Oscar Sosa Sabogal

Sylvie Valin

Sébastien Thiery

Sylvain Salvador

Design and thermal characterization of an induction-heated reactor for pyrolysis of solid waste

Keywords:

A small-scale induction heated reactor (IHR) was specifically developed to study fast pyrolysis, here investigated as the first step of gasification process, representing some of the reaction conditions encountered in a fluidized bed reactor. First, the thermal response of the system was characterized at transient and steady state, and CFD calculations were performed to have a complete description of the temperature profiles inside the reactor. The novel device can handle a few grams of solid at temperatures up to 900 • C, allowing high heating rates (near 80 • C/s) and a uniform distribution of temperature in the sample. Secondly, the pyrolysis of a solid recovered fuel (SRF) sample was carried out at 800 • C, and the distribution and composition of reaction products were analyzed and compared with tests performed in a pilot scale fluidized bed reactor (FBR). The results obtained in the IHR showed a good reproducibility. The same main gas and tar species were measured in the IHR and FBR, with some differences in gas and tar composition that were attributed to the extent of secondary reactions, enhanced by higher heat transfer rates and the presence of bed material in the FBR.

Introduction

Solid waste that cannot be reused or recycled can be transformed through energy recovery processes, an interesting alternative to landfill. Waste derived fuels are produced from industrial or household waste, which include common materials with high calorific values like plastics, textiles, wood, and elastomers [START_REF] Garcés | Evaluation of the potential of different high calorific waste fractions for the preparation of solid recovered fuels[END_REF]. After incineration, pyrolysis and gasification are the most common valorization routes. Pyrolysis is a thermochemical process where the carbonaceous feedstock decomposes in absence of oxygen to produce permanent volatiles (gas), condensable hydrocarbons (tar) and often a solid residue (char). Gasification usually occurs at temperatures above 700 • C, in presence of an oxidizing agent that is fed below the stoichiometric amount needed for total oxidation. * Corresponding author.

The produced gas can be directly burnt to produce energy and heat or, after cleaning, used in a synthesis process to produce biofuels or chemicals. The yields of products and their composition highly depend on reactor design, process parameters, and feedstock characteristics. Among the available technologies in thermochemical conversion, fluidized bed reactors are widely used in the pyro-gasification of biomass and waste since they are suitable for heterogeneous streams [START_REF] Benedikt | Fuel flexible gasification with an advanced 100 kW dual fluidized bed steam gasification pilot plant[END_REF]. Compared to fixed bed reactors, they are characterized by higher mass and energy transfer rates, achieving higher conversion rates and low tar yields [START_REF] Park | A comparative study of the gasification of solid refuse fuel in downdraft fixed bed and bubbling fluidized bed reactors[END_REF].

Testing different feedstocks or conditions in a fluidized bed pilot can be costly in time and resources. Lab scale devices offer a simpler and more flexible solution, however, the reaction conditions found in an industrial fluidized bed reactor are difficult to scale down [START_REF] Leion | Experimental method and setup for laboratory fluidized bed reactor testing[END_REF]. The rate and extent of decomposition of the feedstock during the pyrolysis process, is mostly influenced by the undergone thermal history. This history is classically defined by three parameters: the heating rate, the final temperature, and the total residence time [START_REF] Pasel | Experimental investigations on reactor scale-up and optimisation of product quality in pyrolysis of shredder waste[END_REF]. Slow heating rates induce high residence times and favor char formation, while high heating rates and high temperatures favor gas products [START_REF] Efika | Influence of heating rates on the products of high-temperature pyrolysis of waste wood pellets and biomass model compounds[END_REF].

Most researchers have used thermogravimetric analysis (TGA) to study the pyrolysis of solid carbonaceous feedstocks and char gasification kinetics [START_REF] Aluri | Pyrolysis and gasification studies of model refuse derived fuel (RDF) using thermogravimetric analysis[END_REF][START_REF] Porshnov | Thermal decomposition study of major refuse derived fuel components[END_REF][START_REF] Zhou | Thermogravimetric characteristics of typical municipal solid waste fractions during co-pyrolysis[END_REF]. In this technique, mass loss is continuously measured while the sample is subjected to a temperature treatment at a constant heating rate or a constant temperature under controlled atmosphere. However, conventional thermogravimetric analyzers present some limitations such as low heating rates (∼1 • C/s) and limited gas-solid contact [START_REF] Saadatkhah | Experimental methods in chemical engineering: thermogravimetric analysis-TGA[END_REF][START_REF] Samih | Development of a fluidized bed thermogravimetric analyzer[END_REF]. Sample mass is around 10-100 mg, which makes it difficult to obtain representative results, especially for mixtures as heterogeneous as waste derived fuels [START_REF] Robinson | Sample preparation for thermo-gravimetric determination and thermo-gravimetric characterization of refuse derived fuel[END_REF]. Curie-point and wire mesh reactors achieve very high heating rates (>10 4 • C/s), however sample mass is also in the scale of a few milligrams and reaction products are difficult to quantify [START_REF] Zhu | Fast co-pyrolysis of a massive Naomaohu coal and cedar mixture using rapid infrared heating[END_REF]. Other devices use larger amounts of sample, like fixed bed reactors [START_REF] Hwang | Characterization of products obtained from pyrolysis and steam gasification of wood waste, RDF, and RPF[END_REF], drop tube and boat furnaces [START_REF] Daouk | Thermo-conversion of Solid Recovered Fuels under inert and oxidative atmospheres: gas composition and chlorine distribution[END_REF]. Heat and mass transfer limitations may become significant if the heating rate is not high enough, if large particles are used or if there is not a good contact between the gas and the solid [START_REF] Cortazar | Experimental study and modeling of biomass char gasification kinetics in a novel thermogravimetric flow reactor[END_REF]. Some of the pyrolysis and gasification steps are endothermic, which means that enough heat must be provided to the reactor to sustain these reactions. In fluidized bed reactors, heat can be transferred from the bed material (heated in a separate vessel), from a hot fluidizing gas, by the oxidation of a feedstock fraction (autothermal operation) or by external means [START_REF] Zhang | Catalytic pyrolysis of biomass and polymer wastes[END_REF]. In lab scale installations heat is transferred to the reactor wall externally. Electric resistance heating is one of the most common sources at this scale. It offers a good temperature control; however, it usually takes long time to reach the setpoint temperature due to thermal inertia. High temperature differences appear between the reactor wall and the sample, therefore, a major response delay is observed [START_REF] Latifi | A novel induction heating fluidized bed reactor: its design and applications in high temperature screening tests with solid feedstocks and prediction of defluidization state[END_REF]. Alternative sources that can provide faster and more uniform heating are worth considering.

Widely used in the treatment of metal materials, induction heating is a contactless method in which an AC power source is used to supply an alternating current to a coil, which is wrapped around the work piece. This current generates an electromagnetic field on the work piece and consequently heats it by two phenomena: creation of eddy currents and magnetic hysteresis [START_REF] Latifi | A novel induction heating fluidized bed reactor: its design and applications in high temperature screening tests with solid feedstocks and prediction of defluidization state[END_REF]. Induction heating offers several key features like rapid heating rates, precise temperature control and high energy efficiency, which makes it an interesting energy source for the study of thermal conversion processes [START_REF] Henkel | A study of induction pyrolysis of lignicellulosic biomass for the production of bio-oil[END_REF][START_REF] Mishra | Mathematical modelling, simulation and experimental validation of resistance heating and induction heating techniques for E-waste treatment[END_REF][START_REF] Muley | Pyrolysis and catalytic upgrading of pinewood sawdust using an induction heating reactor[END_REF]. Induction heating has been previously used in a few pyrolysis studies [START_REF] Gauthier | Pyrolysis of centimetre-scale wood particles: new experimental developments and results[END_REF][START_REF] Latifi | Non-catalytic and catalytic steam reforming of a bio-oil model compound in a novel 'Jiggle Bed' reactor[END_REF][START_REF] Muley | Pyrolysis and catalytic upgrading of pinewood sawdust using an induction heating reactor[END_REF][START_REF] Tsai | Production of pyrolytic liquids from industrial sewage sludges in an induction-heating reactor[END_REF], mainly focused on the maximization of the oil fraction, which generally induces temperatures below 600 • C. Therefore, the literature regarding pyro-gasification studies using an induction reactor is very scarce. The present work focuses on the design and thermal characterization of a new induction-heated reactor (IHR), for the study of the thermochemical conversion of solid waste. The characteristics and thermal behavior of the developed reactor are presented in detail. Preliminary pyrolysis experiments were carried out with solid recovered fuel (SRF) samples to validate the setup, and their results are also presented and compared with tests made in a fluidized bed reactor (FBR). Pyrolysis is here studied as the first step of gasification process, and the distribution and characterization of gas and tar products are the main interests.

2.

Description of the experimental setup and procedure

Design requirements

The device developed in this work was designed to reach reaction thermal conditions close to those of a fluidized bed reactor, frequently used in biomass and waste gasification.

These characteristics include heating rates between 100 and 1000 • C/s [START_REF] Nilsson | Gasification reactivity of char from dried sewage sludge in a fluidized bed[END_REF], a temperature range between 750 and 900 • C, and good gas/solid heat and mass transfer conditions. Gas residence times inside the hot reactor are usually between 0.5 and 10 s for bubbling fluidized bed reactors, and between 0.5 and 1 s for circulating fluidized bed reactors [START_REF] Marshall | Commercial application of pyrolysis technology in agriculture[END_REF]. For the present device, a residence time between 1 and 5 s was targeted, long enough to enable significant secondary reactions of volatiles (H 2 , CO, CO 2 , H 2 O and hydrocarbons, including tar species). These reactions take place at temperatures above 600 • C before the volatiles exit the reactor freeboard zone [START_REF] Barr | Influence of reactor design on product distributions from biomass pyrolysis[END_REF].

