Kamaldeep Sharma

Saqib Thomas Helmer Pedersen

Sohail Toor

Yves Schuurman

Lasse Aistrup Rosendahl

Detailed Investigation of Compatibility of Hydrothermal Liquefaction Derived Biocrude Oil with Fossil Fuel for Corefining to Drop-in Biofuels through Structural and Compositional Analysis

Keywords: Hydrothermal liquefaction, Biocrude, Compatibility, Fossil fuel, Corefining, Drop-in biofuels

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

INTRODUCTION

There is considerable interest in developing drop-in biofuels as alternative liquid fuels for the renewable replacement of petroleum, particularly in aviation and heavy transport sectors where there is no real substitute to sustainably produced biofuels. [START_REF] Marsh | Biofuels: aviation alternative?[END_REF] Although the technology used for the production of t r a n s p o r tf u e lf r o mc r u d eo i li sw e l le s t a b l i s h e d ,t h e environmental (e.g., CO 2 and active sulfur species) and sustainability issues of these fuels have prompted growing interest in the development of biofuels from biorenewable feedstocks. [START_REF] Gollakota | A review on hydrothermal liquefaction of biomass[END_REF] Alternative biofuels obtained from biomass feedstock are strong candidates to reduce the environmental impact of aviation exerted during the fuel burning by providing a solution to the current energy and climate problems. [START_REF] Olcay | Techno-economic and environmental evaluation of producing chemicals and drop-in aviation biofuels via aqueous phase processing[END_REF] Hydrothermal liquefaction (HTL) is considered a very promising technology for the conversion of wet biomass into s u s t a i n a b l eb i o c r u d eo i l sw i t hl o wo x y g e nc o n t e n t sa s alternative feedstocks for the production of liquid fuels. [START_REF] Dimitriadis | Hydrothermal liquefaction of various biomass and waste feedstocks for biocrude production: A state of the art review[END_REF] As a wet processing technology, HTL is generally carried out in aqueous media of at least 50%-60% water, around 250-450 °C temperature, and pressures between 10 and 30 MPa, making it very suitable for most natural biomasses and organic residues. [START_REF] Castello | Continuous Hydrothermal Liquefaction of Biomass: A Critical Review[END_REF] Furthermore, the HTL process offers high conversion rates, flexibility with regard to different feedstocks, and catalytic effect of the reaction medium. [START_REF] Castello | Continuous Hydrothermal Liquefaction of Biomass: A Critical Review[END_REF] Comparatively, HTL biocrudes are more stable fuels with high heating value, low oxygen contents, gases, and volatile matters than pyrolysis oils. [START_REF] Baloch | Recent advances in production and upgrading of bio-oil from biomass: A critical overview[END_REF] Although HTL biocrudes with improved fuel properties produced directly from wet biomass feedstocks are attractive from both a fuel market and infrastructure perspective, these biocrudes are not fully compatible with the overall petroleum fuel refining or the existing liquid transportation fuel processing equipment because of high viscosity, large fraction of heavy residue, and heteroatom contents. [START_REF] Chen | Renewable diesel blendstocks produced by hydrothermal liquefaction of wet biowaste[END_REF][START_REF] Bjelic | Detailed Investigation into the Asphaltene Fraction of Hydrothermal Liquefaction Derived Bio-Crude and Hydrotreated Bio-Crudes[END_REF] Therefore, processing of HTL biocrudes in order to improve their chemical and physical properties is a prerequisite to produce drop-in biofuels fully compatible with existing fossil streams for coprocessing in the conventional petroleum refinery. Previously, the upgrading of HTL biocrudes to drop-in biofuels has been extensively studied using the hydrotreating or catalytic upgrading techniques. [START_REF] Cole | From macroalgae to liquid fuel via waste-water remediation, hydrothermal upgrading, carbon dioxide hydrogenation and hydrotreating[END_REF][START_REF] Haghighat | Hydrotreating of Hydrofactionb i o c r u d ei nt h ep r e s e n c eo f presulfided commercial catalysts[END_REF][START_REF] Castello | Catalytic upgrading of hydrothermal liquefaction biocrudes: Different challenges for different feedstocks[END_REF] Compared with the above techniques, the direct use of HTL biocrudes accomplished by blending with fossil streams at a low concentration is potentially an economically feasible drop-in point. [START_REF] Palardy | Fatty Amide Determination in Neutral Molecular Fractions of Green Crude Hydrothermal Liquefaction Oils From Algal Biomass[END_REF] Alternatively, as compared to conventional fuels, the finished fuel prepared by blending HTL bio-oil extract with diesel fuel significantly reduces particulate number and particulate matter without affecting the engine performance. [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] A primary requirement for the conversion of biocrudes to a readily usable biofuel blend is the production of material blends with fuel characteristics comparable to the existing gasoline and diesel standards (ASTM) so that conventional petroleum infrastructures can be implemented. Therefore, methods are required that can efficiently predict the compatibility of biocrude oils with the fossil fuels on the basis of their solubility characteristics for the economic conversion to dropin transportation fuels. In this aspect, a deep understanding of the solubility characteristics and molecular components of HTL biocrude oils is required to ensure the solubility of individual components and the mutual miscibility of constituents in material blends with fossil refinery streams. Solubility parameters as a basic physicochemical property have played a significant role in defining the solubility characteristics and the screening of solvents or materials compatible for a substance. [START_REF] Howell | A Functional Approach to Solubility Parameter Computations[END_REF][START_REF] Romhańyi | Correlations among Miscibility, Structure and Properties in Thermoplastic Polymer/ Lignin Blends[END_REF][START_REF] Barton | Solubility Parameters[END_REF] However, there are only a few reports in the literature regarding the use of solubility parameters for the prediction of solubility of crude oils and bitumen in different solvents. [START_REF] Redelius | Solubility parameters and bitumen[END_REF][START_REF] Wang | Solubility Parameters of Bitumen-Derived Narrow Vacuum Resid Fractions[END_REF] The Hansen solubility parameter (HSP) approach has proven itself to be a valuable predictor of solubility based on solubility parameters of different materials such as polymers, [START_REF] Milliman | Experimental Determination of Hansen Solubility Parameters for Select POSS and Polymer Compounds as a Guide to POSS-Polymer Interaction Potentials[END_REF] adhesives, [START_REF] Barry | The identification and screening of lower toxicity solvents for contact adhesives[END_REF] organic compounds, [START_REF] Guenthner | Solubility Parameters for Octahedral Oligomeric Silsesquioxanes[END_REF] graphene derivatives, [START_REF] Salavagione | Identification of high performance solvents for the sustainable processing of graphene[END_REF] carbon nanotubes (CNTs), [START_REF] Bergin | Multicomponent Solubility Parameters for Single-Walled Carbon Nanotube-Solvent Mixtures[END_REF] medicinal compounds, [START_REF] Turpin | In Silico Screening for Solid Dispersions: The Trouble with Solubility Parameters and χFH[END_REF] asphaltenes, [START_REF] Morimoto | Determination of Hansen Solubility Parameters of Asphaltene Model Compounds[END_REF] ionic liquids, [START_REF] Agata | Determination of Hansen solubility parameters of ionic liquids using double-sphere type of Hansen solubility sphere method[END_REF] and organogels [START_REF] Raynal | Organogel formation rationalized by Hansen solubility parameters[END_REF] in different solvents. Yamamoto et al. [START_REF] Agata | Determination of Hansen solubility parameters of ionic liquids using double-sphere type of Hansen solubility sphere method[END_REF] used the Hansen double sphere method and calculated the HSPs of ionic liquids based on the Hansen solubility approach. The resulting HSPs were used to represent the domain structure and compatibility index of ionic liquids. These reports show that the solubility/ compatibility of different substances can be easily visualized from the Hansen sphere plot using their HSPs. Recently, we have investigated the solubility behavior of renewable HTL bioliquids and refinery streams using the solubility parameters. [START_REF] Pedersen | Understanding and predicting the solubility of bio-crude oils[END_REF] To the best of our knowledge, there is no report in the literature regarding the use of the Hansen double sphere approach for the prediction of compatibility of HTL biocrudes and their components with petroleum refinery streams or fuels. For the first time, the compatibility of HTL biocrude with fossil fuel has been investigated comprehensively by both theoretical predictions and experimental analysis to achieve a biofeed suitable for coprocessing in petroleum refineries. The aim of the present study is therefore to identify the common range of solubility parameters for the deep understanding of solubility characteristics of HTL biocrude and to establish a correlation between miscibility and molecular structure of biocrude to assess its compatibility with refinery streams. It is therefore essential to determine the most appropriate insertion points for HTL biocrude into the conventional petroleum infrastructure for coprocessing. Figure 1 reveals the insertion points for HTL biocrude at different stages to integrate into existing petroleum refineries and distribution infrastructure. The test liquid employed for the miscibility of HTL biocrude is straight-run gas oil (SRGO), a dominant precursor for diesel production, obtained by atmospheric distillation of natural crude oil. [START_REF] Đukanovic | Hydrotreating of straight-run gas oil blended with FCC naphtha and light cycle oil[END_REF] As previously reported, the coprocessing of bio-oil with SRGO leads to the production of an oil rich in diesel fractions. [START_REF] Sauvanaud | Co-processing of lignocellulosic biocrude with petroleum gas oils[END_REF] In the present manuscript, the HSPs of HTL biocrude from pinewood and SRGO were determined from the experimental data obtained on solubility studies in 38 different solvents, which were used to evaluate their extent of compatibility by plotting the Hansen double sphere plot (Figure 2a). Relative energy difference (RED) and R a parameters calculated from the two Hansen solubility spheres of biocrude and SRGO explain the interaction potential and difference in affinity tolerable for the complete mixing of HTL biocrude and SRGO. To amplify the miscibility of the biocrude-SRGO blend, the solvents that occupy a well-defined space with less distance from the junction of the biocrude-SRGO mixture in the Hansen space were selected, and a close agreement with the experimental data from miscibility studies was verified. Furthermore, the HTL biocrude was fractionated into light, heavy, and residual subfractions through the fractional distillation; the compatibility of these individual fractions with SRGO was also determined by both the Hansen double sphere approach and miscibility studies. The complete miscibility of the blends of light, heavy, and residual fractions with SRGO was also indicated from DSC curves and spot tests. The qualitative identification of individual chemical compounds present in all the samples was also achieved by elemental analysis (CHN/O), GC-MS, and GC × GC-MS techniques. We envisioned that the evaluation of interactions between the bio-oil components could provide additional information regarding the molecular structure and the determination of the properties of the blends. Therefore, the effect of the molecular structure of the biocrude, subfractions, and residue on the compatibility are estimated quantitatively by analyzing the contribution of aliphatic, aromatics, and oxygen containing functional groups for miscibility using [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectroscopy. Consequently, the correlations between component interactions and the miscibility as well as between structure and physicochemical properties are established. This study offers a straightforward and flexible approach for estimating the physicochemical properties of biocrudes and light, heavy, and residual subfractions based on the solubility characteristics to optimize their commercial value, and analysis of the solubility parameters may provide a better understanding of the molecular interactions that control miscibility.

