J A García
email: jugarcia@mcm.upv.es

Ll Gascón

F Chinesta

F Trochu

A FLUX LIMITER STRATEGY FOR SOLVING THE SATURATION EQUATION IN RTM PROCESS SIMULATION

Keywords: Resin Transfer Molding, fixed mesh simulation, transport problems, flux limiters

The main aim of this work is the proposal of a numerical procedure for solving the saturation equation in RTM process simulation. In order to analyze in more detail the progressive impregnation of a fibrous preform by a fluid resin, the numerical model here proposed considers the flow through a partially saturated medium, including the dependence of permeability on the saturation degree. The model consists of an elliptic equation governing the pressure distribution and a transport hyperbolic equation governing the evolution of the saturation. A global flux limiter fixed mesh strategy is proposed for solving the transport equation with source term which describes the saturation evolution in RTM process. The flux limiter method has the ability to limit the extra numerical diffusion introduced by standard first-order schemes. This formulation could be an appealing choice for improving RTM flow simulations and optimize injection processes. Some preliminary numerical results are presented in order to validate the proposed numerical strategy.

INTRODUCTION

Liquid Composites Molding (LCM) processes are based on a proper resin impregnation of the reinforcement. Modeling and simulation play an important role in the development and optimization of molds production and in devising appropriate resin injection strategies. Minimization of mold filling time without losing part quality is an important issue in Resin Transfer Molding (RTM). Inadequate injection strategies tend to create macro and microvoids in the part, the formation of which depends on fluid flow velocity.

Over the last decades, different numerical techniques have been used to model the mold filling process in RTM. In general, RTM process simulation requires an accurate treatment of the advection equation which governs the evolution of different fluid properties: fluid presence function, incubation time, temperature, concentration of reacting components, degree of saturation, etc. In some of our former works [START_REF] García | A Fixed Mesh Numerical Method for Modelling the Flow in Liquid Composites Moulding Processes Using a Volume of Fluid Technique[END_REF][START_REF] Sánchez | Towards an efficient numerical treatment of the transport problems in the Resin Transfer Molding Simulation[END_REF] we proposed a new procedure to integrate accurately the transport of different fluid properties. In this work, that numerical procedure is extended for solving the transport equation governing the evolution of the saturation. In this model the permeability is assumed to be a function of saturation [START_REF] Breard | Numerical simulation of void formation in LCM[END_REF], and then the continuity equation that governs the pressure distribution, includes a source term which depends on the saturation. The presence of this source term explains the quadratic spatial pressure distribution in an unsaturated porous medium noticed in unidirectional flows.

To derive a closed model the saturation equation is considered whose source term depends on the micro and macro voids content.

The technique here used is based on a flux limiter fixed mesh strategy for solving the transport equation which governs the evolution of degree of saturation. It is well-known that spurious oscillations in the computed solution can be avoided by using first-order upwind discretization schemes, but unfortunately these first order schemes introduce an excessive numerical diffusion. One alternative for avoiding non-physical oscillations, reducing the extra numerical diffusion, lies in the use of second-order numerical fluxes in the regions where the solution is smooth enough that reduce to first-order in presence of discontinuities. This technique was successfully used for computing the volume fraction evolution in [START_REF] García | A Fixed Mesh Numerical Method for Modelling the Flow in Liquid Composites Moulding Processes Using a Volume of Fluid Technique[END_REF].

GOVERNING EQUATIONS

The model which describe the mould filling process is given by Darcy´s law [START_REF] García | A Fixed Mesh Numerical Method for Modelling the Flow in Liquid Composites Moulding Processes Using a Volume of Fluid Technique[END_REF] combined with the continuity equation, which should account for the loss of resin due to the perform impregnation. This can be done by incorporating a source term in the mass balance equation [START_REF] Sánchez | Towards an efficient numerical treatment of the transport problems in the Resin Transfer Molding Simulation[END_REF] where v is the velocity field, K is the preform permeability tensor, µ is the fluid viscosity, φ is the porosity, p is the pressure and S the degree of saturation. In order to evaluate the permeability, we make use of the model proposed by Breard et al. [START_REF] Breard | Numerical simulation of void formation in LCM[END_REF] for predicting void formation in LCM. Then, the permeability in Darcy's law should be considered as the product of the geometrical permeability, K Sat , and a relative permeability K rel (S), [START_REF] Breard | Numerical simulation of void formation in LCM[END_REF] where the relative permeability depends on the saturation degree [START_REF] Ruiz | Optimization of injection flow rate to minimize micro/macro-voids formation in resin transfer molded composites[END_REF] where β is a fitting factor whose usual values range in the interval [START_REF] Breard | Numerical simulation of void formation in LCM[END_REF]. Combining Eqs. ( 1) and ( 2) yields [START_REF] Trochu | New Approaches to Accelerate Calculations and Improve Accuracy of Numerical Simulations in Liquid Composite Molding[END_REF] Finally, to make a closed description of the flow, we assume the saturation equation proposed in [START_REF] Breard | Numerical simulation of void formation in LCM[END_REF][START_REF] Trochu | New Approaches to Accelerate Calculations and Improve Accuracy of Numerical Simulations in Liquid Composite Molding[END_REF], which governs the transport of the variable S: [START_REF] Sweby | High Resolution Schemes Using Flux Limiters For Hyperbolic Conservation Laws[END_REF] where the source term can take different forms. According to the model proposed by Breard et al. [START_REF] Breard | Numerical simulation of void formation in LCM[END_REF], the source terms writes:

(7) or (8)
where the model proposed by Ruiz et al. [START_REF] Trochu | New Approaches to Accelerate Calculations and Improve Accuracy of Numerical Simulations in Liquid Composite Molding[END_REF] is assumed. In this last model, α M and α m represent the dispersive coefficients of the macro and micro voids, respectively, and Q S is a function of the modified capillary number [START_REF] Breard | Numerical simulation of void formation in LCM[END_REF].

