Le Meur Mathieu

Cohen Grégory

Laurent Mélissa

Höhener Patrick

Atteia Olivier

Effect of NAPL mixture and alteration on 222 Rn partitioning coefficients: implications for NAPL subsurface contamination quantification

Keywords: 222 Rn, Fresh and altered NAPL, Radon Partitioning Coefficient, NAPL Subsurface Contamination quantification Highlights

Soils and groundwater are often contaminated by complex organic mixtures also called Non Aqueous Phase Liquids (NAPLs). Several techniques such as drilling, monitoring of soil gas or injection of tracers are traditionally used to quantify NAPLs in aquifers but are complex to perform. The use of natural soil gas such as 222 Rn could be an easy and cheap alternative. This method requires the knowledge of the radon NAPL-water partitioning coefficients (Kn-w.). Once spilled on soil, NAPL will undergo degradation (evaporation, effects of sun light among others) and this degradation could impact the Knw. This study aims at investigating the partitioning coefficients of complex NAPLs such as commercial diesel fuel and gasoline in relation to degradation such as evaporation and UV-degradation. For that purpose, batch experiments and GCMS investigations were carried out. The results show different Kn-w for the commercial diesel fuel (60.7 ± 6.1) and gasoline (37.4 ± 5.6) The results also show different Kn-w behaviors in relation with degradation. Degraded diesel fuel display opposite Kn-w values (74.8 ± 7.5 and 25.1 ± 2.5 for UV degraded and evaporated diesel fuel, respectively), compared to fresh one.

Degraded gasoline shows no significant variations of the Kn-w compared to fresh one. The molecular investigation reveals the removal of the most volatile fraction for the evaporation treatment, whereas UV-degradation do not have pronounced effects on the chromatogram pattern. For the gasoline molecular investigation, no difference is observed between the treatments excepted a very slight removal of the lightest compounds under evaporation. These results show that NAPL degradation have effects on the Kn-w for diesel fuel and no significant effects for gasoline, at least with these degradation paths. This Kn-w variation will have in fine effects on 222 Rn activity interpretation and NAPL subsurface quantification.

Introduction

Soil and groundwater are often contaminated by complex organic mixtures, such as petroleum products or chlorinated solvents (also known as Non-Aqueous Phase Liquids, or NAPL), and these liquids are recognized as a critical issue in environmental remediation [START_REF] Davis | Effects of heterogeneity and experimental scale on the biodegradation of diesel[END_REF].

These NAPL are frequently encountered in industrial or military sites and are releasing toxic compounds to groundwater. They can persist sometimes for centuries, creating long-term contamination due to their low solubility in water [START_REF] Cohen | Radon-222: environmental behavior and impact to (human and non-human) biota[END_REF][START_REF] Zhang | Effect of vegetation on transport of groundwater and nonaqueous phase liquid contaminants[END_REF].

NAPL can be released to the environment during fueling, maintenance and/or storage operations. Large volume of spilled NAPL can migrate through unsaturated soil zone to the water table [START_REF] Yoon | Using 222Rn as a naturally occurring tracer to estimate NAPL contamination in an aquifer[END_REF]. This migration is complex, following preferential pathways and forming ganglia and small isolated lenses (Fernandez et al., 2013). The light NAPLs preferentially float at the top of the water table and dense NAPLs penetrate into the saturated zone [START_REF] Castelluccio | Using a multi-method approach based on soil radon deficit, resistivity, and induced polarization measurements to monitor non-aqueous phase liquid contamination in two study areas in Italy and India[END_REF]. During the migration through the vadose zone, a certain amount of liquid (up to 20%, known as residual saturation) is retained in the pores by capillary forces forming a source zone [START_REF] Wiedemeier | Natural attenuation of fuels and chlorinated solvents in the subsurface[END_REF] where gaseous and aqueous contaminant plumes are formed [START_REF] Höhener | Radon-222 as a tracer for nonaqueous phase liquid in the vadose zone: Experiments and analytical model[END_REF]. It is then crucial to accurately detect, localize and quantify residual NAPL sources prior to choose efficient remediation procedures.

Traditionally, soil NAPL contamination has been estimated using sampling techniques (drilling and core-sampling) which are of very high quality but are expensive and time consuming [START_REF] Feenstra | Diagnosis and assessment of DNAPL sites. Subsurface. In Dense Chlorinated Solvents and other DNAPLs[END_REF][START_REF] Yoon | Using 222Rn as a naturally occurring tracer to estimate NAPL contamination in an aquifer[END_REF]. In addition, without prior information concerning the contamination pattern, the position of the sampling stations could lead to useless data (Garcia-Gonzalez et al., 2008). Screening method such as gas monitoring (in particular Volatile Organic Compounds, VOCs, [START_REF] Wilson | Persistence of Organic Contaminants in Sewage Sludge-Amended Soil: A Field Experiment[END_REF]) is another non expensive technique that permits to approximately locate the contamination source zone laterally and vertically [START_REF] Robbins | Soil-Gas Surveying for Subsurface Gasoline Contamination Using Total Organic Vapor Detection Instruments Part I. Theory and Laboratory Experimentation[END_REF]. However, NAPL degradation leads to high VOC concentrations that do not reflect the amount of NAPL [START_REF] Höhener | Radon-222 as a tracer for nonaqueous phase liquid in the vadose zone: Experiments and analytical model[END_REF] in the source zone. This last technique is thus only suitable for volatile contaminants and hence not suitable for diesel fuel, fuel, kerosene or hydraulic oil [START_REF] Schubert | Determination of radon distribution patterns in the upper soil as a tool for the localization of subsurface NAPL contamination[END_REF]. The injection of artificial tracers directly in soils is another technique cited in the literature [START_REF] Deeds | Vadose zone characterization at a contaminated field site using partitioning interwell tracer technology[END_REF][START_REF] Brusseau | Partitioning tracer tests for characterizing immiscible-fluid saturations and interfacial areas in the vadose zone[END_REF].

