C Palmier

G Schäfer

On the influence of groundwater table fluctuations on oil thickness in a well related to an LNAPL contaminated aquifer

. It should consider the transient mass exchange between the well and the porous media. Also, the proposed model shows that making the assumption of equilibrium conditions as suggested by Parker et al. (2017) for calculating the volume exchanges between the wells and its surrounding introduced errors. Considering transient transfers of oil better reflects the field observations. This observation is a key outcome for improving field data interpretation (e.g.: bail-down test data) and the remedial approach at site polluted by mineral oils.

Introduction

Since the 1950s, an increasing number of sites contaminated by hydrocarbons or mineral oil have been identified in industrialized countries. These compounds correspond to liquids that are immiscible in water, and because they are generally lighter than water, they are so-called light nonaqueous phase liquids (LNAPL). To recover this oil present in the subsurface, it is of primary importance to estimate the amount of oil present in the porous media and its evolution. The amount of oil retained in the unsaturated and saturated zones is not equivalent to the amount present in a monitoring well, due to the effects of porosity and capillary pressure. Furthermore, the oil distribution in the soil and the oil that will flow to the well is also driven by the groundwater fluctuation [START_REF] Gatsios | LNAPL transmissivity as a remediation metric in complex sites under water table fluctuations[END_REF]. For instance, [START_REF] Deska | Impact of the Water Table Fluctuations on the Apparent Thickness of Light Non-Aqueous Phase[END_REF] showed in a simplified experiment that the LNAPL thickness in the aquifer was different from the one measured in the well. Some simplified field methods [START_REF] De Pastrovich | Protection of groundwater from oil pollution[END_REF][START_REF] Hughes | Two techniques for determining the true hydrocarbon thickness in an unconfined sandy aquifer[END_REF][START_REF] Zilliox | Effects of hydrocarbon processes on the development of ground-water pollution: study on physical models in a saturated porous medium[END_REF] were proposed to estimate the oil thickness in the aquifer but a comparison of these methods at a site [START_REF] Dippenaar | Determining actual LNAPL plume thickness: Review and case study in a fractured aquifer[END_REF] showed results that were not satisfactory, mainly because the methods did not calculate correctly the capillary effects. Several scientific publications addressed the quantification of the LNAPL volume in homogeneous media [START_REF] Charbeneau | Free-Product Recovery of Petroleum Hydrocarbon Liquids[END_REF]Lenhard and Parker, 1990a) or heterogeneous media [START_REF] Johnston | Characteristics of light nonaqueous phase liquid recovery in the presence of fine-scale soil layering[END_REF]. However, temporal variations of oil thickness in a well linked to variations in the water-table levels were rarely studied.

The amount of LNAPL in a well has been shown to vary with the water table. [START_REF] Ballestero | An Investigation of the Relationship Between Actual and Apparent Gasoline Thickness in a Uniform Sand Aquifer[END_REF] showed that the LNAPL thickness in a well increases when the water-table drops and declines when the water-table rises. [START_REF] Steffy | A field study of the vertical immiscible displacement of LNAPL associated with a fluctuating[END_REF] measured in detail the temporal variations of LNAPL thicknesses both in an aquifer and a well. They showed that the LNAPL moves vertically in an aquifer with water-table fluctuations leading to periods of absence of LNAPL in the well when groundwater is high. Other experiments involving water-table fluctuations outlined that after several events of water table rise and fall, the LNAPL layer was also moving [START_REF] Steffy | Numerical simulations and long-column tests of LNAPL displacement and trapping by a fluctuating water table[END_REF], and the oil was spreading laterally in the porous media leading to lower average oil saturations. In a similar way, [START_REF] White | A Practical Model for Mobile , Residual , and Entrapped NAPL in Water-Wet Porous Media[END_REF] showed that during the first drainage stage there is a significant loss of mobile oil into a residual (immobile) saturation, thus reducing significantly the mobile amount. Experimental work showed that during the water-table variation the LNAPL top and bottom position vary both in the well and in the aquifer. Due to the potential delay between the movement in the aquifer compared to movement in the well the thickness of the oil layer in the well can vary significantly and LNAPL can even disappear from the well at high water-table levels.

Additionally, very few papers detail the effects of water-table variations with mainly two different explanations for the origin of the variations. On one hand, [START_REF] Marinelli | LNAPL thickness in monitoring wells considering hysteresis and entrapment[END_REF] and [START_REF] Kemblowski | Hydrocarbon thickness fluctuations in monitoring wells[END_REF] suggest that the thickness variations are mainly due to the difference in residual saturation (Sor) in the saturated and unsaturated zone of the porous aquifer. The authors provide an analytical solution linking the variations in the well to those in the porous media. However, their approach does not quantify transient mass exchanges between the well and the porous media and the solution was not compared to actual field data. On the other hand, [START_REF] Aral | Effect of groundwater table fluctuations on LNAPL thickness in monitoring wells[END_REF] provided a model for the transient exchange between the well and the aquifer, that was based on a simplified homogeneous LNAPL layer, without considering the effect of variable Sor. Recently, [START_REF] Lenhard | A practical tool for estimating subsurface LNAPL distributions and transmissivity using current and historical fluid levels in groundwater wells: Effects of entrapped and residual LNAPL[END_REF] presented a modelling approach to compute the distribution of LNAPL in the porous media from actual and historical well data. Their approach adds the properties of entrapped oil to the classical capillary equilibrium approach introduced by Lenhard and Parker (1990b) and relates the amount of residual oil to the historical positions of the oil in the well. As it is based on an equilibrium assumption, this approach cannot be used to assess the oil permeability of the aquifer.

The objective of this paper is to present a novel modeling approach that considers both the role of the residual oil saturations (Sor) and vertical movement of the LNAPL layer in the aquifer. To our knowledge, this approach is the first to present a simple approach based on a multiphase description of the medium that allows to fully interpret the transient variations of well thickness and position in a well. The approach must remain simple and easy to implement as it is intended to fit field data that were obtained by continuous measurements of the vertical LNAPL position in a well. The analysis concerns two scenarios; a pumping well where the LNAPL layer is unconfined and one where the oil layer is present in a confined porous media. This paper is organized as follows. Section Material and Methods presents ii) the key assumptions to calculate the groundwater fluctuations in both the well and the aquifer, ii) theoretical background proposed to explain how the oil saturation is influenced by the groundwater fluctuation, and iii) the field case study. In the Section Results, the proposed theoretical model is applied for some test cases, and for the unconfined and confined conditions encountered during the field study. Results from the theoretical model are compared to the field measurements. Finally, the sections Discussion and Conclusion expand the conclusions from Section Results comparing the obtained results with other approaches and discussing the domain in which this approach can be applied.

