Dylan Lorfing

Aras Ahmadi

Stéphanie Laborie

Régis Olives

Quentin Falcoz

Xavier Py

Ligia Tiruta-Barna

Energy and environmental performance of a new solar boiler with heat recovery for seawater desalination

Keywords: Solar desalination, concentrated solar energy, life cycle assessment, process modeling, process ecodesign

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

The growing world population, combined with increases in per capita water consumption, has led to an over-exploitation of natural freshwater resources [START_REF] Uhlenbrook | The United Nations world water development report 2019: leaving no one behind[END_REF]. Several geographical areas are already facing freshwater shortages, and climate change could worsen the situation [START_REF] Zhao | Virtual water scarcity risk to global trade under climate change[END_REF], [START_REF] Mekonnen | Four billion people facing severe water scarcity[END_REF]. Because salt water represents 97.5% [START_REF] Center | Volumes of the World's Oceans from ETOPO1[END_REF] of all water on Earth, desalination is one possible response to freshwater scarcity. Desalination has been used for decades, and several countries currently depend on it for their water supply [START_REF] Darwish | Energy water in Kuwait Part I. A sustainability view point[END_REF], [START_REF] Chauhan | A comprehensive review of direct solar desalination techniques and its advancements[END_REF]. Of the proposed technologies, the most widely used at the industrial level are reverse osmosis (RO) and multiple-effect distillation (MED). The first uses semipermeable RO membranes to separate a pressurized flow of seawater into two flows: permeate and brine [START_REF] Kucera | Reverse Osmosis: Industrial Processes and Applications[END_REF]. The second, MED, is composed of a succession of "effects" in which the condensation of the steam of the previous effect enables the vaporization of seawater [START_REF] Chua | Low Grade Heat Driven Multi-Effect Distillation and Desalination[END_REF]. Usually, the feeding steam of the first effect is provided by a boiler powered by fossil fuels. One of the major acknowledged drawbacks of desalination processes, such as classical distillation, multi-stage flash distillation, and MED, is their intensive consumption of heat energy [START_REF] Mannan | Quantifying the energy, water and food nexus: A review of the latest developments based on life-cycle assessment[END_REF]. Despite the considerable progress achieved in this field, following significant research effort and years of feedback, the energy consumption of desalination remains high and is responsible for significant environmental impacts [START_REF] Elsaid | Environmental impact of desalination technologies: A review[END_REF].

Energy transitions linked to the growing needs of water consumption require innovative solutions.

There is a great diversity of solutions proposed to alleviate this energy issue, from the use of geothermal energy to provide heat for thermal desalination processes to the use of wind or tidal energy to supply power to RO installations [START_REF] Koroneos | Renewable energy driven desalination systems modelling[END_REF]- [START_REF] Gude | Renewable and sustainable approaches for desalination[END_REF]. Of the proposed solutions, solar energy has received considerable attention [START_REF] Chauhan | A comprehensive review of direct solar desalination techniques and its advancements[END_REF], [START_REF] Palenzuela | Concentrating Solar Power and Desalination Plants: Engineering and Economics of Coupling Multi-Effect Distillation and Solar Plants[END_REF]. Indeed, solar energy is one of the most explored renewable resources, in particular because there is a strong correlation between areas with high solar potential and areas where freshwater shortages are most significant [START_REF] Servert | Synergies of solar energy use in the desalination of seawater: A case study in northern Chile[END_REF]. These points make solar energy particularly interesting in the context of desalination.

Of the various solutions, the coupling of photovoltaic (PV) electricity production with RO systems has already been extensively studied [START_REF] He | Stand-alone seawater RO (reverse osmosis) desalination powered by PV (photovoltaic) and PRO (pressure retarded osmosis)[END_REF], [START_REF] Espino | Optimised desalination of seawater by a PV powered reverse osmosis plant for a decentralised coastal water supply[END_REF]. Another promising solution is the use of waste heat from concentrated solar power (CSP) plants to feed a thermal desalination system, e.g., MED. Solar stills have also been studied, primarily for small-scale installations, because of their ease of use and their potential in remote areas [START_REF] Trieb | Aqua-CSP Concentrating Solar Power for Seawater Desalination[END_REF], [START_REF] Wellmann | Exergoeconomic evaluation of a CSP plant in combination with a desalination unit[END_REF]. Despite the diversity of the proposed solutions, only a few largescale solar desalination projects have been implemented or even planned.

The alternative solutions that have already been considered are promising but suffer from several limitations. Regarding PV-RO systems, the performance of the entire system is limited by the PV performance. CSP-MED systems appear to have significant potential; however, electricity production is not always required at a given site and increases the complexity of the system. The use of many loops with different fluids requires a large number of heat exchangers between the loops to ensure heat transfer. This complexity is particularly limiting for small-scale applications. Finally, the efficiency of solar stills remains limited and implies the use of a large land area [START_REF] Chauhan | A comprehensive review of direct solar desalination techniques and its advancements[END_REF].

To overcome these difficulties, a new conceptual process for seawater desalination using solar energy as the main energy source is proposed in this study. The proposed process is based on a newly developed solar boiler [20]. The solar boiler permits seawater to be distilled using solar energy concentrated via a "beam-down" optical system. The beam-down system consists of a two-reflection device, which allows the concentration of solar energy at the ground level in a downward-directed beam [21]. This system, initially developed for CSP applications, presents several advantages for use in various applications other than power generation [START_REF] Diago | Net power maximization from a faceted beamdown solar concentrator[END_REF]: (i) the vertical downward concentration and the radiation focused at the ground level facilitate energy use for various processes; (ii) the point concentration allows work over a wide temperature range; and (iii) the construction costs are less than those of conventional solar towers. In this study, the steam produced by the solar boiler (SB) is used as the input stream in the first stage of an adjusted MED system in order to improve the energy efficiency and water productivity.

A comprehensive model coupling the SB with MED (SB-MED) is developed here, complete with all the ancillary processes required for tap water production, from seawater pumping to tap water delivery. The objective of the modelling is to evaluate the entire process in terms of the technical, energetic, and environmental performances. The model considers the particularities of the newly proposed SB (i.e., its shape and material) and the main characteristics of the beam-down solar installation (the reflection surface and optical efficiency). The MED is simulated by rigorously integrating the mass and heat balances, as well as the thermodynamics, for the non-ideal behavior of seawater. The model is applied to a theoretical reference case, a small desalination installation producing drinking water for a small community, with a target annual productivity of 10,000 m 3 of tap water. The environmental performance is assessed using the life cycle assessment (LCA) method [START_REF]2006 -Environmental management -Life cycle assessment -Principles and framework[END_REF] to identify the hot spots of the system and to ultimately compare the new system with conventional technologies. The comparison of the technical, energetic, and environmental performances of SB-MED enables this system to be placed in the context of other desalination systems and highlights its strengths and limitations. To the best of the author's knowledge, this is the first study proposing such solar based desalination technology and its detailed modeling and performance assessment.

2 Materials and Methods

Description of a new process coupling concentrated solar boiling with heat recovery via multiple-effect distillation (SB-MED)

The complete process of tap water production from seawater, shown in Figure 1, is based on a newly developed SB that enables the production of steam from seawater using concentrated solar energy provided by a beam-down system. The steam is condensed to produce distilled water. The condensation heat extracted from the steam is then used as a heat source in a thermal desalination process based on MED. Pumping, pretreatments, and post-treatments, also represented on Figure 1, are considered and are based on conventional treatments currently used in thermal desalination processes; these steps are detailed in Section 2.2.4 [START_REF] Maurel | Dessalement de l'eau de mer et des eaux saumâtres : Et autres procédés non conventionnels d'approvisionnement en eau douce[END_REF].

Figure 1: Layout of the solar boiler (SB)-multiple-effect distillation (MED) system.

The solar boiler (SB)

The central element of the proposed process is the SB, which is composed of three parts. The second element is the conical receiver installed at the focal point. This receiver converts the useful part of the radiative power (𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) into heat and then transfers it to the seawater via boiling (𝑄𝑄 ̇𝑏𝑏𝑠𝑠𝑏𝑏𝑠𝑠𝑏𝑏𝑏𝑏𝑏𝑏 ). The power that is not transmitted to the seawater (𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 ) is lost to reflection, radiation, and convection. The conical receiver and the heat transfer flux are represented in Figure 2B. The SB is especially designed to operate under film-boiling conditions. This choice was motivated by the protective effect on the receiver of the vapor film between the receiver and the seawater, which prevents salt crusting.

Finally, the third part of the SB is the tank, shown in Figure 2C. The tank is supplied with seawater at a given flow rate (𝑚𝑚̇𝑠𝑠 𝑠𝑠 ). A first outlet at the top of the tank allows the recovery of the produced vapor at a flow rate of 𝑚𝑚̇𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 . A second outlet at the bottom of the tank allows the brine, at a flow rate of 𝑚𝑚̇𝑏𝑏 𝑠𝑠𝑏𝑏𝑏𝑏𝑠𝑠 , to be evacuated. Details concerning the modeling and design of the SB are given in Section 2.2.2.

The adapted multiple-effect distillation (MED)

Vapor and brine produced by the SB are routed to an MED whose characteristics have been adjusted (Figure 3B) while keeping its essentials similar to those of conventional installations (Figure 3A) [START_REF] Chua | Low Grade Heat Driven Multi-Effect Distillation and Desalination[END_REF].

As in conventional installations, the adapted MED is constructed of a succession of stages. Each stage consists of a vessel making use of the principle of evaporation and condensation at a reduced ambient pressure. On the hot side of each vessel, inlet steam from the SB or the previous effect is condensed. On the cold side, seawater inlet at a reduced pressure is partially vaporized. The evaporation takes place on the surfaces of the hot heat transfer tubes on which the seawater is sprayed.

Figure 3: Layout of (A) a conventional MED system and (B) one upgraded and adapted for operation with the SB. α: seawater preheating; β: flash chambers

The steam produced at one stage is condensed in the next stage inside the heat transfer tubes and then collected.

