Yassine Rahib
email: yassine.rahib@cnrs-orleans.fr

Toufik Boushaki

Brahim Sarh

Jamal Chaoufi

Combustion and pollutant emission characteristics of argan nut shell (ANS) biomass

Keywords: Biomass combustion, argan nut shell, combustion behaviour, fuel burn rate, pollutant emissions, ash analysis

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

1. Introduction

Nowadays, there is significant interest in biomass feedstock for applications in green energy as these materials represent an abundant, clean and renewable alternative energy resource. In fact, biomass is considered as the fourth largest source of energy following petroleum, coal and natural gas, with a current world demand for energy estimated at 53 EJ [START_REF] Kousksou | Renewable energy potential and national policy directions for sustainable development in Morocco[END_REF]. Most applications of this global energy supply concern an assortment of energy needs, including generating electricity, heating homes, cooking purposes and some industrial applications [START_REF] Balat | Biomass energy in the world, use of biomass and potential trends[END_REF]. However, a major part of the rural population in developing countries is dependent on biomass, mainly as traditional fuel for cooking and heating. Agricultural residues are the most widely available biomass materials with a high energy potential.

Werther et al. [START_REF] Werther | Combustion of agricultural residues[END_REF] estimated that over three billion tons of agricultural residues are generated world-wide. In addition, this resource is considered to be less controversial than fossil fuels, low cost and thus represents an important energy resource for countries with a massive agricultural production.

The present study concerns the energy recovery of agricultural waste in the Mediterranean basin. Argan is one of the agricultural resources producing this waste during the argan oil production process; most of the waste is generated by the argan nut shell (ANS) [START_REF] Zouhair | Typical characterization of argane pulp of various Moroccan areas: A new biomass for the second-generation bioethanol production[END_REF]. The ANS can be considered as an attractive source of biomass, since it is procurable in abundance and does not contend with food production. The raw materials of ANS used in this work were from the region of Sousse-Massa-Draa (southwestern Morocco) in which the development is based on agricultural activities. The annual production of ANS is estimated at 60 000 tons per year.

Among thermochemical conversion processes, combustion is a promising technology and the most common option for biomass conversion [START_REF] Thomas | Combustion and Co-combustion of Biomass: Fundamentals, Technologies, and Primary Measures for Emission Reduction[END_REF]. Fixed-bed combustion is considered a suitable and routine technique to optimize and transform agricultural residues into thermal energy [START_REF] Asthana | Biomass as fuel in small boilers[END_REF]. Studies on the combustion characteristics of fixed beds of biomass have been reported by many papers. Khlifi et al. [START_REF] Khlifi | Investigation of the combustion characteristics of briquettes prepared from olive mill solid waste blended with and without a natural binder in a fixed bed reactor, Biomass Convers[END_REF] studied the combustion of briquettes prepared from olive mill solid wastes in the same reactor as the one used herein. They reported the influence of the binder added to the prepared briquettes on combustion efficiency and pollutant emissions. Khor et al. [START_REF] Khor | Straw combustion in a fixed bed combustor[END_REF] and Cepic et al. [START_REF] Cepic | Combustion characteristics of wheat straw in a fixed bed, Energy Sources, Part A[END_REF] investigated the combustion characteristics of straw in a fixed-bed reactor. Roy et al. [START_REF] Roy | An experimental study of combustion and emissions of biomass pellets in a prototype pellet furnace[END_REF] reported the combustion and emission results obtained during the burning of four biomass pellets in a prototype pellet furnace. Elmay et al. [START_REF] Elmay | Energy recovery of date palm residues in a domestic pellet boiler[END_REF] studied the energy recovery of date palm residues from Tunisia, in a domestic pellet boiler. The combustion parameters such as air flow and fuel particle size have been investigated in the literature. Ryu et al. [START_REF] Ryu | Effect of fuel properties on biomass combustion: Part I. Experiments -Fuel type, equivalence ratio and particle size[END_REF] experimentally investigated the effect of particle size and air flow on the combustion characteristics of four biomass samples by determining equivalence ratio, combustion temperature, ignition and burning rate. Rahib et al. [START_REF] Rahib | Combustion analysis of fixed beds of argan nut shell (ANS) biomass in batch type reactor[END_REF] briefly presented the combustion and emission characteristics of raw argan nut shell (ANS) in a fixed-bed reactor. The focus was placed on the relationship between the nourishing tissue of the argan almond and SO2 emissions. Onabanjo et al. [START_REF] Onabanjo | An experimental investigation of the combustion performance of human faeces[END_REF] studied the combustion performance of human faeces by determining the combustion temperature, the fuel burn rate and the combustion efficiency. They varied air flows, biomass sizes, bed heights, and fuel ignition mode parameters in order to determine the optimum conditions for converting the faecal biomass into energy. Meng et al. [START_REF] Meng | Parametric studies on corn combustion characteristics in a fixed bed: Primary air flow rate and different corn lengths[END_REF] examined the effect of varying corn straw lengths and primary air flow on the combustion characteristics. They suggested that these two parameters directly affect the burning rate, the bed temperature, the combustion emissions and the boiler efficiency. The focus of our experimental research was to identify the conditions that can lead to improved combustion of ANS in biomass combustion installations with ~50 MW output.

To comprehend the combustion process of ANS, the present paper investigates the influence of particle lengths and air flows on combustion quality in a laboratory furnace. To the best of our knowledge, no studies have been reported to date in the literature on the combustion performance of ANS in a laboratory combustor. The first part of this work is a parametric study to analyse the effect of different air flows. Measurements were carried out on raw ANS and three different particle lengths chosen to analyse the size effect on combustion. A comparison with wood pellets was performed. Results include flame structures and stabilities for all the selected samples as well as ash analysis at different running conditions. In view of the absence of ANS combustion studies, this work would be of great interest to biomass combustion studies.

Materials and methods

This study uses the ANS as raw biomass for combustion. Physicochemical characterization was checked through ultimate and proximate analyses as well as the energy content measurement. Ultimate analysis was carried out, using a FLASH 2000 CHNS/O analyser (Thermo Scientific), to determine carbon (C), hydrogen (H), oxygen (O), nitrogen (N) and sulphur (S) weight fractions. Proximate analysis was done using a Shimadzu analyser DTG-60 according to the ASTM standard procedures. A more detailed description of the experimental protocol can be found in our previous work [START_REF] Rahib | Physicochemical and thermal analysis of argan fruit residues (AFRs) as a new local biomass for bioenergy production[END_REF]. A calorimetric bomb (Parr 2100) was used to measure the high heating value (HHV). The low heating value (LHV) was calculated based on water and ash free contents. The energy density was obtained by multiplying bulk density by the LHV. The empirical formula was computed based on C, H and O content (masse fractions from ultimate analysis). By taking Carbone as reference, the empirical formula of ANS is calculated as CH1.46O0.62 (where 1.46 and 0.62 represent H/C and O/C molar ratios). The basic chemical reaction of ANS stoichiometric combustion can be written as: CH1.46O0.62 + 1.05 (O2 + 3.76 N2) CO2 + 0.73 H2O + 3.97 N2 + Q (heat) [START_REF] Kousksou | Renewable energy potential and national policy directions for sustainable development in Morocco[END_REF] This equation was used to determine the theoretical air-fuel ratio.

A scanning electron microscope (SEM) was used to determine the physical nature of raw ANS and ash at different magnifications. The equipment used was a JEOL JSM-IT100 SEM model, connected to a dispersive energy X-ray spectroscopy (EDS) unit which was used to access elemental composition in a semi-quantitative way. To set up this experiment, the tested material was stuck on a thin layer of carbon.

Combustion of the ANS took place in a batch fixed-bed reactor. This device was developed at ICARE-CNRS to investigate the thermochemical conversion process of agricultural biomasses. Fig. 1 shows a schematic diagram of the experimental setup which consists of: (1) an air fan adjusted by a frequency regulator (0-50 Hz), (2) a combustion chamber composed of: a bottom ash recovery, a fixed grate, a rotating leveller, then a confinement where the flame arises, (3) a cyclone connected by a flue pipe from the combustion chamber outlet, (4) a flue gas scrubber. The main components and measuring devices of the experimental rig are also illustrated.

The combustion chamber is divided into two compartments. It can be equipped with ten Ktype thermocouples inserted into the chamber centre to monitor the variation in flame and maximum temperatures. Table 1 summarizes specific positions of the used thermocouples (TC1-TC6). The temperature profiles were recorded every second by a Graphtec data logger.

Table 1 Positions of the thermocouples along the combustion chamber. In the experiments, the composition and temperatures of the combustion gases were measured in-situ at the combustion chamber outlet. Before analysing the flue gas, the apparatus was calibrated. All emission profiles were recorded in the steady state zone. The gas analyser used (Kimo KIGAZ 500) incorporates infrared and electrochemical measurement techniques. The maximum response time of this instrument is less than 50 s. Therefore, a sampling duration of 1 min was used to obtain stable values. At the beginning of each experimental test, 1 kg of ANS is placed on the grate. Then, the leveller is switched on to establish homogeneous distribution of the biomass bed. Afterwards, ignition of the biomass is started on the entire surface of the bed using a gas blow torch and a small amount of liquid fuel to promote the onset of combustion. A long-distributed flame throughout the upper surface of the bed indicates a successful ignition and combustion test (see Fig. 2). The air enters from the boiler bottom through the bed into the combustion chamber. The experimental protocol followed is relevant for fixed grate and domestic boilers since (a) this configuration can present the same contact between biomass particles in the bed, (b) the biomass successively undergoes drying, devolatilization and char combustion and (c) geometric and operational configurations relating to the aspect ratios of biomass particles, dimensions of the bed and the flow paths of combustion gases are the same. Thus, some of the investigations made herein could be quantitatively applicable to industrial combustion systems. The MCE under different operating conditions was calculated based on CO and CO2 emissions as described in equation (2):

MCE (%) = CO2 (%) / [CO2 (%) + CO (%)] (2)
The FBR (g s -1 ) as expressed in equation ( 3) signifies the time required for complete combustion of the biomass fuel consumed, at the end of each individual experiment, in mixture with air. It indicates the rate of energy released into the system. FBR (g s -1 ) = mf (g) / t(s)

The FBR can be used to evaluate the biomass bed velocity (BBV) which was calculated by equation ( 4). Generally, the BBV increases with increase of FBR.

