Guillaume Galliéro

Hai Hoang

Simple Fluids confined in Nanopores: from local transport properties to shear-swelling couplings

Keywords: Molecular Dynamics, Nanopore, Transport properties, Swelling

Introduction

Dense fluids confined between flat solid surfaces are generally strongly inhomogeneous in the direction normal to the fluid-solid interfaces due to surface effects (layering of the molecules of the fluid because of adsorption and molecular packing) [START_REF] Israelachvili | Intermolecular and Surface Forces[END_REF]. Thus, when the solid surfaces are separated by a distance that is smaller than about 10 times the molecular diameters of the fluid, the confined fluid exhibits local and effective transport properties that may strongly differs from those of the bulk [START_REF] Israelachvili | Intermolecular and Surface Forces[END_REF][START_REF] Hoang | Grand Canonical-like molecular dynamics simulations: Application to anisotropic mass diffusion in a nanoporous medium[END_REF][START_REF] Hoang | Local shear viscosity of strongly inhomogeneous dense fluids: From the hard-sphere to the Lennard-Jones fluids[END_REF]. Furthermore, this extreme confinement can induce as well strong forces (solvation) on the solid matrix that may lead to swelling/shrinkage as well known in clays for instance.

Methods and models

To improve the microscopic understanding of the phenomena described above, we have performed extensive molecular dynamics simulations on simple fluids confined between flat solid surfaces. In all cases the solid phase has been modeled using a rigid CFC crystal composed of Lennad-Jones atoms.

Concerning the fluid, different molecular models were employed, from hard sphere to Lennard-Jones, so as to build new weight functions for a non-local model for transport properties based on a local average density model. Furthermore, to ensure the reliability of the model so obtained, various thermodynamic conditions have been explored.

Various non equilibrium molecular dynamics scheme have been developed [START_REF] Hoang | Grand Canonical-like molecular dynamics simulations: Application to anisotropic mass diffusion in a nanoporous medium[END_REF][START_REF] Hoang | Local shear viscosity of strongly inhomogeneous dense fluids: From the hard-sphere to the Lennard-Jones fluids[END_REF][START_REF] Hoang | Couplings between swelling and shear in saturated slit nanopores: A molecular dynamics simulation study[END_REF], see Fig. 1, in order to study the impact of extreme confinement of the dynamic fluid properties. ______________________________________________________________________________________________________ JEMP 2016 -Anglet, France -12-14 Octobre 2016.

Discussion

In the first part of the presentation, we will show how the local variations of the transport properties of the confined fluid (diffusion [START_REF] Israelachvili | Intermolecular and Surface Forces[END_REF], viscosity [START_REF] Hoang | Grand Canonical-like molecular dynamics simulations: Application to anisotropic mass diffusion in a nanoporous medium[END_REF]), induced by density inhomogeneities, can noticeably affect the effective transport properties of the fluid quantified at the pore scale. Furthermore, it will be shown that these local transport properties can be essentially described by a simple local average density model combined with simple weight functions [START_REF] Hoang | Local shear viscosity of strongly inhomogeneous dense fluids: From the hard-sphere to the Lennard-Jones fluids[END_REF], see Fig. 2.

In the second part of the presentation, we will discuss the couplings that occur between shear and swelling at the pore scale because of the strong fluid structure [START_REF] Hoang | Couplings between swelling and shear in saturated slit nanopores: A molecular dynamics simulation study[END_REF]. It will be shown that shear can induce swelling and vice versa because of the confined fluid phase structure, see Fig. 2. This implies that the response to a variation of the external load is a combination of volumetric and shear deformations, because of the fluid.

These phenomena, which are usually neglected in poromechanics modeling, may be non-negligible in highly structured microporous systems such as cementitious or clay-based materials [START_REF] Vandamme | Creep of Lubricated layered Nano-porous solids and application to cementitious Materials[END_REF].

Figure 1 :

 1 Figure 1: Left: Scheme of the molecular dynamics simulation used to study unsteady mass diffusion (blue and green: fluid particles of two species, red: solid particles) in a nanopore. Right: Scheme of the molecular dynamics simulation cell used to study couplings between shear and swelling (green: fluid particles, red: solid particles).

Figure 2 :

 2 Figure 2: Right: Variation of the local shear viscosities perpendicularly to the solid wall. Right: Variation of the distance between the solid surfaces with time during boundary shear.

Acknowledgments

This work has been supported by the "Failflow" project which was funded by an advanced grant from the European Research Council. We gratefully acknowledge computational facilities (in link with a "Conseil Regional d'Aquitaine" project) provided by the Pau University and the I2M Laboratory (Bordeaux University).


Julien Collell
email: julien.collell@total.com

Guillaume Galliero

Romain Vermorel

Philippe Ungerer

Marianna Yiannourakou

François Montel

Magali Pujol

François Gelin

Guillaume Galliéro

Transport of Multicomponent Hydrocarbon Mixtures in Shale Organic Matter by Molecular Simulations

Keywords: Multicomponent Transport, Nanoporous Membrane, Molecular Simulations, Modeling

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Abstract

Hydrocarbon production from shales has significantly increased in the past years. However, the recovery process remains largely unknown, which hinders the sustainability of such resources. In particular, hydrocarbons in shales are mostly located in microporous nodules of organic matter, the so-called kerogen, which are likely to act as selective barriers to hydrocarbon flow [START_REF] Falk | Subcontinuum mass transport of condensed hydrocarbons in nanoporous media[END_REF].

In this work, hydrocarbon transport properties through microporous kerogen membranes [START_REF] Collell | Molecular Simulation of Bulk Organic Matter in Type II Shales in the Middle of the Oil Formation Window[END_REF] were investigated by the means of molecular simulations. To do so, Boundary-Driven Non Equilibrium Molecular Dynamic (BD-NEMD) [START_REF] Frentrup | Transport diffusivities of fluids in nanopores by nonequilibrium molecular dynamics simulation[END_REF] simulations (see figure 1) have been performed to study the mechanisms of pure fluids transport through kerogen porous structure. By expressing the one-dimensional mass flux across the porous structure as a function of chemical potential gradient, mass transfer coefficient (𝜒 𝑡 0 ) through the kerogen membrane has been determined. These mass transfer coefficients were compared to Maxwell-Stefan diffusivities ( 𝐷 ), obtained from Equilibrium Molecular Dynamic (EMD) simulations. Within uncertainties, these two coefficients are equals. As an illustration, in figure 2 are presented the results obtained for pure methane and pure carbon dioxide. Thus, our results show that hydrocarbon transport within kerogen is essentially caused by a diffusion process. In addition, it has been found that Maxwell-Stefan diffusivities could be well approximated by the self-diffusivities, which could be obtained experimentally.

______________________________________________________________________________________________________ JEMP 2016 -Anglet, France -12-14 Octobre 2016. Based on these observations, linear hydrocarbon (n-alkane) diffusion was investigated. The impact of hydrocarbon chain length and the thermodynamic conditions (temperature and adsorbed amount) was quantified and modeled.

Then, from the conclusions drawn on pure compounds, diffusion of binary and ternary hydrocarbon mixtures, as well as a realistic reservoir fluid mimicking a typical condensate gas [START_REF] Collell | Molecular Simulation of Bulk Organic Matter in Type II Shales in the Middle of the Oil Formation Window[END_REF] has been studied. The Onsager's matrix, characterizing the diffusive flux, has been quantified. This matrix is dominated by its diagonal coefficients, whereas Onsager's cross-correlation coefficients are negligible. This indicates that diffusive fluxes induced by interspecies friction are negligible compared to the diffusive fluxes induced by friction with the porous structure. Such behavior can be explained by the important confinement of the fluid species, within the kerogen micropores. Finally, inspired by the Rouse and surface diffusion theories, we propose a simple scaling law that predicts the transport coefficients of linear alkanes in the mixture in good agreement with our simulations data [START_REF] Collell | Transport of Multicomponent Hydrocarbon Mixtures in Shales Organic Matter by Molecular Simulations[END_REF].

Figure 1 :

 1 Figure 1: Schematic representation of NEMD algorithm used in this work. Kerogen membrane is immersed within two fluid reservoirs. A pressure difference is generated between the two reservoirs, thanks to an external field applied in the so-called perturbation region, which results in a fluid flow within the kerogen membrane.

Figure 2 :

 2 Figure 2: Comparison of mass transfer coefficients 𝜒 𝑡 0 with Maxwell-Stefan diffusivities 𝐷 obtained on pure methane and carbon dioxide, as a function of the average reservoir pressure.


Sâm Landier
email: sam.landier@onera.fr

Boolean operations on arbitrary polygonal and polyhedral meshes

Keywords: Boolean Operations, Polyhedral Meshes, Polygonal Meshes, Mesh Intersection, Cell Reconstruction, Conformity, Conservative Remapping, Cut-cell Meshing, Constrained Delaunay Triangulation, Flood Fill Algorithm

An O(nlogn) floating-point arithmetic algorithm designed for solving usual boolean operations (intersection, union, and difference) on arbitrary polygonal and polyhedral meshes is described in this paper. This methods does not approximate the inputs which can be both volume meshes, both surface meshes or one of each. It provides exact and conformal meshes upon exit. It can be used in many pre-and post-processing applications in computational physics (e.g. cut-cell volume mesh generation or conservative remapping). The core idea is to consider any configuration as a polygonal cloud. The polygons are first triangulated, the intersections are solved, the polyhedral cells are then reconstructed from the conformal triangles cloud and finally their triangular faces are re-aggregated to polygons. This approach offers a great flexibility regarding the admissible topologies : non-planar faces, concave faces or cells and some non-manifoldness are handled. The algorithm is described in details and some current results are shown.