RESULTS AND DISCUSSION

Solubility studies of HTL biocrude obtained from pinewood in SRGO were carried out experimentally in 38 different solvents according to the previously reported procedure. [START_REF] Redelius | Bitumen Solubility Model Using Hansen Solubility Parameter[END_REF] The data obtained from the solubility studies of biocrude and SRGO were fitted using the HSPiP software (Fit = 0.982 and 0.934). HSPs for the biocrudes and SRGO were calculated by plotting a 3D Hansen solubility single sphere plot based on the solubility data (Table 1). The resulting HSPs were used to predict the compatibility of HTL biocrude with SRGO via the Hansen double sphere solubility approach, which was verified with the experimental results of miscibility studies. Figure 2a shows the 3D Hansen double sphere plot for the biocrude-SRGO blend with the set of all 38 solvents.

The blue points are good solvents and lie inside the two solubility spheres, whereas the red points reside outside the spheres evaluated as bad solvents for the biocrude-SRGO blend. In the Hansen double sphere plot, the solubility sphere with high δ P value is the biocrude (more polar) as shown in Table 1, and the one with the low δ P value is SRGO (less polar). The yellow point between two spheres is the junction value "sweet spot" that defines the solvents most likely to interact with the blending mixture. Generally, the volume of the area of overlap between the two solubility spheres provides the actual information on the compatibility of two substances. [START_REF] Benjamin | Self-stratifying coatings for metallic substrates[END_REF] The larger the area of overlap between two spheres, the more the compatibility between them. The Hansen double sphere plot for the biocrude-SRGO blend shows weak overlap between the two spheres, which indicates the poor compatibility of HTL biocrude with SRGO (Figure 2a). Furthermore, the experimental solubility parameters such as RED and R a were also calculated for the biocrude-SRGO blend (eqs 2 and 3) which provide the relative energy difference between biocrude and the SRGO as well as the difference in their HSPs, respectively. The higher the value of these solubility parameters, the lower the compatibility. The results mentioned in Table 2 show the high RED and R a values of the biocrude-SRGO blend, which again confirm the poor compatibility of HTL biocrude with SRGO. The miscibility of HTL biocrude in SRGO was also checked by using the procedure as mentioned in the Experimental Section. For this, different proportions of biocrude (1-5 wt %) were mixed in SRGO (95-99 wt %) thoroughly using the vortex mixer for 15 min. The results showed that the HTL biocrude is immiscible in SRGO, which corroborates the theoretically predicted low values of compatibility. These studies show that the compatibility of HTL biocrude predicted from HSPs based on the solubility characteristics are most precise when comparing to those of solution-blended systems.

To amplify the compatibility of HTL biocrude in SRGO, we made a preliminary prediction using the Hansen double sphere approach to determine new solvents compatible with the biocrude-SRGO blend. Generally, solvents that lie within or close to the overlap (junction) of the two-solubility sphere aid the compatibility of the system. Consequently, the solvents occupy a well-defined region in solubility space, and those having a short solubility distance from the junction of the biocrude-SRGO blend were selected. Figure 3A shows a range of good solvents lying close to the junction of the biocrude-SRGO blend. The solvent affinity was also measured in a group of solvents by mixing them in different proportions with biocrude-SRGO blend using the vortex mixer (Table 3). After that, the blending mixture was filtered by vacuum filtration to determine the amount of immiscible residue present in the blend. The results of the miscibility studies displayed a miscibility of 62 and 65% of biocrude in SRGO in the presence of pyridine and cyclohexanone solvents, respectively (Table 3). Based on miscibility studies with pure solvents to enhance the compatibility, solvent mixtures with HSPs fitting with that of biocrude were determined and tested as dispersing agents for the biocrude-SRGO blend. Furthermore, the solvent mixtures such as pyridine-cyclohexanone and pyridine-2-heptanone were also employed to achieve the complete miscibility of HTL biocrude in SRGO (Table 3). The best solvent mixture was pyridine-2-heptanone, which displayed a maximum miscibility of 74%; however, 72% miscibility of biocrude was observed in the presence of the pyridine-cyclohexanone solvent mixture. Figure 3B shows the visual evaluation of miscibility of the biocrude-SRGO blend in the presence of the pyridine-cyclohexanone solvent mixture that demonstrates the affinity of this solvent mixture in significant improvement of the miscibility of biocrude in SRGO. These results are consistent with the theoretical predictions of the solvent affinity for the biocrude-SRGO blend made by using solubility parameters. Thus, the Hansen solubility approach does not only predict the solubility parameters of materials but also predicts the affinities of different solvents to improve their compatibilities in blends.

To get insight into the reason for incompatibility and role of structural components in miscibility, HTL biocrude was fractionated into subfractions from which extensive characterization experiments may impart further information on the contribution of different functional groups and molecular interactions to the compatibility. The fractional distillation of HTL biocrude was carried out in accordance to ASTM D2892 in a two liter 15:5 distillation column as mentioned in the literature. [START_REF] Hoffmann | Co-processing potential of HTL bio-crude at petroleum refineries -Part 1: Fractional distillation and characterization[END_REF] Prior to distillation, the biocrude was dehydrated at the atmospheric equivalent temperature (AET) of 130 °C through vacuum distillation in a stand-alone setup. To avoid thermal cracking of biocrude, the distillation procedure was divided into several steps according to the processing conditions. Initially, the distillation was performed at atmospheric pressure; hereafter, the distillation was continued under vacuum until an end point of approximately 370 °C AET. The distillates were divided into 8 liquid fractions and a distillation residue (Figure 4). The distillation residual fraction defines the bulk of the nonvolatile compounds having boiling points above ∼370 °C (AET). The vacuum distillation was performed by stepwise lowering the vacuum from 100, to 20, and finally to 0.75 Torr.

Depending on the solubility behavior, the distillate fractions were further divided into three main categories: light fractions which include fractions 1-3, obtained at atmospheric vacuum pressure, heavy fractions consisting of fractions 4-8, extracted at low vacuum pressures, and a residual fraction consisting of S2 in the Supporting Information. The total yields of light and heavy fractions distilled during the fractional distillation of biocrude were found to be 10.43 and 22.84 wt %, respectively, while the remaining heavy distillate end of 66.14 wt % was obtained as a residue. The specific requirements to a HTL biocrude for possible coprocessing with the fossil streams depends on the coprocessing conditions and configuration of the particular refinery. The HTL biocrude requires fractional cuts having short chain aliphatics and almost no oxygen contents for the acceptable SRGO blending stock. [START_REF] Deneyer | Direct upstream integration of biogasoline production into current light straight run naphtha petrorefinery processes[END_REF] Figure 5 shows the schematic illustration of the integration of HTL biocrude based on the composition into a conventional petroleum refinery for coprocessing with different fossil streams. Green lines have been used for the HTL biocrude or its components (light fractions, heavy fractions, and residue) whereas red and black lines are for the crude oil and its components. Dashed and solid green lines in Figure 5 represent the possible and actual pathways, respectively, through which HTL biocrude based on its composition and boiling ranges can be integrated into the existing refinery processes. Whereas solid red, dashed red, and dash black lines showed the existing hydrotreating processes in oil refinery for the production of different refinery streams. It was observed that the heavy fractions with low oxygenates and high aliphatic or aromatic contents resemble the SRGO structure in the conventional petroleum refinery. [START_REF] Deneyer | Direct upstream integration of biogasoline production into current light straight run naphtha petrorefinery processes[END_REF] We therefore suggest that the about 22.84 wt % of HTL biocrude (pinewood) is suitable for coprocessing with the SRGO in the petroleum refinery.

The HSPs of light, heavy, and residual fractions were also caculated according to the above-mentioned procedure with fitting values of 1.000, 0.971, and 0.934, respectively. By assigning HSPs of all samples to the Hansen double sphere approach, the predictions of their compatibilities with SRGO were made (Figure 2b-d). Furthermore, RED and R a parameters for all samples were also calculated from the solubility differences between two spheres in each case and compared to assign their relative order of miscibility. The partial overlap between the Hansen spheres of the light fraction-SRGO blend is indicative of a lower affinity of light fractions in SRGO (Figure 2c). Interestingly, the Hansen double sphere plot of the heavy fraction-SRGO blend shows the highest overlap between two spheres, which indicates the high compatibility of heavy fractions with SRGO (Figure 2b). However, the complete immiscibility of the residue in SRGO was predicted owing to the nonoverlap between their corresponding Hansen spheres (Figure 2d). To complement our predictions, RED and R a values for the heavy fraction-SRGO blend were calculated and found to be 0.359 and 4.74, respectively (Table 2). The significantly smaller RED and R a values of the heavy fraction-SRGO blend suggest that the heavy fractions are highly compatible in SRGO. Interestingly, the observed distance value is in accordance with the reported compatibility limit for the center-to-center distance of blends of HTL biocrudes in refinery streams. [START_REF] Pedersen | Understanding and predicting the solubility of bio-crude oils[END_REF] However, the higher RED and R a values of light fractions and residue to SRGO are responsible for their lower interaction potentials (Table 2). These calculations confirm the extreme compatibility of heavy fractions with SRGO as predicted from double sphere plots. The miscibility of subfractions and residue in SRGO was also checked experimentally to verify the theoretically predicted values. Different amounts of each sample were dispersed in SRGO using the vortex mixer for 15 min and observed after a few hours. The light fractions showed a maximum miscibility of 5 wt % while the heavy fractions were completely miscible at any proportions in SRGO. As predicted from the double sphere approach and solubility parameters, the residue did not show any miscibility in SRGO. Moreover, the miscibility of upgraded bio-oil (deoxygenated) in SRGO was also checked for comparison purposes, and a complete miscibility at any proportion was noticed. These studies show that the change in polarity (δ D and δ P ) of the components significantly affects the overlapping of two spheres and, hence, affects their mutual compatibility. The spot tests of the blends obtained during the miscibility studies were also carried out for the visual detection of precipates by casting a drop of the mixture on the filter paper. As shown in Figure 6, the biocrude-SRGO and residue-SRGO blends exhibit the presence of precipitates, whereas no such precipitates were found in the case of heavy fractions in SRGO. These studies reveal the high compatibility of heavy fractions and incompatibility of biocrude and residue in SRGO which are consistent with theoretically predicted values. Therefore, this study highlights a straightforward approach for determining the HSPs, solvent affinity, and compatibility with an acute acuracy of different substances on the basis of their solubility features.