BBV (mm.s -1 ) = FBR (kg.s -1 ) / [Bulk density (kg.m -3 ) * grate area (m 2 )] (

The end of each combustion experiment was selected to be the time moment when the temperature recorded from TC1 or TC2 decreased below 250 °C. At each air supply and fuel particle length, the performance criteria were tested in the steady state zone (flaming mode)

when there was almost no change in flame temperature.

In order to shed light on the evolution of the combustion gas concentrations and temperature, we studied the impact of excess air on the combustion of ANS. The excess air is determined indirectly by measuring the concentration of unreacted oxygen in the flue gaz. A better approximation of the excess air can be computed using equation 5 [START_REF] Tsi | Combustion Analysis Basics: An Overview of Measurements[END_REF].

% = % . ( % ) * 100 (5)
The concentrations of O2 and CO are obtained from sampling the gas at the combustion chamber outlet. The air factor (λ) and the equivalence ratio ( ) are deduced by:

= % !"# $ + 1 ; '( )*+ , *-. ( /) = = $ 0 (6)

Results and discussion

Biomass characterization

Energy content, ultimate and proximate analyses of the raw sample are summarized in Table 2. The relatively high moisture content of ANS (9.5%) is in the range of some biomass sources used in thermal conversions [START_REF] García | Biomass sources for thermal conversion[END_REF]. However, the low ash content will positively impact the combustion efficiency and eliminate slag formation in the boiler. The high content of volatiles (61%) is an attractive characteristic that can improve the ignition process during combustion. The carbon and hydrogen contents were found to be 51.3 and 6.32% respectively. ANS is also listed to have an impressively high heating value (HHV = 18.3 MJ.kg -1 ) despite the significant oxygen content. A critical property of biomass materials is bulk and energetic density, which are linked to storage and transport costs [START_REF] Rahib | Experimental analysis on thermal characteristics of argan nut shell (ANS) biomass as a green energy resource[END_REF]. The values found for these two properties were 596 Kg.m -3 and 10.13 GJ.m -3 (for bulk and energetic density, respectively). This indicates that ANS can be an excellent candidate for thermochemical conversion [START_REF] Rahib | Physicochemical and thermal analysis of argan fruit residues (AFRs) as a new local biomass for bioenergy production[END_REF][START_REF] Rahib | Experimental analysis on thermal characteristics of argan nut shell (ANS) biomass as a green energy resource[END_REF][START_REF] Rahib | Non-isothermal kinetic analysis of the combustion of argan shell biomass[END_REF]. Moreover, the hardness of ANS makes their storage and transport easier and ensures their long durability. The low values of N and S are a good indicator concerning the release of NOx and SOx pollutants to the atmosphere [START_REF] Rahib | Physicochemical and thermal analysis of argan fruit residues (AFRs) as a new local biomass for bioenergy production[END_REF]. The theoretical air volume per kg fuel, calculated based on the ultimate analysis of the fuel, was found to be 4.75 Nm 3 .kg -1 . It refers to the amount of air necessary to complete combustion.

The stoichiometric air fuel ratio (AFR) was also calculated (6.23 kg-air/kg-fuel) to identify the amount of air and fuel required for complete combustion. Energetic density (GJ.m -3 ), AFR: air fuel ratio (kg-air / kg-fuel).

a dry ash free basis, b as received basis

The photo in Fig. 3 shows the morphological characteristics of the raw sample. It was not subjected to any handling apart from natural dehydration in atmospheric air to eliminate external moisture. It can be seen that the ANS presents a polygonal organization composed of smooth and homogeneous zones indicated by the letters (x) and some roughness on its external surface (y). Damage to the external area of the material at the end of some particles (z) was observed, perhaps because of the fruit kernel crushing process. The SEM-EDS results

show that ANS is mainly composed of carbon (C) and oxygen (O). Minor amount of Al and Si were detected in the cracked zone (zone 001). Fig. 3 Fig. 4 shows the microstructure of the ash content of raw ANS. This material was obtained by the LOI (loss on ignition) method, i.e. raw ANS was combusted at 850 °C during three hours in a muffle oven according to the EN NF M03-003 procedure to eliminate all carbon content [START_REF] Leyssens | Energetic performances and environmental impact of the combustion of cardboard/sawdust in a domestic boiler[END_REF]. The morphology of the ash reveals the existence of small agglomerates (not significant) and the amorphous shape of particles (partially molten particles: spot 003). As we can see from elemental analysis, the ash contains mainly oxygen. The amount of carbon was very low and a significant amount of potassium K was identified (spot 1 and 2

Visual observation of the combustion

A general trend of combustion behaviour in fixed beds was observed. Fig. 5 shows the flame images from the videos of ANS as a function of three air flows and the particle sizes.

This flame represents the combustion of pyrolysis gas during the whole process [START_REF] Polesek-Karczewska | Front velocity in the combustion of blends of poultry litter with straw[END_REF]. The wood pellets (WP) were also included for the purpose of comparison. The higher air flow supply (180 m 3 .h -1 ) affected combustion stability, slowed down the combustion process and extinguished the flame (cases LP (large particle) and SP (small particle)). In the RP (raw particle) case, it was noticed that a higher air flow did not extinguish the flame but limited its progress along the combustion chamber. This can be attributed to the presence of broken particles in the raw ANS, which need more oxygen to complete the burning process (see further explanations in section 3.4). In the BP (broken particle) and WP cases, the high air supply did not perturb the flame; the combustion seemed homogeneous, and the flame was very stable. With a lower air flow supply (72 m 3 .h -1 ), the flame images in RP, LP, SP, BP and WP showed intense luminosity, which indicates the existence of some soot because of the rich regime of biomass. The luminosity decreased with increasing air flow, since oxygen addition improved the combustion process (fuel lean conditions). From a structure and stability point of view, flames in the case of BP under the studied air supply were characterized by a regular shape and a relatively smooth and continuous flame front. This can be explained by the existence of a pre-mixed zone in which the volatile gases released by the broken particles mixed well with the surrounding air. This behaviour is similar to premixed gas combustion as in [START_REF] Yuzuriha | Effects of particle size distributions on flame propagation behavior through dust clouds of PMMA[END_REF] where the combustion reactions are mainly affected by chemical kinetics. The LP and SP probably take a lot of time to devolatilize [START_REF] Ryu | Effect of fuel properties on biomass combustion: Part I. Experiments -Fuel type, equivalence ratio and particle size[END_REF][START_REF] El-Sayed | An experimental study of combustion and emissions of wheat straw pellets in high-temperature air flows[END_REF], which contributes to delaying ignition and to a more irregular flame shape. The flame becomes increasingly stable when particle sizes decrease.

Effect of air flow

The combustion tests of raw ANS samples in varying air flow conditions were performed to analyse the effect of this crucial parameter in achieving the highest combustion performances. Fig. 6a-c reveals a typical flame temperature profile (a), combustion behaviour (b) and combustion gas concentration (c) inside the reactor with a 36 m 3 .h -1 air supply (528 kg.m -2 .h -1 ). The process can be divided into four stages as illustrated in Fig. 6a: (1) start-up

(2) steady-state (3) combustion of residual char and (4) switch off. Similar behaviour was identified in the other air supply cases with some oscillation observed in the steady state zone. (stage 4). Fig. 6c shows the gas emission profiles as a function of combustion time. The O2 concentration decreased swiftly as the combustion process proceeded. This was followed by an increase in CO2, CO, CH4 and NOx (NO + NO2). The CO2 content is predominant because of the higher carbon content in ANS. When the biomass flame began to drop (Switch off: char mode), the O2 concentration began to rise, while CO, CO2, CH4, NOx and SO2 declined regularly, indicating the end of combustion stage. Generally, the combustion process of ANS was shown to be dominated by the flaming mode. The combustion of the remaining char, after the extinction of the flame, was not a major event [START_REF] Rahib | Non-isothermal kinetic analysis of the combustion of argan shell biomass[END_REF]. This behaviour was similar to that reported in [START_REF] Calvo | Characterization of operating conditions of two residential wood combustion appliances[END_REF]. The bold arrow (dotted line) indicates the theoretical stoichiometric combustion regime. The instantaneous ER measured at different air flow rates (except for 36 m 3 .h -1 ) is located in the "sub-stoichiometric" fuel lean zone (ER < 1 at the interval of 300 and 700s) of the transient combustion period. With an air flow supply of 36 m 3 .h -1 , the rich regime appears (ER >1) in the combustion period between 370 and 550s. In this zone, all the oxygen was consumed (temporary oxygen deficiencies: O2 < 0.1%) and high emissions of CO and CH4 were observed (see Fig. 6c). Moreover, the intermittent flame zone (ER < 0.45) characterizes the rapid extinguishes of the flame due to convective cooling (when the air flows are not favourable: Fig. 5, air flow rate of 108 m 3 .h -1 ). The results in Fig. 7b reveal that the maximum flame temperature (registered by TC1 or TC2) increased progressively with increasing of the air flow until a value of 886 °C corresponding to an air flow of 108 m 3 .h -1 . Beyond this flow rate, the flame temperature decreased with the increase of the air flow. The exhaust gas temperature had the same behaviour, with a maximum value of 767 °C corresponding to the same air flow. Similar behaviour was also observed in the case of FBR, which presented maximum values of 1.39 and 1.43 g s -1 for an air flow of 108 and 144 m 3 .h -1 , respectively.

The FBR decreased gradually with further increase in the air supply (case of 180 m 3 .h -1 ). Fig. 7c reveals that the modified combustion efficiency ranged from 88 to 97% as a function of the studied range of the air flow (36 to 180 m 3 .h -1 ). It is shown that MCE increased then decreased with the air flow, with a maximum value (97%) observed at 108 m 3 .h -1 . The BBV presented the same behaviour as FBR with maximum values at 108 and 144 m 3 .h -1 corresponding to the same air flows. As noted by Khor et al. [START_REF] Khor | Straw combustion in a fixed bed combustor[END_REF], the combustion temperature and burning rate of straw increased significantly with an increased in air flow velocity until a critical point. Thereafter, they decreased with a further increase in primary air flow due to convective cooling, because the impact of increased convection was stronger than the effect of increased temperature at high flow rate. Onabanjo et al. [START_REF] Onabanjo | An experimental investigation of the combustion performance of human faeces[END_REF] observed that the combustion ,< E## F G 5F H% = ;3., ,-*-.,< = * 20.9 K L%M 20.9 K ;%M < = [START_REF] Khlifi | Investigation of the combustion characteristics of briquettes prepared from olive mill solid waste blended with and without a natural binder in a fixed bed reactor, Biomass Convers[END_REF] where Cmean is the mean pollutant concentration; τ is the time of biomass combustion (s); molar volume at STP (0 °C and 1 atm.) = 22.414 l; L%M is the reference oxygen content in % volume and 7 is the measured concentration.

