Gaël J Cherfallot
email: gael.cherfallot@ifpen.fr

Pierre E Levitz

Pauline Michel

Eric Kohler

Jacques Jestin

Loïc Barré
email: loic.barre@ifpen.fr

Probing Multiscale Structure of Mineral and Nanoporous Kerogen Phase in Organic-Rich Source Rocks : Quantitative comparison of Small-Angle X-ray and Neutron Scattering

 Classically, source rocks are described as a two-phase

define the pore space, including pore size distribution, pore volume fraction, pore connectivity and pore affinity for various fluids. The aim of this study is to achieve such relevant parameters using Xray and neutron scattering techniques complementarity. Rocks thin blades cut normal to bedding plane preserve sample integrity and allow their measurements on both techniques. 2D scattering patterns show anisotropy, due to preferential orientation of lamellar minerals, which allows us to assess an order parameter. This parameter is a valuable tool for mechanical and transport properties. A model based on a three-phase system (minerals, kerogen and pores) is developed through the study of scattering length density of each component within both radiations. The model allows us to fit both Xray and neutrons 1D data using the same model parameters. This later is then considered as selective.

It allows us to extract the kerogen mass density, the kerogen pore size distribution and its associated volume fraction, and the chemical nature of kerogen pore content. This methodology has been applied to a series of five source rocks of increasing maturities, from Barnett Shale Play and Montney-Doig formations. Mature samples show a kerogen density of ~1.6 g.cm -3 , a pore radius distribution centered on 0.5 -0.7 nm accounting for a pore volume fraction of ~ 0.01-0.04. These kerogen nanopores are filled by light condensed hydrocarbons. However, the overmature kerogen exhibit a mass density of 1.74 g.cm -3 , an additional pore radius distribution centered around 3.5 nm with a pore volume fraction of 0.002 and an empty pore space. All these parameters are in agreement with Rock-Eval pyrolysiss measurements and literature data on similar source rocks. These results pointed out that the threephase model associated with X-ray and neutron complementarity could be applied to in-situ studies.

INTRODUCTION

Source rocks formations are one of the most widespread reservoir on earth [START_REF] Kuuskraa | World Shale Gas and Shale Oil Resource Assessment[END_REF] and display a high potential of storage capacity. [START_REF] Godec | Potential Global Implications of Gas Production from Shales and Coal for Geological CO2 Storage[END_REF] Since recent years, gas and oil coming from organic-rich source rocks systems, also known as shale gas, present an increasing interest in North American and Asian system, depending on the matrix (i.e. mineral and organic matter) and the pore space. Then, scattering data are modeled by the polydisperse spherical pore (PDSP) model weighted by a term of contrast between the sample matrix and the pores space. [START_REF] Bahadur | Small-Angle and Ultrasmall-Angle Neutron Scattering (SANS/USANS) Study of New Albany Shale. A Treatise on Microporosity[END_REF][START_REF] Clarkson | Characterization of tight gas reservoir pore structure using USANS/SANS and gas adsorption analysis[END_REF][START_REF] Clarkson | Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion[END_REF][START_REF] Anovitz | Characterization and Analysis of Porosity and Pore Structures[END_REF][START_REF] Bahadur | Hierarchical Pore Morphology of Cretaceous Shale. A Small-Angle Neutron Scattering and Ultrasmall-Angle Neutron Scattering Study[END_REF] The model describes the scattering intensity I(Q) of diluted spherical pores of radius R (Equation 1) as a function of the volume fraction, 𝜙 = ∫ 𝑁(𝑅). 𝑉(𝑅)

𝑅𝑚𝑎𝑥 𝑅𝑚𝑖𝑛 𝑑(𝑅), of polydisperse spheres, the form factor P(Q,R) of spheres, and their volume, V(R). Such model depend on the squared Scattering Length Density (SLD) ρ difference of the considered phases, such as the matrix or the pore space, and can be expressed as follows:

𝑰(𝑸) = (𝝆 𝒎𝒂𝒕𝒓𝒊𝒙 -𝝆 𝒑𝒐𝒓𝒆𝒔 ) 𝟐 ∫ 𝑵(𝑹). 𝑽 𝟐 (𝑹). 𝑷(𝑸, 𝑹)

𝑹 𝒎𝒂𝒙 𝑹 𝒎𝒊𝒏 𝒅(𝑹) (1)
From these modeling a PSD is determined as well as the sample total porosity . Small-angle scattering is one of the rare technique which probe the total pore space. Both SAXS and SANS techniques, are based on the same principle, it is then possible in theory to obtain similar results [START_REF] Radlinski | The microstructure of rocks and small-angle and ultra-small-angle neutron scattering: the coming of age of a new technique[END_REF] .

However, small-angle X-ray scattering on source rocks is less investigated [START_REF] Fischer | Dehydration Effect on Pore Size, Porosity, and Fractal Parameters of Shale Rocks: USAXS Study[END_REF][START_REF] Leu | Multiscale Description of Shale Pore Systems by Scanning SAXS and WAXS Microscopy[END_REF] than SANS owing to the presence of pyrite, with a different SLD than other minerals, introducing a supplementary phase.

Beam types as neutron or X-ray have a different interaction through the material which can be exploited as a complementary. Indeed, the different X-ray and neutron contrast are expected to better define the chemical nature of fluids in pore space.

Herein, this work is focused on the neutron and X-ray scattering profiles similarities and complementarities. The aim is first to provide details on the minerals orientation, the kerogen mass density, pore size contained in the kerogen phase and their associated volume fraction, and then to assess the nature (gas or oil) of fluids in place. A multi-technical approach through the comparison of X-Ray diffraction, Rock-Eval pyrolysis, Headspace gas chromatography, Field-Emission Scanning Electron Microscopy and small-angle scattering techniques, is expected to bring rocks structural information. For that, five source rock samples are selected based on their petrological and geochemical properties to form a continuous sequence of organic matter maturity. Their X-ray and neutron scattering intensities are then compared in order to get new information on (i) minerals orientation relatively to the bedding plane, (ii) the maturity of kerogen, (iii) the pore size distribution and the occupancy of pores in respect to gas or hydrocarbon phase.

MATERIALS AND METHODS

Source rocks.

Source rocks chosen and used in this study were provided by IFPEN and were collected from two geological North-American Formations as part of research projects dedicated to unconventional oil during sediment accumulations in a foreland basin. It is a laminated coarse grained silicate-rich and organic-rich rocks. In the Table 1, general information about the sample geological formation and the depth at which they were collected, are listed.

Sample preparation.

For Rock-Eval pyrolysis and X-Ray Diffraction (XRD) measurements, samples were crushed into < 50 µm powders. HeadSpace Gas Chromatography (HS-GC) analysis was performed on rock sections cut parallel and also cut normal to bedding. These sections were shaped into parallelepiped subsample of about 1 x 2 x 0.2 cm. Field Emission Scanning Electron Microscopy (FESEM) observations and scattering measurements were made on rock thin blade sections cut normal to bedding. A schematic summary for sample preparation according to the technique used is illustrated Figure 1.

Source rocks are a heterogeneous systems where a representative volume is difficult to assess. In addition, the comparison between Small-Angle Neutron Scattering (SANS) and Small-Angle X-ray Scattering (SAXS) measurements requires to be performed on a similar probed volume as both techniques have different beam sizes, classically 0.5 x 0.5 mm for SAXS and 5 x 5 mm for SANS.

Sample thickness optimization is also important as optical path is related both to the sample transmission, different for each radiation, and to multi scattering issues. [START_REF] Eberle | Direct Measure of the Dense Methane Phase in Gas Shale Organic Porosity by Neutron Scattering[END_REF][START_REF] Melnichenko | Small-Angle Scattering from Confined and Interfacial Fluids[END_REF][START_REF] Bahadur | Hierarchical Pore Morphology of Cretaceous Shale. A Small-Angle Neutron Scattering and Ultrasmall-Angle Neutron Scattering Study[END_REF][START_REF] Liu | Investigation of accessible pore structure evolution under pressurization and adsorption for coal and shale using small-angle neutron scattering[END_REF][START_REF] Radlinski | Small Angle Neutron Scattering Signature of Oil Generation in Artificially and Naturally Matured Hydrocarbon Source Rocks[END_REF][START_REF] Hall | Small-angle scattering studies of the pore spaces of shaly rocks[END_REF] In the chosen conditions (see below), transmission is high for SANS about 90 %, and low for SAXS, around 10 %.

From these considerations and prior to this study, the sample thickness and the probed volume were decomposed as the sum of power law trends as A.Q -α . Then, the A or α parameters were used to define the variability of each parameter. The α parameter vary within 1% whereas the prefactor vary within less than five percent. The latter is thought to be correlated with concentration, size and contrast of various scatterers. We conclude from the low dispersion of A and  parameters that with this beam size, the sample phase distribution is almost constant. Moreover, the SAXS intensities measured on 9 or 5 random positions were averaged to get a more representative volume to be compared with neutron measurements.