The gas is directly injected in the vadose zone where it can be transported by advection [START_REF] Mariner | The first vadose zone partitioning interwell tracer test for nonaqueous phase liquid and water residual[END_REF] and/or diffusion (Werner and Hohener, 2002) and the interpretation of the breakthrough curves permits to obtain the localization and the average volumetric NAPL content [START_REF] Dwarakanath | Analysis of partitioning interwell tracer tests[END_REF]. However, this technique is time consuming, expensive [START_REF] Höhener | Radon-222 as a tracer for nonaqueous phase liquid in the vadose zone: Experiments and analytical model[END_REF] and can give quite misleading results in heterogeneous environment [START_REF] Nelson | Partitioning tracer method for the in situ measurement of DNAPL saturation: influence of heterogeneity and sampling method[END_REF]. Due to the limitations of the different techniques cited above, alternative options must be proposed. A simpler way to investigate subsurface contaminations is the use of native soil gas that partitions into NAPLs.

Radon-222 ( 222 Rn) is a good advocacy for the understanding of NAPL behavior in subsurface [START_REF] Barrio-Parra | Field performance of the radon-deficit technique to detect and delineate a complex DNAPL accumulation in a multi-layer soil profile[END_REF]). 222 Rn is a natural component, continuously produced in soil matrices by the alpha-particle decay of 226 Ra in the natural decay of the uranium-238 series [START_REF] Green | Radon-222 as a tracer in the hydrogeologic environment[END_REF]. 222 Rn also decays by alpha-particle decay and has a half-life of 3.82 days [START_REF] Mason | Principles of geochemistry[END_REF]. Uranium is ubiquitous in minerals, as a trace element, permitting almost ubiquity production of radon in the environment. The 222 Rn emanation coefficient corresponds to the gas fraction released from the host materials which is retained in the pore space [START_REF] Andrews | Mechanism of radon release in rock matrices and entry into groundwaters[END_REF]. The composition and mineralogy of the soil, and thus especially the particle size contribute to the emanation coefficient. In general, when the particle size is small, the specific surface area is large and the emanation power of materials containing 226 Ra is higher (Galhadi and Bonotto, 2012;[START_REF] Thu | The effects of some soil characteristics on radon emanation and diffusion[END_REF]. Other chemical and physical parameters can also influence the radon activity such as moisture content and pore size [START_REF] Nazaroff | Radon transport from soil to air[END_REF][START_REF] Galhardi | Radon in groundwater contaminated by dissolved hydrocarbons in Santa Bárbara d´ Oeste, São Paulo State, Brazil[END_REF]Cujic et al., 2020).

The use of natural radon to localize and quantify NAPL amount in subsurface is feasible because its preferential partition into organic phase [START_REF] Horiuchi | A new procedure for the determination of radium in water by extraction of radon and application of integral counting with a liquid scintillation counter[END_REF][START_REF] Hunkeler | Rn-222 as a partitioning tracer to detest diesel fuel contamination in aquifers: laboratory study and field observations[END_REF][START_REF] Nazaroff | Radon transport from soil to air[END_REF][START_REF] Sakoda | A comprehensive review of radon emanation measurements for mineral, rock, soil, mill tailing and fly ash[END_REF][START_REF] Semprini | Laboratory, field and modeling studies of radon-222 as a natural tracer for monitoring NAPL contamination[END_REF][START_REF] Wong | Sorption of radon-222 to natural sediments[END_REF]. When groundwater containing radon migrates towards a residual NAPL contamination area, a local radon deficit in groundwater is then observed [START_REF] Hunkeler | Rn-222 as a partitioning tracer to detest diesel fuel contamination in aquifers: laboratory study and field observations[END_REF]Schubert et al., 2007a).

The radon deficit close to a NAPL-contaminated zone depends on (i) the pore space saturated with residual NAPL and (ii) the radon partitioning coefficient specific for the NAPL present (Schubert et al., 2007a). If the 222 Rn partitioning coefficient of the NAPL is known, it is possible to localize and quantify the residual saturation of the organic phase (Schubert et al., 2007a;[START_REF] Cohen | Laboratory-scale experimental and modelling investigations of 222Rn profiles in chemically heterogeneous LNAPL contaminated vadose zones[END_REF]. The knowledge of the partitioning coefficient is therefore of pivotal importance when dealing with site NAPL contamination delineation. Several partitioning coefficients have been mainly reported for pure organic compounds [START_REF] Clever | Krypton, Xenon and Radon[END_REF][START_REF] Schubert | Determination of radon partition coefficients between water and organic liquids and their utilization for the assessment of subsurface NAPL contamination[END_REF] but few authors reported the partitioning coefficient for commercial NAPL mixtures [START_REF] Schubert | Using radon-222 in soil gas as an indicator of subsurface contamination by non-aqueous phase-liquids (NAPLs)[END_REF]2007a). [START_REF] Schubert | Determination of radon partition coefficients between water and organic liquids and their utilization for the assessment of subsurface NAPL contamination[END_REF] worked on the 222 Rn partitioning between air, water and three artificial NAPL mixtures. They stated the need of experiments on NAPL mixtures in order to verify or modify the theoretical framework. [START_REF] Schubert | Using radon as environmental tracer for the assessment of subsurface Non-Aqueous Phase Liquid (NAPL) contamination-A review[END_REF] also mentioned that NAPL degradation could affect its complex composition, leading in return to a change of the partitioning coefficient. This change of the partitioning coefficient will affect the NAPL quantification in soils. However, to our knowledge, no study in the literature deals with the effect of NAPL alteration on 222 Rn partitioning coefficient.

When spilled on the soil, the NAPL will be exposed to wind and heat for a certain time which might be sufficient to evaporate the light NAPL fraction [START_REF] Villa | Diesel degradation in soil by Fenton process[END_REF]. In soils, NAPL may undergo biodegradation, governed by microorganisms, leading to the loss of contaminants (Wiedmeier et al., 1999) and the modification of initial NAPL composition. Natural NAPL biodegradation takes time and depends on different parameters such as soil properties [START_REF] Jho | Prediction of landfarming period using degradation kinetics of petroleum hydrocarbons: test with artificially contaminated and field-aged soils and commercially available bacterial cultures[END_REF]) and microorganism's ecology in action. These NAPL chemical alterations should thus lead to a 222 Rn partitioning coefficient modification.

