Rachel Balard
email: rachel.calvet@mines-albi.fr

Calvet

K Bendada

B Hamdi

L Boudriche

H Balard

R Calvet

Surface characterization of reservoir rocks by inverse gas chromatography: Effect of a surfactant

Keywords:

Surface characterization of reservoir rocks by inverse gas chromatography: Effect of a surfactant

a b s t r a c t

The description of the surface chemistry of reservoir rock is essential in understanding the physicochemical interaction between the rock surface and its environment. In this study, inverse gas chromatography (IGC) is used to characterize the surface chemistry of rocks extracted from four petroleum reservoirs in Algeria. By means of IGC at infinite dilution (IGC-ID), the dispersive component of the surface energy (␥ s d), the nanomorphological index I M ( t) and the specific component of the surface energy were determined at 100 • C. IGC at finite concentration (IGC-FC) was implemented using n-octane and isopropanol probes, allowing the irreversibility indexes and the adsorption isotherms to be obtained. From the latter, the BET specific surface area and BET constant of the injected probes were determined. Energy distribution functions and indexes of heterogeneity were also computed for the n-octane and isopropanol probes. The results showed that the polar probe, isopropanol, interacts more strongly with the rock surface than the apolar probe. In the second part of this study, the influence of a surfactant used in drilling mud on the heterogeneity of the surface energy was

Introduction

Oil recovery is strongly dependent on the oil wettability of an oilfield reservoir. Wettability describes the tendency of fluid to adhere to a solid surface in the presence of another immiscible fluid [START_REF] Crocker | Wettability and adsorption characteristics of crude-oil asphaltene and polar fractions[END_REF]. For reservoir rock-fluid systems, it is the measure of the affinity that the rock has for either oil or water. Cuiec [START_REF] Cuiec | Mouillabilité et réservoirs pétroliers[END_REF] proved the existence of water-wet, mixed-wet or oil-wet rocks. The wettability of the reservoir rock may change due to the interactions of drilling mud with reservoir rocks. A change in wettability from water-wet to oil-wet conditions is accompanied by a decrease in the relative permeability to oil and a corresponding increase in the water/oil production ratio [START_REF] Sharma | The alteration of rock properties due to interactions with drilling-fluid components[END_REF][START_REF] Skalli | Surface and core wetting effects of surfactants in oil-based drilling fluids[END_REF][START_REF] Yan | Wettability alteration and restoration for cores contaminated with oil-based muds[END_REF].

The wettability properties of reservoir rocks are related to their surface energies and surface heterogeneities. Thus, an accurate description of the surface chemistry of the reservoir rock is essential to improve understanding of the factors affecting reservoir wettability, and thus accurately predict reservoir performance.

Previous studies have mostly been conducted by means of two commonly-used methods to determine the surface energy of a solid: wetting (contact angle) measurements by means of liquid probes, and vapor adsorption measurements (IGC) using vapor probes. Contact angle measurement is one of the most widely-used methods for determining the surface energy of solids. However, the results obtained with this method provide only a macroscopic average of the surface energy of the studied solid and the measurements are difficult to implement on powders due to their surface roughness, porosity and irregular shapes. The limitations of the various methods for measuring contact angles for powders are discussed in a review by Buckton [START_REF] Buckton | Contact angle, adsorption and wettability-a review with respect to powders[END_REF].

Vapor adsorption measurements using IGC-ID are not affected by these surface roughness problems and they provide microscopic variations of the surface properties. This method makes it possible to study the interactions of a probe molecule with the surface adsorption sites. Recently, Arsalan and Palayangoda [START_REF] Arsalan | Surface energy characterization of sandstone rocks[END_REF][START_REF] Arsalan | Surface energy characterization of carbonate rocks[END_REF], successfully quantified the fundamental interactions of the reservoir rock-fluid system by characterizing the surface energy of sandstone and carbonate rocks using IGC-ID.

Despite its huge potential, IGC-ID has its drawbacks when used on heterogeneous surfaces, where only high-energy sites are considered under these conditions. In other words, IGC-ID delivers absolute thermodynamic parameters only on a perfectly homogeneous surface, i.e. a surface for which the interaction potential remains constant from one adsorption site to another. No real solid can be considered as truly homogeneous and the presence of sites having different interaction potentials will influence the behavior of the injected probe, and thus the properties measured by IGC-ID [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations, Acid-Base Interact[END_REF].

It is therefore of great interest to have a method to estimate the degree of heterogeneity of the solid surface. For this reason, IGC-FC was performed in this work after a standard study of the rocks by IGC-ID.

When the concentration of the injected probes is increased, a growing number of less active sites become involved in the interaction with the probe molecules. In this case IGC-FC allows the determination of desorption isotherms and is a suitable method for evaluating the heterogeneity of the surface energy of powders.

To the best of our knowledge, no practical experimental study has been carried out to characterize the surface heterogeneity of natural reservoir rocks at the molecular level. The present paper is an attempt to contribute to this goal.

Theory of inverse gas chromatography

IGC is a well-suited method for exploring the chemical surface properties of non-volatile materials at the molecular scale. It is receiving more attention as it offers several advantages, such as ease and rapidity of measurement, the possibility of using a variety of probes and a large range of temperatures.

The outcome of an IGC measurement is the retention time of the injected probe t r . This value reflects the intensity of interactions between the solid surface and the probe.

The retention volume, namely the volume of the carrier gas required to sweep out an injected probe from the column is related to the retention time by Eq. ( 1):

V n = (tr -t 0 ) × D c (1)
where t r is the retention time of the probe, t 0 the retention time measured with a non-retained probe (methane) and D c is the corrected flow rate, which is related to D m , the flow rate measured with the flow meter, according to Eq. ( 2):

D c = D m × j × T c 273, 15 (2)
where T c is the oven temperature, and j the James Martin coefficient for taking into account the compressibility of the carrier gas under the effect of the pressure drop P, as shown in Eq. (3):

j = 3 2 1 + P P atm 2 -1 1 + P P atm 3 -1 (3)
Depending on the amount of probe molecules injected into the column, two IGC techniques may be distinguished, at infinite dilution (IGC-ID) and at finite concentration (IGC-FC).

Inverse gas chromatography at infinite dilution (IGC-ID)

At infinite dilution conditions, a very small quantity of probe molecules (vapor) are injected in the column at the limit of detector sensitivity, in such a way that the interaction between probe molecules will be negligible and only the solid surface-probe molecule interactions are favored. Under these conditions, Henry's law can be applied and the retention volume is directly related to the free energy of adsorption [START_REF] Lloyd | Inverse Gas Chromatography Characterization Of Polymers And Other Materials[END_REF] according to Eq. ( 4):

-G a 0 = RTLn (Vn) + K ( 4
)
where R is the ideal gas constant, T the temperature, V n the net retention volume and K a constant that depends on the choice of a reference state of the adsorbed probe and also on the total area of the solid accessible to the probe. From the free energy of adsorption and depending on the chemical nature of the injected probe molecule, IGC-ID provides access to many parameters:

The dispersive component of the surface energy

This parameter expresses the ability of the solid surface to establish non-specific interaction with probe molecules. It is calculated according to the Dorris and Gray approach [START_REF] Dorris | Adsorption, spreading pressure, and London force interactions of hydrocarbons on cellulose and wood fiber surfaces[END_REF], by injecting linear alkanes. The slope of the straight line obtained when plotting RT Ln (Vn) versus the number of carbon atoms of the alkane probes, G CH 2 a , gives access to d S by applying Eq. ( 5):

d s = 1 4 CH 2 G CH 2 a Na CH 2 2 (5)
where N is Avogadro's number, a CH 2 the surface area of a methylene group (0.06 nm 2 ), CH 2 the surface energy of a solid made up entirely of methylene groups (i.e. polyethylene), CH 2 = 35, 6 + 0, 058 (293 -T ) in mJ/m 2 , with T being the oven temperature.

The nanomorphological index I M ( t )

This value delivers information about the regularity of the solid surface at the scale of the injected probe. The accessibility to the surface of a solid depends strongly on the probe encumbrances (cyclic and branched probe) and the surface morphology of the studied solid. This effect of the surface morphology can be quantified with the nanomorphological index, by comparison with the adsorption behavior of linear and non-linear alkanes. The nanomorphological index [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations, Acid-Base Interact[END_REF] is obtained according to Eq. ( 6) and illustrated in Fig. 1:

I M ( t ) = exp -ı G M a RT (6)
where -␦ G M a is the variation between the representative point of the branched or cyclic alkane and the reference n-alkane straight line, and t the topology index proposed by Brendlé and Papirer [START_REF] Brendlé | A new topological index for molecular probes used in inverse gas chromatography for the surface nanorugosity evaluation[END_REF] and derived from Wiener's topology indices.

When I M ( t ) is equal to 1, the solid surface can be considered as flat at the molecular scale. Under these conditions, the bulky (branched or cyclic) alkanes and the linear alkanes have access to the same surface.

When the surface roughness increases,I M ( t ) decreases and its value can reach 0.1, as in the case of talc [START_REF] Comard | Coupling of inverse gas chromatography at infinite dilution (IGC-ID) with a controlled modification of a solid surface[END_REF]. Access to the rough parts of the surface is more limited for cyclic (or branched) alkane molecules than for linear ones due to steric hindrance. The term 'specific' includes all type of interactions, i.e. polar, hydrogen bonding, and metallic or magnetic interactions, except the dispersive ones, which are obtained by injecting polar probes [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations, Acid-Base Interact[END_REF]. The difference between the global free energy of the injected polar probe and the straight line of linear alkane probes represents the contribution of specific interactions G sp a also notedI sp (Fig. 1):

G a = G sp a + G d a (7)
The principal advantages and limitations of IGC-ID have been summarized in a review by Balard et al. [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations, Acid-Base Interact[END_REF].