Material and methods

Theoretical background

The floating oil phase thickness in a well can vary rapidly, and this change in thickness in the well cannot reflect the variation in the aquifer itself, particularly in presence of high viscosity oil. The modelling approach described below is based on some elements of [START_REF] Aral | Effect of groundwater table fluctuations on LNAPL thickness in monitoring wells[END_REF] with significant modifications and different notations that require a full description. The non-equilibrium situation can be described as in Figure 1, using, for simplification, a layer of mobile oil of time invariant characteristics. Two main situations may occur, in Figure 1a, the height of the oil-air interface in the well (Zoa) is lower than the one in the aquifer (Noa) therefore oil can move from the aquifer to the well. In the same figure the pressure in the two fluids within the aquifer is drawn, and it can be seen that the oil pressure at the bottom of the oil layer is higher than the oil pressure at equilibrium state (po,stat=pw+pcow) and thus the oil layer will move downward. Figure 1b shows the reverse case with an oil interface Zoa in the well being higher than in the aquifer. Pressure values used in the following explanation are expressed as differential pressures relative to the constant pressure in the atmosphere. The relative pressure in the air of the unsaturated zone is thus considered equal to zero. To calculate the fluctuations in both the well and the aquifer, the following assumptions are made:

1. The pressure equilibrates much faster in the water phase than in the oil. The pressure at the bottom of the well is thus considered to be equivalent to the pressure at the same elevation in the aquifer (inducing blue dotted and solid line to be overlaid in Figure 1); 2. As historical groundwater movements may have reached both higher and lower levels than the current position, a presence of residual oil below and above the mobile oil is considered; 3. The volume of mobile oil moving through a unit surface area is considered to be constant: this arises from the previous assumption of the presence of residual oil and from the negligible volume of oil in the well compared to the aquifer 4. The presence of air on top of the oil leading to an atmospheric pressure at this elevation; 5. The presence of a mobile oil layer in the porous media. 6. A constant value of oil hydraulic conductivity in the oil layer.

Assumption 1 is different from the work of [START_REF] Aral | Effect of groundwater table fluctuations on LNAPL thickness in monitoring wells[END_REF] because here we consider oil with a significantly higher viscosity than water. Assumption 2 was not used by [START_REF] Aral | Effect of groundwater table fluctuations on LNAPL thickness in monitoring wells[END_REF] but can be considered as valid for field conditions [START_REF] Lenhard | A practical tool for estimating subsurface LNAPL distributions and transmissivity using current and historical fluid levels in groundwater wells: Effects of entrapped and residual LNAPL[END_REF][START_REF] Steffy | A field study of the vertical immiscible displacement of LNAPL associated with a fluctuating[END_REF]. Note that the mathematical approach used here to quantify the vertical displacement of the water-oil front resp. oil-air front in an unconfined porous medium is easier to handle than the one introduced by [START_REF] Aral | Effect of groundwater table fluctuations on LNAPL thickness in monitoring wells[END_REF].

Oil Layer in unconfined porous media

If the oil saturation is considered constant in an oil layer having a constant thickness, the vertical movement of the mobile oil layer may be caused by the pressure difference ∆p between the oil pressure due to the height of the mobile oil layer and the pressure of the oil phase at equilibrium state at the water-oil interface. Supposing a simultaneous displacement of both the water-oil and oilair interface, the vertical Darcy velocity of the mobile oil layer uo can be described with the generalized Darcy law [START_REF] Muskat | The Flow of Fluids Through Porous Media[END_REF]:

= - ∆ = - . ∆ (1)
where ρo is the volumetric mass of oil in kg.m -3 , Ko the average oil conductivity of the porous medium in m.s -1 depending on the given oil saturation within the oil layer, k the intrinsic permeability in m² and kr the relative permeability to oil, µ the oil dynamic viscosity in Pa.s -1 , g is the gravitational acceleration in m.s -2 and Bo the oil thickness in the formation in m.

At equilibrium state of an immiscible fluid distribution in the porous medium, the pressure of the water phase and oil phase can be expressed at the water-oil interface (z=Now) as follows (see figure 1a),

= - (2a) = - + ( 2b
)
where ρw is the volumetric mass of water, Zp is the piezometric water head in m and pcow is the capillary pressure in Pa at the water/LNAPL interface (Now) for the considered oil saturation in the oil layer. To displace oil vertically downwards from a given oil layer, the oil pressure needs to be higher than the oil pressure expressed by Equation 2b. For the situation presented in Figure 1a, the vertical movement is potentially possible when the oil pressure caused by the oil layer thickness B0 yields to a pressure difference Given this transient condition, from Darcy's law and the conservation of mass principle for the oil phase, the front velocity of the water/oil interface can be calculated

! " # = - ∆ /( ) ( 4
)
where θo is the volumetric content of the pore space filled by oil. Neglecting the lateral loss of oil to the well, the displacement of the oil/air interface is obtained from the vertical displacement of the water/oil interface, for a given time interval dt as follows:

' ( = ' (5)
Due to the assumption of quasi instantaneous equilibrium and the negligible amount of water in the well compared to the amount of water in the aquifer, the exchange of water between the well and the aquifer is not calculated. The exchange of oil between the well and the aquifer can be calculated using classical fluid flow methods describing the movement of fluid from an unconfined aquifer to a well [START_REF] Thiem | Hydrologische methoden[END_REF]:

) = *+., . -(.(! / ,1 / )2345 (! " ,1 " ) (1 / 2! / ) 67(8 9 /8 " ) (6)
where Re is the equivalent radius and Rw the radius of the well casing (m). The oil head difference is Noa-Zoa and the thickness over which the oil is exchanged is the place where oil is present in both the well and the aquifer. This flux is considered as positive when the flux is going from the well to the aquifer.

The conservation of mass principle applied to the well yields to the velocity of the water/oil interface in the well, calculated as follows:

1 " # = : +; < = ( 7
)
where rc is the radius of the well (m).

During the oil exchange between the well and the aquifer, due to fast water exchanges, and due to pressure equilibrium in the well, we consider that the piezometric head in the well remains equal to the imposed groundwater head in the porous media (Zp) due to fast water exchanges, and due to pressure equilibrium in the well:

= + ; ( ( - ) = (1 -; ) + ; ( (8)
When oil is entering or leaving the well, through the discharge qo, the above equilibrium is conserved. Variation in piezometric head is expected to be very slow compared to the exchange between the well and the aquifer (dZp = 0), Equation 7, combined with Equation 8 yields to the velocity of the oil/air interface in the well, as follows:

1 / # = (1 -; ) : +; < = (9a)
Note that time dependent variation of Zoa is strongly linked to Zow by effect of the oil density:

' = ; : +; < = '? = ' ( @2 (9b)
Equations 4 and 7 can be iteratively solved by an explicit method considering a series of steady-state conditions, requiring short time steps.

Equations currently developed assume a constant residual and maximum oil saturation in the porous medium. However, the residual oil saturation in the non-saturated zone (Sora) zone can be lower than in the saturated zone (Sorw) [START_REF] Bohy | Transport of a mixture of chlorinated solvent vapors in the vadose zone of a sandy aquifer[END_REF]. Moreover, depending on the characteristic of the porous medium, the maximum saturation (Smax(z)) can vary with elevation. This saturation will directly impact the quantification of the vertical displacement of the water/oil interface (dNow) (see Equation 4) as ∆p depends directly on the capillary pressure between the water and oil phase (pcow), a function of the oil saturation itself.

The total specific volume of oil (Vo) is considered to remain constant, therefore dVo=0. Using Equation 3, the specific volume being the height multiplied by saturation and porosity φ:

'A ( = ' ( ∅(C -(. ( ( ) -C ;( ) DE' 'A = ' ∅(C -(. ( ) -C ; ) (10)
where dVa and dVw are the variations of air and water volume per square meter.

In order to maintain a constant volume, the equality of the two volumes is assumed, or:

' ( = ' F G/H (! " )2F " F G/H (! / )2F / (11)
Note that if Smax and Sor are constant over the entire porous media thickness, equation 11 takes the form of Equation 5. On the contrary, the oil layer thickness Bo also varies with time; it is recalculated during each iteration.

Oil layer in confined or semi-confined porous media

In a strictly confined medium, i.e. when the pressure head is always higher than the bottom of the confining medium, the oil cannot move. Thus, the only process that will occur is the variation of water and oil levels in the well to equilibrate the variations of head. In that case we have:

' = ' ( = ' (12)
However, this case is not so common and most of the wells concerned by the present study include a confining layer of thickness smaller than the oil thickness. Several cases, including confinement or semi-confinement, can occur depending on the relative position of the confining layer and the top and bottom of the oil. To analyze these different cases, the confining case was modeled by assigning a low permeability to the confining layer.