Many improvements to increase the performance of conventional MED systems have been proposed in the literature and are used in industry. In the present study, two classical upgrades are considered. The first is seawater preheating (Figure 3B-α). At each stage, a fraction of the produced vapor is extracted and its condensation heat is used to preheat the entering seawater. The second upgrade consists of installing a flash chamber between each stage at the corresponding pressure (Figure 3Bβ). Brine extracted from the different stages is sent to the flash chamber, permitting the extraction of a small portion of vapor that can be used to complement the incoming steam.

In the final stage, steam condensation is ensured in a condenser by an additional flow of seawater. The seawater used for cooling is then mixed with the brine and discharged into the sea. This mixing permits the salt concentration of the brine to be reduced prior to discharge, reducing its impact on the environment. The temperature and pressure levels, design parameters of the MED, and adaptions made to couple it with the SB are presented in detail in Section 2.2.3.

Process modeling and technical and energetic performances of the SB-MED process 2.2.1. Main steps of the modeling approach

The key processes involved in the proposed desalination system are the SB and the MED, which require specific models based on the mass and energy balance and their design and sizing. The SB model was developed and evaluated using an in-house-developed Python program. The simulation of the MED was performed using the state-of-the-art ProSim © chemical engineering simulation software. The pre-and post-treatment processes are not new; they are well-described by conventional models with respect to their material and energy balances and their design. The energy and chemical consumptions of the pre-and post-treatment processes were calculated on an Excel spreadsheet. Details concerning the parameters needed for these estimations are based on the literature and are briefly summarized in Appendix 1.

The global structure of the modeling approach and the tools used for the calculation and simulation are presented in Figure 4.

Figure 4: Architecture of the modeling approach for the SB-MED system and for the energy, productivity, and environmental performance calculations.

The material inventory required for the construction of the system and estimations of the concentrated solar power and the annual operation hours were all made in Excel. Finally, the environmental impacts were calculated using the LCA Umberto © software [START_REF]iPoint-systems gmbh[END_REF], with the foreground inventory provided by the modeling platform and with the background inventory supplied by the ecoinvent database (Section 2.3) [START_REF]ecoinvent[END_REF].

SB and solar concentrator

To estimate the productivity of the process under realistic conditions, a small-scale reference case is proposed and studied here. The reference case is designed for a desalination unit on the Mediterranean island of Corsica. The production goal of the reference installation was set to 10,000 m 3 of tap water per year. A conventional reference DNI value of 1,000 W m -2 was assumed given the sizing. Based on the usual local solar resources [START_REF] Nasa | Configuration Factors for Exchange of Radiant Energy Between Axisymmetrical Sections of Cylinders, Cones, and Hemispheres and Their Bases[END_REF], the operating hours of the installation were then estimated at 1,885 h yr -1 .

The dimensions of the beam-down system used are based on those of a 100-kW laboratory-scale installation [21]. The dimensions of the heliostat field therefore needed to be adjusted to provide the necessary energy to achieve the production goal.

Losses occur during the collection of solar energy. To take this into account and to estimate the power concentrated by the beam-down system, Equation ( 1) is used:

𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = η 𝑏𝑏𝑏𝑏 𝑆𝑆 𝑐𝑐𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑐𝑐 𝐷𝐷𝐷𝐷𝐷𝐷, (1)
where 𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is the power concentrated at the receiver [W], DNI is the direct normal irradiation [W m -2 ], Scollec is the total surface of the primary mirrors [m 2 ], and ηbd is the optical efficiency of the beam-down installation, accounting for the different losses during the collection and concentration of the solar energy. These losses are due to the cosine effect, reflectivity, blocking effect, shadow effect, and aim error. The combination of these losses (or efficiencies, as presented in Table 1) indicates an estimated global optical beam-down efficiency, ηbd, of 0.58. Note that the optical efficiency of the installation depends on the position of the Sun. Here, only the annual mean values are presented. These values are used in this study as a first approximation.

𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 + 𝑄𝑄 ̇𝑏𝑏𝑠𝑠𝑏𝑏𝑠𝑠𝑏𝑏𝑏𝑏𝑏𝑏 = 0, (2)
where 𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 is the concentrated solar energy reaching the receiver, 𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 represents the heat losses resulting from radiation, convection, and reflection on the upper side of the receiver [W], and 𝑄𝑄 ̇𝑏𝑏𝑠𝑠𝑏𝑏𝑠𝑠𝑏𝑏𝑏𝑏𝑏𝑏 is the heat transmitted to the boiling fluid at the lower side of the receiver. These flows are represented in Figure 2B. Then, the following heat and mass balance equations can be written for the fluid in the SB tank.

𝑚𝑚̇𝑠𝑠 𝑠𝑠,𝐻𝐻 2 0 = 𝑚𝑚̇𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠,𝐻𝐻 2 0 + 𝑚𝑚̇𝑏𝑏 𝑠𝑠𝑏𝑏𝑏𝑏𝑠𝑠,𝐻𝐻 2 0

(3)

𝑚𝑚̇𝑠𝑠 𝑠𝑠,𝑁𝑁𝑠𝑠𝑁𝑁𝑠𝑠 = 𝑚𝑚̇𝑏𝑏 𝑠𝑠𝑏𝑏𝑏𝑏𝑠𝑠,𝑁𝑁𝑠𝑠𝑁𝑁𝑠𝑠 (4)
𝑚𝑚̇𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 (ℎ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 -ℎ 𝑏𝑏𝑏𝑏 ) + 𝑚𝑚̇𝑏𝑏 𝑠𝑠𝑏𝑏𝑏𝑏𝑠𝑠 (ℎ 𝑏𝑏𝑠𝑠𝑏𝑏𝑏𝑏𝑠𝑠 -ℎ 𝑏𝑏𝑏𝑏 ) + 𝑄𝑄 ̇𝑏𝑏𝑠𝑠𝑏𝑏𝑠𝑠𝑏𝑏𝑏𝑏𝑏𝑏 -𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 = 0

In Equation ( 4), the mass flow of salt leaving the SB is obtained by assuming that the vapor formed by boiling is pure water.

A nodal method is considered for the resolution. This method considers the temperature at the upper and lower surfaces of the receiver, the boiling temperature of the seawater in the SB, the temperature of the entering seawater, and the ambient temperature.

The liquid-vapor equilibrium condition allows the boiling temperature to be related to the operating pressure in the SB.

𝑃𝑃 = 𝑃𝑃 𝑠𝑠𝑠𝑠 𝑠𝑠𝑠𝑠𝑠𝑠, * (𝑇𝑇 𝑏𝑏 , 𝑠𝑠) (6)
To complete the model, equations for each heat transfer phenomenon are included using expressions from the literature. The radiative and reflective losses are expressed following the method proposed by Modest [START_REF] Modest | Radiative Heat Transfer[END_REF] for a grey surface at a constant temperature. Conduction through a plate is considered for the heat transfer between the upper and lower surfaces of the receiver. The convective phenomena are described via equations for natural convection over a flat plate (for the horizontal part of the receiver) and an inclined plate (for the conical part). These equations are taken from Rohsenow et al. [START_REF] Rohsenow | Handbook of Heat transfer[END_REF]. Free convection is considered in the same manner for the heat lost by the tank. Finally, the heat transfer between the receiver and the boiling fluid is treated as the heat exchange via boiling under film conditions, with equations taken from [START_REF] Rohsenow | Handbook of Heat transfer[END_REF]. The CoolProp library [START_REF] Bell | Pure and Pseudo-pure Fluid Thermophysical Property Evaluation and the Open-Source Thermophysical Property Library CoolProp[END_REF] was employed to calculate the fluid properties and the phase equilibrium conditions in the SB.

The SB model makes it possible to determine the energy efficiency and productivity of the SB depending on the operating conditions (𝑄𝑄 ̇𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 , flow rates, fluid specificity, temperature, and pressure) and the SB design and sizing parameters (e.g., system geometry and material properties).

In the reference case, the geometric parameters of the SB receiver were chosen to maximize the vapor production at the operating point (DNI = 1,000 W m -2 ). Its dimensions were also chosen to maintain a sufficiently high temperature at the lower surface to maintain the film-boiling regime for a DNI as low as 500 W m -2 .

The power input was chosen to ensure the necessary steam production to reach the annual production goal. Because the SB is designed to work with seawater, boiling was assumed at atmospheric pressure at a vaporization rate of 0.65. All the operating conditions used for the calculations are summarized in Table 2.

Simulation and performance of the adjusted MED system

As mentioned in Section 2.2.1, the adjusted MED system was simulated using the state-of-the-art ProSim © chemical engineering simulation software.

In this approach, the seawater is treated as a binary mixture of water and sodium chloride. To account for the discrepancy between an ideal fluid and the seawater (an electrolyte solution), a heterogeneous approach was applied. The activity coefficients were estimated by the e-NRTL model, and the fugacity of pure water was calculated via the Henry law, with the Poynting correction. The Peng-Robinson equation of state was used for the water gas phase.

As mentioned in the process description (Section 2.1), the adjusted MED is based on a conventional MED with preheating of the incoming seawater and flashing of the brine, as can be seen in the layout of the installation (Figure 3B). The number of effects usually varies between 4 and 21 [START_REF] Khawaji | Advances in seawater desalination technologies[END_REF]; in this case, 14 stages were considered, with a top temperature of 70°C. This temperature corresponds to the usual temperature at the top of an MED necessary to avoid corrosion [START_REF] Maurel | Dessalement de l'eau de mer et des eaux saumâtres : Et autres procédés non conventionnels d'approvisionnement en eau douce[END_REF]. The temperature at the last stage was set to 35°C. This value is also usual for an MED system and permits the boiling to occur at a reasonable pressure level. The seawater inlet was set to 20°C at atmospheric pressure. The pressure level was calculated for each stage to ensure a temperature difference between the condensation temperature of the steam and the boiling temperature of seawater of 2.5°C, which is necessary for the heat transfer.