The saturation S takes a unit value in the saturated domain, a zero value in the empty region and varies between 0 and 1 in the partially saturated region. The whole domain has been designated by Ω and its boundary by ∂Ω. Initially, we assume the condition (9) where the saturation function on the inflow boundary is assumed unchanged during the filling process, that is:

(10)
The filling process simulation involves at each time step:

1. The calculation of saturation dependent permeability as well as the calculation of the source term of Eq. ( 5). 2. The calculation of the pressure distribution by applying a standard finite element discretization of Eq. ( 5). 3. The calculation of the velocity field from Darcy´s law (1). 4. The updating of the saturation distribution by integrating Eq. ( 6) using a flux limiter technique.

The boundary conditions are given by: • The pressure gradient in the normal direction to the mold walls vanishes.

• The pressure or the flow rate is specified on the inflow boundary (injection nozzle).

• The pressure is zero in the empty part of mold.

THE ADVECTION EQUATION

The saturation equation has a hyperbolic character, needing for appropriate stabilizations. In this section we propose a flux-limiter technique for its solution. For the sake of simplicity from now on we only consider one dimensional models.

In the one-dimensional case Eq. ( 6) reads:

(11)

and Eq. ( 11) can be integrated by applying a second-order upwind scheme preserving the TVD property [START_REF] Sweby | High Resolution Schemes Using Flux Limiters For Hyperbolic Conservation Laws[END_REF], whose discrete form writes:

where and

(13)

Here h represents the mesh size, Δt the time step and χ(r) is the flux limiter function. For the aproximation of the source term, and considering the model (7)

or using the expression of the source term given by (8)

The superscript UP is associated with the first-order upwind scheme and the superscript SW with the second-order scheme using a modified flux limiter technique (in our case the Sweby flux limiter). To define the coefficient r i+1/2 in Eq.( 13), we propose to define its value comparing consecutive variations of the approximate numerical solution with respect to the flow direction [START_REF] Sweby | High Resolution Schemes Using Flux Limiters For Hyperbolic Conservation Laws[END_REF]:

(16)

The Sweby flux limiter reads [START_REF] Sweby | High Resolution Schemes Using Flux Limiters For Hyperbolic Conservation Laws[END_REF]:

In general, if what guarantees that the scheme will be of in the neighbourhood of a discontinuity, since implies that the slopes of the solution have opposite signs. On the other hand, it is necessary that to obtain a second-order scheme in smooth regions of the solution. The limiter function should be chosen verifying both conditions and maximizing the antidiffusive flux. We remark in Eq.( 13) that the choice gives rise to the original first-order upwind method, whereas the choice defines a fully second-order scheme. Hence, the proposed hybrid scheme, with in Eq. ( 13), is of second-order in smooth regions of the solution but it is a firstorder method when a discontinuity is present. This allows avoid the spurious numerical oscillations associated with the conventional second-order methods in the presence of discontinuities and reduces the excessive numerical diffusion introduced by the first-order upwind schemes.

NUMERICAL SIMULATIONS

In order to analyze the accuracy and efficiency of the proposed numerical scheme just described for the discretization of the transport equation governing the evolution of the saturation, where the source term is given by Eq. ( 8), we analyze some one dimensional described [START_REF] Breard | Numerical simulation of void formation in LCM[END_REF]. A mold of 0.5m length is considered. A constant injection pressure is prescribed (10 -5 Pa) being the saturated permeability K sat and the resin viscosity 5.10 -11 m 2 and 0.1Pa.s, respectively. For the numerical simulation, we consider a time step of 0.1 seconds, α M =α m = 10 -10 , and a constant value R S =0.8. The domain is assumed initially empty, except the first element that represents the injection nozzle that is assumed full-filled.

To analyze the influence of mesh size on the simulated results, three meshes with different nodal distributions are considered, consisting in 30, 60 and 150 nodes, respectively. The associated numerical solutions are depicted in Fig. 1. for a filling time of 700 seconds, using the first-order scheme (Eqs. ( 12)-(13) with χ(r)=0) and using the Sweby flux limiter scheme (Eq. ( 12)-(13) with χ(r) defined by Eq.( 17)). We can notice that the convergence is faster when the flux limiter second-order scheme is considered. Fig. 1. proves also that the diffusivity of the scheme decreases with the mesh refinement. It can be noticed that the use of a first-order scheme introduces a significant numerical overdiffusion. Obviously, there are two terms that contribute to the front smoothing, the one related to the source term, and the one purely numerical introduced by the dicretization scheme. The last one can be reduced by using higher-order schemes and fine enough meshes.

Fig. 2. depicts the saturation profile each 100 seconds by applying both the first-order and the Sweby flux limiter scheme when 150 nodes are used in the space discretization. We can appreciate the significant impact of the discretization scheme on the computed solution. It can be also appreciated that the diffusion is lower, as expected, when flux limiter techniques are employed.

Fig. 2. Saturation profiles each 100 seconds, using the first-order scheme (left) and Sweby flux limiter (right).

To quantify the convergence different computations were performed using different mesh sizes (30, 60, 90, 120 and 150 nodes, respectively). The computed results are illustrated in Fig. 3. that represents the partially filled domain to the total length of the mold for both discretization schemes.