The previous equations have thus to be modified to consider a vertical variation of the medium permeability. For the vertical oil movement, the movement is perpendicular to the layering, and we have:

I = ! / 2! " ∑ 6 K /, K (13)
where li and Ki are the thickness and oil permeability of each layer included in the oil between Noa and Now. As the permeability to oil is generally low in silt layers, this will often lead to very slow vertical movements of oil in the aquifer. For the transfer between the well and the aquifer the averaging is different, as the flow is parallel to the layering:

L = ∑ 6 K , K -(.(! / ,1 / )2345 (! " ,1 " ) (14)
Here a thin layer of sand at any depth can significantly increase the exchange between the well and the aquifer. It can be noted that if the permeability is homogeneous, these equations lead to the same value of Ko and thus to the same equations as in the unconfined case. To maintain the consistency with the unconfined approach, allowing for a very low oil content in the silt layers, the top of the oil in the aquifer (Noa) is at atmospheric pressure (as in Figure 1).

Site and oil thickness measurements

The studied site is a manufacturing facility which started production in 1973 using several types of oil. The site is located on the alluvial plain of the Garonne River in France. The local shallow layers are composed of 12 to 18 m of Pleistocene sediments, mainly gravels and sands, over a thick Tertiary marl layer. From ground surface to the Tertiary marl, this upper layer is vertically and horizontally heterogeneous due to a large grain-size distribution variation from fine sand to gravel, leading to a weak capillary effect. To neglect capillary forces here for modelling of LNAPL displacement between well and porous media is thus justified. In addition, thin silty lenses are randomly encountered across the site. Groundwater beneath this site is unconfined with a seasonal fluctuation between -2 and -3.5 m below ground surface. The hydraulic conductivity of the aquifer has been estimated from pumping tests at four different locations across the site. The values are in close agreement, ranging between 2.6 and 3 × 10 -4 m.s -1 . The hydraulic gradient of the groundwater is quantified to 0.0025 and is oriented from south-west to north-east. The soil and groundwater baseline campaign highlighted four main areas where oil was encountered with a total extent of approximately 15,000 m 2 . The oil thicknesses measured in 120 wells ranged from a few centimeters to 2.5 m. Figure 2 presents the location of key monitoring wells that have been used for this study. Due to the long history of the site and the complexity of past industrial processes, the nature and the released volume of oil are unknown. The oil properties classify it as mostly lubricant oil. With the use of a number of oil products over the years, oil mixing in the soil, precipitation and different degradation stages, the physical properties of the oil slightly vary in space contributing to a range of values as summarized in Table 1. The oil viscosity and relative density have been measured on 25 oil samples, and the interfacial tension on four samples. The positions of the air-oil and oil-water interfaces were continuously monitored using three pressure gauges (Figure 3). Probe 1 provides the atmospheric pressure and Probe 3 measures the total pressure of water and oil (LNAPL) in the well. As probe 2 is located in the water at a fixed distance (L) from the top of the NAPL layer, by knowing the oil density and the three pressures, it is possible to obtain the position of the oil-water and the air-water interface. A regular manual measurement of the interfaces was completed to confirm validation of the automated measurements and to insure the absence of drift.

Results

Test cases

To illustrate the behaviour of the model with simple changes to the piezometric water head for a NAPL of 0.85 relative density, four tests cases were used. For simplification purpose, these test cases do not include capillary effects and thus the oil thickness in the well and in the aquifer will be equal at equilibrium. The obtained results are given in Figure 4. Test case 1 shows a situation where horizontal oil conductivity is equal to 0.02 m.d -1 and the vertical oil conductivity is set to zero which results in fixed Now and Noa. Here, around day 5, 20 cm of raising (peak at day 7) followed up by 20 cm of lowering of the water table were created. The perturbation of the piezometric water head lasts about five days. During that peak, it can be seen that Zoa is rising, and then becomes higher than Noa leading to a discharge of oil from the well to the aquifer. This discharge leads to a decrease of the oil thickness in the well which is marked mainly by the significant rise of the Zow level. Then, at approximately day 9, the vertical position of the oil-air interface becomes higher than Zoa, resulting in a flow back of oil from the aquifer to the well and decrease of the vertical position of the oil-water interface in the well towards its initial position of equilibrium. The second test case starts from the same equilibrium conditions as case 1 and is exposed to the same fluctuation of piezometric water head as before but the vertical oil conductivity in the aquifer is equal to the horizontal one (0.02 m.d -

1

), leading to a vertical movement of the oil in the aquifer. During the 27 days of the numerical experiment, both vertical positions of fluid interfaces, Noa and Now, decrease in the aquifer to equilibrate with the Zp level. This, in turn leads to a decrease of the Zoa level in the long term, and thus a decrease of the oil layer thickness in the well. Therefore, the oil thickness in the well depends on the equilibrium between Zp and the oil in the aquifer. In the case of higher oil conductivity, the oil thickness observed in the well becomes smaller.

Test case 3 uses the same conditions as test case 2 but with a different starting point for Now and Noa.

As the oil in the formation is much higher than the equilibrium state, it leads to an increasing thickness of the oil in the well before day 5. The oil in the aquifer tends to equilibrate with Zp, but at a slower rate, as after 25 days the oil thickness in the well (Zoa -Zow) is still greater than in case 2. Test case 4 illustrates a completely different situation. Here Zp rises steadily and finally reaches an elevation higher than the initial vertical position (at t=0) of the oil-air interface in the porous media, Noa. In that situation all the oil present in the well flows into the aquifer and the oil thickness in the well becomes zero.

From the analysis of all test cases, it can be seen that the variations are quite complex as the vertical positions of the fluid interfaces in the well and in the aquifer equilibrate at different time scales. Moreover, these results clearly illustrate that the oil thickness is almost never the same in the well and in the aquifer.

Application to oil layers in unconfined aquifers

Automatic measurements

The solutions were first applied to the case of an oil layer in unconfined porous media using automatic data measurements of monitoring well PZ262.

After manual tests the optimal values of the parameters given in Table 2 were found using the Excel solver (testing both nonlinear and evolutionary options). Figure 5 shows that a good fit (case 0, Zow on the figure) was finally obtained, with an RMSE (Root Mean Square Error) around 0.09 m (Table 2). The first interesting point is the presence of a significantly lower value of oil conductivity (K2) in the upper part of the unconfined aquifer, visible once the water-table elevation exceeds 3.2 m. The presence of this low conductivity zone is highlighted by the stable value of Zoa after the peak of day 80 and rapid lowering of Zow resulting in a significant increase of the measured oil thickness in the well. After this peak, the low oil conductivity located in the upper part of the aquifer may have limited the decrease of the elevation the oil-air interface. The fitted values of and Sor are also very interesting. To fit the whole curve only a very small difference between Smax and Sor is necessary. This means that a very small proportion of the oil is mobile and may also justify the high value of oil conductivity in the lower part of the aquifer (K1) as only the largest pores contain mobile oil. The fitted values of Sorw and Sora are also quite different, this suggests that the effect mentioned by [START_REF] Marinelli | LNAPL thickness in monitoring wells considering hysteresis and entrapment[END_REF] of a transfer of oil from mobile to immobile, is important. This has an important consequence: during the rise of the water table (between day 60 and day 80 in Figure 5) the thickness of the mobile oil layer in the aquifer declines largely, although an important mass of oil remain in the aquifer as oil reappears when the water-table declines. This is illustrated by the increase of Noa in Figure 5. Several tests were done (case 1 to 4) that can reach the same correctness of fit (Table 2). Sorw, Smax and K2 and the starting position Noa and Now were varied in a realistic range and show a similar value of the RMSE. In case 1 K2 is increased which may result in a decrease of the difference between Smax and Sorw. Case 2 is quite similar to case 0 except that Noa is slightly higher. In case 3, both Noa and Now were slightly higher and the difference between Smax and Sorw is smaller. Case 4 is also similar to case 0 with a smaller difference between Smax and Sorw but the RMSE is then higher than the one of case 0. This analysis indicates that some parameters are correlated, although not in a simple way.