Introduction

Considering two arbitrary polyhedral meshes M 1 and M 2 that are partially or fully overlapping (e.g. one is fully immersed in the other one, or both are representing the same computational domain) and a given tolerance, a floating-point arithmetic method is proposed to solve the geometric intersections and retrieve a conformal polyhedral mesh upon exit that results from the usual boolean operations (intersection, union and difference). A typical target application is related to conservative remapping of some solution fields from one mesh to another [1; 2; 3; 5; 12; 13; 14 ; 19]. In all these works it is assumed that the source and the target are two meshes of the same domain. But if we want to do some conservative remapping in the Chimera context [START_REF] Wang | A fully automated Chimera methodology for multiple moving body problems[END_REF], it is also required to handle partial overlapping, so a general algorithm should not do such assumption and treat the fully-immersion or same-boundary cases as particular cases of a partial overlapping as depicted in Fig. 1. The conservative remapping problem induces necessarily a high computation cost because all the intersections between the polygons must be resolved in the intersecting zone (in green Fig. 1). Applications like conservative interfacing [6; 7] (cf. Fig. 2) for overlapping grids require to build a conformal mesh of a domain where each subdomain has been meshed separately. The conformal assembly is achieved prioritizing some meshes that come fit into non-priority meshes. The intersection zone is therefore reduced to a narrower region in the vicinity of the surface of the prioritized meshes. This is similar to cut-cell meshing (cf. Fig. 3) where the impact on the cut mesh takes place in the vicinity of the cutting surface. Some other applications like Chimera blanking [START_REF] Wang | A fully automated Chimera methodology for multiple moving body problems[END_REF] or Constructive Solid Geometry evaluation [8; 9; 21; 22] works on a reduced sets of large polyhedra (polygonal surface meshes) and their intersecting zone is inherently narrower (cf. fig 4) compared to the same problem with volume meshes (even though [START_REF] Douze | QuickCSG : Arbitrary and Faster Boolean Combinations of N Solids[END_REF] solves very efficiently dense problems with 100,000 polyhedra having millions of intersecting polygons). All these different problems, as for CSG evaluation, can be expressed in terms of boolean operations between two meshes :

• The conservative remapping problem is an intersection operation on meshes without prioritization. • The interfacing problem is a union with prioritization.

• The cut-cell meshing is a mixed-type difference between a volume mesh and a surface mesh.

The proposed algorithm covers all these problems by defining boolean operations on two arbitrary meshes operands :

• polyhedral vs polyhedral (with or without prioritization) • polyhedral vs polygonal • polygonal vs polygonal When a mesh is prioritized, there are two steps in the process : first its outer skin is processed considering the boolean operation between a polyhedral mesh and a polygonal mesh. Then this modified skin is reattached to its interior to get a conformal result (as explained in section 5.6). As a closed surface mesh is a polyhedron, boolean calculation for pure polygonal inputs is seamlessly handled.

Previous 3D works

Among the most recent 3D algorithms, Alauzet [START_REF] Alauzet | A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes[END_REF] focuses on pure tetrahedral mesh intersections. The topological approach fits very well pure tetrahedrons problems. For each pair of intersecting tetrahedrons, the 32 signed distances of each vertices of one tetrahedron versus the four facets of the other one allow to build some topological information that reduces the intersection tests, prevents inconsistencies and ensures robustness. Even though this approach is pragmatic for simplices, pre-computing all the signed distances might be cumbersome for larger polyhedra and not practicable at all for surface mesh inputs since the number of signed distances to compute grows exponentially (for a small polyhedra that is a triangulated hexahedron, we should compute 192 signed distances). Moreover, splitting the intersection zone into tetrahedrons leads potentially to engender a lot of cells and therefore a higher memory usage compared to a polyhedral approach if we want ouput the resulting conformal mesh. An algorithmic advantage however is the fact that the tetrahedrons are convex which greatly facilitates the recovery of intersecting areas (always convex too) and computing the conservative field. In a polyhedral approach, the necessary handling of concavities increases the complexity of the algorithm. Finally, since the geometric kernel (intersection computation) and the conservative remapping are strongly linked as being part of the same iterative loop for each pair of intersecting tetrahedrons, there is no need to keep a geometric representation of the intersections : once two tetrahedrons are processed, every data related to that pair is flushed. This is a good thing for coarse grain multi-threading but induces redundant intersection calculations. The algorithm described in this paper focuses on the geometric construction so it aims at building an explicit polyhedral mesh representation available upon exit. As it is designed, each polygon is processed once. This choice will not prevent to multithread the current sequential implementation though.

Another 3D algorithm designed by Brenner [6; 7] deals with polyhedral (with triangular faces only) mesh intersections over overlapping grids to solve the conservative interfacing problem. It does not give an explicit representation of the resulting mesh : surface vectors and centroids (faces and elements) are instead provided. This is fair enough for the targeted conservative remapping applications but it might be difficult to get to order higher than two or three without the explicit representation. Moreover only few publications of this algorithm are available so it is difficult to analyze it further.

Farrell et al. [1; 2] have proposed an algorithm to solve the conservative remapping problem and their geometric kernel (which is separated from the conservative calculations) has some similarities with the one discussed in this paper, especially their 2D version [START_REF] Farrell | Conservative interpolation between unstructured meshes via supermesh construction[END_REF] : they indeed solve first the edge intersections, and the whole set of split edges is then processed by a constrained-Delaunay triangulator to provide what is called a supermesh. The benefit of this global approach is to avoid intersections calculation redundancy. It might be not necessary though to keep the entire supermesh into memory when the algorithm is purely dedicated to conservative remapping. The 3D version adopts a local approach as in [START_REF] Alauzet | A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes[END_REF] (inducing redundancy) but deals only with convex elements because the clipping Eberly s algorithm [START_REF] Eberly | 3D Game Engine Design : A Practical Approach to Real-Time Computer Graphics[END_REF] is used.

Following efforts have been made by Menon and Schmidt [START_REF] Menon | Conservative interpolation on unstructured polyhedral meshes : An extension of the supermesh approach to cellcentered finite-volume variables[END_REF] to extend the supermesh concept to 3D but the proposed algorithm is restricted to starshaped polyhedra because of their implementation of the algorithm requirement to break down the polyhedra into tetrahedrons. A similar requirement is necessary for the algorithm proposed by Grandy [START_REF] Grandy | Conservative Remapping and Region Overlays by Intersecting Arbitrary Polyhedra[END_REF].

The algorithm described in this paper can deal with almost any type of polyhedral topologies (i.e. useful for practical applications as described in the next section) by solving the intersection between faces avoiding the requirement of such volume decomposition.

Admissible topologies

Here are the characteristics of the geometric entities handled by the algorithm.

Admissible polygon (aPG)

An aPG is a 3D polygon with p vertices forming q edges satisfying the following conditions :

• Its edges are not intersecting each other : it s a conformal set (c1) • Its boundary (its edges excluding the non-manifold bits) form a closed contour confining a non-null surface (c2) • Its boundary is made of a single connected polygonal line : there are no holes nor separate subdomains (c3) • A plane exists such the projected polygon has the same topology (c4) • A triangulation of its boundary exists such all the p vertices lie on the triangulated surface (c5) Conditions (c1) (c2) (c4) are necessary and sufficient conditions to be able to triangulate the polygon as it is required for the algorithm as explained later. Condition (c3) is not strictly necessary but added for convenience and to ease the implementation : with this condition it is always possible to represent the polygon as a sorted vertices list of size q such any two consecutive vertices on this list forms a polygon edge (the first and last too). Condition (c5) is to ensure consistency between the polygon and its triangulated representation. Oddities such as in Fig. 5b are not admissible.

Admissible polyhedron (aPH)

An aPH is a polyhedron with f faces satisfying the following conditions :

• Its faces form a conformal set of aPGs (c6)

• Its boundary (its faces excluding the non-manifold bits) forms a closed contour confining a non-null volume (c7) • Its boundary is made of a single connected polygonal surface : there are no holes (c8) • Any non-manifold entity must be an aPG and has to share an edge with the boundary (c9) Condition (c6) is necessary to build a one-to-one polygons neighborhood information and condition (c8) (c9) ensure that one is able to use that information to traverse totally the polyhedron through its faces. So it implies that if a face has a non-manifold edge, it must be the edge of another face.

We define a minimal aPH (maPH) as an aPH satisfying the following extra condition :

• There are no separate subdomains : any two inside points can be linked by a strictly interior polygonal line that does not intersect the faces (c10)

This condition (c10) is to define the polyhedra upon exit due to the element building process explained later on. The cubes sharing an edge or a face on Fig. 6a are four separate maPHs.

Admissible mesh (aMH) and minimal admissible mesh (maMH)

An aMH (maMH) is a mesh satisfying the following conditions :

• Its elements form a conformal set of aPHs (maPH) (c11)

• The intersection volume between two of its elements is null (i.e. no penetration) (c12) • The outer skin of the mesh (polygonal surface) is manifold in the outer space (c13) Condition (c13) means that for any polyhedron of the outer layer, its nonmanifoldness must be inside (like the Triskaidecahedron s red face on figure 6a) because any outside one (quadrangular face on the cube Fig. 6b) will be lost in the element building process. The algorithm handles as operands any two aMH upon entry and creates a maMH upon exit. As a closed surface mesh is a polyhedron, boolean calculation on surface meshes or mixed types (volume vs. surface) admissible operands are a particular case seamlessly handled.

