Nicolas Macorps

Karyn Le Menach

Patrick Pardon

Sabrina Guérin-Rechdaoui

Vincent Rocher

Hélène Budzinski

Pierre Labadie
email: pierre.labadie@u-bordeaux.fr

Bioaccumulation of per-and polyfluoroalkyl substance in fish from an urban river: occurrence, patterns and investigation of potential ecological drivers

Keywords: PFAS, emerging contaminants, fish, sediment, bioaccumulation Highlights

Per-and polyfluoroalkyl substances (PFAS) are ubiquitous in aquatic environments and a recent shift toward emerging PFAS is calling for new data on their occurrence and fate. In particular, understanding the determinants of their bioaccumulation is fundamental for risk assessment purposes. However, very few studies have addressed the combined influence of potential ecological drivers of PFAS bioaccumulation in fish such as age, sex or trophic ecology. Thus, this work aimed to fill these knowledge gaps by performing a field study in the Seine River basin (France). Composite sediment and fish (European chub, Squalius Cephalus) samples were collected from four sites along a longitudinal transect to investigate the occurrence of 36 PFAS. Sediment molecular patterns were dominated by fluorotelomer sulfonamidoalkyl betaines (i.e. 6:2 and 8:2 FTAB, 46% of ∑PFAS on average), highlighting the non-negligible contribution of PFAS of emerging concern. C 9 -C 14 perfluoroalkyl carboxylic acids, perfluorooctane sulfonic acid (PFOS), perfluorooctane sulfonamide (FOSA) and 10:2 fluorotelomer sulfonate (10:2 FTSA) were detected in all fish samples. Conversely, 8:2 FTAB was detected in a few fish from the furthest downstream station only, suggesting the low bioaccessibility or the biotransformation of FTABs. ∑PFAS in fish was in the range 0.22-3.8 ng g -1 wet weight (ww) and 11-140 ng g -1 ww for muscle and liver, respectively. Fish collected upstream of Paris were significantly less contaminated than those collected downstream, pointing to urban and industrial inputs. The influence of trophic ecology and biometry on the interindividual variability of PFAS burden in fish was examined through analyses of covariance (ANCOVAs), with sampling site considered as a categorical variable.

While the latter was highly significant, diet was also influential; carbon sources and trophic level (i.e. estimated using C and N stable isotope ratios, respectively) equally explained the variability of PFAS levels in fish.

Introduction

Per-and polyfluoroalkyl substances (PFAS) are a group of persistent molecules that have been extensively monitored in the environment and human populations for over 20 years [START_REF] Giesy | Global Distribution of Perfluorooctane Sulfonate in Wildlife[END_REF][START_REF] Hansen | Compound-Specific, 237 Quantitative Characterization of Organic Fluorochemicals in Biological Matrices[END_REF]. Perfluoroalkyl carboxylates (PFCAs) and perfluoroalkyl sulfonates (PFSAs) have been reported to be widely distributed in aquatic ecosystems, including biota [START_REF] Ahrens | Polyfluoroalkyl compounds in the aquatic environment: a review of their 123 occurrence and fate[END_REF]. Perfluorooctane sulfonate (PFOS) and its salts, as well as perfluorooctane carboxylate (PFOA), have been listed under Annexes B and A of the Stockholm Convention, respectively. This pushed towards the production of replacements of long-chain PFAS like perfluoroether sulfonic acid (PFESAs) and carboxylic acid (PFECAs) [START_REF] Xiao | Emerging poly-and perfluoroalkyl substances in the aquatic environment: A 406 review of current literature[END_REF].

As a consequence, emerging PFAS were detected in surface water and sediments in recent years [START_REF] De Silva | Detection of a 194 Cyclic Perfluorinated Acid, Perfluoroethylcyclohexane Sulfonate, in the Great Lakes 195 of North America[END_REF][START_REF] Pan | 346 Worldwide Distribution of Novel Perfluoroether Carboxylic and Sulfonic Acids in 347 Surface Water[END_REF][START_REF] Joerss | Emerging per-and polyfluoroalkyl substances 257 (PFASs) in surface water and sediment of the North and Baltic Seas[END_REF][START_REF] Chen | Occurrence and Distribution of Per-and Polyfluoroalkyl 185 Substances in Tianjin, China: The Contribution of Emerging and Unknown 186 Analogues[END_REF]. These include PFESAs and PFECAs like F-53B, a chlorinated PFESA mainly used in the electroplating industry in China as PFOS alternative [START_REF] Wang | First Report of a Chinese PFOS Alternative Overlooked for 30 391 Years: Its Toxicity, Persistence, and Presence in the Environment[END_REF], HFPO-DA (trade name GenX), ADONA, used as replacement for PFOA as processing aid in fluoropolymer manufacturing [START_REF] Munoz | Analysis of F-53B, Gen-X, ADONA, and 328 emerging fluoroalkylether substances in environmental and biomonitoring samples: A 329 review[END_REF] or perfluoroethylcyclohexane sulfonate (PFECHS), found in hydraulic fluids but phased out since 2002 [START_REF] De Silva | Detection of a 194 Cyclic Perfluorinated Acid, Perfluoroethylcyclohexane Sulfonate, in the Great Lakes 195 of North America[END_REF]. PFECHS presents a lower bioaccumulation factor (BAF) than PFOS in Carassius carassius [START_REF] Wang | 394 Identification, Tissue Distribution, and Bioaccumulation Potential of Cyclic 395 Perfluorinated Sulfonic Acids Isomers in an Airport Impacted Ecosystem[END_REF] while the contrary is observed for 6:2 Cl-PFESA in zebrafish [START_REF] Tu | Bioconcentration and Metabolic Effects of 383 Emerging PFOS Alternatives in Developing Zebrafish[END_REF]. The latter was reported in Greenland marine mammals [START_REF] Gebbink | 220 Observation of emerging per-and polyfluoroalkyl substances (PFASs) in Greenland 221 marine mammals[END_REF], fish and marine organisms from China [START_REF] Shi | Tissue 368 Distribution and Whole Body Burden of the Chlorinated Polyfluoroalkyl Ether 369 Sulfonic Acid F-53B in Crucian Carp (Carassius carassius): Evidence for a Highly 370 Bioaccumulative Contaminant of Emerging Concern[END_REF][START_REF] Liu | Chlorinated Polyfluoroalkyl Ether Sulfonic Acids in Marine Organisms from 284 Bohai Sea, China: Occurrence, Temporal Variations, and Trophic Transfer Behavior[END_REF][START_REF] Wang | Target, Nontarget, and Suspect Screening and Temporal Trends of Per-and 387 Polyfluoroalkyl Substances in Marine Mammals from the South China Sea[END_REF]. HFPO-DA and ADONA have never been measured in aquatic biota and exhibit low bioaccumulation potential [START_REF] Munoz | Analysis of F-53B, Gen-X, ADONA, and 328 emerging fluoroalkylether substances in environmental and biomonitoring samples: A 329 review[END_REF]. Other alternatives that may be transformed into perfluoroalkyl acids (PFAAs) are also of concern [START_REF] Zabaleta | Biotransformation of 8:2 polyfluoroalkyl phosphate diester in 410 gilthead bream (Sparus aurata)[END_REF], like fluorotelomer betaines (FTABs), used in aqueous film forming foam formulations (AFFFs) [START_REF] Place | Identification of Novel Fluorochemicals in Aqueous Film-358 Forming Foams Used by the US Military[END_REF], and fluorotelomer sulfonates (FTSAs), used as a PFOS replacement [START_REF] Field | Properties, occurrence, and fate of fluorotelomer sulfonates[END_REF]. FTABs were previously detected in river sediments at selected locations in France [START_REF] Munoz | Analysis of zwitterionic, cationic, and anionic poly-and perfluoroalkyl 315 surfactants in sediments by liquid chromatography polarity-switching electrospray 316 ionization coupled to high resolution mass spectrometry[END_REF]. 8:2 FTAB was also found in sediment and fish from a e ganti an ha i re River (Canada) after a railway accident, with a gradual concentration decrease within a few years (Munoz et al., 2017b). Furthermore, 8:2 FTSA and 10:2 FTSA were also detected in the ha i re i er after this accident and the latter was also ubiquitous in biota from a small urban river in France [START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF]. Thus, the ever increasing number of identified and detected PFAS advocate for further studies, especially in urban rivers, based on extended lists of target compounds [START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF].