Several trials were done without the presence of a low permeability layer above 3.2 m and gave a correct fit (case 5, RMSE 0.133 m) as long as we keep a small difference between Smax and Sorw. Other tests were done for a small value of the Sorw (the residual oil saturation in the saturated zone), they gave a correct fit (case 6, RMSE 0.118 m) if the low permeability value is kept above 3.2 m. On the contrary, if we remove both the low permeability layer and keep a low value for Sorw, the fit becomes less correct (case 7, RMSE 0.31). These elements tend to suggest that there are two major elements for the given well: (1) presence of a small amount of mobile oil in the porous media and (2) existence of a two-layered porous medium with a low permeability above an elevation of 3.2 m. These two elements seem to co-exist and contribute both to a good fit of the observed measurements. However, only one element is sufficient to fit correctly the observed data. None of the tested parameter set without one of this element can give a correct fit.

Long term series

On the wells with long term manual measurements, we applied the same modeling approach. The piezometric water head data are provided every ten days at the reference points (not at the measured well) while the oil levels were measured every two or three months. It can be seen that for this observation well (pz262) the fit is also correct. However, the sensitivity to the input parameters is small and thus the uncertainty in the parameter's value is high. This has two main reasons: the manual measurements are of worse quality than the automatic measurements, and there is no series of data on a short time scale to fit correctly the oil conductivity. Again the true thickness of the oil in the aquifer is difficult to determine with this approach. were acquired every two hours. In this area of the polluted site some layers of silt were identified, it is therefore possible that the oil movement in this well might be semi-confined or confined. In the measured variations of interfaces positions (Figure 7, Zow_m, Zoa_m) the presence of a confined medium can be detected when their temporal variation is shifted almost parallely to the occurring watertable variation. This implies that the amount of oil in the well is almost independent of the one in the aquifer during this period. This can be due to very low oil conductivity in the aquifer.

Applying a layered aquifer structure composed of a main layer with low conductivity and high permeable layers above and below, the model provide a good fit for Zoa and some slight discrepancies for Zow (Figure 7, reference case ). It can also be seen that, based on the obtained model parameters (Table 3), the resulting Noa and Now are stable, showing an almost immobile oil layer in the aquifer, corresponding to a confinement by a silt or clay layer. When the oil conductivity is low, the other parameters like oil saturation do not play a role in the fitting.

Case 2 shows a trial with only one layer for the oil conductivity. It can be seen that the fit before day 95 is similar to the previous ones, although slightly worse. However, after day 95, when the top of the oil reaches an elevation of 4.5 m, the model significantly underestimates measured vertical position of the oil-water interface. This confirms the presence of a more permeable layer above this elevation. 2). The oil relative density is equal to 0.85. Layers are numbered from top to bottom, zlim1 is the limit between the 1 st and 2 nd layer, same principle applied to zlim2. All N and Z in m, K in m.d -1 , S is unitless.

Parameters

Discussion

Bo-Zow correlations

The correlations found between oil thickness in the well (Zoa -Zow) and the position of the interface Zow were investigated by [START_REF] Kemblowski | Hydrocarbon thickness fluctuations in monitoring wells[END_REF]. If we consider the approach presented here, in an unconfined porous medium these correlations are mainly linked to the equilibrium in the well: when some oil is transferred to the aquifer, due to density effects the major effect is seen on Zow. In theory in a homogeneous unconfined medium with fast exchange, with no movement of the oil in the aquifer, the slope shall be equal to the oil density. Figure 8a shows the relation between Bo and Zow for the well Pz262 which is unconfined. It can be seen that during some period there is no correlation while some points show a clear correlation. This correlation occurs after day 74 (see Figure 5), i.e. when the water table starts to move. The slope of the correlation line is equal to -0.95 which is slightly different from the value of the relative oil density (0.88 in that well). This difference may be justified by the movement of the oil phase in the aquifer as function of time.

In an entirely confined system, the oil thickness in the well does not change. In semi-confined systems there are likely periods similar to the confined situations when the exchange with the well is quite rapid and during these periods the slope may be similar to the unconfined (i.e. equal to the relative oil density). During the period of no exchange the thickness shall not change. There shall also be transition periods when the exchange is rapidly decreasing or increasing, thus with no specific slope. Figure 8b shows the behavior of the well 264 which is semi-confined. For that well a large number of points do not show a clear trend, only a short period, after day 96 (see 8) shows a correlation between Bo and Zow. This period is the only one when the oil is connected to a more permeable part in the well, i.e. the behavior of a part of the oil is close to unconfined. Before this period the well is not totally confined as Bo remains stable during some periods and varies during others.

Comparison with other approaches

As outlined in the introduction, some authors assumed that the oil thickness variations over time observed in the well are due to the difference in the residual oil saturations Sorw and Sora [START_REF] Kemblowski | Hydrocarbon thickness fluctuations in monitoring wells[END_REF][START_REF] Marinelli | LNAPL thickness in monitoring wells considering hysteresis and entrapment[END_REF]. This possible effect is taken explicitly into account in our model: the curve fitting procedure provides different values for the two residual oil saturations. However, the time-dependent fluctuations of the oil thickness observed in the wells could not be reproduced only with these differences; a movement of oil between the well and the aquifer was required. The approach recently proposed by [START_REF] Lenhard | A practical tool for estimating subsurface LNAPL distributions and transmissivity using current and historical fluid levels in groundwater wells: Effects of entrapped and residual LNAPL[END_REF] analyses the oil vertical distribution in relation with historical data. In their approach the authors consider that, due to an equilibrium state, the oil distribution in the formation should be defined by considering only the highest and lowest position of the oil-air interface in the well and the actual oil position in the well. Their equilibrium calculations may not be applicable to field measurements as it leads to a steady thickness of the oil in the well, while our field results indicate that this thickness is highly transient.

Effect of oil viscosity

The model was developed and applied to quite viscous oil (~100 cP) which leads to slow movements of the oil in the formation. This property has consequences on the model itself as it assumes a very fast equilibrium in the water phase compared to the oil phase. To test this assumption, we used the same model for the well Pz262 but multiplied the hydraulic conductivity of the oil by a factor of one hundred to consider an oil of low viscosity, close to the viscosity of water or gasoline. The results are shown in Figure 9. Although the fit is not as good, the figure shows that the oil-water interface in the formation (Now) is closer to Zow than in figure 5, but remain quite different from Zow , so Now variation is much slower than the one in the well. Therefore, the main assumption of our model, i.e. a fast equilibration in the well and a slow one in the formation remains valid. In fact, as only a portion of the porosity is occupied by the oil leading to a low value of kro and thus the assumption of slow oil movement in the formation seems to still be valid. This graph also outlines that even with the low viscosity oil the assumption of a well-aquifer equilibrium for the oil is almost never reached.

The possible difference of the elevation of the fluid interfaces (between the well and the porous medium) resulting from the water-oil capillarity in the porous media has not been taken into account in the interpretation of our field experiments. This is justified by the rather low capillarity of the gravel-sand formation. Note that capillary pressure may modify the oil thickness in the well, but the transient differences between interfaces position in the well and the aquifer shall remain. It is difficult to define precisely the domain of validity of our approach, but the present result suggests that it may be valid for low viscosity oil in formations of hydraulic conductivity as high as 50 m.d -1 . 2 for case 0, and an oil conductivity increased by a factor of 100.

