Motivation Data Empirical specification Results Conclusion

Conclusion

We show that quality management employees:

help firms to export more in value ...

  ... but only to destination-products with NTM Reduce exports on non EU markets without NTM: cost effects? Have a heterogeneous effect according to the type of NTM Future steps: Explore the different type of personnel: Engineer, Technicians Explore the intensity of quality management: number of employees, salaries, working time Look at the effect of quality management on the extensive margin of trade, on unit values and perceived quality (Khandelwal 2010) Emlinger Latouche a AAEC, Virginia Tech b SMAR

  When Quality Management Helps Agri-food Firms to ExportCharlotte Emlinger a , Karine Latouche b Exp fjkt = α 1 Quality ft + ξ jkt + υ f + ε fjktQuality ft is a dummy indicating whether firm f has quality management the year t f fixed effect controls for time invariant firms characteristics jkt fixed effects controls for characteristics of the market of country j and good k the year t → Intensive margin Exp fjkt = lv fjkt log of exports of f to j for the k at t

	Motivation Motivation Motivation Motivation Motivation Motivation Motivation Motivation Motivation Motivation Motivation Motivation Motivation Motivation	Data Data Data Data Data Data Data Data Data Data Data Data Data Data	Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification Empirical specification		Results Results Results Results Results Results Results Results Results Results Results Results Results Results	Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion Conclusion
		Motivation This paper Quality management and control personnel Literature (1) Literature (2) Data sources Data: NTMs Specification Results
				lv fjkt
			(1)	(2)	(3)	(4)
	b SMART LERECO, INRAE IATRC 12/14/2021 Increasing demand for traceability and safety for food products : Investigates the impact of firms' commitment to traceability and food safety on export performance Staff in charge of the firm's products quality: Design quality protocols Quality and trade (Verhoogen 2008, Baldwin and Harrigan 2011, Manova and Zhang 2012...) with different proxy for 0.09** Quality ft 0.02 DADS French administrative employee-firm-level database: Quality ft × EU j 0.13*** -0.05 -0.05 number of employees, working hours, total salary, by firm and 0.02 0.06 0.06 Public regulation (EC regulation 178/2002 of food traceability) Sanitary and Phytosanitary Standards (SPS) and Technical Barrier to trade (TBT) at the border Private certifications (HACCP, ISO, IFS, BRC...) → The ability to produce safe products, ensure their traceability and have it recognized through certification is an important component of competitiveness Conduct inspections and tests quality : occupation Quality ft × nonEU j -0.16*** -0.03*** -0.18** Occurrence of Non-Tariff Measures by country and product (6 0.02 0.14 0.07 Relies on the presence of quality management and control Create quality documentation and traceability systems Prices (Schott 2008) 387d: quality control manager and engineer Quality ft × EU j × NTM jk 0.19*** digits of the Harmonized System) from WITS 0.06 personnel to proxy this commitment Uses firm-level data from 2009 to 2016 Estimates the impact of quality management on the intensive and extensive margin of trade, on trade unit values and perceived quality (Khandelwal 2010) Explores the heterogeneity of the effect by product-destination (presence of Non Tariff Measures) Report feedback from customers and analyse safety issues May impact trade: by reducing hazards, recalls and complains by increasing the efficiency of supply chains by helping the products to comply with regulatory requirement by enhancing the firm's reputation (potentially through Econometric estimation of quality (Khandelwal 2013) 0.14** Quality ft × nonEU j × NTM jk 475b: quality control technician for the processing industries 0.08 We restrict NTMs to Sanitary and Phytosanitary measures -0.24 Quality ft × EU j × SPS jk Expert ranking (Crozet et al. 2012) R&D and Innovation (Curzi et Olper 2012) 0.17 (SPSs), Technical Barriers to Trade (TBTs) and preshipment Quality ft × nonEU j × SPS jk 0.11 French Customs trade data: value and quantity exported by 0.08 inspection -chapters A, B and C of UNCTAD classification Quality ft × EU j × TBT jk 0.43** firm, product (HS6), destination and year 0.18 Professional classification (Hansman et al. 2020, Emlinger and Lamani 2020) → Here a different definition of quality : safety, reliability, ability to follow regulatory requirements Quality ft × nonEU j × TBT jk -0.04 80 countries 0.05 → From 2009 to 2015 -0.13 Quality ft × EU j × Preship jk 0.21 → Agri-food products only -0.18*** Quality ft × nonEU j × Preship jk 0.04 → Focus on Agri-food producing firms (exclusion of wholesalers) Nber Obs. 382,027 329,024 329,024 329,024 certifications) R-squared 0.49 0.50 0.50 0.50
		Firm and destination-product-year fixed effects included
					a AAEC, Virginia Tech b SMAR a AAEC, Virginia Tech b SMAR
			Emlinger Latouche Emlinger Latouche Emlinger Latouche

a AAEC, Virginia Tech Emlinger Latouche a AAEC, Virginia Tech b SMAR Emlinger Latouche a AAEC, Virginia Tech b SMAR Emlinger Latouche a AAEC, Virginia Tech b SMAR Traceability and quality management system on firms competitiveness on domestic markets (Alfaro and Rabade 2009, Epelbaum and Martinez 2014, Aiello et al. 2015) Valuation of food traceability system by consumers (Graia et al. 2013, Liu et al. 2019) → No papers on quality management or traceability system and international trade Emlinger Latouche a AAEC, Virginia Tech b SMAR Emlinger Latouche a AAEC, Virginia Tech b SMAR Emlinger Latouche a AAEC, Virginia Tech b SMAR Data: Trade and quality management Emlinger Latouche a AAEC, Virginia Tech b SMAR Data: Trade and quality management Emlinger Latouche a AAEC, Virginia Tech b SMAR Data: Trade and quality management Emlinger Latouche a AAEC, Virginia Tech b SMAR a AAEC, Virginia Tech b SMAR Data: Trade, quality management and NTM Emlinger Latouche a AAEC, Virginia Tech b SMAR * p < 0.10, ** p < 0.05, *** p < 0.01. Emlinger Latouche a AAEC, Virginia Tech b SMAR


Anthony Trioux
email: anthony.trioux@uphf.fr

Senior Member, IEEE Franc ¸ois-Xavier Coudoux
email: francois-xavier.coudoux@uphf.fr

Patrick Corlay
email: patrick.corlay@uphf.fr

Mohamed Gharbi
email: mohamed.gharbi@uphf.fr

A Comparative Preprocessing Study for SoftCast Video Transmission

Keywords: Wireless Video Transmission, SoftCast, Uncoded Transmission, Preprocessing Method

An original wireless video transmission scheme called SoftCast has been recently proposed to deal with the issues encountered in conventional wireless video broadcasting systems such as cliff effect. In this paper, we first review the SoftCast scheme. We then analyze and compare two simple preprocessing methods that help to increase the quality at the receiver side. Each method consists of the subtraction of either the 8-bit mean gray level 128 or the mean value of all pixels for each video frame. Preprocessing methods are compared and evaluated under different channel signal-to-noise ratios using two metrics: Peak Signal-to-Noise Ratio (PSNR) and Structural SIMilarity (SSIM). Simulation results clearly highlight the importance of the preprocessing block in a SoftCast wireless video transmission scheme. Depending on the video input characteristics, an improvement of the PSNR score up to 2.1dB and 2.5dB can be observed for the average gray level method and for the mean frame method, respectively.

I. INTRODUCTION

Broadcasting video content constitutes a challenge because each user is subject to unreliable and different wireless channel that varies over time. Traditional video coding schemes such as H.264/AVC [START_REF] Richardson | The H.264 advanced video compression standard[END_REF] and HEVC [START_REF] Sullivan | Overview of the High Efficiency Video Coding (HEVC) Standard[END_REF] are not suitable for transmission in such environments and applications. Indeed, the parameters are adjusted to match a bitrate available that is given under predicted or assumed channel state. However, a mismatch between the actual channel state and the predicted or assumed one leads to a cliff effect [START_REF] Kokalj-Filipovi | Suppressing the cliff effect in video reproduction quality[END_REF] or levelling-off effect [START_REF] Liang | Superimposed Modulation for Soft Video Delivery with Hidden Resources[END_REF] in received video quality. The first one refers to the fact that video quality drops quickly when the Channel Signal-to-Noise Ratio (CSNR) is below a presumed value whereas the latter one refers to the fact that video quality stays almost constant even if the CSNR increases. In the last few years, the so-called SoftCast [START_REF] Jakubczak | SoftCast: Clean-slate scalable wireless video[END_REF] has been proposed to deal with these issues.

Different from traditional schemes, SoftCast is a Joint Source-Channel Coding scheme and represents the pioneer work of the uncoded video transmission [START_REF] Xiong | Analysis of decorrelation transform gain for uncoded wireless image and video communication[END_REF] also called the soft video delivery [START_REF] Fujihashi | High-Quality Soft Video Delivery With GMRF-Based Overhead Reduction[END_REF]. In uncoded video transmission the video pixels are processed by successive linear operations and are directly transmitted without neither quantization nor coding process such as entropy and channel coding.