Boolean operations

Considering two sets of arbitrary elements M 1 and M 2 , let s recall first what is meant by boolean operation in algebra of sets :

• M 1 ∩ M 2 : common elements to both M 1 and M 2 • M 1 \ M 2 : elements inside M 1 and outside M 2 • M 1 ∪ M 2 : elements inside M 1 or M 2
These definitions assume that an element can always be classified, i.e. one can tell without any ambiguity this element is either inside or outside a set. Boolean operations make only sense if a predicate "in or out" can be defined. But in our geometrical context dealing with Boundary-Representation volume entities in arbitrary positions, we have to cope with ambiguity, i.e. an entity will often be partially inside. Hence we need to transform the input operands, and in fact the concatenation of them M 1 +M 2 , to make classification possible before being able to answer to any boolean operation. The first step of the transform is to make conformal all the polygons, i.e. solving all the intersections. The second step is to create from that conformal cloud all the possible maPHs. The resulting set is a maMH created from the input operands. Hence for any maPH created it is always possible to find an element of M 1 and/or M 2 that geometrically includes it. A predicate definition P is then possible. Let s note ADM the operator that converts M 1 +M 2 into a maMH. We will see that we won t define our predicate that way but for now, its existence is enough to formalize in our context the boolean operations :

• M 1 ∩ M 2 : elements e of ADM(M 1 +M 2 ) / P(e, M 1 ) and P(e, M 2 ) are both true.

• M 1 \ M 2 : elements e of ADM(M 1 +M 2 ) / P(e, M 2 ) is false • M 1 ∪ M 2 : ADM(M 1 +M 2 )
The main difference with set algebra is hence the requirement of applying the ADM operator to the concatenated mesh. Another difference with this formalism is that upon exit we only have a set of volume entities. So for instance if we compute the intersection of two polyhedra sharing a polygon the result will be empty rather than giving the shared polygon. But this is fine with the current target applications. A common point between the two worlds, the union operation doesn t need a classification step : all considered elements are in the result. Although we will define the ADM operator that turns some meshes into minimal admissible ones, it cannot handle polygons with holes or polyhedra with non-unique contour which won t appear if they are not in the input, so admissibility is a prerequisite to discard those topologies.

The algorithm

Overview

The concatenated mesh M 1 +M 2 as global and unique input needs to be transformed into a maMH. Defining the ADM operator is the main part of the algorithm. Defining the predicate (based on normals orientations) and the consequent classification is more straightforward. The ADM operator breaks down into four steps. The first step is an initialization that focuses on the intersecting zone by discarding any non-colliding polyhedron. An additional but optional treatment can be applied to ensure that the reduced set is oriented consistently meaning that each polyhedra s facet has a normal pointing outward. This treatment is not applied if the input data set is known to be oriented properly. The second step is to make conformal all the polygons seen as a cloud in arbitrary position. Solving intersections for non-planar polygons leads to nonunique solutions because of the multiple definitions of their surface support : we ve therefore made the usual choice to deal with intersections processing at the triangle level and build a conformal triangles cloud first. The third step is to reconstruct the polyhedral elements from the triangles cloud. This is the key step that builds maPHs with triangular faces by detecting any smallest enclosed cavity. The last step is to aggregate the triangular faces to coming from the same initial polygon as long as the aggregate is minimal admissible. These obtained polyhedra are therefore maPHs. The whole process is depicted in the Fig. 7.

Initializing and Pre-conditioning

The two main purposes of this step are to focus on the intersecting zone (keeping apart the elements which are not involved in the intersection) and to prepare the classification step. The latter requires to know which are the outer polygons (all of them in case of a surface mesh, the ones that are not shared in case of a volume mesh) and to have them consistently outward oriented.

A primary coarse decimation is done using the bounding box of the input meshes : any element that is not intersecting or inside both boxes is discarded.

A finer refinement is then applied to the remaining elements using a bounding box tree constructed for the smallest mesh. It is indeed more efficient to construct a small tree and query it intensively rather than the opposite. Any element that is colliding with at least one other element is kept. At the end we get a set of intersecting zones ; one of them is depicted on Fig. 8b. Any outer polygon of these sets that is not already flagged as "pure skin" is flagged as "connection skin" (meaning connected to a discarded set). The discarded elements can already be classified as outside elements and will be agglomerated after the classification step to generate the boolean operation ouput.

The final step of the initialization is to merge the coincident nodes in the set of retained points using a kd-tree. This step facilitates the intersection process by removing one type of degeneracies (cf. 5.4.1). But when two nodes need to be merged, which one has to be moved ? We have chosen to preserve one mesh with respect to the other one : its nodes are attractors in case of merging. This is what is required for instance for a cut-cell mesh : the cutting surface has to be preserved. For a conservative remapping, the target mesh needs as well to be preserved with respect to the source mesh.

Optional reorientation step. Each individual set of skin polygons (pure or connection) forming a closed surface is reoriented consistently (outward) in regard with a reference polygon (one on each set) with a neighborhood traversal algorithm : starting by the reference polygon, we reverse any neighbor with the opposite orientation and so on. For a closed surface it is always possible to find a polygon having a ray perpendicular to it and passing by an arbitrary point on it that does not intersect the surface either above or under the polygon : this indicates the outward so the polygon is flagged and used as a reference after reorienting it properly. This reorientation is crucial for the classification step.

The algorithmic complexity of this initialization step is in O(nlog(n)) (where n is the number of kept cells) because of the bounding box tree constructions and queries. An alternative to bounding box trees through the neighboring s information use is discussed in [2; 12] and might be more efficient for preconditioning in the particular case of a boolean intersection of two meshes of the same domain (which is the context of their conservative remapping).

They will be considered in future work.

From the polygons to a conformal triangles cloud

Each polygon in the cloud is triangulated. Many strategies are available but the choice to use a 2D-Constrained Delaunay approach [START_REF] Borouchaki | Aspects of 2-D Delaunay mesh generation[END_REF] has been made for its robustness dealing with any kind of polygons topology providing they fall into the admissible polygons family. Basic polygons (e.g. convex quads) are obviously processed trivially. Cheaper and therefore faster solutions will be applied in the future to eligible polygons in the cloud : a star-shaped one can be triangulated by linking the centroid to the boundary edges but this tends to produce more triangles and therefore more intersections computations. Other approaches like the Ear clipping algorithm [23; 24] could generate less triangles with an acceptable efficiency. This preliminary step is not a current bottleneck anyway. Once we have a triangle cloud and built the mapping table ancPG giving for each triangle the polygon it belongs to, we can go to the intersections solving process. When this process is done, ancPG is updated accordingly to refer to the new set of triangles that will be used to aggregate back the triangles to make aPGs from them as described in 5.7.

Intersection solving process

If we consider a cloud of intersecting triangles in arbitrary positions (cf. Fig. 9a), the intersection traces in each triangle are of two types : a point or a segment. In case of overlapping, the trace is a polygon so a set of segments too (cf. Fig. 9b). Rather than detecting and resolving on the go one intersection at a time and putting the split triangles back to the pool of triangles to be processed, we ve chosen a two-step algorithm :

• Computing and storing the traces for each triangle • Splitting each intersected triangle along the intersection traces The drawback of this approach is the storage of the traces but the benefit is to avoid an iterative algorithm that would imply redundant queries to the localizing structure (e.g. a bounding box tree). Here, each triangle has a data structure that stores the segments reflecting the intersections traces and the isolated points (degenerated segments) for each pair of intersecting triangles. Each edge has also a list of intersection points that is appended during the process. Once all the traces have been computed, the split can be done (cf Fig. 10a).

Storing the edges (rather than the intersection points only) are necessary because we aim to deal with concave polyhedra, either as input, or as resulting from e.g. a boolean difference between to input meshes having a convex outer surface. It is not therefore possible to assume (as it is done in [START_REF] Alauzet | A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes[END_REF] that the intersection traces and their resulting polygons are convex. This is only true for a boolean intersection over convex polyhedra.

Tolerance and degeneracies handling

An epsilon-approach is used to cope with numerical errors and an interference zone (noted I z ) surrounding any triangle is considered as in [START_REF] Levent Gursoz | Boolean set operations on nonmanifold boundary representation objects[END_REF]. In order to get a robust answer and to minimize the point creation, it is required to handle degeneracies carefully and to prioritize the tests by detecting first if any intersection point is in z N , then in z E and finally in z T . This is approach is opposed to [START_REF] Edelsbrunner | Simulation of simplicity : a technique to cope with degenerate cases in geometric algorithms[END_REF] where degeneracies are rejected : for an intersection problem, degeneracies contain the sufficient intersections information (cf. Fig. 12). The degenerated situations are :

• A vertex falling either on z N , z E or z T of another triangle • An edge intersecting z E or lying on z T of another triangle • Two triangles having their z T interfering (overlapping triangles) Because of the initial nodes merging at the initialization step, if we have two coincident vertices, it means that at least one of them is a created intersection point.

The five following algorithms are necessary and sufficient bricks to cope with all degeneracies and construct a robust Triangle-Triangle intersection algorithm.

Vertex-Inside Edge intersection (same support line). Let P 0 P 1 be the edge, L its length, Q the vertex and s = ||P 0 Q|| L . As it is assumed that P 0 , P 1 and Q are aligned in this test,

   Q ∈ I z ⇐⇒ s ∈ -L , 1 + L Q ∈ z N ⇐⇒ s ∈ -L , L ∪ 1 -L , 1 + L Q ∈ z E ⇐⇒ s ∈ I z \ z E
There is no intersection otherwise.

Vertex-Inside Triangle intersection (coplanar case). The three signed distances between the vertex Q and the edges are computed.

1. Q ∈ z N ⇐⇒ two of them have an absolute value lesser than .

2. Q ∈ z E ⇐⇒ one of them has an absolute value lesser than and the two others are strictly greater than .

3. Q ∈ z T ⇐⇒ the three are strictly greater than .

4. There is no intersection otherwise.

Non coplanar Edge-Plane intersection. Let P 0 P 1 be the edge, L its length. Let s note Q 0 and n the director of the plane. The intersection point I is then given by I = P 0 + sP 0 P 1 , where s = n.Q 0 P 0 n.P 1 P 0 . Then the edge intersects the plane if and only if s ∈ -L , 1 + L .