In the frame of the above discussion, the objectives of this article are (i) to determine the partitioning coefficient of mixed commercial NAPLs, (ii) to investigate the effects of NAPL degradation on 222 Rn partitioning coefficient and (iii) to investigate the relationship between the partitioning coefficient modification and NAPL chemical composition. To reach these goals, batch experiments were conducted to determine 222 Rn soil production and water-NAPL partitioning coefficient (Kn-w) in fresh and degraded complex NAPL mixtures. These experiments aim at better characterizing the ability of 222 Rn method to delineate NAPL pollution at contaminated sites.

Material and methods

Porous media

The porous media used is this study is an alluvial sand from the Aquitaine basin (France). It was sampled in a natural soil and sieved in order to only retain the fine fraction (710 -250 µm) which presents higher 222 Rn emanation coefficient [START_REF] Chitra | Study of Radon and Thoron exhalation from soil samples of different grain sizes[END_REF]. The density of this soil fraction was measured using a pycnometer [START_REF] Rodier | Eaux naturelles, eaux résiduaires[END_REF].

Reagents

Six NAPLs were used in this study. Two of them are commercial "fresh" gasoline (SP98) and diesel fuel, both obtained from a pump at a road fuel station (Casino supermarket, France). Four were obtained from the degradation of both "fresh" NAPLs following two degradation paths (described below). For NAPLs dilution prior liquid GC-MS injections, n-heptane solvent (n-Heptane, 99+%, residues analysis, ACROS Organic, UK) was used.

NAPL characterization and degradation

NAPLs density

As for the porous media, NAPLs densities were characterized using a pycnometer [START_REF] Rodier | Eaux naturelles, eaux résiduaires[END_REF].

GC-MS analysis

In order to characterize chemical compositions of fresh and altered NAPLs, GC-MS analyses were conducted. These analyses were performed using two devices to increase the separation and thus identification ability of this study, the first and second one performing liquid and Head-Space (HS) injections, respectively. Indeed, HS-GC-MS technique permits the detection of the most volatile compounds, and has a low detection limit, suitable for diesel fuel compounds identification (D [START_REF] Auria | Photochemical degradation of crude oil: Comparison between direct irradiation, photocatalysis, and photocatalysis on zeolite[END_REF][START_REF] Safarova | Gas chromatography-mass spectrometry with headspace for the analysis of volatile organic compounds in waste water[END_REF]. The liquid GC-MS is also suitable for NAPL investigation as they contain heavy hydrocarbons with long chain, easily detectable using this technique (D [START_REF] Auria | Photochemical degradation of crude oil: Comparison between direct irradiation, photocatalysis, and photocatalysis on zeolite[END_REF]. For both analytical systems, ultra-high purity He (Alphagaz 2, Air Liquide, France) was used as carrier gas.

Liquid injections were performed on a GC (7820A, Agilent, USA) equipped with a low polarity HP-5ms (30 m × 250 µm × 0.25 µm, Agilent, USA) column and coupled with a mass spectrometer (5977E, Agilent, USA) operated with an electron ionization (EI) source. The GC operating parameters for the liquid injections were: splitless mode injection of 1 µl (NAPLs diluted at 2 mg. L -1 ) at 280°C with a constant flow rate of 1 mL min -1 . The primary oven temperature was programmed at 50°C during 5 min then ramping at 5°C min -1 to 300°C and hold for 20 min.

Head-Space (HS) injections were performed on a GC (8860, Agilent, USA) equipped with an intermediate polarity Rxi-624 Sil MS (30 m x 250 µm x 1.4 µm, Restek, USA) column, which is more appropriate for volatile compounds separation, coupled to a mass spectrometer (5977B, Agilent, USA) containing a EI-Xtr source. The GC operating parameters for the HS injections were: split ratio (20:1) mode injection of 0.5 mL at 280°C with a constant flow rate of 1.5 mL min -1 . The primary oven temperature was 35°C during 1 min, then ramping at 5°C min - 1 to 300 °C and hold for 20 min. Prior HS injections, each vial was incubated at 60°C for 30 min and head-space phase sampled with a syringe heated at 60°C. The MS parameters were the same for both devices: electron ionization mode with an electron energy of 70 eV. The ion source and quad temperatures were 230 and 150°C, respectively. MS acquisition was done in SCAN mode, analyzing m/z between 25 and 300 amu and included a 5 min solvent delay for liquid injections. Chromatograms were interpreted with Masshunter Qual software (Agilent, USA) and mass spectrum compared to the literature [START_REF] Turner | Comparing the effects of weathering and microbial degradation on gasoline using principal components analysis[END_REF][START_REF] Naggar | Hydrocarbon compositions and physicochemical characteristics for the determination of gasoline quality: An implication from gas chromatographic fingerprints[END_REF] and to the NIST MS 2.2 2017 database.

A semi-quantification was applied for the samples. The proportion of different families (linearalkanes, ramified-alkanes, monoaromatics, cycloalkanes) was integrated. For that purpose, the proportion of each family (%) class was calculated by dividing the sum of the area of different compounds of each family by the sum of the peak areas of all analyzed compounds of fresh NAPL (TIC) and multiplied by 100.

Degradation of commercial NAPLs

As it is difficult to mimic natural biodegradation under laboratory conditions "fresh" NAPLs were artificially degraded using two different methods: evaporation and UV degradation.

Concerning the first one, a simple 50% and 30% weight evaporation of the gasoline and diesel fuel, respectively, was performed in order to remove the most volatile compounds. For that purpose, 700 g of fresh NAPLs were placed in a beaker (200 cm 2 ) and exposed at open air under the hood for two weeks and 2 hours for diesel fuel and gasoline, respectively. The photodegradation experiments were carried out in a photolytic reactor which consists in a 1 L glass bottle. A UV light (TUV PL-L 95w/4P HO, 250 nm, Philips) was placed close to the reactor and the set up was wrapped with aluminum foil to avoid radiation release. A mass of 350 g of fresh NAPL was inserted into the reactor and exposed under UV light for two hours at room temperature with magnetic stirring (110 rpm).