A few major properties which makes SoftCast a good candidate for broadcasting video content over wireless channels are listed below:

• Uncoded video transmission can achieve graceful degradation [START_REF] Xiong | Power Distortion Optimization for Uncoded Linear Transformed Transmission of Images and Videos[END_REF]; • For each user, the video quality at the receiver side is a linear function of the CSNR; • A single data stream is delivered and can be decoded by any receivers even if they are subject to bad channel conditions; • SoftCast scheme works without the need of any feedback from receivers [START_REF] Jakubczak | SoftCast: Clean-slate scalable wireless video[END_REF]. Since the original works [START_REF] Jakubczak | SoftCast: Clean-slate scalable wireless video[END_REF], uncoded video transmission has gathered a significant interest from the research community [START_REF] Liang | Superimposed Modulation for Soft Video Delivery with Hidden Resources[END_REF], [START_REF] Xiong | Analysis of decorrelation transform gain for uncoded wireless image and video communication[END_REF]- [START_REF] Shen | Foveation Based Wireless Soft Image Delivery[END_REF]. The authors in [START_REF] He | Structure-preserving hybrid digital-analog video delivery in wireless networks[END_REF]- [START_REF] Zhao | Wireless image and video soft transmission via perception-inspired power distortion optimization[END_REF] propose improvements based on the characteristics of the Human Vision System (HVS) whereas [START_REF] Fujihashi | High-Quality Soft Video Delivery With GMRF-Based Overhead Reduction[END_REF], [START_REF] Xiong | Power Distortion Optimization for Uncoded Linear Transformed Transmission of Images and Videos[END_REF] propose efficient signal energy modeling to better allocate bandwidth resources and therefore improve the received video quality.

In this paper, we first review the original SoftCast scheme and then compare two simple preprocessing methods that has been proposed in the literature [START_REF] Cui | Robust Uncoded Video Transmission under Practical Channel Estimation[END_REF], [START_REF] Hagag | Satellite Images Broadcast Based on Wireless SoftCast Scheme[END_REF]. By preprocessing, we mean the energy reduction before applying all the transformations in the SoftCast scheme. These methods help to increase the received video quality with none to reduce bandwidth consumption. Results underline the importance of the preprocessing block in an uncoded scheme such as SoftCast. The comparison between the two methods shows that depending on the application and the corresponding available bandwidth one may be preferred to the other.

The rest of this paper is organized as follows: Section II gives a review of the SoftCast scheme. Section III introduces the preprocessing methods evaluated in this paper. In section IV, we compare the methods against classical SoftCast scheme based on simulation results. Conclusions and discussions are presented in section V.

II. SOFTCAST OVERVIEW

In this section, the basic scheme of SoftCast [START_REF] Jakubczak | SoftCast: Clean-slate scalable wireless video[END_REF] is given in Fig. 1. We note that the green blocks are not in the original SoftCast scheme but have been added as additional steps and are described in Section III .

A. Compression Step

SoftCast first operates on Group of Pictures (GoP) and decorrelates the signal through a three-dimension full-frame Discrete Cosine Transform (DCT). The 3D-DCT is simply done by exploiting the separability of the DCT transform, i.e., the scheme first transforms each frame with a spatial 2D-DCT and then performs a temporal 1D-DCT over the GoP as shown in Fig. 2. The 3D-DCT [START_REF] Park | A 3D-DCT video encoder using advanced coding techniques for low power mobile device[END_REF] of a GoP f (i, j, k) is denoted by F(u, v, w) and is given by:

F(u, v, w) = P -1 i=0 Q-1 j=0 R-1 k=0 f (i, j, k) • C i,u • C j,v • C k,w (1)
where P, Q denote the frame size and R the GoP-size.

C p,q = 1 √ Z , q = 0 2 √ Z • cos( (2p+1)qπ 2Z ), otherwise (2)
with Z equals to P, Q or R, depending on the selected C p,q . After 3D-DCT, the frames are divided into small blocks called chunks and rearranged to form a new matrix where each row contains a chunk. These chunks are ordered by energy descending order.

In SoftCast scheme, the compression can be done after decorrelation transform by discarding a certain amount of chunks. This amount is fixed by the available bandwidth and the modulation used at the transmitter side. The procedure to determine the number of chunks that can be transmitted is further introduced in subsection II-D.

In uncoded video transmission, the compression ratio [START_REF] Li | Compressed uncoded screen content video transmission in bandwidth-constrained wireless networks[END_REF] is defined by:

CR = K/N (3)
where, K is the number of transmitted chunks and N the total number of chunks within a GoP. This ratio ranges between 0 (no data sent) and 1 (no compression). The number of chunks per GoP N is defined by:

N = nb R • nb C • nb F nb r • nb c , [chunks/GoP] (4)
where nb R , nb C represents the frame size, nb r , nb c the chunk size and nb F refers to the number of frames within a GoP.

B. Error Resilience Step

The next block called Power Allocation or Scaling is used to provide error resilience to the scheme. SoftCast scales the magnitude of the DCT coefficients to offer a better protection against noise that affects the components during transmission. Since the available power transmission P is limited and fixed, it must be distributed to all the chunks in a way that limits the Mean Square Error (MSE). This division is a typical Lagrangian problem and the solution is given by:

g i = λ -1/4 i • P j λ j (5)
where g i , i = 1, 2, . . . , K is the scaling factor for the i th chunk, and

λ i = E[X i 2 ]
is the energy of the i th chunk [START_REF] Xiong | Analysis of decorrelation transform gain for uncoded wireless image and video communication[END_REF]. The resulting scaled-chunks are defined as

U i [j] = g i X i [j] where j = 1, 2, . . . , nb r • nb c represents the j th DCT coeffi- cient in the chunk i.
We note that only one scaling factor per chunk is computed. This is the result of a trade-off between quality received, amount of metadata and computation cost. Readers may refer to [START_REF] Jakubczak | SoftCast: Clean-slate scalable wireless video[END_REF] for further details.

C. Packet Loss Resilience Step

The scaled coefficients are then multiplied by a Hadamard matrix to provide packet loss resilience. The Hadamard matrix is an orthogonal transform composed of +1 and -1 elements.

After 3D-DCT transformation each chunk presents huge discrepancy in terms of energy. The goal of this transformation is to ensure that each packet contains approximately the same amount of information making them equally important for the reconstruction process. This transformation takes the chunks as input and outputs slices. Each slice is simply a linear combination of all scaled-chunks and is defined by

Y i [j] = H i • U i [j]
where H i denotes the i th row of the Hadamard matrix.

D. Modulation Step

After all above listed operations process, the obtained coefficients are directly mapped in pairs (I and Q in OFDM) and transmitted without any coding step in a pseudo-analog manner referred as Raw Orthogonal Frequency Division Multiplexing (Raw-OFDM) [START_REF] Xiong | Analysis of decorrelation transform gain for uncoded wireless image and video communication[END_REF].

In the Raw-OFDM, the Forward Error Correction (FEC) code is bypassed and Pseudo-Analog Modulation replaces the classical modulation part of OFDM. Therefore, instead of bitrate only symbol rate is considered hereafter. Since coefficients are sent in pairs (I and Q planes), the maximal resulting matching channel bandwidth in SoftCast video transmission can be described as follows:

BW max = nb R • nb C • ϑ 2 , [symbs/s] ( 6
)
where ϑ is the frame rate of the video expressed in frame per second (fps).

For instance, a CIF video format with 30fps represents a data volume of 352 • 288 • 30 = 3.04 • 10 6 real values per second to be transmitted [START_REF] He | Structure-preserving hybrid digital-analog video delivery in wireless networks[END_REF]. The resulting matching channel symbol rate is 3.04 • 10 6 /2 = 1.52Msymbols/s. If we consider a wireless bandwidth available of 1MHz per user, nearly 30% of compression is needed. Furthermore, in the case of transmission High Definition (HD) contents or new format such as 4K the wireless bandwidth needed is too large and discarding chunks in the compression step becomes unavoidable in SoftCast scheme. A 4K video format example with 60fps results in 601.3 • 10 6 real values per second to be transmitted corresponding to a wireless bandwidth of 300.6 MHz which is unrealistic.

The Compression Ratio (CR) in (3) can also be expressed as a bandwidth ratio as follows:

CR = BW ava /BW max (7)
where BW ava denotes the available bandwidth at the transmitter.

If the available bandwidth BW ava is less than the maximal resulting bandwidth channel, the number of transmitted chunk K within a GoP is adjusted accordingly.

By using (3), ( 4) and [START_REF] Fujihashi | High-Quality Soft Video Delivery With GMRF-Based Overhead Reduction[END_REF] we get the maximum number of chunks K per GoP that can be transmitted:

K = BW ava • N BW max (8) = 2.BW ava • nb F nb r • nb c • ϑ (9)

E. Metadata

The metadata represent the key elements in SoftCast scheme that are essential to recover video data signal. They represent a small amount of three datasets:

• The mean of each chunk, noted µ i ;

• The variance/energy of each chunk, noted λ i ;

• A bitmap which indicates the positions of the discarded chunks into the GoP.

To ensure a high probability of correct delivery and therefore, a correct decoding process, they are strongly protected and transmitted in a robust way (BPSK for example [START_REF] Fujihashi | High-Quality Soft Video Delivery With GMRF-Based Overhead Reduction[END_REF]). We note that the bandwidth required for transmitting metadata has not been considered above but typical values are given in [START_REF] Fujihashi | High-Quality Soft Video Delivery With GMRF-Based Overhead Reduction[END_REF].

F. LLSE Decoder

At the receiver side, a Linear Least Square Error (LLSE) decoder is used to get the best estimation of received values. The decoded values are then reassembled to form frames that are passed through an inverse 3D-DCT process. In case of bandwidth-constrained environments, the discarded chunks at the transmitter side are replaced by null values.

In SoftCast, an Additive White Gaussian Noise (AWGN) with zero-mean, variance of σ 2 and noted n i [j] is assumed.

After all linear operations in the encoder, Y i [j] is sent and the corresponding Ŷi [j] = Y i [j] + n i [j] is received. SoftCast decodes and gets the best estimate [START_REF] Jakubczak | SoftCast: Clean-slate scalable wireless video[END_REF] as:

Xi [j] = g i λ i g 2 i λ i + σ 2 • Ŷi [j] (10)
The transmitter side can be synthesized into matrix form as follows [START_REF] Jakubczak | SoftCast: Clean-slate scalable wireless video[END_REF]:

Y = HGX = CX ( 11
)
where X is the chunk's matrix and Y the corresponding slices transmitted over the channel. The encoding matrix C is the product of HG where H and G are the Hadamard matrix and the scaling factors matrix, respectively. Therefore, the LLSE equation can be rewritten in matrix form as follows:

XLLSE = λ x C T (Cλ x C T + Σ) -1 Ŷ ( 12
)
where λ x is a diagonal matrix whose diagonal elements are the energy λ i of the i th chunk, and Σ is a diagonal matrix in which the i th element is the channel noise power σ 2 i experienced by the packet carrying the i th row of Y .