As this study is partly focused on the analysis of source rock anisotropy, the samples were cut normal to bedding plane to maximize the occurrence of lamination, as shown in Figure 1. Rocks thin blade sections with a maximum thickness of 200 µm were prepared and stuck to pierced quartz blades with a pinhole of 5.5 mm diameter. This diameter allows to map and to average several SAXS measurements in order to probe about the same volume as SANS ; in this way, the comparison of Xray and neutron scattering intensities are meaningful. Concerning the homogeneous probed volume of samples used in this study, SAXS measurements were performed on five random location for each sample. Obtained scattering intensities were checked and compared to the mean intensity. It reveals no significant variation allowing us to consider that the probed volume display a constant phase distribution.

Figure 1. Schematic representation of sample preparation with in blue normal to bedding plane and

in red the bedding.

Rock-Eval ® 6 pyrolysis.

Geochemical data on organic matter were obtained by Rock-Eval pyrolysis according to the Shale Play method. [START_REF] Romero-Sarmiento | New Rock-Eval Method for Characterization of Unconventional Shale Resource Systems[END_REF][START_REF] Pillot | Method of Assessing at Least one Petroleum Characteristic of a Rock Sample[END_REF] This technique is used to define the TOC content, the organic matter type and the maturity through HI vs Tmax diagram, as shown in Table 1 and in Figure 2. [START_REF] Craddock | Chemical, Molecular, and Microstructural Evolution of Kerogen during Thermal Maturation: Case study from the Woodford Shale of Oklahoma[END_REF][START_REF] Sun | Pore characteristics of Longmaxi shale gas reservoir in the Northwest of Guizhou, China. Investigations using small-angle neutron scattering (SANS), helium pycnometry, and gas sorption isotherm[END_REF][START_REF] Yang | Applying SANS technique to characterize nano-scale pore structure of Longmaxi shale[END_REF][START_REF] Bodhisatwa | TOC calculation of organic matter rich sediments using Rock-Eval pyrolysis: Critical consideration and insights[END_REF][START_REF] Clarkson | Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion[END_REF][START_REF] Han | Influence of particle size on gas-adsorption experiments of shales. An example from a Longmaxi Shale sample from the Sichuan Basin, China[END_REF][START_REF] Li | Estimation of shale gas adsorption capacity of the Longmaxi Formation in the Upper Yangtze Platform, China[END_REF][START_REF] Romero-Sarmiento | New Rock-Eval Method for Characterization of Unconventional Shale Resource Systems[END_REF][START_REF] Anovitz | Characterization and Analysis of Porosity and Pore Structures[END_REF][START_REF] Bahadur | Hierarchical Pore Morphology of Cretaceous Shale. A Small-Angle Neutron Scattering and Ultrasmall-Angle Neutron Scattering Study[END_REF][START_REF] Han | Micro and nano-size pores of clay minerals in shale reservoirs. Implication for the accumulation of shale gas[END_REF][START_REF] Espitalié | La Pyrolyse Rock-Eval et ses Applications : Troisième Partie[END_REF][START_REF] Liao | Kinetic study of marine and lacustrine shale grains using Rock-Eval pyrolysis. Implications to hydrocarbon generation, retention and expulsion[END_REF] Analysis was performed on 60 mg of dry bulk-rock powder and standard deviation was assessed through the repeatability of five measurements of each sample.

Samples have a TOC content ranging from 4.5 %wt (BSP-2 and BSP-3) up to 9.0 %wt (BSP-4). The Figure 2 illustrates sample measurements, all of them are consistent with a kerogen of type II. [START_REF] Ghanizadeh | a A Comparison of Shale Permeability Coefficients Derived using Multiple Non-Steady-State Measurement Techniques: Examples frome the Devernay Formation[END_REF][START_REF] Ghanizadeh | b Petrophysical and Geomechanical Characteristics of Candaian Tight Oil and Liquid-Rich Gas Reservoirs: I. Pore Network and Permeability Characterization[END_REF] These samples follow an increasing depositional depth from BSP-2 (1126 m) to MT-1 (2561 m). BSP samples are mature, as HI range from 146 to 174 mg HC / g TOC and Tmax is close to 445°C. They are in the oil window and the MT-1 sample reach the dry gas window which means that it is overmature (HI = 17 mg HC / g TOC and Tmax = 598°C). As shown by Craddock and coworkers

HeadSpace Gas Chromatography.

To obtain detailed information on Sh0 peak and on the free hydrocarbon composition, samples are characterized by HS-GC. This thermodesorption method is based on a partial pressure equilibrium between the fluid in the source rocks and the vapor outside the rock generated at a given temperature.

For that purpose, this technique is only used as qualitative tool in this study on thin rock section samples whom preparations and representations are described in section 2.2. HS-GC measurements were performed on an Agilent 7890B-GC chromatograph equipped with a Headspace Sampler Agilent 7697A. Samples were put into a 15mL vial at 80°C between 5 minutes to 7 days. Then, a volume of 15 µL is taken from the vapor and injected into the chromatograph. Data on the composition between C 1 and C 11 were acquired using a chromatographic column consisting in a fused-silica capillary coated with Al 2 O 3 of about 30 meters with a flow rate of 1.6.10 -2 mL.s -1 , an input temperature of 160°C and output temperature of 210°C. Data were normalized to the sample weight and compared to a standard (Supelco © n°21823895) for the peak indexation.

The distribution of n-alkane obtained by HS-GC as a function of heating time and retention time is represented in Figure 3 for the BSP-4 sample cut normal to bedding plan. Based on this sample study, light compounds such as C 1 to C 8 are shown to be preserved during the sample preparation. Results from chromatographs reveal that, at t = 4 min to 10 min, the main contribution to hydrocarbon composition are ascribed to light compounds from C 1 to C 5 . Over several heating times, from 5 minutes to 7 days, the gas distribution remains unchanged with an increasing pressure. This reveals an uncompleted gas release as no partial pressure equilibrium between the vapor outside and the fluid in the rock is reached. One may explain it by the rock composition which contains silicates with Si-OH groups and also illite and feldspar with Al 2 O 3 groups which act as retention sites. Such functional groups are classically used in chromatographic fused-silica column as adsorption surfaces. Thus, a chromatographic effect can be observed in the rock as adsorption/desorption can occur on functional groups leading to an uncomplete desorption within the heating time used. Anyway, this suggests that the diffusion through the sample is low which is consistent with a low permeability as source rocks porous media display connected and disconnected pore spaces. 7,[START_REF] Clarkson | Characterization of tight gas reservoir pore structure using USANS/SANS and gas adsorption analysis[END_REF][START_REF] Anovitz | Characterization and Analysis of Porosity and Pore Structures[END_REF][START_REF] Liao | Kinetic study of marine and lacustrine shale grains using Rock-Eval pyrolysis. Implications to hydrocarbon generation, retention and expulsion[END_REF][START_REF] Bernard | Multi-Scale Detection of Organic and Inorganic Signatures Provides Insights into Gas Shale Properties and Evolution[END_REF][START_REF] Bernard | Formation of Nanoporous Pyrobitumen Residues During Maturation of the Barnett Shale (Fort Worth Basin)[END_REF][START_REF] Jayne | Geologic CO 2 Sequestration and Permeability Uncertainty in a Highly Heterogeneous Reservoir[END_REF][START_REF] Medina | Pore System Characterization of Cambrian-Ordovician Carbonates Using a New Mercury Porosimetry-Based Petrofacies Classification System: Application to Carbon Sequestration Reservoirs[END_REF] Measurements on parallel and normal cut to bedding plane were also performed, for heating times ranging from 5 to 480 minutes. Results, shown in supplementary information, reveal that desorption rate, at a given time, is always lower for parallel cuts to bedding plane than for normal ones.

Figure 3. Chromatographs of the BSP-4 sample, cut normal to bedding plan, over several heating

times, from 5 minutes to 7 days, in an oven at 80°C.

XRD Measurements.

The mineral composition was determined using a PANalytical X'pert Pro diffractometer using a detector X'celerator and equipped with a Copper X-ray tube (Cu-Kα = 1.5418 Å). Data were acquired on disoriented powder samples and according to the following analytical conditions: 45 kV, 40 mA, angular sector from 2 to 80 °2θ. Then, minerals quantification in weight percent, was achieved by Rietveld [START_REF] Rietveld | A Profile Refinement Method for Nuclear and Magnetic Structure[END_REF] analysis using the software X'pert High Score Plus.

The mineralogical composition of the five studied source rocks is given in Table 2. The mineral content in weight percent, is then converted in volume percent for the SLD calculation. The major mineral phase encountered in BSP and MT samples are silicates lato sensu with quartz as main mineral (> 30 vol %) followed by illite (4 to 20 vol %) and muscovite (15 to 28 vol%). The second contribution to mineral phase is carbonate minerals with 4 to 27 vol %. Then, pyrite content varies from almost 1 vol % to 2.5 vol %. This mineral composition agrees with other studies on the same geological formations. [START_REF] Ghanizadeh | a A Comparison of Shale Permeability Coefficients Derived using Multiple Non-Steady-State Measurement Techniques: Examples frome the Devernay Formation[END_REF][START_REF] Loucks | Mississippian Barnett Shale. Lithofacies and depositional setting of a deep-water shale-gas succession in the Fort Worth Basin, Texas[END_REF]

Field-Emission Scanning Electron Microscopy.

