J Vaillant

A Clouet

D Alleysson

Color correction matrix for sparse RGB-W image sensor without IR cutoff filter

Keywords: Color restitution, low light level, RGB-W, VIS-NIR hyperspectral images, color correction matrix (CCM), synthetic color chart (SCC), CIE L

Unlike photographic image sensors with infrared cutoff filter, low light image sensors gather light over visible and near infrared (VIS-NIR) spectrum to improve sensitivity. However, removing infrared cutoff filter makes the color rendering challenging. In addition, no color chart, with calibrated infrared content, is available to compute color correction matrix (CCM) of such sensors. In this paper we propose a method to build a synthetic color chart (SCC) to overcome this limitation. The choice of chart patches is based on a smart selection of spectra from open access and our own VIS-NIR hyperspectral images databases. For that purpose we introduce a fourth cir dimension to CIE-L*a*b* space to quantify the infrared content of each spectrum. Then we uniformly sample this L*a*b*cir space, leading to 1498 spectra constituting our synthetic color chart. This new chart is used to derive a 3x4 color correction matrix associated to the commercial RGB-White sensor (Teledyne-E2V EV76C664) using a classical linear least square minimization.. We show an improvement of signal to noise ratio (SNR) and color accuracy at low light level compared to standard CCM derived using Macbeth color chart.

INTRODUCTION

Color correction constitutes an important step in the color image reconstruction pipeline in visible color imaging. Color values of each pixel are spatially interpolated during the demosaicking step [START_REF] Rafinazari | Demosaicking algorithms for RGBW color filter arrays[END_REF]. Then the white balance (WB) and color correction matrix (CCM) [START_REF] Bianco | Color correction pipeline optimization for digital cameras[END_REF] are applied to each pixel to ensure a good color restitution of the acquired scene (see Figure 1). A large majority of color image sensors contains three color channels Red, Green and Blue (RGB) and an infrared filter in front to only acquire visible range wavelengths [START_REF] Teranaka | Single-Sensor RGB and NIR Image Acquisition: Toward Optimal Performance by Taking Account of CFA Pattern, Demosaicking, and Color Correction[END_REF]. CCM are usually computed over commercially available color charts such as MacBeth ColorChecker (MCC) through a linear mean square error minimization method. Such systems are very efficient in terms of color fidelity in high or mid light level. Nevertheless, using only the visible part of the spectrum limits the signal to noise ratio performance under low light conditions. To adress these applications, monochrome sensors without IR cutoff filters are customary used. So signal to noise ratio (SNR) increased, but at price of color information loss. In case of color image sensor, the absence of IR cutoff filter has detrimental impact on color rendering. Nethertheless we investigate the possibility to capture low light images with decent color rendering using the RGB-White image sensor like the Teledyne-E2V Onyx (EV76C664AMT-RTR) product. This sensor has a monochrome pixel array with sparse RGB pattern, delivering four channels RGBW (see Figure 9). With such sensors, color correction matrix and white balance are merged into a single 3x4 matrix converting the raw RGBW output into corrected RGB values to be displayed. In addition, as the sensor is sensitive to near infrared radiation, * jerome.vaillant@cea.fr

Demosaicking

White balance

Color correction (CCM) Raw image

Displayed image the standard color charts, like well-known Macbeth chart (ColorChecker® Classic from X-Rite [START_REF]Color Management Solutions and Products | X-Rite[END_REF]), are not suitable: their properties are defined and controlled only into visible spectrum. This motivates our effort to design a synthetic color chart (SCC) to better constrain the CCM evaluation.

In the following study, we focus on color rendering and we do not address the pixel interpolation part which also requires specific developments. First, we present hyperspectral images databases we consider for the synthetic color chart design.

In a second part, we detail the methodology used to choose representative spectra for SCC construction, by introducing a fourth dimension to CIE-L*a*b* space. Then CCM is computed using our chart and spectral sensitivity of Teledyne E2V Onyx sensor. Finally, we compare the impact of standard CCM versus custom CCM on color accuracy and SNR.

REFLECTANCE DATABASE CONSTITUTION

Standard color charts and limitation for VIS-NIR color restitution

For classical color imaging simulation, reflectance data represented on MCC chart may be used to compute a CCM or adjust white balance (WB) of the imaging device [START_REF] Farrell | Image Systems Simulation[END_REF]. This chart consists of 24 color patches that represent some physical common colors such as skin or foliage colors… sRGB and L*a*b* values of each patch are given by the manufacturer under respectively D65 and D50 CIE illuminants.

Figure 2. MacBeth ColorChecker chart, from X-Rite [START_REF]Color Management Solutions and Products | X-Rite[END_REF] For low light level applications, the infrared cutoff filter is removed from the camera to benefit from the silicon absorbance in this region. In that case, color signals are biased by NIR absorption. To compensate this bias, the NIR content of chart patches need to be known and calibrated. Unfortunately, MCC is not designed to deal with NIR and it is not adapted as reflectance reference for VIS-NIR color restitution. In order to compute a non-biased CCM, we defined a new set of colors with well-known reflectance spectra, based on hyperspectral images databases [START_REF] Skauli | A collection of hyperspectral images for imaging systems research[END_REF].

VIS-NIR reflectance spectra collection

The new reflectance data are collected from open access hyperspectral images. We took in consideration the Stanford Center for Image Systems Engineering database [START_REF] Parmar | A database of high dynamic range visible and near-infrared multispectral images[END_REF] mostly consisting in skins and landscapes (sky, forest..) reflectance data, the 2009 Multispectral Scene Data from ImageVal [START_REF]nm | Imageval[END_REF] consulting, and a set of diverse material reflectance spectra from US Geological Survey [START_REF]USGS.gov | Science for a changing world[END_REF] (see Figure 3). The hyperspectral images are spatially regularly subsampled to extract at first about 200,000 VIS-NIR reflectance spectra. To complete the existing databases, we developed our own VIS-NIR hyperspectral image acquisition bench (see Figure 4). The acquisitions are taken under halogen spots with a VIS-NIR monochromatic 10 bits camera and a set of narrow band-pass optical filters allowing to constitute a scene reflectance data cube of 38 spectral narrow bands from 400nm to 1050nm. The image noise is reduced by averaging several frames. For each monochromatic image, dark current and flat field correction are applied. Knowing all physical acquisition parameters such as optical setup, spectral sensitivity of the acquisition sensor and the illuminance spectrum, the reflectance spectra are extracted [START_REF] Farrell | Image Systems Simulation[END_REF].

SAMPLING THE DATABASE, TOWARDS A NEW "COLOR" CHART

After merging reflectance spectra databases, we want to reduce the number of spectra to constitute a suitable synthetic color chart. The selected 200,000 spectra have to be resampled to uniformly cover the chosen "color" space. Firstly we remind XYZ and L*a*b* spaces formalism, then we detail the extensions we proposed.

CIE formalism and MacBeth ColorChecker

The For that purpose, we add a new component Ir to CIE XYZ space which projects the NIR reflectance data under the chosen illuminant through an 𝑖𝑟 ̅ function. As mentioned before, XYZ are usually computed using CIE illuminants which are not defined outside the visible spectrum. In order to use illuminant with NIR content, we replace the CIE D illuminant by its black body equivalent, and 𝑖𝑟 ̅ (𝜆) is defined by shifting 𝑦 ̅(𝜆) by 400 nm toward the NIR domain (Eq. 3). The projection through CIE 𝑦 ̅ function gives the visible luminance Y of the considered spectrum. As well as for Y, Ir can be considered as a luminance but in NIR domain. This 𝑖𝑟 ̅ function is represented Figure 6.

𝐼𝑟 = 1 𝑁 ∫ 𝑖𝑟 ̅ (𝜆). 𝑅(𝜆). 𝐼(𝜆). 𝑑𝜆 𝑖𝑟 ̅ = 𝑦 ̅(𝜆 -𝜆 𝑠 ) 𝜆 𝑠 = 400 𝑛𝑚 (3)
As for the XYZ to L*a*b* transformation, a new 𝑐 𝑖𝑟 component is calculated using Y and Ir (Eq 4). The 𝑓 function has been defined (Eq 2).

𝑐 𝑖𝑟 = 100. (𝑓 𝑦 -𝑓 𝐼 )

The normalization factor was chosen empirically using the reflectance data collected Section 2. These spectra are projected in the L*a*b*cir space under a black body illuminant with a color temperature of 5000K. The factor is adapted to spread the points over a range about [-40 , +70] on cir alike a* and b* ranges.

Figure 6. CIE standard observer 𝑥̅ , 𝑦 ̅, 𝑧̅ functions for 2° degree and new 𝑖𝑟 ̅ function.

Resampling of the reflectance database and final synthetic chart

COLOR CORRECTION MATRIX FOR RGB-W LOW LIGHT LEVEL SENSOR

In this section the performance of the new synthetic color chart has to be tested and compared to the usual color correction method. For that purpose, the physical configuration of the studied sensor must be known to compute a new suitable CCM.

We present the sensor we considered, then the CCM computation and finally the results in terms of SNR and color accuracy.

Low light level sensor

The study is focused on the commercial low light sensor Teledyne-E2V Onyx EV76C664AMT. Four channels are used on this sensor: classical RGB and an additional "White" W channel which does not have any color filter. The main issue for low light level acquisition is the poor signal to noise ratio. So maximizing the collected signal is mandatory. Integration time has to be kept low to maintain high framerate in video acquisition. For such application, it is usually done by using the sensor without any infrared filtering to gather all the light on pixels. Obviously, this is detrimental for color fidelity: regarding quantum efficiencies of the channels (Figure 9), it is clear that without infrared filter, the color signals are overestimated due to the NIR transmission of the color filters.

Color correction matrix computation, database using

The camera device signal has its own algebraic space where each element (i.e. color) can be decomposed in a 4 components vector 𝑆 = [𝑆 𝑅 𝑆 𝐺 𝑆 𝐵 𝑆 𝑊 ] 𝑇 (S for Sensor, " 𝑇 " exponent for transpose). The acquired video sequence is then displayed on a screen which also has an algebraic space. Display spaces are normalized and we choose the sRGB space in this work.

The CCM is the linear transformation from the camera space to the displayable normalized space while ensuring the color a) b)

fidelity of the scene. The coefficients of the CCM are computed by linear minimum least square method comparing the results of camera output signals to the expected ones (sRGB) under a chosen illuminant.

For the target, we use our synthetic color chart to compute sRGB target coordinates of each patch: first from spectrum to XYZ under D50 illuminant using Eq. 2, the result is then converted into sRGB coordinates under D65 illuminant (Eq.5) applying Bradford adaptation (ABradford) [START_REF] Shevell | The Science of Color[END_REF] and the XYZ to RGB matrix (M) and performing gamma correction (𝛾 = 2.2).

[

𝑅 𝐺 𝐵 ] = (𝑀. 𝐴 𝐵𝑟𝑎𝑑𝑓𝑜𝑟𝑑 . [ 𝑋 𝑌 𝑍 ]) 1/𝛾 ( 5
)
Because sRGB is non-linear due to the application of gamma correction (𝛾 = 2.2), we need to re-linearize targeted RGB coordinates to use the linear minimization formalism. It can be done directly computing RGB coordinates without gamma correction in Eq.5.

For the sensor output, raw RGBW signals are computed considering QE curves shown on Figure 9 over synthetic patches, data are normalized to 255. Then, these vectors are stored in two matrices, defined in Eq. 6: a 4x1498 matrix called 𝑇 for targets and a 5x1498 matrix called 𝑆 for raw Sensor data. The last row composed of ones is added to compute an intrinsic offset signal to subtract.

𝑇 = [ 𝑇 𝑅1 … 𝑇 𝑅1498 𝑇 𝐺1 … 𝑇 𝐺1498 𝑇 𝐵1 … 𝑇 𝐵1498 1 … 1 ] 𝑆 = [ 𝑆 𝑅1 … 𝑆 𝑅1498 𝑆 𝐺1 … 𝑆 𝐺1498 𝑆 𝐵1 … 𝑆 𝐵1498 𝑆 𝑊1 … 𝑆 𝑊1498 1 … 1 ] (6)
The raw correction matrix, denoted 𝑀 ̂, is computed using the linear mean square error minimization, which has a unique analytical solution shown in Eq. 7.

𝑀 ̂= 𝑎𝑟𝑔𝑚𝑖𝑛 𝑀 (ℒ 2 (𝑇 -𝑀. 𝑆))

 𝑀 ̂𝑇 = (𝑆. 𝑆 𝑇 ) -1 . 𝑆𝑇 𝑇 (7)
The 3x4 CCM and the offset vector are extracted from 𝑀 ̂ as shown in Eq. 8.

𝑀 ̂= [ [𝐶𝐶𝑀] [0 ⋯ 0] [𝑉] 1 ]

𝑉 𝑜𝑓𝑓𝑠𝑒𝑡 = -𝐶𝐶𝑀 𝑇 . (𝐶𝐶𝑀. 𝐶𝐶𝑀 𝑇 ) -1 . 𝑉

Finally, Eq. 9 explains how to apply the color correction matrix and the offset vector on any raw sensor data (𝑆 = [𝑆 𝑅 𝑆 𝐺 𝑆 𝐵 𝑆 𝑊 ] 𝑇 ) to get corrected RGB coordinates (𝐶 = [𝐶 𝑅 𝐶 𝐺 𝐶 𝐵 ] 𝑇 ). Note that gamma correction has to be applied on these corrected values to satisfy sRGB specification and properly display them.

[

𝐶 𝑅 𝐶 𝐺 𝐶 𝐵 ] = ( 𝐶𝐶𝑀.
[

𝑆 𝑅 𝑆 𝐺 𝑆 𝐵 𝑆 𝑊 - 𝑉 𝑜𝑓𝑓𝑠𝑒𝑡 𝑅 𝑉 𝑜𝑓𝑓𝑠𝑒𝑡 𝐺 𝑉 𝑜𝑓𝑓𝑠𝑒𝑡 𝐵 𝑉 𝑜𝑓𝑓𝑠𝑒𝑡 𝑊 ] ) 1/𝛾 (9)

SNR and color accuracy results

The first step of the performance evaluation is to verify SNR improvement for the sensor coupled with our new color correction flow. Noise is usually separated in a chrominance and a luminance components, we consider only the latter. We start computing signal values of the different RGBW channels of the Onyx sensor without infrared filter under black body (6500K) illuminant, 20ms integration time, f/1 optics, for a grey surface (reflectance of 18%). The 3x4 CCM and the offset vectors are computed over the synthetic color chart for the same illuminant, then it is applied to the RGBW values to compute the corrected RGB values. Finally, the luminance signal Y is computed using Eq. 10. Noise variances are calculated, considering photon shot noise of the signal and readout noise of the sensor in order to evaluate the noise variance on the Y channel and compute SNRY: the signal to noise ratio on this channel [13][14].

For comparison, we consider a sensor dedicated to color photography under high to mid light level: we use RGB QE curves of Onyx product with an IR cutoff filter (𝜆 𝑐𝑢𝑡𝑜𝑓𝑓 = 650𝑛𝑚) placed in front of it. The raw RGB signal values are computed in the same way, under the same conditions. We apply a 3x3 CCM and white balance classically computed over the MacBeth ColorChecker. SNR is also computed on the Y channel. In each case, the SNR computation is done for a wide range of illumination values: from 1 mlux to 100lux. Table 1 shows a comparison between the two configurations in term SNR performance. Next, color fidelity should be evaluated too. Obviously, the color photography configuration will deliver far better color † and could be considered as upper bound for color fidelity. So we investigated the impact of color chart used to estimate the CCM. This is done quantitatively by computing the color errors over Synthetic Color Chart patches using CIE ΔE2000 metric [START_REF] Shevell | The Science of Color[END_REF]. Table 2 summarizes the results in terms of maximum, mean and minimum errors over the 1498 patches of the synthetic chart. Computing color mismatch over the full 200,000 spectral database confirms that performances are globally increased for a bunch of random spectra, showing that our method is more robust for color rendering when VIS and NIR are acquired with this color camera. In this 4D space we select a limited number of points which are uniformly distributed. These 1498 reflectance spectra constitute our new Synthetic Color Chart, allowing to compute color correction matrix taking into account not only the visible part of the spectrum but also the near-infrared part. Finally, a performance analysis is carried out on the Teledyne-E2V Onyx EV76C664AMT-RTR. We verify that SNR is increased using the low light configuration of the sensor, then we compare color restitution performance between a 3x4 CCM computed over the classical MCC or over our synthetic color chart. The results are illustrated and a CIE ΔE2000 computation over the synthetic chart showing that color restitution under low light conditions is better when CCM is computed using it than using MCC. This is a prior study and we plan to investigate other definition for 𝑖𝑟 ̅ and cir, but also the L*a*b*cir space sampling and CCM calculation. Another perspective is to design a physical color chart, perhaps containing less patches, instead of this synthetic color chart in order to practice real tests with commercial VIS-NIR color sensors.

ACKNOWLEGMENT

We would like to acknowledge B.Diaspara, P.Feyrère, P.Kuntz and T.Ligozat from Teledyne-E2V for the fruitful discussions on the topic.

Reference image (sRGB) RGB sensor with IR cutoff filter

Figure 1 .

 1 Figure 1. Color restitution flow from raw image to displayed image

Figure 3 .

 3 Figure 3. Examples of hyperspectral images and reflectance spectra collected from open access sources: a) SCIEN database b) ImageVal consulting, c) US Geological Survey

Figure 4 .

 4 Figure 4. Examples of sRGB reconstitution of hyperspectral images acquired with our own acquisition bench. a) papers, b) textiles, c) vegetables skins

  International Commission on illumination (CIE) developed the L*a*b* color space to approximate the human vision system [10][11]. To calculate L*a*b* coordinates associated to a surface from a reflectance spectrum under known illumination conditions, several mathematical transformations must be done. First of all, reflectance spectra 𝑅(𝜆) are projected in CIE XYZ space under standard CIE illuminant (either D50 or D65) 𝐼(𝜆) through the CIE standard observer functions 𝑥̅ , 𝑦 ̅ and 𝑧̅ (see Figure 6). (𝜆). 𝑅(𝜆). 𝐼(𝜆). 𝑑𝜆 𝑁 = ∫ 𝑦 ̅(𝜆). 𝐼(𝜆). 𝑑𝜆 non-linear transformation is applied to the XYZ coordinates to compute L*a*b* coordinates [12]: 𝐿 = 116. 𝑓 𝑦 -16 𝑎 * = 500. (𝑓 𝑥 -𝑓 𝑦 ) 𝑏 * = 200. (𝑓 𝑧 -𝑓 𝑦 ) 𝐹𝑜𝑟 𝑈 = {𝑋, 𝑌, 𝑍} 𝑈 𝑊 𝑖𝑠 𝑡ℎ𝑒 𝑤ℎ𝑖𝑡𝑒 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒 𝑜𝑓 𝑖𝑙𝑙𝑢𝑚𝑖𝑛𝑎𝑛𝑡 𝑎𝑛𝑑 *b* coordinates associated to the 24 patches of the MCC are provided by the manufacturer under CIE D50 illuminant. Figure 5 presents the a*b* projection of MCC patches. The points are distributed into a range of [-40,+60] on the a* axis and [-50,+80] on the b* axis.

Figure 5 .

 5 Figure 5. Distribution of the MacBeth ColorChecker chart patches in the L*a*b* space (left) and a* b* plane (right).

3. 2

 2 Near infrared representation, a new 4D L*a*b*cir space Although NIR part is not sensed by human eye and so not represented in L*a*b*, we need to project it in a uniform space. In this context, we decided to treat NIR part with the same kind of transformations than visible part adding a new component to the classical CIE L*a*b* space, we called 𝑐 𝑖𝑟 .

Figure 7 .

 7 Figure 7. Distribution in CIE like a*b*cir space (top left) and according to the 3 main planes of the new color 1498 elements color checker under black body (5000K) illuminant. MCC points colorized on top right plot.A limited number of representative spectra are selected among the 200,000 collected elements to constitute the synthetic color chart. First, we project all spectra into the newly defined L*a*b*cir space, and we take into account only a*b*cir components to subsample data: a* and b* are linked to the hue and saturation, and cir is linked to NIR signal. Then, the a*b*cir space is uniformly binned into 20x20x20 elements according to each axe. In every voxels, only the closest point

Figure 8 .

 8 Figure 8. sRGB representation of the synthetic color chart, hue sorted (a*b* plane)

Figure 9 .

 9 Figure 9. a) Teledyne E2V Onyx E2V76C664 quantum efficiency, b) color filters arrangement (from datasheet). The monochrome channel is called white channel in this paper.

Figure 10 :

 10 Figure 10: Comparison of color correction performance between classical visible case (RGB camera with IR cutoff filter) and low light sensor (RGBW channels without IR cutoff filter)

Table 1 :

 1 SNRY performances of sensor with classical or low light configuration

		Usual color photography	Low light
		configuration	configuration
	Illumination value for 𝑆𝑁𝑅 𝑌 = 1	0.050 lux	0.015 lux
	RGBW sensor implementing our color correction is able to deliver SNRY =1 for 3 times lower illumination than standard
	camera.

Table 2 :

 2 Color mismatch (CIE ΔE2000 error between expected colors and restituted colors over the 1498 patches of the synthetic Visual and qualitative comparison is shown on Figure10. On the upper right corner sRGB image computed using standard observer functions is displayed for reference. The first row shows the case of photographic sensor (RGB channels with infrared filter), on left the raw image, on right after white balance and color correction using CCM evaluation on MCC. The second row presents images for RGBW sensor under consideration (no IR filter), from left to right: raw image, image corrected by CCM computed for RGB equivalent photographic sensors (same as in first row), image corrected by 3x4 CCM computed only on MCC patches and image corrected by 3x4 CCM computed on our SCC. Qualitatively, this last image shows acceptable hue and saturation on the scene.

	color chart
		max(ΔE2000)	mean(ΔE2000)	min(ΔE2000)
	Applied color correction matrix	SCC	Full spectral database	SCC	Full spectral database	SCC	Full spectral database
	3x4 CCM computed
	using MacBeth	33.18	49.24	10.15	22.69	2.24	1.12
	ColorChecker chart
	3x4 CCM computed
	using synthetic color	27.60	42.5	5.2	16.4	0.27	0.01
	chart
	With Δ𝐸 2000 𝑚𝑎𝑥 = 6.75, Δ𝐸 2000 𝑚𝑒𝑎𝑛 = 2.19, Δ𝐸 2000 𝑚𝑖𝑛 = 0.48.

†


Jean-Pierre Leclerc
email: jean-pierre.leclerc@univ-lorraine.fr

Roda Bounaceur

Frédérique Olivier Herbinet

Battin Leclerc

Céline Le Dreff

Sylvain Aguinaga

Mélanie Nicolas

Frédérique Battin Leclerc

Melanie Nicolas

Modelization of the aeraulic in a wood-burning appliance

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

The work presented here deals with the modeling of the flow by Computational Fluid Dynamics, the experimental measurements of RTD and their analysis, as well as the modeling of the aeraulic within the heating appliance using the DTS-Pro software [1].

These early CFD modeling works, as well as the overall flow model proposed using the DTS Pro software based on experimentally measured Residence Time Distributions (RTD), are promising. They made it possible to set up a methodology adapted to the study of the aeraulic in a wood-burning appliance according to two distinct approaches and they provide results that prove to be coherent and complementary.

In this paper, we do not present results coming from CFD modelling.

DESCRIPTION OF THE WOOD-BURNING APPLIANCE 1

Experimental Resident Time distribution have been studied by introducing tracer in different position of a woodburning appliance. We have choose Krypton (m/z 84) as a tracer and the analytical system OmniStar with a mass range of 1-200 amu from PFEIFFER to analyze the gas flow in continue.

Depends on the position of the injection we obtained different kind of signal.

Tracer8, 8th international Conference on Tracers and Tracing Methods, Đà Nẵng , Vietnam, February 26-28, 2019 Using the software DTS-Pro we propose an aeraulic model for the wood-burning appliance. Whatever the position on the injection of tracer, the experimental and simulated result are in good agreement. This model allow us to determine the resident time distribution inside the oven, roughly it take 11 s from the entrance to the outlet.

KEYWORDS: aeraulic, wood-burning appliance, combustion

[1] LECLERC J. P., ANTOINE B., Software "DTSPRO V4.2", PROGEPI LSGC -CNRS -ENSIC, Nancy, 2000

Objective

-The objective of the project research is to take into account the impact of aeraulics in a wood burning appliance, in order to better manage the distribution of gas flows, in view of optimizing combustion and thus reducing pollutant emissions at the source.

-The work presented here deals with the modeling of the flow by experimental measurements of RTD and their analysis, as well as the modeling of the aeraulic within the heating appliance using the DTS-Pro software [1].

RTD Signals

Zone 1

Zone 2 Zone 3

1.Each branches (WD, PAL, etc …) have been modeled with a plug-flow followed by a mixer with back-mixing. For our convenience we have fixed J=2 and =0.27 2.We have used the compartment model to modelized the whole system by varying by simulation the different positions of injection 3.For Cold or Hot Condition, the architecture of the compartment model is conserved 4.For Cold or Hot Condition, we fixe Q 1 and we optimize the different volumes of each modules 5.These volumes are conserved for the simulation with Q 2

Methodology CFD calculation

Presence of 3 zones of recirculation

  aeraulics in a wood-burning appliance Roda BOUNACEUR 1 , Olivier HERBINET 1 , Frédérique BATTIN LECLERC 1 , Jean-Pierre LECLERC 1* , Céline LE DREFF 2 , Sylvain AGUINAGA 2 and Frédéric ROBIC 3 1 LRGP, 2 CSTB, 3 LORFLAM * jean-pierre.leclerc@inrs.fr Mass spectrometer connected in line to a wood stove -Krytpon (m/z 84) was injected with air at different position of the wood-burning appliance -The pulse was measured in continue through a mass spectrometer from Pfeiffer (OMNISTARdetection limit=500ppb) -Volume of the wood stove: V = 70.6 l -Two different flow rates have been studied: Q 1 = 26 m 3 .h -1 and Q 2 = 20 m 3 .h -1 -Free Residence time: and -Flow rates at different positions have been calculated by CFD calculation -Two different conditions: 1. Hot condition -with wood burning 2. Cold condition -without wood burning Experimental approach {1] LECLERC J. P., ANTOINE B., Software "DTSPRO V4.2", PROGEPI LSGC -CNRS -ENSIC, Nancy, 2000 Air + Krypton Results -Good agreement between experiments and simulations whatever the condition and the flow rate -The next step is to couple the RTD model with a full detailed kinetic model for the combustion of wood in order to better understand the formation of pollutant. The kinetic model has already been published: "Development of a detailed kinetic model for the combustion of biomass", Dhahak and al., Fuel, 242, 756-774, 2019.


Amal Dhahak

Roda Bounaceur

Céline Le Dreff-Lorimier

Guillaume Schmidt

Gwenaëlle Trouve

Frédérique Battin-Leclerc
email: frederique.battin-leclerc@univ-lorraine.fr

Development of a detailed kinetic model for the combustion of biomass

Keywords: Combustion, biomass, tars, detailed kinetic model, hydroxyacetaldehyde, Thermo-Gravimetric Analysis (TGA)

In the context of the growing utilization of biomass to produce energy and of the related need to decrease pollutant emissions from domestic wood combustion devices, this paper presents a new kinetic model of wood combustion considering especially in details the gas-phase reactions related to the combustion of the tars produced by the biomass devolatization. The tar production is predicted using a semi-detailed mechanism of the literature. The tar gas-phase combustion model has been built as a compilation of literature mechanisms already proposed for these species, except for hydroxyacetaldehyde for which a new oxidation mechanism has been written. Experiments on the thermochemical behavior of three types of wood (beech, fir and oak) were also performed in parallel of this work using Thermogravimetric Analysis (TGA).

The new detailed kinetic model of wood combustion, BioPOx (Biomass Pyrolysis and Oxidation), has been tested against a wide range of experimental results published in literature.

This model fairly reproduces experimental results for pyrolysis and combustion of biomass and its constituents, key produced tars from biomass pyrolysis, and key compounds for Polycyclic Aromatic Hydrocarbons (PAH) formation, for a wide range of experimental devices and operating conditions.

Introduction

The current global warming issues, especially the concerns about the alarming rise of atmospheric CO2 [START_REF]World Meteorological Organization[END_REF], have increased the importance of the use of fuels from renewable resources, primarily biomass. The use of wood and biomass for domestic small combustion installations (fireplaces, stoves and boilers) is widely widespread in countries where heating is needed in winter [START_REF] Haberle | Numerical models for thermochemical degradation of thermally thick woody biomass, and their application in domestic wood heating appliances and grate furnaces[END_REF]. Residential wood burning significantly affects the air quality because it is one of the largest sources of fine particles (PM2.5, particulate matter of aerodynamic diameter below 2.5 m). In addition, it is responsible for the emissions of a number of other pollutants (carbon and nitrogen monoxides, oxygenated hydrocarbons such as aldehydes and ketones, alcohols, furans and acids, PAH...) [START_REF]Residential heating with wood and coal: health impacts and policy options in Europe and North America[END_REF]. Environmentally sustainable wood heating will require a better understanding of the chemistry of the pollutant formation in such devices. Especially the development of kinetic models involving the chemical reactions responsible for pollutant formation is needed.

Lignocellulosic biomass pyrolysis and combustion are multi-scale, multi-phase, and multicomponent processes [START_REF] Mettler | Top ten fundamental challenges of biomass pyrolysis for biofuels[END_REF], since biomass has a complex structure consisting mainly of a mixture of biopolymers: cellulose, hemicellulose, lignin with a small amount of extractives [START_REF] Liu | Fates of Chemical Elements in Biomass during Its Pyrolysis[END_REF].

Biomass combustion includes four stages: drying, pyrolysis, homogeneous combustion of volatile products and heterogeneous combustion of char. Pyrolysis is the first step in any energy recovery processes such as combustion and gasification [START_REF] Popova | Thermal degradation and combustion of wood fuels, coals and hydrolyzed lignin from the Russian Federation: experiments and modeling[END_REF]. Modeling biomass pyrolysis is therefore essential for understanding combustion [START_REF] Zhou | A thermal decomposition study of pine wood under ambient pressure using thermogravimetry combined with synchrotron vacuum ultraviolet photoionization mass spectrometry[END_REF], which justifies the abundance of work in this field within the literature [START_REF] Papari | A review on the pyrolysis of woody biomass to bio-oil: Focus on kinetic models[END_REF][START_REF] Dhyani | A comprehensive review on the pyrolysis of lignocellulosic biomass[END_REF][START_REF] Kan | Lignocellulosic biomass pyrolysis: A review of product properties and effects of pyrolysis parameters[END_REF][START_REF] Collard | A review on pyrolysis of biomass constituents: Mechanisms and composition of the products obtained from the conversion of cellulose, hemicelluloses and lignin[END_REF].

In the literature, two simplified approaches are generally proposed to describe biomass thermal degradation: the homogeneous approach, where biomass is considered as a homogeneous solid and the heterogeneous approach which takes into account the contribution of each biomass constituents (cellulose, hemicellulose and lignin) to the overall mechanism. According to the first approach, one or some global chemical reactions may be sufficient to describe wood devolatilization. A one-step global mechanism is the most simplified kinetic model used by many works in the literature [START_REF] Larfeldt | Modelling and measurements of heat transfer in charcoal from pyrolysis of large wood particles[END_REF][START_REF] Galgano | Experimental validation of a coupled solidand gas-phase model for combustion and gasification of wood logs[END_REF][START_REF] Yuen | Modelling the pyrolysis of wet wood -I. Three-dimensional formulation and analysis[END_REF][START_REF] Yang | Combustion of a Single Particle of Biomass[END_REF][START_REF] Galgano | Numerical simulation of the glowing combustion of moist wood by means of a front-based model[END_REF][START_REF] Ding | Modeling the pyrolysis of wet wood using FireFOAM[END_REF]. Biomass decomposes into volatile compounds and a solid residue. This type of mechanism is generally used to model mass loss either by pyrolysis or thermogravimetric analysis (TGA) [START_REF] Papari | A review on the pyrolysis of woody biomass to bio-oil: Focus on kinetic models[END_REF]. It is also used to model coupled chemical kinetics and physical phenomena, using for example a CFD (Computational Fluid Dynamics) approach [START_REF] Yang | Combustion of a Single Particle of Biomass[END_REF] [START_REF] Ding | Modeling the pyrolysis of wet wood using FireFOAM[END_REF]. The second common type of kinetic models in the homogeneous approach is independent competitive reaction scheme. According to this model, biomass produces competitively tar, gases, and char [START_REF] Haberle | Numerical models for thermochemical degradation of thermally thick woody biomass, and their application in domestic wood heating appliances and grate furnaces[END_REF]. By using this reaction scheme, yields of tar, char and permanent gases can be predicted, which is not the case with one-step global mechanism.

Generally, this second type of model is coupled to secondary reactions of tars formed during pyrolysis [START_REF] Grønli | Mathematical Model for Wood Pyrolysis Comparison of Experimental Measurements with Model Predictions[END_REF][START_REF] Bryden | Modeling the combined impact of moisture and char shrinkage on the pyrolysis of a biomass particle[END_REF][START_REF] Sand | Numerical prediction of the transport and pyrolysis in the interior and surrounding of dry and wet wood log[END_REF][START_REF] Sadhukhan | Modelling and experimental studies on pyrolysis of biomass particles[END_REF][START_REF] Kwiatkowski | Pyrolysis and gasification of a thermally thick wood particle -Effect of fragmentation[END_REF]. Multistep mechanisms are also discussed. In those schemes, an intermediate solid is formed by the first step and continues to decompose into secondary products [START_REF] Branca | Global interinsic kinetics of wood oxidation[END_REF].

According to the heterogeneous approach, the pyrolytic behavior of biomass is deduced from that of its major constituents: independent parallel reaction mechanisms, representing respectively cellulose, hemicellulose and lignin degradation, have been widely used to model biomass pyrolysis [START_REF] González | Pyrolysis of cherry stones: Energy uses of the different fractions and kinetic study[END_REF][START_REF] Radmanesh | A unified lumped approach in kinetic modeling of biomass pyrolysis[END_REF][START_REF] Barneto | Simulation of the thermogravimetry analysis of three non-wood pulps[END_REF]. This type of mechanism allows a better prediction of product yields.

It can be applied to a variety of biomass since the content of cellulose, hemicellulose and lignin differs from one type to another. Interactions between biomass constituents is neglected. A number of studies uses the Broido-Shafizadeh's scheme (Fig. 1) to model biomass pyrolysis. This scheme, which was developed for the first time for cellulose degradation, has been applied to lignin, hemicellulose and wood pyrolysis. Biomass is converted to intermediate solid called "active biomass" (reaction 1) which decomposes by competitive reactions (reactions 2 and 3) into gaseous, liquid and solid products [START_REF] Papari | A review on the pyrolysis of woody biomass to bio-oil: Focus on kinetic models[END_REF].

Fig. 1. Broido-Shafizadeh's scheme to model biomass pyrolysis [START_REF] Shafizadeh | Thermal degradation of cellulose in air and nitrogen at low temperatures[END_REF].

The most complex reaction scheme in the literature to simulate biomass pyrolysis following the heterogeneous approach is that of Ranzi who developed in 2008 a first multi-step semi-detailed mechanism [START_REF] Ranzi | Chemical kinetics of biomass pyrolysis[END_REF] extending the Broido-Shafizadeh's approach. Dussan et al. proposed a new semi-detailed kinetic mechanism based on a recent Ranzi scheme [START_REF] Debiagi | Extractives Extend the Applicability of Multistep Kinetic Scheme of Biomass Pyrolysis[END_REF] respectively for hemicellulose [START_REF] Dussan | Integrating compositional features in model compounds for a kinetic mechanism of hemicellulose pyrolysis[END_REF] and lignin pyrolysis [START_REF] Dussan | A model of the chemical composition and pyrolysis kinetics of lignin[END_REF]. More advanced approaches would involve microkinetic mechanistic models based on theoretical calculations as proposed by the Broadbelt team for cellulose [START_REF] Broadbelt | Lexicography of kinetic modeling of complex reaction networks[END_REF][START_REF] Vinu | A mechanistic model of fast pyrolysis of glucose-based carbohydrates to predict bio-oil composition[END_REF][START_REF] Zhou | Experimental and Mechanistic Modeling of Fast Pyrolysis of Neat Glucose-Based Carbohydrates. 1. Experiments and Development of a Detailed Mechanistic Model[END_REF] and hemicellulose [START_REF] Zhou | A mechanistic model of fast pyrolysis of hemicellulose[END_REF] and by Horton et al. [START_REF] Horton | Molecular-Level Kinetic Modeling of Biomass Gasification[END_REF] for biomass pyrolysis and gasification.

Compared to pyrolysis, significantly fewer studies were published about the kinetic modelling of biomass combustion. Thermal degradation under oxidative atmosphere is indeed more complex. The presence of an oxidizing agent (air, oxygen, etc.) generates homogenous gasphase reactions between oxygen and volatiles compounds released during devolatilization and heterogeneous reactions between oxygen and char [START_REF] Gil | Thermal behaviour and kinetics of coal/biomass blends during co-combustion[END_REF].

A two-stage reaction kinetic scheme was proposed by Gil et al. [START_REF] Gil | Thermal behaviour and kinetics of coal/biomass blends during co-combustion[END_REF] and Shen et al. [START_REF] Shen | Kinetic study on thermal decomposition of woods in oxidative environment[END_REF] to represent biomass and char combustion. Pérez et al. [START_REF] Pérez | Kinetic analysis of pyrolysis and combustion of the olive tree pruning by chemical fractionation[END_REF] proposed a scheme including three independent reactions to represent respectively, cellulose, hemicellulose and lignin combustion coupled with a fourth reaction representing char oxidation. Wang et al. [START_REF] Wang | Characterisation and model fitting kinetic analysis of coal/biomass co-combustion[END_REF] consider two simultaneous parallel reactions: an overall reaction describing biomass combustion and two individual reactions representing respectively volatiles and carbon residue oxidation. Navarrete Cereijo et al. [START_REF] Navarrete Cereijo | Simplified model and simulation of biomass particle suspension combustion in one-dimensional flow applied to bagasse boilers[END_REF] modeled biomass combustion as three sequential stages, which are drying, pyrolysis and char oxidation. In this work [START_REF] Navarrete Cereijo | Simplified model and simulation of biomass particle suspension combustion in one-dimensional flow applied to bagasse boilers[END_REF], as is shown in Fig. 2, five reactions were used to represent biomass decomposition into tars (reaction 1) , volatiles (reaction 2) , and char (reaction 3), as well as tar degradation in volatiles (reaction 4) and char (reaction 5). The char combustion stage was modeled using three reactions (reactions 6, 7 and 8): direct combustion with oxygen and two reactions respectively with CO2 and H2O. A similar approach was used by Mätzing et al. [START_REF] Mätzing | Modelling grate combustion of biomass and low rank fuels with CFD application[END_REF] to model biomass combustion in fixed bed reactor with a slightly more detailed pyrolysis mechanism considering cellulose, hemicellulose and lignin devolatilization. However, approaches using global reactions cannot be an appropriate method to predict in details pollutant formation during biomass combustion in stoves or industrial systems for instance.

The main aim of this paper is to develop and validate a new detailed kinetic model of wood pyrolysis and combustion in order to predict pollutant emissions. This kinetic mechanism is tested against new TGA results obtained in parallel of this work, as well as a wide range of experimental results published in literature. The used literature results (29 datasets) and the comparisons with the present model predictions have been collected and organized as a database given as two spreadsheets in Supplementary Material (SM).

I/ Description and validations of the chemical model

A new detailed kinetic mechanism, BioPOx, has been developed in Chemkin format. It includes two parts, (1) a semi-detailed mechanism to describe biomass pyrolysis, (2) a detailed mechanism of the gas-phase combustion of the volatiles species.

I.1. Semi-detailed mechanism to describe biomass pyrolysis and char combustion

I.1.a. Description of the model

From 2008, when the team of Ranzi [START_REF] Ranzi | Chemical kinetics of biomass pyrolysis[END_REF] in Milano proposed the first multi-step semi-detailed mechanism to simulate biomass pyrolysis, this model has been progressively up-dated [START_REF] Debiagi | Extractives Extend the Applicability of Multistep Kinetic Scheme of Biomass Pyrolysis[END_REF][START_REF] Ranzi | Kinetic modeling of the thermal degradation and combustion of biomass[END_REF][START_REF] Corbetta | Pyrolysis of Centimeter-Scale Woody Biomass Particles: Kinetic Modeling and Experimental Validation[END_REF][START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF][START_REF] Ranzi | Mathematical Modeling of Fast Biomass Pyrolysis and Bio-Oil Formation. Note I: Kinetic Mechanism of Biomass Pyrolysis[END_REF]. In this work, we used the 2016 version developed by Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] without change.

This last kinetic mechanism consists of 27 semi-detailed reactions and 47 species. 22 species in the solid and metaplastic phase are involved. Thermodynamic data of these solid species are taken from [START_REF] Corbetta | Pyrolysis of Centimeter-Scale Woody Biomass Particles: Kinetic Modeling and Experimental Validation[END_REF]. The method for writing this mechanism is based on grouping similar species and lumping related reactions.

The model of Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] uses a detailed description of biomass, characterized as a mixture of three main constituents: cellulose, hemicellulose and lignin, the contents of which may significantly vary depending on the different types of biomass. Wood, even after drying, can still contains an average of 10-15% in mass of moisture [START_REF] Vassilev | An overview of the chemical composition of biomass[END_REF]. However, since water can be considered mostly as a dilutant gas under the studied conditions, its amount has been neglected in this kinetic work. Hydrophobic and hydrophilic wood extractives, consisting mainly of terpenes, phenolic compounds, fatty and resin acids and triglycerides [START_REF] Dorado | Degradation of lipophilic wood extractive constituents in Pinus sylvestris by the white-rot fungi Bjerkandera sp. and Trametes versicolor[END_REF], were also neglected in our work as a first approach, because they account for less than 10% in mass of the entire biomass [START_REF] Ranzi | Chemical kinetics of biomass pyrolysis[END_REF]. Lignocellulosic biomass is also characterized by a content of minerals (potassium, calcium, sodium, silicon, phosphorus, chlorine and magnesium), less than 1% for wood [START_REF] Sharma | Biomass pyrolysis -A review of modelling, process parameters and catalytic studies[END_REF]. In addition to the three main constituents, extractives and minerals, wood and woody biomass contains 0.1-0.7% of nitrogen and 0.01-0.42% of sulfur [START_REF] Vassilev | An overview of the chemical composition of biomass[END_REF]. The presence of minerals, nitrogen and sulfur was not taken into account in our study.

Each constituent is represented by a pseudo-compound. Cellulose (CELL) is represented by the glucose monomer (C6H10O5). Xylan (C5H8O4) is the monomer chosen for hemicellulose (HCE).

Lignin, having a complex structure, is represented by three reference compounds LIGC (C15H14O4), LIGH (C22H28O9), and LIGO (C20H22O10), richer in C, H and O, respectively. The biomass characterization in this three constituents is a preliminary but a very important step.

The characterization procedure consists of determining from the elemental composition of biomass (C/H/O, corrected by not considering water, N, S and other minerals), the biochemical composition in terms of cellulose, hemicellulose and lignin [START_REF] Debiagi | Extractives Extend the Applicability of Multistep Kinetic Scheme of Biomass Pyrolysis[END_REF].

Assuming that there is no interaction between the three constituents, the devolatilization of biomass is thus considered a straightforward combination of the pyrolysis of the five reference components. As it will be described in part I.2, the produced volatile compounds may undergo secondary pyrolysis or combustion reactions in the gas phase. As shown in table 1, heterogeneous char combustion reactions were added to the model of Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] according to what was proposed by Navarrete Cereijo et al. [START_REF] Navarrete Cereijo | Simplified model and simulation of biomass particle suspension combustion in one-dimensional flow applied to bagasse boilers[END_REF] (see Fig. 2) and by Ranzi et al. [START_REF] Ranzi | Comprehensive and detailed kinetic model of a traveling grate combustor of biomass[END_REF].

I.1.b. Tests of the model

The model described in part I.1.a (in all this part, the model of Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] + the 3 reactions of Table 1 was used) has been tested both on TGA results obtained on purpose for this work, and on a wide range of literature results. The biomass characterization in this three constituents was taken from a database built in Milano [START_REF] Debiagi | Extractives Extend the Applicability of Multistep Kinetic Scheme of Biomass Pyrolysis[END_REF].

I.1.b./ New TGA results

TGA experiments were carried out to study the thermal degradation of beech, oak and fir wood chips locally produced from the Alsacian forest and purchased from Agrivalor (Hirsingue, France). They were ground and sized to 4 mm of particle diameter. Hundred grams of each specie were dried at 105°C for 48h in an oven and then stored in a desiccator for further analyses. The physical and chemical properties of woods, as determined in the study of Schmidt et al. [START_REF] Schmidt | Wood washing: Influence on gaseous and particulate emissions during wood combustion in a domestic pellet stove[END_REF], are shown in table 2. TGA were performed from ground and dry wood samples (masses ranging from 5 to 10 mg) under an oxidative (air) atmosphere in a TA Instruments Q500 thermal analyzer under a temperature ramp equal to 5 °C.min -1 from room temperature to 700°C. To confirm the reproducibility of results, the experiments were carried out at least six times, for each sample. The accuracy of the scale given by the manufacturer is about 0.1 μg.

The standard deviations on the values of the maximum mass loss rates in DTG are from 1 to 2% whatever the nature of the sample. Since the model of Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] has been optimized for low heating rates, this new experimental study under oxidative conditions has been made with a heating rate lower to what can be found in literature. Thanks to the model previously described, the mass loss observed in these TGA experiments can be well predicted. Comparison between experimental results and model predictions of the thermal degradation of raw beech, fir and oak wood under air is shown in Fig. 3. The small overprediction in TGA curves observed below 300°C is due to the fact that water evaporation during the drying step is neglected. The agreement between experimental results and model predictions for TGA is better in case of fir which contains less amount of ashes than beech and oak, as shown in table 2. From DTG (Derivative Thermo-Gravimetric) curves, it is possible to obtain the instantaneous mass loss rates at all temperatures. Three steps can be distinguished as shown by the three peaks: the devolatilization of hemicellulose between 200 and 300°C, the devolatilization of cellulose, between 300 and 350°C, and the devolatilization of lignin accompanied by the char oxidation 400 and 500 °C.

I.1.b./ Tests against literature results

To better know the limitations of this model, we have tested it against the results of a wide range of experimental studies as shown in Table 3. These tests were performed on 10 cases of primary pyrolysis and TGA of wood or wood components (see details and results in a spreadsheet in supporting material).

The experimental studies 1, 2 and 6 were already modeled in the literature [START_REF] Ranzi | Chemical kinetics of biomass pyrolysis[END_REF][START_REF] Dussan | Integrating compositional features in model compounds for a kinetic mechanism of hemicellulose pyrolysis[END_REF][START_REF] Dussan | A model of the chemical composition and pyrolysis kinetics of lignin[END_REF][START_REF] Pérez | Kinetic analysis of pyrolysis and combustion of the olive tree pruning by chemical fractionation[END_REF][START_REF] Navarrete Cereijo | Simplified model and simulation of biomass particle suspension combustion in one-dimensional flow applied to bagasse boilers[END_REF][START_REF] Vassilev | An overview of the chemical composition of biomass[END_REF] while the experimental studies 3-5 and 7-10 are simulated for the first time in this paper.

As shown in Table 3, a majority of studies was performed using TGA. TGA experiments (as well as Derivative thermo-gravimetric (DTG) indicating mass loss rates) are modelled with the software CHEMKIN-PRO [START_REF]ANSYS Reaction Design[END_REF], considering the reactor as a Perfectly Stirred Reactor (PSR) or as a batch reactor if the sample is enclosed in a vessel.

Williams and Besler [START_REF] Williams | The influence of temperature and heating rate on the slow pyrolysis of biomass[END_REF] studied the effect of the heating rate on the degradation of pine wood, cellulose and hemicellulose under an inert atmosphere (nitrogen). Two heating rates were used:

5 and 20° C.min -1 . Fig. 4 compares model predictions and the experimental measurements of Williams and Besler [START_REF] Williams | The influence of temperature and heating rate on the slow pyrolysis of biomass[END_REF] for degradation of pine wood and its constituents (cellulose and hemicellulose). The agreement between experimental results and model predictions is the best in the case of cellulose. The hemicellulose degradation, considered as a polymer of xylan, begins at lower temperatures in experiments than what is predicted, because its decomposition forms more solid residue (20 wt%) than in the case of cellulose (5 to 10 wt%). Consequently, the predicted temperature for the start of the decomposition of the pine wood is also slightly higher than what was experimentally observed. In order to see the effect of adding air in TGA, Fig. 5 reports a comparison between predictions and experiments for oak thermal degradation respectively under air (this study, data of Fig. 3) and argon atmospheres by Le Brech et al. [START_REF] Brech | Mechanisms of biomass pyrolysis studied by combining a fixed bed reactor with advanced gas analysis[END_REF]. The difference between the two curves occurs mainly at high temperatures (>400°C) where char reacts with oxygen from air. The results shown here and in the spreadsheet of supplementary material show that, in most cases, for wood and its constituents, either under inert or oxidative atmosphere, the comparisons between TGA experiments and model predictions show reasonable agreement at low heating rates. The effect of a higher heating rate was studied by Shen et al. [START_REF] Shen | Kinetic study on thermal decomposition of woods in oxidative environment[END_REF] using two types of wood: softwood (pine) and hardwood (birch, aspen and oak). Elemental, approximate and chemical compositions of the studied woods are shown in table 4. The thermal degradation of these biomasses under air, at two heating rates is shown in Fig. 6. The model predictions of woods degradation at 10°C/min are satisfactory while predicted TGA curves at 100°C/min are slower than experiments. This is due to the fact that the model of Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] has been optimized for lower heating rates. Note however that the agreement is slightly better in the case of pine and oak than for Aspens and birch containing more ashes, the possible catalytic effect of which is neglected in the model. Kinetic mechanisms can also be used to predict product yields obtained during wood pyrolysis.

One of the most detailed study of product yields during wood pyrolysis is that performed by Le Brech et al. [START_REF] Brech | Mechanisms of biomass pyrolysis studied by combining a fixed bed reactor with advanced gas analysis[END_REF] in a U-shape fixed bed reactor using two types of wood: oak and Douglas. The reactor was modelled as a Plug Flow Reactor (PFR). Fig. 7a reports the comparison between predictions and experiments for the mass loss during slow pyrolysis [START_REF] Brech | Mechanisms of biomass pyrolysis studied by combining a fixed bed reactor with advanced gas analysis[END_REF] and shows a satisfactory agreement.

Tar, solid and gas yields are shown in Fig. 7b, with an acceptable agreement between experiments and modeling. For the same study [START_REF] Brech | Mechanisms of biomass pyrolysis studied by combining a fixed bed reactor with advanced gas analysis[END_REF], Fig. 8 compares the predicted evolution of CO and CO2, the main gaseous products, to experimental results [START_REF] Brech | Mechanisms of biomass pyrolysis studied by combining a fixed bed reactor with advanced gas analysis[END_REF]. In both model and experiments, CO2 is the major gas compounds. The model predictions overestimate the mass fraction of CO2 and CO for all the studied cases, except for CO mole fraction for oak pyrolysis at 300°C and for CO2 mole fraction for oak pyrolysis at 500°C. Using the same experimental set-up, Le Brech et al. [START_REF] Brech | Mechanisms of biomass pyrolysis studied by combining a fixed bed reactor with advanced gas analysis[END_REF] have also performed a study of Miscanthus pyrolysis (the experimental and simulated data for mass loss and tar, solid and gas (considered as the sum of CO, CO2, H2, CH4, C2H4, C2H6 and C6H6) yields are given in SM). In this study, as is shown in Fig. 9, the authors have also analyzed product yields for products gaseous at room temperature (CO2 (Fig. 9a), CO (Fig. 9b) and CH4 (Fig. 9c), as well as for one of the primary tars, phenol (Fig. 9d). The model predictions of CO2 formation during miscanthus pyrolysis are satisfactory while the mass fraction of CO and that of CH4 are underestimated at high temperatures. The comparison between experimental and model predictions for phenol formation shows a reasonable agreement at low temperatures (< 400°C) for the shape of the temperature dependence.

In summary, thanks to this devolatilization model, for TGA under inert or oxidative atmosphere, the comparisons between experiments and model predictions show an acceptable agreement at low to moderate heating rates. Yields of primary pyrolysis products can also be fairly predicted until moderate temperatures. For high temperatures, gas-phase reactions effect cannot be neglected. Hence the need to consider primary tars degradation mechanism, which will be described in the next section.

I.2/ Detailed mechanism of the gas-phase combustion of the volatiles species

I.2.a. Description of the model

The second part of the BioPOx mechanism considers the gas-phase reactions induced by the combustion of the volatile species produced by the biomass devolatilization. As is shown in table 5, the BioPOx mechanism combines four chemical mechanisms: (1) a first one taken from [START_REF] Husson | New experimental evidence and modeling study of the ethylbenzene oxidation[END_REF] to describe the combustion of usual hydrocarbons, including aromatic compounds, such as benzene or toluene, or oxygenated compounds, such C1-C10 aldehydes or phenol, (2) a chemical mechanism for nitrogen oxides NOx formation [START_REF] Song | The sensitizing effects of NO2 and NO on methane low temperature oxidation in a jet stirred reactor[END_REF], (3) detailed mechanisms of the combustion of volatiles species chosen as surrogates of biomass tars, as shown in the table 6, and finally [START_REF] Mettler | Top ten fundamental challenges of biomass pyrolysis for biofuels[END_REF] the lumped mechanisms of the pyrolysis of levoglucosan (LVG), glyoxal and hydroxymethylfurfural (HMFU) taken from the secondary reactions proposed by Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF]. All together, the BioPOx model (devolatilization + gas phase secondary pyrolysis and combustion) including 710 species and 5035 reactions, is given in Chemkin format in SM.

Hydrocarbon combustion NOx thermal formation

Combustion of key tar compound

Secondary pyrolysis of other volatile species

Husson et al. 2013 [63]

Song et al. 2018 [START_REF] Song | The sensitizing effects of NO2 and NO on methane low temperature oxidation in a jet stirred reactor[END_REF] See Table 6 Debiagi et al. 2016 [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] Detailed oxidation mechanisms of C0-C8 hydrocarbons (e.g. ethylbenzene) and oxygenated compounds including aromatic ones (e.g. phenol, benzaldehyde). Detailed mechanism of NOx formation.

Detailed mechanisms of the combustion of volatiles species chosen as surrogates of biomass tars

Semi-detailed mechanisms of the pyrolysis of levoglucosan (LVG), glyoxal and hydroxymethylfurfural (HMFU).

Table 6 reports the volatiles species chosen as surrogates of biomass tars. These compounds are produced from the primary pyrolysis of the three wood constituents. The mixture cellulose and hemicellulose (holocellulose) is the source of hydroxyacetaldehyde, 5-methylfurfural, furfural and furan and its derivatives. Lignin can lead to the formation of anisole and guaiacol. Except for hydroxyacetaldehyde (HAA) for which a new oxidation mechanism has been written, the model used for the different listed surrogates are taken from literature as is shown in Table 7.

The most detailed models in the literature for LVG, HMFU and glyoxal decomposition are those already included in the lumped model of Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] which contains 3 types of metathesis and 5 unimolecular reactions for LVG, 1 type of metathesis and 2 unimolecular reactions for HMFU and 1 type of metathesis and 1 unimolecular reactions for glyoxal. Because HAA is one of the most important products derived from the pyrolysis of holocellulose and no more detailed model than that of Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] was available, we have developed a new dedicated mechanism. The new detailed kinetic mechanism for the pyrolysis and oxidation of HAA is composed of 29 reactions, including unimolecular initiations, metathesis, decomposition and isomerization as is shown in table 7.

Vinyloxy and hydroxyl radicals are formed by breaking the HO-C bond (reaction 1 in table 7)

while the breaking of C-C bond (reaction 2) leads to formyl radical (CHO) and CH2OH radical.

Hydroxyl-vinoxy radical (R100HOCHCHO) and H-atom are obtained by breaking the OC-H bond (reaction 3). Reactions ( 4) and ( 5

I.2.b. Validation of the model

The BioPOx model has been validated on 19 gas-phase pyrolysis and combustion studies of key compounds of biomass pyrolysis (HAA, anisole, furan and its derivatives, furfural and 5-methylfurfural, guaiacol, phenol and levoglucosan (LVG)), of key compounds for PAH formation (benzene, ethylbenzene, toluene, acetylene ...) and of biomass and its constituents as

shown in Table 8. The experimental studies 1, 3, 4-8, 10-13 and 15-19 were already modeled in the literature while the experimental studies 2, 9 and 14 are simulated for the first time in this paper. Fig. 9 and Fig. 10

display comparisons between model and experiments for two examples

of key primary products from holocellulose. Fig. 10 shows the comparison between BioPOx predictions and experimental results for the decomposition of HAA in an isothermal tubular reactor at different temperatures: 625, 650, 675 and 700 °C [START_REF] Shin | Kinetic analysis of the gas-phase pyrolysis of carbohydrates[END_REF]. These experimental results, which are the only available ones for the decomposition of HAA, were already used as a validation target by Ranzi et al. [START_REF] Ranzi | Chemical kinetics of biomass pyrolysis[END_REF] using their model. Thanks to the newly developed HAA mechanism, BioPOx model predictions are in better agreement with the experimental results than those of the model of Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF], but it will still need refinements when new experimental data are available. Fig. 10. HAA pyrolysis at 625 and 700°C : Comparisons between model predictions (BioPOx model: continuous lines, Debiagi et al. [START_REF] Debiagi | Detailed kinetic mechanism of gas-phase reactions of volatiles released from biomass pyrolysis[END_REF] dashed lines) and experimental data (points) [START_REF] Shin | Kinetic analysis of the gas-phase pyrolysis of carbohydrates[END_REF].

The second example of key products from holocellulose concerns LVG, the major product of cellulose pyrolysis. LVG pyrolysis was investigated by Fukutome et al. [START_REF] Fukutome | Processes forming Gas, Tar, and Coke in Cellulose Gasification from Gas-Phase Reactions of Levoglucosan as Intermediate[END_REF] in a tubular reactor at temperatures between 400 and 900 °C. Fig. 11 reports the comparison between model prediction and experimental results which are in good agreement for LVG consumption and not so far for most of the observed products. that were not present in the original mechanism of Nowakowska et al. [START_REF] Nowakowska | Detailed kinetic study of anisole pyrolysis and oxidation to understand tar formation during biomass combustion and gasification[END_REF]. In contrast, a slightly better agreement was found between experimental points and BioPOx predictions for some products, except for the formation of phenol during oxidation. The difference between the predictions using both models can be partly explained by the presence of a guaiacol sub-mechanism in BioPOx, since guaiacol is an important product of the decomposition of anisole.

As shown in the spreadsheet of supplementary material, BioPOx can also fairly predict the conversion rate of anisole during pyrolysis conducted in a tubular reactor by Zhang et al. [START_REF] Zhang | Experimental and Modeling Investigation on the Effect of Intrinsic and Extrinsic Oxygen on Biomass Tar Decomposition[END_REF] at temperatures between 100 and 1000°C.

Guaiacol, also called 2-methoxyphenol, is another example of key products from the lignin.

The pyrolysis and/or the oxidation of this species used as a surrogate for lignin primary tars, was studied by Nowakowska et al. [START_REF] Nowakowska | Conversion thermique des goudrons provenant de la gazéification de la biomasse[END_REF], Zhang et al. [START_REF] Zhang | Experimental and Modeling Investigation on the Effect of Intrinsic and Extrinsic Oxygen on Biomass Tar Decomposition[END_REF] and Asmadi et al. [START_REF] Asmadi | Thermal reactions of guaiacol and syringol as lignin model aromatic nuclei[END_REF]. Comparisons between experiments and BioPOx predictions, which are in good agreement, are shown in Fig. 13 and in the spreadsheet of supplementary material. predicted by the BioPOx model. On the same way, experiments performed by Zhang et al. [START_REF] Zhang | Experimental and Modeling Investigation on the Effect of Intrinsic and Extrinsic Oxygen on Biomass Tar Decomposition[END_REF] on the pyrolysis of toluene in a tubular reactor are well predicted by the the BioPOx model.

As a last example of those compounds, ethylbenzene pyrolysis was conducted in a tubular reactor by Yuan et al. [START_REF] Yuan | A comprehensive experimental and kinetic modeling study of ethylbenzene combustion[END_REF]. For the different studied pressures, as is shown in Fig. 15, model predictions are in a good agreement with experimental results for ethylbenzene degradation and benzene formation. The BioPox model has also been validated on three pyrolysis and oxidation studies of wood and its components, in particular, in the work of Thimthong et al. [START_REF] Thimthong | Kinetic modeling of non-catalytic partial oxidation of nascent volatiles derived from fast pyrolysis of woody biomass with detailed chemistry[END_REF]. These authors carried out the pyrolysis of cedar wood, as well as the partial oxidation of the produced volatile compounds for two different temperatures (700 °C and 800 °C) in a two-stage tubular reactor.

This reactor was modeled using a network of reactors connecting a PSR for pyrolysis to a PFR for oxidation, using for the CHEMKIN-PRO simulation the flowsheet shown in the spreadsheet in Supplementary Material. Fig. 16. shows major gases (CO, CO2, H2 and CH4) yields as a function of the residence time at 800 °C. Overall, an acceptable agreement is found between model predictions and experimental results.

Conclusion

In the present work, we have developed a new kinetic model of wood combustion. To the best of our knowledge, this is the most detailed mechanism for biomass degradation since it considers in details the gas-phase reactions of the tars produced by the biomass devolatilization.

Contrary to the existing lumped kinetic models, our model involves 710 species and includes 5035 reactions, amongst which 5006 gas-phase elementary reactions. This paper shows that BioPOx (Biomass Pyrolysis and Oxidation) model can predict results obtained for a wide range of experimental devices (tubular, jet stirred reactor, fluidized bed, closed ampoule…) and operating conditions (temperatures from 100 °C to 1327 °C, equivalence ratios from 0.5 to 3

and pressures from 4 kPa to 106.7 kPa).

The first part of BioPOx model consists in a semi-detailed mechanism from the literature used to describe biomass pyrolysis. This devolatilization mechanism was newly tested against TGA results obtained in parallel of this work, and against a set of 10 data from the literature. These comparisons show that the model is able to reproduce experimental results of TGA for wood and its constituents, under inert or oxidative atmosphere at low to moderate heating rates. In future works, this pyrolysis mechanism should be improved to better reproduce results with high heating rates.

Gas-phase reactions induced by the combustion of volatile species produced by the biomass devolatilization are considered in the second part of the BioPOx model. A new detailed kinetic oxidation mechanism was proposed for hydroxyacetaldehyde which is one of the most important products derived from the pyrolysis of holocellulose (cellulose-hemicellulose association).

The new BioPOx model was validated against experimental results for pyrolysis and combustion of biomass, key compounds of biomass pyrolysis, and key compounds for PAH formation (a set of 19 data from the literature). These comparisons show that, as a whole, the model predictions, match reasonably well with experimental data. Note however that, for better validate this model, more studies on a wider range of tars would be needed with especially a more comprehensive analysis of combustion products. For high temperatures and large biomass particles, physical phenomena such as heat and mass transfer cannot be neglected. To predict pollutant emissions from domestic wood combustion appliances, the kinetic model BioPOx

Fig. 2 .

 2 Fig.2. Kinetic scheme used by Navarrete Cereijo et al. to model biomass combustion [41].

Fig. 3 .

 3 Fig.3. TGA and DTG (Derivative Thermo-Gravimetric) curves of beech, fir and oak wood under air at 5 °C/min (points: experimental data obtained in this work; lines: model predictions).

Fig. 4 .

 4 Fig.4. TGA curves of pine wood, cellulose and hemicellulose under nitrogen at 5 °C/min and 20 °C/min (points: experimental data [54]; lines: model predictions).

Fig. 5 .

 5 Fig.5. TGA curves of oak wood (full points: experimental data in air; empty points:

Fig. 6 .

 6 Fig.6. TGA curves of birch, aspen, pine and oak wood for two heating rates (points:experimental data[START_REF] Shen | Kinetic study on thermal decomposition of woods in oxidative environment[END_REF]; lines: model predictions).

Fig. 7 .

 7 Fig.7. Slow pyrolysis of Douglas and oak wood as a function of temperature: (a) mass loss; (b) tar, solid and gas yields from the slow pyrolysis of Douglas and oak (shaded boxes: experimental data [60]; full boxes: model predictions).

Fig. 8 .

 8 Fig.8. Slow pyrolysis of Douglas and oak wood as a function of temperature: CO and CO2 yields (shaded boxes: experimental data [60]; full boxes: model predictions).

Fig. 9 .

 9 Fig.9. Slow pyrolysis of miscanthus: CO,CO2 , CH4 and phenol yields (points: experimental

  R100HOCHCHOH can react by breaking a C-H bond yielding glyoxal (reaction 22). R101OCH2CHO can react by -scissions by breaking a C-C bond to give formaldehyde and CHO radical (reaction 23) and by breaking a C-H bond yielding glyoxal (reaction 24). R102HOCHO can react by -scissions to produce CO and CH2OH radical (reaction 25), which can easily isomerize in formaldehyde, by -scissions by breaking a C-O bond to give ketene and OH radical (reaction 26), and by -scissions by breaking a C-H bond yielding glyoxal (reaction 27). R103HOC2H4O can react by -scissions by breaking a C-C bond to give formaldehyde and CH2OH radical (reaction 28). R104HOCHCHOH can react by -scissions by breaking a C-C bond to form acetaldehyde and OH radical (reaction 29).

Fig. 11 .

 11 Fig.11. LVG pyrolysis: Comparisons between model predictions (lines) and experimental data [77], error bars are the standard deviations provided by the authors.The results shown here and in the spreadsheet in supplementary material show that, in most of

Fig. 12 .

 12 Fig.12. Anisole pyrolysis and oxidation: Comparisons between model predictions (BioPOx : continuous lines, Nowakoswka et al. [68]: dashed lines) and experimental data (points) [68], error bars are the uncertainties provided by the authors.

Fig. 13 .

 13 Fig.13. Guaiacol pyrolysis and oxidation: Comparisons between model predictions (BioPOx: continuous lines, Nowakoswka et al. [68]: dashed lines) and experimental data (points) [67], error bars are the uncertainties provided by the authors.The pyrolysis and combustion of key compounds for PAH formation has also been studied with

Fig. 14 .

 14 Fig.14.Equivalence ratio (ɸ) effect on acetylene oxidation: Comparisons between model predictions (lines) and experimental data (points)[START_REF] Wang | New insights in the low-temperature oxidation of acetylene[END_REF]. Error bars correspond to an uncertainty of 5% as given by the authors.Benzene oxidation was conducted in a tubular reactor by Alzueta et al.[START_REF] Alzueta | Experimental and Kinetic Modeling Study of the Oxidation of Benzene[END_REF] using different

Fig. 15 .

 15 Fig.15. Pressure effect on ethylbenzene pyrolysis: Comparisons between model predictions (lines) and experimental data (points) [86], Error bars correspond to an uncertainty of 25% asgiven by the authors.

Fig. 16 .

 16 Fig.16. Major gases (CO, CO2, H2 and CH4) yields as a function of the residence time during the pyrolysis of cedar wood and the partial oxidation of the volatile compounds: Comparisons between model predictions (lines) and experimental data (points) [85].

  .

Fig. 17 .

 17 Fig.17. Major gases (CO, H2O, H2 ,CH4 and C2H4) and benzene yields as a function of the residence time during the pyrolysis of cellulose: Comparisons between model predictions (lines) and experimental data (points)[80].

Table 1 :

 1 Heterogeneous char reactions (The rate constants [k=AT n exp(-Ea/RT)] are given in mol, s and cal units).

	Reaction	A	n	Ea
	(1) Char+O2=>CO2	1.2e+10	0.0	32300.0
	(2) Char+0.5O2=>CO	2.5e+11	0.0	38200.0
	(3) Char+H2O=>CO2	2.5e+09	0.0	52000.0

Table 2 : Physical and chemical properties of woods used in our TGA experiments according to Schmidt et al

 2

				Elemental (wt%)				Chemical (wt%)	Properties (%)
	Wood	C	H	N	S	O	/	CELL HCE LIGC LIGH LIGO Humidity a Ash contents b
	Fir	48,9 6,0 <0,1 <0,03 41,8 <3,3 45,0	24,4	4,0	21,1	5,5	24,6	0,36
	Oak 48,5 5,9 <0,1 <0,03 42,7 <2,9 45,1	34,7	2,6	1,7	15,9	36,3	0,81
	Beech 48,3 6,0 <0,1 <0,03 43,5 <2,2 53,5	25,1	0,0	5,8	5,8	41,4	1,40

.

[START_REF] Schmidt | Wood washing: Influence on gaseous and particulate emissions during wood combustion in a domestic pellet stove[END_REF]

. a : On raw basis. b: On dried basis. /: Under-determinated

Table 3 : Operating conditions considered for the tests of the model against experimental studies of devolatilization in the literature - Simulations for the studies in bold are shown in the text, simulations for the other studies are shown in SM

 3 . F : Simulated for the first time.

	N° Experimental study	Reactor	Studied compound	Dilutant	Temperature (°C)	Heating rate (°C/min)	Previous simulations
	1	Jakab et al. 1995 [55]	TGA	6 types of lignin	Ar	200-900	20	[28,31,46,52]
	2	Williams and Besler 1996 [54]	TGA	Pine wood, hemicellulose cellulose and	N2	300-720	5, 20, 40 and 80	[28,44,46,52]
	3	Shen et al. 2009 [38]	TGA	Pine, aspen, birch and oak wood	Air	40-800	10 and 100	F
	4	Shen et al. 2013 [56]	TGA	Lignin	He, He + 7%, 20%, 60% O2	20-800	20	F
	5	Shen et al. 2013 [57]	TGA	Cellulose	He, He + 7%, 20%, 60% O2	50-800	20	F
	6	Werner et al. 2014 [58]	TGA (DTG)	Cellulose, Xylan	N2	Final T = 600	10	[30]
	7	Shen et al. 2015 [59]	TGA	Hemicellulose	He, He + 7%, 20%, 60% O2	20-800	20	F
	8	Le Brech et al. 2016 [60]		Miscanthus, douglas, oak		20-Final T = 280, 300, 320, 350, 400 and 500		F
	9	Le Brech et al. 2016 [61]	U-shape fixed bed and TGA	Miscanthus, and cellulose	Ar	Final T = 500	5	F
	10	Chen et al. 2016 [62]	lab-scale fixed bed	Poplar wood	N2	400, 450, 500, 550 and 600	10, 30 and 50	F

Table 4 : Elemental, approximate and chemical compositions of woods used in the study of Shen et al

 4 .[START_REF] Shen | Kinetic study on thermal decomposition of woods in oxidative environment[END_REF].

	Wood		Elemental (wt%)		Approximate (wt%)	Chemical (wt%)
		C	H	N	O	S	Humidity Volatiles	Ash	CELL HCE LIGC LIGH LIGO
	Pine	41,89 4,5 0,22 40,19	/	12,9	71,49	0,3	0,446 0,347 0,032 0,022 0,154
	Aspens 45,84 5,22 0,36 39,97 0,01	8,19	80,37	0,41	0,567 0,274 0,000 0,051 0,108
	Birch	44,41 3,48 0,27 36,65	/	11,39	74,36	0,76	0,526 0,271 0,000 0,099 0,104
	Oak	45,37 5,03 0,28 41,29 0,01	8,78	76,82	0,24	0,451 0,347 0,026 0,017 0,159

Table 5 : Structure of BioPOx: detailed biomass combustion mechanism representing solid devolatilization, gas phase secondary pyrolysis and combustion.

 5

Table 6 : Volatiles species chosen as surrogates of biomass tars. Species (name in mechanism) Chemical name Formula Structure Mechanism

 6

	HOCHO	Formic acid	CH2O2	Battin-Leclerc et al. 2008 [65]
	CH3CO2H	Acetic acid	C2H4O2	Battin-Leclerc et al. 2008 [65]
	C2H4O2	Hydroxyacetaldehyde (HAA)	C2H4O2	This study
	Furan	Furan	C4H4O	Tran et al. 2017 [66]
	MF	2-methylfuran	C5H6O	Tran et al. 2017 [66]
	DMF	2,5-dimethylfuran	C6H8O	Tran et al. 2017 [66]
	furylCHO	Furfural	C5H4O2	Nowakowska 2014 [67]
	C6H5OCH3	Anisole	C7H8O	Nowakowska et al. 2014 [68]
	MF-CHO	5-methylfurfural	C6H6O2	Nowakowska 2014 [67]
	guaiacol	Guaiacol	C7H8O2	Nowakowska 2014 [67] [69]

Table 8 : Operating conditions of the tests of the model against experimental gas-phase pyrolysis and combustion studies. Simulations for the studies in bold are shown in the text, simulations for the other studies are shown in SM.

 8

	N °	Studied compound	Experimental study	Process	Reactor	Temperature (°C)	Pressure (kPa)	Residence time (sec)	Equivalence ratio	Previous simulations	Model*
	Biomass and its constituents
				Pyrolysis and
	1	Cedar wood	Thimthong et al. 2015 [78]	partial oxidation of volatile	Two-stage tubular	700 and 800	/	/	/	[78]	Yes
				compounds
	2	Pine wood	Hoekstra et al. 2011 [79]	Pyrolysis and secondary reactions of volatile compounds	Fluidized bed and tubular series reactor in	500	/	Fluidized sec bed 1.5	/	F	No
				Pyrolysis and
	3	Cellulose	Norinaga et al. 2013 [80]	secondary reactions of volatile	Two-stage tubular	700,750 and 800	/	6	/	[80]	Yes
				compounds
	Key compounds of biomass combustion: holocellulose
	4	HAA	Shin et al. 2001 [76]	Pyrolysis	Tubular	625, 650, 675 and 700	/	/	/	[28],[45]	No
	5	Furan, MF and	Tran et al. 2017 [66]	Oxidation	Tubular	397-897	100	/	~ 0.5 ,1 and 2	[66]	Yes
	6	DMF	Cheng et al. 2017 [81]	Pyrolysis	Tubular	827-1327	4	/	/	[81]	Yes
	7	Furfural	Zhang et al. 2017 [82]	Pyrolysis	Tubular	100-1000	101.3	/	/	[82]	Yes
	8	5-methylfurfural	Nowakowska et al. 2014 [67]	Pyrolysis Oxidation	JSR	400-850 400-725	106.7	2	/ 0.8	[67]	Yes Yes
	9	LVG	Fukutome et al. 2015 [77]	Pyrolysis	Two-stage tubular	400-900	/	0.8-1.4	/	F	No

Acknowledgment

The authors gratefully acknowledges the Agence De l'Environnement et de la Maitrise de l'Energie (ADEME) for the financial support of this work, as well as the team of Prof. E. Ranzi for providing help for first using their biomass pyrolysis mechanism.

Thermodynamic data were calculated based on group additivity Benson method using THERGAS software [START_REF] Muller | THERGAS: a computer program for the evaluation of thermochemical data of molecules and free radicals in the gas phase[END_REF]. Kinetic rate constants were determined by analogy with those of similar reactions (see footnotes in Table 7).

Table 7: Primary mechanism for HAA oxidation. The rate constants (k=AT n exp(Ea/RT) are given in mol, s and cal units). b: Rate constant taken equal to that the unimolecular initiation of acetaldehyde as proposed by Yasunaga et al. [START_REF] Yasunaga | Shock-Tube and Modeling Study of Acetaldehyde Pyrolysis and Oxidation[END_REF] : with the A-factor multiplied by 0.4. c: Rate constant taken equal to that of the recombination of H atoms with alkyl radicals as proposed by Allara et Shaw [START_REF] Allara | A compilation of kinetic parameters for the thermal degradation of n-alkane molecules[END_REF]. d: Analogy-Rate constant taken equal to that of the similar reaction in the case the pyrolysis of acetaldehyde proposed by Yasunaga et al. [START_REF] Yasunaga | Shock-Tube and Modeling Study of Acetaldehyde Pyrolysis and Oxidation[END_REF]. e: Analogy-Rate constant taken equal to that of the similar reaction in the case the pyrolysis or oxidation of methanol or acetaldehyde as proposed by Baulch et al. [START_REF] Baulch | Evaluated Kinetic Data for Combustion Modeling. Supplement I[END_REF]. f: Rate calculated using software KINGAS [START_REF] Bloch-Michel | KINGAS: software for the estimation of kinetic data based on Benson's method[END_REF]. g: Analogy-Rate constant taken equal to that of the similar reaction in the case the oxidation of ethanol as proposed by Tran et al. [START_REF] Tran | An experimental study of the structure of laminar premixed flames of ethanol/methane/oxygen/argon[END_REF]. h: Analogy-Rate constant taken equal to that of the similar reaction in the case the oxidation of ethanol as proposed by Tran et al. [START_REF] Tran | An experimental study of the structure of laminar premixed flames of ethanol/methane/oxygen/argon[END_REF]: C2H4OH=H+CH3CHO.

should be coupled to a thermal model which will be the purpose of a second paper. Note however than before being of use in CFD modelling, the present kinetic model, which includes 710 species and 5035 reactions should be significantly reduced.

Supplementary data

Supplementary data associated with this article can be found, in the on line version:

•