Assuming without loss of generality that a packet contains a single slice, the LLSE decoder can be rewritten in the presence of packet loss as [START_REF] Jakubczak | SoftCast: Clean-slate scalable wireless video[END_REF]:

XLLSE = λ x C T * i (C * i λ x C T * i + Σ ( * i * i) ) -1 Ŷ * i (13)
where C * i and Y * i denote C and Y after removing the i th lost row.

III. PREPROCESSING METHODS

In this section, we study how the preprocessing methods influence the reconstructed video quality after transmission. Recently, Xiong et al. [START_REF] Xiong | Analysis of decorrelation transform gain for uncoded wireless image and video communication[END_REF] introduced the concept of data activity for uncoded transmission. They showed that this term denoted by

H = 1 N N i=1 E[x 2
i ] affect the reconstructed PSNR at receiver side as follows:

P SN R dB = c + CSN R dB -20 log 10 H (14)
with c = 20 log 10 (255). This formula underlines the importance of having a reduced data activity and hence emphasizes the benefit of reducing the energy before applying all the transformations in the SoftCast scheme.

It is well-known that the DC component after DCT transformation carries most of the energy. A simple solution would be to remove the DC component of each frame after 2D-DCT and before applying the 1D-temporal DCT. However, preprocessing method can only work if the removed information is perfectly recovered at decoder level. This is why these data should be transmitted in metadata, recalling that they are strongly protected (FEC) and transmitted in a robust way (BPSK) to ensure correct delivery. Nevertheless, it means that a larger bandwidth must be allocated to the metadata. When the available bandwidth is greater than the needed one, transmitting additional information in metadata is a feasible solution but it is not when the targeted application has bandwidth constraints.

We now show that transmitting DC component directly in metadata is not relevant. To see how, we recall (1) and ( 2) and focus on the 2D-DCT case. We calculate the DC component F(0, 0) as follows:

F(0, 0) = P -1 i=0 Q-1 j=0 f (i, j) • C i,0 • C j,0 (15)
= C i,0 • C j,0 P -1 i=0 Q-1 j=0 f (i, j) = 1 √ P • 1 √ Q • P • Q • f where C i,0 = 1 √ P and C j,0 = 1 √ Q , P, Q denote the
size of the frames and f denotes the mean-pixel value of the frame.

A simple calculation for a CIF video sequence (352 × 288 pixels) shows that each 2D-DC component in SoftCast context should at least be coded on 18 bits (8 bits for the meanpixel value of the frame, 1 sign bit and 9 bits to code the mathematical operation √ 352 • √ 288) whereas only 8 bits are needed for each frame when directly subtracting the mean value in pixel domain and before applying the 2D-DCT. Therefore, we do not consider the preprocessing applied in transformed domain but focus hereafter on pixel domain preprocessing.

The two preprocessing methods are defined as follows:

f proc (i, j) = f (i, j) -p (16)
where f proc (i, j) denotes the pixel frame after preprocessing. The value of p is given differently in the two methods: p = |mean(x)| in the first case and p = 128 in the second. We note that • denotes the rounding operation to the nearest integer.

The first solution has been recently used by Hagag et al. [START_REF] Hagag | Satellite Images Broadcast Based on Wireless SoftCast Scheme[END_REF] whereas the alternative solution has been proposed by Cui et al. [12]. This alternative solution which consists of subtracting an average 8-bit mean gray level (i.e., 128) avoids to increase the allocated bandwidth for metadata transmission. Indeed, adding an offset of +128 for each frame after decoding process does not require any additional information to be transmitted. In the next section, we first compare both methods to the original SoftCast scheme in terms of reconstructed video quality and then evaluate the gap between the two methods.

IV. PERFORMANCE ANALYSIS OF THE PREPROCESSING METHODS A. Simulation Setup

Video sources: We evaluate and compare the preprocessing methods through extensive simulations. The luminance part of video CIF sequences (with a frame rate of 30 fps) from the Xiph collection [16] are used as the inputs. The process is performed GoP by GoP with a GoP-size of 16 frames and each frame is split into 64 chunks of 44 × 36 pixels as in [START_REF] Fujihashi | High-Quality Soft Video Delivery With GMRF-Based Overhead Reduction[END_REF], [START_REF] Xiong | Power Distortion Optimization for Uncoded Linear Transformed Transmission of Images and Videos[END_REF]. For each sequence, we send the first 288 frames.

In the following tests, we choose the Australia, News and Stefan sequences because of their different spatiotemporal characteristics. Stefan contains high temporal and spatial activities. In contrast, Australia and News presents slow motions and low to medium spatial contents, respectively. Results with other CIF sequences are similar.

Wireless characteristics: Transmissions through AWGN channels in the range of [5∼25dB] are considered. The transmission power is normalized to P total = 1. To ensure a fair comparison, the same noise is generated and applied to all methods. Results are averaged over 10 realizations.

Evaluation Metrics: Two commonly used metrics are here considered: the PSNR based on Mean Square Error (MSE) and the SSIM. The PSNR is used as a purely objective metric whereas the SSIM provides a quality index more correlated with the Human Visual System (HVS) [START_REF] He | Structure-preserving hybrid digital-analog video delivery in wireless networks[END_REF]. The SSIM calculation outputs values between 0 (worst quality) and 1 (best quality). The PSNR is given by

P SN R dB = 10log 10 (2 L -1) 2 M SE
and the MSE is defined as M SE = 2 where I ori denotes the original frame and I rec the reconstructed one.

1 P Q P x=1 Q y=1 (I ori (x, y) -I rec (x, y))

B. Simulation Results

Fig. 3 shows the average video quality results in terms of PSNR and SSIM for the original SoftCast scheme where no preprocessing is applied and the two others where subtraction in pixel domain is done before encoding process.

We can firstly note that the PSNR follows a linear relationship. As mentioned in Section I, it is a key feature from SoftCast that has been studied in [START_REF] Xiong | Analysis of decorrelation transform gain for uncoded wireless image and video communication[END_REF].

Then, regardless of the input video sequence, the subtraction of the pixel-mean image before encoding process gives the best results. The biggest difference in quality reconstruction between the classical SoftCast scheme and the preprocessing methods appears for the Australia sequence. This is because Australia contains low spatiotemporal activities making it easy to decorrelate. Most of the energy after 3D-DCT is concentrated in the low frequency bands and protecting almost all the information contained in DC components leads to an improvement bigger than 2dB. In contrast, News and Stefan contains higher spatiotemporal contents, i.e., the energy is spread across more components and therefore the gap becomes lower.

We can also note that the gap between the two methods is higher for the News sequence and almost null for the Stefan sequence. This is because the pixel-mean value of each frame is in average equal to 132 (close to 128) and 78 for the News and Stefan respectively. It is normal to observe better results with the preprocessing block, since the subtraction of the pixelmean value or an average gray level helps to reduce the DC component of each 2D-DCT frames as seen in Section III. The DC component reduction leads to a reduced data activity [START_REF] Xiong | Analysis of decorrelation transform gain for uncoded wireless image and video communication[END_REF] which results in a better reconstructed video quality.

Depending on the video input characteristics, the improvement in PSNR and SSIM between the two methods can be visible or almost null (i.e., when the pixel-mean value of each frame is around 128). As an illustrative example we give numerical values for the News and Australia sequence in Table I. P1 and P2 denote the preprocessing methods, i.e., the subtraction of the pixel-mean value and the subtraction of 128 respectively. Regarding the SSIM curves, we observe that the gap between the three evaluated schemes decreases when the CSNR becomes higher. This is due to the fact that at high CSNR (>25dB) the perturbation of the AWGN noise becomes negligible and therefore the reconstruction of the DC component in classic SoftCast scheme approaches the real DC value before transmission.

Finally, a visual comparison is given in Fig. 4 where the reconstructed frames and the error images are displayed (the error images have been shifted by +128 for viewing purposes). We deliberately set the CSNR to 0dB in order to accentuate the noise during transmission. We can clearly observe that the classical SoftCast gives the lower video quality received. In contrast, the studied preprocessing methods achieve better reconstructed quality under the same channel characteristics.

V. CONCLUSION In this paper, we make a comparative study of two simple preprocessing methods that can be used in a SoftCast context. Results show that depending on the video and its frame-mean value, the pixel-mean subtraction either gets better results (up to 0.67dB for the tested sequences) than average 8-bit gray level method or performs similar (i.e., when the image-mean is close to 128). Regardless of that aspect, the reconstructed video quality at the receiver side is always better than the classical SoftCast scheme. The choice between the two preprocessing method is made according to the available bandwidth. Indeed, the latter one (8-bit gray level method) does not need to allocate more bandwidth for the metadata making it a possible solution in bandwidth-constrained environments.

Fig. 1 :

 1 Fig. 1: Block diagram of the SoftCast video transmission scheme.

Fig. 2 :

 2 Fig. 2: Compression Step in SoftCast scheme. From left to right: GoP in pixel domain, 2D-transformed frames, 3Dtransformed frames, Chunks division after 3D-DCT.

Fig. 3 :

 3 Fig. 3: Average simulation results for classic SoftCast scheme and two added preprocessing methods: Subtraction of the 8-bit mean gray level 128 and subtraction of the mean value of all pixel for each video frame. From left to right: (a), (d) Australia sequence, (b), (e) News sequence and (c), (f) Stefan sequence. First row: Average PSNR results. Second row: Average SSIM results. Please enlarge the figure to observe details.