Visual information on phase distribution is required to determine the occurrence of scattering contrast. For this reason, FESEM was used in order to acquire images on rock structures and organomineral phases distribution at a large scale (from hundreds of microns to dozens of nanometers).

Observations on normal cut to bedding plane samples were made at 12 nm/pxl. Experiments were carried out on a FESEM Nova NanoSEM 450 on cryogenic argon ion polished sample. Images were acquired with a working distance ranging from 5.2 to 5.5 mm and a probe current of 2.5 KV.

The FESEM images of rock structures and phase distributions are shown in Figure 4. Four Fields of View (FOV), from 51 µm down to 2,5 µm, were observed to account for the orientation of micas and clay minerals, the pores in mineral matrix and the pore within the kerogen phase. Five types of structure are identified:

-Pyrite, crystallizing in a cubic system as framboidal and cubic shapes, have a high absorption coefficient leading to white objects on FESEM images, -Dark grey aggregates account for the organic matter as this material is composed of light elements with a low absorption coefficient, -Dark grey level is assigned to pores in both organic and inorganic phases, -Subangular minerals, with a light grey level between the organic matter and pyrite minerals, are attributed to quartz, -Feldspars, with the same grey level as quartz, exhibits an angular shape allowing their identifications, -Carbonaceous minerals, similar to feldspars in shape, have a higher density. These minerals have also an angular shape but some intra-granular pores can be encountered owing to liquid dissolution phenomenon which is used for the identification, -Macroscopic elongated minerals, larger than two microns, are micas, -Fine elongated minerals, lower than two microns, are consistent with clayey mineral such as illite. The anisotropic 2D scattering patterns suggest that in the system some scatterers are preferentially oriented along one direction. Thus, scattering patterns were also azimuthally averaged according to two distinct regions, as shown in Figure 7(b). The first one,

S 1 , is at low Q values, 5.10 -2 < Q < 0.2 Å -1 ,
and the second region, S 2 , is in high Q-region, 0.34 < Q < 0.5 Å -1 . From the 1D curve, illustrated in One popular way to fit anisotropic SAXS data is to use, for a small Q range, the Maier-Saupe function [START_REF] Maier | Theorie der Nematischen Kristallinflüssigen Phase. Teil I[END_REF][START_REF] Maier | Eine Einfache Molekular-Statistische Theorie der Nematischen Kristallinflüssigen Phase. Teil II[END_REF] defined as :

𝒇(𝝋) = 𝑨 + 𝑩. 𝒆𝒙𝒑 (𝒎. 𝒄𝒐𝒔 𝟐 ((𝝋 -𝝍) * ( 𝝅 𝟏𝟖𝟎 ))) (2)
(b) (d) (a) (c)
φ is the azimuthal angle and 𝜓 is the maximum of intensity. Then, the Maier-Saupe data are normalized to their area, to compare results obtained for each sample, according to :

𝑨 = ∫ 𝒇(𝜽). 𝒔𝒊𝒏(𝜽) 𝒅𝜽 𝝅 𝟎 (3)
and

𝒇(𝜽) 𝒏𝒐𝒓𝒎 = 𝒇(𝜽) 𝟐𝝅. 𝑨 (4)
With θ the normal to the angle between the particle and the laboratory frame z axis.

Afterward, the order parameter S is expressed as the mean of a second-order Legendre polynomial :

𝑺 = 〈 𝟑. 𝒄𝒐𝒔 𝟐 (𝜽) -𝟏 𝟐 〉 (5)
And integrated over the whole solid angle sin(𝜃) . 𝑑𝜃. 𝑑𝜑 :

𝑺 = ∫ 𝒅𝝋 𝟐𝝅 𝟎 ∫ 𝒇(𝜽) 𝒏𝒐𝒓𝒎 . 𝟑. 𝒄𝒐𝒔 𝟐 (𝜽) -𝟏 𝟐 . 𝐬𝐢𝐧(𝜽) 𝒅𝜽 𝝅 𝟎 (6)
The order parameter values range from 0, isotropic media, to 1, perfectly oriented particles as columnar or smectitic crystal-liquid phases. [START_REF] Paineau | A Liquid-Crystallin Hexagonal Columnar Phase in Highly-Dilute Suspensions of Imogolite Nanotubes[END_REF] 3. RESULTS

Frame of Scattering modeling

Scattering intensities being related to the so called Scattering Length Densities (SLD) fluctuations,

we first examined what are SLD in source rocks for both neutron and X-ray and secondly how SLD may be taken into account in intensities modeling.

Scattering Length Densities

The SLD of a component or a phase is related to its elemental composition and to the type of radiation used. For each component, SLD is calculated according to the formula: 20,21,27,28,70

𝝆 = 𝟏 𝑽 ∑ 𝒏 𝒊 𝒃 𝒊 𝒊 (7)
Where V is a volume representative of the component, 𝑛 𝑖 the number of atoms of type i contained in the volume V and 𝑏 𝑖 the atomic scattering length. The latter are tabulated for neutrons in the NIST Database (https://www.ncnr.nist.gov/resources/n-lengths/), whereas they are estimated for X-ray according to 𝑏 𝑖 = 0.282.10 -12 Z i (cm) where Z i is the atomic number of atoms of type i. For a mixture of components, the mean SLD, 〈𝜌〉, for both radiation beam is established according to:

〈𝝆〉 = ∑ 𝝓 𝒋 𝝆 𝒋 𝒋 (8)
With ∑ 𝜙 𝑗 = 1 𝑗 , 𝜙 𝑗 the volume fraction of the component j and 𝜌 𝑗 the SLD of the component j.

From FESEM observations, three different phases are observed : mineral, kerogen and pores.

Minerals :

The SLD of the main minerals in our samples are reported on Table 3. For neutrons, minerals SLD are close to each other (~ 4.10 10 cm -2 ) which allows to consider minerals as a homogeneous phase. The corresponding mean value is easily assessed using Equation 8with volume fraction of each mineral determined by XRD. For X-rays, most of the minerals have a SLD value close to 24.10 10 cm -2 , except pyrite. Thus, X-ray perceives the minerals as two distinct phases since differences in SLD give rise to a contrast.

Kerogen:

Kerogen in analogous materials such as coal, 7 is described as a homogeneous phase where its SLD is similar whatever the macerals type.

Since our sample selection was designed to obtain a continuous sequence of increasing maturity, it is mandatory to consider the effect of maturity on kerogen SLD. A recent study on kerogen in source rocks, [START_REF] Thomas | The neutron scattering length density of Kerogen and coal as determined by CH3OH/CD3OH exchange[END_REF] show that neutron kerogen SLD vary from 1.10 10 cm -2 for immature kerogen up to 4.10 10 cm -2

for the overmature one. Elemental compositions and densities of gas shale from various maturities and after acid attack, given by Thomas and coworkers (2014), [START_REF] Thomas | The neutron scattering length density of Kerogen and coal as determined by CH3OH/CD3OH exchange[END_REF] were used here to assess neutron and Xray SLD as well as mass densities of kerogens. Thus, we assumed that all the Fe content in attack acid residues is only due to pyrite FeS 2 . The pyrite contribution, including the sulfur one, has been subtracted to obtain elemental composition and densities of model kerogens containing C, H, O and N atoms. X-ray and neutron SLD were assessed using Equation 7. Results are plotted on Figure 8 as a function of kerogen densities. Indeed, kerogen density vary in the same way as vitrinite reflectance and could be used as a maturity index. with  in cm -2 and d in g/cm 3 .

(10)

Pore space :

For this study, four model fluids are considered : air, methane in gaseous form, toluene and pentane. Pores can be fulfilled by gaseous species and/or by condensed hydrocarbons. If the pore space is fulfilled by a gas, its SLD for both X-ray and neutron is close to 0. If condensed fluids are in the pore space, it is then assumed that neutron SLD is almost null as condensed fluids have a SLD value ranging from 1.10 10 cm -2 , for aromatic fluids, to -0.5 10 10 cm -2 for aliphatic fluids. For X-ray, pore space SLD will be close to 8.10 10 cm -2 for aromatics fluids and around 6.10 10 cm -2 for aliphatic fluids.

SLD values are listed in

From these different SLD values, it appears that since neutron overmature kerogen and minerals SLD values are close, neutron scattering acquired on overmature gas shales could be interpreted in the frame of a two-phases system. As shown in Figure 8, for immature and mature kerogen, SLD values are much lower than the SLD of the mineral phase. Consequently, the two-phase system, which is classically used to described source rock scattering data, is less relevant than a threephases one. Concerning the nature of pore content, it is clear that neutron cannot distinguish gas from hydrocarbons whereas X-ray can. For X-ray SLD values, four phases have different SLD : pyrite, others minerals, kerogen and pore space. From XRD measurements, pyrite content is low, less than 2.5 vol %, in the studied source rocks. Moreover, FESEM observations reveals that a large part of pyrite is present as grains with sizes higher than 1 µm. These grains will contribute to X-ray scattering in a Q range that is not probed by our instrument. Firstly, pyrite is therefore neglected and its contribution will be discussed after data modeling. Hence, for both types of radiation, at least three SLD values has to be considered rather than a two-phase approximation.