The distillate flow rate target at the operating point was set to 5,303 kg h -1 . This rate was fixed according to the annual production goal (10,000 m 3 ) and the number of expected operating hours (1,885 h). The seawater flow rate entering the SB-MED was then determined to ensure the target flow. In this study, the seawater flow was equally spread between the SB and each stage of the MED.

The cooling seawater flow necessary for the final condensation and to cool the distilled water enters the system at 20°C. After its use and before being rejected to the sea, the cooling water is mixed with the brine, lowering the salt concentration of the discharge and decreasing its potential impact on the environment. The flow rate of the cooling seawater was determined to ensure a maximal temperature difference of 10°C between the discharge and the seawater.

The design was adapted to couple the MED with the SB. The vapor coming from the SB is condensed in the first stage of the MED, allowing vaporization of the seawater in this stage. Contrary to a conventional installation, the condensate vapor from the SB is collected with all of the other condensates from the MED and is part of the final distillate production. The brine coming from the SB is collected, as is the other brines from the MED, and sent to the flash chamber to increase the vapor production.

The electricity consumption used for pumping was estimated based on the mass flow and the required pressure drops, with a pump efficiency and an electric motor efficiency of 0.70 and 0.98, respectively [START_REF] Monnot | Integrated approach in eco-design strategy for small RO desalination plants powered by photovoltaic energy[END_REF]. The incondensable gas mass flow that needs to be evacuated to maintain the necessary low pressure was assumed to represent 0.06% of the vaporized seawater mass [START_REF]Lalonde Systhermique -Gaz Incondensables[END_REF].

The parameters necessary for the MED simulation are summarized in Table 2.

Pumping, pretreatment, and post-treatment

The first step in the process is seawater pumping to the facility. Based on current practical operations, it is assumed that the distance between the installation and the seawater intake is equal to 3,500 m. The pressure drop for seawater transport is estimated to be 3.2 bar [START_REF]Mémento des pertes de charges -I.E. Idel'cik -3ème édition -Librairie Eyrolles[END_REF]. The electricity consumption for the pumps is estimated as presented in the previous section. At the seawater intake (Figure 1A), a large mesh filter prevents the intake of large particles and disinfection with hypochlorite prevents the growth of algae or microorganisms (Figure 1-2.1).

To ensure the proper operation of the equipment, the seawater needs to be pretreated before being used in the SB-MED process. The pretreatment consists of adding a coagulant and a flocculant (Figure 1-3) in a mixing and flocculation tank (Figure 1-C). Next, sedimentation is performed in a suitable pond (Figure 1-D). Finally, an antiscalant is added to the seawater (Figure 1234). The chemicals used for these treatments and their required quantities, the size of the necessary equipment, and the associated electricity consumption are estimated using data and methods given in the literature [START_REF] Gille | Seawater intakes for desalination plants[END_REF].

The distilled water obtained at the outlet of the SB-MED system is remineralized in a post-treatment step using lime (Figure 123456789), and then a disinfection step is performed to avoid any contamination (Figure 1-2.2). As for the pretreatment, the type and size of the required equipment were estimated according to conventional methods found in the literature; details are given in Appendix 1.

LCA of the SB-MED system and comparison with conventional desalination technologies

The data, assumptions, and equations presented in Sections 2.1 and 2.2 allow an estimation of the technical performance and energy (electricity) consumption of the proposed system for a given annual production goal, i.e., 10,000 m 3 yr -1 . Based on the calculated performances, the proposed process can be compared with more conventional desalination technologies for the same level of tap water production. The three selected comparative scenarios are presented in Section 2.3.1. The particularities of SB-MED are its use of concentrated solar energy as the main energy source in the SB and its corresponding adjustment of the MED system to maintain a reasonable rate of desalination. For these reasons, a comparison based only on the energy performance cannot fully demonstrate the appeal of the presented process. To obtain a better understanding of the strengths and limitations of the scenario, a full LCA of the SB-MED system needs to be presented with the analysis of the energy performance.

Comparative scenarios

The three conventional desalination scenarios that are compared with SB-MED are (1) a conventional MED using the combustion of natural gas to supply heat; (2) a conventional one-pass RO desalination system; and (3) a one-pass RO system with an integrated turbine to recover energy from the brine under pressure (referred to here as ROR).

Conventional MED

The conventional MED process follows a more or less similar design to that of the MED part of the SB-MED process; see the layout in Figure 3B. The main difference is that the gas boiler of the conventional system is supplied with pure water in a closed loop, where the operating conditions are correspondingly defined to be compatible with the same scale of production as selected for the SB-MED process (see 3.1). Therefore, unlike in the case with the SB, the steam from the hot side of the first evaporator is returned to the boiler and is not extracted with the rest of the distilled water.

The conventional MED process was simulated using the ProSim software. The gas boiler steam flow and the seawater inlet flow were chosen to achieve the same annual productivity of tap water as that with the SB-MED process. Accordingly, the proposed MED was designed and sized to produce 10,000 m 3 of tap water per year. Because the conventional MED operates with fossil fuel, two stops of 48 h per year were included for maintenance, resulting in an estimate of the necessary distillate flow of 1,154 kg h -1 for this scenario. Details concerning the MED characteristics are given in Appendix 2.

RO without energy recovery

The considered RO system is illustrated in Figure 5-RO. It is composed of a pump that pressurizes the seawater and the RO modules, which split the seawater into two flows, i.e., into demineralized water and brine. The demineralized water is sent to post-treatment, as described for the distilled water in the SB-MED process, and the brine is sent back to the sea. The pressure level depends on the number of modules, their organization (in series and/or in parallel), their characteristics, the production objective, and the recovery rate. The annual production objective was set to 10,000 m 3 of tap water.

To determine the number of modules and the required pressure levels, the CSMPRO 6 commercial software was used [START_REF]CSM[END_REF]. This software allows the characteristics of commercial modules to be considered. The global recovery rate was set to 42.5%. The energy demand necessary for the pressurizing seawater was calculated assuming the same efficiency for the pump as in the SB-MED process. In addition, compared with the SB-MED process, the necessary pretreatments are more important in the RO installation to guarantee the performance of the installation before performing RO. Details concerning the process modeling and pretreatment are given in Appendix 2.

RO with energy recovery (ROR)

To reduce the energy demands of RO systems, recent industrial facilities use recovery devices to recapture part of the energy from the brine under pressure. To provide a fair energy-wise comparison, this scenario was also considered in our study. The installation of an ROR system is similar to that of the RO system; however, a turbine is added to the brine outlet to generate electricity (Figure 5-ROR). The produced electricity compensates for part of the electricity consumption needed for the seawater pressurization. The production of electricity can be estimated from the brine and pressure flow rates. The efficiencies of the turbine and generator energy conversions were taken from the literature.

LCA: Goal and scope

In the following, the LCA application to the desalination system is described according to the four steps of the methodology: (1) defining the goal and scope of the LCA study, (2) building an inventory of all the materials and energy flows, (3) calculating the associated impacts using life cycle impact methods, and (4) interpreting the results and making recommendations for improvements.

In this study, the objective of the LCA is to evaluate the potential performance gain, from an environmental point of view, of the proposed SB-MED process with respect to conventional desalination processes. LCA is applied to the reference case presented in Section 2.2 for the proposed process, as well as the three conventional desalination processes presented in Section 2.3.1. The functional unit is the production of 1 m 3 of tap water by a small-scale desalination system over a period of 40 years on a Mediterranean island (Corsica). The production capacity is 10,000 m 3 of tap water per year. A cradle-to-gate boundary is adopted, considering all processes from raw resource extraction to the final product, i.e., tap water. The foreground system encompasses the entire process from seawater pumping to storing the tap water in a tank ready for use. LCA was performed using the Umberto software and the ecoinvent 3.7 database, employing the default allocation model (APOS).

Life cycle inventory

The inventory for the foreground process includes the material and energy consumption for the desalination process operation from seawater to the final tap water, as well as materials used for the equipment and infrastructure.

The material and energy consumptions for the process operation were calculated based on the modeling approaches described in Section 2.2 for the SB-MED process and in Section 2.3.1 for the three conventional processes, with related information concerning the referenced literature and other details given in Appendices 1 and 2.

Except for the beam-down system associated with the SB-MED scenario, it was assumed that all items were placed inside a building, the construction of which needs to be considered. The materials used for construction, the equipment, and the space required for the SB were estimated based on recommendations and data from the literature [21], [START_REF] Voutchkov | Desalination Engineering: Planning and Design[END_REF] and on the models presented in Sections 2.2 and 2.3.1 and in Appendices 1 and 2.

The inventory for the background processes (e.g., material and chemical production, energy production, transportation, and waste treatment) were taken from the ecoinvent database [START_REF]ecoinvent[END_REF].

Regarding the electricity used, the reference mix was set to the Italian electricity mix because of its similarity with the Corsican mix (not present in the database). The process system for LCA, namely the background and foreground processes and their connections and exchanges with the environment, is illustrated in Figure 6 for the SB-MED scenario.

Life cycle impact assessment

The environmental impacts were calculated using the ReCiPe method with the endpoint indicators. This method calculates 17 categories of endpoint impacts, assessing the damages with respect to three areas of protection, i.e., ecosystem quality, human health, and resource depletion. In addition, because it is a major issue of topical interest, the climate change impact was calculated using the IPCC 2013 method.

3 Results and Discussion

Calculated productivity and characteristics of the SB-MED system in comparison with standalone SB

An annual production of 10,000 m 3 of tap water (5,303 kg h -1 ) with a solar resource of 1,885 kWh m -2 yr -1 is considered, corresponding to the demands of 228 persons, assuming a consumption of 120 L day -1 per capita.

The coupled SB-MED model, associated with the input parameters (the available solar energy resources and the required tap water production) and all hypotheses presented in Section 2, allows estimations of the heat and material flows for the entire desalination process, as well as the capacity of the required installations (i.e., the beam-down system, SB, and MED).