In this Figure, the effect of varying air flow on the combustion process is demonstrated.

The CO concentration in the gas was very high (1.5 10 4 mg.Nm -3 ) with an air flow of 36 m 3 .h - 1 because of the rich regime of biomass. It decreased progressively on increasing the air flow until a value of 3973 mg.Nm -3 corresponding to 108 m 3 .h -1 . Afterwards, the CO concentration increased gradually at high air excess (144 and 180 m 3 .h -1 ) due to a high amount of unburnt biomass, resulting in the increase in C char emissions (short residence time of ANS in the combustion zone). The NOx emissions (calculated based on the measured concentrations of NO and NO2) were relatively weak (below 140 mg.Nm -3 referred to 10% O2 in the fume (Fig. 8)). This was an expected positive result given the very low nitrogen content (0.005% on dry ash free basis). Emissions of CH4 decreased from 688 mg.Nm -3 at 36 m 3 .h -1 to 3 mg.Nm -3 at 180 m 3 .h -1 . With a 108 m 3 .h -1 air supply, the CH4 value was found to be very low (44 mg.Nm - 3 ). It is concluded in this first part that the optimal air supply for the fixed-bed combustion of 1 kg of raw ANS was around 108 m 3 .h -1 , which provided the highest flame and exhaust gas temperatures (886 and 698 °C, respectively), the highest FBR and BBV (1.39 g s -1 and 1.35 mm 2 s -1 , respectively), the highest MCE (97 %) and lower concentrations of pollutant (especially CO). In this case, the ash mass was the lowest (<1%) among the other air flows applied, indicating that practically all the biomass was burned. 20

Effect of particle size

The ANS biomass was classified into three different ranges of lengths: large (2.5-3 cm), small (1-1.5 cm) and broken (< 8 mm). Table 3 displays photographs and the calculated bulk densities (BD) of each classified sample. Fig. 9a-f presents the effect of varying ANS length on combustion temperatures, FBR, MCE, and CO and NOx emissions (corrected at 10% O2). For each case, the performances were assessed at three constant air flows of 72, 108 and 180 m 3 .h -1 , corresponding to weak, appropriate and excess air conditions, respectively (based on the results of raw ANS combustion). This can offer the possibility to investigate the effect of air flows and particle sizes at the same time. The results of raw ANS particles (RP) are included and a comparison with wood pellets is also reported. Fig. 9a andb show the influence of varying biomass length on the combustion temperature. For a low air supply (72 m 3 .h -1 ), the small particles (SP) generated the maximum flame temperature while the broken particles (BP) gave the minimum flame temperature. The results show that flame temperature increased from 834 to 900 °C when the broken particles (BP) were replaced by SP. The two other cases (LP and raw particles) fell between the BP and SP. For the appropriate air supply (108 m 3 .h -1 ), the BP and SP induced the same flame temperature, (910 °C), whereas the LP induced the minimum flame temperature (858 °C) due to the short residence time in the combustion zone. Under high excess air (180 m 3 .h -1 ), the difference in flame temperature was very high for the three ANS sizes. For example, the flame temperature was 525 °C for LP and 952 °C for BP. Results concerning the exhaust gas temperature (see Fig. 9b) exhibited the same evolution as that of flame temperature. The exhaust gas temperatures of BP and WP were very close. Fig. 9c shows that the FBR evolution with the air flow was similar for LP and SP. Depending on the air supply, BP had the highest fuel burn rate compared to the other particle sizes and WP. The LP and raw particle (RP) cases yielded the lowest FBR. In the case of the lower air flow, FBR was 1.13, 1.15, 1.29, 1.45 and 1.40 g s -1 for RP, LP, SP, BP and WP respectively. These values increased under moderate air flow (108 m 3 .h -1 ) to reach 1.39, 1.37, 1.49, 1.77 and 1.60 g s -1 for RP, LP, SP, BP and WP, respectively. Under a high air supply, the FBR decreased for RP, LP and SP (1.35, 1.29 and 1.48 g/s, respectively) but continued to increase for BP and WP (1.93 and 1.80 g s -1 , respectively). Fig. 9d presents the particle length effect on the combustion efficiency. The MCE results of the different cases of ANS particle sizes are completely different to the FBR results. The MCE value in the case of a 72 m 3 .h -1 air supply was 94, 93, 80 and 84% for RP + LP, SP, BP and WP respectively. These values were found to rise for all samples in the moderate air flow (108 m 3 .h -1 ) to reach 97, 96, 98, 81 and 91% for RP, LP, SP, BP and WP, respectively. For the highest air supply (180 m 3 .h -1 ), MCE declined for RP, LP and SP (93, 90 and 93%, respectively) but increased for the BP and WP (90 and 97%, respectively). In the literature, some authors have studied the effect of biomass size on combustion. El-Sayed et al. [START_REF] El-Sayed | An experimental study of combustion and emissions of wheat straw pellets in high-temperature air flows[END_REF], found that the larger the size of the fuel particles, the greater the probable residence time of the volatile gases within these particles. Ryu et al. [START_REF] Ryu | Effect of fuel properties on biomass combustion: Part I. Experiments -Fuel type, equivalence ratio and particle size[END_REF] proved that large particles (thermally thick) have a slow devolatilization rate and more distributed heat transfer to the nearby particles. They noted that temperature gradients in the biomass bed during combustion decrease with increasing particle sizes. This led them to conclude that heat penetration to the cold particles below the hot ones is more extreme for smaller particles. Luo et al. [START_REF] Luo | Experimental study on combustion of biomass micron fuel (BMF) in cyclone furnace[END_REF] demonstrated that the biomass fuel burn rate and maximum combustion temperature increased with the decrease in particle size. The large particles present a greater resistance to heat transfer, and therefore their internal temperature was lower. In the present investigation, the optimal air supply for burning LP and SP was found to be similar to that needed for raw ANS particles (108 m 3 .h -1 ). Flame durations of 1kg ANS combustion were 681, 579 and 726s for 72, 108 and 180 m 3 .h -1 , respectively in case of the LP.

In the case of SP, the flame durations were 549, 558 and 628 for 72, 108 and 180 m 3 .h -1 , respectively. These results agree with those of El-Sayed et al. [START_REF] El-Sayed | An experimental study of combustion and emissions of wheat straw pellets in high-temperature air flows[END_REF]. RP, LP and SP showed the same behaviour for the three air flows used. They increased their performance when the air flow was changed from low (72 m 3 .h -1 ) to moderate (108 m 3 .h -1 ) conditions, but decreased regularly in higher air excess (180 m 3 .h -1 ). For the RP, LP and SP, 180 m 3 .h -1 is an excessive air flow during combustion, since it contributes to convective cooling of the biomass bed, slows down the process and extinguishes the flame (see Fig. 3). Contrariwise, the performance of BP and WP revealed an increasing trend when the air flow was increased. The FBR and the maximum combustion temperature of BP were the highest for the high air flows (108 and 180 m 3 .h -1 ) compared to the other sizes. This can be explained by the fact that when raw particles (RP) of ANS were broken, their contact area with air was greater, which leads to higher combustion reaction rates and greater air flow supply needs. The MCE value obtained for air flow rates of 72 and 108 m 3 .h -1 was low (the case of BP), indicative of a poor mixing process (high CO emissions) as indicated in Fig. 9e. However, an air flow of 180 m 3 .h -1 revealed a lower CO emission and a tolerable MCE value. Hence, it could be concluded that broken particles can be burned better than large particles and reach better combustion performances if the required compromise of mixing air and biomass is achieved. The yields of NOx emissions were found to be below 140 mg.Nm -3 for all the experimented conditions (see Fig. 9f). This was expected since fuel-N, considered as the major source of NOx [START_REF] Khodaei | Air staging strategies in biomass combustion-gaseous and particulate emission reduction potentials[END_REF], was very low.