The pressure distribution varies linearly within each saturated element and is continuous between elements. The saturation and pressure distributions for a filling time of 700 seconds are represented in Fig. 4. It can be noticed the presence of three different behaviors: fully impregnation, unsaturated and empty domains. In the fully saturated regions the model reduces to the usual Darcy model, leading to a linear pressure distribution. In the partially saturated regions, the pressure distribution becomes parabolic, as announced in [START_REF] Breard | Numerical simulation of void formation in LCM[END_REF]. Finally, in the empty domain the pressure vanishes.

CONCLUSIONS

A new numerical procedure for simulating LCM processes has been presented. The numerical model is based on the consideration of partially saturated flows. For this purpose, the advection-diffusion equation describing the evolution of the saturation is solved by using a flux limiter upwind scheme. Numerical results confirm that first-order schemes exhibit an excessive and no realistic diffusion due to the numerical approximation of the advective term, while the flux-limiter scheme shows less extra-diffusive effects. Thus, the flux limiter proposed improves significantly the results (with respect to the first-order solutions). The results suggest that the present numerical method has a satisfactory capability of simulating the LCM process but further convergence analysis must be carried out.

Fig. 1 .

 1 Fig. 1. Numerical results for the saturation with the first-order scheme (left) and with the Sweby flux (right).

Fig. 3 .Fig. 4 .

 34 Fig. 3.Convergence analysis.

ACKNOWLEDGEMENTS

This research work is supported by a grant from the Ministerio de Educación y Ciencia (MEC), project DPI2007-66723-C02-01.


Mathieu Cladiere
email: mathieu.cladiere@leesu.enpc.fr

; Gasperi

; Lorgeoux

; Bonhomme

; Rocher

; Tassin

Alkylphenols compounds and bisphenol A contamination within a heavily urbanized area: case study of Paris

Keywords: Nonylphenol, bisphenol A, urban sources, Seine River, atmospheric fallout, heavily urbanized area

This study aims at evaluating the influence of a heavily urbanized area such as the Paris city area on receiving water contamination by bisphenol A (BPA) and alkylphenol ethoxylate by-product (APE). Firstly, concentrations in urban sources were investigated. Therefore, in addition to wastewater treatment plant effluents commonly studied, wet-weather urban sources including combined sewer overflows, urban runoff and total atmospheric fallout were considered. The first results highlight significant contaminations of all urban sources (from few ng/L in atmospheric fallout to several µg/L in other sources) with clearly distinguishable distribution patterns.

Secondly, the concentration changes along the Seine River from upstream to downstream of Paris conurbation were investigated. While concentrations of BPA and nonylphenoxy acetic acid (NP1EC) significantly increase because of urban sources, 4-nonylphenol concentrations are homogeneous along the Seine River. These results suggest a global dissemination of 4nonylphenol at the scale of the Seine River basin. Finally, the relationship between pollutant concentrations and Seine river flow were studied upstream and downstream of the Parisian conurbation. As a result, the clear decrease of NP1EC dissolved concentrations according to Seine River flow underlines the influence of punctual urban pollution on Seine River contamination.

Conversely, 4-nonylphenol dissolved concentrations reinforce the hypothesis of its widespread at the scale of the Seine River basin.

Introduction

Among the pollutants commonly pointed out in the literature for their endocrine disrupting properties, alkylphenol ethoxylates (APE) and the 2,2-(4,4 hydroxydiphenyl) propane commonly named bisphenol A (BPA) deserve special attention because of their global spread in the environment [START_REF] Staples | A review of the environmental fate, effects, and exposures of bisphenol A[END_REF][START_REF] Vethaak | An integrated assessment of estrogenic contamination and biological effects in the aquatic environment of The Netherlands[END_REF]. APE, mainly composed of nonylphenol ethoxylate (NPE: 80%) and octylphenol ethoxylate (OPE: 20%), are widely used for industrial and domestic applications, such as lubricating, oil additives, detergents and antistatic agents [START_REF] Ying | Environmental fate of alkylphenols and alkylphenol ethoxylates--a review[END_REF]. A reasonable estimate of the world annual production of NPE is around 500,000 tons [START_REF] Ying | Environmental fate of alkylphenols and alkylphenol ethoxylates--a review[END_REF]. BPA is mainly used as a monomer in the manufacture of polycarbonate plastics known for its high resistance to shocks and temperature (plastic windows or greenhouses, car bumpers, baby bottles), and in epoxy resins used as food contact lacquer for cans and tin cans. Due to its uses, the world production of BPA was evaluated at about 3,000,000 tons [START_REF] Vandenberg | Human exposure to bisphenol A (BPA)[END_REF] While BPA is recognized as an endocrine disrupting chemical [START_REF] Wetherill | In vitro molecular mechanisms of bisphenol A action[END_REF], NPE and OPE have been of rising concern because of their biodegradation by-products. Indeed, in urban or natural environment NPE can be biodegraded through oxidative or non-oxidative pathways [START_REF] John | Mechanism for Biotransformation of Nonylphenol polyethoxylates to xenoestrogens in Pseudomonas putida[END_REF][START_REF] Jonkers | Aerobic biodegradation studies of nonylphenol ethoxylates in river water using liquid chromatography-electrospray tandem mass spectrometry[END_REF]. Under oxidative biodegradation pathway, NPE turn into carboxylic acids such as nonylphenol acetic acid (NP1EC) while under non-oxidative biodegradation pathway, short chain ethoxylates are produced such as nonylphenol diethoxylate (NP2EO) and nonylphenol monoethoxylate (NP1EO) [START_REF] Giger | Environmental fate of phenolic endocrine disruptors: field and laboratory studies[END_REF]. Finally, NP1EC and NP1EO can be biodegraded into 4-nonylphenol (4-NP) known as the most toxic and persistent by-products of NPE in the aquatic environment [START_REF] Servos | Review of the aquatic toxicity, estrogenic responses and bioaccumulation of alkylphenols and alkylphenol polyethoxylates[END_REF].