Sensitivity study of the obtained model parameters

In the case of oil layers in unconfined aquifers, a sensitivity analysis was performed on the obtained fit parameters to estimate the relative role of each model parameter. The base values obtained from the best fit of the Pz262 data were used (case 0); the sensitivity of each model parameter was calculated by varying these base parameters by 10 % of the potential range for each parameter, called applied δ (Table 4). The potential range was estimated from the knowledge of the site characteristics which are presented in Table 4 as min and max. For the oil conductivities K1 and K2 the 10% range of variation were calculated on the decimal log of their base value, as classically done when using hydraulic conductivities. To quantify the individual sensitivity of each model parameter, we used the calculated vertical positions of the oil-water interface of Zow for different measuring periods.

For each modified model parameter and for four selected measuring periods, the relative difference between the calculated Zow and the reference value (obtained for case0) was quantified and time averaged over the selected period (Figure 10). It appears clearly that the model is not linear as the results for a positive and negative δ can be very different. The first parameter that shows a significant sensitivity is the relative density of the oil (ρ), indicating that this parameter must be measured very accurately at the well. For some periods, a 10% variation of ρ leads to a variation slightly higher than 10% of the Zow range. The initial position of the interface in the porous medium (Now0 and Noa0) also induce a significant variation of Zow. This point raises some difficulties because these elevations cannot easily be measured in the field. The next influencing parameter is Sorw, which plays only a role for a negative δ and for one period. Surprisingly the oil conductivities show a very low sensitivity, meaning that the fitted values will keep a large degree of uncertainty. However the measuring tool allows a precision of 1 to 2 cm leading to a precision equal to the value of δ for K1 and K2. For most of the parameters the sensitivity observed at the first peak period (day 78 to 84) is the most important, underlining the importance of measuring and fitting precisely the peaks of Zow. 4). The blue bar on the left side represents 10 % of the range of variation of Zow.

Conclusion

In this paper a simplified model for analyzing the temporal variation of the water-oil interface and the oil thickness was proposed. This model incorporates the variations of residual saturation between unsaturated and water saturated porous media, but also exchanges between the well and the aquifer and oil movement in the aquifer. The model reproduced quite well the observed characteristics of the two wells located in the field site whether in an unconfined or a semi-confined part of the aquifer. To our knowledge, this is the first study that shows such a fitting of natural transient variations of NAPL levels in wells, that allow to estimate several parameters of the porous medium. The results suggest that the wells are most of the time not at equilibrium with the aquifer, and that the oil in the porous media moves much more slowly than the water table. Thus a continuous record of the oil position in the well can be used to estimate the oil conductivity in the aquifer, but also the oil saturation which can be quite useful for remediation purposes. As it has already been shown in several studies, the apparent thickness of the measured oil in a well is strongly dependent on:

the grain size distribution of the adjacent formation, the condition in which the oil is present in the soil. In an unconfined condition the oil thickness in a well does provide a good indication of head whereas a confined condition results in a misleading oil thickness,

the groundwater fluctuation history.

Based on our modeling approach, the impact of the groundwater fluctuation on the oil thickness in a monitoring well can be explained by the transient transfer of oil between the well and its surrounding area. This is an important conclusion because this phenomenon has real consequences on data interpretation and its use for remediation project management purpose. For example, it impacts the values the hydraulic conductivity of the oil measured from the "bail-down" tests which must then be corrected according to the static level of the water. Therefore, oil thickness measurements for short-term decisions relating to a remediation design is useless and can lead to substantial error. Long-term measurements of both oil thickness in a well along with groundwater fluctuation is a better diagnostic tool. It allows (i) to define the nature of the soil around the well and the confining situation (unconfined or semi-confined), and (ii) to estimate the hydraulic conductivity of the oil in the porous media.

Knowing the evolution of both the thickness of the oil and the hydraulic conductivity of the oil, the recovery of the oil in the well can be optimized according to the variations of the water table and the status of the oil layer (confined or unconfined) in the porous medium. Ultimately, the proposed approach will reduce the cost of a remediation project.

Due to its simplicity the model has limitations, particularly by the use of a vertically constant oil content. This may have consequences on the values of the estimated parameters, but the order of magnitude of the average value of the oil conductivity may be correct. Furthermore, neglecting capillary effects may lead also to errors on the estimated thickness of the oil phase in the aquifer. However, our measurements and simulations show that there is a large heterogeneity of the average physical properties, which may exceed the capillary effect.

Further application of the model to different sites may provide more confidence in the model and its applicability to different cases.

Figure 1 :

 1 Figure 1 : Scenarios of LNAPL positions in a well and formation in unconfined oil, blue is the water, red the mobile oil and red dots represent the residual oil. The solid arrows show potential movement of oil between the well and the formation, the open arrows show the potential vertical movement of the oil in the aquifer. Z presents the vertical position of the interfaces in the well and N in the aquifer. On the right of each sketch, the pressure is drawn, with solid lines for the pressure in the aquifer and dotted lines for the pressure in the well. ΔP is the pressure difference between the oil and water in the porous media.

Figure 2 :

 2 Figure 2 : Monitoring wells locations and oil distribution using kriging interpolation in October 2011

Figure 3 :

 3 Figure 3 : Vertical positions of probes in a well containing LNAPL to continuously monitor oil thickness

Figure 4 :

 4 Figure 4 : Temporal evolution of the vertical positions of fluid interfaces in the well (z) and in the aquifer (N) for four test cases. In test cases 2 -4, two subcases are presented: case a is in full line (Ko = 0.02 m.d -1 ) and case b in dashed lines (Ko = 0.05 m.d -1 ).

Figure 5 :

 5 Figure 5 : Temporal evolution of the measured vertical positions of the oil-water and oil-air interfaces (Zow_m, Zoa_m) on Pz262 shown as dots, the observed piezometric water head (Zp), the vertical positions of the oil-water and oil-air interfaces in the aquifer (Now, Noa). The fitted simulated elevation of the oil-water interface (Zow for case 0, Zow_c1 to c7 for case 1 to 7) superimposed on the measured ones. The oil relative density is equal to 0.88.

Figure 6 :

 6 Figure 6 : Vertical locations of fluid interfaces measured (symbols) at observation well pz262 and modeled (lines); Model results shown here are the best fit in the χ 2 sense 3.3. Application to oil layers in confined or semi-confined aquifers

Figure 7 :

 7 Figure 7 : evolution of the measured and modelled levels in the well and formation for well 264, _m for measured, _c1, c2 mean case 1 and 2. Table 3 : Parameters of the different fits to the measured values of Zow and Zoa for the well PZ264 (same symbols as for Table2). The oil relative density is equal to 0.85. Layers are numbered from top to bottom, zlim1 is the limit between the 1 st and 2 nd layer, same principle applied to zlim2. All N and Z in m, K in m.d -1 , S is unitless.

Figure 8 :

 8 Figure 8 : Relation between the vertical position of the oil-water interface (Zow) and the oil thickness Bo in two wells, (a) well Pz262, unconfined, and (b) well Pz264, semi confined.

Figure 9 :

 9 Figure 9 : Temporal evolution of the interfaces in the well and in the formation for the same values as in Table2for case 0, and an oil conductivity increased by a factor of 100.

Figure 10 :

 10 Figure 10 : Sensitivity of the M NOPPPPP elevation (the presented value is the average for a given period) for different periods, as influenced by a positive or negative variation of δ of each parameter (δ values in Table4). The blue bar on the left side represents 10 % of the range of variation of Zow.