Batch experiments

In order to determine the evolution of 222 Rn partitioning coefficient between gas and NAPL, depending on NAPL chemical composition, eight sets of batch experiments were conducted in this study, each set performed with 6 ( 222 Rn production) or 6 (Kn-w determination) batches presenting different fluids contents. The two first sets were dedicated to the measurement of the 222 Rn production of the porous media coming from the same area, but at different depths (20 and 70 cm) in order to investigate the 222 Rn production variability of a large volume of soil.

The third and fourth sets of batch were dedicated to the determination of the partitioning coefficient of the fresh gasoline and diesel fuel (14 batches). The sets 5-8 permitted this characterization for artificially degraded commercial NAPL mixtures.

All the different sets of experiments were performed using 1 L glass bottles sealed with gas tight pre-perforated rubber stoppers as they prevent any gas linkage [START_REF] Cohen | Laboratory-scale experimental and modelling investigations of 222Rn profiles in chemically heterogeneous LNAPL contaminated vadose zones[END_REF]. Gas leakage was checked for every batch by lowering the pressure in the batch and by monitoring the pressure during 5 min. Then, the atmospheric pressure was restored using a syringe needle.

A mass ms (~ 700g) of sieved soil was chosen for each batch. Different water and NAPL (if applicable) contents were chosen and mixed with the porous media prior insertion of the mixture in the batch. For batches with NAPL, prior NAPL contamination, the dry porous media was moistened with a desired volumetric water content (θw= 0.02) in order to better mimic natural conditions. For each set of batches containing the different NAPLs (fresh and degraded), one batch was dedicated to the measurement of the 222 Rn activity without NAPL at a water content similar to the batches with NAPL (θw=0.02), referred hereafter as "check-batches".

These check-batches were used in order to verify the 222 Rn production for the amount of soil used for each set of batches. The batch reactors were left for 25-30 days to reach radioactive equilibrium before 222 Rn activity measurement [START_REF] Höhener | Radon-222 as a tracer for nonaqueous phase liquid in the vadose zone: Experiments and analytical model[END_REF].

222 Rn activity measurements

Scintillation flasks of 125 cm 3 (Algade, France) were used for 222 Rn measurements. First, a pump (Neuberger 816, KNF, Germany) was used to vacuum the flasks (-850 to -900 mbar).

Then, the soil-gas from the batch was extracted by suction, using a steel needle linked to a valve. The flasks were inserted into the counter chamber of a portable alpha counter (CAPP2, Algade France) and kept in the dark for 10 min. After radioactive equilibrium, 222

Results

Porous media and NAPLs densities

The density of the PM is 2631 ± 4.2 kg.m -3 . Concerning NAPLs, fresh, UV-degraded and evaporated diesel fuel densities are about 813 ± 3.8, 812 ± 3.8 and 843 ± 3.8 kg m -3 , respectively, while they are about 748 ± 3.8, 746 ± 3.8 and 796 ± 3.8 kg m -3 for fresh, UVdegraded and evaporated gasoline, respectively. Thus, significant density differences can be observed for NAPL evaporation with an increase of about 4 and 6% for diesel fuel and gasoline, respectively.

222 Rn production of Porous media

The results concerning the soil 222 Rn production (ECRa) in the different batches are presented in Fig. 1. The results are presented in function of the batches water content (θw). For the 20 cm depth soil, ECRa increases rapidly from 1.49 ± 0.25 Bq kg -1 (dry sample) to 2.65 ± 0.25 Bq kg - 1 (θw 0.02). Then, the ECRa decreases and remain relatively constant (mean of 2.49 ± 0.13 Bq kg -1 ) for larger water contents (θw 0.04 -0.1). Concerning the 70 cm depth soil, the production follows the same behavior but presents lower values, with for the dry sample, an ECRa value of 0.95 ± 0.25 Bq kg -1 which increases to 1.33 ± 0.32 Bq kg -1 (θw 0.1) with a mean of 1.29 ± 0.34

Bq kg -1 . The 222 Rn activities measured in the production batch with a water content of θw = 0.02 are 2090 ± 264 Bq m -3 at 20 cm and 1005 ± 268 Bq kg -1 at 70 cm. In addition, the 222 Rn production measured in the "check-batches" (7 batches coming from the different sets) are comprised between 1.3 and 2.5 Bq kg -1 for the two sets of batches with different soils depth (Fig. 1). Since the production for the "checked batches" is in the range of the production batches, for each set of batch, the "checked batch" corresponding production was chosen instead of the mean production (Fig. 1) due to the 222 Rn production variation. The figure 2b shows the 222 Rn activities for the batches containing UV-degraded diesel fuel for different NAPL contents. This set shows, like for the fresh diesel fuel, but more sharply, a decrease of the 222 Rn activity with the increase of the NAPL content (356 ± 63 Bq.m -3 , NAPL θn = 0.2). The fitted partitioning coefficient for this altered diesel fuel is Kn-w = 74.8 ± 7.5. For the evaporated diesel (Fig. 2c), the 222 Rn activity also decreases, but at a lower intensity than the fresh and UV-degraded diesel. Indeed, the batch without diesel fuel shows a 222 Rn activity of 1413 ± 215 Bq.m -3 which is lower than for the others because of the type of soil used for this batch, and the most NAPL saturated batch presents a 222 Rn activity of 547 ± 28 Bq.m -3 (NAPL θn = 0.2). The partitioning coefficient is Kn-w = 25.1 ±.2.5.