Inverse gas chromatography at finite concentration (IGC-FC)

In the case of an IGC-FC approach, a liquid probe is injected instead of vapor, which leads to the formation of a probe monolayer on the solid surface. Then a strong asymmetric chromatographic peak is obtained when ideal, non linear conditions are fully fulfilled.

Isotherm of adsorption

By applying the elution characteristic point method (ECP) to the reversible isothermal part of the experimental chromatogram, IGC-FC allows access to the desorption isotherm [START_REF] Conder | Physicochemical Measurement by Gas Chromatography[END_REF]. The first derivative of this isotherm is directly related to the net retention time of each point of the diffuse front of the chromatogram through Eq. ( 8):

∂N ∂P L,tr = D C (tr -t 0 ) mRT (8)
where for a given characteristic point of the diffuse front of the chromatogram, N is the number of adsorbed probe molecules, P the partial pressure of the probe at the output of the column, directly related to the height of the signal, t r the retention time and t 0 the retention time of a molecule that is not retained by the solid surface (methane), D c the corrected flow rate, m the masse of the solid contained in the column, L the column length.

The integration of the above equation gives access to the desorption isotherm, from which several items of information can be deduced, such as the specific surface area a BET , the BET constant and Henry's constant.

Irreversibility index

Due to the presence of very high-energy adsorption sites, a nonnegligible part of the injected probe is not necessarily eluted in time for the return of the signal to the base line. In order to assess this irreversibly-adsorbed amount, the temperature of the chromatograph oven is increased to the conditioning temperature, leading to the appearance of a small secondary peak on the right side of IGC-FC chromatogram (Fig. 2).

The irreversible part of the adsorption phenomenon can be accessed from the ratio of the area of the thermodesorption peak to the total area of the chromatogram, and defined as an irreversibility index (I irr ) [START_REF] Balard | Study by inverse gas chromatography of the surface properties of milled graphites[END_REF] according to Eq. ( 9):

I irr = S th S rv + S th (9)
where S rv is the area of the main chromatographic peak and S th the area corresponding to the thermodesorption peak. Moreover, it is obvious that the shape of the desorption isotherm is influenced by the surface heterogeneity. Molecules retained on the sites having the highest energy will remain for a longer time in the chromatographic column than those adsorbed on the sites of lower energy. Hence, the shape analysis of the isotherm will determine the distribution function of the adsorption energies of the probe.

Distribution function of the adsorption energies (DF) and heterogeneity index

The surface heterogeneity is described by a distribution function (DF) corresponding to the relative abundance of each type of domain having the same characteristic energy of interaction. The calculation of the DF is based on a physical adsorption model which admits that the global isotherm may be considered as a sum of local isotherms of adsorption on isoenergetic domains (patchwork model) [START_REF] Rudzinski | Adsorption of Gases on Heterogeneous Surfaces[END_REF][START_REF] Rudzi Ński | Physical adsorption of gases on heterogeneous solid surfaces: evaluation of the adsorption energy distribution from adsorption isotherms and heats of adsorption[END_REF][START_REF] Balard | Estimation of the surface energetic heterogeneity of a solid by inverse gas chromatography[END_REF].

The physical adsorption on heterogeneous solid surfaces was described by the following integral form Eq. ( 10):

N (Pm, T m) = N 0 εmax ε min  (ε, P m , T m) (ε) dε (10)
where N (P m , T m ) is the number of molecules adsorbed at the pressure P m and temperature T m of measurement, N 0 the number of molecules needed for the formation of a monolayer, Â (ε, P m , T m) the local isotherm (generally Langmuir's isotherm) corresponding to adsorption sites having the same characteristic adsorption ε, and (ε) the distribution function (DF) of the sites seen by the probe. The range of adsorption energies is calculated between minimal (ε min ) and maximal (εmax) values.

The characteristic energy (ε) is related to the pressure of measurement by Eq. ( 11):

ε = -RTLn P/K WithK = C10 √ MT ( 11
)
where M is the probe molecular weight and C a constant depending on the pressure unit: C = 2.346 × 10 3 when the pressure is expressed in kPa. The integral equation above is not a trivial task because it has no general solution, except when admitting a step function as a local isotherm known as the condensation approximation. The distribution function for the condensation approximation (DFCA) is then directly related to the first derivation of the isotherm, according to Eq. ( 12):

CA (ε) = P ′ RT d dP ′ N ′ (P ′ ) N 0 ( 12
)
where N ′ and P ′ are respectively the amount of adsorbed probe and the equilibrium pressure of the probe corrected for the multilayer adsorption [START_REF] Messen | Carbon Black using Inverse Gas Chromatography Techniques[END_REF]. This approximation is acceptable only for a measurement temperature approaching absolute zero. In the usual IGC measurement conditions, at room temperature and above room temperature, this approximation is no longer valid, and it becomes necessary to use other approximated forms of the local isotherm. Among them, for Langmuir's local isotherms, the extended [START_REF] Rudzi Ński | Physical adsorption of gases on heterogeneous solid surfaces: evaluation of the adsorption energy distribution from adsorption isotherms and heats of adsorption[END_REF] method allows the computation of the actual distribution function (DFRJ) through a limited development of the even derivatives of the DFCA, according to Eq. ( 13):

(ε) = +∞ j=0 (RT ) 2j b 2j 2j CA (ε) withb 0 = 1 andb 2j = (-1) j 2j (2j + 1)! (13)
On the other hand, by comparing the computed DF with the DF corresponding to a homogeneous surface that fit the left descending branch of the experimental DF, towards the lower interaction energies (Fig. 3), an index of surface heterogeneity I hete [START_REF] Balard | Study by inverse gas chromatography of the surface properties of milled graphites[END_REF] can be found, by using Eq. ( 14):

I hete = 100 A exp -A homo A exp ( 14
)
where A exp is the area under the experimental DF and A homo that of the homogeneous DF. This index is used to compare the surface heterogeneity of the studied solids.

For IGC-FC measurements, all the calculations were performed using special software from the ADSCIENTIS company (Wittelsheim, France).

Materials and methods

Reservoir rocks

In this study, four rocks were collected from four different reservoirs located in the Hassi Messaoud site in south-eastern Algeria and noted OKJ21, OMO62, OKN54 and OKN46.

To remove all liquid from the contaminated core and restore the natural state of the reservoir, the rocks were cleaned of all drilling mud using a distillation/extraction method (Dean-Stark and Soxhlet). Each sample was placed in a Soxhlet or Dean-Stark apparatus and cleaned with refluxing solvent (toluene). In the Dean-Stark apparatus, the toluene is continuously distilled, condensed and then distributed over the top of the sample. In the Soxhlet apparatus, the sample is soaked in the hot solvent, which is periodically siphoned off, then distilled, condensed and distributed back to the extractor [START_REF] Gant | Core cleaning for restoration of native wettability[END_REF].

The cleaned reservoir rocks were ground using a mortar and pestle and were subsequently sieved to obtain a size fraction less than 100 m.

Impregnation protocol

The surfactant used for the preparation of the impregnated rock samples was selected because of its use on drilling mud. Some properties of this surfactant are listed in Table 1. For reasons of confidentiality, no further information was supplied by the petroleum company.

The mass of reservoir rock required to fill the chromatographic column was put in a beaker and mixed with a given mass of surfactant in 20 mL of carbon tetrachloride, used as a solvent, until the mixture became homogeneous (∼5 h). After the evaporation of the solvent in an oven at 333 K, the column was filled with the reservoir rock impregnated with the surfactant.

Depending on the mass of the surfactant, a wide range of impregnation ratios ( ), expressed in% and calculated by Eq. ( 15), were examined:

(%) = m s m r × 100 ( 15
)
where m s and m r were the mass of the surfactant and the mass of the reservoir rock respectively.

Characterization methods

Phase identification was performed on a Panalytical X'PERT-Pro diffractometer (Philips) with an X-ray copper anticathode tube ( = 1.5418). Diffraction data were acquired by exposing the powder samples to Cu-K␣ radiation at a voltage of 45 kV and to a current of 40 mA. The data were collected over a range of 8 • to 90 • with a step size of 0.0167 • . Data analyses were performed with the X'Pert Data Collector software and phase identification was carried out by means of PANALYTICAL High Score Plus software in conjunction with the ICDD Powder Diffraction File 2 database and the Crystallography Open Database.

The elementary analyses were obtained using a PANALYTICAL EPSILON 3XL X-Ray Fluorescence Spectrometer with RX: 50 kV generator power.

Particle morphology was investigated using a scanning electron microscope (SEM) (Philips XL 30 model ESEM-FEG) operating at 10 kV.

Thermogravimetric analysis (TGA) coupled with differential calorimetric scanning analysis (DSC) provided information about the mass changes of the sample according to heating rate. In this study the device used was a ATG-DSC 111 SETARAM. Thermal analysis was performed with a temperature rise of 283 K/min from 293 K to 473 K under nitrogen flow of about 50 mL/min.