Overlapping Edge-Edge intersection. Assuming that four points are supported by the same line, two dot product allows to simply sort the vertices on the line and to retrieve none, one or two vertices for respectively nonoverlapping, single-shared vertex (z N interference) and overlapping cases (z E interference).

Coplanar Edge-Edge intersection. Let P 0 P 1 and Q 0 Q 1 be two edges, L 1 and L 2 their respective lengths. This algorithm is based on the traditional parametric approach [START_REF] Goldman | Graphics Gems[END_REF] for 3D lines :

1. Compute the cross product w = P 0 P 1 × Q 0 Q 1 and its square norm w 2 . 2. If w 2 < 2 then the support lines are parallel, the distance between them is then given by : µ

= ||P 0 Q 0 -Q 0 Q 1 .P 0 Q 0 ||Q 0 Q 1 || || (a)
if µ< the edges are supported by the same line. Do the overlapping Edge-Edge test. (b) Otherwise there is no intersection 3. Otherwise lines are intersecting at a unique point since they are assumed to be coplanar so it cannot be an agonic situation. Hence the two following computed parameters s and t give the common intersecting point :

   P 0 + sP 0 P 1 = Q 0 + tQ 0 Q 1 s = (P 0 Q 0 × Q 0 Q 1 ).w/w 2 t = (P 0 P 1 × Q 0 P 0 ).w/w 2 (a) If s ∈ -L 1 , 1 + L 1 and t ∈ -L 2 , 1 + L 2 ,
ii. If s ∈ L 1 , 1 -L 1 and t ∈ L 2 , 1 -L 2 (z E interference), the
intersecting point is created. (b) In any case the intersecting point is appended to an edge s node list if it belongs strictly to its interior.

Triangle/Triangle intersection

The triangle/triangle intersection algorithm is inspired from the intersection predicate [START_REF] Devillers | Faster Triangle-Triangle Intersection Tests[END_REF] extended to provide the intersection segments. The six signed distances of each vertex to the planar support of the other triangle are first computed. A quick analysis of these values allows discarding any nonintersecting configuration : either one of the two triangles is at a distance from the other triangle s support plane greater than the given tolerance or both are reciprocally positioned as in case b on Fig. 12 meaning that they could share at best a vertex. Fig. 12 illustrates the six possible positions of a triangle regarding the other triangle s plane. The algorithm deals with case f apart from the other cases.

Case b to e (non-overlapping supporting planes).

For each triangle we compute the segment trace by computing the required Plane-Edge intersection points. In case of degeneracies the segment is partially (case d) or fully available (case b and c). So we basically need from zero to four points to create using a Plane-Edge intersection test to get the right intersection trace. We then do an Edge-Edge overlapping test, or a Vertex-Inside-Edge test, or a Vertex-Inside-Triangle test to actually confirm the intersection and update the trace data structure. The trace (point or segment) is appended to the traces of the triangles falling in case d and e. The trace vertices are appended to the appropriate edges nodes list.

Case f (both triangles having the same support plane). We first compute the 18 signed distances between each vertex to the other triangle's edges. If none of the triangles is inside the other one, we compute the appropriate Coplanar Edge-Edge intersections to get the set of intersection points and associated segments. This is the most costly case as we can proceed up to 6 Edge-Edge intersection tests. If any intersection point falls in the edge interior, it is appended to its list. If any intersection point falls inside a triangle interior, the segment is appended to its list as well.

Nodes merging

Coincident nodes need to be merged to ensure overall conformity. The intersection process has produced many redundant points even if a special care has been taken to avoid redundant point creation at the Triangle-Triangle level. Two triangles sharing an edge will indeed produce twice the same intersection point if the shared edge intersects another triangle. This could have been addressed by keeping a record of any Triangle-Edge intersection but this solution is quite expensive in CPU. It has been chosen to proceed with an overall nodes merging (based on a kd-tree structure).

The tolerance used for merging must be the same as for intersection tests to avoid that any edge or triangle gets out of its initial interference zone. It is ensured that way to not create new intersections due to the moving of nodes. This is a major improvement since the initial version [START_REF] Landier | Boolean Operations on Arbitrary Polyhedral Meshes[END_REF], the intersection solving is no more iterative.

Splitting the triangles

The current implementation of this part is based on a constrained Delaunay triangulation [START_REF] Borouchaki | Aspects of 2-D Delaunay mesh generation[END_REF] applied to each triangle to split with its traces. This approach is very robust but too slow in regard with the targeted applications. In the conclusion section the ideas of the future way of proceeding will be given.

Building maPH elements with triangular faces

This geometrical step is done by traversing the conformal triangular cloud and gathering the appropriate set of triangles forming enclosed volumes. Since the cloud is conformal, we can create a neighborhood table that gives for any triangle its neighbors sharing an edge with it. But most of the cloud s edges are non-manifold, i.e. shared by more than two triangles. So we need to select for any triangle and for each orientation of it (both sides) the three right neighbors that will contribute to an enclosed volume. These right neighbors for a given oriented triangle t are those that minimize their dihedral angles with t (cf. Fig. 13.a).

Rather than computing this minimum per edge and per triangle that would lead to a lot of redundant calculations, we sort the triangles (taking into account the two orientations) sharing an edge E 0 E 1 (cf. Fig. 13b) like the pages of a book taking arbitrarily one of them as page number one. In this even sorted list, each pairs of consecutive elements gives the right mutual neighbors. We also add to this list a pair joining the opposite triangles of the first and the last one to close the loop like joining the book s cover. If we note t the opposite orientation of t, the five pairs for the case on Fig. 13b will be : (t 1 , t 2 ), (t 2 , t 3 ), (t 3 , t 4 ), (t 4 , t 5 ), (t 5 , t 1 ).

For the sorting we need to build a monotonically increasing function q for any triangle pair (t i , t j ) sharing an edge E 0 E 1 . Let s note n i and n j their normals. The algorithm proposed here is more robust than the one proposed in [START_REF] Landier | Boolean Operations on Arbitrary Polyhedral Meshes[END_REF]. The split of triangle can indeed generate very poor quality triangles that induce failure on normal computing (cross product error) and orientation predicates. So we rather preserve normals computed on the initial triangles (before splitting) and assign them to split triangles. The inputs for computing the q function are therefore non-degenerated and produce valid results :

q = π + µ * AT AN 2(s, c) (1)
where : Having a sorted list of triangle pairs, we can create a manifold neighboring for the triangles in both orientations by mutually associating as neighbor the triangles of each pair. This information is then used to traverse the triangles cloud with a flood fill algorithm to gather the triangles by element : any triangle set with the same color is a maPH.

       n k = n i × n j µ = SIGN (E 0 E 1 .n k ) s = ||n k ||(sine) c = ||n i .n j ||(cosine)

Building maPH elements for a prioritized mesh

When a mesh is prioritized (the yellow mesh on Fig. 15), it means that is has to be embedded into another mesh. In this case, only its outer skin is involved in the intersection process with the entire embedding mesh (Fig. 15b) because it has to be preserved as much as possible. Once its skin has been imprinted into the embedding mesh, its inner topology needs to be modified in the vicinity of this new surface to match it (Fig. 15c) in order to get a conformal result (Fig. 15d). Rather than computing the intersections again between the new skin and the interior mesh, a topological approach has been chosen : we gather the triangles on the new skin coming from the same initial polygons. We can then tap individually each open cell on the vicinity of the modified surface by refining the outer contour of these open cells (Fig. 16).

Aggregating the triangles : building final aPH elements

For a given maPH with triangular faces, we want to aggregate its triangles to get back to a polygonal representation. The resulting polygons must be admissible and conformity between them must be preserved so we gather the triangles satisfying the following rules :

1. They have the same polygon ancestor (using ancPG mapping, cf. 1.6) 2. They form a connected set with a single boundary loop 3. They are shared by the same two maPHs (for preserving conformity)

We first create a table giving the two polyhedral cells that share each triangle. For each triangle set coming from the same initial polygon, we separate the triangles into smaller subsets that share the same cells. A flood fill algorithm ensures to have at the end only subsets with a single boundary loop.

Optional Concave polygons split. Because concavity can be an issue for some applications (e.g. Finite Volume Method for CFD) requiring having the center of the faces inside the face to be more accurate, an extra feature has been added to optionally split the concave sets into convex ones. Because the entities to split are triangulations rather than meshes the simple following algorithm is enough to get a natural cut for the concave polygons. The algorithm is depicted on Fig. 18 : it starts by finding the worst concavity over the contour (point C). From the oriented edge E ending on C (orange edge) the triangles sharing C are traversed to detect the best cutting edge : the one which makes an angle smaller but as close as possible to 180 • with E (green edge E ). If E ends on a contour node, a convex bit has been obtained and we start again with the remaining contour. Otherwise E becomes E and the cutting is carried on. At the end of this aggregation step, elements are maPH with polygonal faces and we have a new mapping ancPGa giving for each maPH face its original polygon ancestor.

Classification

The classification is not done individually for each maPH. This would imply to geometrically localize the maPH which can be costly. We rather classify them topologically in two steps. First maPHs attached to the pure skin (cf. 1.5) are considered and classified and second the other elements are straightforwardly classified by a flood fill algorithm for which the delimiting boundaries are pure skin polygons (Fig. 19). The classification predicate is based on skin s normal orientation in regards with the considered skin elements. If a skin element has the skin normal inward (yellow and blue elements on Fig. 19), this element is localized without ambiguity as being outside the mesh having the considered skin. Elements sharing the skin face are therefore in the common part (green elements). If no outside elements are found, it means that the input meshes are two meshes of the same domain : their skin fully overlap. We can end up with two zones (rather than three for a partial overlapping) if one mesh is fully inside the other one or if they have a partial contact, i.e. their skin is locally supported by the same surface (and none is inside the other one).