The occurrence of APE and BPA in environment is closely correlated with anthropogenic activities. Many studies suggest that these chemicals preferentially enter into the environment through urban sources [START_REF] Sharma | Nonylphenol, octylphenol, and bisphenol-A in the aquatic environment: A review on occurrence, fate, and treatment[END_REF][START_REF] Ying | Environmental fate of alkylphenols and alkylphenol ethoxylates--a review[END_REF]. Among the urban sources investigated in the literature, the effluents of wastewater treatment plants (WWTP) are frequently studied [START_REF] Hohne | Occurrence and temporal variations of the xenoestrogens bisphenol A, 4-tert-octylphenol, and tech. 4-nonylphenol in two German wastewater treatment plants[END_REF][START_REF] Loyo-Rosales | Fate of octyl-and nonylphenol ethoxylates and some carboxylated derivatives in three American wastewater treatment plants[END_REF][START_REF] Voutsa | Benzotriazoles, alkylphenols and bisphenol a in municipal wastewaters and in the Glatt River, Switzerland[END_REF][START_REF] Zhou | Behaviour of selected endocrine-disrupting chemicals in three sewage treatment plants of Beijing, China[END_REF]). On the contrary, studies on wet weather urban sources such as combined sewer overflows (CSOs) and urban runoff are less available, despite their high contamination [START_REF] Björklund | Phthalates and nonylphenols in urban runoff: Occurrence, distribution and area emission factors[END_REF][START_REF] Gasperi | Priority pollutants in wastewater and combined sewer overflow[END_REF]).

The Seine Basin, located in North-West part of France, drains approximately a 32,000 km² area from its headwaters to Paris. It can be considered as representative of river basins exposed to the impacts of intense human activity (Parisian conurbation: 12 million of inhabitants, among the thirty most populous cities in the world and the third in Europe after Moscow and London) [START_REF] Meybeck | Historical perspective of heavy metals contamination (Cd, Cr, Cu, Hg, Pb, Zn) in the Seine River basin (France) following a DPSIR approach[END_REF]). This basin combines strong anthropogenic pressures with a very limited dilution factor in the Seine River, due to its low flow rate (Seine River median flow at Paris: 350 m 3 /s). Actually, no comprehensive data on the occurrence of APE and BPA are presently available for the upper part of the Seine basin. As far as we are aware, only few studies deal with the influence of such heavily urbanized conurbations (more than 10 millions of inhabitants) on their environment [START_REF] Isobe | Distribution and behavior of nonylphenol, octylphenol and nonylphenol monoethoxylate in Tokyo metropolitan area: Their association with aquatic particles and sedimentary distributions[END_REF] and none of them focus on watershed of European cities.

As a consequence, the study tackles several objectives. The first objective is to assess the occurrence of APE and BPA concentrations and their relative significance in different urban sources of the Parisian conurbation such as the effluents of the major WWTP, the main CSO outfall and urban runoff. Secondly, this study aims at evaluating the influence of the Parisian conurbation on receiving water between upstream and downstream sampling sites. Finally, the last objective is to better examine the concentration variation of target compounds according to the hydrological conditions on upstream and downstream sites.

Materials and methods

Sampling sites / campaigns

Seine River water was collected at three locations (n=11 for each sampling location; Table 1) from February 2010 to February 2011. The first site, Marnay, is located upstream of the Parisian conurbation (weakly urbanized). The second site, Bougival, is located just downstream of Paris City (heavily urbanized). Finally, the last site, Meulan, is located downstream of all Parisian wastewater effluent discharges (heavily urbanized) (Fig. 1). In addition, the Orgeval River in an agricultural experimental catchment [START_REF] Vilain | Budget of N2O emissions at the watershed scale: role of land cover and topography (the Orgeval basin, France)[END_REF]) was also monitored during year 2011 (n=9) (Fig. 1). All samples were manually collected in 2 L glass amber bottles previously pyrolysed at 500°C to avoid sample contaminations. Samples were collected in 2L glass amber bottles also pyrolysed at 500°C. Among these five WWTPs, three different processes of wastewater treatment are considered. Firstly, the WWTP1 use conventional activated sludge (AS) for carbon and nitrogen removal (AS-WWTP), WWTP4 use activated sludge for carbon removal and biofiltration (B) for nitrogen removal (ASB-WWTP), finally the more recent WWTP2, WWTP3 and WWTP5 use biofiltration units for both carbon and nitrogen removals (B-WWTP). The removal efficiencies on organic matter (evaluated with the Chemical Oxygen Demand: COD) and nitrogen (nitrification: Total Kjeldahl Nitrogen (TKN), denitrification: total nitrogen (TN)) are disclosed in Table 1. According to these efficiencies, WWTP1,2,3 and 5 reveal high removals for organic matter and nitrogen. Conversely, WWTP4 which is the largest WWTP of the Parisian conurbation and one of the biggest in the world (more than 1,600,000 m 3 of wastewater treated every day) highlights lower efficiencies for organic matter (COD: 85%), nitrogen (TKN: 70%; TN: 20%) and SS (90%). Measures for the modernization of this WWTP are under way to improve its efficiency for carbon and nitrogen removals. In addition to WWTP effluents, urban sources during wet weather period were also sampled, i.e. combined sewer overflows (CSOs) and urban runoff in separate sewer. CSOs were sampled at Clichy outfall, one of the biggest outfalls of the Parisian conurbation, for 8 events (discharged volumes ranging from 35,000 m 3 to more than 1,000,000 m 3 ) (Fig. 1). Urban runoff was sampled at the outlet of small sub-urban catchment (Sucy-en-Brie) for 4 rain events (Fig. 1). For CSOs and runoff, samplings were performed by an automatic sampler. Flow-weighted composite samples representative of the entire discharges were considered for analyse. At last, TAF were collected at Paris city (heavily urbanized; n=10), Lognes (weakly urbanized; n=5) and at the Fontainebleau forest (n=5) in 10 L glass bottles fitted with 1 m² aluminium funnels (Fig. 1) during 7 periods (15 days) between January and November 2011.