NAPL-gas partitioning coefficient (Kn

Partitioning coefficient (Kn) of fresh and altered gasoline

For the fresh gasoline, the porous media without NAPL shows a lower activity than the diesel fuel batch set, with a 222 Rn activity of 1292 ± 121 Bq.m -3 (Fig. 3a) which is explained by the type of soil used for this batch. The increase of gasoline content in the batches lead to a decrease of the 222 Rn activity (389 ± 52 Bq.m -3 for θn = 0.2). The fitted partitioning coefficient was also calculated and the best fit is obtained for a Kn-w = 37.4 ± 5.6. The UV-degraded gasoline (Fig. 3b) also shows a decrease of the 222 Rn activities, but to a lesser extent, reaching 658 ± 24 Bq.m -3 (θn = 0.2). The partitioning coefficient between NAPL and water is Kn-w = 33 ± 4.9. The evaporated gasoline shows a 222 Rn activity of 1995± 195 Bq.m -3 (θn = 0) decreasing to 673 ± 70 Bq.m -3 (θn = 0.2), leading to a Kn-w of 30.8 ± 4.6. The table 1 summarizes the different Kn-w found is this study (see SI for statistical results).

Molecular investigation of the fresh and degraded NAPLs, identification of byproducts

Chemical composition of diesel fuel

The most volatile compounds identified using the HS-GCMS are presented in the figure 4. The fresh diesel fuel chromatogram (Fig. 4a, Table 2) is principally composed by linear n-alkanes ranging from n-C5 and n-C15 and by branched n-alkanes. Other compounds such as cyclic hydrocarbons, alkenes and BTEX are also encountered. The chromatogram corresponding to the UV treatment (Fig. 4b, Table 2) is rather similar to the fresh diesel without any total loss of compounds. However, a general decrease of the peaks intensity is observed with a TIC area representing 73 % of the fresh diesel fuel. The percentage of the different compounds in the different fractions (<C10 and >C10) confirmed the TIC area decrease, mainly in the <C10 fraction for the UV-degraded diesel fuel. The chromatogram corresponding to the evaporation treatment is different (Fig. 4c, Table 2). The first 12 minutes of the TIC is characterized by an absence of peaks, corresponding to the loss of the most volatile compounds (ranging from n-C5 and n-C8). The area of the evaporated diesel TIC represents 16% of the fresh diesel fuel.

The percentage of the different compounds in the different fractions also shows a decrease in the evaporated diesel fuel mainly in the <C10 fraction.

The liquid GC-MS in scan mode permits to identify the different major hydrocarbons of moderate to low volatility present in the fresh diesel fuel (Fig. 5a, Table 2). The diesel fuel matrix is complex and the separation of the different compounds is limited, reducing the possible identification of the different compounds. The fresh diesel fuel is principally composed by n-alkanes such as linear n-alkanes and branched n-alkanes ranging from n-C8 to n-C27. The diesel fuel is also composed by alkenes, cyclo-alkanes and BTEX. The photodegraded diesel fuel (Fig. 5b) shows a similar chromatogram pattern with the same by-products and similar intensity. The percentages of the different families in the different fractions (< C10, C10 -C15, >C15) do not show high variations for the fresh and UV-degraded diesel fuel. A slight increase of the cycloalkanes and methyl alkanes is observed in the >C15 fraction for the UV-degraded diesel fuel (Table 2). In contrary, the diesel fuel artificially evaporated (Fig. 5c) under the hood (30 % in weight) shows variations of the chromatogram compared to fresh and UV-degraded diesel fuel. The lightest fraction of the diesel fuel (until 17 min) is vaporized resulting in the absence of peaks. The percentages show high decrease of the different compounds in the different fractions, mainly in the <C10 and C10 -C15 fractions, containing in particular cycloalkanes.

Chemical composition of gasoline

The most volatized compounds are presented in the figure 6. The fresh gasoline chromatogram (Fig. 6a, Table 2) is composed by linear n-alkanes, alkenes (n-C5 to n-C8), branched n-alkanes, alkenes and cyclic hydrocarbons. In addition, BTEX represents a large fraction of the chromatogram, eluting between 10 and 20 min. The chromatogram corresponding to the UV treatment (Fig. 6b, Table 2) is rather similar to the fresh gasoline with similar peaks intensity in TIC area. The percentage of the different compounds in the different fractions (<C5 and >C5) also confirms the general observations with the TIC with similar percentages in the different fractions. The chromatogram corresponding to the evaporation treatment is slightly different (Fig. 6c, Table 2). Several peaks at the beginning of the chromatogram, corresponding to alkanes and alkenes, disappeared and the area of the evaporated gasoline TIC represents 96%

of the fresh gasoline. The percentage of the different compounds in the different fractions also shows a decrease in the evaporated gasoline in the <C5 fraction. The >C5 fractions reveals an increase in the different fractions, resulting from a concentration of the compounds into NAPL due to evaporation. Indeed, the evaporation results in the removal of the lower boiling compounds and a relative abundance increase of the higher boiling compounds into NAPL, leading to higher partial pressure in the gas phase (Raoult law).

The fresh gasoline (Fig. 7a, table 2) is characterized by low molecular-mass hydrocarbons mainly eluting before 10 min. Monoaromatic compounds are predominant in the sample.

Alkanes (n-C8 to n-C16), alkenes, cycloalcanes and isoalkanes complete the composition. The UV-degraded gasoline (Fig. 7b, Table 2) chromatogram pattern is similar to the fresh chromatogram pattern with the predominance of low molecular-mass hydrocarbons at similar intensity. In contrast to the evaporated diesel fuel (Fig. 7c), the evaporated gasoline does not clearly show difference with the fresh gasoline. The percentage of the different compounds in the <C10 and >C10 fractions for the fresh, UV-degraded and evaporated gasoline does not show clear and logical variations (Table 2).

Discussion

Radon production in the porous media

Radon production can evolve in two different ways depending on soil moisture. Low soil moisture contents can lead to an increase of soil emanation [START_REF] Nazaroff | Radon transport from soil to air[END_REF][START_REF] Hosoda | Effect of soil moisture content on radon and thoron exhalation[END_REF] in comparison with dry soil. Actually, for dry soil, a significant fraction of 222 Rn that escape from a grain due to recoil enters in another grain and thus does not stay in porosity, inducing low ECRa as can be seen for the first batch without water (Fig. 1). When a small amount of water is added, a higher fraction of 222 Rn is trapped in the porosity, leading to an increase of ECRa. This behavior is also observed in this study with the increase of ECRa for the batches with small content of water (θw 0.01 -0.02) (Fig. 1). However, higher soil moisture reduces gas mobility.