Conservative remapping

Let s consider two intersecting meshes M 1 and M 2 (cf. Fig. 20a) and the mesh M 1 = (M 1 \ M 2 ) ∪ (M 1 ∩ M 2 ) (cf. Fig. 20b). M 1 represents the new mesh of the domain occupied by M 1 . Having the mapping ancPGa (cf. 5.7), we can detect in M 1 any polygon bit from M 1 . We can then use the neighbor graph for M 1 cells to retrieve the mapping M 1 ↔ M 1 using again a flood fill algorithm for which the delimiting boundaries are M 1 polygon bits. Swapping indices in the preceding gives the M 2 ↔ M 2 mapping. The break down for a given M 1 cell is shown on figure 20c.

Applications and results

The method has been implemented in templatized C++ in the Cassiopee Software [START_REF] Benoît | Cassiopee : a CFD pre-and postprocessing tool[END_REF]. This section gives some test results for several ascending size problems covering the different boolean operations on different type of operands. All the test have been done using 1.e-13 as absolut tolerance and all the polygonal aggregations are convex. All the tests and performance measures have been done on a single Intel Xeon core @ 2.8 GHz.

Prioritized union of two volume meshes

We consider a spherical boundary layer mesh immersed in a octal background mesh. This is the simplified typical configuration for a CFD viscous external flow around a body (cf. Fig. 21a). Before processing it, the octree has been decimated by discarding any cell having a node inside the inner sphere because the interior of the boby is irrelevant for that kind of applications. The conformal result is depicted in Fig. 21b and the performances are available in table 1. Step CPU time (s) 1) Init ( 16 Table 1: Performances for the 6.1 case.

Intersection, two volume meshes

Let s consider now two identical conformal polyhedral mesh operands M 1 and M 2 obtained from an octree having a refinement at its centroid (cf. Fig. 22) in an intersecting position. They both have 1,576 polyhedra.

The figures 23 shows the resulting volume meshes of the difference and the non-prioritized intersection of them. It contains 4,821 polyhedra which is less than the double of the initial number of elements. With a tetrahedral approach (i.e. splitting all the polyhedra into tetraherdons first) we would en up with an increase of at least one order of magnitude. The polyhedral approach si therefore better fitted to ouput the resulting mesh for boolean operations. The performance are shown in the table 2.

Union of a surface mesh with a volume mesh

We consider a light triangulated cat surface with 740 triangles (Fig. 24a) fully immersed in a Cartesian grid (29,440 hexs, 91,300 quads). The algorithm generates here the conformal union, i.e. the surface is integrated into the mesh. A view of the clipped mesh is depicted in Fig. 24b and the performance details are given in table 3. A 5.8 speed-up factor has been obtained since [START_REF] Landier | Boolean Operations on Arbitrary Polyhedral Meshes[END_REF].

Union of two surface meshes

Even though this algorithm is more dedicated for cases with at least one volume mesh input, it is interesting to compare it with a pure surface algorithm [START_REF] Douze | QuickCSG : Arbitrary and Faster Boolean Combinations of N Solids[END_REF]. We consider here a case that has been treated in the paper,

Step CPU time (s) 1) Init (11, the union of a Buddha and a lion shown on Fig. 25a. The case is approximatively 1.48 million triangles. In order to make a fair comparison, polygon aggregation has been disabled as the the output mesh is triangular. The time reported by the author for this case is 1.027 sec. for a multithreaded run (4 threads) on a slightly slower processor (@2.7 GHz). Considering that our implementation is sequential, there code is around eight times faster (cf. table 4) than our current implementation. This is mainly due to the cell construct and classification steps that are currently not optimized for surface meshes. But one order of magnitude is acceptable regarding the versatility of our algorithm and the remaining ways of improvement given in the conclusion.

The algorithm shows a good robustness with this case having triangles of very different size at the bottom of the lion model (as depicted in 25b). Step CPU time (s) 6.5. Difference between a volume mesh and a surface mesh : cut-cell meshing No 1 Here we present the bottom part of a landgear (cf. Fig. 26a), having 116,000 triangles immersed into an octal mesh with 303,000 polyhedra (1,067,178 polygons). The resulting cut-cell mesh is shown depicted in Fig. 27a. The performances (cf. table 5 have been significantly improved (speed up factor 20) since [START_REF] Landier | Boolean Operations on Arbitrary Polyhedral Meshes[END_REF]. A lot of ways of improvement remains though as expressed in the conclusion.

Conclusion and perspectives

An algorithm with a O(nlog(n)) algorithmic complexity has been described to resolve boolean operations for arbitrary polyhedral meshes and has been implemented successfully. The current tests have shown that even if some good progresses have been made since the first implementation tests, the current performances are roughly around 1,000 polyhedra constructed per second which is not good enough to deal with transient industrial CFD cases. As a Pre or Post tool, the performance can already be considered as satisfactory though. But there are plenty of ways of improvements.

The first issue of this algorithm comes from the fact that the triangular intersection kernel has been designed to handle any kind of configuration. So it could handle upon entry some non-conformal meshes as long as they are consistently oriented. This is because there are no assumption on the input connectivity, the set of input triangles (once the polygons have been triangulated) is treated as a soup. This is powerful and allows covering a wider range of cases but efficiency would be significantly improved by using this connectivity information for instance for the localization as described in [START_REF] Alauzet | P1-conservative solution interpolation on unstructured triangular meshes[END_REF] or [START_REF] Farrell | Conservative interpolation between volume meshes by local Galerkin projection[END_REF]. Almost all targeted 3D applications deal with conformal meshes upon entry.

The second issue comes from the triangles split stage. Using a constrained-Delaunay algorithm is obviously too heavy for the purpose and is the most sensitive part to robustness issues. Using ear-clipping techniques could be an improvement [ebe98, hel98], but the true enhancement will be to find a solution that does not generate triangles at all. The polygons could still be triangulated to compute the intersections in order to facilitate the intersection kernel design, but we could imagine other ways of cutting the polygons along the intersection traces to work on a polygon cloud rather than a heavy triangular cloud. This would remove the reaggregation stage, woud light the polygon sorting and the cell construction stage would deliver directly the maPHs.

Another way of improvement would be to somehow cut and classify simultaneously the polygon bits. This would avoid to create useless elements, meaning elements rejected at the classification stage.

When all these algorithm changes will be implemented and validated, the code will be multithreaded and specialized to focus on the conservative problem specifically, keeping as an option to output or not the geometry upon exit.

Figure 1 :

 1 Figure 1: Two overlapping meshes, their intersection zone in green.

Figure 2 :

 2 Figure 2: Two overlapping meshes the yellow mesh is prioritized, their intersection zone in green.

Figure 3 :

 3 Figure 3: Cut-cell meshing : a surface mesh cuts a volume mesh (intersection zone in green).

Figure 4 :

 4 Figure 4: Pure surface problem as in a CSG evaluation (intersecting zone in green).

Figure 5 :

 5 Figure 5: (a) aPG ; (b) three non-admissible polygons.

Figure 6 :

 6 Figure 6: (a) and (b) some aPHs ; (c) non-admissible case : a tetrahedron with cubic hole.

Figure 7 :

 7 Figure 7: Algorithm s scheme.

Figure 8 :

 8 Figure 8: (a) initial aMHs M 1 and M 2 ; (b) working set for intersection after initializing a pre-conditioning for a pure polyhedral problem.

Figure 9 :

 9 Figure 9: (a) Triangles cloud ; (b) Intersections traces.

Figure 10 :

 10 Figure 10: (a) Split triangle ; (b) Resulting conformal cloud.

Figure 11 :

 11 Figure 11: Interference zone for a triangle : the location of points at a distance less than the tolerance. z N is a ball around each vertices, z E is a partial cylinder around each edges.

Figure 12 :

 12 Figure 12: one triangle s entities (in red) that are considered for intersection tests with any triangle supported by the plane.

Figure 13 :

 13 Figure 13: (a) t s right neighbors (green) ; (b) sorting the triangle sharing an edge.

Figure 14 :

 14 Figure 14: monotonic angular function q.

Figure 15 :

 15 Figure 15: (a) a prioritized mesh hiding another mesh ; (b) polygon-polyhedron intersection process ; (c) gluing the new skin and the interior mesh ; (d) conformal result.

Figure 16 :

 16 Figure 16: Tapping the open cells to match the new polygonal surface.

Figure 17 :

 17 Figure 17: (a) split triangles on a sphere colored by initial quads ; (b) convex aggregation ensuring conformity with the imprinting mesh.

Figure 18 :

 18 Figure 18: (a) getting the best cutting edge ; (b) split process.

Figure 19 :

 19 Figure 19: (a) skin elements classification ; (b) flood filling.

Figure 20 :

 20 Figure 20: (a) Two intersecting octrees M 1 and M 2 ; (b)M 1 ; (c) one M 1 cell s break down.

Figure 21 :

 21 Figure 21: (a) a spherical boundary layer mesh appended into an octree ; (b) conformal union.

Figure 22 :

 22 Figure 22: (a) Two intersecting octrees M 1 (blue) and M 2 (red) ;(b) octree operand s inner structure.

Figure 23 :

 23 Figure 23: (a) M 1 ∩ M 2 ; (b) M 1 \ M 2 .

Figure 24 :

 24 Figure 24: (a) triangular surface mesh ; (b) conformal union with a cartesian grid.

Figure 26 :

 26 Figure 26: (a) bottom part of a landgear (b) complete model.

Figure 27 :

 27 Figure 27: clipped view of the cut-cell meshes

Table 2 :

 2 Performances for the 6.2 case.

	784 polygons)	0.03
	2) Triangulation (10,322 polygons)	0.21
	3) Intersections(22,757 triangles)	0.67
	4) Triangle split(58,207 triangles)	1.30
	5) Cell construct (5,116 polyhedra)	1.35
	6) Polygons Aggregation	0.6
	7) Classification	0.18
	Total	4.34
	Step	CPU time (s)
	1) Init (92,000 polygons)	0.37
	2) Triangulation (25,460 polygons)	0.02
	3) Intersections(50,182 triangles)	1.29
	4) Triangle split(111,098 triangles)	2.72
	5) Cell construct (10,593 polyhedra)	2.48
	6) Polygons Aggregation	1.4
	7) Classification	1.03
	Total	9.31

Table 3 :

 3 Performances for the 6.3 case.

Table 4 :

 4 Performances for the 6.4 case.

Table 5 :

 5 Performances for the 6.5 case.

	Step

Table 6 :

 6 Performances for the 6.6 case.

Difference between a volume mesh and a surface mesh : cut-cell meshing

No 2 This case is a more complex landgear model : 831,000 triangles (cf. Fig. 26b). The immersing octree has 127,000 polyhedra (450,000 polygons). The resulting cut-cell mesh is shown depicted in Fig. 27b. It took 353 sec. to compute this cut-cell mesh as shown in table 6.