Analytical procedure

Sample preparation

Bisphenol A (BPA), 4-nonylphenol (4-NP), nonylphenol mono-and diethoxylate (NP1&2EO), nonylphenol acetic acid (NP1EC), 4-tert-octylphenol (4-t-OP) and octylphenol mono-and diethoxylate (OP1&2EO) were analyzed in dissolved and SS. After filtration (GF/F, Whatman), 100 mL of dissolved phase for CSOs or 250 mL for all other water samples were spiked with a surrogate standard mixture (BPA-d6, NP1EO-d2, OP-d17) before extraction.

For dissolved phase, samples were extracted by solid phase extraction (Autotrace SPE Workstation, Caliper LifeScience) using OASIS ® HLB cartridges (200 mg, 6 mL). After conditioning with 10 mL of methanol and 10 mL of ultrapure water, dissolved samples were extracted at 5 mL/min, under neutral pH. After drying, elutions were performed with 12 mL of a mixture methanol (MeOH)/Dichloromethane (DCM)/Ethyl acetate (Etace) (40/40/20, v/v).

After freeze-drying, the SS were extracted by microwave assisted extraction using a multiwave 3000 (Antonn Paar). The filters, were extracted using 20 mL of MeOH/DCM (60/40, v/v) mixture at 100°C and 7 bars during 30 min. After extraction, samples were cleaned up by SPE using OASIS ® HLB (200 mg, 6 mL). Basically, after conditioning (3 mL MeOH and 3 mL MeOH/H2O (20/80 v/v), the samples dissolved in 500 µL of MeOH/H2O (50/50 v/v) mixture, were deposited on the top of the cartridges. Then, the cartridges were washed with 3 mL of H2O prior to elution with 9 mL of MeOH/DCM/Etace (40/40/20, v/v/v) mixture.

UPLC-MS-MS analysis

Before analysis, both extracts were concentrated and spiked with internal standard for quantification (BPA-d16, n-NP and n-NP1EO). The analysis was performed by liquid chromatography coupled to a tandem mass spectrometry, LC-MS-MS (AQUITY UPLC / TQD, Waters). APEOs and BPA were separated on an AQUITY UPLC / BEH C18 column, heated at 40 °C, with ultrapure water (A) and methanol (B) each containing 4.5 mM NH4OH. Equilibration takes place with 50 % B at 0.4 mL/min and 10 µL of sample were injected. The mass spectrometer is equipped with an electrospray interface used in positive ionization mode (ESI+) for NP1&2EO and OP1&2EO and negative ionization mode (ESI-) for all other compounds. The compounds were detected in multiple reactions monitoring mode (MRM) with two mass transitions.

In order to assess the variability of the analytical protocol, three surface water samples from the same sampling location (downstream of WWTP 4) were individually analyzed. This variability was only studied for the dissolved phase extraction and UPLC-MS-MS analysis and not for the suspended solids. Actually, in receiving water, alkylphenols and BPA are mostly present in the dissolved phase (4-NP: 80%; 4-t-OP: 90% and BPA: 95%; [START_REF] Cladiere | Alkylphenol ethoxylates and bisphenol A in surface water within a heavily urbanized area, such as Paris[END_REF][START_REF] Isobe | Distribution and behavior of nonylphenol, octylphenol and nonylphenol monoethoxylate in Tokyo metropolitan area: Their association with aquatic particles and sedimentary distributions[END_REF].

The dissolved phases of the three water samples were extracted in triplicates and each extraction was also analyzed in triplicates. Thus, nine concentration values were obtained for each sample and every target compound. The nine values were compared to the median in order to calculate relative deviations that are representative of the analytical variability. Finally, the absolute values of relative deviations generated for the three samples (9x3=27) were represented on Fig. 2 For 4-NP, NP1EC and NP2EO, the relative deviations globally lie within the 0 -15% range while maximum values reach 20% for 4-NP. Thus, in order to account 75% of the relative deviation values (bold lines), the analytical variabilities (±AV) of 4-NP, NP1EC and NP2EO were respectively estimated at 10%, 6% and 13%. For BPA and NP1EO, the relative deviations were calculated only for 21 analyses since their concentrations were close to their limit of quantification (LOQ: BPA: 11 ng/L; NP1EO: 10 ng/L). Similarly to previous compounds and in order to account 75% of the relative deviation values (bold lines), the analytical variabilities of BPA and NP1EO

were respectively evaluated at 35% and 31%. For OPE, the analytical variabilities were not evaluated since these compound concentrations were mostly under their limit of quantification (4-t-OP: 4 ng/L; OP1EO: 12 ng/L and OP2EO: 3 ng/L) in investigated surface water.

Data exploitation

The concentrations presented in this study are total concentrations (expressed in ng/L) calculated by summing dissolved concentrations (ng/L) and SS concentrations (ng/L). For the variations of concentrations with hydrological conditions, only the dissolved phase was considered in order to better assess the origins of target compounds (punctual or diffuse sources) within the Seine River.