Fig. 4 :

 4 Fig. 4: Visual quality comparison at a CSNR equal to 0dB for News sequence (first frame). First row: Reconstructed frames in pixel domain. Second row: Resulting error images. From left to right: (a) Original frame, (b) and (e) Classic SoftCast, (c) and (f) SoftCast with subtraction of the 8-bit mean gray level 128, (d) and (g) SoftCast with subtraction of the mean value of all pixels for each video frame. Please enlarge the figure to observe details.

TABLE I :

 I Evaluation of the maximal quality improvement for the News and Australia sequences

		Maximum Quality Improvement
	Video Sequence	SoftCast vs P2	SoftCast vs P1	P1 vs P2
	News	PSNR = 0.73dB PSNR = 1.4dB SSIM = 0.012 SSIM = 0.023	PSNR = 0.67dB SSIM = 0.011
	Australia	PSNR = 2.1dB SSIM = 0.043	PSNR = 2.5dB SSIM = 0.052	PSNR = 0.41dB SSIM = 0.009

ACKNOWLEDGMENT

We would like to thank Prof. Cagnazzo and Prof. Kieffer for their help during the implementation of the SoftCast scheme.


Laëtitia Lemiere
email: laetitia.lemiere@inrae.fr

Marc Jaeger

Gérard Subsol

Marie Gosme

Augmented reality for agroforestry system design EURAF 2020 Agroforestry for the transition towards sustainability and bioeconomy

Keywords: Augmented reality, Agroforestry system design, Visualization

. In this contribution, we propose a novel application case for agroforestry system design workshops.

Agroforestry system design workshops gather different actors (farmers, extensionists, local policymakers etc.) and aim at collectively decide the tree species to plant, the spatial organisation of the system and the tree and crop management options. Currently, such workshops use whiteboards, maps or physical mock-ups representing the system with tokens, pins or toothpicks. The result of these workshops is a model that represents part of the plot. Such workshops promote discussion between the different actors, but the participants cannot observe the impact of their choices and it is impossible to see the evolution of the plot over the years. Moreover, the model isn't a usable plantation map, an expert must adapt it to the whole plot and translate it into a usable plantation map.

In order to facilitate agroforestry system design and adoption, we propose to use augmented reality both for indoor design workshops and for outdoor field visits. For the indoor design application, our objective is to allow users to easily interact with a physical mock-up in order to facilitate user involvement and visualize quickly modification of the system by providing the users with information relevant to them: tree size, level of tree-crop competition, crop yield heterogeneity, etc. For example, a user could propose a specific tree species and visualize the consequences for the crops, as well as the agronomical or environmental performance of this system. For field visits, our aim is to visualise the impact of trees on the landscape, which would be useful for farmers to help them imagine their system, and for educational purposes, to foster discussions on the impacts of trees on crops, biodiversity, farming operations etc. Finally, the link between the indoor workshop and the in situ visualization, i.e. the implementation of the theoretical pattern in a particular plot of the farm to get the coordinates of the trees, could also benefit from augmented reality, thanks to automatic detection of the agroforestry pattern, replication of this pattern within field borders (with constraints) and generation of geographic coordinates of each tree. Thus, we identified three steps, in which augmented reality could facilitate discussions, projections and help decision-making in the process of agroforestry system design: -

In the, mock-up design stage, augmented reality allows visualizing the evolution of the plants and their constraints (tree growth, competition on light, spreading of diseases…), -

In the mock-up implementation stage, the mock-up instantiation leads to the definition of a 3D scene, representing the future field. This implementation stage involves several processes such as pattern recognition, graph modelling, replication, and georeferencing -At the in situ visualization stage, augmented reality is mobilized for realistic plants (trees, crops) visualisation in the plot including the possibility to simulate plant growth to see the impact on the landscape after 5, 10 or 50 years.

We get some results for the two first steps. Figure 1 shows, on the left, an image acquired by a smartphone or a webcam, of a (simplified) agroforestry system mock-up, with 6 "P" paper markers representing poplar trees, 2 "C" markers representing crops and one "TRI" marker defining the reference coordinate system(trihedron). Augmented reality allows to overlay, in real-time, on this image virtual representations of the trees (green points represent the canopy as the trunk cannot be seen from this viewing angle), crops (currently restricted to the marker surface but the objective is to fill the whole alley between trees) and the coordinate system vectors. On the right part of Figure1, the mock-up has been automatically translated into a 3D scene in the Unity visualisation environment for further analysis.

We propose here a methodology to move from the design stage to the mock-up implementation. It must integrate a complete description of the plot scene extracted from the image (which include to deal with the approximate marker positioning,) and extract automatically relationships such as "the elements P2, P6 and P8 form a line" or "C1 is between the left line of trees and the middle line". We will then use them to infer the Ecosystem Service Functional Motif (ESFM) [START_REF] Rafflegeau | Location-Based Augmented Reality In-situ Visualization Applied for Agricultural Fieldwork Navigation[END_REF]) which is the smallest pattern supporting all the ecosystem services targeted by the designers of the agroforestry system. During the instantiation step, the system repeats the EFSM automatically over the whole plot. An expert could correct, if necessary, to finalize the plantation map.

Further work will focus on: (i) predicting useful information (such as light or water competition) from the ESFM using simulation models and visualising them as augmented reality on the mock-up; (ii) formalising constraints in the implementation step (e.g. no trees in small corners of the plot) to replicate the ESFM throughout the map of the actual plot; (iii) visualising realistic-looking trees in situ, directly in the farmer's fields.

Figure 1 .

 1 Figure 1. Example of mock-up (left) automatically convert into a 3D scene with a script and Unity software (right)


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

Isabelle Bombarda

Magalie Claeys-Bruno

Sandrine Amat

Emmanuelle Myotte

Jean-Paul Nisteron

Christelle Crampon

Elisabeth Badens

Supercritical CO 2 extraction of Moroccan argan (Argania spinosa L.) oil: Extraction kinetics and solubility determination

Keywords:

Experimental and modelling investigations of supercritical CO 2 extraction of oil from Argania spinosa L. kernels were conducted at pressure range from 200 to 400 bar, temperature range of 313-333 K at a CO 2 flow rate of 0.14 kg/h. Regardless of the pressure and the temperature, the highest achievable yield was estimated at 0.63 kg oil / kg biomass . The extraction kinetics were modeled with Sovová's broken and intact cells model. The extraction of type B was found to be the most suited extraction type. Argan oil solubility in supercritical CO 2 was determined and modelled with the Chrastil equation. A retrograde solubility behaviour was observed at 200 bar and the faster extraction kinetics were found at 400 bar and 333 K. The total tocopherols concentration was found between 389.7 and 1688.6 mg/kg extract . Experiments were performed on unroasted and roasted kernels.

Introduction

Argan tree (Argania spinosa L.) is an endemic tree from southern Morocco and Algeria. The oil extracted from argan seeds is mainly composed of monounsaturated and polyunsaturated fatty acids, carotenoids, sterols, tocopherols and squalene [START_REF] Yousfi | Fatty acid, triglyceride and tocopherol composition of Algerian Argan (Argania spinosa) fruit seed lipids[END_REF][START_REF] Kamal | Antioxidant Activities, Total Polyphenolic Compounds and HPLC/DAD/MS Phenolic Profile of Argan Oil Derived From Two Different Methods of Extractions[END_REF][START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF][START_REF] Haloui | Supercritical CO 2 extraction of essential oil from Algerian Argan (Argania spinosa L.) seeds and yield optimization[END_REF]. Argan oil is very well known for its antioxidant properties; it is a product of high added value mainly used in food, cosmetic and pharmaceutical industries in Maghreb and Europe [START_REF] Bennani | Antiproliferative effect of polyphenols and sterols of virgin argan oil on human prostate cancer cell lines[END_REF][START_REF] Cherki | Argan oil: Which benefits on cardiovascular diseases?[END_REF][START_REF] Yaghmur | Evaluation of argan oil for deep-fat frying[END_REF][START_REF] Drissi | Evidence of hypolipemiant and antioxidant properties of argan oil derived from the argan tree (Argania spinosa)*1[END_REF][START_REF] Berrougui | Hypolipidemic and hypocholesterolemic effect of argan oil (Argania spinosa L.) in Meriones shawi rats[END_REF][START_REF] Hilali | Influence of origin and extraction method on argan oil physico-chemical characteristics and composition[END_REF][START_REF] Lybbert | Market-based conservation and local benefits: the case of argan oil in Morocco[END_REF][START_REF] Marfil | Metal content and physicochemical parameters used as quality criteria in virgin argan oil: influence of the extraction method[END_REF]. When argan ripe fruits are collected they are sun dried then the peel is manually removed resulting in argan seeds. The seeds are then broken to collect the white argan kernel. The production of edible oil is performed by mechanical cold-pressing or by traditional hand pressing from roasted argan kernels by using water. The oil extracted from ground unroasted argan kernels using classical solvent extraction process is used as ingredient in cosmetic applications. For industrial cosmetic applications argan oil is extracted from ground kernels using a lipophilic or halogenated solvent such as cyclohexane, petroleum ether, chloroform or dichloromethane [START_REF] Guillaume | Argan oil and other argan products: use in dermocosmetology[END_REF]. After solvent extraction process, the extraction yield is about 45-50 %. It is well-known that extraction processes using organic solvents like cyclohexane or dichloromethane, which are toxic and non-selective, lead inevitably to a separation steps which is time consuming and increase the production costs. A well-known alternative to organic solvent extraction is the supercritical CO 2 (SC-CO 2 ) extraction. SC-CO 2 is a GRAS (Generally Recognized As Safe) solvent, and thanks to its low critical temperature (304.21 K) it can be used to extract heat-sensitive components. Its solvent power and selectivity towards neutral lipids can be improved by tuning temperature and pressure. Moreover, no separation step is needed since CO 2 is gaseous at ambient conditions of pressure and temperature. Lastly, CO 2 is recycled at industrial scale enabling a clean and compact process.