Scattering intensity.

As shown in FESEM observations, samples are described as a four phases system : pyrite, other minerals, kerogen and pores. Even if pyrite is discarded, we will distinguish for scattering four phases, namely minerals, kerogen, pores included in kerogen and pores in minerals. For that purpose, source rocks system can be defined as follows:

∑ 𝑯 𝒊 (𝒓 ⃗ ) = 𝑯 𝑴 (𝒓 ⃗ ) + 𝑯 𝑲 (𝒓 ⃗ ) + 𝑯 𝑷 (𝒓 ⃗ ) + 𝑯 𝑷 ′ (𝒓 ⃗ ) = 𝟏 𝟒 𝒊=𝟏 (11)
Where 𝐻 𝑀 (𝑟 ), 𝐻 𝐾 (𝑟 ), 𝐻 𝑃 (𝑟 ) and 𝐻 𝑃′ (𝑟 ) are respectively, the characteristic functions of the minerals, the kerogen, the pores contained in the kerogen and the pores in minerals. From previous equation, the amplitude 𝐴(𝑄) of neutrons or X-ray can be written as :

𝑨(𝑸) = ∫ [∑ 𝝆 𝒊 𝑯 𝒊 (𝒓 ⃗ ) 𝟒 𝒊=𝟏 ] 𝒆 -𝒊𝒒𝒓 𝑽 ( 12
)
Since ∑ 𝐻 𝑖 (𝑟 ) = 1

𝐴(𝑄) can be rewritten according to the phase of interest through the Fourier transform. We note that the Fourier transform of 𝜌 𝐾 is a dirac centered at Q = 0 and do not appear in the amplitude expression:

𝑨(𝑸) = (𝝆 𝑴 -𝝆 𝑲 )𝑯 𝑴 ̃(𝑹) + (𝝆 𝑷 -𝝆 𝑲 )𝑯 𝑷 ̃(𝑹) + (𝝆 𝑷′ -𝝆 𝑲 )𝑯 𝑷′ ̃(𝑹) (14)
From 𝐴(𝑄), the scattering intensity is expressed according to 𝐼(𝑄) = 𝐴(𝑄)𝐴(𝑄) * . [START_REF] Bazilevskaya | How Oxidation and Dissolution in Diabase and Granite Control Porosity during Weathering[END_REF] The crossed terms are considered negligible owing to FESEM observations revealing no correlation between the kerogen and the pores contained in the mineral matrix. Arthur and Cole (2014) have shown by a FESEM/FIBSEM dual beam analysis that the mesopores are mainly contained in the organic matter. In addition, Bazilevskaya and coworkers (2015) demonstrated that about 50% of the porosity cannot be observed by direct space analysis and may be contained in the organic matter or the interlayer of clayey minerals. Thus, the scattering intensity is expressed as :

𝑰(𝑸) = (
At this point, the scattering intensity as illustrated in Figure 6 can be described as the sum of three contributions depending on a four phase system which are defined using three terms of contrast.

The first contribution is related to the contrast between mineral and kerogen phases. Based on FESEM observations, kerogen is in the form of micrometric to nanometric domains and its volume fraction, related to the TOC content, is few percent. A strong scattering intensity at small Q values is then expected for this contribution. Indeed, at low Q values, the curve trend appears to be a power law which can be expressed as A.Q -α , with  close to 3, A being a prefactor explicited later. In source and sedimentary rocks studies, the α exponent is sometimes related to a surface fractal dimension Ds by 𝛼 = 6 -𝐷𝑠 where Ds is restricted to 2 < Ds ≤ 3. 75-77 Schmidt (1982), [START_REF] Schmidt | Interpretation of Small-Angle Scattering Curves Proportional to a Negative Power of the Scattering Vector[END_REF] shows that the  exponent could be also related to power law size distribution f(R) ~ R - . Whatever the physical meaning of power law intensity dependence, we will consider  as a fitting parameter and concentrate on the prefactor A that could be expressed as the product of squared contrast factor (𝜌 𝑀 -𝜌 𝐾 ) 2 by a factor a related to the structural arrangement of kerogen in the mineral matrix. Hence, the first term of Equation 15 would be a(𝜌 𝑀 -𝜌 𝐾 ) 2 Q -

The second contribution, as highlighted by the FESEM characterizations, is related to pores in mineral phases, which are mainly macropores diluted within the mineral matrix. The mineral/pores interface seems to be smooth and their sizes vary from macrofractures to macropores. Consequently, their contribution likely follows a Porod behavior (I(Q) ~ Q -4 ) which starts at lower Q values and strongly decreases toward higher Q values. At least, this means that this contribution to 𝐼(𝑄) is negligible in the high Q domain probed.

The last contribution is related to the distribution of micropores in the kerogen matrix. As pores shape and size couldn't be well defined, owing to limitations (resolution and/or statistical representativeness), by direct space analysis such as FESEM or transmission electron microscopy, it is assumed that pores have a variety of shape and size as source rocks are natural materials. Both assumptions lead to a smoothing of the scattering curve compared to unique size and shape pores and make difficult to deconvolute both effects. In this study, we fixed the shape of the considered objects as spherical for sake of simplicity and assumed that size are distributed. This assumption preserve the physical meaning of the average size of the pores and it associated volume fraction. In source rocks the pore size distribution is often considered as peaked like in gas adsorption/desorption [START_REF] Chalmers | Characterization of gas shale pore systems by porosimetry, pycnometry, surface area, and field emission scanning electron microscopy/transmission electron microscopy image analyses. Examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig units[END_REF][START_REF] Clarkson | Characterization of tight gas reservoir pore structure using USANS/SANS and gas adsorption analysis[END_REF][START_REF] Clarkson | Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion[END_REF][START_REF] Bodhisatwa | Pore Characteristics of Distinct Thermally Mature Shales : Influence of Particle Size on Low-Pressure CO 2 and N 2 Adsorption[END_REF] or NMR [START_REF] Anovitz | Characterization and Analysis of Porosity and Pore Structures[END_REF][START_REF] Fleury | Comparison of Pore Size Distribution by NMR Relaxation and Nmr Cryoporometry in Shales[END_REF] -a diluted dispersion of pores -where n is the number density of pores, V p (R) stand for the volume of pore of size R, P(Q,R) is the form factor of the pores (P(0,R) = 1) chosen here as spherical, and f P (R) the normalized number size distribution function chosen here for convenience as log normal :

𝒇 𝑷 (𝑹) = 𝟏 𝝈√𝟐𝝅 𝐞𝐱𝐩 (- 𝒍𝒏 (𝑹 𝝁) 𝟐 ⁄ 𝟐𝝈 𝟐 ) (16)
Where μ the mean value of sphere radius and σ the size polydispersity.

Accordingly, for the scattering vector range measured in this study, a three-phase system with two main contributions, is defined and expressed, for X-rays (X) and neutrons (N) as :

In this equation, parameters giving a direct influence on the intensity Q dependence, namely ,  and µ, should be retrieved separately by fitting procedures. They provides details on each contribution prevailing in different Q domains. By contrast, only global prefactors A = a(𝜌 𝑀 -𝜌 𝐾 )² and N = n(𝜌 𝑃 -𝜌 𝐾 )² that adjust the amplitude of each Q dependence, will be extracted from the modeling.

Anisotropy

First, we consider the I(Q) behavior for the two azimuthal sectors φ 1 and φ 2 according to Figure 7(a). Both scattering techniques results are illustrated in Figure 9 for SANS and in Figure 10 for SAXS/WAXS. It is noted that the MT-1 sample gives isotropic 2D pattern. As detailed in the literature, scattering data on source rocks follow at small Q values an algebraic trend assimilated to [START_REF] Gu | Pores in Marcellus Shale: A Neutron Scattering and FIB-SEM study[END_REF][START_REF] Bahadur | Small-Angle and Ultrasmall-Angle Neutron Scattering (SANS/USANS) Study of New Albany Shale. A Treatise on Microporosity[END_REF][START_REF] King | Pore Architecture and Connectivity in Gas Shale[END_REF][START_REF] Eberle | Direct Measure of the Dense Methane Phase in Gas Shale Organic Porosity by Neutron Scattering[END_REF][START_REF] Sun | Pore characteristics of Longmaxi shale gas reservoir in the Northwest of Guizhou, China. Investigations using small-angle neutron scattering (SANS), helium pycnometry, and gas sorption isotherm[END_REF][START_REF] Clarkson | Characterization of tight gas reservoir pore structure using USANS/SANS and gas adsorption analysis[END_REF][START_REF] Bahadur | Hierarchical Pore Morphology of Cretaceous Shale. A Small-Angle Neutron Scattering and Ultrasmall-Angle Neutron Scattering Study[END_REF][START_REF] Thomas | The neutron scattering length density of Kerogen and coal as determined by CH3OH/CD3OH exchange[END_REF][START_REF] Bahadur | Porosity of the Marcellus Shale. A contrast matching small-angle neutron scattering study[END_REF][START_REF] Blach | Fingerprint of hydrocarbon generation in the southern Georgina Basin, Australia, revealed by small angle neutron scattering[END_REF] In both techniques, the α parameter, reported in Table 6, have similar values close to 3 and the intensity ratio between φ 1 and φ 2 remains constant until a breakdown around 0.03 Å - whatever the azimuthal sector. This behavior is ascribed to :