The reactor was designed to handle a few grams of sample and to minimize heat and mass transfer limitations. A homogeneous temperature in the sample was desired along the whole reaction time. Temperature gradients within the reactor were reduced by preheating the carrier/gasification agent gas, before entering into contact with the sample. Finally, another objective was to collect all the reaction products (solids, condensable and permanent gases) for further analyses and quantification.

Detailed description of the setup

The designed and developed lab-scale setup is shown in Fig. 1. It consists of an induction-heated reactor, followed by a condensable and gas products collection system, and analysis modules.

The reactor consists of a stainless-steel tube of 560 mm in height, 31.75 mm in external diameter and with a thickness of 0.8 mm. The type of stainless steel used for the reactor was 316L; it can withstand temperatures up to 900 • C. A constant nitrogen flow fed from the bottom of the reactor is used to purge the system and to sweep the produced volatiles during the course of the experiment. Flowrate is set with a BROOKS's 5851S mass flowmeter controlled by a LabVIEW interface. A custom build heat exchanger helps to preheat the entering gas. The arrangement consists of two concentric metallic Inconel 600 tubes, with a height of 50 mm, a thickness of 0.5 mm and a diameter of 20 mm and 23 mm respectively. Entering gases are forced to pass through the small spaces (2 mm) between the reactor tube and the exchanger walls, for a total of 3 passes (Fig. 2).

The crucible consists in a metallic cylinder (of 27 mm in diameter and 55 cm in height), with the bottom part made of wire mesh, which enables the gas to flow through the sample particles. It can contain up to 10 g of sample, depending on the bulk density of the feedstock. A ceramic ring of 5 mm in height acts as a support and places the crucible at the middle of the reactor tube, just on top of the preheater. A metallic mesh cone of 35 mm height placed below the crucible acts as a diffuser (Fig. 2). Above the sample, an empty region of 320 mm high allows the gas phase reactions to take place during a few seconds.

The reactor is heated externally by an induction setup. The reactor tube is surrounded by a water-cooled copper coil inductor of 24 turns disposed in a parallel layout, for a total height of 420 mm. A generator (HFP 12, EFD induction Gmbh, 12 kW) supplies energy to the induction circuit. Maximal output value is limited to 75% by an internal setting. Setpoint temperature is adjusted with a GEFRAN 2500 PID controller, which is connected to a two-color optical pyrometer (Impac IGAR 6, range between 100 and 2000 • C, response time 2 ms). A quartz tube is placed to create a 5 mm gap between the coil and the reactor (5 mm gap).

Product collection and analysis modules

Product gas flows upwards and leaves the reactor through the outlet line, which goes to the condensable trapping system. The top portion and the outlet line are heated and insulated to keep temperature above 250 • C, to prevent tar and water condensation before reaching the traps. Five gas washing bottles filled with 2-propanol are used to collect condensable species (water and tar) present in the stream. Glass wool and glass beads are used to improve the contact between the gas and the solvent. The first two bottles are installed in an ice bath at 0 • C, while the other three are immersed in a carbonic ice and 2-propanol mixture at -70 • C. One empty bottle is placed at the end of the sampling train. Tar species are subsequently analyzed and quantified using a gas chromatograph with a flame ionization detector (GC-MS/FID, Agilent 7890A).

Non-condensable gases flow towards an online NDIR sensor (Non-Dispersive Infrared Detector), which record the CO, CO 2 and CH 4 concentrations every 1 s. Total volumetric flowrate of the produced gases is determined by a diaphragm gas meter placed at the outlet of the NDIR analyzer. Simultaneously, gases are collected in the Tedlar bag during the whole duration of the test (20 min). The test is finished when no gas concentration change is observed in NDIR. The gas from the bag is then accurately analyzed in the GC. An Agilent 3000A chromatograph equipped with four columns is used.

Reactor thermal characterization

It is common to assume that reaction temperature is that of the heating source, or that the temperature inside the reactor is uniform, although this can lead to major errors [START_REF] Lédé | Biomass fast pyrolysis reactors: a review of a few scientific challenges and of related recommended research topics[END_REF]. When using induction heating, the the position of the coil and of working frequency are crucial to attain a desired temperature profile for a specific workpiece [START_REF] Hadad | Inductive heating with a stepped diameter crucible[END_REF]. For this setup, the space between the coils, uniform at first, was modified to concentrate the magnetic field density along the preheater and the sample zone, where the required power density was higher. The positions of the coil and that of the pyrometer spot were also varied, and the configuration leading to the shorter response time was kept.

Heating profiles inside and at the external surface of the reactor were monitored in various test runs at atmospheric pressure, without and in presence of an inert sample. The reactor was heated from ambient temperature to 800 • C (pyrometer temperature), and then held at stable conditions for several minutes to ensure that steady state was reached. Carrier gas (N 2 ) flowrate was set at 1 NL/min. Temperatures at the wall external surface were measured by five K type thermocouples (TW1 to TW5) of 0.5 mm in diameter, distributed on the outer surface at z = 10, 155, 207, 268, 375 mm as shown in Fig. 2. F AT shaped rod with five K type thermocouples (TS1 to TS5) at different radial (r = 0, 6, 13 mm) and axial positions (z = 185, 210, 235 mm) was introduced into the crucible as displayed in Fig. 2b.

Dynamic temperature profiles

The evolution of temperatures at the external reactor tube surface is shown as a function of time in Fig. 3. Tw1 is the closest thermocouple to gas entrance and is placed outside the heated area, so its temperature was far below the setpoint.

The wall temperature at the sample height (Tw3) reached the setpoint value in 15 s approximately, following a linear behavior with a steep slope of 80 • C/s. At the preheater position (Tw2), the thermal response was slower due to the inertia of the internal elements and to the colder gas flowing along the exchanger walls. Temperatures along the empty zone above the sample (Tw4, Tw5) were similar, reaching a peak temperature just above the setpoint after 60 s followed by a slight decrease before stabilizing around 750 • C. The thermal profile inside the reactor was established for two cases and is shown in Fig. 4. In the first case, the crucible was empty, while in the second case it was filled with a bed of chemically inert material (alumina) with an average particle size of 4 mm. The loading height was about 30 mm. A significant temperature difference was observed between the reactor wall (pyrometer) and the T shaped rod thermocouples for both cases.

Differences between the internal thermocouples (TS1 to TS5) measurements were not significant for the empty case (Fig. 4a), which suggests a uniform temperature profile in both axial and radial directions. For the second case, the fastest response was recorded above the sample (TS5, z = 235 mm), where the thermocouple was subjected to radiant heat incident from the reactor wall and from the top particles of the bed. This explains why the temperature exceeded the setpoint value before reaching a stable value. At the middle of the bed (z = 210 mm) the temperature nearest to the hot reactor wall (TS4) increased faster than the one at the center (TS2), which was expected due to the thermal resistance of the bed material. The gradient in the radial direction was very low when compared with the thermal gradient in the axial direction. A similar result was observed in previous works of [START_REF] Fernández | A radiofrequency heated reactor system for post-combustion carbon capture[END_REF] and [START_REF] Chatterjee | Thermal behavior of a catalytic packed-bed milli-reactor operated under radio frequency heating[END_REF] where negligible radial temperature change was observed on two radio-frequency heated reactors with similar length to diameter ratios. In contrast, temperature differences in the axial direction reached several hundreds of • C. The slowest response was measured at the bottom of the crucible (TS1). In this point, carrier gas coming from the preheater meets the colder solid particles and then must flow through the empty spaces of the bed, which implies an additional thermal resistance. For the conditions of this test, Reynolds number was equal to 11.75, which indicates a laminar flow regime inside the reactor. The main heat transfer mechanisms involved during the heating of the sample were radiation between the inner walls, and bed particles, followed by a smaller contribution of convection, due to the low gas flowrate. It took about 300 s for the thermocouples of the inner bed to reach their endpoint value, compared to only 100 s for the empty crucible case.

The time needed to reach the setpoint temperature depends on the thermal properties of the elements inside the reactor. Thermal diffusivity (␣ = k/ C p )] is an indicator of how fast a material respond to a temperature change. Thermal diffusivity increases with temperature for nitrogen gas, while the behavior is the opposite for alumina. At 800 • C, ␣ is equal to 180,8 mm 2 /s for nitrogen gas and 2.22 mm 2 /s for alumina, which is consistent with the responses observed for the two case studies in Fig. 4. Thermal properties for a solid fuel will depend on its composition, and its heating behavior will be influenced the by the changes it is subjected to during its pyrolysis. In the case of lignocellulosic materials like wood, some part of the feedstock will be released as volatile matter and the rest will remain as char. [START_REF] Redko | Measurement of the times for pyrolysis and the thermal diffusivity of a pyrolysing particle of wood and also of the resulting char[END_REF] found that the effective diffusivity at 600 • C of raw wood (0.03 mm 2 /s) was significantly lower compared to that of its char (0.5 mm 2 /s), and that char diffusivity tended to increase with temperature. For other waste materials like plastics, devolatilization occurs between 400 and 500 • C in a single step without char formation, with the exception of PVC [START_REF] Ranzi | Pyrolysis, gasification, and combustion of solid fuels[END_REF]. Gases produced from plastic pyrolysis present diffusivities in the range of 8-70 mm 2 /s at high temperatures depending on the monomer [START_REF] Honus | Pyrolysis gases produced from individual and mixed PE, PP, PS, PVC, and PET-part I: production and physical properties[END_REF]. The temperature evolution of a solid waste sample will be intermediate between the two cases, first it will behave as the solid, and then once its devolatilization is complete, it will behave as in the case of gas.