In addition, the controlling factors of PFAS bioaccumulation in fish are still not fully understood, although some drivers have been identified. PFAS bioaccumulation can be affected by their structural characteristics such as chain length (i.e. competition between short and long-chain PFAS) and functional group [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants 260 between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF][START_REF] Wen | Long-Chain 398 Perfluoroalkyl acids (PFAAs) Affect the Bioconcentration and Tissue Distribution of 399 Short-Chain PFAAs in Zebrafish (Danio rerio)[END_REF][START_REF] Lee | Concentration and distribution of per-and polyfluoroalkyl substances 268 (PFAS) in the Asan Lake area of South Korea[END_REF]. In addition, the absorption, distribution, metabolism, and elimination of these chemicals is controlled by complex interaction with biomolecules such as proteins, transporters, and phospholipids [START_REF] De Silva | PFAS Exposure Pathways for Humans and Wildlife: A Synthesis of 200 Current Knowledge and Key Gaps in Understanding[END_REF]. However, other environmental factors might also be at play. At some locations, the burden of long-chain PFAS was correlated with fish length (i.e. proxy for age, [START_REF] Mann | Observations on the age, growth, reproduction and food of the chub 295 Squalius cephalus (L.) in the River Stour, Dorset[END_REF]) (Lam et al., 2014;[START_REF] Babut | Per-and poly-fluoroalkyl compounds in freshwater 154 fish from the Rhône River: Influence of fish size, diet, prey contamination and 155 biotransformation[END_REF], while no association was observed at other sites [START_REF] Åkerblom | Variation and accumulation 129 patterns of poly-and perfluoroalkyl substances (PFAS) in European perch (Perca 130 fluviatilis) across a gradient of pristine Swedish lakes[END_REF][START_REF] Langberg | Bioaccumulation of Fluorotelomer Sulfonates and Perfluoroalkyl Acids in 264 Marine Organisms Living in Aqueous Film-Forming Foam Impacted Waters[END_REF]. At some Nordic locations, ∑PFAS was negatively correlated with δ 15 N (i.e. proxy for trophic position), suggesting the absence of biomagnification [START_REF] Lescord | Perfluorinated and Polyfluorinated Compounds in Lake Food Webs 272 from the Canadian High Arctic[END_REF][START_REF] Åkerblom | Variation and accumulation 129 patterns of poly-and perfluoroalkyl substances (PFAS) in European perch (Perca 130 fluviatilis) across a gradient of pristine Swedish lakes[END_REF], while trophic magnification factors > 1 were reported elsewhere [START_REF] Loi | 287 Trophic Magnification of Poly-and Perfluorinated Compounds in a Subtropical Food 288 Web[END_REF][START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF]. Using δ 15 N and δ 13 C (i.e. proxy for carbon sources) as indicators of trophic ecology, diet was identified as a relevant factor to explain the interspecific bioaccumulation pattern of long-chain PFAS in fish from the Rhone River, e.g. perfluorononanoic acid (PFNA), perfluoroundecanoic acid (PFUnDA), PFOS and perfluorooctane sulfonamide (FOSA) [START_REF] Babut | Per-and poly-fluoroalkyl compounds in freshwater 154 fish from the Rhône River: Influence of fish size, diet, prey contamination and 155 biotransformation[END_REF]. Overall, studies combining a wide array of proxies to explain the interindividual (i.e. intraspecific) variability of PFAS contamination levels are relatively scarce. Understanding the relative influence of bioaccumulation determinants is, however, of primary importance for predicting PFAS burden and for risk assessment purposes [START_REF] Lopes | Is PCBs 291 concentration variability between and within freshwater fish species explained by their 292 contamination pathways?[END_REF].The drivers of the intraspecific variability of PFAS burden have generally been studied independently; they are still poorly documented and clearly deserve deeper investigation. This is a major issue to get further insight into the dynamics of PFAS in trophic webs but also to implement biota monitoring strategies, e.g. in the context of the European Water Framework Directive [START_REF] Fliedner | Biota 216 monitoring under the Water Framework Directive: On tissue choice and fish species 217 selection[END_REF].

In this context, the present study focused on the heavily urbanized Seine River basin and on an omnivorous cyprinid, the European Chub Squalius Cephalus, frequently used in biomonitoring studies as it is widely distributed in European freshwaters [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants 260 between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF][START_REF] Nyeste | Age and diet-specific trace element accumulation patterns in 333 different tissues of chub (Squalius cephalus): Juveniles are useful bioindicators of 334 recent pollution[END_REF]. Previous studies have demonstrated the widespread occurrence of PFAS in this river [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants 260 between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF][START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF], resulting from diffuse and point sources (i.e. fluorochemical plant and waste water treatment plants).

To investigate the potential contamination gradient induced by urban and industrial inputs into the Seine River, an extended list of legacy and infrequently reported emerging compounds was analyzed. We explored the PFAS spatial variability in sediment and fish along a longitudinal transect, i.e. upstream and downstream of the Greater Paris conurbation.

Furthermore, tissue distribution was considered (i.e. dorsal muscle vs liver) and we aimed to investigate the potential ecological drivers of PFAS bioaccumulation and its intraspecific variability in a model fish species, through multivariate analysis (i.e. considering biometry and indicators of trophic ecology).

Material and Methods

Chemicals.

The full list of reagents and chemicals is provided in the Supporting information (SI). L-PFOS herein refers to the linear isomer of PFOS and Br-PFOS to the sum of branched isomers. Analyte name, acronym and corresponding internal standard (IS) are provided in Table S1.

Study site

The Seine River flows through the Greater Paris with a relatively low mean daily discharge of 312 m 3 .s -1 over the 1974-2021 period. This flow is lower in summer, i.e. 150 m 3 .s -1 on average over the last 20 years, especially in 2019 (< 100 m 3 .s -1 ) (BanqueHydro). The Seine River basin is under a strong urban influence, hosting a population of approximately 16 million inhabitants.

Based on the hypothesis of a longitudinal contamination gradient in the Seine River basin due to urban inputs, the sampling strategy relied on the fish monitoring scheme implemented for over two decades on the Seine and Marne rivers by the SIAAP MeSeine network [START_REF] Azimi | Influence of the water quality improvement on fish population in 150 the Seine River (Paris, France) over the 1990-2013 period[END_REF]. Four sampling sites were investigated (Figure S1). Gournay-sur-Marne (48.51° N, 2.34° E), located on the Marne River 25 km upstream from its confluence with the Seine River, was used as a relative reference site not directly impacted by the Paris conurbation (Goutte et al., 2018). Levallois (48.54° N, 2.17° E) and Le Pecq (48.53° N, 2.06° E), are situated on the Seine River, 10-30 km downstream of Paris. The farthest downstream site, Triel-sur-Seine (48.98° N, 2.00° E), is located downstream of the Seine and Oise river confluence; it was selected to integrate inputs from the Paris conurbation as well as those from a fluorochemical plant located in the Oise River watershed [START_REF] Boiteux | Concentrations and patterns of perfluoroalkyl and polyfluoroalkyl substances in 171 a river and three drinking water treatment plants near and far from a major production 172 source[END_REF].

Sampling

Composite surface sediment samples (0-2 cm, n = 1 per site) were collected in August 2019 at each location with a stainless-steel spoon and kept in aluminum containers at 4°C. Upon arrival at the laboratory, samples were stored at -20°C until further analysis.

European Chub samples were collected at the same time than sediments, according to [START_REF] Azimi | Influence of the water quality improvement on fish population in 150 the Seine River (Paris, France) over the 1990-2013 period[END_REF]. This bentho-pelagic species is frequently used for biomonitoring studies as chubs are very abundant in European rivers [START_REF] Caffrey | Chub (Leuciscus cephalus): a 178 new potentially invasive fish species in Ireland[END_REF]. In addition, S. cephalus are long-lived omnivorous fishes with large interindividual diet variations [START_REF] Balestrieri | Feeding ecology of 158 Leuciscus cephalus and Rutilus rubilio in southern Italy[END_REF]. Fish were collected by electrofishing (n = 10-12 per site), anesthetized (MS222, 1 g.L - 1 in river water) and euthanized. After sacrifice, sex was determined based on gonad morphology for each individual, then length and weight were recorded (Table S6). Individuals were dissected on site to collect liver (n = 45) and fillets (dorsal muscle) (n = 46). Tissues were stored in polypropylene tubes in a cooler (4°C) and then stored at -20°C upon arrival at the laboratory and until further analysis.

PFAS analysis

Sediment samples were freeze-dried, sieved at 2mm, ground with a ball mill and homogenized before analysis. Fish tissues were also freeze-dried, ground and homogenized.

Fish samples were prepared using a procedure adapted from a previous study by our group [START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF]. Briefly, prior to microwave-assisted solvent extraction using 12 mL of MeOH + 100 mM NaOH (10 min, 70°C), ISs (2 ng each) were added to fish tissues (muscle: 200 mg dry weight (dw); liver: 50 mg dw). Extracts were sequentially cleaned-up on Strata X-AW and ENVI-Carb cartridges before concentration to 300 µL (N 2 , 45°C), transfer to polypropylene injection vials and storage at -20°C until analysis. Sediment samples (1g dw) were processed similarly but clean-up was performed on ENVI-Carb cartridges only.

PFAS analyses were performed using liquid chromatography coupled with tandem mass spectrometry on a 1290 LC system interfaced with a 6495 triple quadrupole mass spectrometer from Agilent Technologies (Massy, France). Further details on chromatographic conditions and mass spectrometry parameters are provided in the SI (Table S2).

Procedural blank consisted of extraction solvent supplemented with ISs. For analytes quantified in procedural blanks (Table S3), data were blank-corrected. Limits of detection (LoDs), based on either blanks or signal-to-noise ratios as described elsewhere [START_REF] Munoz | Spatial distribution and partitioning behavior of selected poly-and 324 perfluoroalkyl substances in freshwater ecosystems: A French nationwide survey[END_REF], were in the range 0.005-1.0 ng g -1 wet weight (ww), 0.02-1.0 ng g -1 ww and 0.05-0.45 ng g -1 dw for fish muscle, liver and sediment respectively (Table S4). The limits of quantification (LoQs) were determined as 10/3*LoD.

Quality assurance and quality control

Whole method recovery rates were assessed through the analysis of common sole (Solea solea) fillets from the Gironde estuary (n = 9, fortified at 5 ng.g -1 ww) and sediment from the Orge River (n = 3, fortified at 5 ng g -1 dw); recoveries ranged between 50 and 105% for all but two analytes in fish muscle, while they were in the range 48-91% for sediments, except for FTABs (Table S5). Accuracy was determined with common sole fillets (n = 16) and sediment (n = 3) spiked with ISs and analytes at the beginning of the procedure (5 ng g -1 each). It was in the range 80-120% in spiked sediment and 52-119% in fish tissues, with relative standard deviation (RSD) between 6 and 21%, except for 6:2 FTAB and 8:2 FTAB (Table S5). The overall lower performances for the determination of FTABs in a complex matrices are not unexpected, considering the lack of appropriate ISs (i.e. isotopologues) and the structural differences with anionic PFAS. This led to the overestimation of their concentration in fish tissues (factor 1.4-1.7) and to the underestimation of their concentrations in sediments (factor 2.9-3.3), which did not affect our conclusions (e.g. see molecular patterns in section 3.2).