A.Q -α .
anisotropic scattering at small Q values likely due to preferential orientation of low dimensionality particles such as clays and micas.

isotropic scattering at large Q values reminiscent of spherical nanopores located in the kerogen A further confirmation of this attribution is shown in supplementary information where the high Q intensity signal is ranked as the one of TOC content. As shown in Table 5, it is possible from these data, to apply the Maier-Saupe fitting function to extract A, B, m and 𝜓 parameters and then to calculate the order parameter S. Values of 𝜓 are close to 90° suggesting that anisotropic particles align preferentially with their long axis parallel to the bedding plane. Order parameters for BSP samples at low Q values are ranking from 0.13 and 0.14, for BSP-3 and BSP-2, up to 0.21 and 0.26, for BSP-5 and BSP-4. Whereas, in the high Q-region, this parameter is quite low, barely reaching 0.09 at its maximum for BSP-4. BSP-2 and BSP-3 exhibit the lowest values with S = 0.06. Then, BSP-5 have an order parameter of 0.08. This seems to indicate that this part of the signal is less anisotropic and is dominated by an isotropic pattern. For MT-1, as its 2D scattering pattern is isotropic, S parameters for both Q regions is equal to 0.

(a) (b)

Table 5. Maier-Saupe function parameters determined on SAXS profiles and their calculated S

parameter for low Q-region (Q = 5.10 -2 to 0.2 Å -1 ) and high Q-region (Q = 0.34 to 0.5 Å -1 ).

Reference

Low Q region : 5.10 -2 to 0.2 Å -1 High Q region : 0.34 to 0.

where the prefactor a has been substituted by a().

Multiscale structure.

We took advantage of anisotropic scattering to consider, in the fitting procedure based on equation 19, the data acquired in azimuthal sector φ 2 . Indeed, for this sector, the scattering intensity from the first term of equation 19 is minimized and allows to better evaluate the second term contribution that remain moderate. This strategy could be optimized by considering a much smaller angular sector φ 2 but it would require much larger acquisition time. Hence, SANS and SAXS/WAXS "φ 2 " data related to the five source rocks were fitted to equation 19 by using SASFit software. [START_REF] Bressler | SASfit: a Tool for Small-Angle Scattering Data Analysis using a Library of Analytical Expressions[END_REF] Results represented in The equation 20b, together with the equations 9 and 10 relating the neutron and X-ray kerogen SLD to the kerogen density d, form a system of three equations with three unknown (𝜌 𝐾𝑁 , 𝜌 𝐾𝑋 and d) that could be easily solved. The extracted parameters are reported on Table 7 for samples of various maturity. It appears that the extracted densities are quite similar -about 1.65 g/cm [START_REF]World Energy Outlook 2007: China and India Insights[END_REF] -for the BSP samples and markedly different -1.74 g/cm [START_REF]World Energy Outlook 2007: China and India Insights[END_REF] -for the MT1. It points out that BSP samples are mature and MT1 overmature source rock as expected from Rock-Eval pyrolysis measurements (section 2.3.).

Regarding the neutron SLD, the one of overmature source rock -3.7.10 10 cm -2 -is quite similar to the one of mineral, suggesting that the scattering data could have been interpreted in the frame of a twophase system. Conversely, the neutron SLD differences between minerals and kerogen for the mature source rocks are noticeable (0.5 -0.7.10 10 cm -2 ), justifying the three phases approximation developed here. Regarding X-ray, the large differences between minerals and kerogen SLD show clearly that the three-phase approximation is mandatory to interpret properly SAXS measurements.

Calculated 𝜌 𝑃𝑋 values are listed in Table 7 and displayed two different values. For BSP samples, a 𝜌 𝑃𝑋 values ranging from 4.3.10 10 cm -2 up to 5.10 10 cm -2 are estimated. This value can be attributed to either light condensed hydrocarbons with SLD values smaller than pentane SLD (6.2.10 10 cm -2 ), or to a mixture of pores fulfilled by a fluid and empty pores. For the overmature MT1 sample, a value of 0 is found for the nanopores (0.5 nm) population and a value slightly negative for the mesopore (3.5 nm) population. The agreement with both a meaningful (positive) 𝜌 𝑃𝑋 value and the best fit intensities gives a null value for mesopores SLD. Hence, for the overmature sample, nano-and meso-pores in kerogen are considered as empty in full agreement with Sh0 and Sh1 values found with Rock-Eval pyrolysis measurements.

From the prefactors 𝑛(𝜌 𝑃 -𝜌 𝐾 ) 𝑋,𝑁 2 and the SLD values, the number density of pores n were easily assessed and their values are reported in Table 7. The nanopores volume fraction  can be inferred from their number density n and their size distribution using = n 4/3  <R 3 > , where <R 3 > is the third moment of the size distribution that can be calculated analytically for the lognormal distribution.

Numerical values are reported in Table 7. They are in the range 1-4% and rank roughly like the TOC content.

Concerning the pyrite influence on SAXS data, calculated intensities for BSP-4 and MT-1 samples, which exhibit the highest pyrite content (2.3 and 2.5 %vol), display the higher discrepancy with measured intensities in the Q range around 0.1 Å -1 . This discrepancy is clearly ascribed to pyrite content that gives an additional intensity contribution. If intensity modeling is still acceptable for these samples, it is clear that for samples containing higher pyrite contents, the fitting procedure will give meaningless parameters, especially for the mesopores SLD. Hopefully, the other estimated parameters would stay unaffected by pyrite.

DISCUSSION

Source rocks is one of the most difficult material to characterize. Indeed, they are multiphase systems (minerals, solid organic matter and pore space filled by various liquid or gaseous hydrocarbons) and the relevant length scales extend from sub-nanometer for nanopores included in kerogen up to few microns for minerals or kerogen domains. Moreover, they are natural materials with inherent composition variability and laminated rocks where bedding could induce a structural orientation leading to anisotropy of properties. Based on these considerations, sample preparation is one of the major concern when studying such materials. Complementary scattering techniques are chosen here for their ability to probe the desired length scales. Herein, an innovative methodology is proposed to overcome (i) composition variability, and (ii) loose of sample integrity and orientation upon grinding. Thin blade samples allows to average several random X-ray scattering measurements in a surface comparable to the section the neutron beam (a 5 mm diameter circular diaphragm). A sample thickness of ~ 200 µm, allow to get usable transmission for both radiation while avoiding multiple scattering. Contrary to scattering measurements on powdered sample [START_REF] Mastalerz | Porosity of Coal and Shale[END_REF][START_REF] Bahadur | Small-Angle and Ultrasmall-Angle Neutron Scattering (SANS/USANS) Study of New Albany Shale. A Treatise on Microporosity[END_REF][START_REF] Bahadur | Hierarchical Pore Morphology of Cretaceous Shale. A Small-Angle Neutron Scattering and Ultrasmall-Angle Neutron Scattering Study[END_REF][START_REF] Radlinski | Small-Angle Neutron Scattering and the Microstructure of Rocks[END_REF] or on thin blade section cut parallel to bedding [START_REF] Sun | Pore structure characterization of organic-rich Niutitang shale from China. Small angle neutron scattering (SANS) study[END_REF][START_REF] Sun | Pore characteristics of Longmaxi shale gas reservoir in the Northwest of Guizhou, China. Investigations using small-angle neutron scattering (SANS), helium pycnometry, and gas sorption isotherm[END_REF][START_REF] Clarkson | Characterization of tight gas reservoir pore structure using USANS/SANS and gas adsorption analysis[END_REF][START_REF] Clarkson | Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion[END_REF] that gives isotropic signal, the thin blades considered here are cut normal to the bedding plane in order to get information on possible structural orientation. [START_REF] Gu | Pores in Marcellus Shale: A Neutron Scattering and FIB-SEM study[END_REF][START_REF] Liu | Anisotropic Pore Structure of Shale and Gas Injection-Induced Nanopore Alteration : A Small-Angle Neutron Scattering Study[END_REF] Finally, this sample preparation allow to compare X-ray and neutron scattering intensities obtained on the same volume and in the same orientation.