To confirm the complete miscibility and phase separation in the blends, DSC spectra were recorded in the course of heating light, heavy, and residual fractions as well as their blends with SRGO (Figure 7). The compatibility of the blending mixtures of distillate fractions and residue with SRGO is evaluated by analyzing the vaporization temperature curves ascribed to the effect of temperature. As suggested, two broad endothermic peaks in the DSC spectra of residue-SRGO and light fraction-SRGO blending mixtures as compared to their starting precursors (e.g., the light fraction and residue) indicate two separate nonmixed phases, which confirm their immiscibility (Figure 7). Whereas, the single endothermic peak in the DSC spectrum of the heavy fraction-SRGO blend identical to pure the heavy fraction indicates a homogeneous phase, which confirms the compatibility of heavy fractions in SRGO. [START_REF] Masson | Melting and glass transitions in paraffinic and naphthenic oils[END_REF] The detailed composition, properties, and distribution of oxygen contents in HTL biocrude and the light, heavy, and residual fractions were investigated using elemental analysis. For comparison, detailed specification of oxygen contents and properties of upgraded biocrude obtained by hydrotreating biocrude (pinewood) in a microbatch reactor was also analyzed. The results of the elemental analysis and properties of all the samples are shown in Table 4. The oxygen to carbon (O/C) and hydrogen to carbon (H/C) ratios indicate the variations of oxygen and aromatic or aliphatic contents present in all the samples, respectively, which may give an estimate about the chemical nature of the functional groups present in the samples. The high O/C ratio in biocrude suggests high oxygen contents (11.5 wt %) which are completely deoxygenated (0 wt %) during the hydrotreating experiment (Table 4, entry 2). Among distillate fractions, the decrease of both the O/C and the H/C ratios with increase in the boiling temperature indicates that the heavy fractions are less oxygenated but more aromatic in structure than the light fractions. These results indicate that the oxygen contents in the distillate fractions decrease with increase in AET. Similar to the heavy distillate fractions, the low H/C (1.48 wt %) and O/C (0 wt %) ratios in the upgraded biocrude allows the extended aromaticity and lack of oxygen containing functional groups which indicate the complete expulsion of oxygen contents via hydrodeoxygenation. These studies reveal that the high compatibility of heavy fractions and upgraded biocrude in SRGO is attributed to their lower oxygen contents (low polarity) being similar to that of the SRGO structure. [START_REF] Wang | Detailed Chemical Composition of Straight-Run Vacuum Gas Oil and Its Distillates as a Function of the Atmospheric Equivalent Boiling Point[END_REF] This observation correlates well with the theoretical predictions of compatibility, made from Hansen double plots. Therefore, fractional distillation plays an important role in dividing biocrude oil into different chemical groups compatible with the fossil fuels to produce drop-in biofuels.

The elemental observation was complimented by identifying the chemical functionalities along with their relative concentrations present in the biocrude and light fractions, heavy fractions, residue, and upgraded bio-oil through GC-MS analysis. GC-MS analysis of the HTL biocrude exhibited the existence of a significant amount of oxygen containing functional groups (e.g., carboxylic acids, ketones, esters, and alcohols), substituted phenolic derivatives, and a small quantity of aromatic as well as aliphatic hydrocarbons (Table S3 in the Supporting Information). The light distillate fractions contain mainly short chain carboxylic acids and cyclic ketones; however, lower concentrations of substituted aromatics, phenol derivatives, and straight chain aliphatic hydrocarbons were also observed (Table S4 in the Supporting Information). The heavy fractions are more dominated by substituted phenol and benzene derivatives, while upgraded biocrude mainly contains aliphatic (straight and branched) and substituted aromatic hydrocarbons (Tables S5 and S7 in the Supporting Information). GC-MS analysis of the residue showed only the chemical compounds below the 300 °C range. The main chemical composition of the residue includes oxygenates (e.g., carboxylic acids, ketones, aldehydes, and alcohols), nitrogenates (e.g., amides, amines, and amino acids), heterocyclic compounds (e.g., pyridine and dithianes), and substituted aromatic hydrocarbons (e.g., benzene and phenol derivatives) with a small quantity of branched aliphatic compounds (Table S6 in the Supporting Information). In contrast, the SRGO is nonpolar owing to the presence of only aliphatic and aromatic hydrocarbons as the main constituents. The presence of heteroatoms in biocrude, light fractions, and residue caused phase partitioning due to the difference in polarities between the oil and SRGO, which resulted in immiscibilities of their components. Whereas hydrodeoxygenation of HTL biocrude completely removed the heteroatoms and increased the H/C ratio to match the polarity of SRGO and, hence, improved the compatibility. [START_REF] Djokic | Quantitative analysis of crude and stabilized bio-oils by comprehensive two-dimensional gas chromatography[END_REF] The GC-MS results showed that the aromatic and aliphatic hydrocarbon constituents present in heavy fractions significantly contribute to the compatibility with SRGO.

The GC × GC technique was also employed to gain further information about the detailed composition of molecular structures of biocrude and distillate fractions as well as to determine the tentative chemical structure of major chemical compounds. A group analysis for the different functional groups was carried out to report overall composition of biocrude and light and heavy fractions. Figure 8 shows the 3D GC × GC plots of the biocrude, light fractions, and heavy fractions with highlighted functional group regions with names of identified compounds. Based on the chemical functionalities, the GC × GC-MS chromatogram of biocrude is broadly categorized into four main groups (Figure 8A). Within the highlighted groups, four different categories of chemical compounds such as ketones (e.g., saturated and unsaturated cyclic ketones), substituted aromatic or phenolic monomers (e.g., arenes, and benzenediols), di-and triaromatics or phenolics (e.g., naphthol, anthracene, phenanthrenes, and biphenyls), and carboxylic acids were identified as the main constituents of biocrude. The presence of oxygenates such as ketones, carboxylic acids, and phenol derivatives in substantial amounts in the HTL biocrude causes a severe threat to the compatibility with SRGO. The chromatograms of light and heavy fractions were also recorded to estimate the distribution of chemical functionalities. The highlighted chemical functionality regions in the chromatogram of light fractions showed three main classes of chemical compounds including ketones (e.g., cyclic ketones), substituted aromatics or phenolics (e.g., arenes, methyl or methoxyphenols, methoxytoluene, naphthalene, and benzenediols), and aliphatics (e.g., n-alkanes) (Figure 8B).

As shown in Figure 8C, the chromatogram of heavy fractions was divided into four different regions with carboxylic acids, ketones, substituted aromatics, or phenolics and aliphatics as the main chemical compounds. The group analysis shows that the areas under the aromatic and aliphatic regions in the chromatogram of heavy fractions are higher than that of light fractions, which indicate the higher aromatic and aliphatic contents in the heavy fractions, whereas the area under oxygen containing functional groups is higher in light fractions. The heavy fractions with higher aromatic and aliphatic contents can be expected to show high compatibility in SRGO. For comparison, the GC × GC color plots of all the distillate fractions (1-8) are also provided in Figures S1-S8 in the Supporting Information. Unfortunately, the GC × GC chromatogram of the residue could not be recorded due to the presence of high boiling complex residual fractions. [START_REF] Van Beek | Comprehensive two-dimensional liquid chromatography of heavy oil[END_REF] The general trend observed on the distribution of functional groups based on identified chemical compounds complies with the results of elemental and GC-MS analysis. These results confirm that the utilization of the GC × GC-MS technique for the estimation of molecular structure plays a crucial role in the determination of the compatibility of biocrude.

To correlate the interactions within the blend components with the compatibility of biocrude, subfractions, and residue, 13 C NMR spectra of all the samples were recorded. Figure 9 shows the overlay [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectra of all derivatives. [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR analyses provide useful information on the type and relative percentage of chemical functionalities present in biooils. A quantitative evaluation of the chemical functional groups present in all the samples was also determined by integrating the specific regions of the [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectra according to different chemical shift values. A summary of the percentage of total carbon contents within a particular chemical shift range is discussed in Figure 10 and Table S7 in the Supporting Information. The observed chemical compositions of all the samples from the 13 C NMR analysis were found to be consistent with the elemental compositions calculated by CHN/O analysis. The whole chemical shift range in each spectrum is distributed into eight regions excluding the CDCl 3 solvent peak (77.2 ppm). These regions are 0-28, 28-55, 55-95, 95-120, 120-150, 150-165, 165-180, and 180-215 ppm which correspond to short aliphatics, branched aliphatics, alcohols, olefins, aromatics, phenols, carboxylic acids, ketones, or aldehydes, respectively. The chemical shift region 0-55 ppm covers all kinds of saturated hydrocarbons including short (0-28 ppm), long, and branched chain aliphatics (28-55 ppm). The region 55-95 ppm in [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectra provides useful information about the oxygen containing functional groups present in all the samples. Particularly, this region corresponds to the carbon adjacent to oxygen, e.g., alcohols, ethers, carbohydrates, and hydroxyl groups from lignin and methoxy-benzenes. The integrated region 95-120 ppm represents the two main categories including acyclic or cyclic olefins and mono-or diolefins. The next chemical shift region is 120-150 ppm which corresponds to aromatic hydrocarbons, including substituted benzene derivatives (e.g., alkyl or aryl benzenes) and heteroaromatics (e.g., pyridine). The chemical functionalities with aromatic contents are important due to their stronger π electron interactions (e.g., π-π stacking interactions) that play an important role in the determination of blend properties. [START_REF] Hung | Intermolecular Interactions of Isolated Bio-Oil Compounds and Their Effect on Bitumen Interfaces[END_REF] The next downfield part of the [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectra lies between 150 and 165 ppm, which accounts for the substituted phenol derivatives. The final integrated region of the spectra is the lowest downfield end that lies between 165 and 215 ppm, which represents the carbonyl group. This region is further subdivided into 165-180 ppm (esters and carboxylic acids) and 180-215 ppm (ketones and aldehydes). Among the above-mentioned regions, the chemical shift regions corresponding to the alkyl hydrocarbons are of main interest due to the significant contribution of aliphatic groups to the energy content of biofuels. 40 13 C NMR results revealed the presence of branched chain aliphatics (27.23 wt %), short chain aliphatics (19.50 wt %), aromatic contents (41.73 wt %), and total oxygenates adjacent to carbon atoms (7.60 wt %) in HTL biocrude (Table S8 in the Supporting Information). Oxygenates in raw biocrude indicate the presence of components with oxygenated polar compounds having moderate-to-high acidity. [START_REF] Kass | Compatibility Assessment of Fuel System Infrastructure Plastics with Bio-oil and Diesel Fuel[END_REF] The carbon contents corresponding to the oxygen containing functional groups are present in higher concentration in the residue (22.57 wt %) than in light fractions (7.48 wt %) and heavy fractions (2.72 wt %). The total aromatic carbon contents including phenols of heavy, light, and residual fractions were found to be 42.77, 21.35, and 12.19 wt %, respectively. These results indicate that the oxygen containing groups such as ketones, aldehydes, carboxylic acids, esters, and alcohols are present in substantial amounts in the HTL biocrude, light fractions, and residue, which affect their stability and compatibility. [START_REF] Djokic | Quantitative analysis of crude and stabilized bio-oils by comprehensive two-dimensional gas chromatography[END_REF] Based on the NMR results the correlations of the carbon contents of the oxygen containing functional groups vs total carbon in aromatics for the increment in miscibility of light, heavy, and residual fractions in SRGO were also demonstrated (Figure S9 in the Supporting Information). It was observed that the molecular structure of the biocrude and its components plays a crucial role in determining their compatibility in the SRGO. The basic differences between the physicochemical properties of these derivatives are attributed to the different functional groups within their molecular structure.