Ash characterization

The ash of fixed beds of ANS is defined as the amount of solid residue that remains at the end of the combustion test. It is considered as a complex inorganic-organic mixture with a heterogeneous and variable composition [START_REF] Kleinhans | Ash formation and deposition in coal and biomass fired combustion systems: Progress and challenges in the field of ash particle sticking and rebound behavior[END_REF]. Knowledge of the physicochemical properties of biomass ash is useful information in predicting the tendency to form deposits in boiler components. In this study, the ANS and WP ash produced during laboratory scale combustion included bottom and fly ash as shown in Fig. 10. In all the experiments, bottom ash represented the major part of total ash. Coarse particles of unburned char end up as bottom ash while finer ones flow out with gases in the form of fly ash. The colour of bottom ash ranged from light grey and brown to black. At first glance, one can see that the ash particles of raw ANS can be classified into three parts: unburned char marked by yellow diamonds (darker coloured biomass ash), incomplete char combustion marked by the red dotted circle, and totally combusted particles corresponding to the clearest particles (inorganic matter, particularly alkali and alkaline earth metals) marked by red circles in the corresponding figures. A high amount of unburned char was identified in the case of a low air supply (36 m 3 .h -1 ), indicating poor combustion efficiency. On the other hand, it can be seen that the residual bottom ash of WP was composed of solid parts (unburned biomass) which have the same colour as the raw sample (yellow square). The completely burned parts of WP are marked by a blue cross. The high unburned WP can be explained by the high biomass regime with an air supply of 72 m 3 .h -1 . No clear sign of sintering and agglomeration was observed from the ANS ash displayed in Fig. 10a. Fly ash collected from the cyclone container was characterized by a black colour, i.e. a high-unburnt carbon content. Fig. 10b shows the EN 5 O "6"F"5P 45 EN Q"E45 Q G *100) of bottom and fly ash of ANS during combustion tests. It is observed that the bottom ash is generally low (<2%) except for raw, large and small particles under excess air conditions (C). This can be explained from the above results, which reveal that these kinds of particles have shown unstable combustion behaviour with limitations in flame mode. Therefore, the bottom ash is mainly generated by the quantity of unburnt particles as shown in the photos included in Fig. 10b. The amounts of fly ash show an increasing trend with increasing air flow rate. The maximum fly ash content is observed for the broken particles at 180 m 3 .h -1 . These particles with high air flow rate show stable combustion and well distributed flame throughout the bed. After the flame was extinguished, the oxidation of the char part, consisting of small particles, was very short, which favoured the transport of ash particles by the fumes. For a low air flow rate (A), fly ash is not detected. SEM/EDS was used to analyse the residual ash of the studied samples by combining a visual image with elemental analysis. Fig. 11a-c illustrates the morphology of bottom ash from raw ANS and wood pellet samples at different operating conditions. Figures X, Y andZ show the zones marked in Fig. 11c at higher magnifications. The ash of BP of ANS was found to be mainly composed of unshaped particles and fine materials (Fig. 11a). These abundant unshaped particles showed a porous microstructure (Fig. 11b). Wood pellet ash showed mixed morphologies with particles of different shapes and sizes. In the X, Y and Z areas, the dominant number of unshaped materials in WP can be clearly seen (Fig. 11c). Fig. 11a-c also shows the selected areas indicated by crosses and rectangles (from 001 to 010) where the semi quantitative elemental analysis (atom %) was performed. The results of the ash analysis are summarized in Table 4. The morphology of ANS ash obtained during fixed-bed combustion was different from that obtained by LOI (see Fig. 4). No visible aggregation or crystal particles were observed. The porous structure (spots 1 and 4) was mainly composed of carbon (76 %), oxygen (18%) and potassium (5%). Other elements were found in minor amounts (Na, Mg and Ca). The Cl and Al percentage in the bottom ash samples was negligible. WP ash (see Fig. 11c) also contained significant quantities of carbon and oxygen. Ca, K, P and Mg were detected as major elements (>1%), and Na, Si and Al as minor elements (<1%). S and Cl elements were not detected. The alkaline index (AI) is the amount of alkaline oxide in the biomass per unit of energy (kg alkaline per GJ). It was used in this study as an indicator of fouling and slag formation. The existence of such problems is likely for an AI greater than 0.17 kg.GJ -1 and certain for a value greater than 0.34 kg.GJ -1 [START_REF] Khor | Straw combustion in a fixed bed combustor[END_REF][START_REF] Ryu | Effect of fuel properties on biomass combustion: Part I. Experiments -Fuel type, equivalence ratio and particle size[END_REF][START_REF] Blomberg | Free alkali-index for optimizing the fuel mixture in biomass co-firing[END_REF]. Fixed-bed combustion of ANS gave an alkaline index of 0.17 kg.GJ -1 and did not contribute to agglomeration. For WP a low AI value was obtained (0.05 kg.GJ -1 ). In other terms, proximate analysis of ANS reveals a very low ash content (<1.5 %). During combustion, the obtained smaller particle size of ash (with no agglomeration) can be justified by the low temperature operation of the boiler (<1000°C). Additionally, the obtained low values of Na and Cl (minor elements: generally, <1%) in ANS ash are a good indicator for limiting the tendency of producing agglomerates. This can be justified with the fact that higher percentages of chloride (NaCl) contribute in a low ash-melting temperature, as reported in [START_REF] Brostrom | Condensation in the KCl-NaCl system[END_REF]. 4. The ANS fly ash examined (Fig. 11d ande) mainly contained particles of various shapes and sizes. In general, prismatic, polyhedral, spherical and fibrous particles were observed. Coarse particles (spots II and III) with high specific surfaces represented typical organic materials. On the contrary, the fine particles were roughly spherical (dotted red circles) and mainly contained O, K, Si and Ca, while the amount of unburned carbon was minimal. Elemental concentrations of P, Na, Mg, Al and S were considerably lower than those of other elements. WP Fly ash (see Fig. 11f) mostly contained coarse and other fibrous particles resembling the original structure of wood fibre. The dark and fibrous particles were mainly formed of carbon and oxygen and came mainly from the unburnt char. In addition, the clearest and brightest particles were composed of inorganic materials, in particular alkali (K) and alkaline earth (Ca), as well as S and Cl (as minor elements: 0.1-1%). The large amount of unburnt carbon in ANS and WP fly ash is mainly due to incomplete combustion of the char part. After flame extinction, the primary air cools the combustion chamber and transports the fine particles of char to the cyclone. Finally, under the moderate air flow (108 m 3 .h -1 ), the bottom and fly ash content of ANS were negligible (<0.5 and <0.05%, respectively), i.e. losses due to unburnt carbon can be neglected. excess reduces the reaction time and consequently the flame temperature and the combustion efficiency since the carbon conversion was limited. With the decrease in ANS length, the combustion duration was shorter, which results in a rise in the FBR. However, the shortest ANS biomass length (broken particles: BP) induced high CO concentration and consequently lower MCE under low and moderate air flows (72 and 108 m 3 .h -1 , respectively). A high excess of air supply, especially for the BP improved the FBR (better than wood pellets), the combustion temperature, the emission of CO and the MCE. In all the cases studied, the average NOx emission was less than 140 mg.Nm -3 at 10% O2. The flame had an irregular shape for the longest ANS biomass but was more stable when the biomass particle size decreased (BP). These facts indicate that a change in fuel specification clearly affects the combustion process. Such results prove that ANS biomass may be an alternative fuel for present and future energy production. Nevertheless, further work is required to study the effect of secondary air on pollutant emissions (especially CO) of BP of ANS to ensure their suitability for combustion. This will not only give further information on the combustion characteristics of this biomass but also validate the presented results in this study.

Nomenclature

ANS

Fig. 1 .

 1 Fig. 1. Experimental combustion setup.

Fig. 2 .

 2 Fig. 2. Experimental procedure of the combustion tests. The flows used in this study were 36, 72, 108, 144 and 180 m 3 .h -1 corresponding to 528, 1057, 1585, 2113 and 2642 kg.m -2 .h -1 , respectively (in mass flow). At the end of each

Fig. 3 .

 3 Fig. 3. Scanning electron microscope image and additional elemental analysis of the outer surface of ANS.

Fig. 4 .

 4 Fig. 4. SEM-EDS analysis of ANS ash obtained by LOI method.

Fig. 5 .

 5 Fig. 5. Images of visible flames from the combustion recording of ANS at different operating conditions and particle sizes. WP are added for comparison.

Fig. 6b illustrates

  Fig. 6b illustrates visual observations of the four stages of the combustion process. The steady

Fig. 6 .

 6 Fig. 6. Typical combustion results: (a) flame temperature (b) visual observation and (c) corresponding combustion gas concentrations (case of 36 m 3 .h -1 air supply).

Fig. 7a -

 7a Fig. 7a-c illustrates the significant impact of air flow on the combustion process of raw

Fig. 7 .

 7 Fig. 7. Influence of the air flow on: (a) equivalence ratio (b) combustion temperature and FBR, (c) BBV and MCE.

Fig. 8

 8 Fig.8shows the mean pollutant concentration calculated, converted and corrected at 10%

Fig. 8 .

 8 Fig. 8. Mean emission concentration during combustion corrected at 10% O2.

Fig. 9 .

 9 Fig. 9. Effect of particle size on combustion temperature (a and b), FBR (c), MCE (d), CO and NOx emission (e and f, respectively).

Fig. 10 .

 10 Fig. 10. Photographs of the ANS and WP combustion ashes in the grate (a) and the distribution of ash percentage mass during combustion tests (b).

Fig.

  Fig. 11d-f shows the morphology of ANS and WP fly ash. Local chemical composition

Fig. 11 .

 11 Fig. 11. SEM images of ANS and WP ash at different operating conditions: bottom ash (a-c) and fly ash (d-f).

Table 2

 2 ANS biomass properties.

	Photograph of the raw ANS particles	C 51.33	H 6.32	Ultimate analysis a (%) O 42.345 0.005 N	S n.d.
			Proximate analysis b (%) and bulk density (BD)
		M	VM	FC	ash	BD
		9.5	61	28	1.5	596
			Energy content b and stoichiometric calculation a
		LHV	ED	Equivalent formula	Stoichiometric air (Nm 3 .kg -1 )	AFR
		17	10.13	CH1.46O0.62	4.75	6.22

n.d.: not detected, M: moisture, VM: volatile matter, FC: fixed carbon, BD: bulk density (Kg.m -3 ), LHV: low heating value (MJ.kg -1 ), ED:

  includes the EDS analysis results.

		O	C	Al	Si
	001	40.48 56.26 1.50 1.76
	002	19.13 80.87
	003	33.98 66.02
	Average 31.20 67.72 1.50 1.76
	Deviation 10.94 12.39 0.00 0.00

Table 3

 3 Classification of the three sizes from the raw ANS samples. Wood pellets are added for comparison purposes.

	Samples	Large particles (LP)	Small particles (SP)	Broken particles (BP)	Wood pellets (WP)
	photograph
	Length	2.5 -3 cm	1 -1.8 cm	< 8 mm	3.15 -4 cm
	BD *	556	592	642	650
	Bed porosity	0.48	0.44	0.39	0.47

* BD: bulk density (kg.m -3 ). Measurement was done in quadruplicate, and the mean value is reported.

suggested that the excess air flow (unfavourable, i.e. convection by cooling) limits the flame propagation, reduces the combustion temperature and affects the combustion stability.

Acknowledgements

This work has been supported by the ANR (Agence National de la Recherche), EranetMed II RenewValue project. The technical help of Radouane Leghrib from LETSMP Ibn Zohr University is gratefully acknowledged.

Conclusion

The understanding of biomass combustion behaviours, performances and their environmental impact is a crucial consideration in terms of sustainable energy development. For this purpose, the most frequent biomass in southwestern Morocco, namely argan nut shell (ANS), was studied. Many conclusions can be drawn based on the experimental results of this work.