Stable isotope analysis

The isotopic composition of fish fillets was evaluated on defatted tissues [START_REF] Bodin | ASE extraction method for 166 simultaneous carbon and nitrogen stable isotope analysis in soft tissues of aquatic 167 organisms[END_REF][START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF]. Samples (0.2 ± 0.1 mg) were weighed in tin capsules and stable isotope ratios were determined using a ThermoFinnigan Delta V elemental analyzer

Statistics

The R statistical software (R version version 4.0.5 R core team 2021) was used to perform statistical analyses. Values <LoD were replaced by 0.5 × LoD and PFAS with detection frequency (DF) < 50 % were not considered for statistics. Since data were not normally distributed (Shapiro-Wilk W-test), statistical differences between groups were perform with Mann-Whitney (paired comparison) or Kruskall-Wallis (comparison of several samples) test, followed by Dunn post-hoc procedure with Bonferroni correction for multiple comparison to specify which groups differed from the others. The Spearman's rank correlation coefficient was used to investigate correlation between individual PFAS and between liver and muscle PFAS concentrations. Analysis of covariance (ANCOVA) was performed to explore the influence of potential explanatory variables (i.e. length, weight, δ 15 N and δ 13 C) on contamination levels; sampling site was considered as a qualitative variable. Variables were centered and reduced to estimate their relative contribution to the regression models. For each model, significant variables were determined by type III sum of square analysis and the improvement of models resulting from the removal of non-significant variables was assessed by the partial F-test. For all analyses, the significance threshold was set at 0.05.

Results And Discussion

Fish biometry and trophic ecology.

To acquire a robust dataset, 46 individuals were collected (i.e. 10-12 per sampling site). Fish length ranged from 176 to 500 mm and from 170 to 354 mm for females and males respectively; weight ranged from 56 to 1572 g and from 47 to 419 g for females and males, respectively. Thus, individuals displayed contrasting features (Table S6) with a RSD of 28% and 103% for length (proxy for fish age) and weight, respectively. No significant difference in length or weight distribution was observed between sampling sites. Based on results acquired in the same biogeographical area and using length as proxy for age, most sampled individuals were likely sexually immature [START_REF] Mann | Observations on the age, growth, reproduction and food of the chub 295 Squalius cephalus (L.) in the River Stour, Dorset[END_REF].

δ 13 C and δ 15 N values ranged from -24.26 to -27.82 ‰ (mean -26.70 ± 0.74 ‰) and 9.40 to 13.32 ‰ (mean 11.47 ± 0.90 ‰), respectively (Figure 1). The wide range of δ 13 C values are in good agreement with the variety of carbon sources utilized by this omnivorous species ( ar o ić et al., 2007). Nitrogen isotope ratios were significantly different between sites, with higher δ 15 N values at Triel-sur-Seine than at Le Pecq and Gournay-sur-Marne. This δ 15 N enrichment may be linked to inputs from a large wastewater treatment (WWTP) [START_REF] Hicks | δ15N tracks changes in the assimilation of sewage-derived 246 nutrients into a riverine food web before and after major process alterations at two 247 municipal wastewater treatment plants[END_REF][START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF]) located a few km upstream [START_REF] Hicks | δ15N tracks changes in the assimilation of sewage-derived 246 nutrients into a riverine food web before and after major process alterations at two 247 municipal wastewater treatment plants[END_REF][START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF].

The lower variability of isotopic ratios at Triel-sur-Seine may also indicate a specialization in S. cephalus diet [START_REF] Hette Tronquart | Stable isotopes reveal food 241 web modifications along the upstream-downstream gradient of a temperate stream[END_REF]. Overall, inter-individual differences are likely due to sampling site specificities and to the omnivorous diet of S. cephalus.

PFAS concentrations and patterns in sediments

Analysis of surface sediments provided a time-integrated estimation of PFAS contamination at the different sampling sites. Among the 36 analyzed PFAS, 17 were detected in this compartment (Table S7). L-PFOS, Br-PFOS, PFDoDA and 6:2 FTAB were systematically detected; 5:3 FTCA was detected at all sites except Le Pecq and 8:2 FTAB levels were > LOD at two sites (Levallois and Triel-sur-Seine). PFAA alternatives such as 6:2 and 8:2 Cl-PFESA or HFPO-DA were never detected but ADONA was quantified at two sites, albeit at low levels (< 0.04 ng.g -1 dw). The low detection frequency of these compounds compared to a recent report for the Bohai Bay, China [START_REF] Chen | Occurrence and Distribution of Per-and Polyfluoroalkyl 185 Substances in Tianjin, China: The Contribution of Emerging and Unknown 186 Analogues[END_REF], illustrates the weakness of their current emissions in the Seine River basin (i.e. few or no industrial sources). ∑PFAS was in the range 0.78-6.7 ng g -1 dw, with individual compounds generally below ng g -1 level (Table S7) except 6:2 FTAB at Triel-sur-Seine (1.70 ± 0.07 ng g -1 dw). Concentrations were in the same order of magnitude than those previously observed in the Seine River [START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF] and in the nearby Orge i er (mean ∑PFAS = 2.28 ± 2.31 ng g -1 dw) [START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF]. At all sites, molecular patterns were dominated by 6:2 FTAB that accounted for 46 ± 19% of ∑PFAS, followed by 5:3 FTCA and L-PFOS (18 ± 14% and 14 ± 4%, respectively); this clearly provided evidence for the non-negligible contribution of several PFAS of emerging concern (Figure S2). A peculiar PFAS pattern was observed at

Triel-sur-Seine, i.e. the presence of 6:2 FTSA (2.6 ± 0.8% of ∑PFAS). Additionally, when PFAS levels were normalized to the total organic carbon content, sediments collected at Trielsur-Seine appeared more contaminated than those from the further upstream locations.

Conversely, [START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF] found no contamination gradient on this river stretch. The difference with our study may arise from specific hydrological conditions, i.e. the particularly low flow rate of the Seine River observed during summer 2019 may have reduced the dilution capacity and sediment transport at the most downstream site. The extended list of PFAS targeted herein (e.g. inclusion of FTABs) may also explain this discrepancy. For instance, 6:2 FTAB proved to be ubiquitous in French river sediments [START_REF] Munoz | Analysis of zwitterionic, cationic, and anionic poly-and perfluoroalkyl 315 surfactants in sediments by liquid chromatography polarity-switching electrospray 316 ionization coupled to high resolution mass spectrometry[END_REF] and predominant in sediments from the Oise River collected downstream of a fluorochemical manufacturing plant [START_REF] Boiteux | Concentrations and patterns of perfluoroalkyl and polyfluoroalkyl substances in 171 a river and three drinking water treatment plants near and far from a major production 172 source[END_REF], thus likely contributing to the higher levels of this compound at Triel-sur-Seine. Inputs from this plant also possibly make for the increased 6:2 FTSA contribution, as observed in periphytic biofilm from the same site [START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF].

The presence of FTSAs in the Seine River could directly originate either from the use or production of these compounds or from the biotransformation of precursors such as fluorotelomer sulfonamidoalkyl betaines found in AFFF formulations [START_REF] Field | Properties, occurrence, and fate of fluorotelomer sulfonates[END_REF].

The peculiar molecular pattern observed at the most downstream site may also be attributed to increased WWTP inputs [START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF].

PFAS levels and patterns in fish

Across all sampling sites, C 10 -C 14 PFCAs, L-PFOS, FOSA and 10:2 FTSA were detected in all fish (Table 1). MeFOSAA was also frequently detected in muscle (96%) while PFOA and PFDS were routinely detected in liver (91% and 98%, respectively). Conversely, most emerging PFAS were less frequently reported. For instance, 8:2 FTSA was more rarely detected than 10:2 FTSA (22 % and 58 % of muscle and liver samples, respectively), while PFECHS was found in 20% of liver samples only and 8:2 Cl-PFESA was detected in a single liver sample at Le Pecq. This further suggests that these PFAS are not widely emitted in the Seine River basin yet. Although FTABs were present in sediments, 6:2 FTAB was never detected in fish and 8:2 FTAB was detected in only 4 individuals from Triel-Sur-Seine, at low level (<LoQ).

∑PFAS was in the range 0.22-3.8 ng g -1 ww and 11-140 ng g -1 ww in muscle and liver, respectively (Table 1); this resulted in an interindividual variability of 52% and 47%, respectively. ∑PFAS was in the same order of magnitude than those reported for S. cephalus elsewhere in Europe. Such concentrations were actually in the same range than those reported for other freshwater ecosystems in France [START_REF] Babut | Per-and poly-fluoroalkyl compounds in freshwater 154 fish from the Rhône River: Influence of fish size, diet, prey contamination and 155 biotransformation[END_REF][START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF] or Germany (Fliedner et al.,208), but somewhat lower than those observed in the Czech Republic [START_REF] Cerveny | Perfluoroalkyl Substances in Aquatic Environment-181 Comparison of Fish and Passive Sampling Approaches[END_REF] (i.e. up to 38 ng g -1 ww in fillets). Higher levels in liver than in muscle are consistent with PFAS affinity for specific proteins, e.g. liver fatty acid-binding proteins [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants 260 between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF].