The specific surface areas and BET constants were determined with an ASAP 2010 Micromeritics Analyser, and evaluated using the Brunauer-Emmet-Teller (BET) equation. Prior to measurements, the samples were degassed by heating to 383 K in a vacuum for 24 h at a pressure of 10 -2 mbar. The analyses were carried out with krypton at a temperature of 77 K (liquid nitrogen temperature).

IGC measurements were performed using an Agilent 7890 apparatus, fitted with sensitive flame ionization detectors (FID). Helium was used as the carrier gas with a flow rate of about 30 mL/min measured with an electronic flow meter (flow 500-Agilent). The temperature of the injector and the detector were respectively 403 and 473 K. Stainless steel columns with an internal diameter of 6.35 mm and a length varying between 10 and 20 cm were filled with a mixture of the reservoir rock and glass beads (90 m median diameter). The interest of glass beads was to reduce the mass of reservoir rocks and so the pressure drop through the column in order to avoid fitting leaks. The powder mass range in the column was generally between 1 and 2 g. The column was then closed with a bit of glass wool at both ends. The columns were then conditioned at 443 K overnight in the oven chromatograph. Net retention times were calculated by subtracting the retention time of a non-retained molecule (Methane) from the retention time of the probe.

The IGC-ID study was performed with an oven temperature of 373 K. The probes used were linear alkanes (n-hexane C6, n-heptane C7, n-octane C8, n-nonane C9), a branched alkane (2,5dimethylhexane 2,5-DMH), a cyclic alkane (Cycloheptane Cycl7) and a polar probe (Dichloromethane CH 2 Cl 2 ). These probes were of chromatographic grade purity (>99%).

The IGC-FC measurements were performed with an oven temperature of 313 K. Two probes were examined in IGC-FC, an apolar probe, n-octane (C8), to study the surface morphology, and a polar probe, isopropanol (IP), to study the surface chemistry. These probes were of chromatographic grade purity (>99%).

Results and discussion

Mineralogical analysis by X-ray diffraction

The diffraction patterns are illustrated in Fig. 4. There was no significant difference in the mineral composition of the four samples. They all contained predominantly Quartz. Apart from quartz, in the OKJ21 and OMO62 samples, the presence of different clay components such as kaolinite and illite was observed but at a very low percentage. Thus it was concluded that the studied rocks were quartz with a high purity.

Chemical composition analysis by elemental analysis

The results of X-ray Fluorescence (XRF) analyses of the studied rocks are summarized in Table 2.

The chemical composition analyses reveal a significant presence of silicon in all samples. The XRF results correlate to a very large extent with the results obtained with XRD, in particular with regard to the dominance of the silicon species in all samples. The presence of other elements was also noted, such as aluminum, iron, calcium and potassium, but at very small percentages.

Morphological analysis by SEM

Observation by SEM (Fig. 5) revealed that the studied rocks showed similar surfaces, composed of small particles that get stuck on the surface of larger ones.

BET surface analysis

Because of the low specific surface areas of the samples, the adsorbed gas selected was krypton at liquid nitrogen temperature (77 K). The molecular size of krypton, 0.152 nm 2 , and its low saturation pressure at liquid nitrogen temperature make it possible to obtain high accuracy on the small adsorbed volume. In other words, Krypton is the suitable gas for the measurement of low specific surface areas [START_REF] Ismail | Adsorption of nitrogen and krypton at 77 K on silicas and graphitized carbons[END_REF]. The values of specific surface area (a BET ), and BET constant (C BET ), obtained by exploiting the adsorption isotherms of Kr at 77 K are produced in Table 3.

The results obtained using gas adsorption manometry indicate that the specific surface areas were very low for all samples 4.

The values of d s obtained with the rocks OKJ21 and OMO62 are close, testifying to similar surface properties. These values are in agreement with those obtained in the literature, for instance, on sandstone originating from Ottawa, (approximately 85 mJ/m 2 , at 353 K), and Berea sandstone originating from Oberlin, Ohio (approximately 60 mJ/m 2 , at 353 K) [START_REF] Arsalan | Surface energy characterization of sandstone rocks[END_REF]. The lowest d s value is obtained with the OKN54 rock. The OKN46 sample stands out from the other rocks, since it gives a high value of d s (137 mJ/m 2 ) reflecting a greater affinity of alkane probes for this rock surface. On the other hand, the dispersive component of the surface energy measured for various silica surfaces in the literature varies from 30 to 156 mJ/m 2 [START_REF] Papirer | Adsorption on Silica Surfaces[END_REF].

This difference in d s values observed on the studied samples can be explained by the surface morphology. To obtain more information about this morphology at the molecular scale, the nanomorphological indexes obtained with cycloheptane (Cycl7) and 2,5-dimethylhexane (2,5-DMH) probes were determined at 373 K (Table 4).

The lower nanomorphological index values obtained with the branched probe, the 2,5-DMH, reflect accessibility to a more limited surface roughness with this probe compared to those obtained with the cyclic one (Cycl7), indicating that the branched probe seems to be more sensitive to the surface morphology of the studied rocks.

The lowest I M ( t ) values are obtained with OKN46, which exhibits the highest value of d s , indicating a high surface roughness for this rock. On the contrary, the highest I M ( t )and lowest By injecting acidic probes, such as dichloromethane, the specific interaction parameter, I sp , was also determined (Table 4). It can be noted that all the samples show almost the same behavior towards the polar probe. However, the measured values of I sp of the studied samples are higher than those determined, for instance, for amorphous and crystalline silica [START_REF] Hadjar | An inverse gas chromatography study of crystalline and amorphous silicas[END_REF], testifying to the strongly acidic character of the studied rocks. This character may results from the higher density of the superficial hydroxyl groups.

When IGC-ID was applied, among the four samples, OKN46 exhibited the highest surface energy, reflecting a high surface roughness. The lowest surface energy was obtained with the OKN54 rock. However, the IGC parameters are clearly related to the adsorption sites having the greatest energy of interaction [START_REF] Balard | Determination of the acid-base properties of solid surfaces using inverse gas chromatography: advantages and limitations, Acid-Base Interact[END_REF]. To provide more information on the whole surface of the studied rocks, IGC-FC experiments were implemented using octane and isopropanol.

Inverse gas chromatography at finite concentration (IGC-FC)

The studied rocks were submitted to IGC-FC analysis using noctane, an apolar probe, which is mainly sensitive to the surface morphology, and a polar probe, isopropanol, which is mainly sensitive to the surface functionality.

Study of desorption isotherms.

From the desorption isotherms of the studied rocks, the specific surface areas and the BET constants of n-octane and isopropanol probes were determined. The results are compared with those obtained by krypton at liquid nitrogen temperature, 77 K, in Table 5.

The organic probes lead to specific surface area values higher than those obtained by adsorption of krypton at 77 K. This deviation was already observed in the study of milled graphite by IGC-FC [START_REF] Balard | Study by inverse gas chromatography of the surface properties of milled graphites[END_REF], and was attributed to the difference in the occupied area by both n-octane and isopropanol probes adsorbed on the solid surface.

Moreover the specific surface areas obtained using n-octane probes are higher than those obtained with isopropanol. This difference could be explained by the more irreversible character of isopropanol adsorption compared to that obtained with n-octane, as testified by their respective irreversibility indexes (I irr ), reported in Table 6.

The values of the irreversibility index of the polar probe obtained for the studied rocks are higher than those obtained using n-octane, reflecting a higher irreversible adsorption of the isopropanol probe compared to the n-octane probe. It should be remembered that the amount of the probe adsorbed irreversibly on the surface of the solid is not taken into account for the calculation of the specific surface area, and contributes to its decrease. This can actually be the reason why the specific surface values measured using an isopropanol probe are lower compared to those obtained with the n-octane probe.

Moreover, it is observed that the irreversibility index I irr obtained with n-octane on the studied rocks follows the same trend as the d s values; the highest values of both parameters were obtained with the OKN46 rock and the lowest ones with the OKN54 rock.

Even if the two parameters are not obtained from the same injection conditions, the first, d s , being obtained under IGC-ID conditions and the second under IGC-FC conditions, both reflect the interactions between the injected probes and the high energy sites. This may be the origin of the good correlation obtained between these two parameters. 4.5.2.2. Characterization of surface heterogeneity. Using the distribution function of the adsorption energies (DF) is a good way to reveal the heterogeneity of the surface of the studied rocks. It was first evaluated with a non polar probe, n-octane (Fig. 6), which exchanges only dispersive interactions with the surface of the studied rocks.

The DFs obtained with n-octane are essentially monomodal and asymmetrical. A maximum is observed at about 22 kJ/mol.

The DF obtained with the OKN46 sample shows a shoulder extending towards the high energies which can be explained by the higher surface heterogeneity of this rock compared to the other samples. The most symmetrical DF is given by the OKN54 rock, testifying to the more homogeneous surface of this rock.

The surface heterogeneity can be quantified with the heterogeneity index (I hete ) obtained from the asymmetrical part of the distribution function and given by Eq. ( 14). The values were determined for n-octane (Table 7). As expected, the highest value of the I hete (33%) was obtained with the OKN46 rock, indicating a more heterogeneous surface than the others from the morphological point of view. Slightly lower values were obtained with OKJ21 and OMO62. The OKN54 sample exhibited a more homogeneous surface with a I hete close to 13%.