Quantifying this orientation has to be taken into account when considering fluid flow properties for transport issues or mechanical properties. Indeed, it is well known that bedding structures modify the rock permeability to fluids according to the considered orientation, [START_REF] Gu | Pores in Marcellus Shale: A Neutron Scattering and FIB-SEM study[END_REF][START_REF] Backeberg | Quantifying the Anisotropy and Tortuosity of Permeable Pathways in Clay-Rich Mudstones using Models based on X-ray Tomography[END_REF][START_REF] Chalmers | Characterization of gas shale pore systems by porosimetry, pycnometry, surface area, and field emission scanning electron microscopy/transmission electron microscopy image analyses. Examples from the Barnett, Woodford, Haynesville, Marcellus, and Doig units[END_REF][START_REF] Kwon | Permeability of Illite-Bearing shale : 1. Anisotropy and Effects of Clay Content and Loading[END_REF] with values ranging from 1.10 -19 m² to 1.10 -21 m², for normal to bedding cut, and 1.10 -21 m² to 1.10 -22 m², for parallel to bedding cut. In soil science, recent studies evidenced the importance of preferred clay orientation on the diffusional properties of water. [START_REF] Dabat | Influence of Preferred Orientation of Clay Particles on the Diffusion of Water in Kaolinite Porous Media at Constant Porosity[END_REF] Here, order parameter vary from 0 (random orientation) up to ~ 0.3.

The random orientation is associated to the coarse grained texture of Montney sample whereas significant values of order parameters are found for fine grained Barnett shales. This striking difference could be the result of various size ratio between low dimensionality particles such as clays or micas and other minerals. Indeed, it has been shown, on model systems of particles mixture (platelets and spheres), that orientation upon sedimentation depend on the diameter ratio. [START_REF] Sui | Stratification in the Dynamics of Sedimenting Colloidal Platelet-Sphere Mixture[END_REF] Anisotropic properties are also illustrated by the HS-GC experiment conducted on thin blade sections where the concentration of thermodesorbed species in the vapor is much larger for normal cut than for parallel cut to the bedding (Supplementary Data).

The quantitative comparisons of X-ray and neutron scattering intensities are based on contrast factor specific to each radiation. The detailed examination of scattering length densities evidence that source rocks could be described for both radiation with three distinct contributions : minerals, kerogen and pores. For overmature kerogens, the neutron scattering could be reduced to the frequently used two phase system approximation, matrix and pores. [START_REF] Gu | Pores in Marcellus Shale: A Neutron Scattering and FIB-SEM study[END_REF][START_REF] Sun | Pore structure characterization of organic-rich Niutitang shale from China. Small angle neutron scattering (SANS) study[END_REF][START_REF] Mastalerz | Porosity of Coal and Shale[END_REF][START_REF] Bahadur | Small-Angle and Ultrasmall-Angle Neutron Scattering (SANS/USANS) Study of New Albany Shale. A Treatise on Microporosity[END_REF][START_REF] Sun | Pore characteristics of Longmaxi shale gas reservoir in the Northwest of Guizhou, China. Investigations using small-angle neutron scattering (SANS), helium pycnometry, and gas sorption isotherm[END_REF][START_REF] Clarkson | Characterization of tight gas reservoir pore structure using USANS/SANS and gas adsorption analysis[END_REF][START_REF] Clarkson | Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion[END_REF][START_REF] Bahadur | Hierarchical Pore Morphology of Cretaceous Shale. A Small-Angle Neutron Scattering and Ultrasmall-Angle Neutron Scattering Study[END_REF][START_REF] Radlinski | Small Angle Neutron Scattering Signature of Oil Generation in Artificially and Naturally Matured Hydrocarbon Source Rocks[END_REF][START_REF] Bahadur | Porosity of the Marcellus Shale. A contrast matching small-angle neutron scattering study[END_REF] This two phases model, based on diluted polydispersed pores, is usually applied to retrieve the pore size distribution and the total porosity. Here, considering three phases allow to broaden scattering techniques to low mature kerogens and to X-ray measurements. A corresponding expression of scattering intensities based on two main contributions is developed. The first one is related to the dispersion of kerogen domains in the mineral matrix, which prevails at low Q values, and turns out to be anisotropic. The second one describes a diluted dispersion of nanopores in the kerogen, giving a dominant isotropic signal at large Q values that remains moderate. We took advantage of anisotropy to consider the azimuthal direction

where the scattering at low Q is reduced in order to better appreciate the contribution, at large Q values, of kerogen nanoporosity. The three phases model allows to fit both X-ray and neutron data with the same geometric parameters which prove the selectivity of the model. Moreover, the intensity ratio between X-ray and neutron prefactors for each contribution allow to retrieve valuable parameters such as (i) the X-ray and neutron kerogen SLD as well as its mass density, both of them being considered as a maturity index, (ii) the nanopore size distribution, the number density of nanopores and their associated volume fraction, and (iii) the X-ray SLD of nanopores that gives a first approximation on the nature of filling fluids. All these parameters are reachable thanks to quantitative comparison of SANS and SAXS measurements, a strategy commonly applied to solve complex nanostructural order. [START_REF] Forny-Le-Follotec | Characterization of Micelles of Small Triblock Copolymer by Small-Angle Scattering[END_REF][START_REF] Eyssautier | Insight into Asphaltene Nanoaggragate Structure Inferred by Small Angle Neutron and X-ray Scattering[END_REF] The pyrite has not been taken into account for SAXS modeling and we show that for pyrite content above ~ 2.5 vol %, the SLD of nanopores is suspicious rendering the nature of filling fluid unclear.

This methodology has been applied to a series of source rocks with an increasing maturity according to Rock-Eval pyrolysis measurements. For mature samples, the SAXS/SANS analysis show (i) a kerogen mass density of ~1.64 g.cm -3 in good agreement with geochemical estimation (ii) a nanopore size radius distribution centered on 0.5-0.7 nm, in agreement with the literature, [START_REF] Bahadur | Small-Angle and Ultrasmall-Angle Neutron Scattering (SANS/USANS) Study of New Albany Shale. A Treatise on Microporosity[END_REF][START_REF] Bahadur | Hierarchical Pore Morphology of Cretaceous Shale. A Small-Angle Neutron Scattering and Ultrasmall-Angle Neutron Scattering Study[END_REF][START_REF] Bahadur | Porosity of the Marcellus Shale. A contrast matching small-angle neutron scattering study[END_REF][START_REF] Bousige | Realistic Molecular Model of Kerogen's Nanostructure[END_REF] with 20% of polydispersity and accounting for pore volume fractions of ~ 0.01 to 0.04. When the volume fraction is compared to the Rock-Eval pyrolysis TOC content (~ 4.5 to 9 % wt), the proportion of pores in kerogen is about a fifth to a half of the kerogen domain. At such pore concentration, the assumption of diluted pores could not always be valid and considering a structure factor S(Q) in the intensities modeling should be taken into account. As any peak in the high Q region, relative to a short range pore ordering, has been detected, a structure factor rather based on pore aggregates should be considered. It would give additional information on nanopore connectivity relevant for future studies and (iii) an Xray nanopores SLD of ~ 4 to 5.10 10 cm -2 . These values can account for either condensed (liquid) light hydrocarbons or a mixture of heavier condensed hydrocarbons and empty pores. For the overmature sample, the kerogen mass density is higher (1.74 g.cm -3 ) as expected, the pore size distribution is bimodal with a mode close to the one of mature sample and an additional distribution of mesopores (with a radius of 3.5 nm) accounting for a small pore volume fraction of ~ 0.1-0.2 %. Both porous media are found to be empty in full agreement with almost null values of free hydrocarbons as measured in the Sh0 and Sh1 values using Rock-Eval pyrolysis.

The developed methodology of sample preparation, measurement and data modeling allow to reach several valuable parameters relevant for source rocks studies. Its application seems to give satisfactory results in comparison with already known parameters. The SAXS measurements could be improved notably. By using shorter wavelength (e.g. molybdenum), transmission would be higher, the exposure time lower and the fluorescence eliminated. If this wavelength is tuned finely around the absorption edge of Fe (ASAXS), the scattering contribution of pyrite should be mitigated rendering the pore content more accurate. As mentioned, data acquired with a better statistic would also allow to consider a smaller azimuthal aperture and to better appreciate the moderate signal of nanopores.

Finally, this fine characterization of the porous media could be seen as a first step before the introduction or the removal of various compounds, including hydrocarbons or CO 2 , from the pores space. The proposed methodology, based on contrasts, would allow to probe the affinity of a fluid to pores contained in kerogen and would provide information on the pore connectivity.