ANS was burnt in the laboratory furnace without any ash agglomeration problem. On increasing the air flow, the combustion temperature, the FBR and the MCE of raw ANS increased until a critical value which corresponds to 108 m 3 .h -1 in our study. At this air flow rate, less CO concentration is obtained and the ash content is almost negligible. High air


Julie Hot
email: hot@insa-toulouse.fr

Erick Ringot

Lounes Koufi

Alexandra Bertron

Modelling of NO photocatalytic degradation in an experimental chamber

Keywords: Langmuir-Hinshelwood, Modelling, Photocatalysis, Nitrogen monoxide, Experimental chamber

Almost real-life" experiments of abatement of a pollutant, actually nitrogen monoxide, were carried out in a 10-m 3 chamber, the walls of which were covered with plasterboard samples, themselves coated with a photocatalytic dispersion. The experimental protocol consisted in first injecting NO polluted air into the chamber to a certain level, then maintaining a steady level of pollution by tuning the flow rate to balance the leaks and, finally, illuminating the chamber. In a first stage of analysis, a three-flow (injection, leakage and renewal flows) model was used in order to characterize the leakage flow rate. This model was based on the difference of NO concentration between the interior and the exterior rather than on a pressure difference. A two-parameter empirical law was specially formulated for this purpose. In a second stage, the photocatalytic phenomenon was described by a four-flow model completing the previous one, the fourth flow being associated with the photocatalytic oxidation of NO. This flow was described by a rate law derived from the Langmuir-Hinshelwood (L-H) law, which was generalized to the experimental chamber. The parameters (adsorption constant) and (abatement kinetics constant) of the rate law were identified using a standardized lab-scale reactor. The equations, integrated by finite differences, fitted the experimental results correctly. The "diffusive zone thickness" was introduced as the thickness of the air layer potentially concerned by the photocatalysis and was quantified. This first attempt to model photocatalysis on a large scale was promising. However, further research work is needed to enable the model to take more parameters into account.

Introduction

Indoor air is polluted by gaseous compounds, which mainly come from building materials, occupant activities and outdoor pollution. As an example, nitrogen oxides, which are harmful outdoor pollutants emitted by transport vehicles and industries, often infiltrate buildings. Two main strategies may be adopted to decrease indoor pollutant concentration: (1) source control, which consists in eliminating individual sources of emissions to reduce the global pollution, and/or (2) remediation action, which involves combatting the existing pollution with techniques such as mechanical ventilation, air cleaning devices or air-depollution coating. However, an improved ventilation system may bring in a higher volume of outdoor air, which can be problematic in the vicinity of heavy traffic areas where levels of traffic-related pollutants are high. Several air purifiers and air-depollution coatings work by using photocatalysis. This well-known technique is based on the photo-activation of a metal-oxide semiconductor. Under irradiation (with photons of higher energy than that of the bandgap), electron-hole pairs are created, leading to the formation of reactive radicals (such as hydroxyl OH • and superoxide O2 •-), which allow the mineralization of gaseous pollutants through redox reactions. This use of heterogeneous photocatalysis to reduce the concentration of nitrogen oxides (NOx = NO + NO2) has been largely reported in the literature. Nitrogen monoxide (NO) has been used as a probe molecule in numerous studies, mainly because it does not adsorb on/react with the surfaces to any notable extent and can be easily measured by a chemiluminescent analyzer [START_REF] Sivachandiran | Investigation of NO and NO2 adsorption mechanisms on TiO2 at room temperature[END_REF].

The successive reactions of its photo-oxidation lead to nitrate species end-products via the formation of NO2 (nitrogen dioxide) [START_REF] Boyjoo | A review on photocatalysis for air treatment: From catalyst development to reactor design[END_REF][START_REF] Zouzelka | Photocatalytic abatement of NOx pollutants in the air using commercial functional coating with porous morphology[END_REF]. The efficiency of the photocatalytic process has been largely evaluated at a lab scale using standardized methods and reactors [START_REF] Boyjoo | A review on photocatalysis for air treatment: From catalyst development to reactor design[END_REF][START_REF] Ifang | Standardization methods for testing photo-catalytic air remediation materials: Problems and solution[END_REF][START_REF] Mills | The nitric oxide ISO photocatalytic reactor system: Measurement of NOx removal activity and capacity[END_REF]. In such conditions, the influence of environmental parameters, such as humidity, temperature, concentration, illumination intensity, substrate type, and of the semiconductor physicochemical properties have been investigated, as they can be controlled [START_REF] Obee | TiO2 photocatalysis for indoor air applications: Effects of humidity and trace contaminant levels on the oxidation rates of formaldehyde, toluene, and 1,3-butadiene[END_REF][START_REF] Yu | Indoor air purification using heterogeneous photocatalytic oxidation. Part I: Experimental study[END_REF][START_REF] Martinez | Degradation of NO using photocatalytic coatings applied to different substrates[END_REF][START_REF] De Melo | Evaluation of the influence of environmental conditions on the efficiency of photocatalytic coatings in the degradation of nitrogen oxides (NOx)[END_REF][START_REF] Hot | Investigation on parameters affecting the effectiveness of photocatalytic functional coatings to degrade NO: TiO2 amount on surface, illumination, and substrate roughness[END_REF]. Several research works have also been carried out at larger scales (tunnel, road pavement, canyons, etc.) under environnemental conditions and ambient pollution [START_REF] Guerrini | Photocatalytic performances in a city tunnel in Rome: NOx monitoring results[END_REF][START_REF] Ballari | Full scale demonstration of air-purifying pavement[END_REF]. The reported observations highlight the variability of the removal rate results because of their dependance on numerous parameters, such as light intensity and energy, wind speed and ambient pollution, which makes it difficult to predict the process efficiency in real conditions. From a modelling point of view, the Langmuir-Hinshelwood (L-H) model has been widely used in the literature to describe the photocatalytic reaction rate of NO and other chemical pollutants at a reactor scale [START_REF] Zhao | Photocatalytic oxidation for indoor air purification: a literature review[END_REF][START_REF] Wang | Photocatalytic oxidation of nitrogen oxides using TiO2 loading on woven glass fabric[END_REF][START_REF] Folli | Role of TiO2 surface hydration on NO oxidation photo-activity[END_REF][START_REF] Khuzwayo | Modelling and simulation of photocatalytic oxidation mechanism of chlorohalogenated substituted phenols in batch systems: Langmuir-Hinshelwood approach[END_REF]. Modelling provides a reasonable interpretation of the experimental data and is an interesting tool to predict the decrease of a gaseous pollutant concentration under various conditions [START_REF] Zhong | Modeling and physical interpretation of photocatalytic oxidation efficiency in indoor air applications[END_REF]. This was notably highlighted by Hunger et al., who derived a model of the NO decomposition process occurring on a photocatalytic concrete paving stone in a reactor cell in order to predict its performance under various conditions and thus to envisage the translation of this process to real-scale applications [START_REF] Hunger | Photocatalytic degradation of air pollutants -From modeling to large scale application[END_REF]. This paper reports the first step of research work aimed at modelling the photocatalytic reaction in an experimental chamber. The objectives were twofold: [START_REF] Sivachandiran | Investigation of NO and NO2 adsorption mechanisms on TiO2 at room temperature[END_REF] to understand the diminution of gaseous pollutant concentration in indoor conditions and, in particular, to identify the contribution of air leakage, air renewal and photocatalytic oxidation (as a technique of air pollution remediation), and

(2) to predict the efficiency of photocatalytic devices/products for improving indoor air quality. The gaseous pollutant and semiconductor tested were nitric oxide, NO, and titanium dioxide, TiO2, respectively. A rate law similar to the L-H model was used at reactor scale to identify the kinetic constant and the NO adsorption coefficient under UV-A and visible light. Then, a model was built at the chamber scale, based on three or four flows depending on whether or not the photocatalysis was active. The NO pollution flows corresponded to the artificial injection, the outdoor pollution, the leakage, and the photocatalytic degradation.

Materials and experimental procedures

Materials

Experiments in the lab reactor were carried out with two common building materials as substrates: painted plasterboard and mortar. The samples placed inside the reactor were rectangular: 100 mm or 250 mm long, 50 mm wide and 10 mm thick. Commercial plasterboard (Placoplatre® BA 13) was cut into samples of the desired dimensions and then painted with orange water-based acrylic paint (LRVision). The formulation and preparation of the mortar were adapted from the NF EN 196-1 standard [START_REF]NF EN 196-1[END_REF]. Siliceous sand and CEM I 52.5 Portland cement were used. They were mixed mechanically with water (at a water to cement ratio (W/C) of 0.5) at ambient temperature and humidity for 3.5 min and then cast in a 300 × 300 × 10 mm 3 steel mold with the aid of a vibrating table. The slab was demolded after 5 days and sawn into samples of the desired dimensions. Finally, the mortar surfaces were ground (120-mm abrasive sandpaper).

Tests in the experimental chamber were conducted with plasterboard samples only. Commercial plasterboards (Placoplatre® BA 13) were cut into pieces of specific dimensions to fit the indoor walls of the experimental chamber (100 × 50 cm², 75 × 50 cm², 50 × 50 cm² and 50 × 25 cm²) and covered an indoor surface of 9.8 m². The edges of each plate were protected with adhesive tape and the surfaces were painted as for samples in the reactor. The TiO2 particles were stabilized in an aqueous suspension to ensure the safety of the operator during the application (no risk of inhalation). The photocatalytic dispersion was applied with a brush at the surface of each substrate. It was prepared from a formulated water-based commercial product (CristalACTiV™ S5-300B, ultrafine TiO2 anatase particles at 18 wt%) by dilution with demineralized water. The TiO2 particles had a diameter of around 50 nm and the TiO2 dry content at the surface after application was 5 g/m 2 for all the samples (used in the reactor and in the experimental chamber). This value was chosen in order to obtain a high photocatalytic depollution efficiency and thus make it possible to carry out the modelling work. ) at the exit of the reactor. In order to control and adjust the NO initial concentration, the polluted air was also sent through a bypass directly to the analyzer. The temperature and the relative humidity were kept constant at 21 ± 2 °C and 50 ± 5 % respectively.