To our knowledge, only two studies dealing with the SC-CO 2 extraction of oil from unroasted argan kernels were reported in the literature [START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF][START_REF] Haloui | Supercritical CO 2 extraction of essential oil from Algerian Argan (Argania spinosa L.) seeds and yield optimization[END_REF]. These studies focused on the effects of pressure and temperature on both the extraction yield and the quality of the extracted oil. Through these studies SC-CO 2 extraction process appears to be a promising method for the extraction of oil from argan kernels. Taribak et al. [START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF] have extracted argan oil from 100 to 400 bar at temperatures from 308 to 328 K with a CO 2 flow rate of 1.2 kg/h. A mass of 15 g of ground argan kernels (mean particle diameter of 800 μm) from southern Morocco was considered for all experiments. The extractions lasted for 3 h.

Comparisons were made with 8 h Soxhlet extraction using n-hexane and semi industrial mechanical cold-pressing without water. The SC-CO 2 extraction yields varied between a few percent (100 bar at 318 and 328 K) to 48 % (400 bar and 318 K) while the extraction yields obtained by Soxhlet and mechanical-pressed were 52 % and 45 %, respectively.

The authors reported that at a set temperature the yield increased with increasing pressure. A retrograde solubility zone was reported for pressures up to 200 bar, at 300 bar the extraction yield was reported to be independent of temperature. Concerning the quality of the oil extracted using SC-CO 2 : no significant differences were observed between the physicochemical parameters of the oils extracted at different conditions of pressure and temperature, the quality of the oil did not vary significantly compared to the oil extracted using press or n-hexane extraction. The extracted oils contained mainly oleic, linoleic, and palmitic acids. The oils extracted by SC-CO 2 and n-hexane Soxhlet had both the required physicochemical properties to be of edible grade according to the recommendations of the official argan oil guidelines (NM 08.5.090, Snima 2003) [START_REF] Rahmani | Composition chimique de l'huile d'argane « vierge[END_REF].

Haloui et al. [START_REF] Haloui | Supercritical CO 2 extraction of essential oil from Algerian Argan (Argania spinosa L.) seeds and yield optimization[END_REF] have performed SC-CO 2 extractions of argan oil from southeast of Algeria (Tindouf). Extraction experiments ranged from 100 to 400 bar, temperatures from 308 to 328 K at a CO 2 flow rate of 0.252 kg/h. Extractions were performed on ground kernels with a mean particle size diameter of 1000 μm for 2 h. The biomass was introduced into an extraction autoclave of 5 cm 3 volume, the mass sample was not mentioned. The highest extraction yield was reported to be 83 % at 250 bar and 308 K on their biomass. At 100 bar, the yield was found be lower than 7 %. The authors have reported a retrograde solubility behaviour at 250 bar. The extracted oils were mainly composed by fatty acids (palmitic, stearic, oleic, and linoleic acid) and squalene.

From these two studies, it appears that compared to classical extraction processes, similar compounds were recovered using SC-CO 2 extraction. A retrograde solubility behaviour was reported at pressures of 200-250 bar. Regardless of the temperature, the extraction yield at 100 bar was reported to be the lowest. Nevertheless, some gaps were identified: the highest extraction yield reported by Haloui et al. was 43.2 % and 38.3 % higher than the highest yield reported by Taribak et al. after SC-CO 2 (48 %) and n-hexane Soxhlet extraction (52-60 %), respectively. No extraction curves were reported in these studies. The extraction kinetics could have led to new insights in the comparison and the understanding of the differences in the reported results. It is worth noting that the extraction curves provide very important information such as the time needed to perform a complete extraction, the effects of process parameters on kinetics and extraction yield. Finally, when modelling studies are performed, a better understanding of the extraction phenomena is possible. Indeed, modelling gives access to very important parameters and data like oil solubility in SC-CO 2 and mass transfer coefficient. These data are of prime importance for theorical knowledge and scale-up studies.

Argan oil is highly prized in cosmetic and food industry and the investigation of green extraction process for its recovery is a subject of prime importance. Hence, the aim of this work is to complement the studies dealing with the extraction of oil using SC-CO 2 from unroasted and roasted argan kernels by providing useful information about extraction kinetics, argan oil solubility in SC-CO 2 , oil analysis and kinetics modelling. Based on previous studies [START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF][START_REF] Haloui | Supercritical CO 2 extraction of essential oil from Algerian Argan (Argania spinosa L.) seeds and yield optimization[END_REF], SC-CO 2 extractions from Moroccan argan kernel ranged from 200 to 400 bar, 313-323 K at a constant CO 2 flow rate of 0.14 kg/h. The effect of mean particle size diameter and roasting on extraction kinetics were also investigated at the experimental condition leading to the highest extraction kinetics from unroasted kernels. Soxhlet extractions using n-hexane were performed to compare the extracted oil yields and oils compositions. As tocopherols are products of high interest, it was chosen to focus on the concentration of tocopherol in the extracted oils. Extracted oils were analyzed by High Performance Liquid Chromatography (HPLC). Sovová's broken and intact cell (BIC) mathematical model [START_REF] Sovová | Mathematical model for supercritical fluid extraction of natural products and extraction curve evaluation[END_REF] was applied to model the extraction curves.

Materials and methods

Raw material and chemicals

Argan fruits were collected in September 2019 from southwest Morocco (Essaouira region). The fruits were sun-dried for few days. The dried nuts were manually shelled to get the kernels.

Unroasted argan kernels were grinded and sieved into three granulometries. The mean particle diameters "d p " considered in this study were 400, 750 and higher than 1000 μm. The highest mass fraction after grinding and sieving was obtained for mean particle size diameter of 750 μm. The mass fraction of the lowest mean particle size diameter considered in this study (d p =400 μm) was lower than 5 % due to a highly fatty biomass. Consequently, SC-CO 2 extraction kinetics were established considering mainly samples of d p =750 μm.

A sample of fresh argan kernels was roasted by conduction at about 423 K for 20-30 min. This sample was then grinded and sieved at d p =750 μm.

Samples were stored at 277 K prior to SC-CO 2 extraction experiments to avoid degradation of oil. The water content of the ground biomass was measured at 3.7 wt % through the mass loss of 5 g of sample after oven drying (Memmert, Schwabach, Germany) at 378 K for 24 h. Hence, no drying was applied on the samples. CO 2 was provided by Air Liquide (France) with a purity of 99. 1. The extraction autoclave is a 20 cm 3 stainless-steel vessel placed in a heater. The CO 2 high pressure pump (3) was a SFC-24 high-pressure liquid CO 2 pump (Interchim France). A high-pressure solvent pump [START_REF] Hilali | Influence of origin and extraction method on argan oil physico-chemical characteristics and composition[END_REF], GILSON 307 Pump with standard head pump of 5SC type (Gilson Inc., USA), was used to clean the pipes and the micrometric valve (V3) with ethanol at the end of each experiment. The pipes and the micrometric valve were dried with a flow of gaseous CO 2 for few minutes (Valves V2, V3 and V5 open, valve V4 closed). Extraction experiments with pure CO 2 were conducted with valves V4 and V5 closed. The CO 2 flow and pressure were controlled with micrometric valve (V3). A flowmeter located at the end of the extraction line ( 8) was used to measure the CO 2 flowrate.

For each experiment, the mass introduced in the extraction autoclave lies between 6 and 7 g. Regarding the small charges used for SC-CO 2 extraction experiments, the mass of extracted oil was estimated relative to the mass losses of the sample in the extraction autoclave. The yield was calculated considering Eq. 1.

Yield ( kg / kg ) = mass of extracted oil (kg) biomass introduced in the extractor (kg) (1)
Experiments were conducted at pressures of 200, 300 and 400 bar, temperatures of 313, 323 and 333 K at a CO 2 flowrate of 0.14 kg/h. The extraction curves were plotted as the variation of the yield as function of the CO 2 /biomass mass ratio.

Soxhlet extraction

Soxhlet extractions, using n-hexane, were performed for 5 and 8 h in two different capacities apparatus. The mass samples were about 7.34 and 14.77 g when extraction was performed at 8 and 5 h, respectively. At the end of extraction, n-hexane was evaporated under vacuum in a rotary evaporator (Heidolph Laborota 4000) at 313 K. The extraction yield was estimated relative to the mass of extracted oil (Eq. 2).

Soxhlet extraction yield (kg

/ kg) = mass of extracted oil (kg) biomass introduced in the Soxhlet apparatus (kg)

(2)

Tocopherol analysis

Tocopherol analysis was carried out using an Agilent 1290 Infinity HPLC system equipped with a Quaternary Pump, an automatic liquid sample and a fluorimetric detector (FLD 1260). The detection was set at 295 nm for excitation wavelength and at 330 nm for emission wavelength. The separation column was a LiChrosorb® SI60 column (250 mm × 4.6 mm i.d., 5 μm, Merck KGaA Darmstadt, Germany). Elution was performed with HPLC grade solvents n-hexane/isopropanol (99/1, v/v) in isocratic mode at a flow rate of 1 mL/min, during 20 min. Column compartment was set at 25 • C. Oil samples were dissolved in 1 mL of mobile phase before injection (1 μL). The identification of tocopherol isomers was confirmed by co-injection of a sample with authentic standards α-, β-, γ-and δ-tocopherols (Sigma Aldrich) then by comparison of retention time. Quantification of the 4 tocopherols was achieved according to the external standard method.

Scanning electron microscopy (SEM)

Grinded and sieved unroasted argan kernels were observed with a scanning electron microscopy (Hitachi TM3000 Tabletop microscope) before and after extraction experiments. The samples were deposited on an adhesive pastille and metallized with a thin layer of Au-Pd to allow a better visualization. The metallization time did not exceed 30 s, the visualizations were done at 15 kV.