Generally, the compatibility of two mixtures depends on the similarity of their compound structure such as mixtures with only alkanes or only aromatics, which exhibit extreme compatibility. [START_REF] Burris | Water solubility behavior of binary hydrocarbon mixtures[END_REF] The NMR analysis showed that SRGO is nonpolar owing to the absence of any oxygen containing carbon atom and phenolic derivatives (Figure 10 and Table S7 in the Supporting Information). Furthermore, the aliphatic and aromatic carbon contents in SRGO were found to be 96.94 and 3.05 wt %, respectively. Therefore, one needs structurally similar compounds to be compatible with SRGO. According to the correlation between carbon containing oxygen atoms and aromatic carbons (Figure S9 in the Supporting Information), the miscibility of distillate fractions of HTL biocrude and its components in SRGO exhibits the following order: residue < light fractions < heavy fractions. The above order of the miscibility is found to be consistent with the theoretically predicted values from the Hansen solubility approach and the experimental data of miscibility studies. The high miscibility of heavy fractions in SRGO is attributed to the presence of aromatic contents, as well as low oxygen contents, which reduce their polar characteristics being similar to the SRGO structure. Aromatic rings present in heavy fractions may interact strongly with the π electron cloud of SRGO through π-π stacking interactions which results in reasonable compatibility. [START_REF] Szabo | Competitive Interactions in Aromatic Polymer/Lignosulfonate Blends[END_REF] Apart from the π-π stacking interactions, the carbonyl groups in heavy fractions can also interact with the aromatic rings of SRGO through noncovalent interactions. [START_REF] Gautrot | Experimental evidence for carbonyl-π electron cloud interactions[END_REF] The competitive interactions between the lone pair of electrons on the carbonyl groups of heavy fractions and the face of the π system of aromatic units of SRGO were confirmed by [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectroscopy. These interactions induced structural changes, as evidenced from the diminishing of carbonyl signals in the [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectrum of the heavy fraction-SRGO blend (Figure S10 in the Supporting Information). These structural changes in the heavy fraction-SRGO blend again confirm the complete miscibility of their corresponding components. [START_REF] Romhańyi | Correlations among Miscibility, Structure and Properties in Thermoplastic Polymer/ Lignin Blends[END_REF] These results showed that the combined effect of π-π and lone pair-π interactions between the functional groups lead to changing structure and properties of the blends. On the other hand, for more oxygen content present in biocrude, light fractions and residue do not match with the SRGO structure, and this mismatch caused their incompatibility. To support our hypothesis, the [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectrum of upgraded biocrude was also recorded. The 13 C NMR spectrum of upgraded biocrude revealed that the hydrodeoxygenation of HTL biocrude not only removed the oxygen contents but also reduced the aromatic contents (Figure 9). Specifically, a single-step hydrotreating of HTL biocrude at a 350 °C temperature and 6 MPa pressure caused a reduction of aromatic carbon from 40.79% to 20.21% (∼50 wt %) aromatic carbons. The decrease of the aromatic carbon contents and the increase of the aliphatic carbon contents indicate that the provided hydrotreating conditions resulted in a high degree of saturation and dearomatization of biocrude, leading to a more aliphatic nature of bio-oil compatible with SRGO (Figure 10). Consequently, the [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectrum of upgraded biocrude exhibited high aliphatic (78.94 wt %) and low aromatic contents (20.26 wt %) with almost no oxygenates (0.14 wt %). These results comply well with the experimental miscibility results of upgraded bio-oil. These results confirmed that the difference in properties and incompatibility of HTL biocrude with those of SRGO is primarily due to the high oxygen contents that should be removed in order to blend appreciable volumes in conventional diesel and gasoline fuels. The present study proved that the fractional distillation is an efficient concept for the separation of oxygen rich light fractions from raw biocrude to improve its compatibility with SRGO. The very low polarity changes by decreasing oxygen contents suggest that these biocrudes would be expected to be highly compatible with the SRGO. It is envisioned that the HTL biocrudes with low oxygen contents (polarity) can be expected to show high compatibility with the fossil fuels compared to SRGO for cost-effective corefining processes.

EXPERIMENTAL SECTION

Materials. Biocrude for the present study was produced from pinewood with supercritical water via HTL at the continuous Bench Scale 1 (CBS1) facility with 1/3 barrel/day capacity at Aalborg University, Denmark. [START_REF] Sharma | Delivery of 50-60 kg of HTL bio-liquid for baseline upgrading activities (M12). Deliverable D2.11 of the European Union's HORIZON 2020 project "4REFINERY[END_REF] The SRGO used in the miscibility studies was provided by MOL refinery, Hungry. All 38 solvents (Table S1 in the Supporting Information) used for the miscibility studies were purchased from Sigma-Aldrich Co. Ltd.

Characterization Techniques. Proton decoupled [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectra of biocrude, subfractions, residue, and upgraded biocrude were recorded in CDCl 3 solvent at 150.9 MHz on a Bruker Avance III 600 spectrometer. Typically, 20-30 mg of each oil sample was completely dissolved in 600 μL of CDCl 3 (chloroform-d 1 ). However, the same amount of residue was maximally dissolved in 1 mL of CDCl 3 , and the resulting solution was filtered to remove the insoluble portion. [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectra of subfractions and upgraded biocrude were acquired at 1024 scans, while 4096 scans were given to record the NMR spectra of biocrude and residue. The baseline corrections, peak integrations, and quantitative analysis of each spectrum were done using the MestReNova software. Elemental analysis of each sample was performed on the elemental analyzer (PerkinElmer, 2400 Series II CHNS/O) using acetanilide as a standard material for the calibration. The analysis was performed in CHN mode, and oxygen contents were calculated by the difference. The moisture contents of the HTL biocrude was measured on a moisture analyzer (Kern, MLS). Qualitative analysis of the biocrude, subfractions, and upgraded biocrude samples was performed by using a GC-MS instrument equipped with a gas chromatograph (Thermo Scientific, Trace 1300) and a mass spectrometer (ISQ QD). For the further identification of chemical compounds, all the samples in the liquid state were also analyzed by a GC × GC spectrometer. The whole setup consists of a 6890N gas chromatograph (Agilent) equipped with a low temperature valve (-100 °C<T < -120 °C) for the narrow pulses, a two stage thermal modulator (Zoex Corporation), and a mass selective detector 5975B (Agilent) for the analysis of column effluents. A thermal desorption of samples occurs at a 280 °C temperature in the first column which injects the trapped solutes into the second column. The raw GC × GC data (cdf files) were processed for 2D and 3D plots using MATLAB software. Component interactions and miscibility of blending mixtures of light fraction, heavy fraction, and residue with SRGO were determined by analyzing the vaporization temperature curves using a DSC instrument (TA Instruments Q2000, Netzsch STA 409 PC, Netzsch STA 409 PC). Fractional distillation of the HTL biocrude was carried out according to ASTM standard D2892 on a lab scale big sized distillation setup containing a 15 theoretical plate column with an internal diameter of 25 mm, surrounded by a heating jacket. The distillation setup consists of a RBF (round-bottom flask) of 2 L at the bottom of the column and 8 fractionation receivers with a capacity of 250 mL each. The HSPiP software package (ver. 5.0.13) 46 was used to access the HSP database of solvents and to construct the Hansen solubility sphere with a fitting algorithm, using solubility test scores of 0 or 1. The Hansen double sphere feature is installed in genetic algorithm mode in HSPiP software for the best-fit results within smallest radius. HSPs for a wide range of solvents and polymers tabulated in the HSPs library can be found in the HSPiP software.

Methods. HSPs and the Hansen Double Sphere Method. According to the Hansen solubility approach, total cohesive energy is decomposed into three main terms of dispersive (δ D ), polar (δ P ), and hydrogen bonding (δ H ) interactions (eq 1).

δδδδ

=++ TDPH 2222 (1)
The extent of affinity of two materials depends on the difference between their HSPs which is evaluated by the relative energy difference (RED) values (eq 2). [START_REF] Morimoto | Determination of Hansen Solubility Parameters of Asphaltene Model Compounds[END_REF] = RR RED / ao (2)

δδ δδ δδ = | - | +| - | +| - | R 4 aD , 1 D , 2 2 P,1 P,2 2 H,1 H,2 2 (3)
where R a and R o are the modified difference between the HSPs of two substances and the radius of the Hansen sphere, respectively. If RED < 1, the two solvents are mutually soluble, if RED = 1 they are partially soluble, and if RED > 1 they are insoluble. In simple terms, if the distance (R a ) between two substances is small then, they have a high tendency of being miscible (eq 3).