On the other hand, by its ability to exchange strong interactions through hydrogen bonding, the isopropanol probe is sensitive to the surface functionality. The DFs obtained with isopropanol (Fig. 7) are all monomodal and highly asymmetrical. They exhibit a main component centered on 18 kJ/mol, while the maximum for the OKN46 rock is situated at a higher value of about 20 kJ/mol. Moreover these DFs exhibit a shoulder towards the high energies up to 45 kJ/mol. A similar DF was also obtained in an Algerian Attapulgite [START_REF] Boudriche | Effect of acid treatment on surface properties evolution of attapulgite clay: an application of inverse gas chromatography[END_REF]. The first peak can be attributed to the siloxane sites and the shoulder towards high energy to other functions, among them silanol groups.

The heterogeneity index values of the isopropanol probe calculated from the obtained DFs, according to Eq. ( 14), are presented in Table 8.

For all the studied samples, the I hete values are higher than 30%. Once again, the OKN46 rock exhibits one of the highest I hete values, 42.0%, compared to 33.6% obtained with the OKN54 rock.

The heterogeneity index (I hete ) of isopropanol is much greater than that of n-octane for all samples, because the former interacts more strongly with the surface functional groups through hydrogen bonds, i.e. with silanol groups, whereas the latter exchanges only non-specific interactions with the surface and is quite insensitive to the surface functionality. IGC-FC allowed us to gain a close insight into the surface heterogeneity of the studied rocks at the molecular scale. Between the four samples, OKN54 exhibited the lowest surface heterogeneity, as shown by the lowest values of heterogeneity indexes obtained with n-octane and isopropanol probes, while OKN46 exhibited the highest.

Good correlation was obtained between the IGC-ID and the IGC-FC results, where OKN46 always exhibiting the highest parameter values, reflecting a more energetic, rough and heterogeneous surface. The lowest values were obtained with the OKN54 rock, testifying to a less energetic, flatter, and more homogeneous surface on this rock. The OKJ21 and OMO62 rocks exhibited almost the same parameters values, testifying to similar surface properties.

Effect of the surfactant impregnation on the surface properties

In this part of this study, the influence induced by a surfactant used in drilling mud was studied on the properties determined by IGC-FC using n-octane and isopropanol probes. A drilling mud additive was used to impregnate the surface of the OKJ21 rock. Before filling the chromatographic columns, thermogravimetric analysis was implemented on the impregnated sample to confirm that it remained stable even at high temperature. The TGA-DSC analysis indicated that the impregnated sample underwent a very weak loss in mass of about 0.4% of the initial mass. This result confirms that the impregnated sample is thermally stable.

Variation of the specific surface area

The isotherms obtained on OKJ21 impregnated with surfactant show a classic type II shape regardless of the impregnation ratio (Fig. 8).

The adsorbed quantities at a given relative equilibrium pressure depend on the impregnation ratio of the surfactant. It decreased from 0% to 5% (Fig. 8).

The variations in specific surface area, the corresponding BET constant, and the irreversibility index as a function of the impregnation ratio, are summarized in Table 9.

It can be observed that whatever the probe used, the specific surface area, the BET constant and the irreversibility index follow the same trend, the weakest impregnation ratio (0.35%) is sufficient to reduce these parameters.

The decrease on the specific surface area and BET constant gives evidence to the recovery of the solid surface with the surfactant, this latter shields the porosity and consequently the highest energy sites since the first impregnation ratio (0.35%). Above this ratio, the polymer covers the most of the surface, and the two parameters obtained with the injected probes remain almost stable and independent of the surfactant coverage rate. On the other hand, the irreversibility index also decreases with the impregnation ratio, testifying that the injected probes interact less strongly with the impregnated samples than with the raw one.

Variation of the surface heterogeneity

The influence of the surfactant impregnation ratio was also examined on the surface heterogeneity. Fig. 9 depicts the variations of the DF of the adsorption energies, for both n-octane (Fig. 9.A) and isopropanol (Fig. 9.B) probes as a function of the impregnation ratio on the OKJ21 rock.

The two probes, n-octane and isopropanol, are sensitive to the surface modification induced by the surfactant impregnation. The progressive disappearance of the shoulder towards high energies can be noted starting from the first impregnation ratio of 0.35%. Above this ratio, the DFs obtained become more symmetrical as the impregnation ratio increases. To support this observation, the variation of the heterogeneity index of n-octane and isopropanol probes was monitored, as a function of the surfactant coverage. The results obtained are illustrated in Fig. 10. As depicted in Fig. 10, the values of the heterogeneity index of the injected probes decrease significantly from 28.1% to 11.4% with n-octane, and from 42.0% to 20.1% with isopropanol, at 0.75% of the impregnation ratio. This decrease in the heterogeneity indexes is consistent with the progressive covering of the solid surface by the surfactant. The hydroxyl chemical functions of the surfactant interact with the isopropanol probe, and make the surface smooth and nearly homogeneous by covering the surface roughness. Above this coverage ratio (0.75%), the heterogeneity indexes obtained with the two probes remain stable and independent of the surfactant coverage. This observation may be related to the fact that above an impregnation ratio of 0.75%, the surfactant covers the entire rock surface and the injected probe interacts with the thick film produced, instead of with the rock surface.

Conclusion

This work provides a comprehensive study of the surface chemistry of four Algerian reservoir rocks, using XRD, XRF, adsorption manometry and IGC. The XRD diffractograms confirmed that the reservoir rocks are quartz-based minerals with traces of kaolinite and illite. The XRF results were in good correlation by exhibiting Silicon as the highest chemical element in the studied rocks. The adsorption manometry analyses were performed with krypton as the adsorbed gas, with results indicating that the specific surface areas were very low for all samples, < 1m 2 /g. IGC was used to investigate the surface properties of the studied rocks. Using IGC at infinite dilution conditions, among the studied rocks, the highest d s value was obtained with the OKN46 rock, indicating a rough, high-energy surface, as shown by the low nanomorphological index values obtained with the cyclic and branched probes. On the other hand, OKN54 exhibited the lowest d s value, demonstrating a smooth, low-energy surface, as shown by the higher values of the nanomorphological index obtained with the cyclic and branched probes on this rock surface.

IGC at finite concentration was used in order to obtain a more realistic description of the whole surface. The DFs obtained with noctane were monomodal and symetrical for two reservoir rocks (OKJ21 and OMO62) and asymetrical for the other ones, while the DFs obtained with the polar probe were highly asymmetrical whetever the solid, exhibiting a large tail towards the high energies up to 45 kJ/mol. Between the four samples, OKN54 exhibited the lowest surface heterogeneity.

The DFs obtained with n-octane were all monomodal and almost symmetrical, while the DFs obtained with the polar probe were asymmetrical, exhibiting a large tail towards the high energies up to 45 kJ/mol. Between the four samples, OKN54 exhibited the lowest surface heterogeneity.

The effect on the surface properties of a surfactant used in drilling mud was further examined by IGC-FC. It was established that the BET surface area, BET constant and the irreversibility index, obtained with n-octane and isopropanol probes, decreased with the increase in the surfactant impregnation ratio, then reached a plateau. The distribution functions of the studied rock also confirm a decrease in the number of the high energy sites according to the impregnation ratio. The disappearance of the tail towards high energy was noted in the first impregnation ratio, and the DF obtained became more symmetrical with the increase in the surfactant impregnation ratio.

This study provides evidence that IGC is a powerful method for obtaining a more realistic description of the surface characteristics of a solid, in particular in studying of the influence of a treatment (e.g. a polymer impregnation) on the physicochemical surface properties of a solid. However care should be taken in interpreting the results with regard to the influence of the surfactant on the wettability of the reservoir rock, owing to the fact that reservoir fluids are usually a mixture of crude oil and brine. Much further work is required to fully utilize the potential of inverse gas chromatography in the study of the effect of drilling mud on the wettability of reservoir rocks.

Fig. 1 .

 1 Fig. 1. Experimental measurements of the free energy of adsorption for different probes. One column.

Fig. 2 . 2 . 1 . 3 .

 2213 Fig. 2. Experimental chromatogram and the associated peak of thermodesorption acquired for the n-octane probe on the reservoir rock. One column.

Fig. 3 .

 3 Fig. 3. Determination of heterogeneity index from DFCA. One column.

Fig. 4 .

 4 Fig. 4. X-ray diffraction patterns of the studied rocks showing the identified minerals (Q: Quartz, KI: Kaolinite, IL: Illite). One column.

Fig. 5 .

 5 Fig. 5. SEM micrographs of the studied rocks. two columns.

ds

  values obtained with the OKN54 rock, indicate a flatter surface compared to the other rocks. The OKJ21 and OMO62 rocks exhibit almost the same values of I M ( t ), indicating similar morphologies.

Fig. 6 .Fig. 7 .

 67 Fig.6. Adsorption energy distribution functions of the n-octane probe on the studied rocks, measured at 313 K. One column.

Fig. 8 .Fig. 9 .

 89 Fig.8. Plots of the n-octane (A) and isopropanol (B) isotherms obtained on OKJ21 impregnated at different surfactant ratios obtained by IGC-FC at 313 K two columns.

Fig. 10 .

 10 Fig. 10. Variation of heterogeneity index (I hete ) of n-octane (C8) and isopropanol (IP) obtained by IGC-FC at 313 K as a function of the surfactant impregnation ratio. One column.

Table 1

 1 The characteristics of the surfactant.

	Product	Supplier	Recommended	Classe	(g/cm 3 )
			use
	VERSAMUL MISwaco/ Shlumberger OBM a emulsify	Cationic 71% 0.928

a Oil Based Mud.

