupled plasma mass spectrometry (ICP-MS) analyses were performed using the metal analysis of total dissolved solutes in water, in order to determine the composition of the ecocatalyst obtained. The samples were acidified with nitric acid 2.5 % and stirred for 30 min. The digestates were diluted to 0.005 g L -1 . Three blanks were recorded for each step of the digestion and dilution procedure on a HR-ICP-MS Thermo Scientific Element XR. Three analyzes were performed for each sample in order to determine the standard deviation of the measurement. Results are summarized in Table 1.

Scheme 1 Retrosynthetic analysis for access to 2Hchromenes

Synthesis

Chemicals

Reagents and solvents were purchased from Sigma-Aldrich and were used without further purification. All reactions were performed under nitrogen atmosphere and magnetic stirring unless otherwise noted. When needed, glassware was dried overnight in an oven (T>100 °C).

Purification and analysis of reaction products

Gas chromatography and mass spectrometry (GC-MS) analyses were performed using electronic impact ionization mode on a Varian Saturn 2000 ion trap instrument, interfaced with a Varian CP-3800 apparatus. The Varian CP-3800 was equipped with a 1079 split-splitless injector (206 °C) and a 30 m× 0.25 mm×0.25 μm film thickness ID WCOT CPSil-8CBfused silica capillary column (Chrompack®, Bergen op Zoom, The Netherlands), with helium as carrier gas (1 mL/ min), and was programmed for 2 min isothermal at 50 °C, then increasing from 50 to 220 °C at 4 °C/min. Mass spectra were recorded in electronic impact (EI) at 70 V and were identified by comparison with data of the NIST 98 software library (Varian, Palo Alto, CA, USA) and by comparison of the retention time of the standard compounds.

Flash column chromatography was performed using Chromagel Carlo Erba Reactifs SDS silica 60A CC 35-70 μm. Reactions were monitored using Merck Kieselgel 60 F254 aluminum. TLCs were visualized by UV fluorescence (254 nm) and then by immersion into KMnO 4 or vanillin ethanolic solutions.

NMR spectra were recorded on a Brüker Avance 300 spectrometer at room temperature, 1 H frequency is at 300 MHz, and 13 C frequency is at 75 MHz. IR spectra were recorded on a PerkinElmer Spectrum 100 FT-IR spectrometer, in ATR mode. Mass spectra were determined with a LC-MS Waters 3695 Separation module, Micromass ZQ 2000 by electrospray ionization (ESI positive or negative mode).

Experimental conditions of synthesis under ecocatalysis

The following syntheses involving the ecocatalysts were conducted in various reaction conditions, such as conventional heating or microwave (MW) activation. The experimental conditions are not necessarily dependent upon the use of a microwave oven. They can be performed in more conventional conditions. Specific examples are described below; the conditions are adapted to the involved reaction mechanisms and the difference in reactivity of the nucleophilic substrate.

Chromenes synthesis -Procedure with electron-rich substituted phenol derivatives In a sealed tube, 0.1 mmol of electron-rich phenolic derivatives, 0.8 mmol of 3-methyl-2butenal, 150 mg of 4 Å activated molecular sieves, 10.1 mg of Eco-Zn (0.01 mmol in Zn), and 2 mL of anhydrous toluene were introduced. The mixture was stirred for 2-4 h at 110 °C (reaction progress followed by GC-MS analysis). 2H-chromenes were isolated after washing with dichloromethane, and filtration, concentration under reduced pressure, and then chromatographic purification on silica gel were performed with a hexane/ethyl acetate mixture (9:1) as an eluent. They were identified by comparison with previously reported spectral data [START_REF] Iyer | Synthesis of 2, 2-dimethyl-2Hchromenes via a palladium (II) catalysed reaction[END_REF][START_REF] Lee | Efficient and general method for the synthesis of benzopyrans by ethylenediamine diacetate-catalyzed reactions of resorcinols with α,β-unsaturated aldehydes. One step synthesis of biologically active (±)-confluentin and (±)daurichromenic acid[END_REF][START_REF] Lykakis | Ph3PAuNTf2 as a superior catalyst for the selective synthesis of 2H-chromenes: application to the concise synthesis of benzopyran natural products[END_REF]).