Modelling

SC-CO 2 extraction curves

The extraction curves were modelled using Sovová's BIC mathematical model [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] 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]. This model considers the structure of the biomass and accounts for the sudden reduction in extraction rate after the first extraction period that is observed during SC-CO 2 extractions from samples. 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. 2).

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 reported in this study exhibits a first part consisting in two straight sections. The extraction type is then B or C. For type C, the second straight line starts very early, at a relative amount of the passed solvent q = q 1 not far from 1. In the results reported in this study, the second straight line starts at q = q 1 >> 1 for all extraction curves indicating that extraction of type B is the most suitable extraction type. The choice of model equations depends on the flow pattern in the extraction autoclave.

In order to optimize the contact between the argan biomass and CO 2 , it is required to have a CO 2 plug flow in the extraction vessel. A CO 2 plug flow means that the CO 2 velocity is uniform throughout the extractor section without any axial dispersion. These flow conditions can be checked using the pore Reynolds number (Re p ) or the modified pore Reynolds number (Re' p ) [START_REF] Mouahid | Supercritical CO2 extraction of neutral lipids from microalgae: experiments and modelling[END_REF][START_REF] Charpentier | Éléments de mécanique des fluides -Application aux milieux poreux[END_REF] in Eqs. 3456.

Re p = ρ CO2 U p CO2 d p μ CO2 (3)
and

Re' p = ρ CO2 V (1 -ε)a g μ CO2 (4) with U p CO2 = V ε τ (5)
and

a g = 6 d g (6)
To avoid axial dispersion, the CO 2 flow regime has to be a linear laminar. The threshold between a linear laminar regime to a transitory regime is 6 for the pore Reynolds number and 1 for the modified pore Reynolds number [START_REF] Charpentier | Éléments de mécanique des fluides -Application aux milieux poreux[END_REF]. The threshold for both pore Reynolds numbers between the transitory regime and a non-linear laminar regime for which axial dispersion may occur is 75.

The tortuosity τ has been considered equal to π/2, corresponding to a CO 2 flow around spherical particles. Under the operating conditions studied in this work, the Re p lies between 3 and 13, while Re' p ranges from 1 to 2. Hence, it can be considered that there is no axial dispersion. The CO 2 flow corresponds to a linear laminar regime or to a transitory regime depending on the operating conditions.

The bed void fraction of argan kernels ε was estimated by immersing a known amount of biomass powder residue in a test tube with ethanol.

The mass of introduced ethanol led to the value of bed void fraction of ε = 0.63 which is similar to the one reported by Taribak et al. [START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF] for a close granulometry. Helium pycnometer (Quantachrome Instruments, Stereopycnometer) was used to measure the biomass solid density, six measurements were performed. The mean argan kernel density was measured at 1228 kg/m 3 .

Equations for plug flow configuration were chosen. In type B extraction, the first part of the extraction curve is composed of two straight lines (Fig. 2) given by Eqs. 8-10. The first straight line (Eq. 8) is controlled by solute solubility in SC-CO 2 . The second straight line (Eq. 10) indicates that the solute concentration in the biomass is considerably reduced and the equilibrium is controlled by solute-matrix interactions. This implies that the solute concentration is much lower than its solubility. The transition between the two straight lines occurs at the transition concentration x t : the solid-phase concentration became lower than "x t " and all the solute interacted with the matrix. Hence, the transfer 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. 11, is controlled by solute diffusion from intact cells to broken cells.

• First part of the extraction curve e = qy s for 0 ≤ q ≤ q 1 [START_REF] Drissi | Evidence of hypolipemiant and antioxidant properties of argan oil derived from the argan tree (Argania spinosa)*1[END_REF] with e, the extraction yield (kg oil /kg insoluble biomass )

q 1 = r (x u -x t ) -γKx t y s -Kx t ( 9
)
e = q 1 y s + (qq 1 ) Kx t for q 1 ≤ q ≤ qc (10)

• Second part of the extraction curve

e = x u [1 -C 1 exp( -C 2 q)]for q > qc (11)
A straight line of slope y s , which represents the solubility of the Fig. 2. Type of extraction in Sovová's BIC model.

extracted oil in SC-CO 2 is to the first part of the extraction curve (Eq. 8).

The values of q c and q 1 were determined by considering that:

-q c is the value of q at the crossing point with the estimate for the second part of the extraction curve and -q 1 is the value of q at the crossing point with the first linear part and the second straight part considering the expression of q 1 in Eq. 9.

The second part of the extraction curve (q > q c ) is described 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. 12 to 17:

r = 1 -C 1 exp( -C 2 q c ) (12)
k s a s = ( 1 -r )( 1 -ε ) QC 2 N m [1 -((1 -r)C 2 /K)] for xt > 0 (13)
With:

e = E N m (14) q = Qt N m ( 15
)
N m = (1 -C u )N (16
)

C u = x u 1 + x u ( 17
)
Where "E" is the amount of extract (kg), " 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 of least squares between the experimental and calculated values of "e". The absolute average relative deviation (AARD) given in Eq. 18, was used to evaluate the efficiency of the model.

AARD ( % ) = 100 n ∑ ⃒ ⃒ ⃒ ⃒ Experimentalyield -Calculatedyield Experimentalyield ⃒ ⃒ ⃒ ⃒ (18)
In this work, the modelled extraction curves were expressed as the variation of the yield (Eq. 1) as a function of the CO 2 /biomass mass ratio.

Argan oil solubility in SC-CO 2

The solubility of argan oil in SC-CO 2 was calculated by considering the slope of the first linear part of the extraction curve (Eq. 8). The experimental data were modelled by the Chrastil model given in Eq. 19. 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.

ln(y

s ) = k ln ρ CO 2 + a T + b ( 19
)
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 calculated by minimizing the sum of least squares between the experimental and calculated values of y s .

Results and discussions

Soxhlet extraction

The yields of argan oil extracted from unroasted kernels by n-hexane Soxhlet were 0.57 and 0.59 kg oil /kg biomass after a period of 5 and 8 h, respectively. These results are in good agreement with the extraction yields reported in the literature: from 0.52 and 0.60 kg oil /kg biomass [START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF][START_REF] Atifi | Fruits Maturity Effect on the Argan Oil Amount, Quality and Chemical Composition[END_REF][START_REF] Haloui | Effects of Extraction Methods on Chemical Composition and Oxidative Stability of Argan Oil[END_REF][START_REF] Kouidri | The chemical composition of argan oil[END_REF][START_REF] Harhar | Effect of argan kernel storage conditions on argan oil quality[END_REF] depending on the harvest location and storage conditions [START_REF] Atifi | Fruits Maturity Effect on the Argan Oil Amount, Quality and Chemical Composition[END_REF][START_REF] Harhar | Effect of argan kernel storage conditions on argan oil quality[END_REF][START_REF] Harhar | Effect of harvest date of Argania spinosa fruits on Argan oil quality[END_REF]. Furthermore, an extraction time of 5 h seems appropriate for n-hexane Soxhlet extraction.

SC-CO 2 extraction kinetics 4.2.1. Repeatability test on unroasted kernels

A repeatability test (Fig. 3) was performed on two sets of measurements at 300 bar and 333 K prior to extraction experiments. The average deviation between the two sets of experiments is about 4.6 % which is satisfactory.

Effects of pressure and temperature on unroasted kernels

The experimental and modelled SC-CO 2 extraction curves are presented in Fig. 4. The effects of pressure are shown in Fig. 4(a)-(c) and the effects of temperature are shown in Fig. 4(d)-(f). One of the major results was observed above 200 bar. At extraction time ranging between 4 and 10 h (corresponding to a CO 2 / biomass mass ratio of 86 and 236, respectively), it was possible to reach an experimental yield of 0.62 kg oil /kg biomass for all extraction experiments which is very close to the highest reachable extraction yield according to n-hexane Soxhlet extraction (0.59 kg oil / kg biomass for 8 h). The residue is dry and discoloured suggesting that almost all neutral lipids were extracted, a similar behaviour was reported for Jatropha curcas oil extraction [START_REF] Mouahid | Supercritical CO 2 extraction of oil from Jatropha curcas: an experimental and modelling study[END_REF].

According to the extraction kinetics reported in Fig. 4, the highest extraction yield reported by Taribak et al. [START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF] (0.48 kg oil / kg biomass at 400 bar and 318 K) should be considered as the extraction yield for a CO 2 /biomass mass ratio of 240 kg/kg at their experimental extraction condition (CO 2 flow rate of 1.2 kg/h, a mass sample of 15 g, d p =800 μm). At 200 bar, regardless of the temperature, the SC-CO 2 extraction curves exhibit very slow extraction kinetics. For a CO 2 /biomass mass ratio ranging between 84 and 113 kg/kg (corresponding to an extraction time ranging between 4 and 5 h), the experimental data exhibits only the two first linear parts of type B extraction curve (Fig. 4(d)).

As the highest extraction yield (0.63 kg oil /kg biomass ) was systematically reached at pressures above 200 bar, the assumption that a similar tendency may be obtained at 200 bar was made. A similar behaviour was reported on the SC-CO 2 oil extraction from Jatropha curcas kernels at 200 bar [START_REF] Mouahid | Supercritical CO 2 extraction of oil from Jatropha curcas: an experimental and modelling study[END_REF]. A linear extension of the second part of the extraction curves was considered to estimate the end of the second extraction period and the beginning of the third extraction period. The BIC model was then used as a predictive tool to obtain a possible shape the overall extraction curves at 200 bar and an order of magnitude of the total extraction times. The predictive curves were given in dotted lines in Fig. 4, the calculated total extraction times were ranging from 17 to 44 h.