Table 2

 2 Atomic composition of studied reservoir rocks.

	Chemical composition (%)
	Element	OMO62	OKJ21	OKN46	OKN54
	Si	94.11	91.46	96.29	94.27
	Al	2.33	2.52	0.33	0.85
	K	-	4.17	0.17	0.33
	Ca	0.77	0.75	0.44	1.14
	Fe	0.27	0.72	0.30	0.70
	Na	0.26	-	0.20	-

Table 3

 3 Values of specific surface areas and BET constants obtained by the adsorption of Krypton at 77 K.

	Reservoir rock	aKr m 2 /g	CBET
	OKN54	0.65	25.8
	OMO62	0.46	18.6
	OKN46	0.44	28.6
	OKJ21	0.36	41.6

Table 4

 4 Values ofd s , IM ( t ), and Isp of the studied rocks determined at 373 K. Parameters such as the dispersive component of the surface energy, d s , the nanomorphological index, I M ( t ), and the specific component of the surface energy, I sp obtained by IGC-ID at 373 K on the studied rocks samples are presented in Table

	Reservoir rocks	d s (mJ/m 2 ) ± 5	IM ( t ) ± 0.1		Isp (kJ/mol) ± 1.6
			2,5-DMH	Cycl7	CH2Cl2
	OKN46	137	0.1	0.2	11.6
	OKJ21	89	0.5	0.6	10.0
	OMO62	80	0.4	0.6	11.0
	OKN54	56	0.5	0.8	9.6
	(<1 m 2 /g). Similar results were obtained by Arsalan on sandstone
	originating from Ottawa, Canada, and on Berea sandstone from
	Oberlin Ohio [7], indicating surface areas varying between 0.2 and
	4 m 2 /g.

4.5. Characterization of samples by IGC 4.5.1. Inverse gas chromatography at infinite dilution (IGC-ID)

Table 5

 5 Values of specific surface areas and BET constants obtained on the studied rocks by krypton adsorption and IGC-FC with n-octane and isopropanol probes.

	Kr			n-Octane		Isopropanol
	Rocks	aKr (m 2 /g) CKr	aC8 (m 2 /g) ± 0.3 CC8 ± 0.5 aIP (m 2 /g) ± 0.3 CIP ± 5.8
	OKJ21	0.36	41.6 3.4	9.0	2.3	11.8
	OKN46 0.44	28.6 1.2	11.2	0.6	14.0
	OMO62 0.46	18.6 0.8	10.0	0.6	13.8
	OKN54 0.65	25.8 1.8	7.0	1.2	8.8

Table 6

 6 Values of irreversibility indexes (I irr ) measured at 313 K using n-octane and isopropanol probes on the studied rocks.

	Reservoir rock	I irr C8 (%) ± 0.7	I irr IP (%) ± 0.8
	OKJ21	3.7	11.8
	OKN46	5.3	7.6
	OMO62	3.2	11.0
	OKN54	1.1	6.5

Table 7

 7 Value of heterogeneity index measured by IGC-FC for n-octane probe on the studied rocks.

	Reservoir rock	I hete (C8) % ± 2.6
	OKN46	33.1
	OKJ21	28.1
	OMO62	28.4
	OKN54	12.8

Table 8

 8 Values of heterogeneity indexes measured by IGC-CF for isopropanol probe on the studied rocks.

	Reservoir rocks	I hete (IP) % ± 2.8
	OKN46	42.0
	OKJ21	41.4
	OMO62	36.8
	OKN54	33.6

Table 9

 9 Values of the specific surface area (aBET), BET constant (CBET), and irreversibility index (I irr ) using n-octane and isopropanol probes on the raw and impregnated rock OKJ21, obtained by IGC-FC at 313 K.

	Impregnation ratio (%)	n-Octane			Isopropanol
		aC8 (m 2 /g) ± 0.1	CC8 ± 0.1	I irr ± 0.6	aIP (m 2 /g) ± 0.6	CIP ± 0.1	I irr (%) ± 0.1
	0	3.4	9.0	3.7	2.3	21.0	11.8
	0.35	1.1	7.7	1.4	0.6	10.5	2.3
	0.75	0.9	6.3	0.7	0.4	7.8	1.0
	3	1	6.5	0.2	0.7	9.5	0.3
	5	0.7	6.8	0.1	0.4	8.7	0.4

Acknowledgment

The authors gratefully acknowledge the contribution of the petroleum company, CRD-SONATRACH, Algeria, for providing the drilling mud additives and the reservoir rocks.


David Guerrero
email: david.guerrero@ifsttar.fr

Fernando Gonzalez Laxe

Maria-Jesus Freire

Carlos Pais Montes

Fernando Gonzalez Laxe

Maria-Jesus Freire Seoane

Fernando González-Laxe

María Jesús Freire-Seoane

Carlos Pais-Montes

Inland accessibility and foreland specialization of European regions

Keywords: foreland, AIS data, inland accessibility, hinterland, OLS regression foreland, AIS data, inland accessibility, hinterland, OLS regression

published or not. The documents may come

Introduction and theoretical background

The heterogeneity of maritime transport supply in regions can be understood as the visible manifestation of two complementary dynamics. On the one hand, there are factors related to demand such as the size of the local market made up of economic activities and population. On the other hand, there are a series of dynamics resulting from strategies pursued by transport companies, which are obviously related to the former but to other structural factors of the foreland as well (i.e. organization of their own transport network). These two dimensions, which are necessary conditions for the success of (maritime) transport terminals, have been conceptualized as centrality and intermediacy. Both are necessary for the success of transport hubs, but their combination can vary considerably from one case to another [START_REF] Fleming | Spatial characteristics of transportation hubs: centrality and intermediacy[END_REF]. Within the context of containerized transport, a high share of transhipment characterizes pure hubs, when intermediacy within the shipping network is the main advantage. On the contrary, gateway ports, where the transhipment rate is lower, are rather characterized by their centrality, namely the geographical proximity vis-à-vis inland markets. It should be however noted that gateways can hardly be "pure" since their large local markets greatly contribute to enhance their intermediacy both within inland and maritime networks, making them attractive locations for transhipment activities as well. In the academic literature of port studies, this issue is not new. A similar debate took place in the aftermath of World War II, on the relative importance of maritime and land-based factors on the success of ports. [START_REF] Amphoux | Les fonctions portuaires[END_REF][START_REF] Amphoux | Géographie portuaire et économie portuaire[END_REF] and [START_REF] Weigend | The problem of hinterland and foreland as illustrated by the port of Hamburg[END_REF] emphasized the prominence of maritime-related factors on the cargo-generating potentials of Le Havre and Hamburg. The success of both ports was not unrelated to the strength of their locally-based shipping companies and, more broadly, to the trade policies implemented by France and Germany. By contrast, the fates of other ports within the Northern Range, such Antwerp and Rotterdam, seemed to be much more related to inland factors such the historical know-how of their local merchants and traders and the high density of shippers in their hinterlands, spreading far beyond national borders [START_REF] Boerman | The need for special examination of particular aspects of port geography[END_REF]. This academic debate was later relativized by those who considered ports as broader systems in which inland, maritime and port-related elements were interrelated but not necessarily in the same proportions (Vigarié, 1964, Robinson, 1970). In the recent decades, the further integration of transport modes allowed by containerization has somewhat blurred the lines between land and sea related factors within the context of a global intermodal transport system. To secure a good access to the hinterlands, containerized shipping lines have been increasingly involved in inland transport, often by investing in deep-sea terminals and sometimes by providing inland transport services (Franc and Van der Horst, 2009). Other intermediaries such freight forwarders have supported this integration as well, by providing integrated door-to-door services [START_REF] Ducruet | Transport integration at European ports[END_REF].

Few works have succeeded to empirically measure the relationship between centrality and intermediacy, mainly because of the lack of data. One of them showed that the rate of transhipment of container ports in the Mediterranean mainly depends on the throughput and on the deviation from the main Europe-Asia maritime route (Zohill and Prijon, 1999). Today, when containerization seems to have reached its stage of maturity [START_REF] Guerrero | The waves of containerization: shifts in global maritime transportation[END_REF] the main challenge for a container port is not just to cumulate high levels of centrality and intermediacy regarding inland markets and shipping networks, but also to maintain and improve their position within value chains (Robinson, 2002). To support the adherence of the local people and economic actors to port expansion projects, ports are also expected to attract activities and jobs related to the maritime flows within the context of international supply chains [START_REF] Hall | Shifting proximities: The maritime ports sector in an era of global supply chains[END_REF]. The existence of frequent services with a wide range of overseas regions port could allow an efficient integration of its inland customers in global production systems. But port performance issues are rarely considered from the point of view of the shippers (inland customers) for whom the frequency of services and their geographical variety are central.

The purpose of this paper is to help to fill this void by a systematic analysis of the contribution of inland potential demand, measured by accessibility to population, to the concentration of container services in Europe by taking in account the diversity of overseas regions involved in maritime trade. While we show that inland accessibility well reflects the geographical concentration of services, we also identify other factors as well. Indeed, we attempt to understand why in some regions the maritime transport supply seems to be less linked than we might expect from its inland market potential. The segmentation of maritime transport supply by overseas regions could deliver some explanation about these deviations.

The rest of this paper is structured as follows. Section 2 presents data and method, which are applied in Section 3 to describe and understand the relationship between maritime services and inland accessibility. We conclude in section 4.