-Procedure for low reactivity derivatives: phenol, naphthol, and 3-bromophenol In a sealed tube, 0.1 mmol of phenol, 0.8 mmol of 3methyl-2-butenal, 150 mg of 4 Å activated molecular sieves, 101 mg of Eco-Zn (0.1 mmol in Zn), and 2 mL of anhydrous toluene were introduced. The mixture was stirred for 20 h at 110 °C and was then submitted to the previously described treatment. The structure of compounds was determined by full spectroscopic characterization and was identified by comparison to previously published spectral data [START_REF] Kureshy | Sulfonic acid functionalized mesoporous SBA-15 as an efficient and recyclable catalyst for the synthesis of chromenes from chromanols[END_REF][START_REF] Zeng | ReCl(CO)5-catalyzed cyclocondensation of phenols with 2-methyl-3-butyn-2-ol to afford 2,2-dimethyl-2Hchromenes[END_REF].

Cannabinoid synthesis Representative procedure with sesamol

In a scintillation tube, 0.5 mmol of sesamol, 0.55 mmol of citral, 50 mg of Eco-Zn (0.05 mmol of Zn), and montmorillonite K10 (500 mg) were introduced. The mixture was placed in a microwave oven for 8 min (mechanic stirring after 1 min) at 500 W. After washing with dichloromethane, filtration, concentration under reduced pressure, and then chromatographic purification on silica gel were performed with a hexane/ethyl acetate mixture (9:1) as an eluent, and 6Hbenzo[b,d]pyran,6a,7,10,10a-tetrahydro-6,6,9-trimethyl-1,3benzodioxole (6a) was isolated as red oil with 90 % yield [IR cm -1 1,478, 1,629, 2,907; 1 H NMR (CDCl 3 , 300 MHz) δ 1.14 (s, 3H), 1.38 (s, 3H), 1.64-1.70 (m, 1H), 1.75 (s, 3H), 1.88-2.01 (m, 2H), 2.13 (m, 1H), 2.52 (brdd, J=16.6 Hz, 5.3 Hz, 1H), 2.63 (dt, J=11.2 Hz, 5.3 Hz, 1H), 5.48 (m, 1H), 5.86 (m, 2H), 6.36 (s, 1H), 6.69 (s, 1H); 13 C NMR (CDCl 3 , 75 MHz) δ 18. 3, 22.9, 27.0, 27.1, 32.2, 36.5, 42.6, 76.5, 98.5, 100.2, 105.1, 116.8, 119.6, 132.8, 140.8, 145.9, 147.3].

Results and discussion

The methodology was based on catalysis with Eco-Zn, with or without supporting on montmorillonite K10 (according to previously described procedures) [START_REF] Laszlo | Catalysis of Friedel-Crafts alkylation by a montmorillonite doped with transition-metal cations[END_REF][START_REF] Nasreen | Montmorillonite[END_REF]). The mixture of aldehyde and phenol derivatives was added to the catalytic system, and then, the reaction was carried out at 110 °C in anhydrous toluene. Experiments aimed at examining the possibility of catalyzing 2Hchromenes synthesis (Scheme 2) with this ecocatalyst gave interesting results. Table 2 presents the data obtained.

The results clearly show the interest of ecocatalysis. The performances of our ecocatalysts are at least similar (entry 3) and even higher (entries 1, 5, 6, and 7) than previous methodologies, allowing the synthesis of 2H-chromenes [START_REF] Adler | Direct, regioselective synthesis of 2,2dimethyl-2H-chromenes. Total syntheses of octandrenolone and precocenes I and II[END_REF][START_REF] Dintzner | Microwave-assisted synthesis of a natural insecticide on basic montmorillonite K10 clay. Green chemistry in the undergraduate organic laboratory[END_REF][START_REF] Lee | Efficient and general method for the synthesis of benzopyrans by ethylenediamine diacetate-catalyzed reactions of resorcinols with α,β-unsaturated aldehydes. One step synthesis of biologically active (±)-confluentin and (±)daurichromenic acid[END_REF][START_REF] Pettigrew | Phenylboronic acid mediated triple condensation reactions of phloroglucinol and unsaturated carbonyl compounds[END_REF][START_REF] Tiabi | Synthese des pecocenes en une seule etape[END_REF][START_REF] Zeng | ReCl(CO)5-catalyzed cyclocondensation of phenols with 2-methyl-3-butyn-2-ol to afford 2,2-dimethyl-2Hchromenes[END_REF]. Moreover, the catalysis by Eco-Zn avoids the use of harsh conditions and sensitive reagents previously reported [START_REF] Sartori | General synthesis of 2H-benzo[b]pyrans (chrom-3-enes) from metal phenoxides and .alpha.,.beta.-unsaturated carbonyl compounds[END_REF]. We tried to perform the reaction under heterogeneous catalysis, by supporting Eco-Zn on montmorillonite K10, but this was associated with a slight loss of yield (entry 2).