Different factors influence the 222 Rn emanation from soils (ie. temperature, soil physical and chemical properties). When the temperatures are lower, the number of radon atoms adsorbed to particles increases, leading to a decrease of the 222 Rn activity [START_REF] Baskaran | Radon: A tracer for geological, geophysical and geochemical studies[END_REF]. The different set of batches were carried out at different time and the room temperature changed slightly (from 25 °C to 15 °C). This temperature change could explain the variation of 222 Rn activity.

Another explanation can come from the soil material used in this study. The soil was sampled from a pond area, close to the laboratory. A large amount of soil was necessary for the different set of batches and a hole of approximately 1.5 m deep was dug. The composition of the soil was not the same from the surface and the bottom with more fine particles encountered deeper.

This soil composition variation could explain the 222 Rn activity variation between the batch sets. [START_REF] Thu | The effects of some soil characteristics on radon emanation and diffusion[END_REF] investigated the 222 Rn emanation and diffusion from soil in function of different soil compositions. They noted a dependence of the radon emanation on iron content and pH.

Molecular composition

Diesel fuel is a complex mixture of different hydrocarbons. The major compounds encountered are straight n-alkanes, isoprenoids (branched n-alkanes), cyclo-alkanes and aromatics [START_REF] Christensen | Solubility of Oil products in groundwater[END_REF]. A typical fresh diesel fuel chromatogram is characterized by a dominance of n-alkanes peaks, appearing in a regular pattern and covering all the chromatogram [START_REF] Christensen | Method for determining the age of diesel oil spills in the soil[END_REF]. Gasoline fuel is obtained from the distillation and cracking of crude oil [START_REF] Naggar | Hydrocarbon compositions and physicochemical characteristics for the determination of gasoline quality: An implication from gas chromatographic fingerprints[END_REF]. Cracking produces, from long chain alkanes, smaller alkenes at high temperature. Typical gasoline fuel is composed by over 200 petroleum-derived chemicals [START_REF] Naggar | Hydrocarbon compositions and physicochemical characteristics for the determination of gasoline quality: An implication from gas chromatographic fingerprints[END_REF] with a dominance of aromatic compounds and branched alkanes over n-alkanes.

The fresh commercial diesel fuel and gasoline used in this study, characterized with MS in scan mode using GC-MS reveals similar patterns than the ones observed in literature. On the contrary, the artificial degradations carried out in this study permit to reveal different behaviors.

The different chromatographic techniques employed in this study do not permit to observe any difference concerning the UV-light degradation with the fresh material except a diminution of the area of the total chromatogram for the UV-degradation compared to the fresh diesel fuel with the HS-GCMS analyses. [START_REF] Garrett | Photooxidation of crude oils[END_REF] also performed artificial weathering of Alaskan crude oil, by its exposure to UV-light, and observed no effect of the illumination on the total ion chromatograms as well. However, the use of thin layer chromatography showed variations with the conversion of the aromatics hydrocarbons to resins or polar compounds. [START_REF] Douglas | The OSSA II pipeline oil spill: the character and weathering of the spilled oil[END_REF] also investigated the effect of UV light on oil molecular composition using Single Ion Monitoring (SIM) mode. They showed that large polycyclic aromatic hydrocarbons are more affected by photooxidation as well as the more alkylated compounds.

Further investigation of the degraded products, focusing on certain molecules could help to distinguish some variations between fresh and UV-degraded chromatograms patterns.

The artificial evaporation effect on the molecular composition is quite different from the artificial photooxidation. In this study, the artificial diesel fuel evaporation under the hood removes the compounds presenting a chromatographic retention time below 12 min, as observed in liquid and head-space chromatographs (Fig 4c and5c). [START_REF] Villa | Diesel degradation in soil by Fenton process[END_REF] studied the effects of the evaporation on the molecular composition of diesel fuel. They showed a loss of hydrocarbons with chain lengths less than 14 carbons in addition to other unsaturated and cyclic hydrocarbons. [START_REF] Prince | The roles of photooxidation and biodegradation in long-term weathering of crude and heavy fuel oils[END_REF] also showed the release of the lightest compounds (C4 -C18) in result to the evaporative process. As a general feature, the evaporative process will start with the removal of all components with short retention times including n-alkanes and isoprenoids. Sometimes, the process can lead to the evaporation of components with higher retention times. However, the ratio between the n-alkanes and isoprenoids will not change [START_REF] Wang | Effect of bioremediation on polycyclic aromatic hydrocarbon residues in soil[END_REF]. In the present study, the gasoline chromatograms do not show any variation of the composition or peak intensity between fresh and evaporated material except a removal of the first peaks (first two minutes, Fig. 7c) and a relative increase of the high boiling compounds in the HS-GCMS. [START_REF] Turner | Comparing the effects of weathering and microbial degradation on gasoline using principal components analysis[END_REF] also studied the effects of weathering (evaporation) on the molecular composition of gasoline using liquid GCMS. They reported no special variation of the chromatogram pattern between a 0% weathered sample and 50%

weathered sample. This could explain the absence of variation in this study with gasoline subject to 50% evaporation in weight.

Determination of 222 Rn partitioning coefficients of fresh and aged NAPLs

Very little data is available concerning the radon partitioning coefficient for NAPL mixtures. 3). To our knowledge, no data is currently available concerning the partitioning coefficient of complex degraded NAPLs.

On the other side, pure NAPLs such as Benzene and Toluene radon partitioning coefficient can be encountered in the literature [START_REF] Clever | Krypton, Xenon and Radon[END_REF][START_REF] Abraham | Hydrogen bonding: XXXV. Relationship between high-performance liquid chromatography capacity factors and water-octanol partition coefficients[END_REF]Schubert et al., 2007a, b).

The table 3 gathers several coefficient partitions of pure NAPLs of interest from the literature.

The next paragraph is dedicated to the comparison of the different complex NAPLs mixtures and pure NAPLs.