Table 1 : Main physical properties of the oil

 1

	Product relative density (15 °C)	0.85 to 0.88
	Viscosity (15 °C)	90 to 115 cP
	Oil/water interfacial tension	16 to 18 dynes/cm
	Oil/air interfacial tension	29 to 31 dynes/cm

Table 2 : Parameters of the different fits to the measured values of Zow and Zoa for the well Pz262 (names are given in the text, K1: oil conductivity below zlim, K2 same for above zlim. All N and Z in m, K in m.d -1 , S is uniteless.

 2

		3.5
		3
	Elevation (m)	2.5									Zow Zoa Now Noa
											Zp
											Zow_m
											Zoa_m
		2									Zow_c1
											Zow_c5
											Zow_c6
											Zow_c7
		1.5
		0	20	40	60	80	100	120	140	160	180	200
							days
	Parameters	case0 case1 case2 case3 case4 case5 case 6 case 7
	Now at t=0	1.92	1.94	1.96	2.00	1.93		2.06	1.90	2.17
	Noa at t=0	3.17	3.17	3.20	3.21	3.17		3.17	3.15	3.19
	Sora		0.05	0.05	0.05	0.05	0.05		0.10	0.09	0.10
	Sorw		0.167	0.233	0.159	0.156	0.200		0.368	0.213	0.25
	K1		0.5	0.5	0.5	0.5	0.5		0.120	0.112	0.111
	zlim		3.26	3.25	3.26	3.26	3.27			3.62
	K2		0.0001	0.001	0.0001	0.0001	0.0001			0.0001
	Smax		0.426	0.46	0.415	0.407	0.412		0.453	0.329	0.293
	RMSE		0.089	0.095	0.089	0.090	0.093		0.197	0.131	0.18

Table 4 :

 4 Parameter range used for the sensitivity analysis (names of the model parameters are given in the text, N is in m, K in m.d -1 , ρ and S are unitless).

		Now0	Noa0	ρ	Sora	Sorw	K1	K2	Smax
	Base	1.917 3.17	0.88	0.05	0.167	10 -0.3	10 -4	0.425
	Min	1.8	3	0.85	0.04	0.15	10 -5	10 -4	0.25
	Max	2.3	3.8	0.92	0.2	0.35	10 -0.3	10 -1.7	0.6
	δ (10% range) 0.05 0.08 0.007	0.016	0.02	10 0.47	10 0.23 0.035


Tianji Ma

Emmanuel Balanzat

Jean-Marc Janot

Sébastien Balme
email: sebastien.balme@univ-montp2.fr

Single conical track-etched Nanopore for a free-label detection of OSCS contaminants in heparin

Keywords: Nanopore, heparin, OSCS, track-etched

The heparin contamination by oversulfated chondroitin (OSCS) was at the origin of one major sanitary problem of last decade. Here we propose a novel strategy to detect OSCS from heparin solution based on conical nanopore functionalized with poly-L-lysine deposition to ensure its re-usability. This sensor is an excellent to detect low heparin concentration (from 25 ng/ml to 3 µg/ml) using the modification of ionic current rectification. It also allows following the kinetic of heparin degradation by heparinase with a good correlation with results obtained by classical methods. The sensor is sensitive to the inhibition of heparinase by OSCS until a concentration of 200 pg/ml representing 0.01 % in weight in a heparin. This resolution is one order of magnitude lower than the one obtained by chromatography. For the first time, it was reached without fluorescence labeling.

Introduction:

Heparin (HEP) is a commonly used anticoagulant to treat several clotting disorders. 10 years ago, a sanitary problem from contamination of oversulfated chondroitin (OSCS) has caused the death of about 200 patients around the world [START_REF] Guerrini | Proc. Natl. Acad. Sci[END_REF]Sasisekharan and Shriver, 2009). Since this event, an effort was made to detect small amount of OSCS from heparin mixture that is not easy due to their close structures (Beni et al., 2011). To this end, the classical methods based on chromatography were the first considered. However they are limited to a detection limit around 0.3 % in weight and required expensive instruments such as mass spectrometer or NMR to identify the OSCS (Liu et al., 2011). More recently, the fluorescence based sensors allow to improve the detection limit until from 10 -2 % until 10 -9 % weight (Kalita et al., 2014). The OSCS detection is usually indirect since they used ability to inhibit the HEP degradation by Heparinase. Despite their low detection limits, the major weakness of these fluorescence sensors is that they require fluorescent probe (Ding et al., 2015;Wang et al., 2016), nanoparticle (Kalita et al., 2014) and/or biomolecule [START_REF] Hu | [END_REF] engineering for the specific detection of heparin as well as fluorescence spectrometer microscope equipment. Thus provide a simple and cheap technology to detect OSCS from HEP sample is still highly challenging.

The single nanopore is versatile method for macromolecule sensing that emerged last two decades (Dekker et al., 2007;[START_REF] Kasianowicz | Proc. Natl. Acad. Sci. U. S. A[END_REF]. Using the resistive pulse technique through solid-state nanopore, a sample of HEP contaminated by OSCS can be identified (Karawdeniya et al., 2018). However, the concentration cannot be obtained by this way. In addition, the major problems of solid-state nanopore are the short lifetime and the low success rate of experiments which limit the real application, despite recent improvement by PEG functionalization (Giamblanco et al., 2018b;Roman et al., 2018Roman et al., , 2017)). The conical track-etched nanopore is a good alternative to design label-free sensor based on the modulation of ionic current rectification (ICR) (Lepoitevin et al., 2017(Lepoitevin et al., , 2016a)). Based on that, small molecules as well as protein can be specifically detected by a ligand/receptor systems (Ali et al., 2016(Ali et al., , 2015(Ali et al., , 2010a(Ali et al., , 2010b)). However, these sensors are often one-off especially when the ligand binding is not totally reversible. Recently, we have shown that the reversible functionalization with poly-Llysine (PLL) could be promised for biosensing applications (Lepoitevin et al., 2016b). Another, advantage to use polyelectrolytes (PE) inside nanopore is that the layer-by-layer deposition can be monitored and the kinetic depends on their properties (size and charge) (Ma et al., 2018).

Following our previous investigations in this field, we propose here to design a reusable sensor for OSCS contained in a HEP sample. Our strategy is based on (i) the reversibility of PLL/HEP functionalization of a conical nanopore and (ii) the degradation of the HEP by heparinase which is inhibited by the OSCS. Here, we assume that action of enzyme will decrease the affinity between degraded HEP and the PLL. This would impact the nanopore surface charge and thus the ICR.

In order to prove the concept that conical nanopore could be a suitable alternative to detect the HEP contamination by OSCS, we present our work in several following step. First, we will demonstrate the reversibility of the PLL/HEP deposition as well as their impact on the IRC.

Then, we will evaluate the impact of the HEP concentration on the IRC in order to evidence a dose-response curve. The OSCS contained in HEP solution will be detected using heparinase.

Thus, we will follow the kinetic of degradation of HEP by heparinase by nanopore and compared the result with classical methods. Then, using this strategy, we will study the relationship OSCS concentration ICR to establish the dose-response dependence. The last sections will be dedicated to discuss the reproducibility of sensing experiments and the nanopore sensor lifetime. This last step will aim to validate our sensor.