Results are displayed in box plots which extend from the 1st quartile (Q1) to the 3rd quartile (Q3)

and thus contain the central half of the distribution score. Dotted lines symbolize 1.5 times the interquartile range while outliers are indicated as points above or below the dotted lines.

Since concentration distributions of each sampling point cannot be assumed to be normally distributed; non parametric tests were performed to compare concentrations found on different sites. The Wilcoxon signed-rank test was selected to compare the Marnay, Bougival and Meulan sites since samplings were collected on the same day at the three sites. For the same reason, the Wilcoxon signed-rank test was also used to compare the WWTP effluents. For all other matrices and sampling sites (TAF, CSO, runoff and Orgeval), the Mann-Whitney U test was selected to compare distributions of different sizes. In accordance with the analytical variabilities, statistical significance was accepted at p < 0.1 for all comparisons.

Results and discussions

Urban sources

Wastewater treatment plants

Results found in WWTP effluents for BPA and NPE are illustrated in Fig. 3. Three groups corresponding to AS-WWTP, ASB-WWTP and B-WWTP as described earlier are considered. By comparing the AS-WWTP and B-WWTP effluents (Wilcoxon signed-rank test), no significant differences of concentrations appear for all target compounds (p > 0.1). The ASB-WWTP effluent does not exhibit any statistical difference compared to AS-WWTP and B-WWTP effluent for BPA and 4-NP (p > 0.1). Conversely, for NPE by-product (NP1EC, NP1EO and NP2EO) significant differences were found between ASB-WWTP and AS-WWTP + B-WWTP effluents (p < 0.05).

The higher concentrations found in ASB-WWTP effluents can be certainly explained by the lower biodegradation rate on organic and nitrogenous matter (COD: 86%, NTK: 70%, TN: 21%) and to a lesser extent by the higher concentration of SS (23 mg/L for WWTP4, against 5 and 10 mg/L for other WWTPs).

Urban sources during wet weather period

Concentrations found in CSOs, runoff and TAF are exhibited in Table 2. The concentrations reported in the Table 2 disclose significant differences between TAF, on the one hand, and CSOs and runoff on the other hand (p < 0.01). For example, while concentrations of BPA range between 10(±4) and 180(±63) ng/L in TAF, concentrations vary between 917 and 2098 ng/L (about 32 times higher) in CSOs and between 287 and 1224 ng/L (about 13 times higher) in runoff. In addition, changes of pattern are clearly noticeable in Table 2. Indeed, while 4-NP has the highest median concentration in TAF (80(±8) ng/L), BPA is the predominant compound in CSOs and runoff (CSO: 1410(±495) ng/L; runoff: 635(±222) ng/L).

TAF concentrations are generally low. Minimal concentrations are lower or close to the limits of quantification whereas median concentrations are always lower than 100 ng/L (Table 2). The non parametric Mann-Whitney U test, performed for the three sampling locations, points out that the concentrations of BPA are statistically greater in Paris (heavily urbanized) and in Lognes (weakly urbanized) than in Fontainebleau (forest) while no significant difference between the three sites is found for NPE.

Higher concentrations in CSOs and runoff compared to those measured in TAF highlight a clear enrichment from atmosphere to catchment outlet. These enrichments could originate from wastewater for CSOs or road and buildings leaching [START_REF] Björklund | Phthalates and nonylphenols in urban runoff: Occurrence, distribution and area emission factors[END_REF][START_REF] Bressy | Alkylphenol in atmospheric depositions and urban runoff[END_REF] for runoff since NPE and BPA are used in building material (concrete, plastics). For both CSOs and runoff, the concentrations measured were close to those reported in untreated wastewaters [START_REF] Zhou | Behaviour of selected endocrine-disrupting chemicals in three sewage treatment plants of Beijing, China[END_REF]). These high concentrations underline necessity to treat wet weather effluents such as CSOs and runoff in order to avoid short-term pollutions of receiving water during wet weather periods especially for BPA.

Comparing CSOs and urban runoff, BPA, 4-NP and NP1EO revealed significant differences of concentrations while NP1EC and NP2EO concentrations were statistically equivalent. Although these results suggest that the wastewater contained in CSOs may play a role in 4-NP, BPA and NP1EO concentrations, no correlation could be drawn between wastewater proportion and total concentrations of compounds in CSOs (R² < 0.25 for all investigated compounds). However, a good correlation between maximum flows discharged by CSOs (Qmax: m 3 .s -1 ) and particulate contents could be drawn for all target compounds (R² ≈ 0.80). The higher the Qmax, the higher the particulate contents. These results may confirm the existence of in-sewer sources such as sewer deposit erosion during high-intensity events. For some events, [START_REF] Gasperi | Contributions of wastewater, runoff and sewer deposit erosion to wet weather pollutant loads in combined sewer systems[END_REF] demonstrated that in-sewer deposit erosion can actually play a major role in the polycyclic aromatic hydrocarbon or suspended solid contaminations of CSOs.

Surface water

Concentration change in relation to urbanization gradient

In order to track the influence of urban sources (WWTPs, CSOs and runoff) on the Seine River, the dissolved organic carbon (DOC) concentrations in Marnay, Bougival and Meulan were analysed in addition to target compounds. As expected, whatever the measurement campaign, a significant increase of DOC concentrations was noticed between Marnay (median: 2.0 mgC/L), Bougival (2.8 mgC/L) and Meulan (3.3 mgC/L) (Wilcoxon signed-rank test; p < 0.05).