It is interesting to note that entries 1-3 led to precocene derivatives. Precocene I (3a) is a natural insecticide with antijuvenile hormone activity in insects [START_REF] Brooks | The action of precocenes in milkweed bugs (Oncopeltus fasciatus) and locusts (Locusta migratoria)[END_REF]). Eco-Zn catalysis allows its synthesis with high yield (91 %) and selectivity (95 %). The efficiency of the Eco-Zn catalyst in precocene I (3a) synthesis was highlighted by a comparison with various commercial Lewis acids derived from Zn, Fe, M n , a nd Ca , u nd e r t he fo r m of c h l or i de s a n d trifluoromethanesulfonates (triflates), often used as powerful Lewis acid catalysts (Table 3). Among the tested Lewis acid catalysts, Eco-Zn clearly showed the highest activity (91 % yield, entry 1), followed by Zn triflate (49 % yield, entry 6) and then by Zn chloride (23 % yield, entry 2). Notable degradation was observed with Ca and Fe triflates, resulting in almost no formation of the expected products (entries 7 and 8). Most of the catalysts displayed a high selectivity toward 3a regioisomer, but only Eco-Zn was able to combine simultaneously high yield and selectivity (Scheme 3).

Under ecocatalysis, synthesis of 2H-chromenes was possible with various nucleophilic substrates. We show here that it is possible to extend this type of reaction to less electron-rich substrates in this type of transformation and, finally, to prepare new structures deemed inaccessible by these synthetic routes. It is important to note that nucleophiles conventionally considered to be insufficiently reactive in this type of reaction can be used here, thanks to ecocatalysis. This is, for example, the case for phenol (Table 2, entry 4) and naphthol (Table 2, entry 5), whose corresponding 2H-chromenes have been accessed in previous reports with toxic or non-eco-friendly catalysts such as rhenium pentacarbonyl chloride [START_REF] Zeng | ReCl(CO)5-catalyzed cyclocondensation of phenols with 2-methyl-3-butyn-2-ol to afford 2,2-dimethyl-2Hchromenes[END_REF], TiCl 4 [START_REF] Sartori | General synthesis of 2H-benzo[b]pyrans (chrom-3-enes) from metal phenoxides and .alpha.,.beta.-unsaturated carbonyl compounds[END_REF], or BF 3 •Et 2 O [START_REF] Madabhushi | An efficient and simple method for synthesis of 2,2-disubstituted-2H-chromenes by condensation of a phenol with a 1,1-disubstituted propargyl alcohol using BF 3 •Et 2 O as the catalyst[END_REF]). However, the Eco-Zn-catalyzed reaction with a substrate bearing an electron-withdrawing substituent, poorer in electrons than phenol, such as 3-bromophenol (Table 2, entry 8) gave only traces of the corresponding chromene. A similar tendance was observed by authors using a phenylboronic-acetic acidcatalyzed methodology on 4-bromophenol, isolated with 35 % yield, one of the lower reported yields in spite of prolonged heating and high loading of catalyst [START_REF] Chauder | Phenylboronic acid-mediated synthesis of 2H-chromenes[END_REF].

The methodology can be extended to bi-or triphenolic structures (Table 2, entries 6 and7). With 3-methyl-2-butenal, the expected 2H-chromenes were formed and the sequential reactions were almost quantitative.