As regards individual PFAS, the highest concentrations were observed for L-PFOS (0.63-13 ng g -1 ww and 5.8-94 ng g -1 ww in muscle and liver, respectively) and even-number longchain PFCAs: PFDoDA (0.37-5.0 ng g -1 ww and 1.6-18 ng g -1 ww in muscle and liver, respectively) and PFTeDA (0.22-3.8 ng g -1 ww and 0.66-12 ng g -1 ww in muscle and liver, respectively). These results were expected due to the greater bioaccumulation potential of long-chain PFAS [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants 260 between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF]. PFOS is regulated under the European Water Framework directive and an environmental quality standard for biota (EQS biota ) was set up to prote t "H man health ia ons mption of fishery pro ts", i.e. 9.1 ng g -1 ww (European Commission, 2013). For chub, whole-body PFOS concentrations can be estimated based on concentrations in fillets and using a conversion factor of 1.908 (Simmonet-Laprade et al., 2019). The exceedance frequency was quite low (i.e. 6.5 % of analyzed fish) but EQS biota compliance for PFOS was observed at two sites only, since levels in two individuals from Levallois and a single one from Le Pecq exceeded the threshold value of 9.1 ng g -1 ww.

This provides further evidence that despite PFOS phase-out in Europe, the contamination of hydrosystems by this chemical remains a long-term environmental issue. The median concentrations of other long-chain PFCAs were in the range <0.03-1.6 ng g -1 ww and 0.12-10 ng g -1 ww in muscle and liver, respectively (Figure 2). The bioaccumulation of the fluorotelomer 10:2 FTSA has seldom been reported so far. Here, its median concentrations were 0.13 ng g -1 ww and 0.74 ng g -1 ww in muscle and liver, respectively. Noteworthy, such values are lower than those observed for PFCAs but much larger than those reported herein for other PFAA precursors. The concentration range of this often overlooked compound was similar to that reported for other cyprinids from the nearby Orge River [START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF] but lower than those observed in the Chaudiere River following the massive use of AFFFs (Munoz et al., 2017b).

In fish tiss es, ∑PFAS an se eral individual compounds exhibited significant spatial differences (Table S9). Fish from Gournay-sur-Marne displayed lower le els of ∑PFAS, ∑PFOS, 10:2 FTSA an FOSA ompare to those obser e at all ownstream sites on the Seine River. Although, the highest me ian ∑PFAS was meas re at e allois, PFAS levels in fish did not differ between sites located downstream of Paris. A contamination gradient in the Seine River was previously observed for dissolved PFAS [START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF] and for other micropollutants in sediment and fish (Teil et al., 2014). Here, we found lower PFAS levels upstream of Paris, which further confirms the impact of dense urban areas on the Seine River contamination. Note that we did not investigate a strict longitudinal gradient since the upstream site was located on the Marne River; however, similar trends were reported for trace metals and Gournay-Sur-Marne can be considered as a suitable reference site at regional scale [START_REF] Elbaz-Poulichet | Short-term 203 variability of dissolved trace element concentrations in the Marne and Seine Rivers 204 near Paris[END_REF][START_REF] Grosbois | The spatial and temporal trends of 231 Cd, Cu, Hg, Pb and Zn in Seine River floodplain deposits (1994-2000)[END_REF].

As stated above, L-PFOS and long-chain carboxylates were the dominant compounds in chub;

this is consistent with previous findings in freshwater fish [START_REF] Labadie | Partitioning behaviour of perfluorinated alkyl contaminants 260 between water, sediment and fish in the Orge River (nearby Paris, France)[END_REF][START_REF] Ahrens | Stockholm Arlanda 126 Airport as a source of per-and polyfluoroalkyl substances to water, sediment and fish[END_REF][START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF]. The relative abundance of emerging PFAS was also examined. When detected, the contribution of 5:3 FTCA to ∑PFAS in muscle was in the range 5-9 % (n = 3) while PFECHS contribution in liver was in the range 0.5-1.8%.

The contribution of FTSAs significantly increased at Triel-Sur-Seine. For instance, 10:2 FTSA accounted at this site for 2.3 ± 0.5% and 1.9 ± 0.4% of ∑PFAS in m s le an li er, respectively. At this site, 6:2 FTSA was found in liver and 8:2 FTSA in both liver and muscle, but their ontrib tion to ∑PFAS was low (i.e. < 1 %) partly because of their lower bioaccumulation potential. This specific pattern is likely related to industrial inputs [START_REF] Munoz | Spatial distribution and partitioning behavior of selected poly-and 324 perfluoroalkyl substances in freshwater ecosystems: A French nationwide survey[END_REF]. When detected, 8:2 FTAB contribution was similar to that of 10:2 FTSA in muscle.

Very few data are available for FTSAs and the existing studies mostly focused on 6:2 FTSA [START_REF] Butt | Biotransformation pathways of fluorotelomer-175 based polyfluoroalkyl substances: A review[END_REF][START_REF] Zhang | Biotransformation of 413 perfluoroalkyl acid precursors from various environmental systems: advances and 414 perspectives[END_REF]. [START_REF] Ahrens | Stockholm Arlanda 126 Airport as a source of per-and polyfluoroalkyl substances to water, sediment and fish[END_REF] found a higher contribution of 6:2 FTSA to ∑PFAS in gonads and lower relative contribution of this ompo n to ∑PFAS in liver and muscle tissues of Perca fluviatilis near Stockholm Arlanda Airport. Our results suggest that a similar relative abundance can be expected for 10:2 FTSA in muscle and liver (Figure 2).

Correlations among individual PFAS were examined separately for muscle and liver samples (Figure S3). Positive associations were observed between most compounds in both matrices, with a few exceptions. For instance, only 10:2 FTSA and PFTeDA were not correlated with each other in liver, suggesting a different behavior between these two compounds (i.e. a PFAA precursor and a potential biotransformation end product). In muscle, PFTrDA and PFTeDA were correlated with neither 10:2 FTSA nor FOSA but showed significant associations with other PFAS. Potential sources for these compounds include the biotransformation of precursors [START_REF] Ahrens | Polyfluoroalkyl compounds in the aquatic environment: a review of their 123 occurrence and fate[END_REF].

For each sampling location, biota-to-sediment accumulation factors (BSAFs) were calculated for selected emerging PFAS and for PFOS (i.e. considered as benchmark compound) (Table S8). For the sake of comparison with the literature, BSAFs were calculated in two ways, i.e.

based on PFAS concentrations in sediments expressed either on a dry weight basis (BSAF) or normalized to the total organic carbon content (BSAF OC ). Overall, log BSAF OC were less variable than logBSAF values (i.e. lower relative standard deviation), thereby highlighting the usefulness of OC normalization. It appeared that the log BSAF OC of these emerging PFAS were lower than those of L-PFOS (in the range -2.3 --1.1 vs -1.3 -0.01). The low log BSAF OC of 8:2 FTAB may result from its strong binding with sediment particles via electrostatic interactions with negatively charged organic matter (Barzen-Hanson et al., 2017;Munoz et al., 2017b). In addition, 6:2 FTAB exhibited a lower biota-to-soil accumulation factor than PFOS [START_REF] Munoz | 310 Bioaccumulation of Zwitterionic Polyfluoroalkyl Substances in Earthworms Exposed 311 to Aqueous Film-Forming Foam Impacted Soils[END_REF]. This may also be related to efficient biotransformation, as observed in zebrafish [START_REF] Shi | Accumulation, Biotransformation, 365 and Endocrine Disruption Effects of Fluorotelomer Surfactant Mixtures on Zebrafish[END_REF]. Likewise, other sulfonamide betaines also proved to be metabolized into PFAAs in earthworm [START_REF] Jin | In Vivo Generation of 253 PFOA, PFOS, and Other Compounds from Cationic and Zwitterionic Per-and 254 Polyfluoroalkyl Substances in a Terrestrial Invertebrate ( Lumbricus terrestris ). 255[END_REF]. 5:3 FTCA may result from the aerobic or anaerobic biotransformation of fluorotelomer-based compounds [START_REF] Liu | 6-2 Fluorotelomer alcohol aerobic biodegradation in soil and 280 mixed bacterial culture[END_REF][START_REF] Chen | 189 Biotransformation and bioconcentration of 6:2 and 8:2 polyfluoroalkyl phosphate 190 diesters in common carp (Cyprinus carpio): Underestimated ecological risks[END_REF]. . In particular, it has been suggested as a marker of landfill leachate [START_REF] Allred | Physical and Biological Release of 133 Poly-and Perfluoroalkyl Substances (PFASs) from Municipal Solid Waste in 134 Anaerobic Model Landfill Reactors[END_REF][START_REF] Hamid | Aerobic biotransformation of fluorotelomer 234 compounds in landfill leachate-sediment[END_REF]. Although frequently detected in sediments, 5:3 FTCA was quantified in three fish muscle samples only, which illustrates its low bioaccumulation potential. Nevertheless, it seemingly displayed the highest log BSAF OC of emerging PFAS; calculations were, however, performed on a limited number of samples (n=3) and results are therefore given as indicative values. Finally, 10:2 FTSA displayed intermediate BSAF, somewhat lower those previously reported for this compound (Munoz et al., 2017b).