At the scale of all investigated sites, the concentrations ranged from < 11 ng/L to 154(±54) ng/L for BPA, from 28(±3) ng/L to 157(±16) ng/L for 4-NP and from 2.1(±0.1) ng/L to 274(±16) ng/L for NP1EC. These concentrations found in surface water within the Parisian conurbation were similar to concentrations reported in Europe [START_REF] Brix | Analysis and occurrence of alkylphenolic compounds and estrogens in a European river basin and an evaluation of their importance as priority pollutants[END_REF][START_REF] Jonkers | Occurrence and sources of selected phenolic endocrine disruptors in Ria de Aveiro, Portugal[END_REF], but lower than in the Seine River estuary (4-NP: 168 ng/L and NP1EC: 544 ng/L; [START_REF] Cailleaud | Seasonal variation of hydrophobic organic contaminant concentrations in the water-column of the Seine Estuary and their transfer to a planktonic species Eurytemora affinis (Calanoïd, copepod). Part 2: Alkylphenol-polyethoxylates[END_REF]).

Concerning the upstream sites Orgeval (representative of rivers not influenced by urban activities)

and Marnay (weakly urbanized) the concentrations of target compounds generally lie close to concentrations found in TAF. As a result, these sites could be considered as In the first group including BPA and NP1EC, significant differences (p < 0.05) of concentrations between upstream sites (medians at Orgeval and Marnay: BPA: 20(±7) ng/L; NP1EC: 16(±1) ng/L) and downstream sites (Bougival and Meulan BPA: 66(±23) ng/L; NP1EC: 124(±7) ng/L) are noticed (Fig. 4). A similar evolution of NP1EC concentrations from upstream to downstream stations of the Glatt River have been pointed out by [START_REF] Jonkers | Mass flows of endocrine disruptors in the Glatt River during varying weather conditions[END_REF]. These significant differences underline the influence of urban sources on receiving water for BPA and NP1EC.

Conclusions

This study aimed at investigating the APE and BPA in urban sources and evaluating the impact of In this study, a significant influence of the Parisian conurbation on NP1EC and BPA concentrations along the Seine River (respectively from 17(±1) ng/L to 124(±7) ng/L and from 20(±7) ng/L to 66(±23) ng/L) was observed. For all other NPE, no significant evolution of concentrations from upstream to downstream sites was noticed suggesting that urban sources of the Parisian conurbation do not have major effect on receiving water and underlining the existence of diffuse sources at the scale of the Seine River basin. Finally, the variation of dissolved concentrations according to the Seine River flow at Meulan and Marnay sites exhibits the importance of spot urban sources for NP1EC, and reinforces the hypothesis of the global dissemination of 4-NP at the scale of the Seine River basin. Unfortunately, the cases of BPA and NP1EO could not be interpreted because of their high analytical variabilities.

In order to better understand the homogeneity of 4-NP concentrations along the Seine River as well as the dynamic of NPE within the Seine River, a further study should be carried out to asses the biodegradation rates of these compounds in receiving water. Finally, the diffuse sources probably linked to river flow origins have to be clearly identified and better assessed in order to understand the widespread of NPE and BPA at the scale of the Seine River Basin.

Fig. 1

 1 Fig. 1 Sampling sites within the Parisian conurbation

Fig. 2

 2 Fig. 2 Distribution histograms of relative deviations of BPA, 4-NP, and NP1EC to the median value. The bold lines represent the third quartile of the relative deviations.

Fig. 3

 3 Fig. 3 Concentrations of target compounds (ng/L) in WWTP effluents. AS: activated sludges; B: biofiltration; ASB: activated sludge (carbon removal) + biofiltration (nitrogen removal)

Fig. 4

 4 Fig. 4 Change of NPE and BPA concentrations according to urbanization gradient

1050 m 3 Fig. 5

 35 Fig. 5 Dissolved concentrations of target compounds (ng/L) versus Seine River flow (m 3 /s) at Marnay (a) and Meulan (b)

a

  heavily urbanized area such as the Parisian conurbation on the receiving water. Hence, urban sources such as WWTP effluents, combined sewer overflows, urban runoff and total atmospheric fallout were studied. Depending on the urban sources considered, differences of concentrations and distribution patterns appear. WWTP effluents are featured by the predominance of NPE, especially NP1EC, due to aerobic biological treatments of wastewater. No seasonal trend of concentration as well as no significant difference of concentration according to the biological treatment of wastewater was noticed. Only the effluent of WWTP4 (one of the biggest WWTP in the world) revealed higher concentrations of NPE and BPA due to lower efficiencies on carbon and nitrogen removals than the other WWTPs. Conversely, wet weather urban sources (CSOs and runoff) are dominated by BPA probably due to wastewater contribution and leaching of building materials.

Table 1 sampling site characteristics

 1

	Sample	n	period	comments / details
	Orgeval River	9	Mar 2011 -Nov 2011	Upstream site  Agricultural watershed Manually collected in 2 L glass bottles
	Seine River	11	Feb 2010 -Feb 2011	3 stations (Marmay, Bougival, Meulan) increasing urbanization Manually collected in 2 L glass bottles
			Jan 2011
	WWTP effluent 11	-
			Nov 2011

WWTP x (vol): process efficiency COD, NTK, TN, SS WWTP

				1 (385,000 m 3 /d):AS,	96% ,	97%,	74%,	98%
				WWTP 2 (48,000, m 3 /d): B,	93%,	95%,	86%,	97%
				WWTP 3 (233,000 m 3 /d): B ,	95%,	96%,	70%,	98%
				WWTP 4 (1,612,000 m 3 /d):AS + B,	86%,	70%,	21%,	91%
				WWTP 5 (92,000 m 3 /d): B ,	94%,	92%,	82%,	97%
	CSO	8	June 2010 -Nov 2010	volume per event: 35,000 to 1,000,000 m 3 automatic samplers 12 bottles  Weighted mean samples
	Total atmospheric fallout	20	Feb 2011 -Nov 2011	3 sites (Paris City, Lognes, Fontainebleau) Total atmospheric fallout (dry + wet) (on 15 days)
	Urban runoff	4	July 2011 -Oct 2011	samples collected at Sucy-en-Brie outfall, separated sewer automatic samplers 12 bottles  Weighted mean samples

