Luc Dormieux

FFT-Based Homogenization of Permeability Using a Hashin-Shtrikman Type Variational Framework

A numerical scheme for the computation of the permeability of complex microstructures is presented. As a darcean counterpart of the Fast Fourier Transform (FFT) based scheme in elasticity, the method is designed to be directly coupled with 3D imaging techniques of porous samples, without meshing or definition of an equivalent pore network. The method relies on the variational principle of Hashin-Shtrikman which ensures a rigorous upper bound status to the estimated permeabilities and provides an energetically consistent discretization of Green operators and of the viscosity of heterogeneous voxels comprising both solid and fluid. A pioneering work (Ene, 1975) early clarified the theoretical link between the macroscopic Darcy’s law for fluid flow in porous media and the microscopic Stokes flow within the pore space. A quantitatively precise prediction of the intrinsic permeability tensor thus requires an accurate description of the pore geometry. Within this framework, successful predictions of the permeability of porous media have been performed, based on different degrees of idealization of the pore/solid phase descriptions, see e.g. (Boutin, 2000) Finer description of the fluid flow requires direct full field simulations on real pore geometries. These geometries may be measured thanks to recent advances in imaging techniques, which allow for precise reconstruction of microstructures down to a few nanometers (Desbois, 2011). Most numerical methods are based on approximate solutions of Stokes equations in the pore space, but suffer from high computational cost (memory and time) or complex meshing. Taking advantage of the fast evaluation of non local terms by FFT, (Wiegmann, 2007) proposed a computationally efficient scheme. Another fruitful approach is the adaptation of the FFT-based scheme initially introduced in linear elasticity (Moulinec, 1994). This scheme was designed to be directly interfaced with imaging techniques and has been adapted to permeability (Monchiet, 2009; Nguyen, 2013). Recently, a variational framework for FFT-based scheme has been introduced in linear elasticity (Brisard, 2010), improving the performances of the so-called basic scheme (Moulinec,

A Micromechanics Approach to the Mechanically-Induced Dissolution in Porous Media

When subjected to a mechanical loading, the solid phase of a saturated porous medium undergoes a dissolution due to strain-stress concentration effects along the fluid-solid interface. Through a micromechanical analysis, the mechanical affinity is shown to be the driving force of the local dissolution. For cracked porous media, the elastic free energy is a dominant component of this driving force. This allows to predict dissolution-induced creep in such materials.