Tissue distribution 5

As expected, PFAS concentrations were higher in liver than in muscle; liver-to-muscle ratios 6 (LMRs) were systematically higher than 1 except for 5:3 FTCA (Table S10). LMRs for 7

PFAAs and FOSA were consistent with previously published values for Cyprinids (Labadie 8 and Chevreuil, 2011;[START_REF] Babut | Per-and poly-fluoroalkyl compounds in freshwater 154 fish from the Rhône River: Influence of fish size, diet, prey contamination and 155 biotransformation[END_REF][START_REF] Wu | Comparisons of tissue distributions and 402 health risks of perfluoroalkyl acids (PFAAs) in two fish species with different trophic 403 levels from Lake Chaohu, China[END_REF]. These are, however, the first data 9 for the emerging PFAS listed in Table S10, which tissue distribution is not documented. 10 Large inter-individual variations LMRs were usually observed: the highest inter-individual 11 variation was for FOSA and 8:2 FTSA (i.e. > 60%), while other PFAS displayed relative 12 standard deviations in the range 33-51%. LMRs computed for 10:2 FTSA, the most recurring 13 FTSA, were similar to those calculated for PFUnDA (5.9±1.9 vs 5.1±1.9), which exhibits a 14 similar perfluoroalkyl chain length, but approximately twice lower than those of L-PFOS 15 (10.7±3.5) likely because of different binding affinity for muscle/liver proteins. 16

Correlations between PFAS levels in liver and muscle were also explored for analytes with 17 DF > 90%. Significant associations were found for all tested compounds and R² ranged from 18 0.31 to 0.70 (Figure S4). This indicated that hepatic and muscular levels were related although 19 the relation was sometimes weak, in good agreement with the variable LMRs presented 20 above. The lowest correlation coefficient reported for FOSA was possibly due to inter-21 individual differences in hepatic biotransformation capacities (i.e. conversion of FOSA to 22 PFOS [START_REF] Letcher | 275 Comparative hepatic in vitro depletion and metabolite formation of major 276 perfluorooctane sulfonate precursors in arctic polar bear, beluga whale, and ringed 277 seal[END_REF]). 23 24

Influence of selected factors on the bioaccumulation of PFAS 25

To investigate the controlling factors of PFAS bioaccumulation in European Chub, an 26 ANCOVA was performed based on PFAS levels in fish muscle. Such analysis is equivalent to 27 a multiple linear regression including quantitative and qualitative variables (Babut et al., 28 2017). As demonstrated above, sampling site was a potential determinant of PFAS levels in 29 fish (i.e. contamination gradient/spatial heterogeneity) and a potential confounding factor (i.e. 30 differences in fish C and N isotopic signatures across sites). Thus, it was included as a 31 categorical variable, along with sex [START_REF] Peng | Tissue Distribution and Maternal 350 Transfer of Poly-and Perfluorinated Compounds in Chinese Sturgeon (Acipenser 351 sinensis): Implications for Reproductive Risk[END_REF]. Explanatory quantitative variables 32 were fish length and trophic ecology proxies (i.e. δ 13 C and δ 15 N). Fish weight was not 33 included as it was strongly correlated with fish length (Figure S5). The latter is often used as a 34 proxy for fish age, thus being more relevant for bioaccumulation studies. PFAS with DF > 35 90% (i.e. C 10 -C 14 PFCAs, PFOS, FOSA and 10:2 FTSA) were chosen as response variables. 36 Significant variables and models coefficients are presented in influence of δ 15 N is consistent with the biomagnification of these PFAS, as observed in 66 various aquatic environments [START_REF] Simonnet-Laprade | Biomagnification of perfluoroalkyl acids (PFAAs) in 374 the food web of an urban river: assessment of the trophic transfer of targeted and 375 unknown precursors and implications[END_REF][START_REF] Penland | Trophodynamics of Per-and Polyfluoroalkyl Substances in the Food Web 355 of a Large Atlantic Slope River[END_REF]Pan et al., 67 2021). Carbon sources in lotic systems are complex [START_REF] Ishikawa | Global meta-analysis for controlling factors on 250 carbon stable isotope ratios of lotic periphyton[END_REF] and more negative 68 δ 13 C are mostly linked to detrital organic matter in river, i.e. a carbon source linked with 69 sediments [START_REF] Finlay | Stable-Carbon-Isotope Ratios of River Biota:implications for Energy Flow 213 in Lotic Food Webs[END_REF]. Since positive coefficients were found for δ 13 C (Table 2), PFAS 70 levels tended to increase with δ 13 C. This strongly suggests that chub that feed more on 71 autochthonous carbon sources (e.g. periphytic biofilm or biofilm grazers) are more exposed to 72 PFAS. Such a result is consistent with PFAS accumulation in biofilms, proven to exceed that 73 observed in sediments [START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF]. 74

In addition, data transformation allowed ranking model coefficients to determine their relative 75 weight. We found that the 95% confidence intervals of model coefficients overlapped for δ 15 N 76 and δ 13 C. Thus, our findings indicate that both factors exhibited similar weights; carbon 77 sources use is therefore equally important as trophic position to explain within-species 78 variability of PFAS bioaccumulation in S. cephalus. 79 Overall, while other exposure pathways are likely important, e.g. respiratory uptake across the 80 gills [START_REF] Armitage | Assessing the bioaccumulation potential of 146 ionizable organic compounds: Current knowledge and research priorities[END_REF], uptake via the diet and dietary habits appeared to significantly 81 influence the interindividual variability of PFAS levels in European chub from a river under 82 urban influence. In such rivers, dissolved PFAS concentrations may rapidly vary depending 83 on hydrological conditions [START_REF] Munoz | Spatio-319 temporal dynamics of per and polyfluoroalkyl substances (PFASs) and transfer to 320 periphytic biofilm in an urban river: case-study on the River Seine[END_REF]. The relative influence of each parameters 84 should be further investigated on different chub populations and different species to confirm 85 these results, while other relevant variables such as protein/phospholipid content could also be 86 considered [START_REF] Armitage | Development and evaluation of a 141 mechanistic bioconcentration model for ionogenic organic chemicals in fish[END_REF]. 87 88

Conclusion 90

This study investigated an extended list of PFAS in sediment and fish along a longitudinal 91 transect in the Seine River basin. The results suggest that the Greater Paris has a strong 92 influence on PFAS inputs in the Seine River. We demonstrated the widespread occurrence in 93 sediment and fish of PFAS of emerging concern such as FTABs and FTSAs, usually linked to 94 point sources related to firefighting or industrial activities. In particular, 6:2 FTAB was 95 prevalent in most sediments, while 10:2 FTSA was ubiquitous in fish. Such findings highlight 96 the need for suitable quantitative analytical methods to address a wide range of target 97 compounds, which is mandatory to better understand PFAS occurrence and fate in 98 hydrosystems. PFAS levels in fish were dependent on the sampling site, but trophic ecology 99 significantly explained interindividual variations; trophic level and carbon sources displayed 100 similar weights. However, while such drivers are influential, they are not sufficient to fully 101 explain PFAS bioaccumulation in European chub at the individual level. Future research is 102 therefore needed to get further insight into this issue. 103 104

Declaration of competing interest 105

The authors declare that they have no known competing financial interests or personal 106 relationships that could have appeared to influence the work reported in this paper.

(

  EA-IRMS) with a Conflo IV interface. Carbon and nitrogen isotopic compositions were expresse as per mil (‰) in the δ notation relati e to Vienna Pee Dee Belemnite (VPDB) an atmospheric N 2 , respectively. Trueness was assessed through replicate analyses (every 10-12 samples) of IAEA-N2 (δ 15 N = 20.3‰) an USG-24 (δ 13 C = -16.05 ± 0.1‰) referen e materials and averaged 20.25 ± 0.23 (n = 10) and -15.94 ± 0.35 (n = 18) for δ 15 N and δ 13 C respectively.

Figure 1 .

 1 Figure 1. Mean stable isotope signature (δ 15 N vs δ 13 C) in European chub fillets collected in

1Figure 2 .

 2 Figure 2. Relative contribution of individual PFAS to ∑PFAS in muscle (top) and liver (bottom). (a) Gournay-Sur-Marne, (b) Levallois, (c) Le 2

  supported by the PIREN-Seine and MeSeine Innovation programs, along with 110 the Investments for the Future Program (Cluster of Excellence COTE, ANR-10-LABX-45). 111 PE A2E (Aq itaine region), E3A (Aq itaine region) an FEDE ("E rope is mo ing in 112

Table 1 .