Size and potential optimization of the solar field

Concerning the beam-down system, to ensure the production required for the reference case, 363,414 W of energy needs to be concentrated at the focal point when the DNI is equal to 1,000 W m -2 . These figures combined with Equation (1) allow an estimation of the required dimensions of the solar concentrator needed to achieve the production goal. The principal characteristics of the beamdown system calculated for this reference case are given in Table 3. For the reference case, the first reflection surface needs to have an area of 625 m 2 and the height of the reflector tower needs to be equal to 20 m. These dimensions appear to be realistic for a small-scale installation. Indeed, these characteristics are slightly larger than those of the experimental beam-down system presented in the literature [21], [START_REF] Kodama | Flux Measurement of a New Beam-down Solar Concentrating System in Miyazaki for Demonstration of Thermochemical Water Splitting Reactors -ScienceDirect[END_REF] but smaller than those mentioned in existing industrial projects [START_REF] Bcp | BCP solar technology[END_REF], [START_REF] Group | Industrila Solar beam down[END_REF]. Note, however, that the heliostat field geometry is not optimized. Moreover, the mean reflectivity considered for the mirrors is very conservative and it is reasonable to consider that an optimized concentrator with a high-performant and well-maintained material could result in a significant reduction in the concentrator size for the same final concentrated power.

Dimension and materials selected for the solar boiler

As explained in Section 2, the SB is the main novel feature of the proposed system. The retained geometric characteristics are presented in Table 3. With this geometry, the model resolution (presented in Section 2.2.2) permits an estimate of the mean expected receiver temperature of approximately 520°C, with a corresponding surface heat transfer of 9.6 W cm -2 . This high temperature required for film-boiling operation is expected to allow seawater boiling in the SB at atmospheric pressure without salt crust formation. The receiver dimensions were chosen to maintain a sufficient temperature to avoid the collapse of the vapor film when the DNI is reduced (i.e., to as low as 500 W m -2 ). With the present design, the temperature of the receiver for a DNI of 500 W m -2 is expected to be around 320°C. The construction material, Steel 304L, was chosen based on previously obtained experimental results [20] because of its resistance to high temperatures (having a fusion temperature of 1420°C). The choice of a metallic receiver with high conductivity allows the temperature difference between the upper and lower sides of the receiver to be limited. The mass flow rate in the SB is equal to 699.2 kg h -1 at 67°C. At the SB outlet, the steam leaves with a flow rate of 454.5 kg h -1 and the rest of the seawater leaves as brine, both flows being at the equilibrium temperature, i.e., 100.86°C, according to the binary mixture model for seawater used in this study.

Integration of the MED part

Concerning the MED part of the system, the temperature and pressure simulation results are presented in Figure 7 for each stage. In addition, Table 4 lists the intermediary mass flows for each of the 14 stages.

It can be seen that the pressure needs to be maintained between 0.290 bars and 0.046 bars for the different stages. This pressure variation permits boiling to occur between 70°C and 32°C; this agrees with data found in the literature [START_REF] Palenzuela | Concentrating Solar Power and Desalination Plants: Engineering and Economics of Coupling Multi-Effect Distillation and Solar Plants[END_REF], [START_REF] Talebbeydokhti | Analysis and optimization of LT-MED system powered by an innovative CSP plant[END_REF]. Table 4: Input-output flow rates in the MED part of the SB-MED system.

Stage Steam inlet

Extracted vapor flow for preheating

Seawater inlet Steam outlet [kg h -1 ] [kg h -1 ] [kg h -1 ] [kg h -1 ]

Comparison of SB-MED with SB in standalone

Before considering the performance of the SB-MED system and comparing it with conventional desalination technologies, we consider a standalone SB, without recovery of the heat of the steam in an MED. In a standalone SB, all the steam produced is condensed. Part of the condensation energy is used to preheat the input water, and the rest is evacuated with the cooling seawater. Heat and mass flows are presented in Table 5 to allow a comparison between standalone SB and SB-MED. It is clear that, for an equivalent flow rate of 5,303 kg h -1 of distilled water, the required energy transmitted to the water by standalone SB is 10 times higher than that by SB-MED. This implies a 10 times larger solar concentrator installation. The associated material requirements, land occupied, and electrical consumption for the heliostats will therefore be significantly higher. Moreover, in the case of standalone SB, the global flow rate of the seawater required, in the SB and for cooling, is also much larger: 8,158.46 kg h -1 for standalone SB versus 699.20 kg h -1 for SB-MED. This significant difference implies greater requirements for pumping and pretreatment. Considering these points, standalone SB is likely not competitive with either conventional technologies or an SB-MED system.

Even from an environmental point of view, even though solar energy has a low impact, the enormous differences in the energy performances between standalone SB and SB-MED or conventional technologies will imply a much greater impact in the first case. For this reason, only the SB integrated with a MED system is investigated herein and is further compared with conventional desalination technologies. This integration is fundamental to optimize operating and structural parameters in order to be competitive against conventional desalination technologies.

Energy performance of the SB-MED process

Here, we analyze the three principal components: the solar concentrator, the SB, and the MED.

The optical efficiency of the solar concentrator is defined by the ratio of the concentrated solar energy arriving on the receiver versus the maximal solar energy available at the first reflector. This efficiency is based on the literature and is fixed at 58.1%. The concentrated solar energy required, 363,414 W, at this optical efficiency implies a large field of heliostats, 629 m 2 for the first reflection mirror. Some improvements can be expected concerning this component that should permit the concentrator size to be reduced at an equivalent productivity.

The SB efficiency can be determined as the ratio of the heat transmitted to the seawater versus the concentrated energy arriving at the receiver. Despite the high temperature of the receiver, the conical shape permits a large part of the radiative losses to be trapped. The chosen design leads to a conversion efficiency of 83.7%, which can be compared with that of conventional boilers (from 95% for a gas boiler to 88%-92% for a coal boiler [START_REF] Esa | Steam Generation from Biomass[END_REF]). Moreover, note that, even if the thermal performance of the SB is slightly smaller, the incoming energy is free and has no environmental impact. In addition, optimization in the design (such as the use of other materials with better characteristics) could increase the overall performance of the SB. The SB is in its early stage of development, significant progress on its performance can be expected in the future. An optimization of its design (including the choice of the material) could bring a significant improvement of the steam production process.Finally, the performance of the MED system should not be defined purely by the energy efficiency because the final product is not energy but water. The gain output ratio (GOR) is conventionally used to evaluate the performance of such a system and is defined as the ratio of the net distilled flow rate versus the first stage steam flow rate. For the present system, the GOR is equal to 11.7; this value can be compared with the ideal case where the quantity of the generated vapor at each stage is equal to the entering quantity of vapor, in which case the maximal GOR is 14.

To place the SB-MED process within the field of desalination technologies, a first comparison with the conventional processes presented in Section 2.3.1 based on the energy consumption defined by the ratio of the consumed energy versus the quantity of distilled water is proposed. Because thermal and electrical energy cannot be directly compared, the electrical efficiency and thermal consumption of the systems will be presented separately.

The results are presented in Table 6. Note that the results obtained for the conventional desalination scenarios agree with data found in the literature. Indeed, for RO, the usual values of the electricity consumption range from 2 kWh m -3 to 6 kWh m -3 [START_REF] Raluy | Life cycle assessment of desalination technologies integrated with renewable energies[END_REF], [START_REF] Qasim | Reverse osmosis desalination: A state-of-the-art review[END_REF]. Regarding MED technology, the heat consumption is generally considered to be between 40 kWh m -3 and 110 kWh m -3 and the electricity consumption is generally between 1.5 kWh m -3 and 2.5 kWh m -3 [START_REF] Trieb | Aqua-CSP Concentrating Solar Power for Seawater Desalination[END_REF], [START_REF] Al-Karaghouli | Energy consumption and water production cost of conventional and renewable-energy-powered desalination processes[END_REF]. In terms of heat, the needs of conventional MED are lower than the amount required by the solar approach; however, the results are very close. This conclusion needs to be tempered by the fundamental difference between the types of energy used: solar, shown in red, versus fossil fuel. Indeed, the efficiency of the SB can be defined by the ratio of heat transmitted to the seawater versus that of the concentrated heat received. This efficiency is equal to 86% and can be compared with the conventional gas boiler efficiency, which is usually close to 95%. Moreover, because of the medium efficiency of the solar field (58%), a large reflector surface is required. However, it is important to emphasize that the environmental and economic cost of the use of solar energy comes only from the construction of the collector and the receiver, unlike the use of fossil energy whose impact and cost are linked to their construction as well as to fuel consumption.

The results presented in Table 6 show the real benefit of the SB-MED solution in terms of electricity consumption. Indeed, even if the SB-MED electricity consumption is slightly higher (13.7%) than that of conventional MED, it is 60.8% lower than that of the ROR scenario, which represents the mostused technology today. The increase in consumption compared with MED can be explained by the heliostat field consumption necessary for solar tracking. Focusing on the electricity in the SB-MED system, the principal consumption points are the following: pumping the seawater from the ocean (42.4%), pretreatment (28.8%), and extraction of the non-condensable gases (17.7%); the rest of the consumption is used for solar tracking and circulation of the water in the SB-MED system.

3.4 Environmental performance of the SB-MED system and comparison with conventional desalination technologies

Life cycle inventory results

The inventory results for the four studied systems (the reference SB-MED system and the three conventional desalination systems) are presented in Table 7. The results are expressed with respect to the functional unit, i.e., 1 m 3 of tap water produced. More details concerning the inventory results are given in Appendix 3.

Regarding infrastructure and equipment, the SB-MED process requires more material than the other scenarios; this is primarily due to the oversizing of the MED to compensate for the lower number of annual operating hours and the construction of the heliostats. Indeed, the use of solar energy implies working with higher flow rates for a shorter period to achieve equivalent annual productivity to that of conventional technologies, which operate nearly all year round. In addition, the RO and ROR scenarios require membrane modules for the RO process.