Steady state conditions

A second two-color optical pyrometer (Impac IGAR 12-LO, 350-1300 • C range) placed on a moving support was used to measure the temperature profile along the reactor external surface in steady state conditions. Both runs (with and without ceramic particle bed) showed the same result, so the mean temperature distribution for the two runs is shown in Fig. 5. The maximum temperature reached inside the sample bulk (located between 180 and 210 mm) is 808 • C. Tempera-ture discrepancies were under 10 • C in the bed (TS1 to TS4), which shows that the temperature is uniform and close to the setpoint temperature once the steady state is reached. The highest wall temperature (TW2 = 825 • C) was measured at 155 mm, where the preheater device is placed. Above the sample, an isothermal zone of about 200 mm long was maintained at 750 • C. This empty zone is analog to the freeboard zone in a fluidized bed reactor. The temperature progressively decreases above this point since the current density is much lower outside the coil.

Reactor modeling

Thermocouple reading inside the tubular reactor can be affected by the radiative heat transfer between the thermocouple and the surrounding walls. The thermocouple thus sees surrounding surfaces at a higher or lower temperature than the real gas temperature. To complete the description of the gas temperature inside the reactor, a finite element thermal modelling was performed at steady state. The commercial software ANSYS FLUENT R19.3 was used to perform these calculations.

Reactor geometry was discretized using a 2Daxysymmetric approach, including the exchanger and the sample holder. The model assumed that gas phase consisted solely of nitrogen, and a carrier gas flow rate was set as inlet boundary condition. Various carrier gas flowrates (0.5 and 4 L/min) were tested to see the preheater performance and the influence of the gas velocity in the temperature profile of the reactor. The solid bed of particles was considered by using the porous media zone condition, which was applied to a specific flow domain created for the zone inside the crucible.

Properties of gas and solid phases were calculated using temperature dependent functions. Atmospheric pressure was defined as the outlet condition. The experimental profile measured previously at the tube surface was implemented to describe the stationary wall temperature. Reactor walls were modeled using no-slip boundary condition for the gas phase. Based on the assumptions listed above, governing equations (mass, energy, and momentum) were solved numerically by a finite volume method. The PRESTO (PREssure STaggering Option) was used as the pressure interpolation scheme, recommended for problems involving flow through porous media. The discreet ordinates radiation model was used to model the radiation heat transfer. The convergence was verified by monitoring residuals and the mass and energy balances.

Fig. 6 shows the temperature distribution of the gas phase inside the reactor at steady state conditions for increasing gas flowrates. At the lowest values, inlet gas was properly heated by the heat exchanger, so its temperature remained above 790 • C in the crucible zone with a rather homogeneous profile in both axial and radial directions. As the N 2 flowrates increased, more pronounced temperature gradients were observed in the crucible zone, especially in the radial direction. Because of enhanced convection, the length of the isothermal empty zone above the crucible increased and the maximum temperature position shifted in the direction of the N 2 flowrate, as observed in the work of [START_REF] Chatterjee | Thermal behavior of a catalytic packed-bed milli-reactor operated under radio frequency heating[END_REF].

N 2 flowrates of 0.5 and 1 L/min are best suited to achieve a homogeneous temperature profile in the sample as desired. Under these conditions, the estimated residence time of the gas in the hot empty zone (temperatures between 750 • C and 800 • C) is between 2 and 4 s. These conditions were selected for the pyrolysis test presented in the next section.

Pyrolysis tests

Preliminary pyrolysis experiments were carried out with solid recovered fuel (SRF) samples to validate the whole setup operation and experimental procedure. Their results are presented in the present section and compared with tests made in a pilot scale bubbling fluidized bed reactor (FBR).

Feedstock

The SRF used for the pyrolysis experiments, was produced from industrial and household waste. The fuel, in the form of pellets of 1 cm in height and 5 mm in diameter, was characterized by ultimate and proximate analyses. Moisture content was determined at 105 • C while ash content was measured at 815 • C according to the ISO 1171standard. Elemental composition (C, H, N, S) was determined with an ELEMENTAR analyzer. Feedstock composition is listed in Table 1.

Test procedure

The crucible was filled with 2.3 g of dried SRF pellets (24 h at 105

• C) and placed in the reactor. Gas washing bottles were placed in the cooling baths and then connected to the reactor outlet.

Nitrogen gas (0.5 L/min) was used to flush the entire system before the test and to carry the produced volatiles. Reactor was heated up to 800 • C and then held at this temperature for about 20 min. All the permanent gases were collected in a Tedlar bag, during the whole test and for an additional 20 min to ensure all the released products were collected. The gas meter reading and the composition of permanent gases as determined using micro GC were used to calculate the molar amounts of permanent gases. Liquid in the washing bottles was sampled and then analyzed by GC-MS/FID. Sample holder was weighed before and after the test to determine the char yield. The carbon conversion was defined as the ratio between the mass fraction of carbon in each product and the carbon content in the feedstock. Two tests were performed under the same conditions and the average values are presented. The values did not differ by more than 2%.

Product yields

The carbon distribution into each of the pyrolysis main products (permanent gases, tar, char) was determined and is presented in Fig. 7. The tar fraction is defined here as all condensable organic compounds with a higher molecular weight than toluene. The results of the present study (named here IHR for "Induction Heating Reactor") were compared with the ones obtained in the work of [START_REF] Valin | Fluidized bed air gasification of solid recovered fuel and woody biomass: influence of experimental conditions on product gas and pollutant release[END_REF] in which pyrolysis tests of the same batch of SRF were conducted at 800 • C in a pilot scale bubbling fluidized bed reactor (FBR) filled with olivine as bed material.

In both cases, most of the initial carbon was converted to gas products. A higher fraction of carbon remained in the char after pyrolysis in the IHR reactor compared with the FBR. This is consistent with the results obtained by [START_REF] Efika | Products from the high temperature pyrolysis of RDF at slow and rapid heating rates[END_REF], where RDF samples were pyrolyzed at different heating rates in a horizontal tubular reactor. Indeed, higher heating rates are encountered in fluidized beds thanks to contact between hot bed material particles, gas, and feedstock particles, which favors the carbon conversion to volatiles. In addition to the heating rate, the higher temperature and residence time also contribute to the cracking of the primary vapors into light molecular weight hydrocarbons, leading to increased gas yield and lower tar yield. Carbon mass balance closure reached about 85 wt% in the IHR reactor and was slightly lower for the FBR (78%). The missing carbon fraction could be attributed to condensable products that are deposited in the reactor outlet despite of tracing, and to hydrocarbons that cannot be identified or quantified in the GC-MS/FID analysis.

Gas products

Produced gas yield and its volumetric composition are compared in Fig. 8 for both setups. In this study, gas species As stated before, total gas production was higher in the FBR reactor. For the IHR reactor, CO was the most abundant gas (29.4%), followed by methane (22%) and hydrogen (21.5%). The fluidized bed gas presented higher concentrations of H 2 (31.9%) and CO 2 (21.7%) compared to the IHR gas. This could be due to higher residence time as well as the presence of bed material in the FBR, which favored hydrocarbon breakdown reactions resulting in more H 2 . Olivine bed improves the reforming of phenol and other tars, as seen in the work of [START_REF] Nitsch | Conversion of phenol-based tars over olivine and sand in a biomass gasification atmosphere[END_REF]. The contents of methane, light hydrocarbons and BTX were slightly lower in the FBR. A similar trend was observed by [START_REF] Pasel | Experimental investigations on reactor scale-up and optimisation of product quality in pyrolysis of shredder waste[END_REF], who compared the benzene yield from shredded waste pyrolysis in various types of equipment, including a tubular and a fluidizing reactor.

Tar products

The condensable fraction recovered in the gas washing bottles contains numerous organic species, which were then analyzed and quantified by GC-MS/FID. Here, the main tar species from pyrolysis in both reactors are shown in Fig. 9. Composition of tar produced from the pyrolysis of SRF in the developed device and a pilot fluidized bed reactor. Fig. 9, and are classified in four groups based on the number of aromatic rings in their structure.

Longer residence times and the presence of bed material possibly favored the extent of secondary reactions in the fluidized bed reactor, which decreased the total amount of tar when compared to the IHR. Most of the tar species generated in the IHR reactor were in the first group, consisting mostly of styrene (74%), and followed by indene and phenol. In the case of the fluidized bed, naphthalene, with two rings, was the most abundant component (70%). Heavier polycyclic aromatic hydrocarbons (PAHs) such as anthracene and pyrene (3 and 4 rings) were present in the tar from the FBR, while their amount for the IHR case was negligible. High temperatures (above 700 • C) promote the appearance of PAHs, as a product of aromatization and rearrangement reactions of aliphatic and monocyclic compounds [START_REF] Pasel | Experimental investigations on reactor scale-up and optimisation of product quality in pyrolysis of shredder waste[END_REF].