Data and method

Data: database on maritime transport supply

This research was carried out using a set of Automatic Information System (AIS) positions, in order to count the number of containerized services to/from each European NUTS3 region. The implementation of this new tracer technology in the ship's bridge begins with the IMO A.917 ( 22) resolution [START_REF] Harati-Mokhtari | Automatic identification system AIS: data reliability and human error implications[END_REF] and it is currently compulsory for all vessels over 300 GT's, which report call, departure and vessel data to the port authorities by mean of this devices. This database has been used by many authors to describe maritime transport trade networks for several different classes of vessel [START_REF] Kaluza | The complex network of global cargo ship movements[END_REF].

A sample of vessel paths was built with the following criteria: (a) not to consider containerships with less than 1000 TEUs to eliminate short range navigation activity noise; (b) consider vessels built before 2007, in order to obtain an equilibrated amount of AIS positions stored per ship; (c) eliminate anchorage, strait or canal positions; and (d) prioritize for the final sample vessels that perform inter-continental activity. This selection procedure guarantees, as a corollary, that at least the most important ports (AIS call -berthingpositions) will be taken into account.

The analysis was conducted by splitting each vessel class sample into two years: 2009 and 2010 AIS positions. So for each year, the sequence of vessel calls defines subsequently another sequence of port of departure-port of arrival pairs. Hence, it can be built, using a programming language with vector calculus features (postgreSQL), a structure of nodes and edges that will allow performing calculus of complex network parameters over this general cargo and containership AIS sets.

An additional layer of meaning was added to the entire set of worldwide call positions, in order to differentiate world trade areas. The division considered can be seen in figure 1, and is roughly based on the geographical regions considered by containerized shipping companies. The final sample composition and its main network features can be seen in Table 1.According to total world fleet supply estimated by UNCTAD [START_REF] Wilmsmeier | Liner shipping connectivity and port infrastructure as determinants of freight rates in the Caribbean[END_REF], database used covers approximately 80% of containership existing fleet. It can be seen a growth in vessels analyzed from 2009 to 2010, with the correspondent increases in total AIS positions.

[Please insert figure 1 and table 1 about here] A very important difference can be seen in the number of different ports considered for containerships. It decreases for containership sample (from 749 in 2009 to 527 in 2010). There are some quantitative approximations, made using complex networks measuring methodologies (Gonzalez-Laxe et al., 2012) explaining part of this behaviour as an outcome of the demand crisis happened in 2008, which caused a severe impact in main containerized lines, having effects in the mean connectivity of world gateways, and causing a conjunctural concentration during 2009-2010 of all the remaining active supply lines in less containerized terminals.

Data: NUTS-3 aggregation of maritime data

Starting from the 2010 version of NUTS3 available at Eurostat, a bijective identification between administrative coastal units and ports has been performed in order to proceed to the analysis: the maximum throughput of all the ports belonging to a NUTS3 unit, has been considered as a proxy of the throughput of the entire NUTS3 region (feasible given the statistical properties of the maximum estimator). Figure 2 is illustrative of how it was made the first step of this attempt to identify ports with those geographical units. Using GIS software it can be seen the superposition between ports and regions along the English Channel. For example in FR232 we can see port complex of Le Havre (633), Antifer (589) and Dieppe (5061). This fact suggest the following identification criteria: the port with maximum throughput in the considered period is the representative of its native NUTS 3, in case of NUTS 3, FR232 region, called Seine-Maritime, will be identified with all network parameters of Le Havre. The size of NUTS 3 appears to be adequate to perform the identification between hinterland parameters and port connectivity as it will be shown in this paper.

Thus, by this method, each NUTS 3 coastal region is associated with the structure of the foreland (network and performance parameters) of its most representative port, and in particular with a unique value of this port's throughput. In a second stage, by postgreSQL programming tasks, the total throughput for each geographical unit will be divided according to the share TEUs moved towards (or coming from) each world partition, taking this parameter as a proxy of the partitioned foreland. This last algorithm will allow obtaining an index of trade importance of each world region with each NUTS 3 unit. Tables 2 and3 present the data on the maritime services aggregated by their level of accessibility and their volume.

[Please insert figure 2 and tables 2 and 3 about here]

Data: road accessibility to population

When studying the links between maritime activity and accessibility to inland markets, the question of the delineation of the hinterlands of the ports is a difficult issue. Even when taking in account large spatial units (i.e. countries, Nuts-2 regions) some large seaports influence the size and shape of hinterlands. Reviewing the recent literature, [START_REF] Chapelon | L'accessibilité, marqueur des inégalités de rayonnement des villes portuaires en Europe[END_REF] propose a first measure of the economic potential of the port cities on the basis of the accessibility parameters, not considering the activity of the ports but just the hinterland influence. Later, [START_REF] Guerrero | Deep-sea hinterlands: Some empirical evidence of the spatial impact of containerization[END_REF] and [START_REF] Notteboom | Concentration and the formation of multi-port gateway regions in the European container port system: an update[END_REF] show that the size of hinterlands varies a lot from one port to another, particularly in relation to their volume, the nature of cargo handled, and the distance towards clients and competing ports. Unfortunately, empirical evidence on the actual hinterlands is only available through enquiries that do not exist on comprehensive, Europewide basis. For these reasons we have decided to use an indicator of accessibility to population, knowing that it is an imperfect proxy of the actual hinterlands.

Practically, we use a measure of accessibility implemented by S&W for the European Spatial Planning Observatory Network [START_REF] Spiekermann | Update of selected potential accessibility indicators[END_REF]Schurmann, 2007, Espon, 2009). This indicator is based on two elements: (1) population in NUTS 3 regions and (2) the effort in time to reach them by road, which is the largely dominant mode of pre and post maritime carriage. The accessibility model measures the minimum time between all NUTS 3 regions by road. The potential accessibility of a NUTS 3 region is calculated by summing up the population in all other European regions, weighted by the transport time to reach them. Compared to the mere consideration of the potential of the region where the port is located, this method allows to take in account the potential of every region, in particular those that are close to the port.

Results

Network vs hinterland differentiation

To evaluate the respective importance of the parameters of hinterland access and maritime connectivity, the variables road access and volume, which are highly correlated, have been converted by Principal Component Analysis into two uncorrelated variables (figures 4 and 5). The first component, associated with the volume and hinterland potential, accounts for 68.5% of the total variance, and has been considered as an indicator of centrality. The second component, explaining the rest of the variance (31.5%), is considered to be a proxy of the intermediacy of the regions within the maritime network. Using the coordinates of the two factors, ports have been aggregated in clusters with Agglomerative Hierarchical Clustering. Five categories of ports are distinguished on the basis of their centrality and intermediacy. "Pure" Mediterranean hubs such Algeciras, Gioia Tauro and Marsaxlokk, with large volumes and low or almost inexistent hinterland, are clustered in a same subgroup together with Piraeus and Limassol. Unsurprisingly, the largest European gateways such Rotterdam, Antwerp and Hamburg are characterized by high levels of centrality and intermediacy.

[Please insert figures 4 and 5 about here]

To provide a description of the foreland orientation of ports, a second Principal Component Analysis has been done on the table of percentages of ports with each of the 12 overseas regions, weighted by the volume (figures 6 and 7). The two main factors represent 51% of the foreland variability of ports. The first one, explaining 29% of the variations is strongly correlated to the shares of Asian and West African forelands which are generally opposed. The second factor, explaining 22% of the variability of foreland orientation of ports, is defined by the opposition between European and North African forelands against American ones. Ports have been aggregated in seven categories. This time, an unequal orientation to African an Asian forelands spreads them in three different categories.

[Please insert figures 6 and 7 about here]

Does inland accessibility provide a good estimation of port volume?

To explain the geography of European supply of container transport, we simply assessed the linear correlations between transport supply and road accessibility to population at the NUTS 3 level (table 4). The correlation is significant (R²=.33), which means that 33% of container supply differences between NUTS 3 regions are described by the road accessibility to population. This is partly due to the importance of the container supply of Northern Range ports that are close to the economic core of Europe, where most of population and wealth is concentrated. However, several other factors, like the strategies of shipping lines (hub & spokes networks) and the proximity of certain European regions to main container routes also explain this geography. In order to distinguish the inland and maritime dimensions, a Principal Component Analysis has been applied to both variables.

According to the model, inland accessibility thus explain to a large extent the spatial variation in European shipping services. This type of analysis naturally raises, however, the question of the deviations from the predictions The relationship is particularly strong with Asian forelands (Far East, South-East Asia) meaning that these regions are rather served by metropolitan ports located near large urban areas or heartland Europe. The relationship with West Africa is good as well, but in this case it is negatively correlated to accessibility, meaning that peripheral regions are more specialized than central ones. This is partly due to containerized cargo related to niche markets (i.e. counter-season fruits, timber, agricultural products) where peripheral ports far from the European core are also important. In the particular case of France, the strong ties of secondary ports with West Africa are partly inherited from the colonial period.

[Please insert table 4 about here]

Results of the OLS Regression

For each geographical aggregate, an approximation of the foreland dependence with respect to the NUTS3 road accessibility parameter (ROAD_ACC) and the NUTS3 hierarchy in terms of shared-with-foreland supply lines (LogVOL), is built, by using an OLS approximation.

In order to improve the accuracy of this approach, two kind of models are computed for each foreland aggregate: one just with the two dependent variables (simple model); and another one (extended model) trying to catch up the effects of the specific features that each European macro-region (Island, Northern Range, Mediterranean, British Islands, Baltic Sea areas and Atlantic Arc) is able to induce, by adding them as a dummy_variable additional dependent regressor.

