We report a Monte Carlo and molecular dynamics simulations study of carbon dioxide in hydrated sodium montmorillonite, including thermodynamical, structural and dynamical properties. In order to simulate the behaviour of a clay caprock in contact with a CO 2 reservoir, we consider clays in equilibrium with H 2 O−CO 2 mixtures under conditions close to relevant ones for geological storage, namely a temperature T =348 K, and pressures P=25 and 125 bar, and under which two bulk phases coexist: H 2 O-rich liquid on the one hand and CO 2-rich gas (P=25 bar) or supercritical fluid (P=125 bar) on the other hand. We first use grand-canonical MC simulations to determine the number of stable states in clay, their composition and the corresponding equilibrium interlayer distances. The vertical, horizontal and radial distribution functions of the confined mixture, subsequently obtained using molecular dynamics, reveal some structural feature induced by the presence of CO 2. Finally, the simulations indicate that carbon dioxide considerably influences the diffusion of mobile species in clays. We discuss these results by comparing them with those obtained for the bulk mixtures, as well as for Namontmorillonite in equilibrium with a pure water reservoir water at the same temperature and pressure.

We report a molecular simulation study of hydrodynamics in clay nanopores, with pore widths ranging from 3 to 10 nm. Understanding mass transfer through clay nanopores is necessary in many contexts such as groundwater hydrology, petroleum and gas reservoir engineering, as well as carbon dioxide sequestration or geological disposal of radioactive waste.Grand-canonical Monte-Carlo simulations first allow to determine the water content in the pores. We then analyze the structure and diffusion of confined water using equilibrium Molecular Dynamics. Finally, Non-Equilibrium MD allow to analyze the hydrodynamic behaviour of the confined fluid and assess the relevance of continuum hydrodynamics to describe the flow under a pressure gradient. The Navier-Stokes equation, using the density and viscosity of the bulk fluid, provides a reasonable description of the flow provided that the pore width is larger than 4 nm and that a slip boundary condition is used. We determine a slip length of 2.

We investigate finite-size effects on diffusion in confined fluids using molecular dynamics simulations and hydrodynamic calculations. Specifically, we consider a Lennard-Jones fluid in slit pores without slip at the interface and show that the use of periodic boundary conditions in the directions along the surfaces results in dramatic finite-size effects, in addition to that of the physically relevant confining length. As in the simulation of bulk fluids, these effects arise from spurious hydrodynamic interactions between periodic images and from the constraint of total momentum conservation. We derive analytical expressions for the correction to the diffusion coefficient in the limits of both elongated and flat systems, which are in excellent agreement with the molecular simulation results except for the narrowest pores, where the discreteness of the fluid particles starts to play a role. The present work implies that the diffusion coefficients for wide nanopores computed using elongated boxes suffer from finite-size artifacts which had not been previously appreciated. In addition, our analytical expression provides the correction to be applied to the simulation results for finite (possibly small) systems. It applies not only to molecular but also to all mesoscopic hydrodynamic simulations, including Lattice-Boltzmann, Multiparticle Collision Dynamics or Dissipative Particle Dynamics, which are often used to investigate confined soft matter involving colloidal particles and polymers.

International audienceRandom walk (RW) or Continuous Time Random Walk (CTRW) are recurring Monte Carlo methods used to model convective and diffusive transport in complex heterogeneous media. Many applications can be found, including fluid mechanic, hydrology, and chemical reactors modeling. These methods are easy to implement, very versatile and flexible enough to become appealing for many applications because they generally overlook of deeply simplify the building of explicit complex meshes required by deterministic methods. RW and CTRW provide a good physical understanding of the interactions between the space scales of het-erogeneities and the transport phenomena under consideration. In addition, they can result in efficient up-scaling methods, especially in context of flow and transport in fractured media. In the present study, we review the applications of RW or CTRW for several situations coping with various spatial scales, and different insights into up-scaling applications. RW and CTRW advantages and downsides are also discussed, thus providing a few avenues for further works and applications

We report on a molecular simulation study of the origin of non-slip or slip hydrodynamic boundary conditions in clay nanopores, focussing on the role of electrostatics. We simulate hydrodynamic and electro-osmotic flows and consider both charged (montmorillonite) and uncharged (pyrophyllite) clays. We further use two commonly used force fields to analyze the effect of local interactions, in particular the effect of the polarity of the surface, in addition to the mere effect of the presence or absence of a net charge and counter-ions. For the 6 nm pore investigated here, the molecular velocity profile can be well described by continuum hydrodynamics only if (a) proper boundary conditions, with a slip or stagnation length determined from molecular simulation, are taken into account and (b) the ionic density profiles from MD simulations are used in the case of electro-osmotic flow, since the Poisson-Boltzmann equation fails to reproduce the ionic profiles, hence the force acting on the fluid. Among the considered force fields only CLAYFF predicts a hydrophobic pyrophyllite and hydrophilic montmorillonite, as expected from experimental behaviour. The non-slip or slip boundary conditions at clay surfaces strongly depend on electrostatic interactions of water molecules with the surface. The presence of a net charge results in an average electric field experienced by surface water molecules between the charged surface and the condensed layer counter-ions, which influences their orientation. The charge distribution inside the clay layer determines the polarity of the surface and hence the strength of hydrogen bonds donated by water molecules to surface oxygen atoms.

We present an analytical and numerical investigation of the finite difference computation of the equivalent conductivity of heterogeneous porous media. The customary harmonic scheme to evaluate finite difference internodal transmissivities produces a systematic bias in the numerical results unless an extremely fine grid is used. In order to quantify such effects, we have developed an analytical approach in the form of a series expansion of the equivalent numerical conductivity in powers of the conductivity variance. This leads to an expression of the numerical answer as a function of the grid block size. The calculation confirms the existence of a strong bias and of a very slow convergence. We propose a simple method to correct it, which is well suited for upscaling. Numerical experiments performed with more contrasting heterogeneous media show similar results. This allows the use of coarser gridding and consequently an appreciable speedup in the numerical simulation approach.

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HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow B Noetinger To cite this version: B Noetinger. A quasi steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow. Journal of Computational Physics, Elsevier, 2015, 283, pp.16 Barenblatt et al [2] remain still the base of most industrial fluid flow simulators [3-10]. Homogenization techniques [11-17 14], or Volume averaging techniques [15-17] allow a formal derivation of the double porosity equations, starting from 1s the detailed DFN, at least in the Darcy hypothesis, and in the case of a well connected fracture network. Numerical 19 solution of the associated closure problems permits to evaluate the parameters of the dual porosity madel as a function 20 of the geometry of the DFN. Useful connections with random walk theory providing efficient computational tools were 21 made by several authors [18-22]. In the case of badly connected networks, modelling approaches involving percolation 22 theory background are more appropriate [27-29]. But a complete workflow remains to be developed, especially if 23 strong couplings with the matrix are involved, and in situations in which non linear transfers, like multiphase flow, 24 are to be accounted for [8-10]. Direct simulations of flows in 2D or 3D DFN were already performed by several groups 25 ([5, 30-40]). The underlying numerical methods involve finite volume, finite elements techniques. Sorne groups intend 26 to couple the high resolution DFN model with a flow in the matrix [41]. 21Here, we focus on the simplest problem: fractures (here 2D abjects like closed polygons or ellipses of small thickness 2s