Conclusions

An induction-heated reactor was developed to perform pyrolysis experiments of waste derived fuels and its constituent materials. Some of the features of the developed device included a gas preheating system, high heating rates and the possibility of recovering and analyzing all reaction products. Experimental and CFD results provided a complete description of the temperature profiles for the surface, the sample and the gas inside the reactor. Heat provided by the induction circuit enabled to maintain a uniform temperature inside the sample carrier gas flowrates between 0.5 and 1 NL/min. The IHR was used to perform the pyrolysis of a SRF sample and the results were compared with tests made in a pilot scale fluidized bed reactor. Reaction conditions in the IHR reactor were close to intermediate to fast pyrolysis (heating rate 75 • C/s, volatiles residence time ≈ 4 s). Char yield indicates that the heating rate in the solid sample is lower in the IHR compared to the FBR.

Main permanent gas products were similar for the two reactors; however, residence time and the presence of the bed material had an influence on the extent of secondary reactions, which modified the distribution of the permanent gas species and tar products. In the future, experiments will be performed with raw materials used as model constitutents of wastes (such as plastic polymers, woody biomass, paper or cardboard), and their mixtures. Results obtained in the IHR reactor, carried out under controlled and well characterized conditions, will then be useful for the development and improvement of prediction models of the reaction products, and thus contribute to the understanding of pyrolysis and gasification at various scales.

Fig. 1 -

 1 Fig. 1 -Experimental setup of the induction heated reactor (IHR).

Fig. 3 -

 3 Fig. 3 -Temperature evolution at different locations along the reactor outer wall.

Fig. 4 -Fig. 5 -

 45 Fig. 4 -Temperature evolution a) in the empty crucible and b) in the crucible filled with ceramic material.

Fig. 6 -

 6 Fig. 6 -Contour plots of temperature distribution in the gas phase for different gas flowrates (left). Close up at the exchanger and sample zone (right).

Fig. 7 -

 7 Fig. 7 -Carbon distribution into products obtained from RDF pyrolysis at 800 • C in the induction heating reactor and a pilot fluidized bed reactor.

Fig. 9 -

 9 Fig. 9 -Composition of tar produced from the pyrolysis of SRF in the developed device and a pilot fluidized bed reactor.

  The species that can be quantified are O 2 , CO 2 , CO, CH 4 , N 2 , H 2 , C 2 H 2 , C 2 H 4 , C 2 H 6 , C 3 H 8 , C 6 H 6 (benzene), C 7 H 8 (toluene), C 8 H 10 (xylene and ethylbenzene), H 2 S, COS, and H 2 O in vapor phase. Remaining solid products in the sample crucible are weighed and collected for further analyses once the reactor has cooled down to ambient temperature.

Table 1 -Chemical composition of the feedstock.

 1

	SRF

ar: as received; db: dry basis. a By difference.

Fig. 8 -Yield of non-condensable gases from RDF pyrolysis at 800 • C for the developed device and a pilot fluidized bed reactor.

	included H 2 , CO 2 , CO, CH 4 , light hydrocarbons from two to four
	carbon atoms (C 2 H 2 , C 2 H 4 , C 2 H 6 , C 3 H 8, C 3 H 6, C 4 H 6 -butadiene)
	and light aromatic species like C 6 H 6 (benzene) and C 7 H 8
	(toluene), grouped and named here BTX.

Declaration of competing interest

The authors declare that they have no known competing commercial interests or personal relationships that could have appeared to influence the work reported in this paper.


Philippe Le Coent
email: p.lecoent@brgm.fr

Nina Graveline

Monica A Altamirano

Nabila Arfaoui

Camilo Benitez-Avila

Thomas Biffin

Javier Calatrava

Kieran Dartee

Ali Douai

Amandine Gnonlonfin

Cécile Hérivaux

Roxane Marchal

David Moncoulon

Guillaume Piton

Is-it worth investing in NBS aiming at reducing water risks? Insights from the economic assessment of three European case studies

Keywords:

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

Introduction

In Europe, climate change is expected to increase the frequency of extreme weather events. The IPCC indeed predicts that annual damages due to climate risk will rise by 77% in 2030 (IPCC 2014). Water related risks will be particularly affected with an increased occurrence of droughts and floods. For example, the number of centennial floods is expected to double in the next three decades [START_REF] Alfieri | Global warming increases the frequency of river floods in Europe[END_REF] . Engineered solutions or so-called grey infrastructure (e.g. floodwall) have been historically largely used to manage flood risks. The reliance on these solutions has nevertheless showed limits: limited adaptability in front of the expected modification of risks due to climate change [START_REF] Milly | Climate change: stationary is dead: Whither water management?[END_REF] , adverse environmental effects through the modification of ecosystems [START_REF] Van Slobbe | Building with Nature: in search of resilient storm surge protection strategies[END_REF] , the limited capacity of sewer systems to manage urban flooding with negative effects on water quality and the transfer of flood management risk downstream [ 30 , 60 ] and the tremendous investment and maintenance costs they generate [START_REF] Wilderer | Applying sustainable water management concepts in rural and urban areas: some thoughts about reasons, means and needs[END_REF] .

There is a growing recognition and awareness that nature can help provide protection to humans through risk reduction properties of ecosystems [ 5 , 14 , 32 ]. The EU Floods Directive of 2008 already opened the way for more integrated flood management and a plurality of measures including the resort to Nature-Based-Solutions (NBS). River restoration, the restoration of wetlands and flood plains in rural context and a number of green infrastructure in urban contexts such as bioswales, green roofs, and vegetated open retention basins are increasingly considered as alternative or complementary solutions, to manage flood risks. Besides their impact on water risks, ecosystems generate a wide diversity of ecosystem services essential to human life, understood as the benefits people obtain from ecosystems [START_REF] Ma | Millenium Ecological Assessment. Millennium Ecosystem and Human Well-being: A framework for Assessment[END_REF] . Recently in urban contexts, the need for services provided by ecosystems, has been increasingly highlighted [START_REF] Raymond | A framework for assessing and implementing the co-benefits of nature-based solutions in urban areas[END_REF] . For example, urban trees included in many NBS for water risks have been estimated to have an impact on carbon storage and sequestration. An estimated 2,367,000 tonnes (approximately 15t/ha) of carbon is stored in London's trees [START_REF] Rogers | Valuing London's Urban forest[END_REF] . Zinzi and Agnoli [START_REF] Zinzi | Cool and green roofs. an energy and comfort comparison between passive cooling and mitigation urban heat island techniques for residential buildings in the Mediterranean region[END_REF] estimate a 10-14% energy saving for buildings with green roofs in Barcelona due to reduced heating in winter and cooling effect in summer. Aevermann and Schmude [START_REF] Aevermann | Quantification and monetary valuation of urban ecosystem services in Munich, Germany[END_REF] provide a review of amounts for air pollution removal associated with urban green ranging from 1.97 to 3.80 g/m 2 /yr of O 3. Other examples of ecosystem services generated by NBS include twater cycle regulation, the creation of new habitats for biodiversity and recreational services [START_REF] Hérivaux | Natural Capital and Ecosystem Services to Valuate Co-Benefits of NBS in Water Related Risk Management[END_REF] . The need for these services is expected to become even stronger in the context of climate change, with for example the expected increase in occurrence of heat waves [ 28 , 37 ]. However, the production of these services is increasingly threatened due to the degradation of ecosystems resulting from urban sprawl, pollution and climate change.

The terminology used to denominate these solutions is diverse: ecosystems based adaptation, green infrastructure, ecosystem based disaster risk reduction, natural water retention measures [START_REF] Kabisch | Nature-Based Solutions to Climate Change Mitigation and Adaptation in Urban Areas : Perspectives on Indicators, Knowledge Gaps, Barriers[END_REF] and sustainable urban drainage systems (SUDs) [START_REF] Fletcher | BMPs, WSUD and more -the evolution and application of terminology surrounding urban drainage[END_REF] . More recently, the concept of Nature Based Solutions (NBS) has gained momentum. NBS can be considered as an umbrella term for these approaches that is defined by the EC 1 as "solutions to societal challenges that are inspired and supported by nature, which are cost-effective, simultaneously provide environmental, social and economic benefits and help build resilience ".

Interestingly, the economic advantage of NBS is generally assumed, as in the EC definition, with limited evidence to support this "fact ". The economic assessment of NBS is however a key step in the evaluation of NBS. Indeed, assessing the value of costs and benefits of NBS and being able to compare them to alternative strategies such as business as usual grey solutions is fundamental for decision makers to develop these solutions and eventually turn them into implementable projects. The limited adoption of NBS aiming at reducing water risks may actually be attributed to uncertainties regarding their economic performance, as in the case of SUDs [ 47 , 53 ]. Some evidence mainly focused on SUDs actually show that risk reduction benefits may often not exceed the costs they generate [ 30 , 33 , 34 , 47 ]. But one particularity of NBS is their capacity to generate a multiplicity of co-benefits [START_REF] Raymond | A framework for assessing and implementing the co-benefits of nature-based solutions in urban areas[END_REF] , such as biodiversity conservation, water availability and quality, air pollution, the regulation of air temperature. Economic assessment frameworks that accounts for the multifunctional impacts of NBS are thus required. The aim of this paper is to develop this framework for the economic assessment of NBS including specific methodologies to assess costs and benefits. We then apply our methodology to three case studies of the H2020 "NAture Insurance value: Assessment and Demonstration " (NAIAD) project, two in France and one in the Netherlands, in order to bring new evidence on the economic efficiency of NBS projects.