Christelle Miqueu

Frederic Plantier

Kamila Marques Fernandes

Carine Malheiro

Bernard Delanghe

Water Vapor Adsorption/Desorption on Two Fully Characterized Commercial Activated Carbons

Keywords: microporous, activated carbon, water

Introduction

Activated carbons (ACs) are widely used as adsorbents for removing pollutants from streams in industrial processes because of their powerful and various adsorption properties. The presence of water in ACs is known to have an important negative impact both on the capacity and on the selectivity for the removal of organic or inorganic contaminants in the industrial ACs [1][2][3].

The adsorption mechanism of water on ACs is quite different from that of simpler fluids such as nitrogen or alkanes [4]. While these simple compounds (e.g. nitrogen, argon, methane) present most usually type I isotherms (IUPAC classification) on ACs, water adsorption isotherm is S-shape, similar to type IV or V depending on the density of active sites. The difference in these behaviours is classically assigned both to the weak water-carbon interactions and to the strong hydrogen bonds that lead to water clusters formation (see the two interesting reviews of water behaviour in porous carbons by Brennan et al. [START_REF] Brennan | Colloids Surfaces A Physicochem[END_REF] and Mowla et al. [START_REF] Mowla | Adsorption of Water Vapor on Activated Carbon: A Brief Overview[END_REF]).

Several investigations have been carried out on the measurement and the understanding of water adsorption on graphitic microporous materials (e.g. AC, ACF, SWNT) [7][8][9][10][11], sometimes with a complete surface chemistry and pore structure analysis [12,13]. However, the experiments have always been performed at a unique temperature, close to the ambient one, except in the work of Ohba et al. [14] and Nastaj and Aleksandrzak [15]. In this work, the adsorption behaviour is analysed on a wide range of temperature thanks to new experiments and modelling.

Methods

Experimental section

In the present study, the adsorption/desorption of water vapor on two commercial microporous ACs is measured at three temperatures (353, 369 and 386 K) by means of a magnetic suspension balance, in order to investigate the influence of temperature on the adsorptive properties. The two ACs are fully characterized in terms of structural properties and surface activity. The difference in their Pore Size Distribution (PSD) -more or less extended -allows discussing the impact of PSD on water adsorption.

Thermodynamic modelling

Few years ago, Do and Do [16] developed a model (DD) able to explain the role of active sites and microscopic structure of AC in the adsorption of water. This model is based on a two-step mechanism: a water cluster formation on active sites followed by the penetration of the clusters into the micropores. Since its introduction, several modifications concerning the size of clusters or the adsorption on actives sites have been proposed for this model. In their critical review of analytic approaches for the modelling of water adsorption on carbons, Furmaniak et al. [17] have shown the efficiency of DD derived models on water adsorption on ACs. In the present study, we test the DD model and its two principal modifications [18,19] on the experimental isotherms of the two ACs.

Results

The effect of temperature is clearly shown on the adsorption/desorption hysteresis but is negligible on the total adsorptive capacity of the AC. The different textural properties (specific surface area, pore volume and pore size distribution) of the two ACs have an evident impact on both the slope of the isotherm corresponding to the adsorption in micropores and the total capacity of adsorption of the AC.

  The original DD equation and two of its modifications were used to model the measured isotherms. All the isotherms could only be well-fitted by the version of Do and Do model improved by Furmaniak et al. (HDD).

Figure 1 :

 1 Figure 1: water vapor adsorption isotherm on Carboxen-1012® : o experiments, ---DD equation, ⎯ DDN equation, ⋅⋅⋅⋅ HDD equation [19].


Julien Lemaire
email: julien.lemaire@centralesupelec.fr

Claire-Line Blanc

Marc-André Fannyduval

Dominique Pareau Theoleyre

Lgpm

Centralesupélec

Purification of pentoses from hemicellulosic hydrolysates with sulfuric acid recovery by using electrodialysis

Keywords: electrodialysis, pentoses, purification, acid recycling, green chemistry. Highlights

The valorization of lignocellulosic biomass as a renewable carbon source is growing in chemical industries, particularly in the agro-industrial sector. Many chemicals compounds and bio-based intermediates can be produced but their production needs to be more costcompetitive. The valorization of pentoses in hemicellulosic hydrolysates, obtained by using dilute sulfuric acid, is of growing interest. However, current downstream processes which involve a partial or complete neutralization of the acid are not satisfactory for economic and environmental reasons.

This work presents a method of purification of pentoses with sulfuric acid recovery which reduces water and chemicals consumptions. The results obtained at the laboratory scale with wheat bran hydrolysates are very promising. The process is based on the combination of ultrafiltration, conventional electrodialysis and ion-exchange. A special organic UF membrane (Alpha Laval -UFX10pHt), resistant to acidic conditions, removed totallymacromolecules which can damage the electrodialysis unit by precipitation, with good mean permeate flow rate (24 L.h -1 .m -2 till VCF = 4.4). Then, conventional electrodialysis was performed to recover most of sulfuric acid (>80%) without losing sugars (< 1%) with an acceptable faradic yield (70%). The specific energy consumption of the electrodialysis stack was interesting (0.6 kWh per kgof H 2 SO 4 recovered and 4.2 kWh per m 3 of hydrolysate).

Finally, the complete demineralization (conductivity < 10 µS.cm -1 ) and discoloration (420 nm absorbance < 0.01) of the pentoses solution was obtained by ion-exchange with about a 10fold increase of resins capacity (20 BV) compared to conventional processes with a neutralization step (2 BV).

Introduction

Lignocellulosic biomass is an attractive renewable carbon source for agro-industries, such as food or forestry industries. Actually, it generates large amounts of coproducts (wheat straw and bran, sugar beet pulp, wood waste …) which are often poorly valued [START_REF] Jacquemin | Evaluation of the technical and environmental performances of extraction and purification processes of arabinoxylans from wheat straw and bran[END_REF]. Many chemicals compounds and bio-based intermediates can be produced from these lignocellulosic residues such as sugars, paper pulp, surfactants, polymers or bioethanol. In the frame of sustainable development, the green chemistry and the valorization of these coproducts to produce bio-based molecules is of growing interest [START_REF] Cheng | Sugarcane bagasse hemicellulose hydrolysate for ethanol production by acid recovery process[END_REF][START_REF] Huang | A review of separation technologies in current and future biorefineries[END_REF].

Lignocellulosic biomass is mainly composed of cellulose (40 to 50% w ), lignins (10 to 35% w ) and hemicellulose (20 to 45% w ) which is a copolymer of pentoses and hexoses.

Generally, the hydrolysis of lignocellulosic biomass is very difficult because of its recalcitrant structure (low porosity, crystallinity, high molecular weights). This treatment aims at extracting cellulose fibers by solubilizing lignins and hemicellulose. Three main processes are used at industrial scale: Kraft process using alkaline solution like caustic soda in paper industry, "Organo-solv" processes using organic solvents such as acetone, ethanol or acetic acid, and hydrolysis with dilute inorganic acids [START_REF] Fitzpatrick | A biorefinery processing perspective: treatment of lignocellulosic materials for the production of value-added products[END_REF][START_REF] Sarkar | Bioethanol production from agricultural wastes: An overview[END_REF]. However, others methods using steam, hot water or a combination of enzymes can also be used. After treatment, a complex mixture of pentoses, hexoses, lignins and mineral salts must be separated to value them.

The present article deals with the valorization of pentoses in hydrolysates obtained by using dilute inorganic acids, more particularly sulfuric acid. Indeed, pentoses have found many applications recently (xylitol, bio-based building blocks, surfactants and biopolymers).

Currently, the industrial methods begin with a partial or complete neutralization of the inorganic acid in order to precipitate lignins, proteins and eventually metal residues by using caustic soda or lime. Then pentoses are purified by ion-exchange [START_REF] Asko | Process for making xylose[END_REF][START_REF] Ballerini | Procédé et unité de production en continu d'un mélange de sucres contenant au moins 80% de xylose à partir d'un substrat lignocellulosique[END_REF][START_REF] Ferreira | Process for the production of crystalline xylose from sugar cane bagasse, crystalline xylose obtained by said process, process for the production of xylitol from the said xylose and crystalline xylitol obtained thereby[END_REF], adsorption, chromatography or crystallization [START_REF] Heikkilä | Method for recovering xylose[END_REF][START_REF] Heikkilä | Method of producing xylose[END_REF][START_REF] Heikkilä | Process of producing xylose and dissolving pulp[END_REF]. This process is not satisfactory for economic and environmental reasons. Indeed, large amount of base is required, resulting in greatly increased amount of salts, needing more water and chemical reagents to separate them.

Moreover it generates large volume of effluent and the acid catalyst cannot be recycled to the hydrolysis step.