CONCLUSION

This study was performed to better characterize source rocks for transport or mechanical issues. For that, a new methodology based on SAXS/SANS complementarity is developed. The sample preparation, thin blade section cut normal to bedding, allow to compare directly the anisotropic X-ray and neutron patterns. From 2D scattering analysis, an order parameter likely related to the preferential orientation of lamellar minerals is inferred. It represents a valuable parameter that could be used for mechanical or transport properties issues. At large Q values, an additional isotropic scattering contribution, ascribed to nanopores in kerogen, is evidenced and mostly apparent at specific azimuthal angles. For these later, the 1D scattering profiles are modeled by two contributions related to three distinct phases : minerals, kerogen and pores. These two contributions are weighted by prefactors that are different for each radiation. The exploitation of both prefactor, together with the one of the scattering model allow to retrieve valuables parameters such as a kerogen maturity index, number density of nanopores leading to their size distribution and also their associated volume fraction. The

  and gas reservoirs (GASH European program (2009-2012) and MGH IFPEN internal research program). Four samples named as BSP-2, BSP-3, BSP-4 and BSP-5 come from the Mesquite 1 well of the Barnett Shale Play (BSP) (Texas -United States). The BSP samples were deposited in a foreland basin in the Fort Worth Basin. These rocks are fine grained laminar silicate-rich and organic-rich source rocks. The last sample MT-1 originates from the Cypress field (well C-30-l / 94-b-15) of the Montney-Doig Formation (MT) (Alberta and British Columbia -Canada). This sample was deposited

  homogeneity were assessed on a sample, called MT-2, with a low Total Organic Carbon (TOC) content (1.4 %wt), extracted from the well 0/14-32-073-08W6 of the Montney-Doig formation at a depth of 2070 meters. This well is located at 270 Km South-East of MT-1 sample. MT-2 was chosen to evaluate the effect of mineral variability on scattering intensity, as it have a low TOC content. The influence of sample thickness on SAXS data were analyzed to determine the occurrence of multiple scattering effects. SAXS measurements were conducted on MT-2 normal cut to bedding thin blade sections within a thickness of 100, 140 and 210 µm. Scattering intensities were normalized to the sample thickness and transmission. Results (supplementary information) show that intensities in absolute units are about the same according to three different sample thickness suggesting (i) no multiple scattering in this Q range and (ii) measurements are performed in an almost homogeneous probed volume. The multiple scattering effect was only checked on SAXS data assuming, as suggested byAnovitz and Cole (2015), the fact that if the transmission is greater than 90 %, the multiple scattering effects remains small.To complete our view on probed volume homogeneity, SAXS measurements were performed on 9 and 5 random positions on the 140 µm thick MT-2 sample with a 200 x 200 µm beam size. Results

Figure 2 .

 2 Figure 2. HI as a function of Tmax diagram with delineations 1, 2 and 3 defining the limit of the oilgas window for kerogen of type I, II and III. 54 BSP samples are represented by triangles and MT-1 is

Figure 4 (Figure 4 .

 44 Figure 4(a), Figure 4(b) and Figure 4(c) display macroscopic observations (FOV = 51 µm and

Figure 5 .

 5 Figure 5. Schematic representation of SAXS/WAXS configuration with respect to the laboratory frame

Figure 6 .

 6 Figure 6. (a) Example of fluorescence subtraction on BSP-4_φ 2 SAXS data. (b)Example of incoherent subtraction on BSP-4_φ 2 SANS data. Both scattering profiles are displayed as a function of two contributions, log normal (dark green dash lines) and A.Q -α (orange dash lines).

Figure 7 ( 67 Figure 7 .

 7677 Figure 7(d), the variation of the scattering intensity is plotted as a function of the azimuthal angle φ

Figure 8 .

 8 Figure 8. X-ray and neutron kerogen SLD as a function of kerogen densities based on data fromThomas et al., 2014. 71 X-ray linear regression (black curve) and neutron linear regression (red curve)

4 𝑖=1

 4 and fluctuations of SLD occur, an arbitrary SLD reference can be chosen to determine 𝜌 𝑖 𝐻 𝑖 (𝑟 ) in regard to the phase of interest, the kerogen, as : ∑ 𝝆 𝒊 𝑯 𝒊 (𝒓 ⃗ ) 𝟒 𝒊=𝟏 = (𝝆 𝑴 -𝝆 𝑲 )𝑯 𝑴 (𝒓 ⃗ ) + (𝝆 𝑷 -𝝆 𝑲 )𝑯 𝑷 (𝒓 ⃗ ) + (𝝆 𝑷′ -𝝆 𝑲 )𝑯 𝑷′ (𝒓 ⃗ ) + 𝝆 𝑲

Figure 9 .Figure 10 .

 910 Figure 9. (a) Samples SANS profiles according to the azimuthal area of interest. Full dots represent

Figure 11 .

 11 Figure 11. SAXS azimuthal integration profiles of BSP and MT samples within (a) low Q-region (Q = 5.10 -2 to 0.2 Å -1 ) and (b) high Q-region (Q = 0.34 to 0.5 Å -1 ). Integrated azimuthal angle regions

Figure 12 (Figure 12 .

 1212 Figure 12(a) for SANS data and in Figure 12(b) for SAXS/WAXS measurements shows a good

Table 1 . Rock-Eval pyrolysis data obtained within the Shale Play method on the five source rock samples. (a) Data expressed in mg HC / g rock.

 1

			Well	Depth	Maturity	Sh0	Sh1	Sh2	Tmax	HI	TOC
	Formation	Reference
				m		(a)	(a)	(a)	(°C)	mg HC / g TOC	wt %
		BSP-2	Mesquite 1	1126.7	Mature	2.36	2.7	7.5	439	168	4.5
	Barnett	BSP-3	Mesquite 1	1130.5	Mature	2.55	3.5	7.8	438	174	4.5
	Shale Play	BSP-4	Mesquite 1	1142.4	Mature	2.09	3.0	14.5	453	159	9.0
		BSP-5	Mesquite 1	1145.4	Mature	1.57	2.5	11.9	449	146	8.1

Table 2 .

 2 Normalized

		Density	BSP-2	BSP-3	BSP-4	BSP-5	MT-1
	Phase
		(g/cm 3 )	(vol %)	(vol %)	(vol %)	(vol %)	(vol %)
	Quartz	2.65 (a)	41.9	41.7	30.1	31.6	36.4
	Albite	2.62 (a)	12.0	9.0	15.4	12.5	6.5
	Muscovite	2.90 (a)	15.6	13.7	28.0	22.5	17.9
	Illite	2.75 (a)	12.4	14.8	19.8	12.8	4.1
	Calcite	2.71 (a)	8.5	12.7	-	17.4	8.6
	Dolomite	2.87 (a)	8.5	7.1	-	1.4	18.3
	Apatite	3.19 (a)	-	-	4.3	-	-
	Pyrite	4.93 (a)	1.1	0.9	2.3	1.8	2.5

mineral compositions of BSP and MT samples converted in volume percent (vol %) using the mineral density (a) defined in the database www.webmineral.com.

Table 3 .

 3 neutron and X-Ray SLD values of minerals. (a) Data coming from the mineralogical database webmineral, on : http://webmineral.com/

				SLD
			Density (a)
	0Phase	Chemical formula (a)	(g/cm 3 )	X-rays	Neutrons
				(x 10 10 cm -2 )	(x 10 10 cm -2 )
	Quartz	SiO2	2.65	22.5	4.2
	Albite	NaAlSi3O8	2.62	22.1	4.0
	Muscovite	KAl2(AlSi3O10)(OH)2	2.90	24.5	3.9
	Illite	K(Al,Fe,Mg)2(Si,Al)4O10(OH)2	2.75	23.1	3.7
	Calcite	CaCO3	2.71	23.0	4.6
	Dolomite	CaMg(CO3)2	2.87	24.3	5.4
	Apatite	Ca5(PO4)3(OH,F,Cl)	3.19	26.9	4.1
	Pyrite	FeS2	4.93	40.5	3.7

Table 4

 4 below.

Table 4 .

 4 Model Fluids SLD calculated from equation 7.

		Neutrons SLD	X-Ray SLD
	Model fluids
		(x 10 10 cm -2 )	(x 10 10 cm -2 )
	Toluene	0.9	8.0
	Pentane	-0.6	6.2
	Methane(g)	0.0	0.0
	Air	0.0	0.0

  𝑰(𝑸) 𝑿,𝑵 = 𝒂(𝝆 𝑴 -𝝆 𝑲 ) 𝑿,𝑵𝟐 𝑸 -𝜶 + 𝒏(𝝆 𝑷 -𝝆 𝑲 ) 𝑿,𝑵

		𝑹 𝒎𝒂𝒙
	𝟐	∫ 𝒇 𝑷 (𝑹)𝑽 𝑷 𝟐 (𝑹)𝑷(𝑸, 𝑹) 𝒅𝑹
		𝑹 𝒎𝒊𝒏

  The separation of the global signal into an anisotropic and an isotropic contribution allows to specify a more accurate expression for Q dependence of intensity : 𝑰(𝑸) 𝑿,𝑵 = 𝒂(𝝋)(𝝆 𝑴 -𝝆 𝑲 ) 𝑿,𝑵 𝟐 𝑸 -𝜶 + 𝒏(𝝆 𝑷 -𝝆 𝑲 ) 𝑿,𝑵

										5 Å -1
		A	B	m	𝜓	S	A	B	m	𝜓	S
	BSP-2	418.6	168.8	2.0	92	0.14	28.6	4.4	1.8	91	0.06
	BSP-3	324.8	181.1	1.6	94	0.13	22.6	5.6	1.4	95	0.06
	BSP-4	304.1	96.6	3.1	91	0.26	32.3	1.1	3.6	90	0.09
	BSP-5	342.1	177.1	2.4	87	0.21	28.9	2.5	2.5	87	0.08
	141 MT-1	423.4	0.0	0.0	0.0	0.0	24.7	0.0	0.0	0	0.0
								𝟐 ∫ 𝑹 𝒎𝒊𝒏 𝑹 𝒎𝒂𝒙	𝒇 𝑷 (𝑹)𝑽 𝑷 𝟐 (𝑹)𝑷(𝑸, 𝑹) 𝒅𝑹

Table 6 .