The quantities of seawater pumped for the SB-MED and MED systems are greater than those pumped for the RO and ROR systems, that is, 5.15 m 3 and 5.11 m 3 per 1 m 3 of tap water for the SB-MED and MED processes, respectively, versus 2.33 m 3 per 1 m 3 of tap water for the membrane processes. The additional seawater flow in the SB-MED and MED systems is necessary for the cooling of the final stage of the MED. Similarly, the brine outlets differ in the two situations (brine is rejected to the sea). For the thermal systems, it is possible to mix the brine with the cooling water, which leads to a smaller salinity difference between the brine outlet and the seawater compared with the case in membrane technologies. The discharged effluents for the SB-MED and MED systems also carry heat because their temperatures are higher than the seawater temperature. Salt and heat returning into the sea have no global impact but could have local impacts on restricted areas [START_REF] Petersen | Impact of brine and antiscalants on reef-building corals in the Gulf of Aqaba -Potential effects from desalination plants[END_REF], [START_REF] Jones | The state of desalination and brine production: A global outlook -ScienceDirect[END_REF]. Because of the current lack of assessment models, it is not possible to properly quantify these impacts at the moment.

Regarding the end-of-life processes, materials such as concrete or steel were not considered because they can easily be recycled. Only waste destined for disposal, such as membrane modules and cartridge filters, were considered in the landfill disposal. These materials are a mixture of plastic and polypropylene waste. In addition, the pretreatment step produces sludge, which needs to be further treated. The larger quantity of seawater pretreated in thermal desalination systems implies the production of 2.2 times more sludge than in membrane systems.

Environmental impact results

The endpoint impact results estimated using the ReCiPe (Endpoint (H,A)) method are presented in Figure 8 for the production of 1 m 3 tap water by each of the four scenarios.

The total impact of SB-MED is 6.4 times lower than that of conventional MED. Because of the similarities of the MED processes in the two scenarios, the categories "end of life," "electricity," and "chemicals" have roughly the same impact in both cases. The impact of "building and infrastructure" is considerably higher in the SB-MED scenario, 3.3 times larger than that in the conventional MED scenario. This difference is explained by the construction of the large solar installation for the SB and because of the oversizing of the MED necessary to compensate for the discontinuity in the solar energy received. However, this is more than compensated for by avoiding the impact associated with burning fossil fuels. Indeed, 88.3% of the impact of conventional MED is caused by the generation of heat from the combustion of natural gas.

The total impact of SB-MED is slightly lower than those of the two RO scenarios. Similar to the abovediscussed case, the infrastructure of the SB and the oversizing of the MED installation lead to a 2.6 times higher impact of the SB-MED system than those of the RO systems. The end of life also has a greater impact, 0.09 for SB-MED versus 0.05 for RO. This difference is due to the large quantity of sludge from the water treatment, that is, the water necessary for cooling the final MED stage (as explained in Section 3.3.1). The main advantage of the SB in terms of impact comes from the reduction in the electricity consumption. Indeed, a 0.20 and 0.12 point of impact difference are noted relative to RO and ROR, respectively. Figure 9 details the endpoint impact results for the different ReCiPe impact categories. For all scenarios, the greatest impact is related to the use of fossil fuels. Indeed, "climate change, ecosystems," "climate change, human health," and "fossil depletion" are linked to the extraction of fossil fuels and the emissions of greenhouse gases during their combustion. This link is direct in the case of the MED with the gas burner or indirect in all cases with the production of electricity and materials.

Regarding the other impacts, the land occupation" impact of the SB-MED system is greater than those of the other scenarios. This impact is due to the large field of heliostats required for the solar concentration. Note that parallel use of the land under the heliostats field may be possible, for example, for forage or other vegetation growth. This possibility has not been considered in this study but can significantly reduce this impact. The metal required for the equipment also has a large impact on the "metal depletion" category. Climate change was identified as the main contributor to the ReCiPe endpoint impacts. Figure 10 shows the complementary climate change impact calculated via the IPCC2013 method using GWP100 (the global warming potential at 100 years) and expressed in kg CO2-eq. Focusing on this point, the appeal of SB-MED is even greater and the difference between SB-MED and ROR is more significant, with 20.6% kg CO2-eq less emissions for the reference case. Regarding the impact contributions of the different processes, the proportions remain roughly the same. The energy contribution to the impact is definitively lower in the case of SB-MED than in the other scenarios.

As observed above, an important aspect to be considered is the electricity mix used: depending on the electricity mix, the ranking of the scenarios could change. As presented in Section 2.3, the calculation was performed with an Italian electricity mix used as the reference. Electricity is one of the most important sources of impact, especially for the RO scenarios. Accordingly, the use of an electricity mix that emits more CO2, which is the case in many countries using desalination (e.g., Kuwait, Saudi Arabia, or Australia) [START_REF]ecoinvent[END_REF], will degrade the environmental performance of the system. Moreover, in case of SB-MED, the location will have important consequences on the share of impacts between the infrastructure and the functioning. Indeed, with better solar power, given the same installation, the tap water productivity will be greater. Figure 11 shows the climate change impact calculated with IPCC2013 using three different electricity mixes: the reference (e.g., Italy), a lowcarbon mix (e.g., France), and a high-carbon mix (e.g., Australia). Because SB-MED consumes less electricity, the impact of the electrical mix is less important for SB-MED. Switching from an Italian mix to an Australian mix increases the CO2-equivalent emission by 35.2%, while using a French mix decreases it by 26.9%. The same modification increases the emission for the ROR scenario by 71.4% for the Australian mix and decreases it by 54.7% for the French mix. In addition, it appears that, in the case of a low-carbon electricity mix, the ROR solution becomes even more advantageous in terms of its climate impact than the SB-MED solution. This analysis of the electricity-mix impact considers only the climate change impact; other considerations (e.g., other environmental impacts and technological risks) are beyond the scope of this analysis.

Note that the SB-MED system is a new concept and complementary work needs to be done to prove its feasibility at the industrial level. Despite there being much room for improvement in this technology, the current results indicate that this process could be environmentally competitive with the currently most-advanced RO desalination process.

Regarding the main aspects that need to be investigated, the design of the collector system could be improved. Construction has a significant impact, and improving the performance of the solar collector or reducing the material consumption for an identical technical performance could greatly improve the environmental performance of the system. Furthermore, the scale-up of the SB needs to be investigated at larger scales and the scale effect on the overall performance needs to be evaluated.

Concerning the design of the MED part, the chosen configuration with 14 stages enables a performance that is representative of what could be observed at an industrial scale but is not necessarily the best performance that can be obtained. Different design improvements (such as increasing the number of stages) may lead to an increase in the productivity of the system.

The substantial difference in the environmental impact between conventional MED and SB-MED suggests that the addition of an SB to an already existing MED installation is a mitigation solution worth exploring. Indeed, many countries that use desalination have available land and a strong solar potential. In this context, SBs could be very effective and relatively easy to connect to already existing thermal desalination facilities. Considering the significant impact of burning fossil fuels in a conventional MED facility (15.43 kg CO 2-eq per m 3 of tap water in the considered example), replacing at least part of this energy source with concentrated solar energy could save enough emissions to offset the impact of the construction of the solar installation (approximately 0.51 kg CO2-eq per m 3 of tap water in the considered example). This could, in time and with reasonable investment, significantly reduce the fuel consumption and associated impact of thermal desalination plants already in operation.

Conclusions

In this study, an innovative process coupling a beam-down concentrator with a solar boiler and multiple-effect distillation (SB-MED) was proposed, allowing an alternative approach in the field of water desalination. A theoretical model was developed to describe this new process "from sea and sun to tap water". Applied to a reference case, the model allowed to investigate the feasibility of tap water production for a small community, i.e., an annual production of 10,000 m 3 . The facility was sized in terms of equipment, materials, and energy consumption.

The energy consumption of this process was estimated to be 1.58 kWh of electricity and 117.7 kWh of direct solar energy per 1 m 3 of tap water produced. An area of 3,485 m 2 is needed to supply the target annual production, this area primarily being occupied by the concentrating solar facility.

The appeal of coupling SB and MED was demonstrated. Indeed, if the SB uses low-impact solar energy resources, its standalone use suffers from a lack of efficiency compared with the SB-MED system. The required energy for boiling in a standalone SB system is 10 times higher than that in an SB-MED system. This implies a 10 times larger solar concentrator installation in the case of standalone SB. The SB-MED system is therefore particularly competitive in terms of both energy performance and environmental impact. The energy reuse strategy enabled by this solution gives results equivalent to the best RO technologies in the field. These results were obtained for the reference case, and further optimizations could improve them.

A significant part of the impact in the proposed solution is caused by the construction of the equipment. The integration of heat storage could be beneficial in terms of the environmental performance by allowing more stable operation and a reduction in the dimensions of the MED, pretreatment, and post-treatment installations, with an associated reduction in their impacts.

This comparison of the SB-MED system with conventional desalination technologies demonstrated that, at equivalent productivity, the SB-MED system requires less electricity than the best-case RO scenario. Compared with conventional MED, a reasonable increase in the electricity consumption permits the use of fossil fuels to be avoided. In addition, considering the low level of modifications to the MED part of the SB-MED system compared with conventional MED, consideration should be given to installing SBs as plug-in modules in already operational MEDs. This addition could significantly reduce the impacts of existing desalination plants. The overall endpoint impact of SB-MED, estimated via the ReCiPe method, was significantly lower than that of MED and was in the range of those of the RO processes. The same trend was observed for the climate change impact. The presented results emphasize the potential interest of this new process, which could be an alternative solution to RO when solar energy is abundant and the electricity mix is highly CO 2 emitting.

In perspective, pilot experiments and optimization of the process design are needed together with an iterative, environmental and economic assessment, including the regional specificities in terms of solar energy availability and energy storage.