Experimental protocol

The experimental protocol took its inspiration from standard ISO 22197-1 [START_REF]Test method for air-purification performance of semiconducting photocatalytic materials -Part 1: Removal of nitric oxide[END_REF]. The NO flow rate was set at 1.50 ln/min. Initial NO concentrations varied between 50 and 400 ppb. Two lighting conditions were tested: visible light (fluorescent tube, Osram T8 Lumilux Cool White L 18W 840) and UV-A light (fluorescent tube, Narva LT-T8 Blacklight blue 30W 073). The lighting intensity received by the sample surface was measured by a radiometer (Gigahertz-Optik) using two detectors (UV-A, UV-3717 model and visible, RW-3703 model). The values obtained were 6 W/m 2 for visible wavelengths (400-800 nm) and 1 W/m² for UV-A wavelengths (315-400 nm). The light spectrum of the visible fluorescent tube is shown in [START_REF] Topalov | In situ NO abatement by photocatalysis-study under continuous NO injection in a 10-m3 experimental chamber[END_REF]. The main steps of the protocol were: (1) injection of NO polluted air through the bypass to check the initial level -light off (5 min), (2) injection of NO polluted air through the reactor containing a sample -light off (15 min), (3) switching on of the light to activate the photocatalysis (60 min), (4) switching off of the light to stop the photocatalysis (15 min), and (5) calculation of the NO photocatalytic efficiency (in %) (cf. part 3.1). The steps of this protocol are schematically represented in [START_REF] Hot | Investigation on parameters affecting the effectiveness of photocatalytic functional coatings to degrade NO: TiO2 amount on surface, illumination, and substrate roughness[END_REF][START_REF] Hot | Titanium valorization: From chemical milling baths to air depollution applications[END_REF]. The experiments carried out in the reactor allowed the two constants of the assumed L-H kinetics to be identified, as explained in part 3.1. Each experiment (same initial concentration and lighting condition) was conducted three times with a different mortar sample each time.

Experiments at chamber scale 2.3.1. Description of the setup

The macro-scale experiments were carried out in an experimental house located at the LMDC (France). This setup was previously described in [START_REF] Topalov | In situ NO abatement by photocatalysis-study under continuous NO injection in a 10-m3 experimental chamber[END_REF][START_REF] Hot | Photocatalytic degradation of NO/NO2 gas injected into a 10-m3 experimental chamber[END_REF]. It was divided into two rooms of 10 m 3 each.

One room -the experimental chamber -was used as a photocatalytic reactor and contained the samples (covering a wall surface area of 9.8 m²), and ventilation and lighting systems. The second room -the monitoring chamber -was equipped with a NOx analyzer (HORIBA APNA370) and a gas cylinder (45 ppm of NO stabilized in N2, Air Liquide) connected to an MFC (M+W Instruments™ Mass-Stream). A fan was necessary to homogenize the atmosphere. The two rooms were connected with stainless steel tubes: one enabling the NOx analyzer to sample gas for measurement, the other for injecting the pollutant from a gas cylinder through the MFC. Meteorological data (environmental parameters) were acquired using a weather station (DAVIS Vantage Pro2™). Humidity and temperature inside the photocatalytic room were also acquired using a data logger (KIMO KH60). The values were 50 ± 10 % and 20 ± 5 °C, respectively. Moreover, indoor/outdoor exchanges occurred due to 'natural' leakage because, among other reasons, the joinery was not perfectly airtight.

Experimental protocol

NO artificial pollution was injected into the experimental chamber as described in [START_REF] Topalov | In situ NO abatement by photocatalysis-study under continuous NO injection in a 10-m3 experimental chamber[END_REF]. Two protocols were followed to identify the model parameters as explained in part 3.2. Each protocol consisted of 4 main steps; the first three, conducted in the dark, were identical for both protocols, the last one was different as described below:

(1) background NOx level assessment;

(2) fast NO dynamic injection at 1.5 ln/min until the desired concentration was reached inside the chamber;

(3) NO injection at a lower flow rate to compensate for air leakage and maintain the pollution at the desired concentration (concentration plateau), and Experiments with three different maximum concentrations, expressed in ppb, were carried out. Their values and the corresponding injection flow rates used to maintain a constant pollution level are summarized in Table 1. Experiments without the photocatalytic activity were carried out three times for each concentration (cf. part 4.2.1). Only one experiment was conducted with the photocatalytic activity for each lighting condition, UV-A and visible light (cf. part 4.2.2).

Table 1. Maximum concentrations injected in the experimental chamber and the corresponding injection flow rates to maintain the concentration at a stable level.

Maximum concentration reached in the experimental chamber (ppb)

Injection flow rate to maintain the concentration constant in the chamber (ln/min) 300 0.45 200 0.30 100 0.20

Differences between the reactor and the chamber

In the lab-scale reactor, the gas flow is pushed from one edge to the other by a piston effect. The pollutant concentration decreases progressively during its journey along the photocatalyst applied to the sample surface. The thickness of the air layer is 5 mm according to standard ISO 22197-1 [START_REF]Test method for air-purification performance of semiconducting photocatalytic materials -Part 1: Removal of nitric oxide[END_REF].

Therefore, all the pollutant flow is assumed to be concerned by the abatement.

The experimental chamber is not standardized. Its interest is that it simulates a room close to a real one (even if the size of 10 m 3 remains modest in regard to the volume of real rooms). The pollutant invades all the volume so a significant part of the polluted gas, far from the walls, is little concerned by the abatement, if at all.

The lab-scale enables the set {surface + photocatalyst + illuminant} to be characterized via coefficients and of the L-H-like model. In turn, these factors are used in the four-flow model, provided the walls were coated by the same materials and lit by the same light.

The reactor is airtight; the chamber presents a slight air infiltration/exfiltration, which is not controlled but is taken into account in the modelling (cf. part 3.2).

Model description

The following sections discuss the model development.

Langmuir-Hinshelwood-like model in the reactor

The Langmuir-Hinshelwood (L-H) approach has been widely used to analyze the kinetics of heterogeneous photocatalysis at a lab scale. The photocatalytic reaction is closely related to the L-H adsorption model as its rate depends on the coverage of the semiconductor particle surface by the gaseous pollutant. Peral and Ollis notably employed this model to describe the photocatalytic oxidation of 1-butanol, formaldehyde, and m-xylene when the surface of a porous fritted glass plate covered with a P25 TiO2 powder layer (anatase) was irradiated under UV [START_REF] Peral | Heterogeneous photocatalytic oxidation of gas-phase organics for air purification: Acetone, 1-butanol, butyraldehyde, formaldehyde, and m-xylene oxidation[END_REF]. Sleiman et al.

investigated the photocatalytic removal of toluene at indoor air levels using an annular flow-through reactor with TiO2 as photocatalyst [START_REF] Sleiman | Photocatalytic oxidation of toluene at indoor air levels (ppbv): Towards a better assessment of conversion, reaction intermediates and mineralization[END_REF]. They showed that the experimental data complied with the L-H rate expression. Such a model was also applied to describe NOx photocatalytic oxidation. In the reactor presented previously, the air flow is "pushed" along the photocatalytic surface of a sample (mortar or plaster), and becomes less and less polluted, provided the irradiation is sufficient to activate the semiconductor particles. A rate law, inspired from the L-H model, whose expression is given by equation ( 1), was used to describe the kinetics of the NO consumption in the reactor due to the photocatalysis process. The negative sign of this expression is consistent with the abatement of NO due to photocatalysis.

= = - = - (eq.1)
In this equation, represents the disappearance rate of the reactant (the variation of the NO pollutant concentration per increment of time) expressed in ppb/min and is the reactant concentration in ppb ( being the concentration at the entrance of the reactor). As for the L-H law, this model involves two specific coefficients: , expressed in ppb -1 , which is the adsorption equilibrium constant and defines the gas/surface adsorption affinity, and , expressed in ppb/min, which is the reaction rate constant. The latter parameter has to be considered as a pseudo-first order factor describing the kinetics of NO abatement, involving the intermediate reactions of oxygen, vapour, hydroxyl radical formation and combination with NO.

! = # = $ %& (eq.3)
From equations 1 and 3, the variation of the concentration in the reactor ( ) can be given as a function of the sample length ( ) (equation 4):

= - ' = - %& $ (eq.4)
Equation 4 can be integrated with respect to the limits: = at = 0 and = at = , thus reducing the rate expression to equation 5:

-+ ln # + = - %& $ (eq.5)
which leads to equation 6 at the exit of the photocatalytic reactor: = for = :

-+ ln + = - %& $ (eq.6)
The photocatalytic efficiency ( ) is defined by equation 7 as the relative difference between the NO concentration at the entrance of the reactor, , and the NO concentration at the exit of the reactor, :

= + , + (eq.7)
Therefore, equation 6 can be rewritten as:

-ln 1 -= . / $ (eq.8)

where 0 1 = is the volume of the air layer above the upper surface of the sample in the reactor. which can be simply expressed as:

5 = 67 + 8 (eq.10)
where 7 and 5 are two intermediate variables, defined as follows: (eq.11)

Like 7, 5 is positive as ∈ [0; 1]; 6 and 8 are two constants, the slope and the intercept of the straight line respectively, defined by: @ 6 =

. / $ 8 = -(eq.12)

It should be noted that the L-H model is a local adsorption-reaction law, which means that, at reactor scale, a number of influencing parameters are assumed to be uniform as the sample is small. This notably concerns the nature of the substrate, the light intensity, the photocatalytic dispersion applied to the sample surface, the relative humidity and temperature in the vicinity of the photocatalytic surface, and the residence time of the gaseous pollutant in the reactor.

Three-and four-flow model in the experimental chamber

The model describing the evolution of NO concentration in the experimental chamber was developed in two steps:

• Step 1: modelling without the photocatalytic activity,

• Step 2: modelling with the photocatalytic activity under artificial light (visible or UV-A).

Step 1 allows the air leakage kinetics to be characterized. As reported previously by the authors [START_REF] Hot | Photocatalytic degradation of NO/NO2 gas injected into a 10-m3 experimental chamber[END_REF],

in the case of a static injection (i.e. the quantity of pollutant injected was controlled by setting the flow rate and the injection volume), the NO concentration naturally decreased when the injection was stopped. This diminution was attributed to the air leakage of the experimental chamber because of imperfect airtightness of the joineries, which allowed part of the polluted air to be exhausted to The conservation law for flow rate leads to equation 13:

A;B + C&; -:&1 = 0 (eq.13)

Equation 14 describes the variation of NO concentration ( ) as a function of time in an experimental chamber of volume 0:

A;B A;B ' + C&; ' -:&1 ' = 0 (eq.14)

The air leakage is triggered by the difference between the indoor NO concentration ( ) and the outdoor NO concentration ( ). The relationship between the leak rate :&1 and the difference of NO concentration is expressed via an empirical law introduced by equation 15:

:&1 = DE F -1G H , > ̅ (eq.15)
where is a flow rate-like constant, K is a positive dimensionless number and > since the pollutant was artificially injected into the experimental chamber. These two constants are assumed to characterize the behavior of the room. Obviously, :&1 vanishes as → ̅ . This empirical law also works when ̅ > , provided that it is rewritten:

:&1 = sign -̅ × QE F -1Q H (eq.15')
In this way, equation 15' also allows for the possibility that the NO outdoor concentration becomes higher than the NO indoor concentration; in such a case, the flow rate is reversed.