At a set temperature, increasing the pressure from 200 to 400 bar leads to an enhancement of the extraction kinetics (Fig. 4(a)-(c)). At 313 K some differences were found: increasing the pressure from 300 to 400 bar did not lead to a significant enhancement of the extraction kinetics. Furthermore, at 400 bar the second part of the extraction curve exhibits stronger solute-matrix interaction compared to the extraction curve at 300 bar due to a lower value of partition coefficient K (Table 1). The highest extraction kinetics were obtained at the highest studied pressure and temperature: 400 bar and 333 K.

Modelling

The model parameters are reported in Table 1. The AARD ranges between 2.72 and 9.53 % suggesting the extraction of type B from the BIC model is well suited for describing the SC-CO 2 extraction curves from argan kernels. It denotes the presence of solute-matrix interactions when oil is extracted by SC-CO 2 from unroasted argan kernels. Applying Sovová's mathematical model led to an accurate determination of the highest achievable yield of C u = 0.63 kg oil / kg biomass .

Regardless of the extraction conditions, the calculated transition concentrations x t and grinding efficiency parameter r remained relatively constant around an average value of 1.633 kg oil / kg insoluble solid and 0.93, respectively. The calculated values of r imply a high volumetric fraction of broken cells in the particles suggesting that the grinding pre-treatment was efficient.

Operating conditions at 333 K, 300 and 400 bar seem to be the most interesting ones from kinetic point of view as they allow a longer extraction period related to solubility (q 1 ) associated to high solubility of oil in SC-CO 2 (y s ), a short solute-matrix interaction period (q c ) and an enhanced transfer of oil in SC-CO 2 (K). Indeed, by considering the association effect of all parameters (Table 1), it was found a relatively long solubility period (relative high value of q 1 ), a short solute-matrix interaction period (low value of q c ), high values of solubility and partition coefficients.

SEM images were performed on unroasted argan kernel samples before and after extraction (Fig. 5). After both SC-CO 2 and n-hexane Soxhlet extraction (Fig. 5(b) and(c)), the surface aspects were very similar. The residues exhibit a porosity confirming a high surface area favouring solute matrix interactions and the use of type B in the BIC model.

Solubility of argan oil from unroasted kernels in SC-CO 2

Chrastil equation was chosen to model the experimental data of argan oil solubility y s in SC-CO 2 (Eq. 20). This equation is relatively simple and provides a very good fit between calculated and experimental data as the AARD is about 1.

The evolution of argan oil solubility according to SC-CO 2 density (ln (y s ) = f(ln(ρCO 2 )) is given in Fig. 6. Above 200 bar, increasing both pressure and temperature leads to an increase of argan oil solubility in SC-CO 2 . The highest solubility, y s = 10.6 g oil /kg solvent was found at 400 bar and 333 K which correspond to the faster extraction kinetics' experimental conditions.

Predictive correlations were developed by Del Valle et al. and Sovová et al. [START_REF] Del Valle | An improved equation for predicting the solubility of vegetable oils in supercritical carbon dioxide[END_REF][START_REF] Sovova | Solubility of two vegetable oils in supercritical CO 2[END_REF][START_REF] Del Valle | A refined equation for predicting the solubility of vegetable oils in high-pressure CO2[END_REF] for the determination of vegetable oil solubility in SC-CO 2 . These correlations allow the solubility assessment of several vegetables' oil solubility in SC-CO 2 and hence can be used for predictive studies. It is interesting to check their ability to assess the solubility of argan oil in SC-CO 2 . The calculated solubilities were compared to the experimental argan oil solubility in SC-CO 2 (Table 2).

The deviations between experimental and calculated values ranges between 0.4 and 59.8 %. The highest deviations (57.3 up to 59.8 %) were found at 400 bar and 313 K. These correlations gave an estimation with a correct order of magnitude when pressures are lower than 400 bar. The deviations between the experimental values and the calculated ones be explained by several factors: the solubility was calculated considering the straight line of the first part of the extraction curve considering one experimental point, which can lead to some approximation, the extracted mixture from the other vegetable oils may have a different composition according the operating conditions of extraction finally, the correlation proposed by Del Valle 2012 [START_REF] Del Valle | A refined equation for predicting the solubility of vegetable oils in high-pressure CO2[END_REF] can predict solubility of vegetable oils within +/-40 %. Nevertheless, it is recommended to use Chrastil model (Eq. 20) for accurate determinations of argan oil solubility in SC-CO 2 from 200 to 400 bar.

Effects of particle size and roasting on extraction kinetics

The effect of particle size distribution on extraction kinetics was investigated on unroasted kernels at 400 bar and 333 K at a CO 2 flow rate of 0.14 kg/h corresponding to the faster extraction kinetics. The extraction kinetics were reported in Fig. 7(a). Regardless of the granulometry, the slopes of the first part of the extraction curves have very close values (about 10 g oil / kg CO2 ) confirming that it is linked to the solubility of argan oil in SC-CO 2 and that argan kernels contain a high amount of free solute on its surface.

Surprisingly, the extraction kinetics at d p =400 μm were not found to be the highest ones. The highest and lowest extraction kinetics were obtained for d p =750 μm and d p > 1000 μm respectively (Fig. 7(a)). The adjusted model parameters are given in Table 3. As expected, the fraction of broken cell r was lower when the mean particle diameter of the biomass was higher than 1000 μm (0.8 and about 0.93 for d p > 1000 μm and 400 < d p < 750 μm, respectively). Usually, the transition concentration x t was slightly lower (average of 1.56 kg oil /kg insoluble solid ) than the one obtained with a mean particle size diameter of 750 μm (1.597 kg oil /kg insoluble solid ). The partition coefficient K was of the same order of magnitude than the one obtained with d p =750 μm for pressures higher than 200 bar (average of 2 × 10 3 ).

When the extraction was performed on a biomass with a mean particle size of 400 μm, the parameter k s a s has a value of the same order of magnitude than the one obtained when extraction was performed at 200 bar (on the average of 0.05 × 10 -5 s -1 ). This parameter is the product of the solid-phase mass transfer coefficient (k s ) and the specific area between the regions of intact and broken cells (a s ). Considering that the parameter a s for d p =400 μm should be higher than the one for d p =750 μm, the parameter k s should also be higher. The low value obtained is probably due to the low extraction kinetics observed indicating that channelling of SC-CO 2 in the extraction autoclave may probably occur due to sticky kernels caused by the high amount of oil on the biomass surface (oil which should have been expelled from cells after grinding).

It is then advised to perform SC-CO 2 extraction at particle size diameter close to 750 μm.

The effect of roasting on extraction kinetics at 400 bar and 333 K was reported on Fig. 7(b). It shows that the extraction kinetics are lower when SC-CO 2 extraction is performed on roasted kernels probably due to a different oil composition due to roasting. The highest extraction yield achieved was the same the one reported in section 4.2.1 (0.63 kg oil / kg biomass ). It was achieved after an extraction duration of about 5.1 h. The solubility of the oil extracted from roasted samples in SC-CO 2 was found to be 8.4 g oil /kg CO2 which is about 21 % lower than the solubility reported from unroasted kernels. The extraction curve is also of type B and exhibits a short extraction period related to solubility of oil in SC-CO 2 and a long solute-matrix extraction period. For all extraction experiments, the extracts were composed in average of 6.7 % of α tocopherol, 87.6 % of γ tocopherol and 5.7 % of δ tocopherol. A similar ratio was found in the literature when conventional extraction methods were applied [START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF][START_REF] Haloui | Effects of Extraction Methods on Chemical Composition and Oxidative Stability of Argan Oil[END_REF][START_REF] Matthäus | Effect of processing on the quality of edible argan oil[END_REF][START_REF] Gharby | Oxidative stability of edible argan oil: a two-year study[END_REF]. For all extraction experiments, the amount of total tocopherols is at the same order of magnitude than the one reported by Taribak et al. [START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF]. Nevertheless, the values reported in this study are slightly lower probably due to SC-CO 2 extraction conditions and harvest location [START_REF] Atifi | Fruits Maturity Effect on the Argan Oil Amount, Quality and Chemical Composition[END_REF][START_REF] Harhar | Effect of harvest date of Argania spinosa fruits on Argan oil quality[END_REF]. The oil extracted from roasted kernels have a lower concentration of tocopherols than the commercial one, the order of magnitude is however similar. This lower concentration may be not only due to harvest location but also to the differences in roasting methods and conditions [START_REF] Demnati | Effect of roasting temperature and time on the chemical composition and oxidative stability of argan (Argania spinosa L.) oils[END_REF][START_REF] Demnati | Optimum roasting conditions of argan kernels (Argania spinosa L.) for the production of high-quality edible argan oil[END_REF]. The highest concentration of tocopherols in the extracts were obtained at 200 bar due to a low amount of extracted oil E compared to the ones obtained at higher pressure. Indeed, at 200 bar the extraction could not have been performed until its end due to very slow extraction kinetics contrary to the extracts obtained at pressure higher than 200 bar (Fig. 4). This interesting result means that tocopherols were mainly extracted at the beginning of the extraction period.

When pressure was higher than 200 bar, the concentration of tocopherols in the extracts was found to be close than the ones obtained after Soxhlet extraction. The closest concentrations were found for the extracts obtained at 300 bar and 313 K. The concentrations of total tocopherols were found to range between 389.7 and 555.4 mg/kg which is in the same order of magnitude than the results reported in the literature when conventional extraction methods were applied [START_REF] Taribak | Quality of cosmetic argan oil extracted by supercritical fluid extraction from Argania spinosa L[END_REF][START_REF] Haloui | Effects of Extraction Methods on Chemical Composition and Oxidative Stability of Argan Oil[END_REF][START_REF] Matthäus | Effect of processing on the quality of edible argan oil[END_REF][START_REF] Gharby | Oxidative stability of edible argan oil: a two-year study[END_REF], as well. Nevertheless, the concentrations of tocopherol reported by Haloui et al. [START_REF] Haloui | Effects of Extraction Methods on Chemical Composition and Oxidative Stability of Argan Oil[END_REF] were higher probably due to a different harvest location or period [START_REF] Atifi | Fruits Maturity Effect on the Argan Oil Amount, Quality and Chemical Composition[END_REF][START_REF] Harhar | Effect of harvest date of Argania spinosa fruits on Argan oil quality[END_REF]. The highest concentration of γ-tocopherol was obtained at 300 bar and 333 K.