In the Hansen single sphere plot, the HSPs of different solvents and a substance are plotted in a three-dimensional space in which good solvents for the substance exist inside the sphere while the poor solvents are placed outside the sphere. The HSPs of the final substance are represented by the center of the three-dimensional sphere with the radius of the sphere considered as the radius of interaction. In comparison to the single sphere plot, the double sphere plot is extremely explicit in determining the volume of area overlap between the two spheres which provides actual information on the extent of compatibility of two substances. [START_REF] Benjamin | Self-stratifying coatings for metallic substrates[END_REF] Furthermore, the difference in HSPs (RED) and solubility distance (R a ) between two substances can be easily determined from the center of each sphere. [START_REF] Agata | Determination of Hansen solubility parameters of ionic liquids using double-sphere type of Hansen solubility sphere method[END_REF] Additionally, the affinity of different solvents for the immiscible substances can be easily determined from their distance from the junction between the two spheres. HSPs can help to determine and improve the compatibility of biocrudes, heavy fractions, bitumens, asphaltenes, and residues with existing petroleum crudes to achieve a drop-in biofuel for processing in conventional refineries. In the present work, we used the Hansen double sphere method to determine the compatibility of HTL biocrude, light fraction, heavy fraction, and residue with SRGO, which were found to be consistent with the experimental miscibility results. Furthermore, the affinity of different solvents for the biocrude-SRGO mixture was also studied from their distance (R a ) from the junction of the blending mixture, and a close relationship with experimental data on miscibility was verified.

Determination of HSPs. The solubility of each of the samples was measured experimentally in 38 different solvents using the standard procedure [START_REF] Redelius | Bitumen Solubility Model Using Hansen Solubility Parameter[END_REF] (Table S1 in the Supporting Information), and corresponding HSPs (Table 1) were calculated by plotting a threedimensional Hansen solubility plot. Typically, approximately 0.5 g of each sample is blended in 5 mL of different solvents using a vortex shaker for 10-15 min. Then, the blends are left undisturbed for 48 h to allow for complete dissolution or settlement. Hereafter, each of the test solvents is evaluated as good and bad on a binary scale; 1 means completely soluble and hence a "good" solvent and 0 for insoluble and hence a "bad" solvent for that particular sample. Due to the dark black color of the solutions (except for SRGO), visual inspection of the obtained solutions was done by the spot test on a filter paper. If a black ring structure was found on the filter paper, the test solvent was assigned to be a bad solvent (score 0), while the completely soluble solutions were contemplated to designate a good solvent (score 1). HSPiP software (Ver. 5.0.13) was employed to plot Hansen solubility spheres for each sample, and HSP values were calculated from the center coordinates of the resulting solubility sphere.

Fractional Distillation of Biocrude. Prior to fractional distillation, approximately 1.2 L of HTL biocrude was dehydrated at a vacuum pressure of 100 bar and vapor temperature of 130 °C through vacuum distillation in a stand-alone setup. To ensure the bubbling, 15 g of boiling stones have been added into the flask. To ensure the adiabatic conditions, the jacket temperature was kept at 0-5 °C lower than the AET vapor temperature during the distillation and a total reflux for around 15 min was carried out. The fractional distillation of biocrude was performed at different conditions ranging from atmospheric pressure to 0.75 Torr vacuum pressures and 75 to approximately 370 °C AET temperature. A column to fraction collector reflux ratio of 5:1 was maintained during the distillation for vacuum pressure >10 Torr and a reflux ratio of 2:1 for <10 Torr. The fractions were collected at different vacuum pressures from atmospheric to 0.75 Torr with a temperature interval of 25 °C. To avoid the thermal cracking, the RBF temperature and the vapor temperature were maintained below 310 and 210 °C, respectively. 47 Vapor temperature, vacuum pressure, RBF temperature, RBF skin temperature, and volume of fractions are recorded about every 2 min. The vapor temperature recorded during the collection of the different fractional cuts was converted to AET by using the ASTM standard D5236. [START_REF]D5236 standard test method for distillation of heavy hydrocarbon mixtures (vacuum potstill method)[END_REF] Miscibility Studies. HTL biocrudes obtained from pinewood (1-5 wt %) and SRGO (95-99 wt %) were blended in a dry plastic vial using the vortex mixer for 15 min. To improve the miscibility of the blending mixture, pyridine, cyclohexanone, and their respective (1:1) mixtures (20 wt %) were mixed to blend with biocrude (5-10 wt %) and SRGO (70-75 wt %) under continuous stirring at ambient conditions. The resulting mixture was heated at 60 °C on a stirrer for 1 h, and nonionic surfactants (span 80 and Tween 80) were also employed to facilitate the miscibility of biocrude in SRGO. Furthermore, the miscibility of different proportions of residue and light and heavy fractions obtained from fractional distillation of biocrude were also checked in SRGO under similar conditions to evaluate the effect of molecular structure on the compatibility of HTL biocrude. Additionally, the spot tests were also performed by spreading a drop of blends of subfractions, biocrude, and residues in SRGO on the filter paper for the visual evaluation of the compatibility of the blending mixtures.

CONCLUSION

For the first time, the Hansen double sphere approach has been successfully applied to predict the compatibility of the HTL biocrude and subfractions with SRGO. Furthermore, this approach also described the affinities of different solvents and solvent mixtures in term of their polarities to enhance the compatibility of a material blend. The correlation between the compatibility and the molecular structure of the HTL biocrude was established by investigating the compatibility of light fractions, heavy fractions, and residue obtained by the fractional distillation of HTL biocrude. The compatibility of blends was verified from the R a and RED values as well as experimental miscibility studies. The DSC thermograms and spot tests showed complete miscibility of heavy fractions in SRGO. The qualitative techniques like elemental analysis (CHN/O), GC-MS, and GC × GC spectroscopies showed the presence of high aromatic and oxygen contents in HTL biocrude. Quantitative 13 C NMR analysis of all the samples revealed that the nonaromatic oxygenates present in HTL biocrude, light fractions, and residue pose a severe threat to the compatibility, while the heavy distillate ends and upgraded biocrude oil with low oxygenates improve the compatibility. Both theoretical predictions and experimental investigation showed that a change in the polarity of the components affects their physicochemical properties and, hence, alters their compatibility. The present study proved that fractional distillation is an efficient concept for the separation of biocrude into the chemical groups of different polarities, having high compatibility and affinity for the fossil fuels. Furthermore, we believe that the use of the Hansen double sphere approach will be advantageous toward developing a mixing strategy to assess the compatibility of biocrude oils, heavy distillate fractions, asphaltenes, residues, and polymers with existing petroleum infrastructure for the cost-effective and sustainable biorefinery processes.

ASSOCIATED CONTENT

* sı Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acssuschemeng.9b06253. Detailed illustration of solubility scores, biocrude distillation, GC-MS, GC × GC, and [START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectra of distillation products as well as correlation between carbon containing oxygen atoms and aromatic carbons (PDF)

Figure 1 .

 1 Figure 1. Insertion points for HTL biocrude to integrate into existing petroleum refineries and distribution infrastructure.

Figure 2 .

 2 Figure 2. Hansen double sphere plot showing the compatibility of (a) HTL biocrude, (b) heavy fraction, (c) light fraction, and (d) residue with SRGO.

Figure 3 .

 3 Figure 3. (A) Hansen solubility map showing the affinity of different solvents for the biocrude-SRGO mixture (50:50) in terms of their polarities. (B) Visual inspection of the biocrude-SRGO blend (a) without cosolvent and (b) in the presence of pyridine-cyclohexanone as cosolvent.

Figure 4 .

 4 Figure 4. Picture shows the light fractions (1-3, left to right), heavy fractions (4-8, left to right), and residue (last) obtained by the fractional distillation of HTL biocrude (pinewood).

Figure 5 .

 5 Figure 5. Schematic illustrative integration of HTL biocrude based on the boiling range of different fractional cuts into the conventional petroleum refinery for the production of drop-in biofuels.

Figure 6 .

 6 Figure 6. Spot tests for the visual detection of miscibility of 5 wt % (a) HTL biocrude oil, (b-d) light fractions, (e-i) heavy fractions, and (j) residue in SRGO (95 wt %).

Figure 7 .

 7 Figure 7. DSC spectra showing vaporization temperature curves of light fraction, heavy fraction, residue, light fraction-SRGO, heavy fraction-SRGO, and residue-SRGO blends.

Figure 8 .

 8 Figure 8. GC × GC-MS (3D) surface plots with group type analysis and identified major compounds in (A) HTL biocrude, (B) light fraction, and (C) heavy fraction.

Figure 9 .

 9 Figure 9. 13 C NMR spectra of biocrude, light fraction, heavy fraction, SRGO, and upgraded bio-oil.

Figure 10 .

 10 Figure 10. Quantitative analysis of[START_REF] Nabi | Fuel characterisation, engine performance, combustion and exhaust emissions with a new renewable Licella biofuel[END_REF] C NMR spectra of biocrude, light fraction, heavy fraction, residue, SRGO, and upgraded biocrude oil by integration of the defined chemical shift range.

Table 1 .

 1 Calculated HSPs for Selected Derivatives and Solvents from Solubility Studies Results

	sample	δ D	δ P	δ H	δ	R 0	fit	wrong in	wrong out
	biocrude	17.44	10.67	8.58	21.90	10.2	0.982	1	1
	heavy fraction	16.81	9.13	7.90	21.3	11.9	1.000	0	0
	light fraction	18.77	9.92	9.81	21.9	12.0	0.971	1	0
	residue	20.51	8.03	8.64	23.7	9.1	0.914	1	2
	SRGO	16.22	3.98	9.76	18.1	11.0	0.934	1	2
	pyridine	19	8.8	5.9
	cyclohexanone	17.8	8.4	5.1
	pyridine-cyclohexanone (50%)	18.4	8.6	5.5

Table 2 .

 2 Calculated HSPs, RED, and R a Values for Selected Blending Mixtures from Miscibility Study Results the Using Hansen Double Sphere Plot a

						distance
	blends	D j	P j	H j	RED	(R a )
	pinewood biocrude-	17.60	5.60	6.20	0.607	6.25
	SRGO
	heavy fraction-SRGO	16.70	6.30	9.40	0.359	4.74
	light fraction-SRGO	16.70	6.80	9.60	0.465	5.86
	residue-SRGO	18.60	6.10	8.60	0.935	8.51

a D j , P j and H j are the HSPs for the junction of the selected blending mixtures.