The results are expressed in the tables 5 and 6, with which several important outcomes can be highlighted:

•

The 12 forelands are able to produce 10 meaningful relations, sometimes with the ROAD_ACC parameter acting as the main controller (case of West Africa and Oceania), in other cases with the LogVOL parameter as the key element to catch the meaning of the relationship analyzed (Caribbean, South America Pacific, Indian Ocean, South East Asia and Far East). In one case, for the simple model computed for Far East foreland, the two dependent variables ROAD_ACC and LogVOL do succeed in achieving joint significance (which should be the ideal model sought).

•

The relations in which ROAD_ACC is the significant regressor are elusive, but if appearing, they could allow a highly suggestive set of possible interpretations:

• For the influence of road access and volume of TEUs shared with West Africa, the extended model suggest that belonging to a peripheral EU region (coef=-0.001) improves the network influence with respect this foreland aggregate. Said in another words: for each additional unit of ROAD_ACC gained, 0.1% of influence units with respect West Africa foreland could be lost.

In this case, it must be noted the negative influence of the Atlantic Arc on the West Africa foreland (coef=-0.171), hence setting the European Mediterranean macroregion (West Med range) as the main service area for the containerized trade with West Africa, with important global hubs as Lagos (Nigeria), Abidjan (Iv. Coast), or Dakar (Senegal).

This coefficient also confirms that the remarkable box-transhipment activity of Sines (Portugal, Atlantic Arc) is still centered exclusively in the services to East Asia-Northern Range lines. o There's a slightly positive effect for the influence of Australasia foreland with respect being well located in terms of ROAD_ACC (coef=0.0002), which must be interpreted as a sign of the capacity for the best connected NUTS3 regions to establish containerized relations even with the farthest forelands.

•

The relations in which LogVOL is the significant regressor appear more frequently:

o The Caribbean foreland do prefer European small-sized containerized terminals to perform trade operations (coef=-0.054), i.e., each additional TEU moved by a NUTS3 region with some Caribbean node, yields a penalty of e1(-0.054)=-14.7% units of influence with the box trade on this area.

o The South America Pacific, Indian Ocean, South East Asia and Far East still prefer the Northern Range European hubs to perform their containerized trade operations, with different significant intensities (coefficients of 0.069, 0.042, 0.069, 0.025, respectively).

•

In the South America Atlantic model, there is an evidence of the high connectivity with respect to European Atlantic hubs that can be seen in the significant 0.118 coefficient.

•

The case of the simple model for the Far East positions, without including the modulation coming from European macro-regions dummy-variables, allows a richer interpretation than in the extended case (although less powerful in terms of ROAD_ACC influence): a joint positive effect both of road connectivity and throughput capacity of the NUTS3 region can be detected by the common positive influence of the two regressors (0,0003 for ROAD_ACC and 0,028 for throughput). This higher correlation would result from two dynamics. On one hand, shipping lines may give priority to the gateways with fast and easy access to European heartland, in order to partly offset the length of the maritime voyage. On the other hand, the increasing size of container vessels on Europe-Asia trade also emphasizes the need for concentrating the calls on a few large ports in order to achieve economies of scale. Although Mediterranean hubs are used for serving Sourthern Europe and Africa, Northern Range gateways (Rotterdam, Antwerp, Hamburg) -located at the vicinity of Europe's heartland-are extensively used in the the trade with East Asia.

[Please insert tables 5 and 6 about here] Figures 8 and9 present the residuals of the simple model for South East Asia. The main overestimations (negative residuals) can be founded mostly in the core European regions with high accessibility to markets but with a lower share of direct trade with South East-Asia, either because they are close powerful gateways (ex. Felixtowe in Southern England), or because their foreland mix is highly diversified. That is the case of the top-ranked Antwerp and Bremerhaven, where all forelands are well represented, particularly those of North America and Caribbean. The underestimations of the model (positive residuals) follow a more complex pattern, partly resulting from historical ties of ports resulting from colonial relationships of the countries (i.e. Southampton, Amsterdam) or from hubbing strategies of shipping companies (ie. CMA at Marsaxlokk and Evergreen at Taranto). We also see, in a lesser extent, excess supply in highly industrial peripheral regions such Bilbao and Gdansk.

[Please insert figures 6 and 7 about here]

Conclusions

This paper attempts to measure the linkage between maritime transport supply and inland accessibility in Europe, both for container and general cargo services. The results of this paper support the expectation that maritime transport supply is strongly dependent on the demographic size and economic potential of hinterlands. More specifically, the findings here suggest that inland accessibility to population explains at least the 33% of the geographic variations in the maritime transport supply for containers. Hence, it should be noted that the relationship between accessibility and maritime transport is strong, ensuring to the shippers a minimum amount of cargo, but it also varies considerably depending on the overseas market served.

The East and South-East Asia markets seem to be more linked to inland accessibility than the other forelands. This relation has been amplified along the last years with the increase in the commissioning of New-Panamax and Triple-E vessel classes, exclusively operating the Europe-Asia pendulum services, and marginalizing some secondary ports within these routes. It's commonly accepted that this increasing vessel size (and the derived new round-the-world services due to the Panama Canal widening) is going to change the hub-spoke relations currently established in the central/peripheral ports, and at this precise moment, European hubs like Le Havre or Algeciras are losing direct connections indeed.

In the American markets three different pattern emerges regarding the transatlantic trade: for the North Atlantic (NAA) foreland, the European Atlantic Arc façade (ATL) shows potential for taking additional advantages of an improved network of inland corridors connecting this peripheral area with the European Backbone; for the Caribbean hubs, the European subsidiary and small ports have the best opportunities to establish new trade links with some of the strong hubs located in this area (Kingston, Caucedo, Cartagena, Altamira, etc.); for the countries located in the South Atlantic (SAA) foreland, there are some evidence of some kind of penalty linked with traders who are native English speakers.

Regarding African forelands (NAF, WAF and IND), the difference between center and periphery is less clear, due to the specific nature of the trade (primary sector and raw materials), in which the European secondary ports play an important role. There are also evidences of a inertia in the colonial relations with certain countries like France or Portugal.

The work explains an accurate GIS methodology to put in relation port activity with hinterland flows, using a very simple indicator: the number of direct links with different overseas regions. But it opens a wide field of study which might be completed, in further research, adding on the foreland side, the port specialization and the specific network features; and on the hinterland side parameters such GDP, industrial indexes, etc… This work raises questions about the opportunities for peripheral regions having good connections with specific forelands if they can take advantage of their situation, for example by choosing suppliers in countries with low labor costs. Since many of these peripheral regions have large port capacities there is potential for the development of new traffic. However, this approach is not without risk, since sudden changes on the strategies of shipping companies may have repercussions on the entire production network, increasing the vulnerability of these regions to external shocks. Table 1 - 0.12 0.04 ISLAND-1 -0.12 -0.04 -1.00 NR-0 -0.67 -0.25 -0.28 0.28 NR-1 0.67 0.25 0.28 -0.28 -1.00 MED-0 0.40 -0.01 -0.08 0.08 -0.44 0.44 MED-1 -0.40 0.01 0.08 -0.08 0.44 -0.44 -1.00 BRI-0 -0.21 -0.02 0.70 -0.70 -0.22 0.22 -0.39 0.39 BRI-1 0.21 0.02 -0.70 0.70 0.22 -0.22 0.39 -0.39 -1.00 BALT-0 0.24 0.21 -0.10 0.10 -0.09 0.09 -0.16 0.16 -0.08 0.08 BALT-1 -0.24 -0.21 0.10 -0.10 0.09 -0.09 0.16 -0.16 0.08 -0.08 -1.00 ATL-0 0.19 0.26 -0.20 0.20 -0.18 0.18 -0.32 0.32 -0.16 0.16 -0.07 0.07 ATL-1 -0.19 -0.26 0.20 -0.20 0.18 -0.18 0.32 -0.32 0.16 -0.16 0.07 -0.07 -1.00 %EUR -0.22 -0.20 -0.08 0.08 0.22 -0.22 -0.30 0.30 0.10 -0.10 0.13 -0.13 -0.06 0.06 %NAF -0.13 -0.11 -0.12 0.12 0.13 -0.13 -0.40 0.40 0.13 -0.13 0.12 -0.12 0.17 -0.17 0.84 %WAF -0.33 -0.22 0.21 -0.21 0.21 -0.21 0.06 -0.06 0.16 -0.16 0.00 0.00 -0.59 0.59 0.16 -0.18 %NAA -0.17 0.00 -0.12 0.12 0.12 -0.12 -0.03 0.03 -0.07 0.07 -0.08 0.08 0.23 -0.23 -0.13 -0.21 -0.10 %SAA -0.07 -0.16 -0.22 0.22 0.08 -0.08 0.13 -0.13 -0.31 0.31 0.07 -0.07 -0.02 0.02 0.09 0.07 0.09 0.06 %CAR -0.04 -0.40 -0.03 0.03 0.04 -0.04 0.13 -0.13 -0.01 0.01 -0.22 0.22 -0.09 0.09 -0.32 -0.44 -0.02 0.37 -0.10 %OCE 0.19 -0.08 0.11 -0.11 -0.12 0.12 0.07 -0.07 0.09 -0.09 -0.14 0.14 -0.03 0.03 -0.17 -0.