Dienals, such as citral, were also effective in this reaction. Optimization of reaction conditions revealed that microwave irradiation proved to be much more efficient than thermal heating. Indeed, when carried under MW irradiation, the reaction was completed in 8 min, whereas more than 20 h was necessary under conventional heating, even with electron-rich substrates. By contrast with the previous 2H-chromene synthesis, the final reaction after dehydration of adduct was not an intramolecular 6π-electrocyclization, but a hetero Diels-Alder reaction, involving the terminal double bond (Scheme 4). The product obtained was not a 2Hchromene, but a cannabinoid-related structure (Table 4). Interestingly, structure 6 was formed in situ after migration of the C=C double bond of the initially expected structure 5 which is not isolated. Structure 6 is suggested by the 1 H NMR signal of the olefinic proton, at 5.48 ppm, which would have been deshielded to values superior to 6 ppm in structure 5, because of an induced diamagnetic field arising from the aromatic ring, as already described on similar compounds [START_REF] Choi | NMR assignments of the major cannabinoids and cannabiflavonoids isolated from flowers of Cannabis sativa[END_REF][START_REF] Taylor | Active constituents of Hashish. Synthesis of Dl-Delta6-3,4-trans-tetrahydrocannabinol[END_REF]. The coupling constant of protons at cycle junction (J=5.3 Hz) indicated a cis configuration. No trans form was detected during analysis of the reaction products. This result shows the interest of the methodology, giving access with high selectivity to structures similar to natural products such as Δ 8 -tetrahydrocannabinoids derivatives [START_REF] Goujon | Expeditious preparation of various delta(9)-6a,10a cis and trans 2-substituted tetrahydrocannabinoids[END_REF].

Results in entries 1 and 2 show that irradiating the mixture for 8 min allows to obtain high yields of products. The yield can be increased to 98 % when the time reaction was nearly doubled (15 min instead of 8 min), according to entries 2 and 3. As montmorillonite K10 was used as a solid medium for the reaction, we investigated the catalytic activity of the sole clay. It appeared that only 20 % of the product was formed in these conditions, demonstrating that the efficiency of the methodology is due to the Eco-Zn catalyst. However, for less electron-rich substrates like phenol, the previous conditions did not lead to the same efficiency (10 % yield, entry 5). We then investigated for a better ecocatalyst by using Eco-Mn. The yield was then slightly increased when using Eco-Mn in the same conditions (20 % yield, entry 6). After optimization of the reaction conditions, we were able to obtain the cannabinoid 6c in 72 % yield, by using an excess of citral and one equivalent on Mn from Eco-Mn. It is important to note that the synthesis of cannabinoid 6c was not previously described under Lewis acid catalysis in the literature, probably because of the low activation of the starting aromatic ring. Moreover, the ecocatalyst efficiency can be pointed out by comparison w i t h p r e v i o u s c a t a l y t i c s y s t e m s s u c h a s dichlorophenylboranes which led to lower yield (30 %) of the product similar to 6b (Kun [START_REF] Lau | Dichlorophenylborane a new reagent for the preparation of 2-phenyl-4H-1,3,2-benzodioxaborins[END_REF]. Ecocatalysis allowed equally the access to new structures, such as the cannabinoid 6a whose synthesis was not previously described.

Conclusion

The aim of this work was to describe an efficient green access to the emerging biopesticides, which are eco-friendly substitutes to conventional toxic pesticides. It was possible to access complex benzopyrans, some of which are natural products belonging to the chromene group, in good to excellent yields. These molecules were prepared by ecocatalysis, an innovative methodology involving the use of biomass from phytoextraction processes as a valuable source of metallic elements for catalysis. Eco-Zn and Eco-Mn catalysts were able to promote addition reactions on enals and dienals of various reactivities with phenol nucleophiles. Moreover, this methodology provides an efficient access to cannabinoidrelated structures, including the new product 6a which could find an interest in further studies.

a

  Reaction conditions: phenol derivative (0.1 mmol), 3-methyl-2-butenal (0.8 mmol), 4 Å activated molecular sieves (150 mg), Eco-Zn (amount corresponding to indicated values), anhydrous toluene (2 mL), 110 °C b Yield determined by GC-MS with biphenyl as internal standard c Isolated yield d Eco-Zn was supported on montmorillonite K10