First, a solar

  collector concentrates solar energy in a downward vertical flow. The concentrator is based on the beam-down concept, shown in Figure2A. The beam-down apparatus consists of a field of heliostats (Figure2A-1) that reflect the solar direct normal irradiation (DNI) at the top of a structure supporting a secondary reflector (Figure2A-2). The secondary reflector redirects the collected solar energy toward the ground to the focal point (Figure2A-3).

Figure 2 :

 2 Figure 2: Illustration of the SB showing (A) the beam-down concentrator, (B) the receiver, and (C) the tank.

Figure 5 :

 5 Figure 5: Layout of the reverse osmosis facilities in the cases of RO (without energy recovery; top) and ROR (with energy recovery; bottom).

Figure 6 :

 6 Figure 6: Life cycle assessment (LCA) process system diagram for the SB-MED scenario.

Figure 7 :

 7 Figure 7: (A) Pressure and (B) temperature levels in the different stages of the MED part of the SB-MED system.

Figure 8 :

 8 Figure 8: ReCiPe endpoint impact results for the four desalination scenarios.

Figure 9 :

 9 Figure 9: Impact results for SB-MED in comparison with the conventional scenarios.

Figure 10 :

 10 Figure 10: Climate change impact results according to the IPCC2013 (GWP100) method.

Figure 11 :

 11 Figure 11: Climate change impact results for SB-MED and ROR for the Corsican (Italian, IT), French (FR) and Australian (AU) electricity mixes.

Table 1 :

 1 Various estimated efficiency factors[START_REF] N'tsoukpoe | Integrated design and construction of a micro-central tower power plant[END_REF].

	Efficiency	Reflectivity	Cosine effect	Blocking and shadow effect	Aim error
	Value	0.85	0.90	0.95	0.97
	The method proposed by Lorfing et al. [20] was used to model the receiver and the tank of the
	concentrated SB. Concerning the modeling of the concentrated SB, the following energy balance
	equation is considered around the receiver:

Table 2 :

 2

	Principal characteristics of the SB-MED calculation
	SB
	Operating pressure	101,325 Pa
	Vaporization rate	0.65
	MED
	Number of stages	14
	Top-stage temperature	70 °C
	Last-stage temperature	35 °C
	Temperature change (ΔT) between	2.5 °C
	each stage
	Maximal discharge temperature	Tsw + 10 °C
	Total distillate water flow	5,303 kg h -1
	Inlet seawater
	Salinity	0.039 kgNaCl kgsw -1
	Temperature	20 °C

Operation conditions at the inlet for the simulation of the solar boiler (SB)-multiple-effect distillation (MED) system.

Table 3 :

 3 Design and principal characteristics of the beam-down system and the receiver facility.

	Item	Value	Unit
	Beam-down system
	Number of heliostats	74
	Reflective area per heliostat	8.5 m 2
	Primary reflective area	629 m 2
	Occupied land	3,350 m 2
	Height of the reflector	20 m
	Receiver (specific design calculated for this study)
	Diameter	1.02 m
	Thickness	0.08 m
	Cone half-angle	15 °
	Material	Steel 304L

Table 5 :

 5 Heat and mass flows in an SB-MED system and an SB-standalone system for comparison.

	Unit	SB-MED	SB-standalone
		system	system

Table 6 :

 6 Heat and electricity consumption of the four compared desalination systems, where RO indicates reverse osmosis and ROR indicates reverse osmosis with energy recovery.

	Scenarios	Consumption [kWh m -3 ] Electricity Heat
	SB-MED	1.39	58.9 (solar)
	MED	1.58	58.4 (fossil)
	RO	5.37	-
	ROR	4.03	-

Table 7 :

 7 Inventory and ecoinvent unit processes for the four desalination scenarios.

			Input		Quantity per m 3 of produced water
	Category	Material	/							Unit	ecoinvent process
			output	SB-MED	MED	RO	ROR
		Building construction	In	3.38 × 10 -4	2.99 × 10 -4	3.18 × 10 -4	3.18 × 10 -4 m 2	market for building, hall, steel construction [GLO]
		Charcoal for filtration	In	-		-		1.70 × 10 -3	1.70 × 10 -3 kg	market for charcoal [GLO]
		Concrete	In	18.60 × 10 -5	5.75 × 10 -5	3.68 × 10 -5	3.68 × 10 -5	m 3	unreinforced concrete production, with cement CEM II/B [RoW]
		Land occupation	In	34.85 × 10 -2	1.20 × 10 -2	1.27 × 10 -2	1.27 × 10 -2 m 2 year N/A
	Equipment and building	Heliostat mirror Membrane module Motor Pipe Cartridge filter Pump	In In In In In In	1.69 × 10 -2 -939.75 × 10 -6 11.67 × 10 -3 -2.73 × 10 -4	--5.00 × 10 -6 7.00 × 10 -3 -0.68 × 10 -4	-1.25 × 10 -3 5.00 × 10 -6 5.37 × 10 -3 1.78 × 10 -4 9.50 × 10 -4	-1.25 × 10 -3 5.00 × 10 -6 5.37 × 10 -3 m kg m 2 kg 1.78 × 10 -4 kg 9.50 × 10 -4 unit	flat glass production, coated [RER] seawater reverse osmosis module production, 8-inch spiral wound, enhanced [GLO] market for electric motor, for electric scooter [GLO] polyethylene pipe production, corrugated, DN 75 [RER] polypropylene production, granulate [RER] market for pump, 40W [GLO]
		Pump station	In	84.81 × 10 -8 18.29 × 10 -8	9.02 × 10 -8	9.02 × 10 -8 unit	pump station construction [RoW]
		Sand for filtration	In	-		-		1.02 × 10 -3	1.02 × 10 -3 kg	market for sand [GLO]
		Steel	In	1.36 × 10 -1 0.04 × 10 -1	0.03 × 10 -1	0.04 × 10 -1 kg	hot rolling, steel [RER]
		Stainless Steel	In	19.64 × 10 -3	1.08 × 10 -3	-	-kg	steel production, chromium steel 18/8, hot rolled [RER]
		Carbon dioxide	In	4.40 × 10 -2	4.40 × 10 -2	4.40 × 10 -2	4.40 × 10 -2 kg	carbon dioxide production, liquid [RER]
		Scale inhibitors	In	5.65 × 10 -3	5.60 × 10 -3	2.55 × 10 -3	2.55 × 10 -3 kg	polycarboxylates production, 40% active substance [RER]
		Citric acid	In	-		-		5.61 × 10 -4	5.61 × 10 -4 kg	citric acid production [RER]
	Chemical	Disinfectant Hydrogen peroxide Coagulant	In In In	3.57 × 10 -3 -5.65 × 10 -2 5.623 × 10 -2 2.34 × 10 -3 -	2.15 × 10 -3 2.80 × 10 -5 2.56 × 10 -2	2.15 × 10 -3 2.80 × 10 -5 2.56 × 10 -2	kg kg kg	sodium hypochlorite production, product in 15% solution state [RER] hydrogen peroxide production, product in 50% solution state [RER] market for iron(III) chloride, without water, in 14% iron solution state [GLO]
		Minerals	In	1 × 10 -1	1 × 10 -1	1 × 10 -1	1 × 10 -1 kg	lime production, milled, packed [RoW]
		Dechloration products	In	-		-		4.62 × 10 -4	4.62 × 10 -4 kg	chlor-alkali electrolysis, mercury cell [RER]
		Water for cleaning	In	-		-		2.74 × 10 -2	2.74 × 10 -2	kg	tap water production, underground water without treatment [Europe without Switzerland]
	Electricity	In		1.58		1.39	5.37	4.03 kWh	market for electricity, low voltage [IT]
		Seawater (inlet)	In		5.15		5.11	2.33	2.33 m 3	N/A
		Solar energy	In	117.89	-		-	-	kWh	N/A
		Heat	In	-			58.36	-	-	kWh	heat production, natural gas, at boiler modulating <100 kW [Europe without Switzerland]
		Seawater (outlet)	Out		4.15		4.11	1.33	1.33 m 3	N/A
		Chloride	Out		21.47		21.47	22.32	22.32 kg	N/A
		Sodium ions	Out		11.94		11.94	12.41	12.41 kg	N/A
		Sulfate	Out		3.01		3.01	3.13	3.13 kg	N/A
	Process	Magnesium Calcium ions	Out Out	1.43 4.56 × 10 -1	1.43 4.56 × 10 -1	1.49 4.74 × 10 -1	1.49 kg 4.74 × 10 -1 kg	N/A N/A
		Potassium ions	Out	4.29 × 10 -1	4.29 × 10 -1	4.46 × 10 -1	4.46 × 10 -1 kg	N/A
		Hydrogen carbonate	Out	1.17 × 10 -1	1.17 × 10 -1	1.22 × 10 -1	1.22 × 10 -1 kg	N/A
		Bromide	Out	7.41 × 10 -2	7.41 × 10 -2	7.70 × 10 -2	7.70 × 10 -2 kg	N/A
		Strontium	Out	7.80 × 10 -3	7.80 × 10 -3	8.11 × 10 -3	8.11 × 10 -3 kg	N/A
		Boron	Out	5.07 × 10 -3	5.07 × 10 -3	5.27 × 10 -3	5.27 × 10 -3 kg	N/A
		Fluoride	Out	1.56 × 10 -3	1.56 × 10 -3	1.62 × 10 -3	1.62 × 10 -3 kg	N/A
		Heat waste	Out		41.42		41.42	-	-	kWh	N/A
	End of life	Membrane waste Sludge Waste from caterbridge	Out Out Out	--	28.26	--	28.15	1.73 × 10 -3 12.82 1.78 × 10 -4	1.73 × 10 -3 12.82 kg kg 1.78 × 10 -4 kg	treatment of waste plastic, mixture, sanitary landfill [Europe without Switzerland] drying, sewage sludge [RoW] treatment of waste polypropylene, sanitary landfill [RoW]

Acknowledgments

This research was funded by INSA (Institut National des Sciences Appliquées) Toulouse, and CNRS (Centre National de la Recherche Scientifique), France. We thank Martha Evonuk, PhD, from Evonuk Scientific Editing (http://evonukscientificediting.com) for editing a draft of this manuscript.