The cost-benefit balance of NBS for water-related risks requires the comparison between the cost of implementing and maintaining these solutions, and their opportunity costs, with the multiple benefits they generate: i) the cost of damages they prevent due to the reduction of water risks and ii) the co-benefits they provide. The evaluation of benefits of these NBS therefore calls for the combination of state of the art methods for the estimation of flood damages prevented by NBS solutions with methods for the estimation of the monetary value of the diversity of co-benefits they generate. In the scientific literature, previous studies tend to focus on either one benefit or the other. Some papers 1 https://ec.europa.eu/research/environment/index.cfm?pg = nbs . carry out a thorough evaluation of the impact of NBS on the reduction of risks, based on physical modelling mainly focusing on the impact on hazard [ 16 , 36 , 38 , 56 ] and in some cases on the reduction of damages they generate [START_REF] Vincent | Enhancing the Economic Value of Large Investments in Sustainable Drainage Systems (SuDS) Through Inclusion of Ecosystems Services Benefits: Water[END_REF] . Other authors rather focus on the advanced valuation methods of ecosystem services generated by different types of NBS or of combinations of NBS: river restoration (Arfaoui and Gnonlonfin, [START_REF] Arfaoui | The economic value of NBS restoration measures and their benefits in a river basin context : a meta-analysis regression[END_REF] for a meta-analysis), urban parks (e.g [START_REF] Aevermann | Quantification and monetary valuation of urban ecosystem services in Munich, Germany[END_REF] ), Sustainable Urban Drainage Systems [START_REF] Johnson | Are neighborhood-level SUDS worth it? An assessment of the economic value of sustainable urban drainage system scenarios using cost-benefit analyses[END_REF] , green roofs [ 6 , 46 ], façade greening [START_REF] Perini | Is greening the building envelope economically sustainable? an analysis to evaluate the advantages of economy of scope of vertical greening systems and green roofs, Urban Forest[END_REF] and a meta analysis of stated preference valuation of blue and green Nature in cities [START_REF] Bockarjova | Economic valuation of green and blue nature in cities: a meta-analysis[END_REF] . Studies that combine both type of assessments generally have a simplified approach of risk reduction or ecosystem services, using only value transfer methods.

This study therefore brings a novel contribution in the sense that it provides a methodological framework for an advanced assessment of both NBS benefits on the reduction of water-related risk and for their co-benefits. The evaluation of the reduction of water risk is based on physical models of the impact of NBS on the reduction of flood hazard and on the use of sophisticated damage valuation methods (in two case studies out of 3). This evaluation is combined with thorough assessment of co-benefits that does not only rely on value transfer but rather on stated preferences or direct valuation methods (see the methods section for details). Finally, the paper presents the application of this common methodological framework to different scales in three sites in two European countries: from the city neighbourhood (Dutch case), to the river catchment level mixing urban, peri-urban and rural contexts (two French cases).

The paper describes in section 2 the economic assessment framework and its application to the case studies. Section 3 presents the main results that can be drawn from the economic assessment carried out in the three case studies. In section 4, we discuss the results and conclude.

Economic assessment methodology of NBS aiming at reducing water risks

General methodology of the economic assessment

The aim of the economic assessment methodology is to assess the relative economic value of alternative strategies, through a Cost benefit Analysis (CBA). The relative economic value provides an evaluation of the economic efficiency of a programme. CBA was initially developed to support policy development and justify environmental regulations in the US [START_REF] Pearce | Cost-Benefit Analysis and the Environment: Recent Developments: Organisation for Economic Co-operation and development[END_REF] . The method aims at ascertaining that benefits (gains in human well-being) exceed costs (losses in human well-being) before implementing projects or programmes and if investable funds are limited, which one of these projects or programmes should be selected [ 42 , 48 ]. The monetary value of these benefits and costs, revealed through choices in markets, is expected to reflect human preferences [START_REF] Pearce | Cost-Benefit Analysis and the Environment Recent Developments[END_REF] . Its application to environmental economics has raised the need to assign a monetary value to environmental externalities, with methods mentioned in section 2.6.

In our context, the CBA aims to compare alternatives to manage water risks. Depending on the case study, one or several alternatives are compared which incorporate different levels of NBS and traditional grey infrastructure. NBS strategies are here the alternative projects we evaluate that may incorporate a combination of NBS and grey infrastructure. The CBA performed compares strategies without NBS (considered as the Business as Usual (BAU) strategy) with one or several strategies including NBS measures.

The CBA requires the estimation of all direct and indirect costs and benefits for the different NBS strategies under study in monetary value. The following typology of monetary values associated with NBS strategy are considered:

• Cost of implementation are those that are necessary for the implementation and maintenance of the NBS included in the NBS strategy;

Fig. 1. description of the cost-benefit analysis approach for the economic valuation of NBS within NAIAD (modified from Graveline et al [START_REF] Graveline | General Framework for the Economic assessment of NBS and their insurance value[END_REF] )

• Opportunity costs are those that are foregone with the NBS strategy, for instance areas that are taken out of production, or land that is used for NBS and that cannot be used for other purposes such as the construction of building. They are the indirect costs of the NBS strategy. • Avoided Damage Costs are the damages avoided due to the reduction of water risks 2 generated by NBS strategies. Avoided costs are the primary benefit generated by NBS strategies aiming at reducing water risks. • Co-benefits are the additional environmental, economic, and social benefits generated by NBS. In the CBA, we will focus on the ones that can be evaluated monetarily although they cover only part of the co-benefits generated by NBS strategies or only a portion of their overall value.

The methods used to estimate the monetary value of these different costs and benefits are described in details in section 2.4 to 2.6. In Fig. 1 , we present a schematic representation of the CBA method applied to the evaluation of NBS aiming at reducing water risks.

Several indicators can be calculated to carry out a CBA. In this study, we mainly report on the Benefit Cost Ratio that is estimated with the following formula, where 𝐶 𝐵 𝑡 is the Co-benefits in year t, 𝐴 𝐷 𝑡 is the Avoided Damage in year t, 𝑟 3 is the discounting factor, 𝐶 𝑡 and 𝑂 𝐶 𝑡 are Implementations Costs and Opportunity Costs in year t and T is the time 2 In this paper, the NBS considered are designed to reduce damages arising from pluvial and fluvial flooding (see section 2.3 for case study description). The general approach could nevertheless apply also to reduce other types of water risks such as coastal flooding or drought. 3 Discounting arises because of the underlying value judgement in CBA taken from welfare economics, that individuals give a higher value to a present benefit or cost than to a future one. The discounting factor is thus determined by the rate at which individuals express. this "time preference " [START_REF] Pearce | Cost-Benefit Analysis and the Environment Recent Developments[END_REF]. The European Commission recommends a discount factor ranging from 3 to 5% (European Commission, 2014) whereas the French Quinet report recommend a value of 2.5% (CGSP, 2013). In practice, the discounting factor varies in the different case studies (2.5% to 3%) considering the value prevailing in the evaluation of investment projects at the country level. The value of the discounting factor may affect negatively the benefits associated with long-term sustainabil-horizon of the assessment.

𝐵𝐶𝑅 = ∑ 𝑇 𝑡 =0 [ 𝐴 𝐷 𝑡 + 𝐶 𝐵 𝑡 (1+ 𝑟 ) 𝑡 ] ∑ 𝑇 𝑡 =0 [ 𝐶 𝑡 + 𝑂 𝐶 𝑡 (1+ 𝑟 ) 𝑡 ]
A BCR superior to 1 means that a project is economically efficient, i.e. that it improves the economic welfare and that it should be eligible for investment by public funds. Decision makers may want to invest in the alternative that present the highest BCR among different courses of action.

In this study, we also look at partial CBA indicators in which we focus on the primary benefit and consider only the direct cost of implementation. Although partial in economic terms, this indicator provides indicators that may be contemplated by decision makers specifically interested in the risk reduction challenge.

Avoided damage ∕ Cost ( rate ) = ∑ 𝑇 𝑡 =0 [ 𝐴 𝐷 𝑡 (1+ 𝑟 ) 𝑡 ] ∑ 𝑇 𝑡 =0 [ 𝐶 𝑡 (1+ 𝑟 ) 𝑡 ]
Finally, we also report on a cost effectiveness indicator, which indicates the cost incurred to achieve an output, expressed by a physical indicator. This physical indicator is a proxy of the effectiveness of the measure such as m 3 of water retention for flood management. This indicator is compiled only for individual NBS measures and not for NBS strategies.

Cost ef fectiveness =

∑ 𝑇 𝑡 =0 [ 𝐶 𝑡 (1+ 𝑟 ) 𝑡 ]

𝐼𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟 𝑜𝑓 𝑒𝑓 𝑓 𝑒𝑐𝑡𝑖𝑣𝑒𝑛𝑒𝑠𝑠

The stepwise approach A stepwise approach was used for the economic assessment of NBS in this project. This approach could be replicated in other contexts. 1. Set scale and time horizon. The time horizon at which the strategies are evaluated defines the number of years for which the benefits ity, since long term benefits will be discounted strongly especially when high discount factor are used.

and costs are taken into account in the economic analysis. This time horizon varies depending on the type of investment and is usually set at the expected lifetime of the considered investment. 2. Define and describe strategies. This step is crucial for the analysis.