Table 3 .

 3 Results of Miscibility Studies of HTL Biocrude in SRGO in the Presence of Different Solvents and Solvent Mixtures

	biocrude (wt %)	solvents	SRGO (wt %)	biocrude miscible	immiscible residue	miscibility
	5	pyridine (20 wt %)	75	0.310 g	0.190 g	62%
	5	cyclohexanone (20 wt %)	75	0.325 g	0.175 g	65%
	5	pyridine-cyclohexanone (20 wt %)	75	0.360 g	0.140 g	72%
	5	pyridine-2-heptanone (20 wt %)	75	0.370 g	0.130 g	74%
	10	pyridine-cyclohexanone (20 wt %)	70	0.650 g	0.350 g	65%
	10	pyridine-2-heptanone (20 wt %)	70	0.670 g	0.330 g	67%

Table 4 .

 4 Elemental Composition, Properties, and Miscibility Studies of Biocrude, Upgraded Bio-oil, Light Fractions, Heavy Fractions, and Residue

	elemental analysis [wt %]

a Calculated by the Channiwala equation. b Calculated by difference.

ACKNOWLEDGMENTS

This research acknowledges support from "4REFINERY" (Grant Agreement No. 727531) project, funded by the European Union's Horizon 2020 research and innovation programs.


A Gauguet

T E Mehlstäubler

T Lévèque

J Le Gouët

W Chaibi

B Canuel

A Clairon

F Pereira

Dos Santos

A Landragin
email: arnaud.landragin@obspm.fr

Off-resonant Raman transitions impact in an atom interferometer

We study the influence of off-resonant two photon transitions on high precision measurements with atom interferometers based on stimulated Raman transitions. These resonances induce a two photon light shift on the resonant Raman condition. The impact of this effect is investigated in two highly sensitive experiments: a gravimeter and a gyroscope-accelerometer. We show that it can lead to significant systematic phase shifts, which have to be taken into account in order to achieve best performances in term of accuracy and stability.

I. INTRODUCTION

In the field of atom interferometry, the improving sensitivity of inertial sensors [1,2,3,4] is paving the way for many new applications in geophysics, navigation and tests of fundamental physics. Most of these experiments are based on Raman transitions [5] to realize beamsplitters and mirrors, which manipulate the atomic wave-packets. Among others, this technique has the advantage of an internal state labelling of the exit ports of the interferometer [6], enable an efficient detection methods. Moreover, the atoms spend most of the time in free fall, with very small and calculable interactions with the environment. The inertial forces are then determined by the relative displacement of the atomic sample with respect to the equiphases of the laser beams, which realise a very accurate and stable ruler. This makes this technique suitable for high precision measurements, as required for instance for inertial sensors and for the determination of fundamental constants [7,8,9,10,11].

A limit to the accuracy and the long term stability of these sensors comes from wave-front distortions of the laser beams. This wave-front distortion shift appears directly on the signal of an interferometer when the atoms experience different wave-fronts at each Raman pulse. This effect thus depends on the actual trajectories of the atoms, so that a precise control of the initial position, velocity and temperature of the atomic clouds is required [12,[START_REF] Landragin | Proc. of the Enrico Fermi International School of Physics[END_REF]. A convenient technique to reduce this bias is to minimize the number of optical components in the shaping of the two Raman laser beams and by implementing them in a retro-reflected geometry [1,3,[START_REF] Cheinet | [END_REF]. Indeed, as long as the two beams travel together, wave-front aberrations are identical for the two beams and thus have no influence on their phase difference. This geometry also provides an efficient way to use the k reversal technique, which allows to diffract the atomic wavepackets in one or the opposite direction and thus to separate effects of many major systematic errors such as gradients of magnetic fields or light shifts [15]. The main drawback of this geometry arises from the presence of off-resonant Raman transitions, which induce a light shift on the resonant Raman transition and thus a phase shift of the atom interferometer.

In the following, we investigate this effect called two photon light shift (TPLS) [16]. We first show that the TPLS arises from several off-resonant transitions and evaluate each contribution. We then derive the impact onto the phase of an atom interferometer and use our gravimeter and gyroscope-accelerometer for quantitative comparisons. In particular we measure the systematic shifts and we investigate the influence on the long term stability. The study demonstrates that the precise control of experimental parameters, in particular the Raman laser intensities and polarisations, is needed to reduce the influence of this effect for such interferometers.

m F =0 m F =0 0 1 , k 1 2 , k 2 D 2 -line P 3/2 = i i e, F = F + 1 g,F m F =1 m F =2
a)

II. LIGHT SHIFT DUE TO OFF-RESONANT RAMAN TRANSITIONS

A. Raman Spectroscopy

The two experiments are using different alkali-metal atoms: 87 Rb in the case of the gravimeter and 133 Cs in the case of the gyroscope. As hyperfine structures, transition selection rules and Raman laser setups are similar (see figure 1), their results can be compared easily. The Raman transitions couple the two hyperfine ground states of the alkaline atom (labelled |g and |e ) via an intermediate state (labelled |i ) and two lasers with frequencies (labelled ω 1 and ω 2 ) detuned by ∆ i on the red of the D 2 line. During the interferometer sequence, a bias magnetic field is applied along the direction of propagation of the Raman laser beam to lift the degeneracy of the magnetic sublevel manifold. The two Raman lasers are overlapped with orthogonal linear polarisations and delivered within the same polarisation maintaining optical fiber to the vacuum chamber. After the fiber, the Raman beams pass through a quarter-wave plate to convert the initial linear polarisations into circular polarisations, noted σ i+ 1 for the Raman laser at the frequency ω 1 and σ i- 2 for the orthogonal polarisation at ω 2 . These beams are then retro-reflected through a quarter-wave plate to rotate the polarisation of each beam into its orthogonal polarisation (σ +r 2 , σ -r 1 ). For m F = 0 to m F = 0 transitions, there are two pairs of beams (σ + /σ + and σ -/σ -), which can drive counterpropagating Raman transitions with effective wave-vectors ±k eff = ±(k 1 -k 2 ). Then, the ground state |g, p is coupled with the excited state |e, p + hk eff by the pair of Raman laser (σ +i 1 /σ +r 2 ) and to the excited state |e, p -hk eff with the pair of Raman laser (σ -i 2 /σ -r 1 ). We use the Doppler effect to lift the degeneracy between the two resonance conditions. Indeed, if the atoms have a velocity in the direction of propagation of the Raman lasers, the Doppler shifts are of opposite sign for the two counter-propagating transitions. The resonance condition for each of these couplings is ∆ω laser = ω 0 + ω r ± ω D , where ω 0 is the hyperfine transition frequency, hω r = hk 2 eff /2m is the recoil energy and ω D = -k eff .v the Doppler shift due to the atomic velocity v in the reference frame of the apparatus. Consequently, the detuning between the two resonances is 2ω D , therefore we can discriminate between the two transitions when the Doppler shift is large enough compared to the linewidth of the Raman transition. This linewidth is characterised by the effective Rabi frequency Ω eff , which depends on the product of the two Raman lasers intensities and inversely to the Raman detuning ∆ i [15].

In this first part, we use the gyroscope-accelerometer experiment described in detail in [3]. The experiment has been performed with a cloud of cold Caesium atoms (1.2 µK) prepared initially in the |F = 3, m F = 0 state. The atoms are launched at 2.4 m.s -1 with an angle of 8 • with respect to the vertical direction. The Raman lasers are implemented in the horizontal plane with a 6 • angle with the normal of the atomic flight direction. Thus, to select only one Raman transition for the interferometer, the frequency difference between the two Raman lasers can be tuned to be resonant with either the +k eff or the -k eff transition.

Figure 2 shows the transition probability as a function of the detuning of the Raman transition with respect to the FIG. 2: Transition probability as a function of the frequency difference between the two Raman lasers when the atoms have a non-zero velocity in the direction of propagation of the Raman laser beams. The frequency is referenced to the microwave hyperfine transition (ω0). The data have been recorded with laser parameters corresponding to a π pulse of 135 µs duration. Lines (1,1') correspond to the two counter-propagating transitions, line 2 to the copropagating transition between the two mF = 0 states and lines 3 to the copropagating magnetic sensitive transitions.

hyperfine transition frequency. One can identify the two velocity selective counter-propagation transitions (labelled 1 and 1'), whose widths reflect the velocity distribution of the atomic cloud. In addition to the counter-propagating transitions, we observe transitions due to residual co-propagating Raman coupling, also detuned from resonance by a Doppler shift (lines 2, 3 and 3'). When the frequency difference of the Raman lasers is tuned to be resonant with one of the counter-propagating transitions, the second counter-propagating transition and the co-propagating ones induce a light shift (TPLS) on the selected Raman transition used for the interferometer.

B. Frequency shift due to the 2nd pair of Raman laser beams

The TPLS is the differential shift between the two atomic levels corresponding to the atomic states |g, p and |e, p ± hk eff involved in the atomic interferometer. The energy of the state |g, p is shifted of ε g by the off-resonant |g, p ↔ |e, p ∓ hk eff transition detuned by ±2ω D (eq. 1), while the energy of the state |e, p ± hk eff is shifted of ε e by the off-resonant |e, p ± hk eff ↔ |g, p ∓ 2hk eff transition detuned by h(∓2ω D + 4ω r ) (eq. 2). The two levels are shifted in opposite directions as illustrated in figure 3, here for the case of a Raman transition resonant with +k eff .

1 i e, p + hk eff g, p 2 r 1 r 2 i 1 r g, p + 2hk eff e, p hk eff 2 D 2 D + 4 r i i, p hk 1 i, p + hk 1 i, p + h k eff + k 1 ( ) 2 i g e FIG.
3: Scheme of the effect on the non-resonant coupling on the two atomic states |g, p and |e, p + hk eff involved in the atomic interferometer. The two states are coupled together through the selected Raman transition (+k in this particular case). But each state is also coupled to an other one, through an off-resonant Raman transition of opposite wave-vector.