 1 PFAS occurrence in European chub muscle and liver (all sites considered) (DF: detection frequency).

		Muscle (n = 46)		Liver (n = 46)
		DF (%)	Range (ng.g -1 ww)	Median (ng.g -1 ww)	DF (%)	Range (ng.g -1 ww)	Median (ng.g -1 ww)
	PFHxA	0	<0.02	<0.02	0	<0.02	<0.02
	PFHpA	2	<0.005-0.02	<0.005	0	<0.005	<0.005
	PFOA	2	<0.06-0.13	<0.06	33	<0.06-0.26	<0.06
	PFNA	28	<0.03-0.11	<0.03	91	<0.03-0.78	0.12
	PFDA	100	0.09-1.6	0.58	100	0.56-10	2.8
	PFUnDA	100	0.06-1.2	0.35	96	<0.53-5.1	1.7
	PFDoDA	100	0.37-5.0	1.6	100	1.6-18	7.0
	PFTrDA	100	0.07-1.6	0.39	100	0.25-3.3	1.0
	PFTeDA	100	0.22-3.8	0.90	100	0.66-12	3.1
	PFBS	0	<0.07	<0.07	0	<0.42	<0.42
	PFHxS	11	<0.02-0.10	<0.02	42	<0.17-1.6	<0.17
	PFHpS	2	<0.05-0.09	<0.05	44	<0.32-0.66	<0.32
	Br-PFOS	93	<0.06-3.29	0.14	100	1.1-7.6	3.2
	L-PFOS	100	0.63-13.3	2.6	100	5.8-94	28.7
	PFDS	28	<0.06-0.27	<0.06	98	<0.10-1.5	0.27
	4:2 FTSA	0	<0.004	<0.004	0	<0.02	<0.02
	6:2 FTSA	0	<0.12	<0.12	18	<0.12-0.37	<0.12
	8:2 FTSA	22	<0.01-0.03	<0.01	58	<0.02-0.42	0.08
	10:2 FTSA	100	0.03-0.24	0.13	100	0.16-1.5	0.74
	FOSAA	0	<0.008	<0.008	0	<0.05	<0.05
	N-MeFOSAA	96	<0.05-0.09	0.07	58	<0.28-0.50	0.31
	N-EtFOSAA	0	<0.15	<0.15	24	<0.002-0.02	<0.002
	FOSA	100	0.01-0.14	0.05	100	0.04-0.70	0.20
	N-MeFOSA	0	<0.01	<0.01	0	<0.06	<0.06
	6:2 diPAP	4	<1.0-2.1	<1.0	7	<1.0-4.0	<1.0
	8:2 diPAP	9	<0.08-0.27	<0.08	2	<0.21-1.2	<0.21
	6:2 FTAB	0	<0.34	<0.34	0	<2.0	<2.0
	8:2 FTAB	9	<0.13-0.20	<0.13	2	<0.47-0.77	<0.47
	HFPO-DA	0	<0.30	<0.30	0	<0.35
	ADONA	0	<0.01	<0.01	0	<0.01	<0.01
	6:2 Cl-PFESA	0	<0.01	<0.01	0	<0.06	<0.06
	8:2 Cl-PFESA	0	<0.006	<0.006	2	<0.20-0.22	<0.20
	PFECHS	0	<0.19	<0.19	20	<0.46-0.66	<0.46
	5:3 FTCA	7	<0.09-0.75	<0.09	0	<0.36	<0.36
	∑PFAS	100	0.22-3.8	7.4	100	11-140	54

Table 2 .

 2 37 38

Table 2 .

 2 ANCOVA results for selected PFAS. Regression coefficients for significant quantitative variables are given in the right-hand column.

	39
	40	CI: confidence interval.
		Variables	Adjusted R²(p-value)	Variables (p-value)

Aq itaine with the E ropean egional De elopment F n ") are also acknowledged for 113 funding. PFAS and stable isotope analyses were performed using the technical facilities from 114 the PLATINE mass spectrometry platform at UMR 5805 EPOC. We are grateful to V. 115 Lespannier (Aquascope) for his support on the sampling campaign and to A. Coynel


S De Hoop
email: dehoop-1@tudelft.nl

D Voskov
email: d.v.voskov@tudelft.nl

E Ahusborde
email: etienne.ahusborde@univ-pau.fr

B Amaziane
email: brahim.amaziane@univ-pau.fr

M Kern

Reactive Multiphase Flow in Porous Media at the Darcy Scale: a Benchmark proposal

Introduction and context of the proposal

This document presents a proposal for a benchmark on reactive multiphase flow. The proposal was put together as a followup of the first SITRAM meeting https://sitram19.sciencesconf.org/, which took place in Pau in December 2019. The topic is increasingly important for modern energy applications.

The content of the benchmark was initially written by SdH and DV, and the current version is the result of discussions between the five authors. The proposal is still work in progress. Preliminary results were reported by seveal teams in two sessions of a minisymposium at the upcoming SIAM Conference on Mathematical and Computational Issues in the Gesociences, and it is the organizers' hope that input form the participants will enable the model to be extended towards more realistic geometries as well as physical and chemical phenomena.

A second workshop SITRAM21 https://sitram21.sciencesconf.org/ was organized in December 2022 at the Inria Centerin Paris, where participants showed further results. A special issue of the journal "Computational Geosciences" is planned, where participants will be able to present and compare their work.

The proposal was written to address several challenges commonly met in applications:

1. Robust coupling of chemical reactions with multiphase flow in porous media, 2. Phase behaviour coupling with equilibrium reactions, 3. Conservative treatment of solid phase dissolution and precipitation, 4. Effective coupling of equations in the case of multiple (concurrent) reactions.

The general structure of the physical and chemical model is described in Sections 2 to 5, while the specific data for the proposed cases are given in Section 6, and requested output is specified in Section 7.

Governing equations

This section briefly covers the governing equations of the multiphase multi-component reactive transport framework for the proposed benchmark study. We start with the basic mass balance equations including the

1 effect of chemical reactions as source/sink term following [START_REF] Kala | Element balance formulation in reactive compositional flow and transport with parameterization technique[END_REF]:

∂n c ∂t + l c + q c = K k=1 v ck r K k + Q q=1 v cq r Q q , c = 1, . . . , C + M, (1)
where C is the number of fluid species and M is the number of mineral species, n c is the overall mass of component c, l c is the total flux associated with that component, q c is the total well flow rate associated with that component, v ck is the stoichiometric coefficient associated with kinetic reaction k for the component c and v cq is the stoichiometric coefficient associated with equilibrium reaction q for component c, r K k is the rate for kinetic reaction and r Q q is the equilibrium reaction rate. The overall mass of components is defined as n c = φ T P j=1 (ρ j s j x cj ), c = 1, . . . , C.

(2)

Here P stands for the total number of fluid phases and x cj is the molar fraction of component c in phase j. This term indicates the total mass of component c in all the fluid phases. For the solid mineral components, we use the following relationship :

n m = φ T ρ m ŝm , m = C + 1, . . . , M, (3)
where ŝm is the mineral (solid) saturation. The total porosity φ T term will be explained later (see equation 15). The term l c defines the flux of component c and is given as:

l c = ∇ • P j=1
(ρ j x cj u j -ρ j φs j d cj ∇x cj ) , c = 1, . . . , C,

where the term d cj corresponds to the dispersion of component c in phase j. The term u j is the velocity of the phase j and is defined by Darcy's law:

u j = -k k rj µ j (∇p -ρ j g∇h) j = 1, . . . , P, (5)
where k is the rock permeability. In this benchmark capillary pressure effects are ignored, so there is only a single pressure for all phases. Equation 1 can be written in a vector form:

∂n ∂t + l + q = V Q r Q + V K r K , (6)
where n = (n 1 , . . . , n C+M ) T , l = (l 1 , . . . , l C , 0, . . . , 0) T , q = (q 1 , . . . , q C+M ) T is the well flow rate, V Q and V K are the stoichiometric matrices respectively for the equilibrium and kinetic reactions, while

r Q = (r Q 1 ,. . . ,r Q Q ) T and r K = (r K 1 ,. . . ,r K K )
T are the equilibrium and kinetic reaction rate vectors.

Phase behavior of compositional system

The following equations are used for thermodynamic equilibrium of multicomponent system. A component is in thermodynamic equilibrium if the chemical potentials of the components in both phases are equal:

f c1 -f cj = 0, c = 1, . . . , C, j = 2, . . . , P. (7)
The fugacity of a component in a particular phase is given by

f cj = φ cj x cj p, c = 1, . . . , C, j = 1, . . . , P, (8)
where φ cj is the fugacity coefficient of an ideal mixture. Equation ( 7) can also be written in terms of the partition coefficients K cj = φ cj /φ c1 :

K cj x c,1 -x cj = 0, c = 1, . . . , C, j = 2, . . . , P. (9)
The system of equations ( 7) or ( 9) can be directly coupled with the conservation equations ( 6) and solved in a fully coupled manner using the global Newton solver. Such formulation is often called global or natural formulation. However, when a new phase appears in the process of simulation, the phase equilibrium should be calculated based on the local approximation of the mass from equation (6).

The system of equations can be closed with the following algebraic constraints:

P p=1 s p = 1, (10)
and

C c=1 x cj = 1, j = 1 . . . , P (11)
In case of equilibrium reactions, we need to add the law of mass action to either global or local systems (depending on the preferred nonlinear formulation), which is given as:

Q q -K q = Π C c=1 a vcq cw -K q = 0, q = 1, . . . , Q. ( 12
)
Here Q is the number of equilibrium reactions, Q q is the reaction quotient whereas K q is the equilibrium reaction quotient or equilibrium solubility limit in case of dissolution/precipitation of minerals, a cw is the activity of the component c in the aqueous phase, and v cq is the reaction stoichiometric coefficient.

Porosity treatment

For an accurate treatment of solid phase dissolution and precipitation at the continuous level, the treatment of the rock porosity should be adjusted. Conventionally the control volume (denoted as bulk volume) is subdivided into two regions, void space (occupied by all mobile phases, such as liquid and vapor phase) and solid skeleton (occupied by immobile species, for example, carbonate rock).

In most contributions from the literature, the porosity φ depends on the concentrations of the minerals according to the relationship:

φ = 1 - M m=1 M m c ms ρ m = 1 - M m=1 ŝm , ( 13
)
where M is the number of reactive minerals, M m is the molar mass of mineral m, ρ m is the mass density of mineral m and c ms represents and the molar concentration of mineral m. Here we introduced saturation of the mineral (solid) phase ŝm .

In equation ( 13), it is not clear which properties are spatially correlated and which are changing in time due to dissolution or precipitation reactions. Following the approach suggested in [Farshidi, 2016], we can subdivide the volume of the solid skeleton further into a reactive part which can be modified by chemical reactions and a non-reactive part (which is unaltered by any chemical reaction, and therefore constant throughout the simulation), see Figure 1.