The following differential equation (equation 16) is then obtained from equations 13, 14 and 15:

= . R A;B E STU -1F -E -1F H V (eq.16)
Equation 16 expresses the variation of the NO indoor concentration in the experimental chamber as a function of time. The solution of this non-linear differential equation is ' = W $ X,H ' . However, it has no analytical expression. Therefore, it was solved by the finite difference method by running incremental calculations according to the scheme shown in Figure 3. The volume of the experimental chamber (0), the injected flow rate ( A;B ), the concentration of injected NO ( A;B ) and the NO outdoor concentration ( ) are experimental parameters, which were obtained by measurement. Δ'

is the timestep and was equal to 5 min here (time interval between two measurements displayed by the analyzer). Parameters and K were obtained by the least-squares method (a spreadsheet solver was used).

Their optimal values were found by minimizing equation 17, i.e. the sum (Z [ ) of squared differences between the measured experimental concentrations B and the concentrations predicted by the model W $ X,H \' B ] .

Z [ = ∑_ B -W $ X,H \' B ]`[ (eq.17)
Step 2 consists in adding a new flow to the model to take the photocatalytic oxidation of NO into account. This additional flow, noted a , is shown in Figure 2.b and is defined according to equation 18:

a = b × ′ × a = 0 a × a (eq.18)
where b is the surface fonctionnalized by the photocatalytic dispersion, ′ is the thickness of the air layer along the sample surface concerned by diffusive, adsorption or degradation phenomena, 0 a is the volume of the polluted air concerned by the photocatalysis and a is the disappearance rate of the NO due to photocatalysis. The thickness of the air layer, which is associated with the free space above the sample surface in the reactor, is unknown in the experimental chamber. This air layer corresponds to the diffusive zone of the reactive radicals (created by the irradiation of the semiconductor particles), which can react with NO molecules, as shown in Equations 13 and 15 defined in step 1 are kept. However, equation 14 changes to equation 20 to take the variation of the NO concentration due to the photocatalysis into account (the new flow a is added).

A;B A;B ' + C&; ' -:&1 ' + V h a = 0 (eq.20)

The combination of equations 13, 15, 19 and 20 leads to the following differential equation, the solution of which is ' .

= . R A;B E STU -1F -E -1F H V - . e .
(eq.21)

which can be simplified to:

= . R A;B E STU -1F -E -1F H V -A a (eq.22)
where

A a = . e .
is expressed in min -1 .

Parameters and K were defined in step 1 (experiments without photocatalysis) and their values were kept for step 2. The only unkown variable for step 2 was A a . The non-linear equation 22 was solved by the finite difference method by running incremental calculations according to the scheme shown in Figure 5. (cf. equations 9 and 11). A linear relation is clearly observed for both UV-A and visible light, meaning that the L-H-like law was valid. The expressions of the trend lines are reported on Figure 7. Their equations allowed the adsorption coefficients to be identified (5 =for 7 = 0) and the values of (reaction rate constant) to be determined from the slopes (cf. equations 10 and 12). However, the values obtained for the adsorption coefficient were negative under both lighting conditions.

These results are unexpected and can be explained by the lack of precision of the experimental points -the lines go through the vicinity of the coordinate system origin, near the 0 value, probably because of the low NO adsorption capacity of the exposed surfaces. The uncertainty on the coefficient therefore becomes higher than the value of the coefficient itself. To overcome this problem, the authors decided to increase the length of the sample in order to obtain higher abatement values. A new series of experiments was conducted with longer samples (250 mm in length instead of 100 mm) and thus with a higher quantity of TiO2 particles at the surface (the TiO2 dry content per m² was kept constant). 2. Considering the uncertainty related to the experiments, the coefficient was assumed to be similar for both substrates and independent of the lighting conditions (errors on were: ± 2.20 or 2.38 or 1.76 or 2.52 ppb -1 ). However, the coefficient seemed to be impacted by the nature of the substrate and the light (the uncertainty on the values was quite low: ± 0.07 or 0.08 ppb/min). Lower values were obtained under visible light for both substrates: k. = 1.15 × "AlA%:& for mortar and plasterboard samples, and higher values were obtained for mortar: mnC 1C = 1.10 × o:1l &C%n1C

for both lighting conditions. Such results were expected as the photocatalytic activity, and thus the degradation of NO, is wavelength selective and accelerated by UV light [START_REF] Yu | Indoor air purification using heterogeneous photocatalytic oxidation. Part I: Experimental study[END_REF][START_REF] Hüsken | Experimental study of photocatalytic concrete products for air purification[END_REF]. The semiconductor TiO2 is activated for wavelengths below 388 nm, which explains the higher reaction rate constant obtained under UV-A light. The degradation of NO observed under visible light could be explained by:

(i) the non-zero value of the light intensity of the fluorescent tube between 380 and 400 nm (the lowest wavelength of the visible light spectrum may be considered equal to 380 nm), and/or (ii) the doping of TiO2 nanoparticles in order to make them sensitive to the visible blue light (the formulation of the commercial product was not known). The influence of the irradiance on constants and was highlighted by Hunger et al. [START_REF] Hunger | Photocatalytic degradation of air pollutants -From modeling to large scale application[END_REF]. They showed that the reaction rate constant, , was dependent on the irradiance while the adsorption coefficient, , remained unaffected. Moreover, the synergic effect between the cementitious matrix and NO could explain the higher value of the reaction rate constant obtained with mortar samples. Cassar notably suggested that the cement hydrates could highlighted the reaction of NO2 with strongly alkaline hydrates [START_REF] Horgnies | NOx de-pollution by hardened concrete and the influence of activated charcoal additions[END_REF]. The values of and obtained at the reactor scale for plasterboard were used for the modelling at the experimental chamber scale. the model throughout the experiment for the three concentrations tested. The parameters and K were identified and the following values were selected to obtain the best fit: = 26 ~z/ yz and K = 0.25. The NO outdoor concentration ( ) was not monitored and was assumed to be constant throughout a test. Its value was adjusted for each experiment in a way that best fitted the experimental points. The model response to this parameter was assessed however. Figure 10 shows the model sensitivity to different values of for the experiment conducted with a maximum indoor NO concentration of 200 ppb ( X and K being unchanged). In this case, 5 ppb was the value selected for , as it enabled the best fit between experimental and modelled values to be obtained. To go even further, the NO outdoor concentration could be monitored with an additional analyzer and its evolution law taken into account in equation 14. Moreover, the three-flow model allowed the values of the flow rates reported in Table 1 (and defined experimentally) to be calculated. During the NO injection at a low flow rate (constant level of pollution inside the chamber), the variation of the concentration was taken to be 0, which meant that = 0. In such conditions, Equation 16 allows us to write:

R A;B E STU -1F -E -1F H V = 0 (eq.23)
Therefore, the injected flow rate during the constant phase is defined by equation 24: This value is consistent with the injected flow rate defined experimentally A;B &#o = 0.30 ~z/ yz (cf. Table 1). In the case of 300 ppb, equation 24 gives A;B = 0.47 ~z/ yz ( A;B &#o = 0.45 ~z/ yz).

A;B = E , F ۥ E STU , F (
For 100 ppb, the value given by equation 24 is slightly underestimated: A;B = 0.12 ~z/ yz versus However, in this case, the injection was not stopped at the end of the concentration plateau. At 50 min, the lighting was switched on to activate the photocatalysis: under UV-A (cf. Step 2 allowed the parameter 6 a to be identified, its value being dependent on the lighting conditions; the higher the photocatalytic activity, the higher the 6 a value: 6 a = 8.561 yz , for UV-A light and 6 a = 6.640 yz , for visible light.

The thickness ′ of the diffusive zone above the plasterboard samples was therefore determined for both lighting conditions according to the following equations: (eq.26)

Therefore, ′ = ‡ e .

…

(eq.27)

where the constants and were determined at the reactor scale under UV-A and visible light (cf.

Table 2). photocatalytic oxidation -on the evolution of NO indoor concentration, and allowed the thickness of the air layer involved in the photocatalysis to be estimated. Because the chamber was not airtight, leaks were observed and had to be taken into account in the model. They could not be explained by the overpressure due to the injection phase of the NO pollutant; such a phenomenon was never observed in spite of the accuracy of the barometric instruments. Instead, the leakage was explained by the difference of NO concentration between the interior and the exterior, which was expressed through an appropriate but empirical law. The percentage of decrease in the (amount of) pollution when the light was switched on was, obviously, attributed to the photocatalytic effect of the dispersion coating the plasterboard samples. This percentage did not constitute a real flow rate but nevertheless contributed to the disappearance of NO. It was taken into account through a rate law inspired by the Langmuir-Hinshelwood model. Thus, the adsorption and the abatement kinetics parameters were identified in a lab reactor. However, the following reservations should be made on the use of the L-H-like law in the four-flow model:

• The rate law has a "local" character. At lab scale, the samples had small sizes and the law was assumed to apply uniformly because the local characteristics listed here are reputed to be uniform: porosity, roughness, amount of TiO2 at the surface of samples, lightning, temperature, humidity.

• Therefore, the generalization of the use of the rate law to a greater volume, as in the experimental chamber, necessitated the assumption that the local conditions were uniform.

For instance, the lighting was implicitly averaged over the whole area of the walls.

• Another issue concerns the thickness of the air layer involved in the photocatalysis phenomenon. At reactor scale, it is generally accepted that this thickness corresponds to the distance between the surface of the sample and the borosilicate upper surface. In the case of the chamber, no equivalent assessment could be made: the model provided an answer but the order of magnitude was about 20 times larger than in the reactor (81 mm or 98 mm versus 5 mm). It is too early to claim that the values found in this range have physical significance.

In order to provide answers to these concerns, the model has to be refined. Further studies, like the ones listed below, need to be carried out:

• Check on the general scope of the model. New experiments could be performed with other illuminants, other substrates, other pollutants. For instance, experiments conducted with NO2 should show a greater adsorption ability. Will this phenomenon be correctly expressed by the model?