Table 2

 2 Total atmospheric fallout, CSO and runoff concentrations (ng/L)

	Compound TAF n=20 (ng/L)	CSO n=8 (ng/L)	Runoff n=4 (ng/L)
		min-max (median)	min -max (median)	min -max (mean)
	BPA	10 -180 (40)	917 -2098 (1410)	287 -1224 (635)
	4-NP	<LQ 1 -167 (80)	445 -1208 (668)	272 -533 (400)
	NP1EO	<LQ 1 -65 (21)	357 -1257 (598)	47 -401 (184)
	NP2EO	<LQ 1 -301 (10)	138 -401 (250)	146 -847 (402)
	NP1EC	2 -63 (15)	220 -591 (251)	193 -426 (128)

1 : <LQ: lower than limit of quantification

Acknowledgment

This study was carried out within the framework of PIREN-Seine and OPUR research programs.

Urban runoff was studied within the framework of the INOGEV French ANR project. The authors want to gratefully acknowledge the Parisian public sanitation service (SIAAP) and more especially Céline Briand and Jean Daste-Blanc for their helpful assistance for WWTP effluent and CSO samplings. The authors also want to thank Mohamed Saad, Cécile Mirande-Bret, Alex Segor, Philippe Dubois and Lila Boudahmane for their valuable assistances.

However, while Bougival and Meulan sites exhibit similar concentrations of BPA, a significant difference could be noticed for NP1EC between both sites (p < 0.05). This difference is linked to the large volume discharged by WWTP4 coupled with high concentrations of NP1EC (median: 861±51 ng/L). Thus, whereas the NP1EC was the lowest NPE by-product in upstream sites, it becomes predominant at Meulan. Similarly, the prevalence of NP1EC on a large range of organic pollutants in the Danube River has been reported by [START_REF] Loos | Occurrence of polar organic contaminants in the dissolved water phase of the Danube River and its major tributaries using SPE-LC-MS2 analysis[END_REF].

The second group of compounds (NP1EO and NP2EO) reveals no significant difference of concentrations between all sites (NP1EO: 45(±14) ng/L and NP2EO: 50(±6) ng/L). The concentrations found in the Orgeval River (agricultural basin) are statistically similar to those found at Meulan site (p > 0.5). A large variation of NP1EO concentrations is observable at Bougival site (min: 20(±6) ng/L; max: 213(±66) ng/L) (Fig. 4). The highest concentrations found at Bougival could be the consequence of the activities generated by Gennevilliers Harbour (the greatest of Île-de-France) located upstream of the sampling site.

Finally, the last group (4-NP and 4-t-OP) reveals a contrasted pattern. A significant difference (p < 0.05) of concentrations between Orgeval River (agricultural basin) and Seine River sites (Marnay, Bougival and Meulan) could be noticed on Fig. 4. The occurrence of 4-NP in the Orgeval River (median: 61(±6) ng/L) could be imputed either to mixture of diffuse sources such as TAF (median: 80(±8) ng/L) and groundwater [START_REF] Latorre | Presence of nonylphenol, octyphenol and bisphenol a in two aquifers close to agricultural, industrial and urban areas[END_REF], and/or to agricultural activities [START_REF] Zgola-Grzeskowiak | Determination of nonylphenol and short-chained nonylphenol ethoxylates in drain water from an agricultural area[END_REF]). Conversely, Marnay site could be partially impacted by urban sources and by biodegradation of precursors (NP1EC, NP1&2EO) into 4-NP along the Seine River.

Nonetheless, no statistical difference between Marnay (weakly urbanized), Bougival and Meulan (heavily urbanized) sites could be drawn (p > 1). This homogeneity of concentrations along the Seine River suggests that urban sources are probably not predominant sources of 4-NP on receiving water. Thus, diffuse sources such as TAF, groundwater and biodegradation of 4-NP precursors could play a key role in the occurrence of 4-NP in the environment and the homogeneity of its concentrations along the Seine River. This observation is in agreement with a previous study reporting the same observation on the Glatt River in Switzerland [START_REF] Jonkers | Mass flows of endocrine disruptors in the Glatt River during varying weather conditions[END_REF]).

The concentrations found in the Seine River are far lower than concentrations leading to an acute lethal effect on aquatic wildlife (lethal concentration (LC50) for rosy barb: 344 µg/L; [START_REF] Bhattacharya | Toxicity studies of nonylphenol on rosy barb (Puntius conchonious): A biochemical and histopathological evaluation[END_REF]). However, these authors have claimed that concentration closer to those reported in the Seine River could lead to histopathological effects on gills, liver and kidney of the same fish. In addition [START_REF] Brian | Evidence of estrogenic mixture effects on the reproductive performance of fish[END_REF] have highlighted the mixture effects of 4-NP, 4-t-OP and BPA. They have reported that the mixture of these three compounds has a greater estrogenic effect on fish's reproduction than each compound separately. Therefore, even the low concentrations found in the Seine River may have chronic effects en aquatic wildlife.

Variation of pollutant concentrations according to hydrological conditions

The dissolved concentrations of BPA, 4-NP and NP1EC measured at Marnay and Meulan were compared to the Seine River flow on the Fig. 5. During the sampling period, from February 2010 to February 2011, the Seine River flow ranged from 13 to 228 m 3 /s at Marnay and from 157 to