The identification of NBS strategies is undertaken using a participatory process involving stakeholders of the territory. NBS strategies are identified as a response to the main territorial challenges in terms of water risks and other territorial issues that may be addressed by NBS. 3. Impact assessment. The impacts of NBS strategies must be established against a reference scenario in order subsequently assess the economic value of these impacts. This requires first that NBS strategies be translated into usable inputs for modelling. Either this can be done through a simple quantification of some physical variables that characterize strategies (such as the number of trees planted in the different NBS strategies) or by developing maps that locate the different NBS and associated variables (land use change, retention volume). This quantification of NBS strategies is then used to estimate their impact using a diversity of models. Given the focus of this study on water risks, detailed hydrologic and hydraulic models are developed to estimate the impact of NBS strategies on flood damage. Other simplified models have been mobilized to estimate the physical impact of NBS on co-benefits. 4. Assessment of costs and benefits: The details of the economic assessment methods are presented in section 2.4 to 2.6. 5. Cost Benefit Analysis: Finalization of the CBA by compiling the benefits and costs defined above.

Description of the case studies

This paper reports on the economic assessment of NBS in three case studies: the Brague and the Lez case in southern France and the Rotterdam case in the Netherlands. The results presented here are based on original data collected during the H2020 Naiad Project by the authors of this article. The paper presents a cross-caste studies analysis of the results presented in project deliverable 6.3 of the H2020 NAIAD Project [ 11-13 , 21 ]. A diversity of contexts in terms of water risk, scale and urban/rural setting were selected in order to increase the robustness of the economic results: a neighbourhood scale with pluvial flooding issues in urban context (Rotterdam), a watershed scale with pluvial flooding issues in an urban context (Lez Catchment) and a watershed scale with a river flooding issue in an urban-rural context (Brague River catchment).

The Lez catchment in France (746 km 2 ) is characterized by a rapid urbanization around the city of Montpellier and pluvial flooding risks (78% of damages in the last major event of 2014 [START_REF] Coent | Demo Insurance Value Assessment[END_REF] . The catchment also faces typical challenges of large Mediterranean cities: heat island effects, air pollution, water scarcity and biodiversity loss mainly due to urban sprawl. Two NBS strategies based on two levels of development of green infrastructures in cities were designed to address these issues based on a stakeholder consultation process: i) "NBS 1 " includes small bioswales, city deproofing and permeable pavement, and ii) "NBS 2 " includes NBS1 measures plus green roofs, open retention basins, larger vegetated bioswales. The paper presents the results of the economic assessment of these strategies compared to a business as usual strategies with no intervention.

The Brague River catchment in France (68 km 2 ) meets the Mediterranean Sea in the city of Antibes. The catchment mid part is hilly and forested while the upper part is a plateau with a suburban land use. The flat floodplain of the lowlands experiences high flood risks, e.g., in Oct. 2015, an extreme flash flood caused 4 casualties and triggered dozens M € of damages. The grey strategy initially proposed was to build large flood retention dams. The NBS strategy under study relies on small natural retention measures spread in the catchment over 200 ha, along with an ambitious river corridor restoration to give room to the river in the lowlands. It consists in building five light structures aiming to trap woody debris, widening the channel by 50-100%, modifying 3 bridges and restoring 13 ha of riparian forest and 11 ha of wetlands. It would also require buying and demolishing 50 to 70 houses.

The Rotterdam case study focuses on Spangen, a low-lying neighbourhood in the West of the city, spanning roughly 65 ha with around 10,000 inhabitants. With the low elevation and shortage of pervious surface area due to intense urbanisation, the neighbourhood has been suffering frequent pluvial flooding during heavy rain events. To add retention capacity to the area for dealing with these rain events, and to sustain a reliable supply of fresh water in times of droughts, a so-called Urban Waterbuffer (UWB) was realised on the square next to the Sparta Stadium in 2018. As the Rotterdam case study is interlinked with this implemented piece of hybrid infrastructure, it provides important insights that may not have been gleaned from modelling and forecasting alone. The Rotterdam case study also constitutes a comparison of three (green -grey -hybrid) neighbourhood wide strategies to address the economic impact of NBS approaches for the area.

Assessment of implementation and opportunity costs

The evaluation of implementation costs was estimated following the Life cycle costs (LCC) principles, also named Total Cost of Ownership (TCO). It considers the total cost of acquisition, use/administration, maintenance and disposal of a given item/service [START_REF] Ellram | Total cost of ownership: an analysis approach for purchasing[END_REF] . The accurate identification of LCC provides the information to assess the magnitude of investments for maintaining socio-technical system functionality over time. This methodology focuses on identifying the generating activities and cost determining factors to maintain the main functionality of NBS: avoiding water-related risks. Cost generating activities can be grouped into six LCC components namely: 1) capital expenditures, 2) operating and minor maintenance expenditures, 3) capital maintenance, 4) expenditure on direct support, 5) expenditure on indirect support and 6) cost of capital.

In the Rotterdam case study, the full LCC method was mobilized to directly estimate cost figures for costs related to measures and activities related to the realized UWB, as data could be collected in the pilot project. For the other NBS included in Rotterdam and in the Lez and Brague case studies, cost were estimated based on reference values from the scientific literature, national databases of market prices and expert opinions. Cost per units of surface (or volume) of individual NBS measures, composing NBS strategies were first evaluated, then these costs were extrapolated at the NBS strategy levels, to estimate the overall cost associated with NBS strategies. The estimation of costs based on value transfer presents large range of uncertainty, which is reported.

The opportunity costs are those costs associated with the foregone alternative, which can be measured by the net foregone benefit (because the resources that provide the services cannot be used in their next beneficial use, [START_REF] Tietenberg | Environmental & Natural Resource Economics/Tom Tietenberg[END_REF] ). NBS implementation because of its relatively large spatial footprint usually requires large-scale land use changes from productive uses to other uses. When NBS are implemented on private land, the cost can be integrated in the capital expenditure related to land purchase, but when NBS are mainly implemented on public owned land, opportunity cost should be considered [START_REF]Guide to Cost-Benefit Analysis of Investment Projects[END_REF] 4 . However, in urban cases NBS are implemented on marginal spaces, such as on a share of the sidewalk or even on concrete spaces, without specific use or value (roundabouts, forecourts, plaza etc.). Sometimes the use value will not be altered (e.g. greening parking spaces) so there are no opportunity costs. Sometimes the question of whether a change of land use generates an opportunity Fig. 2. The principle for assessing avoided damage costs cost is subject to interpretation when public road or parking space is concerned.

In the Lez and Rotterdam case, we applied a conservative approach, which is to consider land market prices as a proxy of opportunity costs, although alternative possible use of this land is uncertain. We therefore estimate an upper bound of opportunity costs. In Brague, NBS strategies involve privately owned land use change. In this case, following recommendations from the water agency 5 , land acquisition costs were included in investments costs while additional opportunity costs were estimated based on profits private landowners could have obtained from the use of this land (estimated by revenues they could have perceived over this land).

Assessment of avoided damages Overall approach to the assessment of avoided damages

The overall approach to the estimation of the avoided damage associated with NBS strategies comprises two main steps: 1) estimation of the relation between water related hazards and damages (catastrophe risk models (CAT) model) and 2) estimation of the impact of NBS strategies on the modification of hazard (droughts or floods) through physical models 5 . The combination of these two steps leads to the estimation of damages under different NBS strategies and without these (BAU) ( Fig. 2 ). The difference between damages in the BAU and NBS strategies provides an estimation of the avoided damage, which is expressed in Mean Annual (Avoided) Damage (MA (A) D) and can be integrated in the overall economic evaluation. The general approach was adapted to each case study according to specificities and data availability.

Estimating the relation between hazard and damage costs: the CAT model framework

The CAT model aims to establish the costs of an event based on its magnitude, its spatial distribution (event intensity), and the vulnerability of the elements at risk [START_REF] Naulin | Estimation of insurance-related losses resulting from coastal flooding in France[END_REF] . This involves the following steps [ 20 , 39 ]:

• Mapping of event's hazard intensity.

• Assessment of the exposure of the assets/elements at risk. • Definition of damage functions/models. • Calculation of the value of the damage cost.

Consequently, the structure of CAT models relies on three units: hazard, vulnerability and damage ( Fig. 3 ).

Overall the total damage computed for one event is:

𝐷 𝐸 = 𝑁 𝐸 ∑ 𝑖 =1 𝑉 𝑖 ( 𝐻 𝐸 ( 𝑋 𝑖 , 𝑌 𝑖 ) )
Where D E is the damage of event E, 𝑁 𝐸 is the number of assets at risk for event E, i is the index of each asset, X i Y i are the coordinate of asset i, H E is the hazard intensity for event E and 𝑉 𝑖 is the vulnerability of asset i which is usually computed using a damage curve, i.e., a curve relating the vulnerability to the hazard intensity 𝐻 𝐸 . This approach was followed in the Lez and Brague cases, while a simplified approach was used in the Rotterdam case to better suit the small scale of the focus area. The strategies in the Rotterdam case were designed to all provide a similar level of flood risk reduction to assess which is the most favourable choice in terms of associated costs and co-benefits provided, when comparing a grey, a hybrid and a green strategy for mitigating a T10-rain event (52,9 mm of rain over 12 h) in Spangen. An estimation of the magnitude of avoided damages was derived from another recent study on climate risk mitigation in the neighbourhood of Spangen [START_REF] Arcadis | MKBA Klimaatbestendige Inrichting Pilotwijken: Pilot Spangen (Rotterdam) en Mariahoeve[END_REF] .