First of all, the results show that, in spite of a wide range covered by the radon partitioning coefficients , the different commercial NAPLs investigated have a strong affinity with radon. The fresh diesel fuel shows higher partitioning coefficient than fresh gasoline. For both fresh NAPL used in this study, the partitioning coefficient Kn-w are similar to those presented in [START_REF] Schubert | Determination of radon partition coefficients between water and organic liquids and their utilization for the assessment of subsurface NAPL contamination[END_REF] (60.7 ± 6.1 vs 60 ± 1.3 and 37.4 ± 5.6 vs 38.9 ± 0.9, for diesel fuel and gasoline, respectively), despite the fact that this study used commercial mixture while [START_REF] Schubert | Determination of radon partition coefficients between water and organic liquids and their utilization for the assessment of subsurface NAPL contamination[END_REF] used simplified synthetic mixtures. Indeed, the gasoline used in [START_REF] Schubert | Determination of radon partition coefficients between water and organic liquids and their utilization for the assessment of subsurface NAPL contamination[END_REF] study was a laboratory made mixture composed by 50 % of iso-octane, 40 % of BTEX and 10 % alkene while the commercial gasoline used in this study is composed by multiple compounds and especially a large proportion of BTEX. Coefficient partition of several BTEX has been determined in the literature indicating intermediate table 3). This could explain the lower Kn-w encountered for gasoline.

The diesel fuel used in [START_REF] Schubert | Determination of radon partition coefficients between water and organic liquids and their utilization for the assessment of subsurface NAPL contamination[END_REF] was composed at 60% by hexadecane and 15% cyclohexane while the one used in this study is mainly composed by different alkanes from C8 to C27. One explanation for this Kn-w similarity is that the compounds used by [START_REF] Schubert | Determination of radon partition coefficients between water and organic liquids and their utilization for the assessment of subsurface NAPL contamination[END_REF] may drive the partitioning coefficient behavior. The main result brought by this study is the variation of the partitioning coefficient (compared to fresh NAPLs) when the diesel fuel is degraded. On the other hand, the gasoline did not show any significant variations related to degradation, probably due to the too slight degradation (see part 4.2). The evaporation of 50% in weight of the gasoline was extremely rapid. However, the chromatogram pattern does not show large differences for the evaporation treatment. This could be due to the evaporation of an extremely volatile compound. The evaporation leads to a reduction of the diesel fuel affinity for 222 Rn, whereas the UV-degradation engenders higher affinity of diesel fuel for 222 Rn. This feature demonstrates that for diesel, the degradation processes will change the affinity of NAPLs toward 222 Rn compared to fresh products. The partitioning coefficients gathered in the literature (Table 3) may explain the variations of Kn-w. When a diesel fuel is artificially evaporated, the results show a removal of the lightest fraction which is composed by short alkanes chains and cycloalcanes. The Kn-w of hexane and cyclohexanes are 58.1 and 63.3, respectively. When those molecules are removed by evaporation, a modification of the Kn-w is then expected, as measured in this study. In addition, the hexadecane Kn-w has also been reported with a value of 33.3 [START_REF] Abraham | Hydrogen bonding: XXXV. Relationship between high-performance liquid chromatography capacity factors and water-octanol partition coefficients[END_REF].

As Schubert et al., (2007a) stated, the use of Radon method is not applicable without restrictions. Indeed, as found in this study, the partitioning coefficient evolves in relation with the NAPL alteration. This change in the partitioning coefficient will lead to incorrect interpretation of the Radon Deficit Factor. A simple calculation of the NAPL saturation (eq. 3)

permits to estimate the NAPL saturation changes in relation with the Kn-w. The use of a fresh diesel fuel Kn-w (60) instead of a Kn-w of evaporated diesel fuel (26) in an area where diesel fuel has been exposed to air will lead to an overestimation of approximatively 50% of the NAPL saturation. In the same way, if a Kn-w of a fresh diesel fuel is used instead of fresh gasoline, the overestimation of the NAPL saturation would be about 30%. However, semi-quantitative measurements are still operable since 222 Rn shows a strong affinity to NAPLs either fresh or degraded.

In this study, the different pure compounds forming the diesel fuel and gasoline present a Kn-w ranging from 33 to 63 (fresh compounds). The fresh diesel fuel detains a Kn-w of 60.7 and the gasoline a Kn-w of 37. This could suggest that the Kn-w for this kind of NAPLs mixtures should reasonably ranging between 30 and 60. Despite the remaining uncertainty in the Kn of one degraded NAPL, the presented results allowed to specify the full range of Rn for field NAPL.

Conclusion

This study investigates the variations of the partitioning coefficient (Kn-w) of different fresh commercial NAPL mixtures (diesel fuel and gasoline) and commercial NAPL mixtures degradations (evaporation and photooxidation). The results show different partitioning coefficients of the fresh diesel fuel and gasoline which are similar with previous Kn-w reported in the literature. The NAPL artificial degradations carried out in this study engender variations of the Kn-w. The evaporated diesel fuel shows lower Kn-w than the fresh diesel fuel whereas the UV-degraded diesel fuel shows higher Kn-w than fresh diesel fuel. For the gasoline, the variations of the Kn-w in relation with the degradation processes are more tenuous. The molecular characterization of the diesel fuel, using GCMS in scan mode, do not permit to differentiate fresh and UV-degraded products (except the diminution of the intensity concerning the HS approach). The evaporated diesel fuel chromatogram is different with the absence of peaks at the beginning of the chromatogram (first 17 min). The gasoline molecular composition is not variable between the different treatments using the GCMS method in scan mode, except a removal of the first peaks (first 2 min) in the HS approach. As previously reported in the literature, the 222 Rn is a good proxy parameter for soil NAPL delineation. In the calculation and modelling, the partitioning coefficient is of pivotal importance. This study emphasis the importance of the study of the Kn-w variability as it can lead to an false estimation of NAPL saturation. Therefore, it is extremely important to explore the effects of different parameters that could modify the Kn-w. This study reveals that NAPL degradation modify the partitioning coefficient in relation with the molecular composition. Future researches are thus needed to decipher the relationship between NAPL molecular composition and 222 Rn partitioning coefficient Kn-w in order to:

better understand the evaporation intensity effects on the diesel fuel and gasoline Kn-w