For a decade, the use of electrodialysis (ED) has been growing because of its efficiency to separate ions without consuming chemical reagents or water. ED is an electrochemical separation technique which uses an electric potential as driving force to move ions through selective ion-exchange membranes in order to separate them from others molecules present in solution [START_REF] Cheng | Fermentation of pretreated sugarcane bagasse hemicellulose hydrolysate to ethanol by Pachysolentannophilus[END_REF][START_REF] Vyas | Separation of inorganic and organic acids from glyoxal by electrodialysis[END_REF]. ED has been applied to demineralize aqueous solutions, desalinate seawater and purify wastewater [START_REF] Park | Removal of hardness ions from tap water using electromembrane processes[END_REF][START_REF] Thang | Detailed investigation of an electrodialytic process during the separation of lactic acid from a complex mixture[END_REF][START_REF] Thang | Electrodialysis versus chromatography for desalting silage juice: Comparison of both processes with regard to energy consumption[END_REF]. Besides, ED has been widely used in bioprocesses to separate organic acids (lactic, citric, acetic, succinic oxalic) and amino acids [START_REF] Huang | Application of electrodialysis to the production of organic acids: State-of-the-art and recent developments[END_REF][START_REF] Blanc | Purification of organic acids by chromatography: Adsorption isotherms and impact of elution flow rate[END_REF][START_REF] Lee | Recovery of lactic acid from fermentation broth by the two-stage process of nanofiltration and water-splitting electrodialysis[END_REF][START_REF] Lee | A feasibility study on the multistage process for the oxalic acid pretreatment of a lignocellulosic biomass using electrodialysis[END_REF].

Within the framework of pentoses purification in hemicellulosic hydrolysates, ED proved to be an alternative promising demineralization method but partial or complete neutralization was still required [START_REF] Cheng | Sugarcane bagasse hemicellulose hydrolysate for ethanol production by acid recovery process[END_REF][START_REF] Park | Method of producing xylitol using hydrolysate containing xylose and arabinose prepared from byproduct of tropical fruit biomass[END_REF][START_REF] Lee | Economic process for producing xylose from hydrolysate using electrodialysis and direct recovery method[END_REF]] so as to eliminate macromolecules (lignins and proteins) which could precipitate during ED. Indeed, ED membranes are quite expensive and are dramatically damaged by clogging.

The objective of this study was to investigate the feasibility of sulfuric acid recovery from lignocellulosic hydrolysates in the frame of pentoses valorization. The present process combines ultrafiltration (UF), conventional electrodialysis and ion-exchange (IE) and does not need neutralization step, that is a significant advantage in terms of economy and environment. First, the influence of the nature (mineral or organic) and the cut-off of UF membranes on the elimination of macromolecules precipitating during ED, due to a pH increase, were studied. Then the ED performances were investigated for acid recovery and demineralization. Finally, a polishing treatment by IE was performed to get a solution of sugars with very low conductivity (< 10 µS.cm -1 ) and totally discolored. This work proposes an eco-efficient process to purify pentoses from hemicellulosic hydrolysates.

Materials and methods

Hemicellulosic hydrolysate

The lignocellulosic hydrolysate was produced from wheat bran milled then mixed with a dilute sulfuric acid solution (≈ 10 g.L -1 ). Its main properties are given in table 1. Before performing ultrafiltration, centrifugation was required to remove suspended matter, whose content is about 1.5 g.L -1 . The centrifugal pump could reach 60 bars and the cross-flow rates were generally comprised between 5 and 100 L.h -1 .m -2 with operating conditions recommended by suppliers.

The temperature was controlled between 20 to 80°C by using a heat exchanger combined with a thermostat. The volume of the UF tank containing the retentate was about 8 L.

Conventional electrodialysis unit

Our conventional ED unit (EurodiaIndustrie) is composed of one stack with 10 unit cells, a voltage generator, three tanks (capacity = 2 L) containing the brine, the product and the electrolyte and three pumps ensuring the flow of each solution through the corresponding compartment (table 3). Conventional ED was used to transfer acids and salts from the product to the brine. The conductivity, pH, acid concentration, sugar concentration and ion concentration of the brine and the product were monitored as well as the current intensity.

This unit was optimized for demineralization by the manufacturer. Operating conditions (flow rates, current, voltage, electrolyte and initial brine composition) were fixed according to manufacturer's recommendations. Conventional ED is generally performed with a constant tension so the limiting current density is not a constant and decreases during demineralization. Tension (12 V) was determined to work always under the limiting current density so as to optimize energy consumption and faradic yield.

Ion-exchange system

The polishing treatment by ion-exchange (IE) was performed at laboratory scale in two vertical double jacket glass columns operating in series, filled respectively with 350 mL of a strong anionic resin (LEWATIT S7468) in the OH form and a strong cationic resin (LEWATIT S2528) in the H form. Their inner diameter was 25 mm and the bed height 70 cm. A thermostat was used to maintain the water jacket at 40°C while the product was injected at room temperature at 4 BV.h -1 . BV is a common unit used to express volumes or flow rates as a function of the bed volume.

The flow rate was controlled by a peristaltic pump and the mobile phase flew from the top to the bottom of glass columns. An automatic sampling system was used at the output in order to monitor pH, conductivity, acid concentration, sugar concentration and ion concentration of the product.

The regeneration procedure for the anionic and cationic resins begins with the elution of 2 BV at 2 BV.h -1 of respectively 1M NaOH solution and 1M HCl solution in separated columns.

Then, columns are connected and resins are rinsed with reverse osmosis water till the conductivity of output solution remains constant (close to input conductivity).

Analytical methods

Conductivity and pH were measured with a 340i conductimeter/pH-meter from WTW. Dry matter was estimated by refractometry using a brixmeter (RFM732 Bellingham+Stanley).

Sample color was estimated by measuring absorbance at 420 nm with a spectrophotometer (UV-1800, Shimadzu). H 2 SO 4 concentration was evaluated by titration with 0.1 M NaOH from the volume required to reach pH 4.0, so as to consider only strong acidity.

Sugars were analysed with an HPLC system (Ultimate 3000, Dionex) equipped with a pump, an auto sampler and a RI-101 refractometer at 35 °C (Shodex). The analytical column was an Aminex HPX-87H (Biorad) along with a matching guard column (Micro-Guard cartridge, Biorad). The column temperature was maintained at 45 °C with a column oven controller. The mobile phase was 2 mM H 2 SO 4 in milli-Q water (Direct 8, Millipore),degassed by an on-line vacuum degasser. The flowrate was set to 0.5 mL.min -1 and the injection volume to 10 µL.

Anions and cations were analysed with an HPIC system (ICS-5000 + , Thermo Scientific Dionex) equipped with two pumps, an auto sampler, two eluent generators, a column oven controller set to 35 °C and two suppressors. Detection is performed by conductivity. For anion analysis, the column was an Ionpack AS11HC 2x250 mm along with a matching guard column (AG11HC 2x50 mm). The eluent generator produced a 30 mM KOH solution for the mobile phase. The flowrate was set to 0.3 mL.min -1 , the suppressor to 23 mA and the injection volume to 2.5 µL. For cation analysis, the column was an Ionpack CS16 3x250 mm along with a matching guard column (CG16 3x50 mm). The eluent generator produced a 30 mM methanesulfonic acid solution for the mobile phase. The flowrate was set to 0.36 mL.min - 1 , the suppressor to 32 mA and the injection volume to 10 µL.

Results and discussion

Removal of macromolecules by ultrafiltration

Macromolecules like lignins or proteins must be removed from the hydrolysate before performing ED because they will damage the electrodialysis stack by precipitation due to pH increase during the treatment. UF with ceramic membranes and organic membranes (2 flat sheets, total surface = 0.036 m2) was investigated to remove macromolecules, without pH adjustment so without reagents consumption in contrast with existing processes.

Temperature was set to 40°C and transmembrane pressure to 6 bar. So as to evaluate their performance, the amount of precipitates in hydrolysate samples before and after UF was measured at different pH, which was adjusted with soda (table 4). Precipitates were filtered on 0.22 µm PTFE filter then their dry weight was measured by a moisture analyzer (Sartorius MA150). Only the organic membranes (10 to 50 kD) were efficient to retain totally macromolecules which precipitate with increasing pH, although some of them had a higher cut-off than the ceramic membranes. These results highlighted the great influence of the membrane nature on macromolecules retention. Liu et al. [START_REF] Liu | Application of inorganic membranes in the alkali recovery process[END_REF] also found that permeate flux and rejection rate (for lignin removal) were not only determined by pore size of inorganic membrane, but also by membrane charge and hydrophobicity.The influence of membrane nature for the treatment of hemicellulosic hydrolysates is not well detailed in literature. Besides, the membrane geometry (tubular or flat sheets in a plate-and-frame module) can play also a significant role. Indeed, it affects the membrane fouling, concentration polarization or cake formation which impact the permeate flux and retention rates.

Initial permeate fluxes were respectively equal to 25, 28 and 94 L.h -1 .m -2 with 10, 20 and 50 kD organic membranes. A more detailed experiment was performed with the 10 kD organic membrane to evaluate UF performances till a volumetric concentration factor (VCF) equal to 4.4 (table 5). Indeed, generally the permeate flux decrease progressively owing to membrane fouling. The dead volume of the UF device was about 1 L, so the feed was initially slightly diluted with the rinsing water retained inside. Till VCF = 4.4, the mean flow rate of permeate remained quite good (24 L.h -1 .m -2 ), so the implementation at industrial scale is conceivable. Besides, the retention of macromolecules was highlighted by the drop of the absorbance at 420 nm below 0.5. Indeed, some of them are the main coloring agents.

Acid recovery and demineralization by conventional electrodialysis

Conventional ED was used to extract most of the sulfuric acid present in the lignocellulosic hydrolysate which is partially demineralized in the same time. Two hydrolysate samples, previously ultrafiltered with 10 kD organic membranes, were treated successively with the same brine. The brine was reused for the second treatment in order to increase its H 2 SO 4 concentration and made it reusable in hydrolysis step of lignocellulosic biomass.