The characterisation of the flood hazard event ( 𝐻 𝐸 ) in the different case studies has been done by using or adapting hazard models. In the Lez a 25 m-resolution runoff model developed at the French scale by the CCR [START_REF] Moncoulon | Analysis of the French insurance market exposure to floods: a stochastic model combining river overflow and surface runoff[END_REF] has been adapted to integrate the local information about land use and slopes taking into account water heights on each mesh. This method sprawls water along short watercourses, instead of being blocked in the banks and is possible in terms of calculation duration. It was calibrated on the Oct. 2014 event. In the Brague, a 2D model computed on a 2 m mesh represented the flooding in the whole floodplain [START_REF] Bladé | Iber: herramienta de simulación numérica del flujo en ríos[END_REF] . The model was built using topographical data and land use maps. It includes bridges and culverts. It was calibrated on the Oct. 2015 event and validated on the Nov. 2011 event

Estimating the impact of NBS on hazards

This step involves modelling how NBS strategies would change the intensity and location of the hazard (hazard unit). For the Lez case, the hydraulic model used could not directly model the impact of NBS on flood hazards because of model limitations: too large resolution of the model and underlying equations (description of flow not integrating small-scale obstacles). An inverse approach was thus undertaken to approach the avoided damages related to NBS. Various values of runoff reduction (in %) were forced in the model and their effects in terms of damage reduction was computed. A relationship between the reduction of runoff and the reduction of damage was therefore estimated. The reduction of runoff (in %) resulting from NBS strategies was estimated simply by considering it equal to the % of rainfall stored in NBS (due to water retention capacity). Both, these estimations provided the building block to assess avoided damages due to NBS.

In the Brague case, the NBS strategy was directly included in the model by modifying bridge geometries, widening the river channel, lowering ground level on wetlands, changing the roughness coefficients where land use changed and removing effects of woody debris

Assessing avoided damages

The Mean Annual Avoided Damages (MA(A)D) is evaluated by estimating the reduction of damages obtained with NBS strategies for different return period and by summing the product of the avoided damages multiplied by the probability of occurrence of each rainfall event.

In the Lez and Brague case studies, the calibrated damage curves on residential houses has been used to simulate the effect of runoff reduction (Lez) and flow depth reduction (Brague) on damage. Damage was computed for several return periods [START_REF] Cgsp | Rapport Quinet: Évaluation Socioéconomique Des Investissements Publics[END_REF][START_REF] Foudi | Integrated spatial flood risk assessment: the case of Zaragoza[END_REF][START_REF] Perini | Is greening the building envelope economically sustainable? an analysis to evaluate the advantages of economy of scope of vertical greening systems and green roofs, Urban Forest[END_REF] and 100 years in the Lez, 20, 100 and 500 years in the Brague) and then averaged. Differences between BAU and strategies enabled to compute the avoided damages. In the Lez case, an increase of 28% was subsequently applied as compared to residential damages to account for total direct damages (This ratio was estimated for the 2014 events). [ 20 , 39 ]).

Fig. 4.

Stepwise approach for ES valuation when direct valuation approaches are used [START_REF] Herivaux | Natural Capital and Ecosystem Services to Valuate Co-Benefits of NBS in Water Related Risk Management[END_REF] Co-benefits assessment

The co-benefits assessment was carried out with a two-stage approach with (1) the identification of co-benefits and (2) the monetary valuation of those co-benefits. As recommended by Nesshöver et al. [START_REF] Nesshöver | The science, policy and practice of nature-based solutions: an interdisciplinary perspective[END_REF] , a strong involvement of local stakeholders was organised throughout the process in order to integrate their perceptions and knowledge.

Identification of co-benefits

In the three case studies, the identification of co-benefits relied on the organisation of focus groups in which potential benefits of NBS strategies were discussed with local stakeholders. Three existing co-benefits classifications and frameworks were used as a basis for discussion: (i) the Millennium Ecosystem Assessment [START_REF]Ecosystems and Human Well-being: Biodiversity Synthesis[END_REF] , (ii) the common international classification of ecosystem services (CICES) [START_REF] Haines-Young | Common International Classification of Ecosystem Services (CICES) V5.1 and Guidance on the Application of the Revised Structure[END_REF] , (iv) the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES) framework [START_REF] Díaz | Assessing nature's contributions to people[END_REF] for the identification ecosystem services. The EKLIPSE framework was used [START_REF] Raymond | A framework for assessing and implementing the co-benefits of nature-based solutions in urban areas[END_REF] for the identification of challenges in urban contexts.

These frameworks were finally combined in order to embrace a wide range of potential co-benefits and specific local issues. In the Lez case study, for instance -a watershed with 50% of natural areas and 30% of agricultural areas-ecosystem services classifications (MEA and IPBES) were used, while in the Rotterdam case study -an urban neighbourhood -the EKLIPSE framework was used as a core framework for co-benefits identification due to its comprehensive coverage of urban issues. In the Brague, the co-benefit list was tailored after three focus group meeting dedicated to flood protection, environment and quality of life.

Co-benefits valuation

Despite our acknowledgement of the diversity of values associated with NBS co-benefits [START_REF] Jacobs | A new valuation school : integrating diverse values of nature in resource and land use decisions[END_REF] , we focus in this paper only on the monetary valuation of co-benefits with the view to carry out the CBA. Two different valuation techniques were used to undertake a monetary valuation of co-benefits in the different case studies: direct valuation approaches and stated-preference approaches.

Direct valuation approaches (market price and cost-based methods) were used in the Rotterdam case study, to valuate seven co-benefits, namely climate mitigation through carbon storage, air quality regulation, water cycle regulation, urban regeneration, human health and wellbeing, and aesthetic amenities. These approaches rely on two main steps ( Fig. 4 ):

• Step 1: the quantification of the level of ecosystem services provided by the NBS strategy (compared with the baseline) with bio-physical indicators (e.g., annual carbon sequestration expressed in t-eqCO2/year; water availability expressed in m3/year) derived from models, functions or reference values obtained in similar contexts; • Step 2: the monetary valuation of the change in the ecosystem service level derived from market prices (when market exists), replacement costs (costs required to provide a similar ecosystem service with a human engineered solution) or avoidance costs (costs that would occur if the ecosystem service were lost).

These approaches provide biophysical and monetary indicators for each ecosystem service. However, they do not reflect the total economic value of these ecosystem services, as they only capture direct use values. Results should thus be considered as lower bound estimates.

Stated preference approaches, namely the Contingent Valuation Method and the Discrete Choice Experiment [START_REF] Vic | Contemporary guidance for stated preference studies[END_REF] , were used in the Brague and the Lez case respectively. These approaches rely on representative surveys of the population to estimate people's willingness to pay for a hypothetical modification of the environment (400 respondents in the Lez and 405 in the Brague), here the implementation of NBS strategies. In both cases, the survey aims at evaluating residents' Willingness to pay for different NBS strategies. They allow the estimation of total monetary values of NBS strategies and associated bundles of ecosystem services, without seeking to evaluate ecosystem services one by one. The stated preferences surveys are detailed in Gnonlonfin et al. [START_REF] Gnonlonfin | DELIVERABLE 6.3 DEMO Insurance value assessment report-Part 7: France -Brague DEMO[END_REF] and Hérivaux and Le Coent [START_REF] Hérivaux | Introducing nature into cities or preserving existing peri-urban ecosystems ? analysis of preferences in a rapidly urbanizing catchment[END_REF] .

Cost-Benefit Analysis of NBS in the three case studies

The results of the monetary assessment in the three case studies are summarized in Table 1 and Fig. 5 .

In Brague and Rotterdam the cost of implementation and maintenance of grey solutions is higher than the cost of NBS strategies for the same level of risk management (grey alternatives were not evaluated in the Lez case). This confirms statements mentioning that NBS may be more cost effective solutions than grey solutions as they are less costly. Indeed, for the same level of avoided damage, the NBS solutions are 15% and 63% less costly than the grey solutions, in the Rotterdam and the Brague case study respectively.

The cost effectiveness of individual NBS measures has also been investigated in the Lez. In this case, the cost of different measures is compared with a proxy of the level of service: here the cost per m 3 of water retention. This analysis shows a very large heterogeneity of costeffectiveness of individual NBS measures. For example, in the Lez case study, the cost-effectiveness of green roofs is extremely low because of the large cost of green roofs as compared to their limited water storage capacity with 1282-1582 € of investment/m 3 of retention while vegetated bioswales cost 102-131 of investment/m 3 of water retention. This large difference of magnitude is confirmed in the Rotterdam case (See Appendix A)

In urban areas, taking into account the opportunity costs of NBS can totally change the estimation of their cost advantage. Considering that NBS require a large spatial extent as compared to traditional grey strategies, the inclusion of opportunity costs has a strong weight in the overall cost estimation, especially in urban areas where land value is high. As mentioned in the methodological section, we however estimate higher bound of opportunity cost. This point is discussed in the last section.

In the three cases, avoided damages benefits are not sufficient to cover investment and maintenance costs, as can be seen in the three case studies. This result needs to be nuanced because our estimations only accounts for a share of the avoided damages, with a restriction on direct damages. Indirect damages, such as the macro-economic impact of floods, due to their effect are not considered, although they can be significant. The assessment also does not consider the potential of protection measures on other non-monetary but essential indicators such as the capacity to reduce the exposition (number of residents in flood prone areas), limiting risk of deaths, injuries or post-traumatic stress.

Co-benefits represent the largest share of the value generated by NBS strategies in all three studies. This result does not depend on the method used for the estimation of co-benefits, since revealed preference methods have been used in the Lez and Brague case studies while direct valuation has been used in Rotterdam.