According to representative surveys, the level of unionization in the 1970s would not have been 20%, but almost 40%, which is similar to that of our European neighbors.

Our time series is consistent with official estimates from the 1990s onwards. This means that the extent of deunionization in the 1980s may also have been significantly underestimated.

We also provide an estimate of the level of unionization between 1949 and 1969. Here again, our estimates are above those currently in circulation.

Based on representative surveys of the French population, including polls and international surveys, we estimate that the level of unionization was underestimated until the late 1970s.

Introduction

According to DARES (Direction de l'Animation de la Recherche, des Études et des Statistiques), the statistical service of the Ministry of Labor, France has had one of the lowest levels of unionization in Europe since the 1960s [START_REF] Pignoni | Which side are you on? A historical perspective on union membership composition in four European countries[END_REF]. According to these estimates, France is an exception, since it has had few unionized workers despite numerous social struggles in the 1970s, which are a sign of strong union power.

How do we measure the level of unionization, defined as the proportion of employees who are unionized? In most developed countries, official estimates are based on self-reporting by workers in national surveys. 1 Thus, a worker is considered to be a member of a trade union if he or she declares to be so when questioned in a survey. Since 1996, France has also used this approach, without revising the series prior to 1996. Before this date, the level of unionization in France is estimated by relating the amounts of union dues paid to the main unions to the dues payable by each member. In other words, only workers who pay their dues regularly are considered to be truly unionized. The choice between these two methods, although seemingly trivial, can lead to significant differences in the estimate of the number of unionized workers and thus in the calculation of the level of unionization. These differences are particularly apparent for France when we compare two historical series: the one proposed by DARES, based on union dues data until 1996, and the one we estimate from polling and survey data that have not been used until now (Figure 1). The estimates of the level of unionization based on surveys are clearly higher than the DARES series in the 1970s, but then converge from the end of the 1980s.

In this policy brief, we propose a new historical series of the level of unionization of employees in France, based on polls and representative surveys of the French population from 1970 to 2018 as well as a retropolation for 1949 to 1968. This new series has the advantage of being based on a uniform definition of the notion of a unionized worker over the entire period. For this reason, and others that we will discuss below, we believe that this series provides a better approximation of the level of unionization than the currently available series. 2 This policy brief details the possible causes of discrepancies between levels 1 Since 1973, the Bureau of Labor Statistics in the United States has used the Current Population Survey (CPS). The question used is: "In this job, are you a member of a trade union or an employee association similar to a trade union?" In Germany, too, surveys have been used since 1980, and in the UK since 1989.

2 Other series measuring unionization in France coexist with the DARES series: the Institutional Characteristics of Trade Unions, Wage Setting, State Intervention and Social Pacts (ICTWSS) project, hosted by the Organisation for Economic Co-operation and Development (OECD), and a new series produced by Andolfatto and Labbé (2021). Both of these series are also based on contributions from major unions and are very similar to the DARES series, although somewhat higher.

of union membership measured by representative surveys from the 1970s onward and those based on membership dues data provided by unions. Finally, we provide estimates for the 1950s and 1960s. 1958[START_REF]Unionization rate 1958[END_REF][START_REF]Unionization rate 1958[END_REF][START_REF]Unionization rate 1958[END_REF][START_REF]Unionization rate 1958[END_REF][START_REF]Unionization rate 1958[END_REF]2018 Dares Dares Author's estimation

Measuring union membership from dues data

Measuring CGT and CFDT membership

Until the 1980s, union members paid their dues each month by buying stamps to stick on their membership card (Figure 2). The number of members of a union can then be obtained by dividing the number of stamps sold in a given year by an estimate of the average number of stamps paid per year per member (Box 1). This is what [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF] does for the Confédération générale du travail (CGT) and the Confédération française démocratique du travail (CFDT), which are historically the two main unions in France. He assumes that the average annual number of stamps paid per member is constant and equal to 9. [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] and [START_REF] Andolfatto | Histoire des syndicats[END_REF] follow this choice, but have more recently settled on the assumption of 8 stamps [START_REF] Andolfatto | Un échec français : la démocratie sociale[END_REF]Andolfatto and Labbé, 2021).

However, there is little accurate and reliable information

The total number of stamps sold also includes those purchased by retired members. In theory, these should be subtracted to obtain the net unionization rate. Here, [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] and Pignoni (2016) take different approaches. [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] does not subtract anything. For his part, Pignoni (2016) makes a uniform subtraction of 13%, without justifying this figure as far as we know. This corresponds roughly to the proportion of retirees in the membership of the CGT, according to its statements (see [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF], p. 45). But Andolfatto and Labbé (2021) point out (p. 11) that retirees are supposed to buy only one stamp per quarter, so their share of stamps is smaller than their share of union members.

The proportion of stamps to be deducted is therefore certainly somewhere between Labbé's 0% and Pignoni's 13%. But here we come back to the same problem: we would need to know the average number of stamps paid by active workers on the one hand, and by retirees on the other, in order to establish an exact correction coefficient. We can only point out that our series (see Fig. 6) is clearly above Labbé's, even though he does not subtract any retirees, which suggests that the stamps paid by unionized retirees represented only a small proportion of the total.

Box 1 : Retired members' stamps Box 1 : Retired members' stamps

Figure 2: A 1949 CGT member's union card with seven stamps on the average number of stamps per member. In the 1950s, the CGT counted the number of annual cards sold, and found a number fluctuating between 7.0 and 8.5 stamps per card. [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF] suggests that the reason the CGT stopped publishing the information was to mask the decline in the number of stamps paid per member, as suggested by several calls to order issued by the CGT in the 1960s. [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF] quotes Le Peuple, the CGT newspaper, which gives averages "depending on the year [...] of 6, 7 or 8 monthly dues per year". 3 It thus seems that Bevort maintained the figure of 9 stamps in spite of the to which he had access, for the sake of homogenization. It seems clear that, for the CGT, the average number of stamps per member in the 1970s was well below 9.

From CGT and CFDT membership to unionization rate

In addition to the choice of average number of paid stamps per member, an additional step is needed to go from the membership of the CGT and CFDT to the total level of unionization. This involves measuring the relative importance of these unions compared to the others. According to a method introduced by Labbé (1995), we can extrapolate the unionization level by assuming that the share of a confederation in the total union membership is the same, at a given moment, as its vote share in workplace elections. This hypothesis is reasonable in principle, but [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] cannot test it directly.4

However, while the hypothesis of alignment between the relative importance of unions among members and the results of workplace elections is plausible a priori, one can also imagine several reasons for rejecting it. For example, it is possible that the extreme left-wing militancy typical of the post-1968 period in France, and the creation in 1968 of sections syndicales d'entreprises (unions at the level of the establishment which are not obliged to affiliate to a confederation), led to an increase in membership of small local unions which did not participate in workplace elections in the 1970s. More generally, the two main unions, the CGT and the CFDT, may have more resources and expertise to mobilize voters in workplace elections, which could lead to an under-representation of other unions in these elections compared to their relative importance among members.

In conclusion, while the assumptions necessary to move from membership data to unionization level are credible, they introduce an additional degree of uncertainty to that of the number of stamps. It is for these two reasons that we adopt a different method for estimating the unionization level. 1977,1978,1981,, 2017 opinion polls post-election surveys International Eurobarometer, 1970, 1971, 1975-1977, 1983, 1985, surveys European Value survey 1987, 1989-1992, 1994, 1996Public surveys EPCV, SRCV 1996-2004[START_REF]Unionization rate 1958[END_REF], 2010, 2013[START_REF] Pignoni | Which side are you on? A historical perspective on union membership composition in four European countries[END_REF] Measuring union membership from survey data

Our method exploits data from national and international surveys, and opinion and post-election polls, to estimate the unionization level for each survey-year pair. This approach uses the same type of data: representative surveys of the French population (Table 1); and a fortiori uses the same definition of unionization, which is the one used by DARES since 1996. Another advantage is that this measure of unionization is transparent. It uses the answer to a simple question: "Are you a member of a trade union?" Finally, this method does not require any extrapolation or arbitrary assumptions. The quality of the estimate of union membership depends entirely on the quality and reliability of the surveys.

We have several reasons to consider that our sources are reliable. First, although they are different in nature and collected by different organizations, they give consistent results. In particular, in the 1970s, they all lead to a considerable increase in the estimate of the unionization rate (Figure 3).

From 1990 onwards, we observe a convergence of our series with the official series. This date corresponds to the development of the automation of stamp payments, which generalizes the purchase of 12 stamps per year for each member. It should be noted that after 1996, our main source is the same as that of DARES: the EPCV survey (Enquête permanente sur les conditions de vie des ménages). However, DARES [START_REF] Pignoni | Which side are you on? A historical perspective on union membership composition in four European countries[END_REF], as well as the OECD, revised the unionization rate upward by 2.5 percentage points because the question about unionization in the EPCV is inserted into a more general question about participation in associations (parent-teacher associations, tenants' associations, etc.) which could lead some respondents to skip the question about union membership. Comparative work with other European countries is underway [START_REF] Batut | Which side are you on? A historical perspective on union membership composition in four European countries[END_REF]. It shows that surveys and polls in Italy, Germany, and Great Britain give results in line with the official series (Figure 6). This supports the use of surveys to estimate the unionization level in France.

The new estimates we propose challenge the idea that France is an exception in terms of unionization and instead point to a strong mobilization, comparable to other European countries, in the years following the May 1968 labor and student protests.

Moreover, according to our data, unionization rates fell by more than a factor of three over a decade during the 1980s. This is a much more rapid decline than previously estimated. However, a similar decline can be observed in the number of days not worked due to strikes: according to DARES (2021),5 it fluctuated around 4,000 days per year per 1,000 employees in employment between 1972 and 1977, and fell below 1,000 for the first time in 1985 (Figure 4). Interpretation: In 1976, there were 4,000 days lost per 1,000 employees in employment. In 2019, there were 161.