These experiments aimed at proving the feasibility of acid recovery in the frame of pentoses purification in lignocellulosic hydrolysates.

The 1 st ED was performed with 2 L of hydrolysate and 2 L of fresh brine. The dead volume of the ED unit is about 0.5 L. So the feed was again slightly diluted with the rinsing water retained inside. Figure 1 presents the variation of conductivity, pH, current intensity and faradic yield over time. The product was almost totally demineralized (conductivity < 1 mS.cm -1 ) after 20 min of treatment, meanwhile its pH reached 2.9. The faradic yield decreased below 50% after 14 min and was equal to 62% on average. This low faradic yield was expected because of high mobility of H + that are difficult to keep in brine compartment. According to table 6, about 90% of sulfuric acid was transferred into the brine, meanwhile sugars remained almost completely in the product (> 99%). H 2 SO 4 concentration of the brine reached 5.9 g.L -1 , which was not enough to be used for hydrolysis step. This is the reason why this brine was reused for the 2 nd ED. The 2 nd ED was performed with 2.2 L of hydrolysate and 1.2 L of the brine recovered after the 1 st ED so as to get a H 2 SO 4 concentration up to 15 g.L -1 . As previously, the product was almost totally demineralized after 20 min and the same pH, conductivity and current intensity profiles were observed over time. About 80% of sulfuric acid was recovered in the reused brine, meanwhile most of sugars (> 99%) remained in the product (table 6). The H 2 SO 4 concentration of the brine reached 14.2 g.L -1 and its pH was equal to 1. So, this time, the brine could be recycled to the hydrolysis step.

A last ED experiment was performed with 2 L of hydrolysate and 2 L of fresh brine in order to study the transfer rate of acids and different salts during the treatment. Indeed, if acids are extracted faster than other salts (mainly sodium, potassium, ammonium, magnesium and calcium salts), ED could be performed advantageously in two steps: a first one with a reduced operation time to recover most of acids in a first brine, a second one to extract most of other salts in a second brine. This method could be used to limit the accumulation of other salts in the brine intended to be recycled for hydrolysis step. Figure 2 presents the recovery rates of acids and other salts in the brine over time. ED was performed during only 12 min so as to recover most of acidsand keep the faradic yield above 50%. In this case, the faradic yield remained acceptable (70%) and the specific energy consumption of the electrodialysis stack was quite interesting (0.6 kWh per kg of H 2 SO 4 recovered and 4.2 kWh per m 3 of hydrolysate). The recovery rates of major cations and anions are detailed. We observed that acids are transferred slightly faster than other salts but not enough to recover most of them without most of other salts. Consequently the implementation of ED in two steps did not appear advantageous for this kind of hydrolysates, containing mainly ammonium, potassium and calcium salts (table 1). Indeed, these cations were extracted as fast as acids (mainly sulfuric acid). Nevertheless, it could be advantageous for hydrolysates containing almost sodium or magnesium salts since these cations were recovered quite slower than acids (figure 2). The accumulation of ammonium, potassium and calcium salts in the brine recycled for hydrolysis step has to be watched and might require a periodic purge.

As the concentration of cations is quite low compared to acid, we expect that their accumulation in brine will be relatively slow. Thus, if a periodic purge is sometimes necessary, it must be only occasional. Currently, in a pilot scale study, the brine reused for hydrolysis was as efficient as fresh sulfuric acid to treat wheat bran. Indeed, hydrolysates produced with reused sulfuric acid had exactly the same content except for salts. The brine which has to be purged could be considered as a waste or might be valorized if it is relevant economically. For example, it could be treated by chromatography with ion-exchange resins to separate acids from salts.

Finally an additional polishing treatment by IE was required to remove salts completely and economically. Indeed, the faradic yield of ED dropped below 30% after 20 min when the product conductivity was around 1 mS.cm -1 .

Polishing treatment by ion-exchange

The product of ED was treated by IE to remove totally the salts and organic impurities which could be retained in the polymer matrix of resins. The strong anionic and cationic resins have respectively a total capacity of 1.0 and 1.75 eq. L bed -1 . Figure 3 presents the product pH and conductivity as a function of the volume injected. The same treatment was applied to a sample of hydrolysate neutralized with lime as in conventional processes, in order to highlight the advantages of the present process. were completely demineralized (conductivity < 10 µS.cm -1 ) before saturation of one of the resins, while only 2 BV of hydrolysate neutralized with lime were treated before saturation.

Consequently, the present process greatly reduces water and chemical reagents needs, particularly in the resin regeneration and rinsing steps. Besides, the product was totally discolored (absorbance at 420 nm < 0.01). Finally, the separation of sugars (glucose, xylose and arabinose) can be achieved classically by continuous chromatography (SMB, SSMB or ISMB methods) or crystallization [START_REF] Heikkilä | Method for recovering xylose[END_REF][START_REF] Heikkilä | Method of producing xylose[END_REF][START_REF] Heikkilä | Process of producing xylose and dissolving pulp[END_REF].

Conclusion

The developed process is a promising pathway to reduce energy, water and chemicals consumptions, the cost of pentoses purification and the impacts on environment. Currently, the improvement of downstream processing is a key factor to make biorefinery productions more cost-competitive. The results at the laboratory scale proved that pentoses can be purified eco-efficiently from dilute sulfuric acid hydrolysates of wheat bran, with acid recovery.

This new process is based on the combination of ultrafiltration, conventional electrodialysis and ion-exchange. First, the ultrafiltration step with organic membranes can efficiently remove macromolecules which can damage irreversibly the electrodialysis unit by precipitation. Then, most of the sulfuric acid can be recovered effectively by conventional electrodialysis. Most of other salts (mainly ammonium, potassium and calcium salts) are coextracted and their accumulation in the recycled brine has to be watched and might require anoccasional purge. Nevertheless, the recycling of sulfuric acid keeps very interesting economically. Finally, the polishing treatment by IE can fully demineralize and discolor the solution of pentoses whose purification can be achieved classically by continuous chromatography or crystallization.

In comparison with traditional processes that involve hydrolysate neutralization with lime or caustic soda, the present method gets several economic and environmental advantages: a) recovery of most of sulfuric acid that can be reused for hydrolysis step, b) saving of lime or caustic soda that would be required for neutralization, c) consecutive decrease of salts to be removed, resulting in energy, water and chemicals savings for demineralization, d) reduction of effluents and other wastes.

Further investigations will be done at a larger scale in order to study the process feasibility and reliability, meanwhile to optimize its performances.

Figure 1 -

 1 Figure 1 -Monitoring of conductivity and pH of brine and product and variation of current intensity and faradic yield during the 1 st ED with fresh brine

Figure 2 -

 2 Figure 2 -Recovery rate of acids and other salts over time during ED with fresh brine

Figure 3 -

 3 Figure 3 -Monitoring of the product pH and conductivity during demineralization by ion-exchange

Table 1 -Physico-chemical properties and composition of the lignocellulosic hydrolysate treated

 1

	Dry weight	8.2	%w
	pH	1.1	-
	Conductivity	34.5	mS.cm	-1
	Absorbance at 420 nm	2.2	-
	H 2 SO 4	8.7	g.L	-1
	Glucose	12.8
	Xylose	21.3	g.L	-1
	Arabinose	10.6
	Sodium	1.9
	Potassium	4.7
	Ammonium	14.8
	Magnesium	2.8
	Calcium	4.6
	Total cations	28.8	mEq.L -1
	Chlorure	2.0
	Nitrate	0.9
	Phosphate	24.3
	Sulfate	175.2
	Total anions	202.4
	2.2. Ultrafiltration device
	Our pilot device can perform cross-flow filtration through different kinds of membrane with
	various cut-offs for microfiltration (MF), ultrafiltration (UF), nanofiltration (NF) or reverse
	osmosis (RO). Two ceramic tubular membranes in series (TAMI) and up to 40 organic flat
	sheet membranes (Alpha-Laval), composed of polysulfone and polypropylene, in a plate-
	and-frame module can be used (table 2).

Table 2 -Characteristics of UF ceramic membranes and UF organic flat sheet membranes

 2

			UF ceramic	UF organic
	Surface (cm	2 )	50	180
	Length (cm)	25	-
	Diameter (mm)	6	100
	pH		0 to 14	1 to 13
	Pressure (bar)	1 to 15	1 to 10
	Temperature (°C)	< 120	< 75
	Cut-off (kD)	8 (TAMI) 15 (TAMI)	10 (UFX10pHt) 20 (GR61PP) 50 (GR51PP)

Table 3 -Operating conditions of the conventional electrodialysis unit

 3

	Stack	10 unit cells

Table 4 -Amount of precipitates (gdryperkg of hydrolysate sample) before and after different UF treatments as a function of pH

 4

	pH	Before UF	Ceramic 15 kD	Ceramic 8 kD	Organic 10/20/50 kD
	1.1	0	0	0	0
	2	0.22	0.19	0.19	0
	2.5	0.42	0.42	0.38	0
	3	0.62	0.60	0.53	0
	6	0.80	0.81	0.71	0

Table 5 -Properties of feed, retentate and permeate at VCF = 4.4 with the 10 kD organic membrane

 5

			Feed	Retentate Permeate
	Volume (L)		8.0	1.8	6.2
	Dry weight (% w )		7.3	11.6	7.0
	pH		1.3	1.3	1.3
	Conductivity (mS.cm	-1 )	31.5	30.2	34.5
	Absorbance at 420 nm	2.1	6.5	0.5

Table 6 -Analysis of brine and product after the 1 st ED with fresh brine and the 2 nd ED with brine reuse

 6

	Volume (L)	pH	Conductivity (

Acknowledgements

The authors would like to thank Fondation Paris-Reims, Région Champagne-Ardenne, Département de la Marne and Reims Métropole for their financial support and ARD for the hydrolysate supply.