Conclusions

The extraction of argan oil by SC-CO 2 is very promising. The extraction kinetics established in this study show that regardless of the pressure and the temperature, the maximal extraction yield (0.63 kg oil / kg biomass ) could be reached. Extraction conditions of 200 bar exhibit very slow extraction kinetics (the maximal extraction yield can be reached after an estimated time between 17 and 44 h depending on the temperature) and a retrograde solubility zone. The best extraction kinetics were found at 333 K at 300 and 400 bar, the highest solubility of argan oil in SC-CO 2 was obtained at 400 bar and 333 K. A mean particle diameter of 750 μm leads to the best extraction kinetics, a lower mean particle diameter leads to channelling due to a very fatty biomass.

The application of Sovová's mathematical model gave access to mass transfer coefficients which are very useful for scale-up studies. The model shows that solute-matrix interactions occur during the SC-CO 2 extraction probably due to oil desorption from porous biomass (confirmed by SEM analysis). The model was also applied to predict the complete shape of the extraction curves at 200 bar.

Tocopherols were mainly extracted during the first period of SC-CO 2 extraction. The ratio and the composition of tocopherols were close and of the same order of magnitude than the one obtained after conventional extraction methods. When pressure was higher than 200 bar, the extraction yield was higher than those obtained by mechanical pressing or traditional extraction and the extraction yield was at the same order of magnitude than organic solvent extraction. Nevertheless, for the fastest extraction kinetics conditions (400 bar and 333 K) the extraction time for reaching the maximum yield was about 4 h, two times lower than Soxhlet extraction, and no separation step between oil and solvent is needed (contrary to Soxhlet or organic solvent extractions) as CO 2 become gaseous at ambient condition.

Considering all the data reported in this study, SC-CO 2 extraction performed at 400 bar and 333 K is the best compromise between yield, extraction duration and concentration of total tocopherols.

Fig. 1 .

 1 Fig. 1. Process diagram of the extraction setup: (1) CO 2 tank, (2) cooler, (3) CO 2 high pressure liquid pump, (4) pressure gauge, (5) extraction apparatus heater, (6) extraction vessel, (7) glass vessel, (8) flowmeter, (9) ethanol tank, (10) Gilson high pressure solvent pump.

Fig. 3 .

 3 Fig. 3. Reproducibility test performed on unroasted argan kernels (d p =750 μm) at 300 bar and 333 K.

  A retrograde solubility behaviour was observed at 200 bar (Fig. 4 (d)), a similar observation was reported by Taribak et al. Above 200 bar, increasing the temperature leads to faster extraction kinetics. Nevertheless, at 323 and 333 K at 300 bar, the extraction kinetics were found to be very close (Fig. 4(e)). Considering these results, pressure of 200 bar should be avoided.

Fig. 4 .

 4 Fig. 4. Experimental and modelled SC-CO 2 extraction curves from unroasted argan kernels (d p =750 μm). Effects of pressure (a) 313 K, (b) 323 K, (c) 333 K; effects of temperature (d) 200 bar, (e) 300 bar, (f) 400 bar.

  3 %. ln(y s ) = 7.715 ln ρCO 2 -5716.71 T -39.72

Fig. 5 .

 5 Fig. 5. SEM images of unroasted argan kernels: (a) before extraction, (b) after SC-CO 2 extraction at pressures above 200 bar, (c) after 8 h n-hexaxe Soxhlet extraction.

Fig. 6 .

 6 Fig. 6. Experimental and modelled solubility of argan oil from unroasted kernels in SC-CO 2 from 200 to 400 bar and 313 to 333 K.

  7 %, and n-hexane (VWR, HPLC grade, France) was used to perform Soxhlet extraction.

	2.2. Extraction methods
	Nomenclature	q	relative amount of the passed solvent (kg CO2 /kg insoluble
	a g 2.2.1. SC-CO 2 extraction specific surface area of the microalgae powder (m -1 ) SC-CO 2 extraction experiments were performed on a laboratory scale	q'	biomass ) specific flow rate (kg solvent /kg solid /s)
	a s extractor supplied by Separex (Champigneulles, France). The process specific area between the regions of intact and broken cells (m -1 ) flow diagram of the facility is given in Fig.	Q r	solvent flow rate (kg/s) grinding efficiency or fraction of broken cells
	C u D 21	solute content in the untreated solid (kg oil /kg biomass ) Diffusion coefficient of oil (2) to CO 2 (1) (m 2 /s)	T t	temperature (K) extraction time (s)
	d p e	mean particle diameter (m) extraction yield of mathematical model (kg oil /kg insoluble	t f V	extraction time to achieve the SC-CO 2 extraction (h) CO 2 velocity in empty autoclave (m/s)
	E k f k s	biomass ) amount extracted (kg) fluid-phase mass transfer coefficient (s -1 ) solid-phase mass transfer coefficient (m/s)	x t x u y s	transition concentration (kg oil /kg insoluble solid ) concentration in the untreated solid (kg oil /kg insoluble biomass ) solute solubility (kg oil /kg CO2 )
	K n N N m P	partition coefficient number of experimental points solid charge in the extractor (kg) charge of insoluble solid (kg) pressure (bar)	Greek letters γ solvent to matrix ratio in the bed (kg solvent /kg insoluble solid ) ε bed void fraction τ Tortuosity

Table 1

 1 BIC model parameters for d p =750 μm from unroasted kernels.

	P (bar)	T (K)	N (g)	y s (g oil / kg CO2 )	C 1	C 2	K s a s (s -1 ) × 10 5	r	K × 10 3	x t (kg oil / kg insoluble solid )	q 1 (kg solvent / kg insoluble solid )	q c (kg solvent / kg insoluble solid )	γ (kg CO2 / kg insoluble solid )	AARD (%)
		313	6.44	2.250	-	-	0.030	0.93	0.940	1.654	63.497	1015.025	1.144	-
	200	323	6.479	2.229	-	-	0.020	0.93	0.794	1.670	33.088	1195.253	1.072	-
		333	6.221	2.114	-	-	0.010	0.93	0.457	1.662	27.386	2070.917	0.995	-
		313	6.536	6.114	7.915	0.011	0.894	0.92	2.289	1.640	23.183	379.135	0.730	9.19
	300	323	6.152	6.857	2.181	0.009	0.036	0.88	2.821	1.641	22.198	304.364	1.203	5.42
		333	6.902	7.086	6.896	0.011	0.465	0.95	2.222	1.586	29.910	414.493	1.147	9.53
		313	6.538	5.114	518.879	0.019	10.058	0.91	1.999	1.661	18.751	442.487	1.328	3.04
	400	323	6.503	8.114	130.601	0.021	1.944	0.93	2.591	1.632	15.580	353.554	1.282	3.43
		333	6.652	10.600	4.962	0.019	0.906	0.94	4.433	1.597	25.649	205.841	1.235	6.20

Table 3

 3 BIC model parameters for unroasted samples (d p =400 μm and d p > 1000 μm) and roasted samples (dp =750 μm) at 400 bar and 333 K.

	Roasting	d p (μm)	N (g)	C 1	C 2	K s a s (s -1 ) × 10 5	r	K × 10 3	x t (kg oil / kg insoluble solid )	q 1 (kg solvent / kg insoluble solid)	q c (kg solvent / kg insoluble solid)	γ (kg CO2 / kg insoluble solid )	AARD (%)
	no	400 >1000	5.369 7.721	0.095 0.952	0.001 0.004	0.051 0.696	0.93 0.80	2.721 2.352	1.59 1.54	18.385 20.259	344.302 325.143	1.235 1.235	4.24 9.09
	yes	750	5.965	75.418	0.026	2.115	0.93	3.5	1.64	19.343	254.933	1.235	3.60

Table 4

 4 Tocopherols concentration in the extracted oils.

	P (bar)	T (K)	t (min)	α tocopherol (mg/kg extract)	γ tocopherol (mg/kg extract)	δ tocopherol (mg/kg extract)	Total tocopherol (mg/kg extract)
		313	231	55.9	575.1	52.7	683.6
	200	323	246	80.6	941.9	68.0	1090.5
		333	316	119.3	1471.3	97.9	1688.6
		313	472	33.9	454.9	27.1	515.9
	300	323	610	24.3	346.2	19.2	389.7
		333	524	33.3	490.1	31.9	555.4
		313	471	28.9	394.4	25.2	448.5
	400	323	405.8	27.7	399.8	23.0	450.5
		333	336	28.0	383.6	21.9	433.5
	Soxhlet		483	34.0	446.6	24.4	505.0
	Roasted		305	27.5	366.2	18.9	412.6
	Argapur*		-	35.8	484.7	32.8	553.2

Journal of CO2 Utilization 46 (2021) 101458

* commercial food oil.

Acknowledgments

The authors gratefully acknowledge the support of Giovanna Maria Belogi, Mohammed Mouahid and Moroccan supplier "Chez Brahim, vente de produits naturels Miel et Argan, Av. Mohamed Zerktouni N • 41, Essaouira, Morocco" (Agricultural cooperative: Khiorate Biladina).

Tocopherols concentrations in the extracted oils

Tocopherols concentration in the extracts is reported in Table 4. The composition of the oil extracted from the roasted sample was compared to the composition of a Moroccan commercial food oil named "Argapur"

Author contribution

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. These authors contributed equally.

CRediT authorship contribution statement

Declaration of Competing Interest

The authors report no declarations of interest.