Understanding fluid transport through the multiscale pore network of a natural shale

The pore structure of a natural shale is obtained by three imaging means. Micro-tomography results are extended to provide the spatial arrangement of the minerals and pores present at a voxel size of 700 nm (the macroscopic scale). FIB/SEM provides a 3D representation of the porous clay matrix on the so-called mesoscopic scale (10-20 nm); a connected pore network, devoid of cracks, is obtained for two samples out of five, while the pore network is connected through cracks for two other samples out of five. Transmission Electron Microscopy (TEM) is used to visualize the pore space with a typical pixel size of less than 1 nm and a porosity ranging from 0.12 to 0.25. On this scale, in the absence of 3D images, the pore structure is reconstructed by using a classical technique, which is based on truncated Gaussian fields. Permeability calculations are performed with the Lattice Boltzmann Method on the nanoscale, on the mesoscale, and on the combination of the two. Upscaling is finally done (by a finite volume approach) on the bigger macroscopic scale. Calculations show that, in the absence of cracks, the contribution of the nanoscale pore structure on the overall permeability is similar to that of the mesoscale. Complementarily, the macroscopic permeability is measured on a centimetric sample with a neutral fluid (ethanol). The upscaled permeability on the macroscopic scale is in good agreement with the experimental results

Dynamic permeability of porous media by the lattice Boltzmann method

International audienceThe lattice Boltzmann method (LBM) is applied to calculate the dynamic permeability K(omega) of porous media; an oscillating macroscopic pressure gradient is imposed in order to generate oscillating flows. The LBM simulation yields the time dependent seepage velocity of amplitude A and phase shift B which are used to calculate K(omega). The procedure is validated for plane Poiseuille flows where excellent agreement with the analytical solution is obtained. The limitations of the method are discussed. When the ratio between the kinematic viscosity and the characteristic size of the pores is high, the corresponding Knudsen number Kn is high and the numerical values of K(omega) are incorrect with a positive imaginary part; it is only when Kn is small enough that correct values are obtained. The influence of the time discretization of the oscillating body force is studied; simulation results are influenced by an insufficient discretization, i.e., it is necessary to avoid using too high frequencies. The influence of absolute errors in the seepage velocity amplitude delta A and the phase shift delta B on K(omega) shows that for high omega even small errors in B can cause drastic errors in Re[K(omega)]. The dynamic permeability of reconstructed and real (sandstone) porous media is calculated for a large range of frequencies and the universal scaling behavior is verified. Very good correspondences with the theoretical predictions are observed. (C) 2013 Elsevier Ltd. All rights reserved

Lattice Spring Models

International audienceSolid mechanics can be addressed by a Lattice Spring Model whose major ingredients are briefly described. It is applied to solve the dynamic equations of motions and the static equations derived by homogenization. Results relative to the macroscopic properties of solids are successfully compared to the ones obtained by analytical methods and by other techniques of numerical calculations. Wave velocities derived by direct simulations are in good agreement with the ones derived by homogenization

Prediction of the macroscopic mechanical properties of carbonate from nano-indentation tests

Copyright © 2018 ARMA, American Rock Mechanics Association. The nano-indentation technique was applied to microporous carbonates from the Easter Parisian Basin made of nearly 100% calcite. Room-dried, small, irregular pieces, 5mm thick and with a polished surface of about 1 cm2 are used. Then, the distribution function and the linear auto-correlation of the indentation modulus are derived from these data. The numerical analysis consists in generating random three dimensional media with a local indentation modulus M(x) which has the same statistical properties as the measured ones. This is achieved via a non linear transformation of normal correlated Gaussian fields. Then, the elasticity equation with variable Lamé coefficients is solved by a code based on lattice springs. The elastic velocities are derived and compared to the measured ones

Two-phase-flow pore-size simulations in Opalinus clay by the Lattice Boltzmann Method

International audienceThe experimental determination of transport properties of low permeability clay rocks, especially of relative permeabilities and capillary pressure curves for water and gas, is a very challenging issue, in particular at high water saturation (very low gas permeability resulting in long equilibration times) and for gaseous hydrogen (due to the high pressures involved and the resulting explosion risk). Navier-Stokes equations are solved inside a porous medium on the pore scale, so as to derive the absolute and relative (two-phase-flow) permeabilities. For this purpose microtomography data of Opalinus clay samples acquired in the Mont Terri Ventilation Experiment are used to visualize the pore space in 3D at a micrometric scale (porosity size .0.7 mm). The corresponding percolating porosity is mainly composed of micrometric cracks parallel to the bedding and attributed to shrinkage. Two-phase flow is calculated in the percolating cracks by an immiscible Lattice Boltzmann (LBM) code. In addition, some validation results of the LBM model for three-phase systems (liquid-gas-solid) are presented. © The Geological Society of London 2014

Acoustic properties of porous media: an overview

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Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures

The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass–Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures