Lucie Merlier

Jérôme Jacob
email: jerome.jacob@univ-amu.fr

Pierre Sagaut

Lattice-Boltzmann Large-Eddy Simulation of pollutant dispersion in street canyons including tree planting effects

Keywords: Computational Fluid Dynamics, Lattice Boltzmann Method, Simulation, Urban pollutant dispersion, 3D

This study assesses the performance of a large eddy simulation (LES) based on the lattice Boltzmann method (LBM) in predicting near field dispersion in street canyons with tree planting. Based on a benchmark test case benefiting from wind tunnel measurements (CODASC), this study qualitatively and quantitatively discusses the prediction of traffic-induced pollutant concentration with respect to several reference studies. It also analyses the physics of the flow and concentration fields. Although the problem might seem rather simple, the flow is highlighted to be strongly three dimensional and transient. These properties enhance pollutant dispersion in the empty street canyon but air flow velocity and turbulence intensity tend to decrease in tree crowns. This effect of trees increases both mean and peak concentration levels at pedestrian level, which may be problematic in cities with dense traffic. These results show that LBM-LES is particularly well suited to study dispersion problems towards the development of more breathable cities.

Introduction

In the current context of environmental stress, near-field pollutant dispersion issues due to anthropogenic activities are of major concern. According to the World Health Organization's urban ambient air pollution database, more than 80% of people living in cities, for which monitored data are available, face pollution concentration levels that exceed recommendations. This is especially the case in low-income regions (World Heath Organization, 2016).

A large part of pollutant emission in urban areas is due to transport. Vehicles emit 30% of particle material in European cities. This ratio reaches 50% in the OECD countries, especially because of diesel use. This pollution substantially increases risks of diseases and prematured death rates in cities (World Heath Organization, 2018). Hence, while greenery is currently promoted as a solution to improve urban environmental quality including urban micro-climates and air quality thanks to filtering and deposition on plant foils, the inverse effect of trees on pollutant dispersion in dense cities with street canyons may be problematic (Gromke andRuck, 2007, 2009;[START_REF] Janhäll | Review on urban vegetation and particle air pollution -Deposition and dispersion[END_REF][START_REF] Abhijith | Passive control potentials of trees and on-street parked cars in reduction of air pollution exposure in urban street canyons[END_REF][START_REF] Abhijith | Air pollution abatement performances of green infrastructure in open road and builtup street canyon environments -A review[END_REF][START_REF] Jeanjean | Air quality affected by trees in real street canyons: The case of Marylebone neighbourhood in central London[END_REF][START_REF] Santiago | On Dry Deposition Modelling of Atmospheric Pollutants on Vegetation at the Microscale: Application to the Impact of Street Vegetation on Air Quality[END_REF][START_REF] Xue | The impact of roadside trees on traffic released PM 10 in urban street canyon: Aerodynamic and deposition effects[END_REF]: tree crowns also tend to curb airflow and reduce the natural ventilation potential of streets, thus increasing pedestrian exposure to high levels of pollutant concentration. Wise urban planning choices should consequently be made to improve the breathability of urban areas in a context of climate change. However, in urban environments that M A N U S C R I P T

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include sharp-edged buildings and trees, air flows and pollutant dispersion processes are complex [START_REF] Britter | Flow and dispersion in urban areas[END_REF][START_REF] Ahmad | Wind tunnel simulation studies on dispersion at urban street canyons and intersections -A review[END_REF][START_REF] Lateb | On the use of numerical modelling for near-field pollutant dispersion in urban environments -A review[END_REF], making predictions and thus decisions more difficult.

Hence, for several decades now, different approaches to study urban flow and dispersion issues were developed. Thanks to the recent progress in computational capabilities, the use of detailed numerical approaches -typically computational fluid dynamics (CFD) -has increased, improving the accuracy of predictions. Capable of providing whole flow field data, this investigation technique advantageously completes experimental approaches and systematic field measurements. Although requiring an appropriate use and implementation, CFD is especially beneficial to highlight basic aerodynamic mechanisms underlying dispersion and to study virtual scenarios [START_REF] Vardoulakis | Modelling air quality in street canyons: A review[END_REF][START_REF] Moonen | Urban Physics: Effect of the micro-climate on comfort, health and energy demand[END_REF][START_REF] Tominaga | CFD simulation of near-field pollutant dispersion in the urban environment: A review of current modeling techniques[END_REF][START_REF] Blocken | Computational Fluid Dynamics for urban physics: Importance, scales, possibilities, limitations and ten tips and tricks towards accurate and reliable simulations[END_REF][START_REF] Lateb | On the use of numerical modelling for near-field pollutant dispersion in urban environments -A review[END_REF]. In urban physics, most studies rely on steady statistically averaged methods (Reynolds Averaged Navier-Stokes -RANS), because of the smaller computational costs involved. However, the accuracy of usual steady RANS approaches for studying dispersion in built environments is often found rough because of their inherent limitation in solving transient processes and turbulent transfers, which are important for dispersion [START_REF] Tominaga | CFD modeling of pollution dispersion in a street canyon: Comparison between LES and RANS[END_REF][START_REF] Salim | Performance of RANS, URANS and LES in the Prediction of Airflow and Pollutant Dispersion[END_REF][START_REF] Tominaga | Ten questions concerning modeling of near-field pollutant dispersion in the built environment[END_REF]. The use of time dependent approaches that resolve large scales of turbulence -typically large eddy simulation (LES) -appears therefore effective, but this also raises additional modeling challenges compared to RANS [START_REF] Blocken | 50 years of Computational Wind Engineering: Past, present and future[END_REF][START_REF] Blocken | Computational Fluid Dynamics for urban physics: Importance, scales, possibilities, limitations and ten tips and tricks towards accurate and reliable simulations[END_REF]. Especially, suitable boundary conditions should be specified (Tabor and Baba-Ahmadi, 2010), and the efficiency of the solver

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used is critical due to the increased computational costs LES involves in comparison to RANS.

The development and use of effective simulation approaches such as Lattice Boltzmann Method (LBM [START_REF] Chen | Lattice Boltzmann method for fluid flows[END_REF][START_REF] Succi | The lattice Boltzmann equation for fluid dynamics and beyond[END_REF][START_REF] Shan | Kinetic theory representation of hydrodynamics: a way beyond the Navier-Stokes equation[END_REF][START_REF] Guo | The Lattice Boltzmann Method and its applications in engineering[END_REF][START_REF] Krüger | The Lattice Boltzmann Method[END_REF])-based LES approaches appear thus promising for urban applications. Indeed, thanks to its local and explicit formulation compared to Navier-Stokes-based approaches, this method is inherently parallel and very efficient to simulate low Mach separated flows. Regarding urban applications, first uses of this method addressed the simulation and visualization of contaminant dispersion using GPU (Graphics Processing Unit) for civil security [START_REF] Qiu | Dispersion simulation and visualization for urban security[END_REF][START_REF] Qiu | Dispersion simulation and visualization for urban security[END_REF]. Ten years later, this approach is receiving more and more interest because of its efficiency, although being still an emergent method. Contemporary studies especially address its accuracy and computational performance when implemented on GPUs [START_REF] Obrecht | Towards aeraulic simulations at urban scale using the lattice Boltzmann method[END_REF][START_REF] King | Modelling urban airflow and natural ventilation using a GPU-based lattice-Boltzmann method[END_REF], take advantage of this massively parallelizable method to discuss the link between urban morphology and pedestrian comfort [START_REF] Ahmad | Large-Eddy Simulation of the gust index in an urban area using the Lattice Boltzmann Method[END_REF]Jacob and Sagaut, 2018), or to quantify uncertainties or assimilate data for pollutant dispersion [START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript | A hybrid anchored-ANOVA POD/Kriging method for uncertainty quantification in unsteady highfidelity CFD simulations[END_REF][START_REF] Mons | Data assimilation-based reconstruction of urban pollutant release characteristics[END_REF].

To examine further the applicability and performance of LBM LES for urban issues, the present paper discusses qualitatively and quantitatively the accuracy of such an approach to address dispersion problems in the urban canopy layer. More specifically, the present study discusses results of LBM LES performed using ProLB (CS, 2018;M2P2, 2018) The present paper is organized as follows. First, Sec. 2 presents the key features of the LBM LES approach used for this study. Second, Sec. 3 is dedicated to the CODASC benchmark in terms of experiment (Sec. 3.1) and related numerical studies (Sec. 3.2). Then Sec. 4 discusses the modeling we developed using ProLB (Sec. 4.1). It also presents the grid sensitivity analysis results (Sec. 4.2) and qualitatively and quantitatively discusses simulation results with respect to experimental data (Sec. 4.3). On this basis, Sec. 5 analyses the physics of the flow and the associated turbulent dispersion processes. Finally, Sec. 6 synthesizes the main results of this study and gives outlooks.

The hybrid LBM LES approach

General approach. The Boltzmann equation is a statistical equation, which describes the evolution of the distribution function f of a particle of mass m and speed ξ undergoing an external force F in a fluid:

∂f ∂t + ξ • ∂f ∂x + F m • ∂f ∂ξ = Ω(f ) (1)
where Ω(f ) is a collision operator standing for particle interactions during shocks. After projection and integration of Eq. 1, and neglecting at first external forces, the LBM BGK formulation reads:

M

f α (x + c α ∆t, t + ∆t) -f α (x, t) = - ∆t τ (f α (x, t) -f eq α (x, t)) (3)
The left hand side of Eq. 3 corresponds to the stream phase and the right hand side of Eq. 3 corresponds to the collision phase. The development of the equilibrium function to the second order is given by :

f eq α (x, t) = ρω α 1 + c αi u i c 2 s + 1 2c 4 s Q αij u i u j (4) M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT with:     
ω α and c s : weight and sound velocity constants depending on the lattice used,

Q αij = c αi c αj -c 2 s δ ij .
From LBM, usual macroscopic quantities such as the fluid density ρ and flow momentum ρu can be recovered as follows:

ρ = α f α ; ρu = α f α c α (5)
Also, with the the BGK collision operator, the kinematic viscosity ν is related to the relaxation time τ , following:

ν = c 2 s τ - ∆t 2 (6)
This general LBM framework model allows to recover the Navier-Stokes equation to the second order and is the basis of the CFD solver ProLB. Nevertheless, in order to enhance the stability of computation while keeping the simplicity and accuracy of the scheme, a third-order expansion of the equilibrium function was used in the present study, along with a hybrid Recursive Reconstruction procedure for the non-equilibrium part of the distribution function f neq α = f α -f eq α (see Jacob et al. (2018) for details). Using the Chapman Enskog expansion, it is possible to show that :

f neq α ≈ Q αij 2c 4 s α c αi c αj (f α -f eq α ) f neq,LBM α = - τ ω α 2c 2 s Q αij ∂ρu j ∂x i + ∂ρu i ∂x j f neq,DF α (7)
According to Eq. 7, f neq could be estimated using the local distribution functions (f neq,LBM α

) or the derivatives of the macroscopic values (f neq,DF α ), which may be evaluated using second order finite differences. Hence, in order

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to enhance stability while limiting numerical dissipation, f neq is computed in our model as follows:

f neq α = σf neq,LBM α + (1 -σ)f neq,DF α (8) with σ ∈ [0; 1].
Treatment of external forces. In order to take source terms ( S) into account, the right hand side of Eq. 3 can be modified as follows:

f α (x + c α ∆t, t + ∆t) -f α (x, t) = - ∆t τ (f α -f eq α ) + S α (x, t) (9)
According to [START_REF] Guo | Discrete lattice effects on the forcing term in the lattice Boltzmann method[END_REF], the following development of an external force (S non-dimensionalized following S = S ∆t 2 ∆x ) can be more particularly considered in order to accurately recover the Navier-Stokes equations :

S α (x, t) = ρ 1 - 1 2τ ω α c α -u c 2 s + c α (c α • u) c 4 s • S (10)
The macroscopic velocity is then given by:

u(x, t) = 1 ρ α c α f α (x, t) + ∆t 2ρ S (11)
In the present study, the aerodynamic drag of trees is taken into account by introducing a volumic Forchheimer force (F por [N m -3 ]) designed to account for porous media effects on turbulent flows:

F por = -ρ × R × |u| × u × Φ (12)
with:

     R : the drag force coefficient [m -1 ],
Φ : the ratio of porous media immersed in the volumic cell.

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Hybrid approach. To solve the conservation equations for species (passive scalar) while remaining within the LBM framework, it is possible to use a multidistribution approach. Multidistribution means that an additional superimposed lattice is considered to solve passive scalar transport. Nonetheless, given the correspondence between the LBM and Navier-Stokes approaches, it is also possible to develop a hybrid approach to solve passive scalar transport when basically using the LBM. In such an approach, the mass and momentum conservation equations are solved using the LBM while the species conservation equations are solved using a usual finite volume / finite difference method. This method allows thus to consider only one additional unknown per additional equation. Typically, in ProLB, the species conservation equation is solved using a finite difference vertex centered scheme. A centered scheme using the 18 neighbors defined in the LBM lattice mixed with a first order upwind scheme is used for the advective term whereas a standard centered second order scheme is used for diffusion term.

Boundary conditions. As most of LBM solvers, ProLB uses the immersed boundary method to include solid boundaries. This method decouples the triangular surfacic mesh from the cubic volumic mesh. As each near wall node do not have all its neighbors in the fluid domain, the lattice Boltzmann algorithm cannot be applied. For these particular nodes, macroscopic quantities are computed using an interpolation (Dirichlet condition) or an extrapolation (Neumann condition) between the fluid and the solid boundary, or wall functions. The distribution functions are then reconstructed from equations ( 4) and ( 7). This method substantially reduces meshing costs compared to usual unstructured meshes based on surface discretization.

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Large eddy simulation. The LBM is inherently well suited to dynamically solve flows using the LES technique. With LES, the most energy carrying and problem dependent eddies are solved. Conversely, eddies smaller than the spatial filter -typically the grid mesh-are modeled. For this purpose, the Smagorinsky [START_REF] Smagorinsky | General circulation experiments with the primitive equations. 1. The basic experiment[END_REF] subgrid viscosity model is commonly used:

ν t = (C∆) 2 |S| (13)
with:

                  
ν t : the subgrid scale eddy viscosity, ∆ : the width of the filter, taken equal to the mesh size in the present study, C : the Smagorinsky constant, taken equal to 0.18 in the present study,

|S| = (2S ij S ij ) 1/2
: the magnitude of the resolved strain rate tensor.

In ProLB, the subgrid scale viscosity is added to the molecular viscosity of Eq. 6 to perform LES.

The CODASC benchmark

Wind tunnel setup and results

[Figure 1 about here.]

The CODASC database [START_REF] Kit | CODASC: COncentration DAta of Street Canyons -Karlsruhe Institute of Technology[END_REF]Gromke et al., 2008;Gromke andRuck, 2009, 2012) provides detailed reduced-scale measurements of traffic-like induced pollutant concentration next to the walls of a street canyon model.

The CODASC deals with different configurations, including different aspect ratios (H/W), wind incidences and artificial tree plantings. The present study

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focuses on the H/W = 1 configuration with a wind direction perpendicular to the street canyon axis with and without continuous tree planting.

Reference experiments were carried out in a boundary layer wind tunnel with smooth walls and ceiling. This ceiling was adjusted in order to obtain a zero pressure gradient in the streamwise direction. The cross section is 2 m large (Y direction) and 1 m high (Z direction).

According to Figure 1 The CODASC database reports measurements for λ = 0 m -1 (no tree), λ = 80 m -1 and λ = 200 m -1 .

λ = p ww -p lw ( 1 2 ρu 2 )d (14) M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT with:                           
The traffic-like pollutant release was modeled using four line sources of equal strength located on the street canyon ground. These sources are more precisely composed of equidistant little openings with high pressure drop to ensure that the release remains unaffected by local pressure fluctuation induced by the street canyon flow. Emissions consisted of a mixture of sulfure hexafluoride (SF6, Q SF 6 = 6.5 cm 3 min -1 , tracer gas) and dry air (Q air = 7 × 10 3 cm 3 min -1 ). Mean tracer gas concentrations were measured at x + = 0.04167 x H from street canyon building walls using electron capture detectors.

The 700 molar concentration measures (c mol ) distributed over the 7 horizontal lines available for each wall were normalized as follows:

c + = C mol HU H Q l ( 15
)
with:

                   c + : the normalized concentration [-] H : the building height [m]

Related studies

The CODASC benchmark was considered by several studies to assess the performance of different CFD approaches in predicting pollutant dispersion in the presence of trees. Studies often considered the H/W=1 configuration with a wind incidence perpendicular to the canyon axis (Gromke et al., 2008;[START_REF] Balczó | Numerical modeling of flow and pollutant dispersion in street canyons with tree planting[END_REF][START_REF] Salim | Numerical simulation of dispersion in urban street canyons with avenue-like tree plantings: Comparison between RANS and LES[END_REF][START_REF] Moonen | Performance assessment of Large Eddy Simulation (LES) for modeling dispersion in an urban street canyon with tree planting[END_REF]Gromke and Blocken, 2015a;[START_REF] Vranckx | Impact of trees on pollutant dispersion in street canyons: A numerical study of the annual average effects in Antwerp, Belgium[END_REF][START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript | Development of a computational fluid dynamics model with tree drag parameterizations: Application to pedestrian wind comfort in an urban area[END_REF], or the H/W=0.5 configuration [START_REF] Buccolieri | Aerodynamic effects of trees on pollutant concentration in street canyons[END_REF][START_REF] Buccolieri | Analysis of local scale tree-atmosphere interaction on pollutant concentration in idealized street canyons and application to a real urban junction[END_REF][START_REF] Abhijith | Passive control potentials of trees and on-street parked cars in reduction of air pollution exposure in urban street canyons[END_REF][START_REF] Xue | The impact of roadside trees on traffic released PM 10 in urban street canyon: Aerodynamic and deposition effects[END_REF]. Table 1 gives an overview of the different CFD studies performed for the H/W=1 configuration.

[Table 1 about here.]

Studies referenced in Table 1 generally highlighted that simulation is capable of reproducing the main flow and concentration patterns highlighted in the experiment. However, quantitative analysis generally exhibits discrepancies between predictions and measurements. In particular, using steady RANS, the street canyon vortex is generally predicted weaker than observed in the wind tunnel experiments or more detailed approaches (Gromke et al., 2008;[START_REF] Salim | Numerical simulation of dispersion in urban street canyons with avenue-like tree plantings: Comparison between RANS and LES[END_REF][START_REF] Vranckx | Impact of trees on pollutant dispersion in street canyons: A numerical study of the annual average effects in Antwerp, Belgium[END_REF]. This behavior can be explained by the underprediction of the turbulent kinetic energy at the canyon top, which induces too small shear at the canyon top. Regarding dispersion, studies pointed out the unequal performance of turbulence models (RSM was

Numerical modeling and performance evaluation

Numerical settings

To assess the applicability and performance of the LBM LES approach we developed in ProLB for urban pollution issues, this study focuses on a bad case for dispersion: the street canyon perpendicular to the wind incidence.

The studied configuration corresponds to the reduced scale (1:150) H/W=1 street canyon, containing, or not, continuous avenue-like tree plantings (λ = 0, 80 and 200 m -1 ).

[Figure 2

U (y) U H = y y H ku (16) M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT with:             
k u = 0.3 : the power law exponent, y H = H = 0.12 m : the canyon height, U H = 4.65 m s -1 : the wind velocity at y=H.

The Synthetic Eddy Method [START_REF] Pamiès | Generation of synthetic turbulent inflow data for large eddy simulation of spatially evolving wall-bounded flows[END_REF] was used to provide the turbulent contribution of the approaching flow, based on the following profile of turbulence intensity [START_REF] Moonen | Performance assessment of Large Eddy Simulation (LES) for modeling dispersion in an urban street canyon with tree planting[END_REF]:

I(y) I H = y + y D y H + y D k I (17)
with: To model pollutant sources, 1.42×1.25×10 -3 m 2 lines sources were created on the domain bottom boundary (Figure 3(b)) and activated at t = 8 s. With a massic emission concentration of 4.786×10 -3 kg kg -1 and a vertical velocity equal to 0.2054 m s -1 , the mass flow rate of SF 6 is 2.094 × 10 -6 kg s -1 . The corresponding mass flow rate of air is 4.375 × 10 -4 kg s -1 . Diffusivity of SF6 was set to 2.3 × 10 -5 m 2 s -1 and the subgrid Schmidt number to 0.7.

                     k I = -
Although an influence of the turbulent Schmidt number was observed on previous RANS studies, only one value of the subgrid Schmidt number was used. Indeed, since a LES model is used the main part of turbulent effects is resolved and only a small part is modeled, which decreases the importance of that numerical parameter.

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According to convergence analysis, the last 10 s of simulation were kept for post processing and time averaging of results. For physical analysis, velocities (u i ) were normalized (u + i ), as follows:

u + i = u i U H (19)
and concentration results (c m ) were normalized following:

c + = c m × U H × H Q SF 6 /l × M air M SF 6 (20)
with:

                                  
c + = : the normalized concentration, H = 0.12 m : the height of the street canyon, l = 1.42 m : the length of the line sources, Q SF 6 = 1.359 × 10 -6 m 3 s -1 : the volumic flow rate of SF6, M air = 28.966 g mol -1 : the molar mass of air, M SF 6 = 146.055 g mol -1 : the molar mass of SF6.

Grid sensitivity analysis

In order to analyze the grid influence on the results, the configuration without trees was tested using the grid defined on Sec. 4.1 and a coarser grid with dx = H/48 in the street canyon. Figure 5 shows the normalized concentration c + profiles in front of wall A and B for the two simulated grids and the measurements. A better agreement is observed for the finest grid at wall A, however, there is no significant differences at wall B.

[Figure 5 Quantitative evaluation.

[Figure 9 about here.]

Figure 9 summarizes the quality metrics defined in Table 2 computed Differences between predictions and observations may be explained by some modeling assumptions, which do not strictly correspond to the experimental configuration. In particular, deviation might be explained, at least partly, by the fact that a smooth boundary condition was specified at walls A and B in the numerical model, which appears not to be exactly the case in the experiment according to Figure 1(b): joints between blocks as well as taps modify the Plexiglas wall surface. Also, roughness on the street canyon floor differs from around in the experiment while a uniformly rough floor was assumed in the numerical model. In addition, regarding the effect of trees, the metallic lattice is not taken into account in the present numerical model whereas wind tunnel experiments found that the presence of the empty lattice cage induces an increase of pollutant concentration by 18 % on wall A and a decrease of 16 % on wall B with respect to the fully empty case. Thus, the accumulation of these apparently small differences in the geometric models could lead to significant deviation in concentration results by modifying flow properties in the street canyon.

Physical analysis of flow and concentration fields

Results presented in Section 4. Crosses are related to outliers.

As expected, results show that mean velocity and fluctuations are generally higher at y/H = 5 than at y/H = 0 for both points M and A. The direct lateral interactions with the general boundary layer, induces standard deviations that are generally more than 3 times higher at y/H = 5 than at y/H = 0. Without trees, the corner vortex also induces relatively high mean velocities at point M (v = -1.25 m s -1 ) as the flow enters the street canyon from its sides. On the contrary, velocity at point M is rather low at y/H = 0, because the canyon vortex is almost centered in the canyon. Being located on the edge of this vortex, point A shows higher velocities (u = -0.35 m s -1 ).

Regarding the effects of trees, Figure 12 show that concentration levels are about one order of magnitude higher at y/H = 0 than at y/H = 5 for point M, where concentration at y/H = 5 are very low. This difference is also substantial at point A, for which concentration levels at y/H = 5 are also low. The denser the crowns, the greater the difference. Standard deviations are also significantly higher at y/H = 0 than at y/H = 5.

Still conversely to velocity, the influence of trees on concentration differs depending on the considered location: tree crowns increase concentration levels at y/H = 0 and slightly decrease it at y/H = 5 for points A and M.

More specifically, at y/H = 0, dense tree crowns increase mean concentration substantially exceeds 100 several times when trees are present, even if mean concentrations may be less than the half of this peak value.

Hence, the reduction of velocities by trees tends to increase mean concentration and associated fluctuations at y/H = 0, i.e. where concentration levels are the highest. Very high instantaneous concentrations might occur at point A, where the mean concentration levels significantly exceed the median values. This means that instantaneous concentration can be much higher than the mean value, which can be prejudicial for people's health in case of short time exposure to some specific pollutants.

Concluding remarks

This study assesses the performance of a LBM-LES approach in predicting pollutant dispersion in street canyons in the presence or absence of trees. Simulation results compare very satisfactorily to state-of-the-art results obtained for the same benchmark configurations using Navier-Stokesbased LES approaches. Predictions exhibit a very satisfactory agreement with experimental data on wall A, which is critical as this wall shows the highest concentration levels, while larger differences are observed on wall B (as in all previously reported numerical results), where concentration levels are relatively low. The general effect of crowns on dispersion observed in the experiment is well reproduced by simulations, but with less accuracy when decreasing crown permeability. This deviation may be explained, at

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least partly, by differences between the numerical and experimental models, as the flow, and thus dispersion processes, are very sensitive to geometric details at this scale.

Further, present results show that the developed unsteady high-fidelity approach is valuable to predict and understand air flows and dispersion processes and thus the local urban breathability [START_REF] Panagiotou | City breathability as quantified by the exchange velocity and its spatial variation in real inhomogeneous urban geometries: An example from central London urban area[END_REF]. In particular, effects of tree crowns on the development of usual canyon and corner vortices have been studied in detail. The analysis of the results especially pointed out the alteration of the general mean flow structures as well as of intermittent processes at different locations in the street canyon.

Such results enable turbulent dispersion to be better predicted, and rapid phenomena that are critical for short term exposure issues to be identified.

Hence, this study shows that the LBM-LES yields state-of-the-art results, while allowing the use of very fine spatial and temporal resolutions thanks to its computational efficiency. In addition, the use of embedded uniform meshes with immersed boundary conditions allows to handle complex geometries in a very easy way, which reduces pre-processing efforts for urban problems. Therefore, based on present results, this approach appears well suited to further study dispersion in realistic urban environments including complex building and street geometries, different atmospheric stability states or even moving bodies such as motorized engines or people.

  with respect to a benchmark test case: the COncentration DAta of Street Canyons -CODASC (KIT, The CODASC focuses on pollutant dispersion in a street canyon with traffic-like pollutant emissions for different configurations of avenue-like tree planting. This configuration is used to analyze the physical processes that underlay dispersion in the urban canopy layer, as made possible by high fidelity modeling approaches.

  mesoscopic description, the LBM aims at simulating the fluid behavior by resolving a discretized version of the Boltzmann equation in phase space, using (CS, 2016): 1. a discrete velocity model c α,α=0...Q-1 in a space of dimension D. A D3Q19 scheme is typically used for 3D problems; 2. a collision model towards relaxation. The simplest model is the single relaxation time Bhatnagar-Gross-Krook (BGK) model: an equilibrium function model. This function generally corresponds to the development of the Maxwell-Boltzmann distribution function.

  (b), small solid elements on the floor were used as roughness to reproduce a typical urban boundary layer mean velocity profile. A 0.3 power law profile for the mean velocity of the boundary layer was achieved. Considering U H = 4.65 m s -1 at the building height (H), the Reynolds number of the test equals 3.7 × 10 4 , so the flow is turbulent.The measured turbulence intensities are characterized by a decreasing -0.36 power law profile with height.As shown in Figures1(a) and 1(b), the street canyon model consists of two H = 0.12 m high, L=10 H long rectangular obstacles made of contiguous blocks of plexiglas. When present, tree crowns were modeled with rectangular volumes made of a fiber like wading material enclosed in suspended metallic lattice cages(Gromke and Ruck, 2009). Trunks were neglected. Different tree crowns types were realized by varying the mass of wading material in the lattice cage. Corresponding porosity properties were experimentally determined and characterized with a normalized pressure loss coefficient (λ [m -1 ]), as follows:

p

  ww : the windward pressure [Pa], p lw : the leeward pressure [Pa], ρ : the fluid density [kg m -3 ], u : the mean streamwise velocity [m s -1 ], d : the streamwise thickness of the wadding material [m].

U

  H : the wind velocity at H [m s -1 ] Q l : the emission rate of the line source [m 2 s -1 ] M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT Experimental measures available in the database were symmeterized. Experimental results show weaker concentration levels on the windward wall (wall B) than on the leeward wall (wall A). This distribution is explained by the formation of a street canyon vortex, which is driven by the above flow (Gromke and Ruck, 2009). The canyon vortex drives pollutant from the street canyon ground towards wall A, and upwards. Part of pollution is then mixed with the above flow at roof level. The other part is re-entrained in a new cycle of the canyon vortex, which explains the presence of pollutant next to wall B. In addition, corner eddies enhance ventilation in the canyon after separation at the lateral edges of block A, which decreases pollution at street canyon ends. In the absence of trees, these typical flow structures of 3D street canyons induce an averaged concentration level on wall A that is 3.8 times higher than on wall B. The presence of trees reduces exchanges between the street canyon and the ambient flow. Corner eddies are blocked at the street canyon ends, and the canyon vortex is highlighted weaker in the central part of the street than in the empty street canyon. Velocity is substantially reduced next to wall B. Velocity next to wall A is also reduced. These modifications induce a substantial increase of pollutant concentration levels next to wall A, as well as a decrease of pollutant concentration at wall B. As explained in Gromke et al. (2008), the rotating fluid mass decreases when trees are located in the street, leading to a reduction of the pollutant mass ejected above wall A to wall B and a decrease of pollutant concentration close to wall B. Thus, higher concentrations are observed in the street canyon with tree planting than in the empty street canyon: the total pollutant increase is about 28 % for M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT λ = 80 m -1 and 36 % for λ = 200 m -1 . Additional experiments highlighted no substantial change in wall-averaged pollution concentrations for higher values of λ.

  perform better than k -ε) and the dependence of predicted concentrations with respect to the choice of the turbulent Schmidt number as well as the limitation of steady state approaches in reproducing the mixing processes, which are intrinsically transient(Gromke et al., 2008;[START_REF] Salim | Numerical simulation of dispersion in urban street canyons with avenue-like tree plantings: Comparison between RANS and LES[END_REF] Gromke and Blocken, 2015b). These reasons could explain the variable behaviors of RANS results in terms of concentrations on walls A and B in the reviewed studies. Nonetheless, overall, studies generally concluded that RANS approaches may constitute an acceptable compromise between prediction accuracy, applicability and computational costs. Using unsteady RANS,[START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript | Development of a computational fluid dynamics model with tree drag parameterizations: Application to pedestrian wind comfort in an urban area[END_REF] found also a relatively satisfactory agreement between predictions and measurements in terms of flow and concentration patterns for the different tested tree configurations, but concentrations were underestimated for wall A and overestimated for wall B.When comparing LES to RANS,[START_REF] Salim | Numerical simulation of dispersion in urban street canyons with avenue-like tree plantings: Comparison between RANS and LES[END_REF] found a substantially better performance of LES than that of RANS, especially with respect to the consistency of concentration distributions. The better performance of LES was explained by its ability to reproduce intermittent turbulent fluctuations. LES predictions were found almost satisfactory on wall A, but deviations were still highlighted on wall B[START_REF] Salim | Numerical simulation of dispersion in urban street canyons with avenue-like tree plantings: Comparison between RANS and LES[END_REF][START_REF] Moonen | Performance assessment of Large Eddy Simulation (LES) for modeling dispersion in an urban street canyon with tree planting[END_REF]. Moreover,[START_REF] Salim | Numerical simulation of dispersion in urban street canyons with avenue-like tree plantings: Comparison between RANS and LES[END_REF] and[START_REF] Moonen | Performance assessment of Large Eddy Simulation (LES) for modeling dispersion in an urban street canyon with tree planting[END_REF] emphasized that LES enables the instantaneous and intermittent behavior of the flow to be analyzed, thus providing information on dispersion processes as well as short term exposure problems.These advantages of LES involve nonetheless significant additional computational costs with respect to RANS, which may be limiting for its develop-applications. As a matter of fact,[START_REF] Salim | Numerical simulation of dispersion in urban street canyons with avenue-like tree plantings: Comparison between RANS and LES[END_REF] indicates that performing LES instead of RANS induced an increase of computational costs of one or two orders of magnitude. Hence, given the addressed problem and the conclusions of related studies, this benchmark appears well suited to highlight and discuss the performance of innovative CFD approaches, such as the present LBM LES.

  Figure 2(a) depicts the L D × W D × H D = 3 × 2 × 1 m 3 computational domain set for simulation to reproduce the experimental test section. The fetch equals 7 H and the inflow was specified with a velocity inlet condition, as follows (Moonen et al., 2013):

Figure 4

 4 Figure 4 displays the mesh used for simulation, which includes five nested refinement zones. Spatial discretization involves dx = H/96 lattices in the canyon. The corresponding basic time step equals 1.44 × 10 -5 s in order to fulfill CFL and low Mach flow requirements. Overall, 4.1 × 10 7 grid points are used to mesh the full domain. Simulations were performed on the French GENCI's Occigen supercomputer using 240 cores and run over 25 s of physical time.

Figure 6

 6 Figure6firstly compares the simulated w + field, at y/H = 0.5 with LDV measurements reported inGromke et al. (2008).Gromke and Ruck (2009) show that wall averaged c + is not very sensitive to λ value for λ ≥ 200 m -1 , which means that the flow in the street canyon is quite independent of λ in that range of values. From this result, Figure6(b) compares velocity fields considering λ = 200 m -1 for simulation results and λ = 250 m -1 for experimental results. Results highlight that predicted and observed velocity distributions are in good agreement, showing both the development of a street canyon vortex, and reduced velocities in and around tree crowns when present, especially next to wall B.

Figure 7

 7 Figure 7 also highlights the effects of the finite length of the street canyon. The formation of the corner vortices induces a decrease of concentration distribution on walls A and B from y/H = 0 to the street canyon ends. According to simulation, c + values are on average more than 2.3 times higher in the fifth central part of wall A (|y/H| < 1) than on the rest of the wall when trees are present. This ratio equals 2.1 without trees. Because of the blocking effect of trees, concentration increases on wall A and decreases on wall B for |y/H| > 2.5. Such a trend is also highlighted in experimental results, although the measured c + show smoother gradients in the y direction in the central part of the canyon than simulated, especially when trees are present. Simulation results also exceed experimental data on wall B at this location. On average, comparing simulation results to measurements, results show that simulation satisfactorily predicts wall averaged concentration on wall A (c + sim,A = 18.6 vs c + exp,A = 19.6), but overpredicts that of wall B (c + sim,B = 9.6 vs c + exp,B = 5.4) in the absence of trees. Including trees in the modeling also induce a limited relative modification of concentration levels on walls A and B compared to the experiment: c + sim,A increases by 18 % and 23 %, and c + sim,B decreases by 11 % and 15 %, for λ = 80 and 200 m -1 respectively according to current results, whereas c + exp,A increases by 41 % and 58 %, and c + exp,B decreases by 37 % and 49 %, for λ = 80 and 200 m -1 respectively according to Gromke et al. (2008) and Gromke and Ruck (2009).

  Figure9summarizes the quality metrics defined in Table2computed for both or only wall A and wall B, along with values available in literature that were obtained by[START_REF] Moonen | Performance assessment of Large Eddy Simulation (LES) for modeling dispersion in an urban street canyon with tree planting[END_REF] and[START_REF] A N U S C R I P T A C C E P T E D Accepted Manuscript | Development of a computational fluid dynamics model with tree drag parameterizations: Application to pedestrian wind comfort in an urban area[END_REF]. Results show that current quality metrics mostly belong to the recommendation ranges when considering both walls A and B. However, wall-by-wall results analysis confirms previous statements: quality metrics are mostly close to target values for wall A but half of indicators fall out of recommendation ranges for wall B, for which reference concentrations used for scaling are low. Also, the denser the crowns, the further apart the predictions from experimental

  Figure 12(a): point M is located in the middle of the street canyon and point A is located in the bottom leeward part of the street canyon, i.e. where concentrations are the highest. The central line of boxplots indicate the median value, the circle corresponds to the mean value, boxplot edges are the 25 and 75 percentiles and the ends of the whiskers represent the extreme values.

  confirms previous results: trees significantly alter mean velocities as well as fluctuations at point M, which is located in tree crowns. More specifically, at y/H = 0, the alteration of the canyon vortex due to the presence of dense trees reduces u by a factor of 7 at point M, i.e. down to nearly zero (with a change of sign), while w is increased by a factor of 17, making w non null. Corresponding standard deviations are factor about 5 for both components. Regarding point A, u is divided by a factor of 6 and w is reduced by a factor of 2. Standard deviations are less altered by trees than for point M, as they are reduced by less than 15 % and 30 % respectively for u and w. Standard deviation is even increased by 35 % for v. At y/H = 5, tree crowns limit v at point M by a factor of 3 and u by a factor of 12 (with a change of sign). Corresponding standard deviations are reduced by a factor of 1.6. Considering point A, u and w are reduced by less than a factor of 2, and v by a factor of 6 (with a change of sign). Standard deviations are only reduced by 10 % for u and w and by 20 % for v.Hence, these results highlight that trees alter velocities at points A and M, which is related to the alteration of the general flow structures in the middle and at the end of the canyon, i.e. in the canyon and the corner vortices. However, while both mean velocities and fluctuations at point M are generally reduced because of tree crowns, effects of trees on fluctuations at point A are less straightforward.5.2. Effect of turbulence on dispersion[Figure13about here.] According to Figures10 and 7, clean air entering the canyon from above in front of the windward wall and from the sides of the street canyon pushes pollutant towards the central leeward part of the canyon. A jet raises there and drives the pollutant out, especially when trees are present. Focusing on this critical part of the street canyon, Figure13clearly shows how the reduction of turbulence and velocities induced by tree crowns affect pollutant reduced ventilation potential of the street canyon increases pollutant concentration levels within it. More precisely, while pollutant is driven by the main street canyon vortex from line sources to the top mixing layer in the absence of trees, porous zones favor the diffusion and the residence of pollutant inside the street canyon. The less porous the crown, the higher the concentration. Pollutant is especially retained below and inside tree crowns, as well as in the leeward part of the street canyon. The flow developing there extends further above wall A at the canyon top and in the mixing layer, which contaminates the separation bubble above block A.[Figure14about here.] Similarly to Section 5.1, Figure 14 displays boxplots of instantaneous c + at y/H = 0 or at the street canyon ends (y/H = 5) for a point M and A in order to analyze more quantitatively the effects of trees on turbulent dispersion processes. As opposed to velocity, and as highlighted in Section 4.3, results

  of 2 at point M and 1.8 at point A compared with the configuration without trees. Corresponding standard deviations are increased by a factor of 2.7 and 1.3 respectively. Reached peak values are very high as c +

Figure 4 :

 4 Figure 1: CODASC experimental model c CODASC, KIT.

Figure 5 :Figure 7 :

 57 Figure 5: Comparisons between measured ( ) and simulated c + vertical profiles for the coarse () and fine ( ) grid

Table 1 :

 1 Overview of CFD studies dealing with the CODASC benchmark, H/W=1, trees and a wind perpendicular to the street canyon

Table 2 :

 2 Statistical model performance indicators

Acknowledgments

The authors acknowledge support from several French institutions. This work was supported by the French project CLIMB, with the financial sup-

ACCEPTED MANUSCRIPT

Tabor, G., Baba-Ahmadi, M., Apr. 2010. Inlet conditions for large eddy simulation: A review. Computers & Fluids 39 (4), 553-567.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

In order to assess more quantitatively the accuracy of simulation and evaluate the general model performance as recommended in [START_REF] Chang | Air quality model performance evaluation[END_REF]; [START_REF] Hanna | Acceptance criteria for urban dispersion model evaluation[END_REF]; [START_REF] Moonen | Performance assessment of Large Eddy Simulation (LES) for modeling dispersion in an urban street canyon with tree planting[END_REF], several integrated indicators were also estimated:

• the fraction of predictions within a factor of two of observation (FAC2)

• the fractional bias (FB),

• the root normalized mean square error (RNMSE),

• the geometric mean bias (MG),

• the geometric variance (VG),

• and the correlation coefficient (R).

[Table 2 about here.] Their meaning as well as target values and acceptable range for urban problems according to [START_REF] Chang | Air quality model performance evaluation[END_REF] are synthesized in Table 2.

The different indicators computed for the two grids are listed in Table 3. All of them are located in the acceptable range for coarse and fine grid which means that the model is consistent with grid refinement. Furthermore most of the quality metrics computed for the finest grid are closer to the target values than the ones computed for the coarse grid. Since the results presented in Figure 5 and Table 3 are slightly better for the finest grid, this grid with dx = H/96 in the street canyon was selected for the actual study.

[Table 3


Adil Mouahid
email: adil.mouahid@univ-amu.fr

Halima Bouanga

Christelle Crampon

Elisabeth Badens

Supercritical CO 2 extraction of oil from Jatropha curcas: An experimental and modelling study

Experimental and modelling investigations of supercritical CO 2 extraction of oil from Jatropha curcas were conducted at a pressure range of 20-40 MPa and a temperature range of 313-333 K at a CO 2 flow rate of 0.4 kg/ h. The extraction yield was estimated to be about 0.6 kg oil /kg biomass for all experiments. The model of broken and intact cells published by Sovová was applied. It was found that the extraction of type B was the most suited extraction type to apply as the experimental extraction curves exhibit three parts. Whatever the pressure and the temperature applied, the asymptotic yield at infinite time was found to be the same. At 20 MPa, increasing the temperature from 313 to 323 K enhances the extraction kinetics. A retrograde solubility zone was found at 30 and 40 MPa. The Jatropha curcas oil solubility in SC-CO 2 was determined and the data were modelled with the Chrastil equation.

Introduction

On a worldwide scale, the demand for energy continues to increase while fossil fuels are increasingly being discredited. One of the current ways intended to supplant fossil fuels is the production of biofuels. Jatropha curcas (JC) is a promising plant for such application as its oil can contain more than 75% of total lipids and is present in the range of 40-60 g oil/100 g [START_REF] Achten | Jatropha biodiesel fueling sustainability? Biofuels Bioprod[END_REF][START_REF] Pandey | Jatropha curcas: a potential biofuel plant for sustainable environmental development[END_REF][START_REF] Ong | Production and comparative fuel properties of biodiesel from non-edible oils: jatropha curcas, Sterculia foetida and Ceiba pentandra, Energy Convers[END_REF][START_REF] Van Eijck | Prospects for jatropha biofuels in Tanzania: an analysis with strategic niche management[END_REF][START_REF] Mofijur | Prospects of biodiesel from Jatropha in Malaysia[END_REF][START_REF] Yang | Review and prospects of Jatropha biodiesel industry in China[END_REF][START_REF] Achten | Jatropha bio-diesel production and use[END_REF]. The advantage of JC compared to rapeseed or sunflower seeds, is that this plant adapts well to dry and hot climates and as such, does not require much water. Above all, the cultivation of this plant does not compete with food crops. As a consequence, JC seeds represent an encouraging source of oil from which biodiesel may be derived by transesterification [START_REF] Ong | Production and comparative fuel properties of biodiesel from non-edible oils: jatropha curcas, Sterculia foetida and Ceiba pentandra, Energy Convers[END_REF][START_REF] Van Eijck | Prospects for jatropha biofuels in Tanzania: an analysis with strategic niche management[END_REF][START_REF] Mofijur | Prospects of biodiesel from Jatropha in Malaysia[END_REF][START_REF] Yang | Review and prospects of Jatropha biodiesel industry in China[END_REF][START_REF] Atabani | A comparative evaluation of physical and chemical properties of biodiesel synthesized from edible and non-edible oils and study on the effect of biodiesel blending[END_REF][START_REF] Sánchez | A comparative study of the production of esters from Jatropha oil using different short-chain alcohols: optimization and characterization[END_REF][START_REF] Silitonga | A global comparative review of biodiesel production from jatropha curcas using different homogeneous acid and alkaline catalysts: study of physical and chemical properties[END_REF][START_REF] Go | A new approach in maximizing and direct utilization of whole Jatropha curcas L. kernels in biodiesel production -Technological improvement[END_REF][START_REF] Lim | A review of processing and machinery for Jatropha curcas L. fruits and seeds in biodiesel production: harvesting, shelling, pretreatment and storage[END_REF][START_REF] Sánchez-Arreola | Biodiesel production and de-oiled seed cake nutritional values of a Mexican edible Jatropha curcas[END_REF][START_REF] Huerga | Biodiesel production from Jatropha curcas: integrated process optimization[END_REF][START_REF] Baldini | Seed processing and oil quality of Jatropha curcas L. on farm scale: a comparison with other energy crops[END_REF][START_REF] Nazir | Extraction, transesterification and process control in biodiesel production from Jatropha curcas[END_REF]. JC oil can be extracted by different methods, however mechanical extraction methods [START_REF] Baldini | Seed processing and oil quality of Jatropha curcas L. on farm scale: a comparison with other energy crops[END_REF][START_REF] Subroto | Mechanical extraction of oil from Jatropha curcas L. kernel: effect of processing parameters[END_REF][START_REF] Subroto | Optimization of mechanical oil extraction from Jatropha curcas L. kernel using response surface method[END_REF][START_REF] Siregar | Comparison of oil press for jatropha oil: a review[END_REF] are generally preferred because the operational costs are low and they can easily be carried out by semi-skilled operators. Furthermore, the residue can be used for biogas production. On the down side, however, the extraction yield is lower than solvent extraction methods. Indeed, the rate of oil recovery obtained by mechanical press methods is comprised between 69 and 86% while the yield obtained by classical organic solvent, such as n-hexane, extraction methods are comprised between 70 and 99% depending on extraction time and solvent type [START_REF] Sánchez-Arreola | Biodiesel production and de-oiled seed cake nutritional values of a Mexican edible Jatropha curcas[END_REF][START_REF] He | Nontoxic oil preparation from Jatropha curcas L. seeds by an optimized methanol/n-hexane sequential extraction method[END_REF][START_REF] Qian | Preparation of biodiesel from Jatropha curcas L. oil produced by two-phase solvent extraction[END_REF]. However, classical organic solvents are known to be pollutant and non-selective, which has led to the investigation of other extraction methods for JC oil [START_REF] Nazir | Extraction, transesterification and process control in biodiesel production from Jatropha curcas[END_REF][START_REF] Liu | Extraction of oil from Jatropha curcas seeds by subcritical fluid extraction[END_REF][START_REF] Kumar | Ultrasonic-assisted reactive-extraction is a fast and easy method for biodiesel production from Jatropha curcas oilseeds[END_REF][START_REF] Go | A new approach in maximizing and direct utilization of whole Jatropha curcas L. kernels in biodiesel production -Technological improvement[END_REF][START_REF] Severa | Bio-oil extraction of Jatropha curcas with ionic liquid co-solvent: fate of biomass protein[END_REF]. The supercritical CO 2 (SC-CO 2 ) extraction method allows a green and rather selective extraction, depending on the operating pressure and temperature, of non-polar compounds, particularly triglycerides that lead to biodiesel after transesterification. These advantages encourage researchers to evaluate the feasibility of SC-CO 2 oil extraction from JC and its use for biodiesel production [START_REF] Ghoreishi | Biodiesel Production from Natural Resources via Supercritical Fluid Extraction and Catalytic Transesterification Reaction[END_REF][START_REF] Chen | Biodiesel production from supercritical carbon dioxide extracted Jatropha oil using subcritical hydrolysis and supercritical methylation[END_REF][START_REF] Chen | Green production of energetic Jatropha oil from de-shelled Jatropha curcas L. seeds using supercritical carbon dioxide extraction[END_REF][START_REF] Lim | Influences of different co-solvents in simultaneous supercritical extraction and transesterification of Jatropha curcas L. seeds for the production of biodiesel[END_REF][START_REF] Mićić | Kinetic modelling of supercritical carbon dioxide extraction of sage (Salvia officinalis L.) leaves and jatropha (Jatropha curcas L.) seeds[END_REF][START_REF] Breet | Supercritical carbon dioxide extracted oil from Jatropha curcas: directive for the biodiesel industry?[END_REF][START_REF] Chen | Supercritical carbon dioxide extraction of triglycerides from Jatropha curcas L. seeds[END_REF][START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF][START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF][START_REF] Tsuchiya | Study on the performance and emissions of diesel engines fueled by jatropha crude oil extracted with supercritical CO 2[END_REF][START_REF] Tsuchiya | Solubility characteristics and selective extraction of jatropha oil by super-and subcritical CO2 extraction[END_REF]. For the sake of simplicity, the operating conditions of the studies dealing with the SC-CO 2 extraction of oil from JC with pure CO 2 are reported in Table 1.

In 2009, Chen et al. [START_REF] Chen | Supercritical carbon dioxide extraction of triglycerides from Jatropha curcas L. seeds[END_REF] studied the effects of pressure, temperature and solvent to solid ratio on the extraction efficiency of triglycerides from JC seeds by using SC-CO 2 extraction. The authors used a response surface methodology to determine the effects of the operating conditions on the concentration of triglycerides present in the extracted oil. They showed that pressure is most effective in enhancing the recovery of triglycerides, however the main factor that affects the concentration of triglycerides is temperature and solvent to solid ratio value. They also demonstrated that SC-CO 2 extracts exhibit a higher concentration of triglycerides than Soxhlet extracts obtained at 342 K with n-hexane. Chen et al. [START_REF] Chen | Biodiesel production from supercritical carbon dioxide extracted Jatropha oil using subcritical hydrolysis and supercritical methylation[END_REF] investigated the SC-CO 2 extraction of triglycerides from powdered JC kernels followed by subcritical hydrolysis and supercritical methylation of the extracted oil. They demonstrated that supercritical methylation preceded by subcritical hydrolysis of the extracted oil is a feasible two-step process for producing biodiesel. Chen et al. [START_REF] Chen | Green production of energetic Jatropha oil from de-shelled Jatropha curcas L. seeds using supercritical carbon dioxide extraction[END_REF] investigated the use of the SC-CO 2 for the extraction of triglycerides from de-shelled JC seeds. They used a response surface methodology to evaluate the effects of pressure, temperature and solvent to solid ratio on total yield, concentration of triglycerides and recovery of triglycerides. They showed that pressure and solvent to solid ratio significantly affect the quality of the extracted oil. Ghoreishi et al. [START_REF] Ghoreishi | Biodiesel Production from Natural Resources via Supercritical Fluid Extraction and Catalytic Transesterification Reaction[END_REF] used SC-CO 2 to extract oil from JC seeds in order to study two different catalytic reactions (transesterification with an alkali catalyst and esterification with an acidic catalyst) for biodiesel production. They showed that the alkali catalyst transesterification reaction is more effective than the acidic esterification. Tsuchiya et al. [START_REF] Tsuchiya | Study on the performance and emissions of diesel engines fueled by jatropha crude oil extracted with supercritical CO 2[END_REF] evaluated the performance of an unpurified extracted SC-O 2 oil as a fuel. The authors used a large extraction device to produce adequate amounts of oil for the combustion tests. In order to use the extracted oil as a substitute of biodiesel they performed the extraction at operating conditions which allowed the selective extraction of triglycerides from JC seeds [START_REF] Tsuchiya | Solubility characteristics and selective extraction of jatropha oil by super-and subcritical CO2 extraction[END_REF]. According to this study, when the extracted oil was used to fuel a diesel engine, no remarkable differences in thermal efficiency and specific fuel consumption was noticed compared with diesel fuel. Nevertheless, it is necessary to perform a long-term evaluation as the combustion tests were conducted for very short duration. Min et al. [START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF] investigated the extraction kinetics of JC oil and its solubility in SC-CO 2 . The solubility

Nomenclature a g

Specific surface area of the microalgae powder (m -1 ) a s Specific area between the regions of intact and broken cells (m From these studies, it appears that the quality of the oil extracted by SC-CO 2 extraction from JC is suitable to biodiesel application. However, it is necessary to emphasize that the study of the SC-CO 2 extraction kinetics has only been investigated in two articles [START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF][START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF] and only one study has dealt with the modelling of the extraction curve at 30 MPa, 323 K and a CO 2 flowrate of 3.23 × 10 -3 kg/min [START_REF] Mićić | Kinetic modelling of supercritical carbon dioxide extraction of sage (Salvia officinalis L.) leaves and jatropha (Jatropha curcas L.) seeds[END_REF]. Few studies deal with the solubility of JC oil in SC-CO 2 by taking into account the slope of the first part of the extraction curve [START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF][START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF] or by direct experimental measurements [START_REF] Breet | Supercritical carbon dioxide extracted oil from Jatropha curcas: directive for the biodiesel industry?[END_REF][START_REF] Tsuchiya | Solubility characteristics and selective extraction of jatropha oil by super-and subcritical CO2 extraction[END_REF][START_REF] Chen | Solubility of Jatropha and Aquilaria oils in supercritical carbon dioxide at elevated pressures[END_REF]. Furthermore, the growing environment of JC is different in each study (Table 1) which can lead to different oil compositions and hence differences in solubility values. The aim of this work is to study the extraction kinetics of the extracted oil from JC by using the model of broken and intact cells (BIC) developed by Sovová [START_REF] Sovová | Mathematical model for supercritical fluid extraction of natural products and extraction curve evaluation[END_REF]. The BIC model was chosen because it is accurate, well adapted to natural products and versatile: it has been applied as much as for plant materials as for microalgae [START_REF] Sovová | Mathematical model for supercritical fluid extraction of natural products and extraction curve evaluation[END_REF][START_REF] Mouahid | Supercritical CO2 extraction of neutral lipids from microalgae: experiments and modelling[END_REF][START_REF] Mouahid | Effects of high water content and drying pre-treatment on supercritical CO2 extraction from Dunaliella salina microalgae: experiments and modelling[END_REF][START_REF] Solana | Exploiting microalgae as a source of essential fatty acids by supercritical fluid extraction of lipids: comparison between Scenedesmus obliquus, Chlorella protothecoides and Nannochloropsis salina[END_REF][START_REF] Mouahid | Supercritical CO 2 extraction from endemic Corsican plants; comparison of oil composition and extraction yield with hydrodistillation method[END_REF]. The solubility of JC oil in SC-CO 2 was also calculated and oil analysis for each experiment was performed.

Materials and methods

Raw materials and chemicals

JC seeds were obtained from the Indian company Vanashree Agrotech. The seeds were de-shelled and the kernel were grinded and sieved at a particle size distribution of 300-500 μm. The water content of the grinded kernels was estimated at about 4 wt%, hence water should not affects the extraction as the value is lower than 20 wt% [START_REF] Mouahid | Effects of high water content and drying pre-treatment on supercritical CO2 extraction from Dunaliella salina microalgae: experiments and modelling[END_REF]. Before SC-CO 2 extraction, the grinded biomass was stored at 274 K to avoid the chemical degradation of the lipids. CO 2 was provided by Air Liquide (France) with a purity of 99.7%, n-hexane (99.8%, Carlo Erba, France) was used to make the organic solvent extraction to determine the total oil content of the kernels.

Experimental setup

The extraction unit used for this study is a laboratory scale extraction device supplied by Separex (Champigneulles, France). The extraction autoclave is a stainless-steel vessel of 10 cm 3 placed in a heater. This autoclave has at its ends two flat stainless-steel frit filters (pore diameter distribution of 5-15 μm). The operating and the details of the extraction device has already been described in other studies [START_REF] Mouahid | Effects of high water content and drying pre-treatment on supercritical CO2 extraction from Dunaliella salina microalgae: experiments and modelling[END_REF][START_REF] Mouahid | Supercritical CO 2 extraction from endemic Corsican plants; comparison of oil composition and extraction yield with hydrodistillation method[END_REF]. For each experiment, the mass introduced in the extraction autoclave was comprised between 7 and 8 g. Regarding the small charges used for SC-CO 2 extraction experiments, the efficiency of the extraction was estimated relative to the mass losses of the sample in the extraction autoclave (Eq. ( 1))

= × e'(%) mass extracted (kg) mass introduced in the extractor (kg) 100

SC-CO 2 extraction experiments were conducted at pressures of 20, 30 and 40 MPa, temperatures of 313, 323 and 333 K, and a CO 2 flowrate of 0.4 kg/h. The extraction curves were plotted as the variation of the mass losses of the sample as a function of the CO 2 /biomass mass ratio. At the end of an extraction experiment, the extracted oil was collected in 5 mL of n-hexane.

Scanning electron microscopy (SEM)

JC grinded kernels were observed with a Scanning Electron Microscope before extraction experiments. The visualizations were made on a Hitachi TM3000 Tabletop Microscope at 15 kV. The sample powders of JC were deposited on an adhesive pastille and metallized with a thin layer of Au-Pd to allow a better conduction of the sample and a better visualization. The metallization time did not exceed 30s.

Assumptions

The supercritical fluid extraction models presented in the literature have been built by making different assumptions on the flow pattern and the interactions between the extracted solute and the solid matrix. Those characteristics depend on the experimental conditions and on the extraction autoclave dimensions. In order to target the appropriate equations to our system, we have determined the flow pattern and the type of interactions which may occur during the SC-CO 2 extraction process. The internal diameter (D) of the autoclave is 12.5 mm and the length (L) is 160 mm. The Reynolds number (Re) describing the flow of SC-CO 2 in the empty autoclave is 184. This value of Re corresponds to a laminar flow in a cylindrical tube. For fluid flow through a porous media, the Reynolds number Re p is given by Eq. ( 2)

= - ρ V μ a ε Re (1 ) p CO g 2 (2)
Where ρ CO2 is SC-CO 2 density, V is the SC-CO 2 velocity, μ is the solvent dynamic viscosity, a g is the specific surface area of JC powder and ε is the bed void fraction. As the extraction bed was supposed to be composed of spherical particles, a g is then equal to 6/d p where d p is the mean JC particle diameter. The bed void fraction ε of JC was estimated by immersing a known amount of biomass powder residue (powder of JC after extraction) in a test tube containing a known volume of absolute ethanol. The volume displaced allows us to calculate the density of JC ρ s . The JC density ρ s was estimated at 642.5 kg/m 3 . Knowing the bulk density ρ b it is possible to determine ε by using Eq. ( 3).

= - ε ρ ρ 1 b s (3)
The value of the bed void fraction ε of JC was estimated at 0.7 after a repeatability test consisting of three experiments. This value was the same whatever the operating conditions of the extraction experiments. The calculated values of Re p varied from 1.8 to 3.3. In all cases, the values of Re p are lower than 10 and close to 1, which correspond to the laminar or transitory flow regime. Considering that L > > D and the values of Re and Re p , we can assume that the flow pattern of SC-CO 2 in the extraction autoclave is plug flow. Therefore, axial dispersion was supposed to be negligible.

Modelling

SC-CO 2 extraction curves

The extraction curves were modelled using Sovová's mathematical model for supercritical fluid extraction of natural products [START_REF] Sovová | Mathematical model for supercritical fluid extraction of natural products and extraction curve evaluation[END_REF]. This model takes into account the structure of the biological material studied and accounts for the sudden reduction in extraction rate after the first extraction period that is observed during SC-CO 2 extractions from seeds.

According to the study published by Sovová, the extraction can be of type A, B, C or D. In the decision on extraction type it is possible to refer to the aspect of the extraction curves (Fig. 1): if the first part of the extraction curve consists of one straight section, the type is A or D. If it consists of two straight sections, it is of type B or C. The shape of the extraction curves obtained in this study exhibits three parts, this observation was also pointed out by Min et al. [START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF]. Hence, the extraction type is B or C. For type C, the second straight line starts very early, at a relative amount of the passed solvent q not far from 1. In this study the second straight line starts at q > > 1 for all extraction curves. Hence, extraction of type B is the most suitable extraction type to describe the extraction curves in this work.

In extraction of type B, the first part of the extraction curve is composed of two straight lines (Fig. 1) given by Eqs. ( 4)- [START_REF] Yang | Review and prospects of Jatropha biodiesel industry in China[END_REF]. The first straight line (Eq. ( 4)) is controlled by solute solubility in SC-CO 2 . The second straight line (Eq. ( 6)) indicates that the solute concentration in the biomass is considerably reduced and the equilibrium is controlled by solute-matrix interactions. This implies that the fluid-phase equilibrium is much lower than the solute solubility. The transition between the two straight lines occurs at the transition concentration x t . The phase equilibrium no longer depends on solubility but on the partition coefficient K which represents the constant of proportionality of the linear relationship between solid and fluid-phase concentrations. The transition concentration x t is equal to the matrix capacity for interaction with the solute, if x t = 0 there is no solute-matrix interaction. Solute-matrix interactions can be related to the desorption of the solute from the biomass. The last part of the extraction curve, described by Eq. ( 7), is controlled by solute diffusion from intact cells to broken cells. The extraction curve of type B are described by considering Eqs. ( 4), ( 6),( 7):

• First part of the extraction curve e = q y s for 0 ≤ q ≤ q 1 [START_REF] Van Eijck | Prospects for jatropha biofuels in Tanzania: an analysis with strategic niche management[END_REF] with e, the extraction yield (kg oil /kg insolublebiomass )

= - - - q r x x γ K x y K x ( ) u t t s t 1 (5)
e = q 1 y s + (qq 1 ) K x t for q 1 ≤ q ≤ q c (6)

• Second part of the extraction curve

e = x u [1 -C 1 exp(-C 2 q)]for q > q c (7)
A straight line of slope y s , which represents the solubility of the extracted oil in SC-CO 2 is fitted to the first part of the extraction curve (Eq. ( 4)).The values of q c and q 1 were determined by taking into account the fact that:

-q c is the value of q at the crossing point with the estimate for the second part of the extraction curve according to Eq. ( 6) and -q 1 is the value of q at the crossing point with the first linear part (Eq. ( 4)) and the second straight part (Eq. ( 6)) considering the expression of q 1 in Eq. ( 5).

The second part of the extraction curve (q > q c ) is described by Eq. ( 7) by adjusting constant parameters C 1 and C 2 . Estimations of parameters k s a s , the mass transfer coefficient, and r, the fraction of the broken cells, can be obtained by considering Eq. ( 8) to 13:

= - - r C C q 1 e x p( ) c 1 2 (8) = - - - - > k a r εQC N rCK x (1 ) (1 ) [1 ((1
) / ] for 0

s s m t 2 2 (9)
With:

= e E N m (10) = q Q t N ˙m (11) = - N C N (1 ) m u (12) = + C x x 1 u u u ( 13
)
Where E is the amount of extract (kg) and Q ˙is the solvent flowrate (kg/ s) and C u is the solute content in the untreated solid. The solute concentration in the untreated solid x u (with insoluble solid as reference) was supposed equal to the asymptotic extraction yield at infinite time. The adjustable parameters C 1 and C 2 were calculated by minimizing the sum of least squares between the experimental and calculated values of e. The absolute average relative deviation (AARD) given in Eq. ( 14), was used to evaluate the efficiency of the model.

For more details on the assumptions made in this section and the determination of the model parameters, one can refer to previous works [START_REF] Sovová | Mathematical model for supercritical fluid extraction of natural products and extraction curve evaluation[END_REF][START_REF] Mouahid | Supercritical CO2 extraction of neutral lipids from microalgae: experiments and modelling[END_REF][START_REF] Mouahid | Effects of high water content and drying pre-treatment on supercritical CO2 extraction from Dunaliella salina microalgae: experiments and modelling[END_REF]. The modelled extraction curves were expressed as the variation of e' as a function of the mass ratio CO 2 /biomass. As additional information, which can be useful for further studies, it was decided to give the binary diffusion coefficient D 21 and the fluid phase mass transfer coefficient k f of the extracted JC oil in SC-CO 2 . These properties were calculated by the correlations given in the works of He [START_REF] He | Prediction of binary diffusion coefficients of solutes in supercritical solvents[END_REF] and Tan et al. [START_REF] Shi | Correlation of mass transfer coefficient in the extraction of plant oil in a fixed bed for supercritical CO2[END_REF]. The average molar mass of JC oil was calculated at

JC oil solubility in SC-CO 2

The solubility of JC oil in SC-CO 2 was calculated by considering the slope of the first part of the extraction curve (Eq. ( 4)). The experimental data were modelled by the Chrastil model given in Eq. ( 15). This model considers that one molecule of solute can associate with k molecules of solvent forming a solvated complex molecule in equilibrium with the fluid.

= + + y k ρ a T b ln( ) ln s CO 2 (15)
With:

-k: the association number -a: which depends on the heat of solvation and vaporization of solute -b: a parameter which is dependent on the molecular weight of species

The parameters k, a and b were adjusted on the experimental data of y s .

Results and discussions

n-hexane extraction

The total oil content of the JC kernel was determined by n-hexane extraction carried out on 6 g of grinded and sieved (300-500 μm) JC kernels in 100 mL of n-hexane. The extraction was performed at 323 K over 3 days. The total mass loss of the oil extracted from JC kernels was determined at about 61.7 wt%. This result is in good agreement with a previous study [START_REF] Lim | Influences of different co-solvents in simultaneous supercritical extraction and transesterification of Jatropha curcas L. seeds for the production of biodiesel[END_REF].

SC-CO 2 extraction experiments 4.2.1. General finding

The extraction curves are presented in Fig. 2. It can be seen that for all experiments, when it was possible to perform extraction until its end, the maximal mass loss reached is about 60%. This value is very close to the value obtained by n-hexane extraction (61.7 wt%). The aspect of JC powdered kernels before and after SCCO 2 extraction is given in Fig. 3. Before extraction (Fig. 3(a)) the biomass aspect is very colored (yellow) and oily, after extraction (Fig. 3(b)) the residue aspect is dry and totally discolored. It was noticed that after SC-CO 2 extraction the biomass residue still have the same aspect. This aspect suggests that all neutral lipids were extracted. Consequently, it can be considered that it was possible to extract all the oil contained in JC kernels by SC-CO 2 whatever the operating conditions. This result is of prime importance for modelling studies as it gives the possibility to make predictions if the experimental extraction curve could not be performed until the end. Furthermore, this tendency is in agreement with previous studies [START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF][START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF]. Indeed, it can be seen in these studies that the asymptotic yield at infinite time seems to reach a same maximal value (about 52 wt%), close to the value obtained by Soxhlet extraction method (about 56 wt%), whatever the conditions of pressure and temperature at a constant CO 2 flowrate. Hence, the value of C u was fixed at 0.6 kg oil /kg biomass for all modelling calculations.

The surface structure of JC observed by SEM at scales of 300 and 500 μm is shown in Fig. 3(c) and (d). It can be seen that the surface structure is highly craked by the grinding process indicating that the latter was very effective.

Effects of pressure and temperature

The modelled extraction curves showing the effects of pressure and temperature are respectively given in Figs. 2 and4. In Fig. 2, at a fixed temperature, increasing pressure from 20 to 40 MPa enhances the extraction kinetics. This tendency is in good agreement with the studies of Min et al. [START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF] and Fernandez et al. [START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF]. In Fig. 4, at a pressure of 20 MPa an increase of temperature from 323 to 333 K leads to a decrease in the extraction kinetics. The same tendency was observed at 30 and 40 MPa when increasing the temperature from 313 to 333 K. At 40 MPa, the extraction curves were found to be close at 323 and 333 K. The deviation between the two extraction curves was about 5%. The effects of temperature observed in this study can be explained by the presence of a retrograde solubility zone at a pressure of 20 and up to 40 MPa. In SC-CO 2 extraction, when the temperature increases the solute vapor pressure increases while the SC-CO 2 density decreases. Increasing the solute vapor pressure enhances the extraction but the decrease of the SC-CO 2 density disadvantages the extraction. In this study, when increasing the temperature at 20 up to 40 MPa, the decrease of SC-CO 2 density overtakes the increase of solute volatility.

The extraction curves published by Min et al. [START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF] were plotted reporting the variation of oil yield (Y) pressures versus the volume of CO 2 (VCO 2 ) at different pressures for a fixed temperature. In order to make comparisons with our results, it was decided to plot their results by showing variation of temperature at single pressure in Fig. 5. The authors reported that increasing the temperature from 308 to 328 K at 20 MPa (Fig. 5(a)) decreased the oil yield Y (amount of oil extracted as a mass percentage of the original kernels). From Fig. 5, the following remarks can be made: at 30 MPa (Fig. 5(b)) the extraction curves overlap whatever the temperature. At 40 and 50 MPa Fig. 5(c) and(d), the extraction curves are very close to each other (the deviation was about 5%) even if the extraction kinetics are slightly improved by increasing the temperature from 308 to 328 K. Fernandez et al. [START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF] reported the effects of temperature at 50 MPa, pointing out that increasing the temperature from 313 to 333 K increased the extraction kinetics but from 323 to 333 K, this increase was less pronounced as the two extraction curves reported at these temperatures are very close to each other and reach the same asymptotic yield.

The differences between our study and the results reported by Min et al. [START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF] can be explained by the different growing environments and harvest time of JC. Considering the results reported by Min et al. [START_REF] Min | Supercritical CO 2 extraction of jatropha oil and solubility correlation[END_REF] and Fernandez et al. [START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF], it is possible to suppose that the retrograde solubility zone ends at a pressure threshold below 40 MPa while in this study, the retrograde solubility zone goes up to 40 MPa. It was not possible to determine the threshold in this study since the maximum working pressure of the extraction apparatus is 45 MPa. The best

JC oil solubility in SC-CO 2

The solubility of JC oil was determined by calculating the slope of the first part of the extraction curve. The solubility y s with the SC-CO 2 density ρCO 2 , the mass transfer coefficient k f and the diffusion coefficient D 21 of the extracted oil are reported in Table 2. Fig. 6(a)-(c) shows the plot of ln (y s ) versus ln (ρ CO 2 ) at 313, 323 and 333 K, the linearity is very good. In Fig. 6 (d) the experimental data of y s were correlated with the Chrastil equation. The correlation obtained in the study conditions is given in Eq. ( 16), the corresponding AARD is about 1.3%. s CO2 [START_REF] Nazir | Extraction, transesterification and process control in biodiesel production from Jatropha curcas[END_REF] The experimental data were compared to the estimations made by Fernandez et al. [START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF] in Fig. 6(a)-(c). The solubility calculated in both studies is at the same order of magnitude. Moreover, the value of the oil solubility estimated in this present work is of the same order of magnitude as that calculated with the results of Micic et al. [START_REF] Mićić | Kinetic modelling of supercritical carbon dioxide extraction of sage (Salvia officinalis L.) leaves and jatropha (Jatropha curcas L.) seeds[END_REF] and presented in part 4.2.4.

The highest value of the oil solubility was obtained at 40 MPa and 313 K, which was expected since the retrograde solubility zone goes up to 40 MPa. These operating conditions correspond otherwise to the most rapid extraction kinetics.

Modelling

The values of the model parameters fitted on the experimental data of JC are reported in Table 3. The AARD is comprised between 2.65 and 3.91% for the modelling performed on the experimental data reported in this study, suggesting that the extraction of type B from the BIC model is very well suited for describing the extraction curves from JC. Thanks to the modelling, it was possible to estimate the extraction time needed to complete the extraction by SC-CO 2 . The estimates of the extraction times t f for total oil extraction by SC-CO 2 were also reported in Table 3.

At 40 MPa and 313 K (Figs. Fig. 22(a) and Fig. 44(c)), the experimental data obtained exhibits only the solubility part, the last experiment point is very close to maximal yield. Due to the lack of experimental points, it was not possible to complete the modelling. Nevertheless, at these operating conditions the solute-matrix interactions are supposed to be very low and close to solubility. At 20 MPa and 333 K, the experimental extraction curve was not performed until its end, nevertheless the first and the second part of the extraction curve were visible. Hence, it was possible to make a predictive estimation to complete the extraction curve by using the BIC model. In this case, the model gives an order of magnitude of the parameters that should be obtained. A possible shape of the complete extraction curve at 20 MPa and 333 K is given in Figs. Fig. 22(c) and Fig. 44(a).

The model parameters calculated show that, for a fixed pressure, the transition concentration x t is larger for smaller values of partition coefficient K. An increasing value of parameter x t associated to a decreasing value of parameter K highlights an increase of the solute-matrix interactions. When the value of parameter x t increases, it can be observed that the transition between the first and second straight line of the extraction curve becomes sharper. The transitions became smooth with a decrease in the solute-matrix interactions (decreasing of x t ).

In the retrograde solubility zone, the solute-matrix interactions increased with an increasing temperature and with a decreasing pressure. When the value of parameter K is low, the second straight line of the extraction curve is longer because of the low mass transfer. Hence, the time required to complete the extraction increases. The calculated values of grinding efficiency r were found to be very close to 0.9 indicating that the pre-treatment applied in this study (grinding and sieving) was efficient. This result confirms the observations made by SEM. It was decided not to fix parameter r at a single value as the grinded and sieved biomass introduced into the extraction autoclave is different in terms of shape of the powder from one sample to another involving differences in mass transfer.

When the solute-matrix interactions are weak, the transition between the second straight line and the diffusion part of the extraction curve is smooth. This transition became sharp when the solute-matrix interactions were high. Hence, when the solute matrix interactions are stronger, the diffusion process starts very late and appears to be fast. The end of the extraction curve (second and third part) is governed by solute-matrix interactions followed by fast diffusion. On the contrary, when solute-matrix interactions are low, the end of the extraction curve is mainly governed by diffusion. The transition can be evaluated by the value of the parameter k s a s , when the value of the parameter increases for a fixed value of pressure, the diffusion appears to be important at the end of the extraction curve.

To our knowledge, no modelling data using the BIC model have been reported about the extraction of oil from JC or about the use of the BIC model involving the extraction of type B. Consequently, it is not possible to make a comparison between the literature and the values of the parameters reported in this study. Hence, it has been decided to apply the type B, BIC model to the data published by Micic et al. [START_REF] Mićić | Kinetic modelling of supercritical carbon dioxide extraction of sage (Salvia officinalis L.) leaves and jatropha (Jatropha curcas L.) seeds[END_REF]. The JC seeds used in this study came from Malaysia, the extraction was not performed until the end and the maximal extraction yield was not indicated. The pre-treatment applied was drying, milling and sieving to a mean particle diameter of 900 μm. Lim et al. [START_REF] Lim | Influences of different co-solvents in simultaneous supercritical extraction and transesterification of Jatropha curcas L. seeds for the production of biodiesel[END_REF] studied SC-CO 2 extraction with co-solvents using JC seeds from Malaysia, they also performed Soxhlet extraction on the kernels. They found that the total oil content in JC kernels was about 64.59 wt%. Considering this data, the value of C u was fixed at 0.6 kg/kg for the modelling calculations. The bed void fraction ε was fixed at 0.7. The modelled extraction curve considering the data reported by Micic et al. [START_REF] Mićić | Kinetic modelling of supercritical carbon dioxide extraction of sage (Salvia officinalis L.) leaves and jatropha (Jatropha curcas L.) seeds[END_REF]. is presented in Fig. 7, and the adjusted parameters are reported in Table 3.

The AARD was found to be 2.26% which is very satisfactory, and the calculated parameters are at the same order of magnitude than those obtained in this study. The parameter r was found to be low: 0.28 showing that the pre-treatment was not efficient. The sieving should probably be lower than 900 μm to increase the efficiency and then the value of parameter r. The parameter k s a s was found to be very low, indicating that the diffusion at the end of the extraction process is very slow at can be seen in Fig. 7. Finally, at the same operating conditions [START_REF] Lim | Influences of different co-solvents in simultaneous supercritical extraction and transesterification of Jatropha curcas L. seeds for the production of biodiesel[END_REF] and Fernandez et al. [START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF]. Indeed, in the study published by Min et al. [START_REF] Lim | Influences of different co-solvents in simultaneous supercritical extraction and transesterification of Jatropha curcas L. seeds for the production of biodiesel[END_REF], the values of the extraction yield were reported as a function of the volume of CO 2 measured by a gas wet meter. The pressure and temperature of volume measurements were not reported making the conversion of the volume of CO 2 into mass impossible. In the study of Fernandez et al. [START_REF] Fernández | Supercritical extraction and fractionation of Jatropha curcas L. oil for biodiesel production[END_REF], the extraction curves were plotted according to the mass of oil collected at the end of the extraction line. On the extraction curves, it was not possible to clearly detect the three parts of the extraction curves.

JC oil analysis

Oil analysis was performed by gas chromatography coupled with mass spectrometry and a flame ionization detector (GC/MS-FID) equipped with an Agilent ZB-WAX column (0.25mm × 30m), the carrier gas used was hydrogen. Fatty methyl esters were analyzed after transmethylation. The reagents were sulfuric acid in methanol with a concentration of 5%, the temperature of reaction was 358 K and the reaction time 1h30. The JC kernel oil before extraction is rich in neutral lipids, indeed the content of polar lipids towards neutral lipids is about 2.3% (7 μg/mg) and the percentage of free fatty acids towards triglycerides is about 25%. Among polar lipids, can be quantified 28% of Phosphatidylcholine, 21% of Phosphatidylinositol and 23% of Phosphatidylethanolamine. The FAME profile of JC oil before extraction is given in Table Compared to the composition reported in the literature [START_REF] Nazir | Extraction, transesterification and process control in biodiesel production from Jatropha curcas[END_REF], the values reported appeared to be low. These differences are probably due to the variety and the growing conditions of the biomass used in this study. The composition of the SC-CO 2 extracted oil is given in Table 5. As expected, the composition varies with the pressure and the temperature. The highest amount of total fatty acids is about 599 μg/μL and was obtained at 30 MPa and 323 K. At the operating conditions leading to the best extraction kinetics, the amount of fatty acids is about 519 μg/ μL. The lowest amount (485 μg/μL) was obtained at 40 MPa and 323 K. Whatever the operating conditions used for SC-CO 2 extraction, no polar lipids were extracted. In the oil obtained at 40 MPa, 313 K, the amount of free fatty acids towards triglycerides is close to 0.

The composition of the n-hexane extracted oil is also given in Table 5. The amount of total fatty acids is about 441 μg/μL which is lower than the amounts extracted by SC-CO 2 . The percentage of free fatty acids towards triglycerides is about 6%. Furthermore, polar lipids were also extracted (1.8 mg/mL). To complete the extraction of total fatty acids by n-hexane extraction, a higher extraction time is needed. Whatever the operating conditions used for SC-CO 2 extraction no polar lipids were extracted. In the oil obtained at 40 MPa, 313 K, the amount of free fatty acids towards triglycerides is close to 0. It appears that the FAME profile is independent of the extraction method and remains the same than in the initial biomass.

Conclusion

In this work, an experimental campaign of supercritical extraction of oil from Jatropha curcas kernels has been performed. The modelling of the extraction kinetics was studied by applying the BIC model with extraction of type B. Extraction of type B implies that the first part of the extraction curve can be divided into two distinct linear parts: one controlled by the JC oil solubility in SC-CO 2 and the second linear part highlighting solute-matrix interactions. The following part of the extraction curve is controlled by solute diffusion from intact cells to broken cells.

It was found that this model was very well suited to the SC-CO 2 oil extraction from JC. Whatever the conditions of pressure and temperature applied in this study, the asymptotic yield at infinite time was found to be always the same. The solubility of JC oil in SC-CO 2 was determined by the slope of the first extraction curve and was successfully modelled by the Chrastil equation.

The grinding of the biomass was the only pre-treatment applied and was found to be sufficient to obtain rapid extraction kinetics. A retrograde solubility zone was found at 20 MPa and up to 40 MPa. The best extraction conditions in terms of kinetics, were obtained at 40 MPa and 313 K. Nevertheless, the highest amount of total fatty acids in the extract (599 μg/μL) was obtained at 30 MPa and 323 K. The FAME profile was found to be independent of the extraction method.

Fig. 1 .

 1 Fig. 1. Shapes of the extraction curves for the different types of extraction reported in the Sovová's mathematical model.

Fig. 2 .

 2 Fig. 2. Experimental and modelled JC SC-CO 2 extraction curves: effects of pressure (a) 313 K, (b) 323 K, (c) 333 K.

Fig. 3 .Fig. 4 .

 34 Fig. 3. grinded and sieved JC kernels (a) before extraction, (b) after extraction, (c) & (D) SEM before extraction.

Fig. 5 .

 5 Fig. 5. Experimental SC-CO 2 extraction curves plotted according to the data published by Min et al: Effects of temperature (a) 20 MPa, (b) 30 MPa, (c) 40 MPa, (d) 50 MPa.

Fig. 6 .

 6 Fig. 6. JC oil solubility in SC-CO 2 , plot of ln (y s ) versus ln(ρ CO2 ): (a) 313 K, (b) 323 K, (c) 333 K, (d) Chrastil modelling at pressure from 20 up to 40 MPa and temperature from 313 up to 333 K.

Fig. 7 .

 7 Fig. 7. JC SC-CO 2 extraction curve published by Micic et al. and modelled with BIC model (extraction of type B, P = 30 MPa and T = 323 K).

Table 1

 1 Experimental operating conditions of the SC-CO 2 extraction studies performed on JC kernels. (-) no data reported.

	Refs. Year T(K)	P(MPa) CO 2 flowrate *	t(min)	d p (μm)	Growing	N ** × 10 3 (kg) Study of SCeCO 2	Determination of oil	Extraction
					environment	extraction	solubility in SCeCO 2	curve
						kinetics		modelling

Table 2

 2 Transfer properties of JC oil in SC-CO 2 : oil solubility, fluid phase mass transfer coefficient and diffusion coefficient.

	P (MPa) T (K) ρCO 2	y s × 10 3 (kg oil /	k f × 10 5	D 21 × 10 9 (m 2 /s)
			(kg/m 3 )	kg CO2 )	(m/s)
	40	313	958	5.878	5.15	5.10
		323	925	4.735	5.68	5.55
		333	891	4.150	6.25	6.04
	30	313	907	4.585	5.82	5.62
		323	868	4.080	6.52	6.20
		333	827	1.783	7.32	6.90
	20	323	773	2.383	8.25	7.51
		333	717	1.024	9.76	8.70

Table 3

 3 BIC model parameters (extraction of type B) evaluated from experimental data on JC.

	This study
								ϒ (kg CO2 /	q 1 (kg CO2 /	q c (kg CO2 /	AARD (%) t f (h)
								kg insolublesolid )	kg biomass )	kg biomass )
	40	313	8.776	-	-	-	-	-	-	-	-	2.2-3.3
		323	8.537	1.4471	0.94 2.55	1.28	3.36	134.11	364.98	2.65	4.3
		333	7.465	0.1713	0.98 2.36	1.40	3.36	101.28	415.75	2.93	5.6
	30	313	7.085	1.6719	0.92 2.25	1.16	3.29	154.40	394.36	3.35	5.3
		323	7.055	0.3680	0.96 1.61	1.19	3.15	133.88	591.35	3.51	7.1
		333	7.019	0.4168	0.98 0.92	1.37	3.00	229.47	1031.60	3.91	8.8
	20	323	7.039	0.6551	0.80 0.70	1.20	2.81	62.04	387.68	3.52	24.6
		333	7.087	0.0271	0.98 0.28	1.28	2.61	317.48	3516.87	3.00	35.4
	Micic et al.
	30	323	50	0.0686	0.28 1.50	1.04	3.15	30.28	72.05	2.26	519

P (MPa) T (K) N × 10 3 (kg) k s a s × 10 5 (s -1 ) r K× 10 3 x t (kg oil / kg insolublesolid )

Table 4

 4 Fatty acids composition of fresh JC kernels.

	Fatty acid	μg/mg	mass fraction (%)
	Palmitic C16:0	54.0	5.4
	Palmitoleic C16:1	2.8	0.3
	Stearic C18:0	20.6	2.1
	Oleic C18:1	112.3	11.2
	c18:1b	4.0	0.4
	Linoleic C18:2	100.1	10.0
	Total	293.8	29.4

Table 5

 5 Comparison of the FAME profile of the JC oil (before and after extraction).

	Fatty acids (%)
	P (MPa)	T (K)	C16:0 C16:1 C18:0 C18:1 C18:1b C18:2
	40	333	21.30	0.90	7.87	37.58	1.35	31.00
		323	19.46	1.18	6.85	38.33	1.42	32.76
		313	20.63	1.20	6.48	38.72	1.37	31.60
	30	333	19.29	1.07	7.21	39.52	1.35	31.58
		323	20.46	1.02	7.41	38.11	1.32	31.70
		313	19.87	1.09	7.21	37.99	1.30	32.54
	20	323	18.69	1.09	6.73	38.76	1.35	33.38
		313	17.88	1.15	7.23	39.87	1.54	32.31
	n-hexane extraction	18.45	1.09	6.73	38.25	1.36	34.13
	JC oil before extraction	18.37	0.97	7.01	38.23	1.37	34.05

Acknowledgment

This work was conducted with financial support from Biocarb company France.

performed because of the lack of information in the reported studies. ** N:solid charge in the extractor.