Mathematically this is expressed as follows

V b = V f + V r + V nr , (14)
where V r denotes the reactive volume and V nr represents the non-reactive volume (not altered by any chemical reaction). Dividing this by the total (bulk) volume gives

1 = φ + φ r + φ nr = φ T + φ nr , (15)
where φ r represents the reactive volume fraction, φ nr is the non-reactive volume fraction, and φ T is the total porosity defined as the sum of the fluid porosity and reactive volume fraction. Since only the reactive volume and fluid porosity can change due to chemical reactions, it follows directly that the total porosity remains constant throughout the simulation (when compressibility is neglected). This and the changes in volume fractions due to precipitation and dissolution is illustrated in Figure 1.

Note that the fluid porosity can always be obtained from the following constitutive equation

φ = φ T 1 - M m=1 ŝm , ( 16
)
where M is the number of solid phases (occupying the reactive volume fraction) and ŝm is the saturation of the solid phase. Please note that the s α is the fluid saturation (defined over the pore volume) while ŝm is the solid saturation of mineral phase m (defined over the pore and reactive rock volume). Solid saturation in the total porosity formulation can be found with the following equation

ŝm = V r,m V r + V f , (17)
where V r,m is the volume of mineral phase m defined as

V r,m = M m ρ m n r m , (18)
where n r m is the total number of moles of mineral m that can participate in any reaction. The permeability dependence on porosity is approximated using the following power-law equation

k = k 0 φ φ 0 A . ( 19
)
where k 0 and φ 0 are initial porosity and permeability respectively.

Additional description for fluid and rock parameters

The relative permeability functions used in this benchmark consist of the Brooks-Corey description, more precisely

k r,α = k e r,α s α -s r,α 1 -p∈P s r,p nα , (20)
where k r,α is the relative permeability, k e r,α is the maximum relative permeability, s r,α is the residual saturation, and n α is the Corey exponent of phase α respectively. In the absence of any residual saturation and taking P = {w, g} (i.e., assuming liquid (water) and vapor (gas) are the fluid phases present in the system), this results in

k rw = k e rw (s w ) nw , (21)
for the water and

k rg = k e rg (1 -s w ) ng , (22)
for the gas relative permeability.

For the phase density, a simple linear compressibility model is assumed, particularly

ρ α = ρ α,0 (1 + C α (p -p 0 )). ( 23
)
Here C α is compressibility and ρ α,0 is density at pressure p 0 . This is assumed to hold for each of the three phases present in the system, water, gas, and solid. Additional physical complexity can be obtained by adopting a fully compressible model for the gas phase. Finally, the activity of each component in the water phase can be written using the following equation

a cw = γ cw m cw , (24)
where γ cw is the activity coefficient and m cw is the molality of component c in the water phase, which in turn can be written as

m cw = M w ( x cw x ww ), ( 25
)
where M w is the number of moles of H 2 O per kilogram of aqueous phase (typically taken as 55.508), x cw is the mole fraction of component c and x ww is the mole fraction of H 2 O in the aqueous phase respectively. For this benchmark the assumption of an ideal solution is made and hence the activity coefficient is taken as 1.

6 Benchmark scenarios [10 -6 , 10 -4 , 10

-7 ] [1/bar] Phase viscosity, µ w,g [1, 0.1] [cP] End-point relative permeability, k e rw,rg [1, 1] [-] Corey exponents, n w,g [2, 2] [-] Residual saturation, s rw,rg [0, 0] [-] Phase partition coefficients, K H2O,CO2 [0.1, 10] [-] Diffusion coefficients, d cj = d 10 -9 [m 2 /s] Activity coefficients, γ cw = γ 1 [-] Porosity-permeability dependence factor, A 3 [-]
Table 2: Values for all the relevant fluid and rock properties.

The model is setup with an injection well (i.e., source term) in the first block and a production well in the last block, no flow boundary conditions from left and right (i.e., ∂p ∂x | x=0 = 0 and ∂p ∂x | x=∆xNx = 0). These are typical boundary conditions for reservoir simulation. It is possible to replace the wells and no-flow boundary condition with a Neumann boundary condition at x = 0 and a Dirichlet at x = ∆xN x . Table 3 summarizes the initial, injection and production conditions and simulation time. Table 3: Boundary conditions and other simulation parameters.

… p prod Q inj , z c,inj p 0 , z c,0 Q = 0 Q = 0
Note that the injection and initial compositions are given in terms of the overall mole fractions z i , i = 1, . . . , C, defined as

z i = P j=1 x ij ν j , i = 1, . . . , C, with ν j = ρ j S j P k=1 ρ k S k
, j = 1, . . . , P.

We refer to [START_REF] Kala | Element balance formulation in reactive compositional flow and transport with parameterization technique[END_REF] for more details. Note that composition for the C-th component can be obtained by z C = 1 -C-1 j=1 z j and is not a primary unknown (hence the initial and injection composition doesn't contain the composition of z C ), and the primary unknowns in this system are X = [p, z 1 , . . . , z C-1 ]. The initial and injection composition expressed in terms of molar fraction of individual species and saturation of each phases are given in Appendix A.

We now describe the chemical reaction used for this first case. It consists of a single chemical reaction (i.e., we cannot reduce the global system of nonlinear equation using the element reduction). The system consists of the following components:

z c = [ H 2 O, CO 2 , Ca +2 , CO -2 3 , CaCO 3 ]. The kinetic reaction equation consists of CaCO 3 ----Ca +2 + CO -2 3 . (26)
We distinguish two cases according to whether the reaction is modelled as kinetic or at equilibrium.

Two-phase flow with kinetic chemistry

Here we assume that the chemical reaction ( 26) is kinetic. The kinetic rate (i.e., the right-hand-side of equation ( 6)) is written as

r k = AK k 1 - Q K sp ( 27
)
where A is the reactive surface area, which is a linear function of the solid saturation (A = A 0 ŝs = (1-φ 0 )ŝ s ), K k is the kinetic reaction constant, Q is the activity product (to simplify Q = x ca,w × x co3,w ) and K sp is the equilibrium constant.

The values of the reaction constants are given in Table 4. K sp is equal to 0.25 × 0.25 = 0.0625 to ensure that the initial state is in equilibrium and no dissolution occurs.

Property

Value Units Kinetic constant, K k 1 [kmol / m 3 / day ] Solubility constant, K sp 0.0625 [-] Table 4: Kinetic and equilibrium constants.

Two-phase flow with equilibrium chemistry

The second test case is similar to the first one, except that now the reaction is treated as an equilibrium reaction. Mathematically, this adds an additional constraint equation of the form

Q -K sp = 0, ( 28
)
where Q is the activity product of the equilibrium reaction as defined in equation ( 12) (which is taken here to have the same form as in Section 6.1.1) and K sp is the solubility constant, with the value given in Table 3.

All the other parameters, fluid/rock/boundary condition/simulation parameters (as specified in table 2 and3), are the same as for the previous case (including of course the stoichiometry of the reaction).

2D Heterogeneous domain

The third test case consists of a two-dimensional heterogeneous domain. In the model, a zone of high porosity (and permeability) is embedded within a lower porosity (and permeability) zone. The domain extends for 10[m] in the y-direction (all the other measures are mentioned in Figure 3). Kinetic chemistry is used to model the dissolution of CaCO 3 . See Tables 5 and6 for all the parameters Property Value Units

x CO 2 ,w 3.9624 × 10 -10

[-]

x Ca 2+ ,w 2.1703 × 10 -6 [-] x H + ,w 2.3507 × 10 -12 [-] x OH -,w 1.5475 × 10 -6 [-] x HCO - 3 ,w 1.5467 × 10 -6
[-]

x CO -2 3 ,w 6.2315 × 10 -7

[-]

Table 8: Initial molar fractions for the extended chemical model .

GROUP is a (4 to 6 character) unique identifier, selected by each group;

CASE is a 2 character identifier for the specific benchmark case, as follows 11 for 1D, kinetic chemistry;

12 for 1D, equilibrium chemistry;

21 for 2D, simple chemistry;

22 for 1D, extended chemistry.

LOC is the location of the variables in the file (such as t1000 or x25);

VAR gives additional information, such as grav or nograv depending on whether or not gravity has been included.

1D homogeneous domain

• Text output of all variables as a function of space at time 1000 days in a CSV file named (with case = "11" or "12") GROUP_CASE_t1000.csv , containing (x, S g , P g , φ, x H 2 O,w , x CO 2 ,w , x Ca 2+ ,w +x HCO - 3 ,w ); • Text output of all variables as a function of time at x = 25 in a CSV file named GROUP_CASE_x25.csv, containing (t, S g , P g , φ, x H 2 O,w , x CO 2 ,w , x Ca 2+ ,w + x HCO - 3 ,w ); • It is suggested to include a numerical convergence study.

2D heterogeneous domain

Simple chemical model

• Plot CO 2 fraction, ion mole fractions, gas saturation and porosity as a space maps at time 1000 days;

• Write the same variables as in 1D on a cross-section along the vertical line at x = 40m in a CSV file named GROUP_21_x40_VAR.csv, containing (y, S g , P g , φ, x H 2 O,w , x CO 2 ,w , x Ca 2+ ,w + x HCO - 3 ,w ); • Write the same variables as in 1D on a cross-section along the horizontal line at y = 50m in a CSV file named GROUP_21_y50_VAR.csv, containing (x, S g , P g , φ, x H 2 O,w , x CO 2 ,w , x Ca 2+ ,w + x HCO - 3 ,w ).