 6 Fitting parameters of SANS and SAXS data obtained for the α parameter and the term of contrast 𝐴 = 𝑎(𝜑)(𝜌 𝑀 -𝜌 𝐾 ) 𝑁 2 related to the A.Q -α contribution and also the radius (µ) and the term of contrast 𝑛(𝜌 𝑃 -𝜌 𝐾 ) 𝑁 2 related to the log normal contribution.

	(a)			(b)
		mu	Neutrons	X-rays
	Reference	α
		(nm) 𝒂(𝝋)(𝝆 𝑴 -𝝆 𝑲 ) 𝑵 𝟐	𝒏(𝝆 𝑷 -𝝆 𝑲 ) 𝑵 𝟐	𝒂(𝝋)(𝝆 𝑴 -𝝆 𝑲 ) 𝑵 𝟐	𝒏(𝝆 𝑷 -𝝆 𝑲 ) 𝑵 𝟐
	BSP-2	3.20 0.7	4.4	0.6	4.9	0.6
	BSP-3	3.25 0.5	3.4	4.4	4.4	3.5
	BSP-4	3.10 0.5	6.4	3.6	7.2	5.6
	BSP-5	3.10 0.5	7.6	6.3	11.0	5.2

Table 7 .

 7 Values for 𝜌 𝑀𝑁 and 𝜌 𝑀𝑋 are calculated from equation 7. Kerogen densities, 𝜌 𝐾𝑁 , 𝜌 𝐾𝑋 and 𝜌 𝑃𝑋 are estimated from, respectively, equation 21, 9, 10 and 22. Estimated n values for kerogen pores and the associated volume fraction.Knowing kerogen SLD for both SAXS and SANS techniques, 𝑅 𝑁 ratios may provide fluids in place SLD values assuming 𝜌 𝑃𝑁 ~ 0. Then, 𝜌 𝑃𝑋 can be expressed as :

	Sample	mu	n	Volume fraction	Kerogen density d	𝝆 𝑴𝑵	𝝆 𝑴𝑿	𝝆 𝑲𝑵	𝝆 𝑲𝑿	𝝆 𝑷𝑿
		(nm)	(x 10 19 cm -3 ) (x 10 -2 )	(g/cm 3 )	(x 10 10 cm -2 )	(x 10 10 cm -2 )	(x 10 10 cm -2 )	(x 10 10 cm -2 )	(x 10 10 cm -2 )
	BSP-2	0.7	0,5	1.0	1.66	4.0	21.3	3.4	14.5	4.3
	BSP-3	0.5	4.7	3.0	1.67	4.0	21.3	3.4	14.6	5.1
	BSP-4	0.5	6.0	3.8	1.59	3.7	20.3	3.0	14.0	4.4
	BSP-5	0.5	5.7	3.6	1.65	3.8	20.2	3.3	14.4	4.9
	MT-1	0.5	2.6	1.6	1.74	4.1	21.6	3.7	15.1	0
	MT-1	3.5	7.10 -4	0.15	-	-	-	-	-	0
					𝝆 𝑷𝑿 =	-𝝆 𝑲𝑵 + √𝑹 𝟐𝑵 𝝆 𝑲𝑿 √𝑹 𝑵

in SANS and 0.1 Å -1 in SAXS/WAXS. For larger Q values the scattering intensity is quite similar

agreement between model and data for the both radiation on the whole Q range. Geometrical parameters (, µ and reported in Table 6, are first assessed by fitting SANS data as the Q dependence of these latter are more pronounced than for SAXS data. Then, modelling was performed based on a simultaneous scattering fit of SAXS/SANS data to obtain the pre-factors 𝑎(𝜌 𝑀 -𝜌 𝐾 ) [START_REF] Godec | Potential Global Implications of Gas Production from Shales and Coal for Geological CO2 Storage[END_REF] and 𝑛(𝜌 𝑃 -𝜌 𝐾 ) [START_REF] Godec | Potential Global Implications of Gas Production from Shales and Coal for Geological CO2 Storage[END_REF] , containing the SLD of each phase and depending on the type of radiation.

Results obtained for geometrical parameters indicate that both SANS and SAXS/WAXS scattering intensity can be described as the sum of two types of contributions using the same parameters giving the Q dependence, namely , µ and . These results also validate the SANS incoherent scattering background subtraction based on mean value measured at high Q values .

The  parameters, that are close to each other (3.1 -3.25) for BSP samples and slightly higher (3.4) for MT1, are in the range of reported values. [START_REF] Gu | Pores in Marcellus Shale: A Neutron Scattering and FIB-SEM study[END_REF][START_REF] Sun | Pore structure characterization of organic-rich Niutitang shale from China. Small angle neutron scattering (SANS) study[END_REF][START_REF] Mastalerz | Porosity of Coal and Shale[END_REF][START_REF] Bahadur | Small-Angle and Ultrasmall-Angle Neutron Scattering (SANS/USANS) Study of New Albany Shale. A Treatise on Microporosity[END_REF][START_REF] Sun | Pore characteristics of Longmaxi shale gas reservoir in the Northwest of Guizhou, China. Investigations using small-angle neutron scattering (SANS), helium pycnometry, and gas sorption isotherm[END_REF][START_REF] Clarkson | Characterization of tight gas reservoir pore structure using USANS/SANS and gas adsorption analysis[END_REF][START_REF] Clarkson | Pore structure characterization of North American shale gas reservoirs using USANS/SANS, gas adsorption, and mercury intrusion[END_REF][START_REF] Bahadur | Hierarchical Pore Morphology of Cretaceous Shale. A Small-Angle Neutron Scattering and Ultrasmall-Angle Neutron Scattering Study[END_REF][START_REF] Radlinski | Small Angle Neutron Scattering Signature of Oil Generation in Artificially and Naturally Matured Hydrocarbon Source Rocks[END_REF][START_REF] Bahadur | Porosity of the Marcellus Shale. A contrast matching small-angle neutron scattering study[END_REF] The widths  of nanopore size distributions are quite narrow, always close to 0.2 and the fitted parameters given here are obtained with values of  set to 0.2 for a better visibility. The mean radius of nanopores is close to 0.5 nm, a value commonly found for this type of material. [START_REF] Bahadur | Small-Angle and Ultrasmall-Angle Neutron Scattering (SANS/USANS) Study of New Albany Shale. A Treatise on Microporosity[END_REF][START_REF] Bahadur | Porosity of the Marcellus Shale. A contrast matching small-angle neutron scattering study[END_REF] For the overmature sample, the curves at high Q values show clearly two separate bumps assigned here to two pore size distributions. The first one has a mean radius of 0.5 nm in the same range as the mature samples and the second one has much higher values close to 3.5 nm. In addition, it appears that SAXS techniques can also provide information on porous media in the kerogen phase as both SANS and SAXS/WAXS profiles are in good agreement using pore size define from SANS modeling. From fitting data, BSP samples are described as source rocks with pore radii varying from 0.5, for BSP-3, BSP-4 and BSP-5, up to 0.7 nm, for BSP-5. MT-1 sample displays two pore radii 0.5 nm and 3.5 nm. In addition, fit sensitivity on the pore size radius was tested as shown in supplementary information. It shows that radii nanopore measurements are sensitive within ~ 1-2 Å range. latter being related to the kerogen maximum storage capacity for gaseous species or condensed fluids. Moreover, X-ray pore space SLD gives some indications about the nature of filling fluids. This methodology is tested on a series of source rocks of increasing maturities. The same set of geometrical parameters allow to fit both X-ray and neutron data proving the selectivity of the model.

The kerogen maturity index is in agreement with the Rock-Eval pyrolysis maturity approximation. The nanopore sizes and their associated volume fraction are in the range of, respectively, 0.5-0.7 nm and 0.01-0.04 for mature source rocks. They are likely filled either by light hydrocarbons, or a mixture of heavy hydrocarbons and empty pores. For the overmature one, an additional pore size of 3.5 nm, accounting for a volume fraction of ~ 0.2%, is evidenced. For both population, pores appears empty in full agreement with Rock-Eval pyrolysis measurements. This new methodology proved to be efficient and open a new way to look quantitatively at nanoporous kerogen phase and its in-situ evolution upon treatment such as emptying or filling it with various fluids.

ACKNOWLEDGEMENT

The authors are grateful to IFP Energies Nouvelles and PHENIX laboratory for their financial and scientific support. We thank E. Bemer (IFPEN) and W. Sassi (IFPEN) for providing the source rock samples as part of GASH and MGH projects. We also thank M. Detrez for his technical support on PA20 and the Laboratoire Léon Brillouin which provide SANS instrumentation and the financial support for this experiment. We are grateful to P. Hayrault and F. Moreau for their help respectively on HS-GC interpretation and FESEM experiment. All authors contributed to the discussion, the writing and the review of this paper .