Scheme 4

 4 Scheme 4 Extension of the reaction sequence to dienal

a

  Reaction conditions: phenol derivative (0.5 mmol), citral (0.55 mmol), Eco-Zn (amount corresponding to indicated values) and montmorillonite K10 as solid medium (500 mg), MW irradiation at 500 W b Yield determined by GC-MS with biphenyl as internal standard c Isolated yield d Montmorillonite K10 only, without ecocatalyst e Eight equivalents of citral were used

Table 1

 1 Metallophyte species and derived ecocatalyst

	Ecocatalyst	Mg	Ca	Al	Mn	Fe	Zn	Pb	Cd
		wt% (±sd)	wt% (±sd)	wt% (±sd)	wt% (±sd)	wt% (±sd)	wt% (±sd)	wt% (±sd)	wt% (±sd)
	Eco-Zn from	3.76 (±0.10) 35.81 (±0.50) 1.74 (±0.049) 0.071 (±0.0027) 1.80 (±0.028) 6.57 (±0.059) 0.73 (±0.0048) 0.35 (±0.0040)
	Noccaea
	caerulescens
	Eco-Mn from	5.26 (±0.086) 10.44 (±0.17) 0.24 (±0.015) 6.72 (±0.037) 0.90 (±0.0075) 0.06 (±0.0025) nd	nd
	Grevillea exul
	rubiginosa
	nd not determined (<10 ppm)

Table 2

 2 Scope of the Eco-Zn-catalyzed synthesis of 2H-chromenes

	Entry	Product	a	Eco-Zn (equiv of Zn)	Time (h)	Yield % b (regioisomers ratio)
	1			0.1	2	91 (82) c
						(3a/3a' = 95/5)
	2			0.1	2	62 d
						(3a/3a' = 95/5)
	3			0.1	4	98 (76) c

Table 3

 3 Test of various Lewis acid catalysts in precocene I synthesis

	Entry Lewis acid	Catalyst	Yield % b 3a/3a′ regioisomers
		catalyst a	equivalents		ratio b
	1	Eco-Zn	0.1 (Zn)	91	95/5
	2	ZnCl 2	0.1	23	97/3
	3	C a C l 2	0.1	1	nd c
	4	FeCl 3 •6H 2 O	0.1	11	89/11
	5	MnCl 2 •4H 2 O	0.1	1	nd c
	6	Zn(CF 3 SO 3 ) 2	0.1	49	94/6
	7	C a ( C F 3 SO 3 ) 2	0.1	0	nd c
	8	F e ( C F 3 SO 3 ) 3	0.1	1	nd c
	9	Mn(CF 3 SO 3 ) 2 0.1	12	98/2
	a Reaction conditions: 3-methoxyphenol (0.1 mmol), 3-methyl-2-butenal
	(0.8 mmol), 4 Å activated molecular sieves (150 mg), Lewis acid catalyst
	(0.01 mmol), anhydrous toluene (2 mL), 110 °C, 2 h
	b Yield and regioisomer ratio was determined by GC-MS with biphenyl as
	internal standard
	c Not determined

Table 4

 4 Scope of the methodology with dienal (citral)

	Entry	Product a	Ecocatalyst	Time (min)	Yield % b
	1		Eco-Zn (0.1equiv Zn)	8	9 7 ( 9 0 ) c
	2		Eco-Zn (0.1equiv Zn)	8	9 2 ( 6 8 ) c
	3		Eco-Zn (0.1equiv Zn)	15	98
	4		-	8	2 0 d
	5		Eco-Zn (0.1equiv Zn)	8	1 0
	6		Eco-Mn (0.1 equiv Mn)	8	2 0
	7		Eco-Mn (1equiv Mn)	8	7 2 e

Acknowledgments The authors would like to thank the Agence Nationale de la Recherche (ANR 11ECOT 011 01), Centre National de la Recherche Scientifique (CNRS), Agence de l'Environnement et de la Maîtrise de l'Energie (ADEME), and Fond Européen de Développement Régional (FEDER) program for their financial supports.