TPLS corrections are calculated from fourth order perturbation theory. In the case of our system, the level shifts ε g and ε e for a ±k eff interferometer are given by:

ε g = ∓h Ω 2 eff 4 (2ω D ) (1)
ε e = h Ω 2 eff 4(±2ω D + 4ω r ) , (2)
where Ω eff is the effective Rabi frequency corresponding to counter-propagating Raman transitions. Thus, the shift of the resonance condition depends on the sign of direction of the selected Raman laser pair (i.e. ±k eff ), quadratically on the Rabi frequency and inversely to the Doppler detuning:

δω (TPLS±) = 1 h (ε e -ε g ) = Ω 2 eff ±8ωD + Ω 2 eff 4 (±2ωD+4ωr)
(3)

Variation with Ω eff

The frequency shift is measured from fits of the spectrum lines, as displayed in figure 2, with different Raman intensities (Ω 2 eff is proportional to the product of the intensity of the two lasers). Note that we discriminate it from the shifts independent of k eff , like quadratic Zeeman effect or AC Stark shift, by alternating measurements +k eff and -k eff , leading to a differential determination of the effect. The difference in the resonance condition ∆ω = 2k eff v + 2δω (TPLS) depends only on the TPLS and the Doppler effect. The Doppler effect does not depend on the Rabi frequency and can be determined by extrapolating ∆ω to Ω eff = 0. The results of these measurements are displayed in figure 4 as a function of Ω 2 eff . The curve clearly shows the quadratic dependence of the frequency shift with Ω eff . For this experimental configuration the Doppler shift was 85 kHz, and the value of δω (TPLS) for the largest Ω eff (2π × 27 kHz at the center of the beam) is 2.1 kHz in good agreement with the expected 2.4 kHz.

Position dependance in the Raman laser beams

The laser beams have a Gaussian shape, with a 15 mm waist (radius at 1/e 2 in intensity). In order to evaluate the phase shift, we first measure the TPLS for different atomic positions by scanning the resonance along their trajectory. As the Raman beam are horizontal, the Doppler shift is constant for the three pulses and the TPLS varies only with the Raman laser intensity. Figure 5 displays the measured TPLS, proportional to the laser intensity, which follows exactly the Gaussian profile of the laser beams.

C. Frequency shift due to the co-propagating transitions

In an ideal experiment, with perfect circular polarization and a Raman detuning ∆ i large compared to the hyperfine structure of the intermediate state (201 MHz in the case of the Caesium atom), co-propagating transitions are forbidden. In a real experiment, with imperfect polarization and/or finite Raman detuning, co-propagating transitions are slightly allowed, and will lead to additional TPLS. Imperfect polarization leads to a residual combination of σ + 1 /σ + 2 and σ - 1 /σ - 2 in the co-propagating beams and allows coupling between m F = 0 states. As the momentum exchanged hk eff = h(k 1k 2 ) ≃ 0, the Doppler and recoil effect are negligible and the resonance condition is ∆ω laser = ω 0 (line 2 of figure 2). The Rabi frequency corresponding to the transition ∆m F = 0 is determined experimentally using the residual co-propagating transition probability, P = 0.1 at full Raman laser power. It gives Ω eff Ω00 = 5, which can be explained by an error of linear polarization of one of the Raman laser of 2% in power. The detuning of this transition, compared to the two counter-propagating transitions, depends on the Doppler and recoil shift:

δω 00 (TPLS±) ≃ 1 4 Ω 2 00 ±ω D + ω r (4)
For ω D = 2π × 85 kHz and Ω eff ≃ 2π × 27 kHz we find an effect due to this coupling smaller than 100 Hz. The second source of residual co-propagating transitions stems from the coupling of |F,

m F = 0 ↔ |F ′ , m F ′ = ±2 by the co-propagating Raman laser pairs (σ + 1 ,σ - 2 ) and (σ - 1 ,σ + 2 )
. Because of the hyperfine splitting in the intermediate state, there are two paths for the Raman transition. Both transitions interfere destructively when the detuning compared to the intermediate state ∆ i is larger than the hyperfine splitting of the intermediate state, and so in this case the transition strength is zero. However, in our experimental set up, with ∆ i ≃ 2π × 780 MHz and the ∆ HF S = 2π × 201 MHz the ratio between the Rabi frequency of counter-propagating transitions Ω eff and the Rabi frequency of the co-propagating ∆m F = ±2 transition Ω 02 is 6.1, leading to a transition probability of 6.4 % in good agreement with the experimental value (see figure 2). These transition resonance conditions depend on the magnetic field amplitude as ∆ω laser = ω 0 ± 2αB, where α = 2π × 350 kHz/G for Caesium. With a calculation similar to the one used to obtain eq.3, we deduce the two photon light shifts δω 02 (TPLS±) induced by the magnetically sensitive transitions for the ±k eff case to be:

δω 02 (TPLS±) = Ω 2 02 4 1 ±ωD+ωr+2αB + 1 ±ωD+ωr-2αB (5)
The first term in eq. 5 is due to the coupling with |F ′ , m F ′ = +2 whereas the second term is induced by the coupling with |F ′ , m F ′ = -2 . It is clear from eq. 5 that a residual magnetic contribution appears in the half difference and creates a magnetic sensitivity in addition to the standard quadratic Zeeman effect. This contribution to the two photon light shift is measured by changing the bias field in the Raman interaction zone. Using the differential method previously described, we show in figure 6 the variation of the total TPLS with the bias field. The resonance around 130 mG corresponds to the case where a magnetic co-propagating transition and the counter-propagating transition are resonant simultaneously. Previous measurements have been performed with a 31 mG magnetic field bias.

III. IMPACT ON THE INTERFEROMETER PHASE SHIFT

A. Theoretical derivation of the phase shift

In the following we will consider interferometers constituted of three Raman pulses in a π/2 -π -π/2 sequence. If the TPLS is constant during the interferometer it is equivalent to a fixed frequency shift of the Raman transition. In that case, It is well known that no phase shift is introduced in the interferometer. On the contrary, a fluctuation of the TPLS during the interferometer sequence leads to a phase shift given by:

Φ TPLS = +∞ -∞ g(t)δω TPLS (t)dt. ( 6
)
where g(t) is the sensitivity function of the atom interferometer, defined in [17].

1. Case Ω eff τ = π/2
In the case where the interaction pulses are short enough that one can neglect the variation of the TPLS during the pulses, and that the area of first and last pulse fulfils the Ω eff τ = π/2 condition, the two-photon interferometer phase shift can be approximated by:

Φ TPLS = δω (1) TPLS Ω (1) eff - δω (3) TPLS Ω (3) eff , (7) where ω (i)
TPLS and Ω (i) eff are the TPLS and the Rabi frequencies of the i-th pulse, respectively. One might notice that the frequency shift during the π pulse does not contribute to the interferometer phase shift. Moreover, as all components of the TPLS, counter-propagating and co-propagating terms, increase as the square of the Rabi frequencies, the interferometer phase shift scales linearly with the Raman laser power.

In the limit where the co-propagating transitions are negligible (perfect polarization and very large Raman detuning) and the dominant source of TPLS is due to the counter-propagating transition, the phase shift of the interferometer can be simplified as:

Φ counter TPLS = Ω (1) eff 4δ (1) D - Ω (3) eff 4δ (3) D , (8)
where δ i D is the Doppler shift for the i-th pulse.

Case

Ω eff τ = π/2
More generally, the interferometer phase shift can be calculated when the π/2 pulse condition is no longer fulfilled. This appears when the Rabi frequency drifts due to changes in power or polarization of the Raman lasers. Generalising the formalism of the sensitivity function to the case where Ω eff τ = π/2 allows deriving the interferometer phase shift:

Φ TPLS = δω (1) TPLS Ω (1) eff tan Ω (1)
eff τ (1) 2

- δω (3) TPLS Ω (3) eff tan Ω (3) eff τ (3) 2 (9)
Usually, the Rabi frequencies and pulse durations can be taken equal for the first and the last pulses; the expression of the interferometer shift is then:

Φ TPLS = δω (1)
TPLS -δω

(3) TPLS Ω eff tan Ω eff τ 2 (10)
As before, for a dominant counter-propagating transition, the previous expression can be simplified to:

Φ counter TPLS = Ω eff 1 4δ (1) D - 1 4δ (3) D tan Ω eff τ 2 ( 11
)
An other aspect of the influence of the TPLS on the atomic phase shift concerns the stability of the experiment versus the experimental parameters fluctuations, in particular the Raman laser power. As Rabi frequency fluctuations are small in relative values (typically smaller than 10 %), we can develop eq. 11 to first order in δΩ eff close to the usual conditions Ω eff τ = π/2 and find:

δΦ TPLS = 1 + π 2 δΩ eff Ω eff Φ TPLS (12)
Similar calculations may be derived to extract the dependance on the duration of the pulse or the Doppler detuning.

As the stability of the latter parameters is much better controlled in cold atom interferometers, no measurable influence on the short term stability of the interferometer is expected.

B. Case of a gravimeter

We first consider the case of the gravimeter developed at SYRTE and described in detail in [START_REF] Cheinet | [END_REF]18]. In this compact experimental set-up, cold 87 Rb atoms are trapped in a 3D MOT in 60 ms and further cooled during a brief optical molasses phase before being released by switching off the cooling lasers. During their free fall over a few centimetres, the interferometer is created by driving the Raman laser in the vertical direction, with pulses separated by free evolution times of T = 50 ms. The first Raman pulse occurs 17 ms after releasing the atoms. The Doppler shift at the first pulse is thus relatively small, about 400 kHz, and gets large, about 3 MHz, for the last pulse. With a Rabi frequency of 40 kHz, this leads to a TPLS of about 22 mrad for counter-propagating transition. Following the method of paragraph II C, we find a 11 mrad for co-propagating ones. This corresponds to a large shift for the gravity measurement of about 8.10 -8 g.