There are no clear-cut conclusions on the overall economic efficiency of NBS in our assessments. Indeed, NBS strategies have a BCR close to 1 or slightly superior on average in Lez and Brague and below one in Rotterdam whatever the strategy. The picture is more positive if we exclude opportunity costs from the economic analysis. Interestingly however, for Brague and Rotterdam, the economic efficiency of NBS strategies is nevertheless much higher than the one of grey strategies.

The Benefit Cost ratio should however not be the only criteria considered. For example, the level 1 NBS strategy in the Lez has the highest Cost-Benefit ratio however, the rate of avoided damages on implementation cost is extremely low, since this strategy has very limited effect on flood protection and is thus not satisfactory to reach flood risk reduction goals. Although this strategy may be cost-efficient if all benefits are considered, it could not be considered a valid alternative for municipalities aiming at addressing flood risks and should therefore be combined with other flood management strategies.

Discussion and conclusion

This article presents a methodological approach for the evaluation of NBS aiming at water risk and the results of its application to three case studies. This process has led to the identification of lessons learnt on the methodology.

The economic valuation of NBS strategies first requires a large effort for the design of strategies. This step requires the participation of stakeholders and preliminary modelling approaches. It is fundamental because the quantification of the physical characteristics and impacts (e.g. retention capacity, number of trees) is the basis for the estimation of their costs and benefits. The design of alternatives is also a key step in the economic assessment of any project. The innovative nature of NBS strategies as compared to traditional solutions nevertheless requires an additional effort in that aspect, since knowledge is not always available; participants need to be informed and engineering capacity for the design of option may not be available.

Second, cost estimates mainly rely on the transfer of existing values evaluated in other projects except in the Rotterdam case in which specific cost evaluation was undertaken for some NBS measures. This reliance on a diversity of sources gives rise to a high level of uncertainty. Costs can indeed vary greatly depending on the exact feature of the NBS and on local contexts. In order to reduce uncertainty, costs should either be directly valued locally or rely on local references presenting the same technical specifications.

Third, on opportunity cost, the approximation we used to estimate opportunity costs is relatively coarse and may lead to an overestimation of this cost. In Lez and Rotterdam, two urban cases, land price is used as a proxy of opportunity costs, even though NBS are developed on public areas. It provides an estimation of the fact that this space cannot be used for other profitable uses. Whether all public space may have other profitable use, such as sidewalks for example, is unclear. This area may need further investigation in the future.

Forth, in order to assess the avoided damages granted to NBS strategies, both simple, straightforward methods and advanced models are necessary to estimate fully the effect of NBS on the intensity and spa-Fig. 5. Net Present Value of the costs and benefits included in the CBA of Brague, Rotterdam, Lez and Medina for the various strategies. The average BCR is indicated above histograms. tial extent of hazards, especially when assessments are carried out at the catchment scale. The evaluation of avoided damages depends on the availability of data to be able to link the reduction of hazard to a reduction of damages. The synthetic character of this paper presenting multiple case studies should not mask the important disciplinary and interdisciplinary work behind each economic analysis [START_REF] Coent | Demo Insurance Value Assessment[END_REF] .

Fifth, we report on the assessment of co-benefits through monetary approaches. The valuation of nature or ecosystem with monetary approaches is a highly divisive question among scholars. These last years, there is a growing number of scientists and practitioners who explore how combinations of ecological, socio-cultural and economic valuation tools can support environment valuation and land-use decision-making. In fact, there is a growing body of literature, which argues that valu-ation approaches of ecosystem services that target single value-types, be it economic, ecological or socio-cultural values fail to capture the importance of nature and to represent fully the society and its worldviews, interests and preferences. As a response, integrated valuation approaches are increasingly put forward (Gómez-Baggethun and Barton, 2013; [START_REF] Jacobs | A new valuation school : integrating diverse values of nature in resource and land use decisions[END_REF] ). In this article, we only report on the monetary valuation of co-benefits that could be integrated in the CBA, although other valuation methods of co-benefits using socio-cultural or ecological methods could be integrated.

Finally, our economic assessment methodology bears the limits inherent to every economic analysis with ecological or environmental variables. The multiplicity of models required for the estimation of the different costs and benefits increases their overall uncertainty. Only the magnitude of costs and benefits should be compared rather than the precise values we have presented. In addition, only indicators that could be evaluated monetarily are included in this study. Other indicators such as non-monetary impacts on flood risk, co-benefits that could not be or partially be valued monetarily such as social and environmental indicators are important in the decision making process for the development of NBS. Their inclusion would require the development of a Multi Criteria Decision Analysis framework. Some recommendations can be drawn from the main results of this study. First, NBS aiming at reducing water risks cannot be assumed to improve systematically economic welfare, since BCR lie between 0.5 and 1.3. It is therefore fundamental to carry out thorough case-specific economic valuations of a diversity of strategies, involving NBS, grey and hybrid solutions, in order to identify the most adequate strategy for water risk management and to address territorial challenges. In a context of limited public resources, economic valuation can help identifying the adequate solution to address water risks.

A preliminary step to screen measures to improve the overall economic efficiency of NBS strategies would be to carry assessments of the cost effectiveness (in terms of risk reduction) of the individual measures constituting these strategies. This preliminary assessment could help designing economically efficient NBS strategies, with combinations of cost-effective NBS measures (e.g. [START_REF] Bokhove | A cost-effectiveness protocol for flood-mitigation plans based on leeds' boxing day 2015 floods[END_REF][START_REF] Cgsp | Rapport Quinet: Évaluation Socioéconomique Des Investissements Publics[END_REF] ). This rule of thumb should however not overlook the importance of co-benefits in the value of NBS. For example, small bioswales with simple plant cover may be more cost effective for water retention than large bioswales planted with trees but their production of co-benefits is also very limited; in this case, public money available for biodiversity or nature in city might help decide upon the two strategies.

The large share of co-benefits in the overall value of NBS aiming at reducing water risks combined with the limited avoided damages has strong implications on NBS funding and business models. Indeed, support from sectoral policies is generally conditioned to a positive costbenefit analysis on the specific benefit they target, such as for example flood risk reduction in our cases. However, NBS appear to be economically efficient only when all the benefits they generate are considered. Implications for project set up and financing are very significant. Rules applying for the public funding of NBS should therefore be adapted in order to take into account cross-sectoral benefits of NBS. This requires modifications of the silo approach currently still prevailing in the application of public water risk policies. On the other hand, considering the significance of co-benefits for NBS economic value, it is important to ensure that the co-benefits are maximized during NBS design and implementation. For example, if an open retention basin is created in an urban environment, the vegetation included as well as its facilities for recreational activities should be considered with as much care as the technical specifications required for flood management. This conclusion invites decision makers to consider non-built environment, especially in urban environment, as rare multifunctional space for which the production of overall benefits should be maximized (risk reduction and "co "-benefits). This also suggests developing research methodologies that facilitate the identification of optimal spatial layout of NBS in a constrained urban environment [ 27 , 59 ].

Fig. 3 .

 3 Fig.3. Structure of any CAT models (adapted from[ 20 , 39 ]).

"Many public investment projects use land as a capital asset, which may be stateowned or purchased from the general government budget. Whenever there are alternative options for its use, land should be valued at its opportunity cost[…]. This must be done even if land is already owned by the public sector. If it is reasonable to assume that market price captures considerations about land's utility, desirability and scarcity, then it can generally be considered reflective of the economic value of land. "

AERMC (2011). Elaboration d'un outil de détermination des coûts de restauration hydromorphologique des cours d'eau du bassin versant local et des bassins RMC. Agence De l'Eau Rhone Mediterranee Et Corse.

Acknowledgement

This research was funded by the H2020 project NAIAD (Grant 730497) from the European Union's Horizon 2020 research and innovation programme. We are grateful to Elena Lopez-Gunn and Laura Vay for their dedicated coordination of the project. We also want to thank local stakeholders for their involvement in the design and implementation of the economic assessments in the three case studies.

Table 1

Overview of results of the economic analysis in net present value in millions € discounted over the time horizon of the evaluation. Average values are indicated in bold and value ranges reflecting uncertainty (when evaluated) are indicated in italic between brackets.

Declaration of Competing Interest

The authors whose names are listed immediately below certify that they have NO affiliations with or involvement in any organization or entity with any financial interest (such as honoraria; educational grants; participation in speakers' bureaus; membership, employment, consultancies, stock ownership, or other equity interest; and expert testimony or patent-licensing arrangements), or non-financial interest (such as personal or professional relationships, affiliations, knowledge or beliefs) in the subject matter or materials discussed in this manuscript.

LE COENT Philippe, GRAVELINE Nina, ALTAMIRANO Monica, AR-FAOUI Nabila, BENITEZ-AVILA Camilo, CALATRAVA Javier, DOUAI Ali, GNONLONFIN Amandine, HERIVAUX Cécile, MARCHAL Roxane, MONCOULON David, PITON Guillaume Thomas Biffin and Kieran Wilhelmus Jacobus Dartée, hereby declare that Field Factors B.V., nor their personal affiliation with Field Factors B.V. as employees raise any pecuniary or other conflicting interests, direct or indirect, in any matter with their contribution to the research conducted for the paper "Is-it worth investing in NBS aiming at mitigating water risks? Insights from the economic assessment of NAIAD case studies. "

Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi: 10.1016/j.nbsj.2021.100002 .