• Measurement of the external pollution. Rather than taking a constant value for the external pollution level, the model, in its current version, already enables the real-time evolution ̅ ' to be taken into consideration.

• Introduction of a model for the illumination of the walls, provided that a correlation can be established between i) the wavelength and the intensity of the light, and ii) the coefficients and .

The model presented fitted the experimental data well in the specific conditions of this chamber.

Improving this model according to the above suggestions could make it possible to evaluate the efficiency of various indoor air depollution techniques or devices, available commercially or as part of research works. It could even contribute to an assessment of the influence of various parameters (such as the lighting, the substrate nature, etc.) on the air depollution function.

Conclusion

The main aim of this study was to make a contribution to a predictive model of pollution abatement in a room. The gas targeted was nitrogen monoxide. The suggested four-flow model was built in three steps. First, the adsorption and the abatement kinetics parameters were identified in a lab reactor, using a rate law mathematically similar to the L-H model. Then, a three-flow model was developed at the chamber scale, taking the NO injection phase, the air leakage and the air renewal into account. The flow associated with the photocatalytic oxidation (occurring when the light was switched on) was introduced as a third step based on an L-H-like law. Results showed good agreement between predicted values and experimental data, meaning that the suggested models described the evolution of NO well at the experimental chamber scale. A parameter not previously considered was extracted from the four-flow model: the thickness of the diffusive zone in which the process of abatement was assumed to take place. This thickness was estimated at between 80 and 100 mm depending on the illuminant involved in the photocatalysis (visible or UV-A light). The firstintention model presented here is ambitious but suffers from several deficiencies, which could be overcome thanks to further investigations as suggested in the discussion. Such modelling work could enable future prediction of the photocatalytic process under various environmental conditions and thus its translation towards real environments.

2. 2 .

 2 Experiments at reactor scale 2.2.1. Description of the setup The experimental setup used to assess the photocatalytic degradation of NO at a lab scale is described in more detail in [10]. It consisted of three parts: (1) a polluted air supply mixing NO (8 ppm of NO stabilized in N2, Air Liquide™) with humidified and dry air streams adjusted by mass flow controllers MFC (Bronkhorst); (2) the lighting system and the photocatalytic reactor (cylindrical shape, free volume = 424 cm 3 ) containing a sample, which was swept by the polluted air; (3) a NOx chemiluminescent analyzer (ENVEA Environnement SA, France, model AC32M), which measured the concentration of NOx, NO and NO2 ([NO2] = [NOx] -[NO]

( 4 .

 4 a) stopping of the injection (cf. part 3.2, modelling without the photocatalytic activity), or (4.b) keeping the low injection rate and switching on the light to activate the photocatalysis (cf. part 3.2, modelling with the photocatalytic activity under artificial light). The photocatalysis was activated with visible light (4 fluorescent tubes, Sylvania T8 Luxline Plus 30W 840) or UV-A light (4 fluorescent tubes, Narva LT-T8 Blacklight blue 30W 073).

  Devahasdin et al. showed that the steady-state experimental data obtained for space time and inlet concentration effect studies were well fitted by the L-H kinetic model, which took the reaction rate constants of the catalyst TiO2 and the adsorption equilibrium constants of NO, NO2 and H2O into account[START_REF] Devahasdin | TiO2 photocatalytic oxidation of nitric oxide: transient behavior and reaction kinetics[END_REF]. Moreover, Ballari et al. proposed an extended kinetic model based on L-H, which included the relative humidity and irradiance effects. They showed good agreement between the model predictions and experimental results for NO and NO2 concentrations[START_REF] Ballari | Modelling and experimental study of the NOx photocatalytic degradation employing concrete pavement with titanium dioxide[END_REF].

Figure 1

 1 Figure1gives a schematic representation of the polluted air flowing on the surface of a sample in the reactor. The sample is characterized by its length, , and width, . The air layer above the sample, i.e. in the space between the sample surface and the upper surface of the reactor, has a thickness = 5. At steady state and + abscissa, the concentration inside the reactor is equal to

Figure 1 .

 1 Figure 1. Schematic representation of the polluted air flow on the surface of a sample along the x-axis. : length, : width, : concentration at the entrance and : concentration at the exit.In the reactor, the volume of air is injected at a constant flow rate at a speed ! . The flow rate is defined by equation 2 and the speed by equation 3:

Equation 8

 8 implicitly expresses the photocatalytic efficiency as a function of the concentration of polluted air at the entrance of the reactor. This equation can be rewritten as a linear function (equation 9):

  the outside. Because no differential pressure was detected during experiments, the suggested model is based on the NO concentration difference between indoors and outdoors, which drives the air leakage. As shown in Figure 2.a, three flows are considered, each of them being associated with an NO concentration: 1. A;B is the flow rate of NO injected into the experimental chamber at the concentration A;B ; A;B being the NO concentration in the gas cylinder, i.e. 45 ppm; 2. :&1 is the flow rate of the air leakage and is the indoor NO concentration; 3. C&; is the flow rate of the air renewal and the outdoor NO concentration.

Figure 2 .

 2 Figure 2. Schematic representation of: a) the three-flow model (step 1), and b) the four-flow model (step 2) in the experimental chamber.

Figure 3 .

 3 Figure 3. Scheme showing the method implemented to solve equation 16 and identify parameters and K (step 1).

Figure 4 .

 4 The rate law inspired from the L-H model, defined by equation 1, was used to express a . The assumptions made at the reactor scale (cf. part 3.1) were assumed to be valid for a larger volume. Moreover, equation 1 was simplified to equation 19 as the NO concentrations were around 100 ppb and constant was of the order of 10 -4 ppb -1 (1 ≫).

Figure 4 .

 4 Figure 4. Schematic representation of the thickness ′ of the air layer affected by the photocatalysis above the sample surface in the experimental chamber.

Figure 5 .

 5 Figure 5. Scheme showing the method implemented to solve equation 22 and identify the parameter 6 a (step 2).

4. Results and discussion 4 . 1 .STEP 2 :

 412 Figure 6 shows the photocatalytic efficiency as a function of the NO concentration injected into the reactor for mortar samples with the shorter length (100 mm) under visible and UV light. Various

Figure 6 .Figure 7 .

 67 Figure 6. Photocatalytic efficiency ξ (cf. equation 7) as a function of the NO concentration injected into the reactor for 100 mm long mortar samples under UV-A and visible light (VIS).

Figure 8

 8 Figure8shows the results obtained with 250 mm long mortar and plasterboard samples for various concentrations of NO, from 100 to 400 ppb with a concentration step of 50 ppb, under visible light and UV-A light. As explained above, the variable 5 was plotted as a function of the variable 7. Again, a linear correlation was observed. The trend lines are indicated in Figure8. The adsorption coefficients obtained with the longer samples were positive for the two substrates tested under UV-A and visible light. Their values, together with those of the reaction rate constant , are reported in Table2. Considering the uncertainty related to the experiments, the coefficient was assumed to

  nitrate salt formed during the photo-oxidation of NO[START_REF] Cassar | Photocatalysis of Cementitious Materials: Clean Buildings and Clean Air[END_REF], and Horgnies et al.

Figure 8 . 2 .Figure 9 Figure 3 .

 8293 Figure 8. Variable 5 versus variable 7 (cf. equation 11) for 250 mm long mortar and plasterboard samples under 2 lighting conditions: UV-A and visible light (VIS).Table2. Mean values of rate law coefficients obtained for mortar and plasterboard samples under UV-A and visible light. Adsorption coefficient is espressed in ppb -1 and reaction rate constant is expressed in ppb/min.

Figure 9 .

 9 Figure 9. Comparison between the measured concentrations of NO and the values obtained with the threeflow model. Three maximum concentrations were injected: a) plots of the three concentrations, b) 300 ppb, c) 200 ppb and d) 100 ppb, at different scales.

Figure 10 .

 10 Figure 10. Model sensitivity to different values of for the experiment conducted with a maximum indoor NO concentration of 200 ppb.

  eq.[START_REF] Peral | Heterogeneous photocatalytic oxidation of gas-phase organics for air purification: Acetone, 1-butanol, butyraldehyde, formaldehyde, and m-xylene oxidation[END_REF] which gives, in the case of the experiment carried out at = 200 uu :

AFigure 5 .

 5 Figure 11 shows the NO experimental concentrations measured by the analyzer (each point is the average of three values) and the concentrations calculated with the four-flow model according to Figure 5. Experiments were carried out only with the NO concentration of 200 ppb. The increasing concentration phase and the constant phase were obtained as described previously for step 1.

  Figure 11.a) and visible light (cf. Figure 11.b). The NO concentration decreased rapidly: it reached a background value of around 20 ppb after 50 min. The experimental data were again well fitted by the model. The values of and K obtained during step 1 were used.

Figure 11 .

 11 Figure 11. Comparison between the measured concentrations of NO and the values obtained with the fourflow model. A maximal concentration of 200 ppb was injected under: a) UV-A and b) visible light.The values of the parameters of the four-flow model are summarized in Table3. The thickness ′ was dependent on the lighting conditions (98 mm for UV-A versus 81 mm for visible light): the UV-A radiation led to a higher photocatalytic thickness, and therefore to a larger spread of the reactive radicals in the air layer above the sample surfaces. The increase of ′ with UV-A light was consistent with the increase of the reaction rate constant observed at the reactor scale. Moreover, in[START_REF] Topalov | In situ NO abatement by photocatalysis-study under continuous NO injection in a 10-m3 experimental chamber[END_REF],Topalov et al. compared the photocatalysis efficiency with respect to NO obtained in this experimental chamber using various lighting systems; the same fluorescent tubes as the ones used in the present study and halogen and LED bulbs in the visible spectrum. Lower NO abatement values were reported for the halogen and LED bulbs. Modelling has not yet been conducted with these two lighting systems. However, a smaller thickness ′ can be expected under halogen and LED bulbs, as their lighting intensities were low for wavelengths below 388 nm.

Table 3 .

 3 Parameters of the four-flow model: 0 and b are characteristics of the experimental chamber, and were determined at the reactor scale, and K were determined during step 1, and ′ during step 2.

	Parameters	UV-A light	Values	Visible light
	0, volume of the chamber b, plasterboard surface area on the indoor walls		10.3 ˆ 9.8 [

Acknowledgments

The authors are grateful to Mr. Jivko Topalov for his collaboration in this work, in particular his contribution to the carrying out of the experiments.