Tables

FiguresFigure 1 -Figure 3 -Figure 5 -Figure 6 -Figure 7 -Figure 8 -

 135678 Figures

Sample composition Containerships (supply in TEUs)

		Time scope sample	2009	2010
	Number of vessels analyzed	2,032	2,144
	Number of AIS positions analyzed	126,920	145,736
		Maximum	15,550	15,550
	Vessel capacity	Minimum	450	1,057
		Average	4,533	4,730
	Total fleet supply present in sample	9,211,236	10,142,327
	Total world fleet supply estimated*	10,760,173 12,142,444
	Number of different ports of call (World sample) 749	527
	Number of different ports of call (Europe)	162	124
	Source: own calculations from AIS data from Lloyd's Registry Database (2010)

Table 2 -Breakdown of maritime connections, by location

 2

	South	North
	America

Table 4 -Correlations between the main variables

 4

	Variables	ROAD_	ACC	VOL(Log	)	ISLAND-	0	ISLAND-	1	NR-0	NR-1	MED-0	MED-1	BRI-0	BRI-1	BALT-0	BALT-1	ATL-0	ATL-1	%EUR	%NAF	%WAF	%NAA	%SAA	%CAR	%OCE	%NAP	%SAP	%IND	%SEA
	ROAD_ACC
	VOL(Log)	0.33
	ISLAND-0

Table 5 -Simple and extended model for foreland aggregates' influence (part 1)

 5

		%EUR		%NAF		%WAF		%NAA		%SAA		%CAR
		coef	p>|t|	coef	p>|t|	coef	p>|t|	coef	p>|t|	coef	p>|t|	coef	p>|t|
						EXTENDED MODEL
	Constant	0.4726	0.0071	0.3237	0.0035	0.3992	0.0047	-0.2048	0.2353	0.1265	0.0254	0.3282	0.0016
	ROAD ACC	0.0000		0.0005	0.2706	-0.0008	0.0158	-0.0002	0.3674	-0.0004	0.0918	0.0003	0.4027
	VOL(Log)	-0.0349	0.1855	-0.0323	0.2508	0.0000		0.0000		-0.0094	0.2696	-0.0539	0.0040
	ISLAND-0	-0.0618	0.3423	-0.1304	0.0812	0.0666	0.0575	0.0000		0.0179	0.4326	-0.0274	0.5651
	ISLAND-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	NR-0	0.0000		0.0000		-0.0686	0.1961	0.0690	0.1794	-0.0342	0.1631	0.0000
	NR-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	MED-0	-0.0892	0.0713	-0.1351	0.0070	-0.0414	0.2557	0.0725	0.0704	0.0000		0.0174	0.5914
	MED-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	BRI-0	0.0371	0.6530	0.1071	0.2346	-0.0993	0.1033	0.0532	0.2484	-0.0717	0.0158	0.0308	0.5917
	BRI-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	BALT-0	0.0815	0.4703	0.0000		0.0000		0.0557	0.3437	0.0375	0.3014	-0.0931	0.2419
	BALT-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	ATL-0	-0.0577	0.4084	0.0000		-0.1706	0.0001	0.1175	0.0103	0.0000		0.0000
	ATL-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	F P>F	1.8140 0.1140		3.1342 0.0148		7.0258 < 0.0001		1.6823 0.1435		1.8722 0.1029		2.2311 0.0542
	R2	0.1704		0.2249		0.4430		0.1600		0.1749		0.2016
	Adj-R2	0.0765		0.1532		0.3800		0.0649		0.0815		0.1113
	Model	0.2215		0.3771		0.1949		0.0409		0.0247		0.1319
		0.1704		0.2249		0.4430		0.1600		0.1749		0.2016
	Residual	1.0784		1.2995		0.2450		0.2145		0.1166		0.5224
		0.8296		0.7751		0.5570		0.8400		0.8251		0.7984
	rootMSE	0.1426		0.1551		0.0680		0.0636		0.0469		0.0993
						SIMPLE MODEL
	Constant	0.4526	< 0.0001	0.2621	0.0054	0.1589	0.0006	0.0781	0.0305	0.0608	0.0243	0.2713	< 0.0001
	ROAD ACC	-0.0005	0.2089	-0.0003	0.4447	-0.0005	0.0309	-0.0002	0.1840	0.0000	0.8547	0.0002	0.4307
	VOL(Log)	-0.0276	0.2896	-0.0165	0.5841	-0.0143	0.3284	0.0050	0.6686	-0.0093	0.2886	-0.0581	0.0014
	F	2.0498		0.6590		4.0983		0.9046		0.7356		5.6985
	P>F	0.1381		0.5213		0.0217		0.4104		0.4837		0.0055
	R2	0.0671		0.0226		0.1257		0.0308		0.0252		0.1666
	Adj-R2	0.0344		-0.0117		0.0950		-0.0032		-0.0090		0.1374
	Model	0.0872		0.0379		0.0553		0.0079		0.0036		0.1090
	Model (%)	0.0671		0.0226		0.1257		0.0308		0.0252		0.1666
	Residual	1.2126		1.6387		0.3846		0.2475		0.1378		0.5453
	Residual (%)	0.9329		0.9774		0.8743		0.9692		0.9748		0.8334
	rootMSE	0.1459		0.1696		0.0821		0.0659		0.0492		0.0978
		Source: Own calculations from AIS data from Lloyd's Registry (2010) and ESPON (2006)

Table 6 -Simple and extended model for foreland aggregates' influence (part 2)

 6

		%AUS		%NAP		%SAP		%IND		%SEA		%FAE
		coef	p>|t|	coef	p>|t|	coef	p>|t|	coef	p>|t|	coef	p>|t|	coef	p>|t|
						EXTENDED MODEL
	Constant	0.0153	0.6438	-0.0177	0.5630	-0.1874	0.0559	0.0529	0.5475	-0.1874	0.0559	-0.0552	0.4389
	ROAD ACC	0.0003	0.0434	0.0000		0.0002	0.4551	0.0000		0.0002	0.4551	0.0002	0.3860
	VOL(Log)	-0.0051	0.3124	-0.0026	0.6489	0.0695	< 0.0001	0.0417	< 0.0001	0.0695	< 0.0001	0.0254	0.0169
	ISLAND-0	-0.0073	0.5884	0.0236	0.0964	0.0096	0.7306	-0.0099	0.6280	0.0096	0.7306	0.0000
	ISLAND-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	NR-0	0.0126	0.3888	0.0000		0.0091	0.8110	-0.0245	0.3393	0.0091	0.8110	-0.0148	0.6053
	NR-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	MED-0	0.0000		0.0000		0.0000		-0.0149	0.4735	0.0000		0.0000
	MED-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	BRI-0	0.0214	0.2180	-0.0219	0.1645	0.0000		0.0000		0.0000		-0.0101	0.6662
	BRI-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	BALT-0	-0.0307	0.1591	0.0423	0.0815	0.0382	0.5533	-0.0502	0.2572	0.0382	0.5533	0.0354	0.4086
	BALT-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	ATL-0	0.0000		0.0218	0.1181	0.0575	0.1233	-0.0137	0.6432	0.0575	0.1233	0.0207	0.3963
	ATL-1	0.0000		0.0000		0.0000		0.0000		0.0000		0.0000
	F P>F	1.1991 0.3213		1.4760 0.2129				3.8569 0.0029		6.4132 < 0.0001		3.5620 0.0049
	R2	0.1195		0.1202				0.3039		0.4206		0.2874
	Adj-R2	0.0198		0.0388				0.2251		0.3550		0.2067
	Model	0.0057		0.0074				0.0646		0.2647		0.0664
		0.1195		0.1202				0.3039		0.4206		0.2874
	Residual	0.0417		0.0544				0.1480		0.3645		0.1646
		0.8805		0.8798				0.6961		0.5794		0.7126
	rootMSE	0.0280		0.0317				0.0528		0.0829		0.0557
						SIMPLE MODEL
	Constant	0.0210	0.1656	0.0240	0.0038	0.1246	0.0006	-0.0405	0.1437	-0.1074	0.0172	-0.0437	0.1396
	ROAD ACC	0.0001	0.0827	0.0001	0.1425	0.0002	0.2218	0.0000		0.0003	0.2503	0.0003	0.0272
	VOL(Log)	-0.0059	0.2396	0.0000		-0.0352	0.0029	0.0408	< 0.0001	0.0759	< 0.0001	0.0285	0.0046
	F	1.7661		2.2101		4.8688		22.6361		18.4101		10.2337
	P>F	0.1802		0.1425		0.0112		< 0.0001		< 0.0001		0.0002
	R2	0.0584		0.0367		0.1459		0.2807		0.3925		0.2642
	Adj-R2	0.0253		0.0201		0.1159		0.2683		0.3711		0.2384
	Model	0.0028		0.0023		0.0399		0.0597		0.2469		0.0610
	Model (%)	0.0584		0.0367		0.1459		0.2807		0.3925		0.2642
	Residual	0.0446		0.0596		0.2334		0.1529		0.3823		0.1699
	Residual (%)	0.9416		0.9633		0.8541		0.7193		0.6075		0.7358
	rootMSE	0.0280		0.0321		0.0640		0.0513		0.0819		0.0546

Corresponding author. E-mail: david.guerrero@ifsttar.fr

Source: Own calculations from AIS data from Lloyd's Registry (2010) andESPON (2006)

David Guerrero is a researcher on the freight transportation team (Ame-Splottmaritime transportation research, with relevant contributions to the analysis of a port's foreland and hinterland. Since 2010, she's

Figure 2 -NUTS-3 Regions and ports identification used in this study Source: Own calculations from AIS data from Lloyd's Registry (2010) and Espon (2006)