Material and methods

Materials

Poly(ethylene terephthalate) (PET) film (thickness 13 µm, biaxial orientation) was purchased from Goodfellow (ES301061). Sodium chloride (71380), potassium chloride (P3911), sodium hydroxide (30603), hydrogen chloride (30721), trizma hydrochloride (T3253), CAPS (C2632), sodium acetate (W302406), ethylenediaminetetraacetic acid (EDTA) (E5513), Poly-L-lysine hydrobromide (PLL) (30 kD-70kD P2636), Heparin sodium salt from porcine intestinal mucosa (HEPep) (H4784), Heparinase I and III Blend from Flavobacterium heparinum (H3917), Heparinase II from Flavobacterium heparinum (H6512) were purchased from Sigma-Aldrich.

Over Sulfated Chondroitin Sulfate (OSCS) Standard (3125401) was purchased from SERVA.

Ultra-pure water was produced from a Q-grad®-1 Milli-Q system (Millipore).

Track-etching nanopores and current -voltage measurements

The PET films (13 µm) were irradiated by a single Xe irradiation (8.98 MeV) (GANIL, SEM line, Caen, France) to create single tracks and thus a single nanopore. Then, the latter was exposed to UV irradiation during 9 hours for tip side and 15 hours for base side (Fisher bioblock; VL215.MC, λ = 302 nm). The activated PET film was mounted between two chambers of a Teflon cell. The etchant solution (NaOH 9 M, 1.6 ml) was added on the base side and the stopping solution (KCl 1M and CH3COOH 1M, 1.6 ml) on the tip side. An electrode (Pt) is immersed in the stop solution and the working one (Pt) in the etchant solution and then a potential of 1 V was applied across the membrane. The nanopore opening was characterized by the current as a function of time recorded by a patch-clamp amplifier (EPC-10 HEKA electronics, Germany). The etching process was stopped by replacement of the etching solution by the stop one when the current reach a value of several hundred pA.

The tip diameter d of the conical nanopore was determined from the dependence of the conductance G measured in the linear zone of the I-V curve (typically between -60 mV to 60 mV) assuming a bulk-like ionic conductivity inside the nanopores (equation 1).

=

(1)

Where, κ is the ionic conductivity of the solution, L is the nanopore length (13 μm) and D is based diameter which was calculated from the total etching time t using the relationship D = 2.5t

(the factor 2.5 was determined in our experimental set up using multipore track-etched membranes).

The I-V curve were obtained from the current traces recorded as a function of time from 1 V to -1 V by 100 mV steps for 2 s and from 100 mV to -100 mV by 10 mV steps for 2s using a sampling rate 50 kHz.

Nanopore functionalization and reversibility of PLL/HEP layer

The same buffer solution (50 mM Tris-HCl, 75 mM CH3COONa, 100 mM NaCl) was used for polyelectrolyte adsorption and enzymatic degradation. The pH is adjusted to 7.5 by addition of chloride acid and sodium hydroxide. For the functionalization with PLL, 10 µl of the polyelectrolyte solution (1mg/ml) was added in the tip side of the nanopore. A voltage -1V was applied from the tip side to the base one during 3 minutes. Then a various volume of HEP (1mg/ml) was added in 1.6 ml buffer solution at tip side of the cell. The 1 V for HEP was applied for 3 min. The I-V curves were recorded after replacing polyelectrolyte solution by buffer. After each detection of HEP, the PLL-HEP layer was desorbed using a buffer at pH 12 containing 100 mM KCl, 5 mM Trizma-HCl and 1 mM EDTA.

Enzymatic degradation

50 U of Heparinase I and III was dissolved in 2.5 ml of storage solution containing 20 mM Tris-HCl, 100 mM NaCl, 1 mM EDTA at pH 7.5. 10 U of Heparinase II is dissolved in 1 ml of the same buffer. 0.25 ml of Heparinase I and III at 20 U/ml and 0.5 ml off Heparinase II at 10 U/ml are mixed and then diluted 10 times. So the final solution has a concentration of 1.33 U/ml of total enzyme.

The enzymatic reaction is carried out at ambient temperature ~25°C during time from 0 to 250 min in the buffer solution pH 7.5 containing 50 mM Tris-HCl, 75 mM (CH3COO)Na, 100 mM NaCl . For each essay, 3 µl of HEP (1 mg/ml) and 5 µl of enzyme cocktail solution (1.33 U/ml) are added in 1.5 ml of the reaction buffer solution. So the concentrations of HEP and Heparinase for reaction are 2 µg/ml and 4.43 mU/ml respectively.

For OSCS detection, 2 mg OSCS is dissolved in 20 ml storage solution described above. Then 1 ml of this solution is dissolved by 10 times (10 µg/ml) and 1 ml dissolved by 1000 times (0.1 µg/ml). To obtained the OSCS/heparin ratio 10%, 1%, 0.1%, 0.01% w/w, 30 µl, 3 µl of OSCS (10 µg/ml) or 30 µl, 3 µl of OSCS (0.1 µg/ml) was added in 1.5 ml of reaction solution containing HEP at 2 µg/ml. Then 4.43 mU/ml of enzyme solution was added. The enzymatic reaction was carried out at 25 °C during 200 min.

Results and discussions

The strategy to obtain the nanopore sensor is illustrated on the figure 1 3.1 Heparin detection by conical nanopore decorated with PLL

The PET single conical nanopores were obtained by track-etched methods under dissymmetrical condition as previously described (Lepoitevin et al., 2015). Shortly, we used the electrostopping method. The Dbase is deduced from the etching time. In order to confirm the factor used is suitable and evaluate the impact of the dispersity of the base diameter, we performed the same experiment on low density membrane (10 5 pores/cm 2) to avoid the nanopores overlap. In Figure S1 are reported the SEM of several nanopores obtained after etching time 156 min. From the etching time and conductance measured on a single nanopore performed in the same condition, we obtained a Dbase = 390 nm and a dtip = 22.5 nm. Accoring to the dispersity observed on the multipore membrane (Figure S1) the error on the dtip about 1.5 nm. After alkaline etching, the nanopore inner wall exhibits carboxylate moieties which confer it a negative surface charge. The I-V dependence recorded at pH 7 NaCl 100 mM shows ICR behavior characterized by the rectification factor Rf = |I(1V)/I(-1V)| < 1 (Figure 2). The first set of experiment is dedicated to show the nanopore functionalization by PLL and the HEP detection. To do so, the PLL was added in the tip chamber and a voltage -1 V was applied until inversion of I-V curve that is characteristic to the inversion of the nanopore surface charge (Figure 2 and S2). After washing, the heparin was added to the tip chamber under 1 V during 3 min. The I-V curve was again inversed due to the excess of negative charge from heparin. This evidences that each polyectrolyte can be detected by the conical nanopore. The first targeted property of our nanopore sensor is its reusability. To prove that, we have performed several cycles of PLL/HEP adsorption followed by a washing at pH 12 under 1V during 5 min to remove the PE layers on different nanopores with similar size. The Rf as well as the conductance recorded after each step are similar for the 18 cycles (Figure 2 and S3) and 4 cycles (SI-3). This confirms as expected that conical nanopore is reusable for the heparin detection. Our nanopore is suitable to detect HEP using the IRC. We have to demonstrate if the value of Rf is dependent on the HEP concentration in order to establish a dose-response curve. We can notice that at low concentration, the adsorption of PE onto a charged surface is usually described by a Langmuir model. Here, the detection method by ICR does not give the exact interfacial concentration of PE but it is sensitive to the modification of the global surface charge. We measured the I-V dependence after adsorption of HEP for different bulk concentrations following the cycle PLL/HEP adsorption and washing at pH 12 (Figure 3). The rectification factor after each step for two consecutive quantitative analyses was reported on figure S54 to confirm the constant values after PLL adsorption and after washing. Conversely, the rectification factor decreases with the heparin concentration in the bulk. This means that the positive charges of PLL are counterbalanced by the increase of HEP amount adsorbed inside the nanopore.