Extended chemical model

Same output as for the simple chemical model, with the addition of all chemical species:

• Plot CO 2 fraction, ion mole fractions, gas saturation and porosity as a space maps at time 1000 days;

• Text output of the same variables as 1D cross-section along vertical line at x = 40m in a CSV file named GROUP_22_x40.csv, containing (y, S g , P g , x H 2 O,w , x CO 2 ,w , x Ca 2+ ,w , x H + ,w , x HCO - 3 ,w , x CO 2- 3 ,w , φ); • Write the same variables as in 1D on a cross-section along the horizontal line at (y = 50m in a CSV file named GROUP_22_y50.csv, containing (y, S g , P g , x H 2 O,w , x CO 2 ,w , x Ca 2+ ,w , x H + ,w , x HCO - 3 ,w , x CO 2- 3 ,w , φ).

Liquid MoleFrac

5.00e-01 3.33e-12 2.50e-01 2.50e-01 0.00e+00 Vapor MoleFrac 5.00e-01 3.33e-12 2.50e-01 2.50e-01 0.00e+00 Solid MoleFrac 0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.00e+00 ----------------------------------------------------------------------------------------------------------------------------------------------------- -------------------------------------------------------------------------- -------------------------------------------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------ ------------------------------------------------------------------------------------ --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Vapor Liquid Solid Phase MoleFrac 0.0000000e+00 1.0000000e+00 9.9997788e-13 Mass Density 1.0094000e+02 1.0000940e+03 2.0000000e+03 Viscosity 1.0000000e-01 1.0000000e+00 0.0000000e+00 Sat. phi_tot 0.0000000e+00 1.0000000e+00 9.9997788e-13 Sat. phi_fluid 0.0000000e+00 1.0000000e+00 0.0000000e+00 -------------------------------------------------------------------------------------

2D injection (gas stream)

Properties based on injection state: state = [P, z_CO2, z_Ions, z_H2O] injection state = [9.50000000e+01 1.00000000e+00 1.00000000e-12 9.99977878e-13] -------------------------------------------------------------------------------------CO2 Ions H2O CaCO3 Composition, z_c 1.0000000e+00 1.0000000e-12 9.9997788e-13 9.9997788e-13 Vapor MoleFrac 1.0000000e+00 9.0008986e-13 9.9997788e-13 0.0000000e+00 Liquid MoleFrac 1.0000000e-01 9.0008986e-01 9.9997788e-12 0.0000000e+00 Solid MoleFrac 0.0000000e+00 0.0000000e+00 0.0000000e+00 1.0000000e+00 --------------------------------------------------------------------------------------------------------------------------------------------------------------------------Vapor Liquid Solid Phase MoleFrac 1.0000000e+00 1.2478907e-13 9.9997788e-13 Mass Density 1.0094000e+02 1.0000940e+03 2.0000000e+03 Viscosity 1.0000000e-01 1.0000000e+00 0.0000000e+00 Sat. phi_tot 1.0000000e+00 1.4150213e-14 9.9997788e-13 Sat. phi_fluid 1.0000000e+00 1.4150213e-14 0.0000000e+00 -------------------------------------------------------------------------------------

Figure 1 :

 1 Figure1: Schematic of the different volumes in the domain. The domain consists of three distinct regions, particularly the fluid volume which is occupies by all the mobile phases (liquid and gaseous in the case of two phase flow), the reactive volume which consist of solid phases that can react or precipitate, and finally the nonreactive volume (the part of the control volume which doesn't participate in any chemical reaction).

Figure 2 :

 2 Figure2: One dimensional domain setup. Injection on the left is constrained with rate and composition Q inj and z c,inj respectively. Production on the right is constrained with pressure p prod . Initial condition for pressure and composition is defined as p 0 and z c,0 respectively. No flow boundary condition is imposed on both the left and right boundary.

Figure 3 :

 3 Figure 3: Configuration of the 2D test case (Section 6.2). Constant injection rate on the left boundary (Neumann) and constant pressure (Dirichlet) on the right. The domain extends 10[m] in the y-direction.

-

  2D initial (void, Ω 1 )Properties based on initial state: state = [P, z_CO2, z_Ions, z_H2O] initial state = [9.50000000e+01 2.66666667e-12 4.00000000e-01 4.00000000e-01]

-

  2D injection (water stream)Properties based on injection state: state = [P, z_CO2, z_Ions, z_H2O] injection state = [9.5e+01 2.0e-12 1.0e-12 1.0e+00]

Table 1 :

 1 Table 1 describes how each component distributes over all phases. Component-Phase distribution matrix.

	Component Liquid (water) Vapor (gas) Solid
	H 2 O
	CO 2
	Ca +2
	CO -2 3
	CaCO 3

  The first case is a basic 1D model. The rock and fluid properties are shown in Table2.

	6.1 1D homogeneous domain
	Property	Value	Units
	Permeability, k x,y,z	[100, 100, 100]	[mD]
	Total porosity, φ T	1	[-]
	Porosity, φ	0.3	[-]
	Control volume dimension, ∆x, y, z	[1, 1, 1]	[m]
	Number of control volumes, N x	1000	[-]
	Phase density at p 0 , ρ w,g,s	[1000, 100, 2000]	[kg/m 3 ]
	Phase compressibility, C w,g,s

-

  2D initial (rock, Ω 2 )

	Properties based on initial state: state = [P, z_CO2, z_Ions, z_H2O]
	initial state = [9.5e+01 1.0e-12 1.5e-01 1.5e-01]

Acknowledgements

The authors are grateful to Eric Flauraud (IFPEN) for providing the initial values for the "Extended chemical model" in Section 6.2.2, as well as for a careful reading of the paper.

used in this model. Note that we have provided the initial values both in terms of the overall mole fractions and in terms of the individual mole fractions (computed with the same python code listed above), and also that the concentration of the calcite can be directly computed as a function of the porosity (see equation 13). All fluid and chemical parameters (e.g., kinetic constants, reference mass density, etc.) are the same as in test case 6.1.1.

In addition to the two chemical systems described later, this test case can be executed with or without gravity (i.e. g = 0). We note that when gravity is included, it would have been more natural for the initial pressure to follow a hydrostatic law. However, the effect is quite small, and the simpler constant initial pressure was retained.

Property

Value Units

Gas injection rate,

Table 5: Boundary conditions and other simulation parameters.

Property

Value Units

Table 6: Values for all the relevant fluid and rock properties.

Simple chemical model

In that case, only one chemical reaction is included, and the chemical model is the same as in Section 6.1.1. However, one further simplification may be necessary: one may encounter convergence problems when running the system as described previously. If that is the case, it may be helpful to consider a single "meta-ion" Ca 2+ + CO 2- 3 in the liquid phase.

Extended chemical model

We consider a somewhat more realistic (albeit still quite small) chemical system, including dissociation of water and of carbonic dioxide, as this makes it possible to take into account the influence of pH.

The system is composed of 4 reactions:

Note that this increases the total number of species by three, particularly to z c = [ H 2 O, CO 2 , Ca +2 , CO -2 3 , H + , OH -, HCO -3 , CaCO 3 ]. However, this allows to represent the CaCO 3 reaction (last equation in ( 29)) with an explicit dependency on the pH of the solution.

The first three reactions are at equilibrium, the logarithms of the equilibrium constants are given in Table 7, while the fourth reaction is kinetic, and the rate for the last reaction is given by equation ( 27), with Q now defined by: Q = a Ca,w a HCO3,w a H,w .

(30) 95 -6.293 -10.279 -1.899 Table 7: Log 10 of the equilibrium constants for extended chemical system (29).

For this last case, the mass actions laws are expressed in activities:

Initial conditions computed using Arxim [START_REF] Moutte | Arxim, a library for thermodynamic modeling of reactive heterogeneous systems, with applications to the simulation of fluid-rock system[END_REF] are given in table 8. All other physical are the same as in test 6.2.1.

Expected output

Participants are expected to provide the following output, in the form of a CSV file for 1D output and a figure for 2D output. To make it easier to organize the results from different participants we ask that the submitted files follow a specific naming scheme, as detailed below. Each filename name has four parts: GROUP_CASE_LOC_VAR, where

A Appendix

1D injection

Properties based on injection state: state = [P, z_h2o, z_co2, z_ca, z_co3] Injection state = [1.65e+02 1.00e-12 1.00e+00 1.00e-12 1.00e

CO3-2 CaCO3 Composition, z_c 1.00e-12 1.00e+00 1.00e-12 1.00e-12 1.00e-12 Liquid MoleFrac 1.00e-11 1.00e-02 4.94e-01 4.94e-01 0.00e+00 Vapor MoleFrac 1.00e-12 1.00e+00 4.94e-13 4.94e-13 0.00e+00 Solid MoleFrac 0.00e+00 0.00e+00 0.00e+00 0.00e+00 1.00e+00 ------------------------------------------------------------------------------------------------------------------------------------------------------Liquid Vapor Solid Phase MoleFrac 1.02e-12 1.00e+00 1.00e-12 Mass Density 1.00e+03 1.01e+02 2.00e+03 Viscosity 1.00e+00 1.00e-01 0.00e+00 Sat. phi_tot 1.17e-13 1.00e+00 1.00e-12 Sat. phi_fluid 1.17e-13 1.00e+00 0.00e+00 ---------------------------------------------------------------------------

1D initial

Properties based on initial state: state = [P, z_h2o, z_co2, z_ca, z_co3] Initial state = [9.5e+01 1.5e-01 1.0e-12 7.5e-02 7.5e-02] ---------------------------------------------------------------------------H2O CO2 Ca+2 CO3-2 CaCO3 Composition, z_c 1.50e-01 1.00e-12 7.50e-02 7.50e-02 7.00e-01