To measure the bias on the atomic interferometer phase due to TPLS, we exploit its dependence with the Rabi frequency. The principle of this measurement is based on a differential method, where one performs an alternating sequence of measurements of the interferometer phase with two different Rabi frequencies Ω eff and Ω ′ eff , but keeping the areas of the pulses constant by changing the duration of the pulses τ . The Rabi frequency is modulated with the power of the Raman lasers. In practice, the differential measurement is performed by alternating sequences of measurements with four different configurations : (Ω eff , +k eff ), (Ω eff , -k eff ), (Ω ′ eff , +k eff ) and (Ω ′ eff , -k eff ). After averaging for 5 minutes, we extract the difference of the TPLS between the two Rabi frequencies with an uncertainty below 1 mrad. This measurement was repeated for various Ω ′ eff , keeping Ω eff fixed. The phase differences are displayed in figure 7 in according to the ratio of the Rabi frequency Ω ′ eff /Ω eff . The results clearly demonstrate the linear dependence of the phase shift with the Rabi frequency. The fit of the data allows to extract a 32 mrad shift, in very good agreement with the expected value (33 mrad), deduced from eq. 7. Deviations from the linear behavior and discrepancies (up to ±10%) between different measurements that correspond to the same ratio cannot be explained by uncontrolled fluctuations in the Rabi frequencies, as the simultaneous monitoring of the laser intensities showed stability at the per cent level during the course of the measurements. We demonstrated that these fluctuations were correlated with changes of the polarization of the Raman beams, which modulate the contribution to the phase shift of the undesired co-propagating transitions.

We perform a complementary measurement by changing the duration of the first and last pulse simultaneously, while keeping Ω eff constant. The acquisition is performed with a similar differential method than previously, but now alternating between different pulse durations and a pulse duration of 6 µs, when the π/2 pulse condition is fulfilled. The data are then shifted by the bias deduced from previous measurements with τ = 6 µs (result of figure 7) and displayed in figure 8 . Using eq. 10, the fit of the data gives a Rabi frequency of 39 kHz , in very good agreement with the expected value (42 kHz). A small deviation appears for long pulse durations when the areas of each of the two pulses is close to π.

In the case of our gravimeter, where cold atoms are dropped from rest, the TPLS is very large, almost two orders of magnitude above the pursued accuracy. In principle, this effect can be measured accurately by alternating measurements with different Rabi frequencies. But, it seems desirable to decrease the effect by operating with lower Rabi frequencies, the drawback being an increased velocity selectivity of the Raman pulses. A more stringent velocity selection, or smaller temperatures, are then required in order to preserve a good fringe contrast. In the case of a fountain gravimeter, where the atoms are launched upwards at a few m/s, the Doppler shift at the first and last pulse is much larger, considerably reducing this effect. For the parameters of the Stanford gravimeter [1] (long pulse duration of 80 µs and time between pulses of 160 ms), we find a phase shift of 0.8 mrad, which corresponds to 2.10 -10 g.

C. Case of a gyroscope-accelerometer

In the case of the gyro-accelerometer, the mean velocity of the wave-packet is not collinear with the effective Raman wave vector. Consequently, the atomic phase shift measured with the interferometer is sensitive to the rotation rate Ω in addition to the acceleration a. As in the case of the gravimeter, the atomic phase is shifted by the TPLS and by other systematics (labelled Φ 0 ), for instance the phase shift induced by the laser wave-front distortions [12]. The total phase shift is expressed by :

Φ = k eff • aT 2 + 2k eff • V × ΩT 2 + Φ 0 + Φ TPLS (13)
Our gyroscope-accelerometer uses a double interferometer with two atomic clouds following the same trajectory but with opposite directions to discriminate between acceleration and rotation phase shifts. Moreover, our experiment is designed to measure different axis of rotation and acceleration according to direction of propagation of the Raman laser beams. We will illustrate the impact of the TPLS on the interferometer in the configuration where the Raman lasers are directed along the vertical direction.

The measurement is realized in the same way than for the gravimeter experiment by comparing atomic phases with high and low Rabi frequency, changing the Raman laser power but keeping the pulse duration constant to 7.6 µs. In order to enhance the TPLS signal we decrease the time between pulses to 20 ms. Indeed, the Doppler effect is reduced and the available laser power on the side of the Gaussian laser profile is increased. The first pulse occurs 15 ms before the apogee and the third 25 ms after the apogee, corresponding respectively to a Doppler shift of about ω

D = 2π×574 kHz. The Rabi frequency for each pulse is approximately 33 kHz, then the TPLS expected from eq.7 is about 38 mrad for each interferometer. As this shift is similar for the two interferometers when the two atomic clouds perfectly overlap and experiment the same TPLS, it bias the acceleration signal only. Figure 9 displays the variation of the acceleration and rotation signals with the Rabi frequency. Acceleration shift (squares) varies in a good agreement with expected shift (continuous curve) calculated from eq. 9. Rotation shift (circles) shows no dependance on the Rabi frequency and illustrates that the rejection from the acceleration signal is efficient. Nevertheless, fluctuations from expected behaviour are clearly resolved and repeatable. We attribute these deviations to wave-front distortions of the Raman laser beams. Indeed, when the atomic trajectories do no perfectly overlap, a residual bias appears on the rotation due to unperfected cancellation. This bias depends on the details of the wave-front distortions weighted by the actual atomic cloud distributions, and is modified when the Rabi frequency is changed. In the usual conditions, with interrogation time of 80 ms, the acceleration shift is reduced to about 12 mrad thanks to the increase of the Doppler shift and reduction of the Rabi frequency on the side of the Gaussian Raman beams.

We finally estimate the impact of the Raman laser power fluctuations on the stability of the rotation signal in usual conditions (interrogation time of 80 ms). We performed a complementary measurement by recording the interferometer signal and the Raman laser power in the same time when applying a modulation of the laser powers of 10%. The modulation is applied by attenuating the radio-frequency signal sends to the acousto-optic modulator used to generate the Raman pulses. The power of the lasers was recorded during the third pulse thanks to a photodiode measuring the intensity on the edge of the laser beams. We found a small dependance of the rotation signal on the power fluctuation of 6.10 -9 rad.s -1 /%, which can limit the long term stability of the gyroscope. As no dependance was expected, we attribute it again to non perfect superimposition of the two atomic clouds trajectories, leading to a different Rabi frequencies experienced by the two clouds.

IV. CONCLUSION

We have shown that the use of retro-reflected Raman lasers in atom interferometers induces off-resonant Raman transitions, which have to be taken into account in order to achieve best accuracy and stability of interferometers. We have first quantitatively evaluated the effect on the resonance condition for each off-resonant line: the other counter-propagating transition, which can not be avoided in the retro-reflected design, and co-propagating transitions arising mainly from imperfections in the polarisation. Then, we have measured the impact of this two photon light shift on the phase of two atom interferometers: a gravimeter and a gyroscope. In particular, we show that this shift is an important source of systematic errors for acceleration measurements. Nevertheless, it can be measured accurately by modulating the Raman laser power and/or the pulse durations. Our study has also shown that it can impact the stability of the two sensors if the polarization and/or the power of the Raman lasers fluctuate.

The TPLS appears as a drawback of using retro-reflected Raman laser beams. But, as it can be well controlled, it does not reduce the benefit from this geometry, whose key advantage is to drastically limit the bias due to wave-front aberrations, which is larger and more difficult to extrapolate to zero.

This study can be extended to other two photon transitions (like Bragg transitions) and to other possible polarization configurations (when using linear instead of circular polarizations), when using the Doppler effect to select the transition. If the signal is generated from the subtraction of the phase shifts of two independent atomic clouds, e.g. gradiometers or gyroscopes, perfect common mode rejection, is required to suppress this effect. In our case this means a perfect overlap of atomic trajectories.

Finally, the two photon light shift can be drastically reduced by increasing the Doppler effect and/or using colder atoms, allowing to reduce the Rabi frequency during the Raman pulses. By contrast, for set-up with intrinsic small Doppler effect, as for space applications [START_REF] Landragin | Proc. of the Enrico Fermi International School of Physics[END_REF][START_REF]see for instance Apll[END_REF], this effect becomes extremely large and has to be taken into account in the design of the experiment.

1 2FIG. 1 :

 11 FIG.1: Scheme of our Raman laser setup. a) Scheme of the Raman transition between the two hyperfine ground states of an alkaline atom. b) Implementation of the Raman laser beams. The two Raman lasers of orthogonal polarisations are guided to the experiment through the same polarization maintaining fibre. The two lasers are represented respectively by the solid and dashed lines. The lasers go through a first quater-wave plate (λ/4), cross the experiment and are reflected by a mirror, crossing twice a second quater-wave plate. The wave-plates are set in such a way that counter-propagating Raman transitions are allowed but co-propagating Raman transitions are forbidden.

FIG. 4 :

 4 FIG. 4: Variation of the frequency shift of the counter-propagating Raman transition versus the square of the Rabi frequency. The Rabi frequency is controlled by changing the Raman laser intensities.

FIG. 5 :

 5 FIG. 5: Variation of the two photon light shift with the position in the Gaussian beam of the Raman lasers. The dots correspond to the measurement of the shift and the line to the fit of the data by a Gaussian function.

1 .

 1 TPLS induced by mF = 0 to mF = 0 co-propagating transitions

2 .

 2 TPLS induced by mF = 0 to mF = ±2 co-propagating transitions

FIG. 6 :

 6 FIG.6: Variation of the two photon light shift versus the bias magnetic field. A resonance appears when the Zeeman shift equals the Doppler shift.

FIG. 7 :

 7 FIG.7: Variation of the gravimeter phase shift due to the two photon light shift versus the Rabi frequency ratio, keeping the pulse area constant. To remove drifts from other sources, the phase shift is measured in a differential way by changing the Rabi frequency up to 40 kHz, which is the maximum available. The dotted line is a linear fit of the shifts.

FIG. 8 :

 8 FIG.8: Variation of the gravimeter phase due to the two photon light shift versus the pulse duration ratio, keeping the the Rabi frequency constant (40 kHz). To remove drifts from other sources, the phase shift is measured in a differential way with respect to the optimum pulse duration (6 µs). The line corresponds to the calculated shift.

FIG. 9 :

 9 FIG. 9: Variation of the rotation and acceleration phases (resp. circles and squares) due to the two photon light shift versus the Rabi frequency ratio, keeping the pulse duration constant (7.6 µs). Acquisitions have been recorded for a total interaction time between the first and the last pulse of 40 ms. To remove drifts from other sources, the phase shift is measured in a differential way with respect to the maximum Rabi frequency available at the location of the π/2 pulses (33 kHz). The line shows the calculated shift for acceleration signal.

Acknowledgments

We express our gratitude to F. Biraben for pointing out this effect and to P. Cheinet for earlier contributions to the gravimeter experiment. We would like to thank the Institut Francilien pour la Recherche sur les Atomes Froids (IFRAF), the European Union (FINAQS contract), the Délégation Générale pour l'Armement (DGA) and the Centre National d' Études Spatiales (CNES) for financial supports. B. C., J. L.G. and T. L. thank DGA for supporting their work.