Assuming that the HEP adsorption on PLL is mainly governed by the electrostatic interactions, the amine groups of PLL layer can be seen as binding sites for acidic moieties of the HEP. In this case the rectification factor can be assimilated to the bound fraction of HEP on PLL as following equilibrium.

[

PLL] + [HEP] ⇄ [PLL -HEP]

The plot of rectification factor as a function of HEP concentration in the bulk can be fitted by a classical sigmoidal equation (eq. 2) equation where the asymptotic values are the rectification factor induced by only the PLL (Rf PLL) and after saturation by HEP (Rf HEP). The sigmoidal curve comes from the fact that to modify the IRC a sufficient amount of HEP has to be adsorbed to impact the nanopore surface charge. At low concentration, the amount of HEP adsorbed is not sufficient to significantly modify the nanopore surface charge and thus the IRC. In this case, the transport is mainly dominated by the PLL charge. With the increase of HEP concentration, more and more HEP are adsorbed and thus affect the IRC. In this range, the nanopore sensor is suitable to obtain the dose-response of HEP based on the Rf. Finally, when HEP concentration reaches a certain value the adsorption is very fast and the Rf become constant.

= + ( !)# (2)
where the half maximal effective concentration EC50 is the bulk concentration where HEP reaches 50% of PLL coverage, c the concentration of HEP in the solution and p the equivalent of Hill coefficient which gives information about degree of interaction between the binding sites of PLL and the HEP. The non-linear fit (Figure 3b) gives an EC50 = 435.9 ng/ml and a p= -2.79 10 - 3 . The p value below 1 means that when a HEP is bound on PLL its affinity for another HEP molecule decrease. This result highlights that the HEP adsorption inside the nanopore should not be described by a Langmuir isotherm since this model assumes that binding sites are completely independent. This result opens numerous questions about our basic conception of polyelectrolyte adsorption under confinement that is crucial for the understanding the membrane functionalization using such macromolecules.

3.2 OSCS detection by conical nanopore decorated with PLL Our concept for OSCS sensing is based on its ability to inhibit the HEP degradation by heparinase. As first step, we have to establish a correlation between the IRC and the degradation degree of HEP. To do so, we adsorbed the HEP after different degradation time by heparinase..

As shown on figure 3, the rectification factor increases with the degradation time of HEP. This can be explained by a weaker affinity of oligosaccharide from the HEP with the PLL due to their lower molecular weight. The kinetic of HEP degradation obtained by nanopore experiment is compared with the one obtained by a classical method which consists of dose the oligosaccharide by absorbance at 214 nm (Figure 4 and SI-6). It follows an order 1 kinetic law (eq. 3).

$%& = $% &exp(-+,)

where P is the product of Hep degradation. The value of kinetic constant k obtained by nanopore detection (k =1.12 10 -2 ±0.6 10 -2 ) and absorbance (k =1.56 10 -2 ±0.06 10 -2 ) are very close proving that the nanopore functionalized with PLL is a good candidate to follow easily the enzymatic degradation of PE. It could be noticed that using a single nanopore, the enzymatic degradation was only characterized by resistive pulse method (Fennouri et al., 2013;Giamblanco et al., 2018a).

Because the IRC depends on the degree of heparin degradation, we expected that the inhibition by OSCS can be also detected by nanopore. The first experiment was to compare the I-V curves after addition of heparine degraded by heparinase after 200 min incubation at 25°C with and without 10 % weight of OSCS (Figure 5a). Without the inhibitor, the rectification factor decreases from 5.22 to 1.86 because the affinity of oligosaccharides with PLL is too weak to provide efficient charge compensation. In presence of OSCS the heparinase is inhibited and the HEP is less degraded. The long chains of heparin have a better affinity with the PLL inducing more efficient charge compensation characterized by a decrease of Rf until 0.9. The range of OSCS dose-response is reported on Figure 5b

Stability and reproducibility of nanopore sensor

As mentioned in introduction, the main bottlenecks to use solid-state nanopore as sensor are their short lifetime and the difficulties to reproduce similar experiments several consecutive days without constraining experiments. We discuss now about the stability and the lifetime of our nanopore. For the heparin sensing, the experiments shown in figures 2, S-2 and S3 where 18 cycles performed in the same day are reported. For the dose response experiments (Figure S5), on the reversible functionalization with PLL allows using the same nanopore for several experiments with a good reproducibility of results. The experiments about the OSCS sensing (Figure 5b and S7) were performed during two consecutive days. In order to provide a clear proof of the nanopore stability, we show in figure 6, a series of HEP and HEP after degradation with by heparinase in presence of OSCS 1% detection experiments performed during 18 days.

Between each experiment the nanopore was conserved in milliQ water. The result show that a good reproducility of results. Typically after each step the rectification factor stay comparable along the day. We notice also that after 18 days the nanopore is still working.

Conclusion

To sum up, the single nanopore sensor described herein can be used to detect easily a wide range of OSCS concentration contained in heparin sample. The detection limit about 0.01 % weights that is less sensitive compared methods based on fluorescence but in the good range for the characterization of contaminated sample of heparin. In addition, our approach does not require the synthesis of fluorescent dyes, specific DNA ligands or nanoparticles nor expensive instrumentation. Indeed, the nanopore functionalization requires a couple of minutes and it is totally reversible which allows quantifying the OSCS after performed a calibration curve. It is also perfectly conceivable the integration of the nanopore inside a microfluidic device and use a miniaturized amplifier to build a portable system to analyze heparin sample. So, we could expect that this nanopore sensor will enhance the quality control chain of heparin allowing avoiding the risk of patients' death. Beside the detection of heparin contaminant, two other applications are possible with our nanopore: the characterization of enzymatic degradation of PE and the mechanism of PE layer formation. Globally, this study highlight that a conical nanopore simply functionalized with PLL is powerful for many applications from enzymology to controlling quality of drug.

Supporting Information:

Additional results (S1 -S7) (PDF) is available in supporting information.

Acknowledgement:

Single tracks have been produced in GANIL (Caen, France) in the framework of an EMIR project. The authors thank Laurent Bacri from LAMBE university of Evry for the discussion about heparin contaminants.

  . It consists to open a single conical nanopore on a PET film and decorated it by adsorption of PLL. Then, as mention in introduction, our methodology has follow three steps of detection (i) the HEP (ii) the HEP degraded by heparinase and (iii) the the HEP degraded by heparinase in presence of OSCS.

Figure 1 .

 1 Figure 1. Sketch of experimental methodology follows in this work. The first step is the

Figure 2 .

 2 Figure 2. (a) Sketch of experimental functionalization and heparin detection using conical

Figure 3 .

 3 Figure 3. (a) I-V dependence after HEP adsorption at different bulk concentrations (b) Rf as a

Figure 4 .

 4 Figure 4. Enzymatic degradation of HEP by heparinase follows by absorbance-based methods

  and S7. The experiments conducted on two individual nanopores with tip diameter 12 nm and 36 nm show the same trend. The value Rf decreases with the OSCS concentration. For both nanopores the Rf is boundary between two asymptotic values the one obtained after heparin degradation without inhibitor and the one 14 obtained after adsorption of non-degraded heparin. For all tested nanopores, the detection range where the Rf is dependent on the OSCS concentration is found from 0.1 to 10 -4 w/w.

Figure 5 .

 5 Figure 5. (a) Sketch of the OSCS detection using single PLL functionalized nanopore (b) I-V

Figure 6 .

 6 Figure 6. Nanopore sensor stability and reproducibility: Rectification factor obtained for

cycles was performed during two consecutive days. These results confirm that approach based