Reconstructing a historical series of the level of unionization

Explaining the differences between survey estimates and those of DARES

Our sources identify, in addition to union membership at the time of the survey, the name of the union to which the worker belongs. This allows us to compare our estimates of CGT and CFDT union membership with those estimated by [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF] and those obtained from membership figures reported by the unions themselves, and also compiled by [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF] for the two main unions: CGT and CFDT (Figure 5).

The surveys give a significantly higher rate of CGT unionization than [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF]. To find a series consistent with our observations -a "CGT+CFDT" unionization rate of 18-20% -we would have to assume an average annual number of stamps between 6 and 7, as opposed to the 8 or 9 used by [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] and [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF]. We therefore have good reason to believe that [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF] and [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] overestimate the average number stamps paid each year in 1970s. Moreover, our estimates are slightly higher than those calculated from the membership figures reported by the CGT itself, which indicates that the unions were probably not over-reporting their membership. The discrepancy with the declarations of the unions themselves can be explained by an indeterminacy inherent in the very definition of "union member": a former member who has not regained union membership in a new job, or a member who only pays dues very irregularly, may consider themselves to be union members and declare this in the surveys, without being considered [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF], from union data and from survey data

Note: The graph compares CGT and CFDT union membership rates according to CGT and CFDT figures, the estimates of [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] as such either by the method of [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF] or by their union.

This upward revision of about one-third for the combined CGT and CFDT membership in the 1970s is not sufficient to explain all of the discrepancy between our estimate of the unionization level and the official estimates at that time. To do this, we must also take into account the second stage in the construction of the official series, i.e. the transition from the CGT and CFDT figures to the total unionization rate thanks to the results of workplace elections. As we have already explained, we believe that the extrapolation of [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] may lead to an underestimation of the importance of the smallest unions, especially those not participating in workplace elections.

A new historical series of unionization levels

We propose a new historical series of employee unionization levels since 1970 (Figure 6). It is calculated by taking a five-year rolling average of all estimates from survey and polling data. However, we do not use the EPCV survey, which may underestimate the unionization rate because of the wording of the question.

We supplement this estimate with two proposals for estimating changes in the level of unionization between 1949 and 1968. Since this exercise requires a number of as-

Conclusion

The first contribution of this policy brief is methodological: we confirm that the use of surveys is preferable to more indirect extrapolation methods. As recently shown by [START_REF] Farber | Unions and inequality over the twentieth century: New evidence from survey data[END_REF] in the United States, the combination of opinion surveys, political polls and international surveys allows for a robust historical estimate of unionization. At the same time, our estimates of union membership in the CGT and CFDT are close to what the unions themselves report. This attests to the quality of the figures released by the unions during this period. The declarations of the unions are therefore not necessarily to be discarded and can, on the contrary, constitute a valuable source of information.

The second contribution is factual. On the comparative level, we question the idea of exceptionally low unionization in the early 1970s in France: in our view, the level of unionization in France in the 1970s was higher than in West Germany and close to that of Italy and the United Kingdom.

This changes the story that follows in the 1980s. Historically, the official series suggested a brutal deunionization in France, comparable in scale but more rapid than in other countries. In the United Kingdom, it took about 30 years, from 1980 to 2010, to halve the unionization level, compared with only about 10 years in France, from the late 1970s to the late 1980s, according to the existing series. According to our revised series, the fall was even more precipitous, with unionization dropping to less than a third of its original level in this period. This is consistent with the social, economic and institutional history that makes the 1980s a pivotal decade. Indeed, these years of brutal deunionization were those of the collapse of strike activity, as we have noted above, but they also witnessed, for example, the decline of the labor share in value added [START_REF] Cette | The Labor Share in the Long Term: A Decline?[END_REF], and the rise in the share of total income for the richest 10% [START_REF] Garbinti | Income inequality in France, 1900-2014: evidence from distributional national accounts (DINA)[END_REF].

  The Institut des politiques publiques (IPP) has been created by PSE and is developed through a scientific partnership between the Paris School of Economics (PSE) and the Groupe des écoles nationales d'économie et de statistique (GENES). The aim of the IPP is to promote quantitative analysis and evaluation of public policy using cutting edge research methods in economics.RecountingFrance's trade unions Is France characterized by a particularly low level of unionization compared to other European countries? This is what the comparative literature on trade unions suggests. In this policy brief, we question this idea and trace a different history of the evolution of the level of unionization in France. Current estimates are based on a double extrapolation of membership data from the two main unions -the Confédération générale du travail (CGT) and the Confédération française démocratique du travail (CFDT)and the results of workplace elections.

Figure 1 :

 1 Figure 1: Comparison of the unionization level in France estimated by the authors from survey data or by DARES from administrative data Note: The graph shows the distribution of unionization levels estimated from several surveys since the 1970s and compares them with the DARES time series. Interpretation: The graph shows the distribution of unionization levels estimated from several surveys since the 1970s and compares them with the DARES time series. Sources: Dares, authors' calculations based on polls, international surveys and public surveys. Coverage: All French employees.

Figure 4 :

 4 Figure 4: Individual days not worked due to strike action Source: DARES (labor inspectors' reports until 2004, then the Acemo-Dialogue social survey).Interpretation: In 1976, there were 4,000 days lost per 1,000 employees in employment. In 2019, there were 161.

Figure 5 :

 5 Figure 5: Comparison of CGT and CFDT membership estimates by[START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF], from union data and from survey data

Table 1 :

 1 Surveys and polls mobilized to estimate the unionization level between 1970 and 2017

	Type of source Name	Years
	Post-election & Crédoc, Agoramétrie,

  After 2013, the SRCV survey (Statistiques sur les ressources et conditions de vie) and the Conditions of Work survey isolate the unionization question from other associations and both find a unionization rate above 10%, while another component of the SRCV survey, in which the union question is framed as in the EPCV survey, finds a rate of 8%. : The graph presents the distribution of unionization levels estimated from several surveys since the 1970s and compares them to the DARES time series. Interpretation: In 1978, the unionization level in the Agoramétrie survey was 30%, whereas it is 20% in the series published by DARES.

		.5
		.4
	Unionization rate	.2 .3
		.1
		0
		1948 1958 1968 1978 1988 1998 2008 2018
		SRCV	EPCV
		Electoral survey	Agoramétrie
		Credoc	Eurobarometer
		European Value Survey	Dares
	Figure 3: Comparison of unionization levels in France
		estimated from survey and administrative data

NotesSources: Authors' calculations based on multiple polls, international and public surveys. Coverage: All French employees.

More precisely, Le Peuple reports 7 stamps (n°814, December16- 25, 1970), "between 7and 8" (n°893-894, May 1-15, 1972), 7.1 (n°969, July 1975) and 8 (n°1040, June 16-30, 1978).

[START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] confirms this hypothesis by examining three sectors for which the membership of the CGT, the CFDT and the FO (Force ouvrière) is known: public finance; post, telegraph and telephone (PTT); and public and health services. He notes that in each of these sectors, the vote shares of the three unions in the workplace elections are relatively close to the directly known shares of the workforce (the error is less than 10%). However, these sectors can hardly be considered as representative, since all three are in the public sector. Moreover, these verifications concern the 1980s and 1990s, or the 1960s in the case of the PTT, but not the 1970s, which is our subject here.

[START_REF] Mercier | Les conflits en 1999: une reprise sensible[END_REF] and[START_REF] Camard | Comment interpréter les statistiques des grèves?[END_REF] point out the limitations of these data, but do not suggest that the trend over time is biased. The volatility of strikes is higher than that of union membership, but the trends are similar.

Recounting France's trade unions Since we do not have reliable survey data before 1970, a we cannot estimate a unionization level prior to that date. Nevertheless, we believe that our methodological criticisms of the DARES and ICTWSS series are equally valid for this period. In particular, [START_REF] Bevort | Compter les syndiqués, méthodes et résultats la CGT et CFDT 1945-1990[END_REF] himself cites a ratio between the number of membership cards and the number of stamps sold annually by the CGT from 1945 to 1957 that oscillates between 7 and 8.5, which contradicts the assumption of 9 stamps. In order to construct a new historical series, in the absence of more reliable data, we propose to base it on the number of active members declared by the CGT itself. b Indeed, the 1970s polls allowed us to rule out, for this period, the suspicion of overestimation by the union. Our hypothesis consists in transposing this result to earlier decades. It then remains to move from this estimate to the level of unionization. To do this, we propose two methods (Figure 6). The first, which allows us to go back to 1949, consists of adopting the method used by [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] based on the results of workplace elections: Total unionizationt = CGTt/ct, where ct is the share of the CGT in the results of workplace elections in year t. Indeed, we have shown that this method led to an underestimation of total membership in the 1970s, but we have attributed this effect to the specific institutional and political context of the years after May 1968. We note that this series is very close to the one proposed by Andolfatto and Labbé (2021), based on the hypothesis of 8 stamps.

The other series we propose assumes, on the contrary, that the negative bias of [START_REF] Labbé | La syndicalisation en France depuis 1945[END_REF] would have already been present 1968: we replace the coefficient ct for earlier years by 40%, the share of the CGT in the total workforce estimated from polls in 1970. Since the relative weight of the CGT has changed over the decades, this hypothesis can only be considered plausible in the 1960s, and we therefore restrict this second series to that period. The first series based on Labbé's method can therefore be considered as a conservative estimate, and the second as a high estimate.

a There is a survey in 1958 and one in 1962 with a question on unionization, but their results are contradictory to each other. b Before 1960, the CGT does not distinguish between active and retired members. For the period 1949-1959, we subtract a fixed share of 10% corresponding to the share of retirees in 1960. sumptions, which we detail in Box 2, we recommend that the reader exercise some caution in using the proposed figures. The main lesson we wish to emphasize is that we obtain higher estimates than those of DARES before 1970, as we do after 1970 and even under conservative assumptions.

Authors