  Rn activity in each flask was determined six times with counting times of 20 min. Radon background, referred as blank values was measured on the same flask, under the same counting conditions and were subtracted. The yields of each flask were taken into account and the radon activity expressed in Bq m -3 was obtained using previously established calibration. The 222 Rn production (Bq kg -1 ) was then calculated (equation 1) taking into account the batch properties (mass of soil, water and gas contents):222 Rn activity (Bq.m -3 ), θw the water content ( -), KH the gas-water partitioning coefficient ( -), θg the gas content ( -), Kn the NAPL-gas coefficient ( -), θn the NAPL content, ms the mass of soil (kg), Vg the volume of gas (m 3 ), E the 222 Rn emanation coefficient ( -) and CRa the solid226 Ra content (Bq kg -1 ). The NAPL-water partitioning coefficient was also calculated: Eq. (2) Kn-w = Kn×KH In order to test the effect of Kn-w modification on NAPL saturation (Sn), the equation presented in[START_REF] Hunkeler | Rn-222 as a partitioning tracer to detest diesel fuel contamination in aquifers: laboratory study and field observations[END_REF] was used:Eq. (3) Sn = (Ae napl=0 /Ae napl>0 -1)/(Kn-w-1)With Sn the NAPL saturation ( -), Ae napl=0 the 222 Rn activity in the batches without NAPL (Bq.m -3 ), Ae napl>0 the 222 Rn activity in the batches with NAPL (Bq.m -3 ) and Kn-w the NAPL water partition of 222 Rn ( -).

  coefficient (Kn) of fresh and altered diesel fuelThe222 Rn activities in the batches containing fresh diesel fuel at different volumetric contents are presented in Figure2a. The Supplementary Information (SI) presents the statistical results permitting to conclude to the significant difference between the calculated Kn-w. The 222 Rn activities are presented in function of the batch NAPL contents. The batch without NAPL shows a 222 Rn activity of 1991 ± 114 Bq.m -3 , similar to the production experiment(2210 ± 200 Bq.m -3 ). The increase of the NAPL content in the porous media leads to the decrease of the 222 Rn activity reaching a value of 429 ± 24 Bq.m -3 for θn = 0.2. The theoretical Rn activity calculated from Eq.1 with different NAPL contents are also presented in figure2a(black curve). The best fit with the experimental data is obtained using a Kn-w = 60.7 ± 6.1.

  [START_REF] Hunkeler | Rn-222 as a partitioning tracer to detest diesel fuel contamination in aquifers: laboratory study and field observations[END_REF] measured the 222 Rn partitioning coefficient for an unspecified diesel fuel and Schubert et al. (2007a) determined 222 Rn partitioning coefficient for three synthetic NAPL mixtures representing gasoline, and diesel fuel (Table

Fig. 1 .

 1 Fig. 1. 222 Rn production (ECRa) for the soil used in this study in relation with the water content (θw). Grey dashed line corresponding to ECRa mean (dry sample not included).

Fig. 2

 2 Fig. 2 Experimental (black dots) and theoretical (black curve) 222 Rn activity (Bq.m -3 ) for (a) Fresh diesel fuel, (b) UV-degraded diesel fuel and, (c) evaporated diesel fuel as a function of the NAPL content (θn). Dotted lines represent errors of 15% in the gas-diesel partitioning-coefficient.

Fig. 5

 5 Fig. 5 Liquid GC-MS in scan mode chromatograms of the (a) fresh diesel, (b) UV-degraded diesel and, (c) evaporated diesel. The C8 to C27 corresponds to the linear n-alkanes, triangle refers to ramified alkanes, circle refers to cycloalkanes, stars correspond to BTEX.

Fig. 6

 6 Fig. 6 Head-Space GC-MS in scan mode chromatograms of the (a) fresh gasoline, (b) UV-degraded gasoline and, (c) evaporated gasoline. The C4 to C8 correspond to the linear n-alkanes, triangle refers to ramified alkanes, circle refers to cycloalkanes.

Fig. 7

 7 Fig. 7 Liquid GC-MS in scan mode chromatograms of the (a) fresh gasoline, (b) UV-degraded gasoline and, (c) evaporated gasoline. The C4 to C10 correspond to the linear n-alkanes, triangle refers to ramified alkanes, circle refers to cycloalkanes.

Acknowledgements

The authors would like to thank the financial support of the Carnot ISIFoR and IdEx for this study.

-Investigate the effects of different degradation processes on the same NAPL mixture (evaporation coupled to photooxidation, evaporation coupled to microbial degradation).

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Diesel fuel Gasoline

Fresh 60.7 ± 6.1 37.4 ± 5.6

UV-degraded 74.8 ± 7.5 33 ± 4.9 Evaporated 25.1 ± 2.5 30.8 ± 4.6

Table 1. NAPL-water partitioning coefficient for the fresh and altered diesel fuel and gasoline.

Supplementary information

This supplementary material presents the statistical results permitting to indicate that the Kn-w calculated from the equation 1 in the paper are significantly different. To test the significant differences between the groups, ANCOVA was used. For the ANCOVA, NAPL content (θ)

was treated as fixed factors and the activity as the covariates. Statistical tests were performed using the software Xcel Stat (version 2021.1) with the significant level set at 0.05. All the variables were normalized by 1/A transformation prior to analysis.

Step 1: linear approximation of the equation : 𝐴 = The linear approximation is: We found a significant linear regression between the NAPL content and the fresh diesel (F = 3.72; p < 0.05). However, the NAPL did not show significant linear regression between UV degraded diesel fuel and evaporated diesel fuel (F = 2.45 p > 0.05; F = -0.20 p> 0.05). We can state that the different 1/A of the diesel are significantly different. We found a significant linear regression between the NAPL content and the evaporated gasoline (F = 4.96; p < 0.05). However, the NAPL did not show significant linear regression between UV degraded gasoline and fresh gasoline (F = 0.49 p > 0.05; F = 0.55 p> 0.05). We can state that the different 1/A of the diesel are significantly different.